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Institute of Transportation Studies ◊ University of California, Davis One Shields Avenue ◊ Davis, California 95616 PHONE: ( 530) 752 6548 ◊ FAX: ( 530) 752 6572 WEB: http:// its. ucdavis. edu/ Year 2006 UCD— ITS— RR— 06 14 Techno Economic Models for Carbon Dioxide Compression, Transport, and Storage & Correlations for Estimating Carbon Dioxide Density and Viscosity David L. McCollum Joan M. Ogden Techno Economic Models for Carbon Dioxide Compression, Transport, and Storage & Correlations for Estimating Carbon Dioxide Density and Viscosity David L. McCollum* Joan M. Ogden Institute of Transportation Studies University of California, Davis One Shields Avenue Davis, CA 95616 * Corresponding Author E mail: dlmccollum@ ucdavis. edu October 2006 ABSTRACT Due to a heightened interest in technologies to mitigate global climate change, research in the field of carbon capture and storage ( CCS) has attracted greater attention in recent years, with the goal of answering the many questions that still remain in this uncertain field. At the top of the list of key issues are CCS costs: costs of carbon dioxide ( CO2) capture, compression, transport, storage, and so on. This research report touches upon several of these cost components. It also provides some technical models for determining the engineering and infrastructure requirements of CCS, and describes some correlations for estimating CO2 density and viscosity, both of which are often essential properties for modeling CCS. This report is actually a compilation of three separate research reports and is, therefore, divided into three separate sections. But although each could be considered as a stand alone research report, they are, in fact, very much related to one other. Section I builds upon some of the knowledge from the latter sections, and Sections II & III can be considered as supplementary to Section I. * Section I: Techno Economic Models for Carbon Dioxide Compression, Transport, and Storage – This section provides models for estimating the engineering requirements and costs of CCS infrastructure. Some of the models have been adapted from other studies, while others have been expressly developed in this study. * Section II: Simple Correlations for Estimating Carbon Dioxide Density and Viscosity as a Function of Temperature and Pressure – This section describes a set of simple correlations for estimating the density and viscosity of CO2 within the range of operating temperatures and pressures that might be encountered in CCS applications. The correlations are functions of only two input parameters— temperature and pressure— which makes them different from the more complex equation of state computer code based correlations that sometimes require more detailed knowledge of CO2 properties and operating conditions. * Section III: Comparing Techno Economic Models for Pipeline Transport of Carbon Dioxide – This section illustrates an approach that was used to compare several recent techno economic models for estimating CO2 pipeline sizes and costs. A common set of input assumptions was applied to all of the models so that they could be compared on an “ apples to apples” basis. Then, by averaging the cost estimates of the models over a wide range of CO2 mass flow rates and pipeline lengths, a new CO2 pipeline capital cost model was created that is a function only of flow rate and pipeline length. Keywords: carbon dioxide, CO2, CO2, CCS, pipeline, transport, compression, injection, storage, sequestration, techno economic, cost model, climate change, greenhouse gas, correlation, density, viscosity SECTION I: Techno Economic Models for Carbon Dioxide Compression, Transport, and Storage David L. McCollum dlmccollum@ ucdavis. edu Institute of Transportation Studies University of California One Shields Avenue Davis, CA 95616 ABSTRACT This report provides techno economic model equations for estimating the equipment sizes and costs of compression, pipeline transport, and injection and storage of carbon dioxide ( CO2). Models of this type are becoming increasingly important due to the recent heightened interest in carbon capture and storage ( CCS) as a climate change mitigation strategy. The models described here are based on a combination of several CCS studies that have been carried out over the past few years. Because the models are laid out step by step, the reader should be able to understand the methodology and replicate the models on his or her own. Keywords: carbon dioxide, CO2, CO2, CCS, pipeline, transport, compression, injection, storage, sequestration, techno economic, cost model, climate change, greenhouse gas 1 PART I: CO2 COMPRESSION Nomenclature m = CO2 mass flow rate to be transported to injection site [ tonnes/ day] Pinitial = initial pressure of CO2 directly from capture system [ MPa] Pfinal = final pressure of CO2 for pipeline transport [ MPa] Pcut off = pressure at which compression switches to pumping [ MPa] Nstage = number of compressor stages [] CR = compression ratio of each stage [] Ws, i = compression power requirement for each individual stage [ kW] Zs = average CO2 compressibility for each individual stage [] R = gas constant [ kJ/ kmol K] Tin = CO2 temperature at compressor inlet [ K] M = molecular weight of CO2 [ kg/ kmol] ηis = isentropic efficiency of compressor [] ks = ( Cp/ Cv) = average ratio of specific heats of CO2 for each individual stage [] Ws total = total combined compression power requirement for all stages [ kW] ( Ws) 1 = compression power requirement for stage 1 [ kW] ( Ws) 2 = compression power requirement for stage 2 [ kW] ( Ws) 3 = compression power requirement for stage 3 [ kW] ( Ws) 4 = compression power requirement for stage 4 [ kW] ( Ws) 5 = compression power requirement for stage 5 [ kW] Ntrain = number of parallel compressor trains [] Wp = pumping power requirement [ kW] ρ = density of CO2 during pumping [ kg/ m3] ηp = efficiency of pump [] myear = CO2 mass flow to be transported and stored per year [ tonnes/ yr] CF = capacity factor [] mtrain = CO2 mass flow rate through each compressor train [ kg/ s] Ccomp = capital cost of compressor( s) [$] Cpump = capital cost of pump [$] Ctotal = total capital cost of compressor( s) and pump [$] Cannual = annualized capital cost of compressor( s) and pump [$/ yr] CRF = capital recovery factor [/ yr] Clev = levelized capital costs of compressor( s) and pump [$/ tonne CO2] O& Mannual = annual O& M costs [$/ yr] O& Mfactor = O& M cost factor [/ yr] O& Mlev = levelized O& M costs [$/ tonne CO2] Ecomp = electric power costs of compressor [$/ yr] pe = price of electricity [$/ kWh] Epump = electric power costs of pump [$/ yr] Eannual = total annual electric power costs of compressor and pump [$/ yr] Elev = levelized O& M costs [$/ tonne CO2] 2 Calculation of Compressor & Pump Power Requirements After CO2 is separated from the flue gases of a power plant or energy complex ( i. e., captured), it must be compressed from atmospheric pressure ( Pinitial = 0.1 MPa), at which point it exists as a gas, up to a pressure suitable for pipeline transport ( Pfinal = 15 MPa), at which point it is in either the liquid or ‘ dense phase’ regions, depending on its temperature. Therefore, CO2 undergoes a phase transition somewhere between these initial and final pressures. When CO2 is in the gas phase, a compressor is required for compression, but when CO2 is in the liquid/ dense phase, a pump can be used to boost the pressure. It can be assumed that the ‘ cut off’ pressure ( Pcut off) for switching from a compressor to a pump is the critical pressure of CO2, which is 7.38 MPa. Hence, a compressor will be used from 0.1 to 7.38 MPa, and then a pump will be used from 7.38 to 15 MPa ( or to whatever final pressure is desired). This line of reasoning has been adapted from [ 1]. Pinitial = 0.1 MPa Pfinal = 15 MPa Pcut off = 7.38 MPa The number of compressor stages is assumed to be 5 (= Nstage), and the equation for the optimal compression ratio ( CR) for each stage is given by Mohitpour [ 2]: CR = ( Pcut off / Pinitial)^( 1/ Nstage) ( where Nstage = 5) The compression power requirement for each stage ( Ws, i) is given by the following equation, which is adapted from [ 1] and [ 2]. ( ) ⎥⎦ ⎤ ⎢⎣ ⎡ − ⎟ ⎟⎠ ⎞ ⎜ ⎜⎝ ⎛ − ⎟ ⎟⎠ ⎞ ⎜ ⎜⎝ ⎛ ⎟⎠ ⎞ ⎜⎝ ⎛ ∗ = − 1 24 3600 1 1000 1 , s s k k s s is s in s i CR k k M W mZ RT η Based on some assumptions and CO2 property data from the Kinder Morgan company [ 3], the following values can be used in the above equation:  For all stages:  R = 8.314 kJ/ kmol K  M = 44.01 kg/ kmol  Tin = 313.15 K ( i. e., 40 oC)  ηis = 0.75  1000 = # of kilograms per tonne  24 = # of hours per day  3600 = # of seconds per hour  For stage 1:  Z s = 0.995  k s = 1.277  These values correspond to a pressure range of 0.1 0.24 MPa and an average temperature of 356 K in the compressor. 3  For stage 2:  Z s = 0.985  k s = 1.286  These values correspond to a pressure range of 0.24 0.56 MPa and an average temperature of 356 K in the compressor.  For stage 3:  Z s = 0.970  k s = 1.309  These values correspond to a pressure range of 0.56 1.32 MPa and an average temperature of 356 K in the compressor.  For stage 4:  Z s = 0.935  k s = 1.379  These values correspond to a pressure range of 1.32 3.12 MPa and an average temperature of 356 K in the compressor.  For stage 5:  Z s = 0.845  k s = 1.704  These values correspond to a pressure range of 3.12 7.38 MPa and an average temperature of 356 K in the compressor. Thus, the calculation for compressor power requirement must be conducted five times, since this is the number of stages that have been assumed. Although, this procedure may seem a bit more tedious than simply assuming average values for Zs and ks over the pressure range and using the equation only once, it is prudent to break up the calculation by stage due to the unusual behavior of CO2’ s properties, which are different at each stage. The compressor power requirements for each of the individual stages should then be added together to get the total power requirement of the compressor. Ws total = ( Ws) 1 + ( Ws) 2 + ( Ws) 3 + ( Ws) 4 + ( Ws) 5 According to the IEA GHG PH4/ 6 report [ 1], the maximum size of one compressor train, based on current technology, is 40,000 kW. So if the total compression power requirement ( Wstotal) is greater than 40,000 kW, then the CO2 flow rate and total power requirement must be split into Ntrain parallel compressor trains, each operating at 100/ Ntrain % of the flow/ power. Of course, the number of parallel compressor trains must be an integer value. Ntrain = ROUND_ UP ( Ws total / 40,000) To calculate the pumping power requirement for boosting the CO2 pressure from Pcut off ( 7.38 MPa) to Pfinal ( 15 MPa), the following equation has been adapted from [ 1]: ( ) ⎥ ⎥⎦ ⎤ ⎢ ⎢⎣ ⎡ − ⎟⎠ ⎞ ⎜⎝ ⎛ ∗ = − p final cut off p m P P W 24 36 ρη 1000 * 10 4 ( where ‘ m’ is the CO2 mass flow rate [ tonnes/ day], and the following values can be assumed: ρ = 630 kg/ m3, ηp = 0.75, 1000 = # of kilograms per tonne, 24 = # of hours per day, 10 = # of bar per MPa, 36 = # of m3* bar/ hr per kW) The following figure shows the total power requirement for the compressor( s) and pump over a range of flow rates. Notice that the dependence of compression power on flow rate, ‘ m’, is linear, as would be expected from the equation for Ws. Also, notice how small pumping power is relative to compression power. This is because the compressor raises the CO2 pressure from 0.1 to 7.38 MPa— a total compression ratio of 73.8— whereas the pump raises the pressure from 7.38 to 15 MPa— a total compression ratio of only 2.0. Power Requirement of Compressors and Pumps 0 20,000 40,000 60,000 80,000 100,000 120,000 0 5,000 10,000 15,000 20,000 25,000 CO2 Mass Flow Rate [ tonnes/ day] Power [ kW] Compressor Power ( W_ s) Pump Power ( W_ p) Figure 1: Power Requirement of Compressors and Pumps as a Function of CO2 Mass Flow Rate Capital, O& M, and Levelized Costs of CO2 Compression/ Pumping *** All costs are expressed in year 2005 US$ The CO2 mass flow rate through each compressor train ( mtrain) in units of ‘ kg/ s’ is given by: mtrain = ( 1000 * m) / ( 24 * 3600 * Ntrain) The capital cost of the compressor can then be calculated based on the following equation, which has been slightly adapted from Hendriks [ 4] and scaled up into year 2005$. 5 ( )( ) ( )( ) ⎥⎦ ⎤ ⎢⎣ ⎡ ⎟ ⎟⎠ ⎞ ⎜ ⎜⎝ ⎛ = × − + × − − initial cut off comp train train train train P P C m N 0.13 106 m 0.71 1.40 106 m 0.60 ln The units on the constant terms ( 0.13 x 106 and 1.40 x 106) are ‘$/( kg/ s)’. Therefore, the compressor capital cost ( Ccomp) is given in ‘$’. The capital cost of the pump can be calculated based on the following equation, which has been slightly adapted from [ 1] and scaled up into year 2005$. Cpump = {( 1.11 x 106) * ( Wp / 1000)} + 0.07 x 106 The following graph shows the capital costs of both the compressors and pumps in term of [$/ kW]. As one would expect, at the higher CO2 mass flow rates the values fall in the $ 1000 2000/ kW range, which is consistent with other studies. Note the cost curve for compressors is not entirely smooth. This has something to do with the fact that at a certain level of compression power demand, another compressor train is added, which adds to the capital costs, but not significantly to the power demand. No such restriction is placed on pumps, so the cost curve for pumps is smooth. Capital Costs of Compressors and Pumps 0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 1,000 2,500 5,000 10,000 15,000 20,000 25,000 CO2 Mass Flow Rate [ tonnes/ day] Compressor [$/ kW] 0 200 400 600 800 1,000 1,200 1,400 1,600 Pump [$/ kW] Compressor Pump Figure 2: Capital Costs of Compressors and Pumps as a Function of CO2 Mass Flow Rate The total capital costs are thus: 6 Ctotal = Ccomp + Cpump The capital cost can be annualized by applying a capital recovery factor ( CRF) of 0.15. Cannual = Ctotal * CRF ( where CRF = 0.15/ yr) The total amount of CO2 that must be compressed every year is found by applying a capacity factor ( CF) of 0.80. myear = m * 365 * CF ( where CF = 0.80) The levelized capital costs ( Clev) are thus: Clev = Cannual / myear The annual operation and maintenance costs ( O& Mannual) can be found by applying an O& M factor ( O& Mfactor) of 0.04 to the total capital cost. O& Mannual = Ctotal * O& Mfactor ( where O& Mfactor = 0.04) The levelized O& M costs ( O& Mlev) are thus: O& Mlev = O& Mannual / myear The total electric power costs of the compressor ( Ecomp) and pump ( Epump) are calculated by multiplying the total power requirement by the capacity factor ( CF) of 0.80 and price of electricity ( pe). It can be assumed that the electricity price is $ 0.065/ kWh, based on estimates by Kreutz et al. [ 17] for a coal to hydrogen plant that employs CO2 capture. Eannual = Ecomp + Epump = pe * ( Ws total + Wp) * ( CF * 24 * 365) ( where pe = $ 0.065/ kWh, and CF = 0.80) The levelized power costs ( Elev) are thus: Elev = Eannual / myear Finally, the total annual and levelized costs of CO2 compression/ pumping are: Total Annual Cost [$/ yr] = Cannual + O& Mannual + Eannual Total Levelized Cost [$/ tonne CO2] = Clev + O& Mlev + Elev The following two figures show the contribution of capital, O& M, and power to the total levelized cost of CO2 compression/ pumping. The reason for the cost curves not being smooth is because of the maximum power constraint of 40,000 kW per compressor train. In other words, as the flow rate of CO2 increases, the compression power reaches a threshold point where a new 7 compressor train is needed. This new compressor train causes a spike in the capital cost ( and thus, O& M and total costs). The total power requirements and cost, however, are unaffected by the number of compressor trains that are required. Furthermore, the figures show that there are economies of scale associated with CO2 compression/ pumping— i. e., the capital cost becomes a smaller percentage of total cost as the CO2 flow rate increases. The last figure shows the dependence of levelized power cost and, thus, total levelized cost on the price of electricity. Since electric power is so important to the process of CO2 compression/ pumping, it makes up an increasingly larger share of total costs as electricity becomes more expensive. Levelized Cost of CO2 Compression/ Pumping 0 4 8 12 16 20 0 5,000 10,000 15,000 20,000 25,000 CO2 Mass Flow Rate [ tonnes/ day] $/ tonne CO2 Total Levelized Cost Levelized Power ( E_ lev) Levelized Capital ( C_ lev) Levelized O& M ( O& M_ lev) Figure 3: Levelized Cost of CO2 Compression/ Pumping as a Function of CO2 Mass Flow Rate 8 Component Contribution to Total Levelized Cost of CO2 Compression/ Pumping 8.52 4.95 3.30 3.29 2.60 2.78 2.45 2.27 1.32 0.88 0.88 0.69 0.74 0.65 6.81 6.81 6.81 6.81 6.81 6.81 6.81 0 2 4 6 8 10 12 14 16 18 20 1,000 2,500 5,000 10,000 15,000 20,000 25,000 CO2 Mass Flow Rate [ tonnes/ day] $/ tonne CO2 Levelized Power ( E_ lev) Levelized O& M ( O& M_ lev) Levelized Capital ( C_ lev) Figure 4: Contribution of Capital, O& M, and Power to Total Levelized Cost of CO2 Compression/ Pumping ( Dependence on CO2 Mass Flow Rate) Component Contribution to Total Levelized Cost of CO2 Compression/ Pumping 3.30 3.30 3.30 3.30 3.30 3.30 0.88 0.88 0.88 0.88 0.88 0.88 4.19 6.29 8.39 10.48 12.58 14.68 0 2 4 6 8 10 12 14 16 18 20 0.04 0.06 0.08 0.10 0.12 0.14 Electricity Price, pe [$/ kWh] $/ tonne CO2 Levelized Power ( E_ lev) Levelized O& M ( O& M_ lev) Levelized Capital ( C_ lev) m = 5,000 tonnes/ day Figure 5: Contribution of Capital, O& M, and Power to Total Levelized Cost of CO2 Compression/ Pumping ( Dependence on Electricity Price) 9 PART II: CO2 TRANSPORT Nomenclature D = pipeline diameter [ in] m = CO2 mass flow rate in pipeline [ tonnes/ day] Pin = inlet pipeline pressure [ MPa] Pout = outlet pipeline pressure [ MPa] Pinter = intermediate pipeline pressure [ MPa] ΔP = pressure drop in pipeline = Pin  Pout [ MPa] T = CO2 temperature in pipeline [ oC] μ = CO2 viscosity in pipeline [ Pa s] ρ = CO2 density in pipeline [ kg/ m3] ε = pipeline roughness factor [ ft] Re = Reynold’s number [] Ff = Fanning friction factor [] L = pipeline length [ km] Ccap = pipeline capital cost [$/ km] Ctotal = total pipeline capital cost [$] FL = location factor [] FT = terrain factor [] CRF = capital recovery factor [/ yr] Cannual = annualized pipeline capital cost [$/ yr] O& Mannual = annual O& M costs [$/ yr] O& Mfactor = O& M cost factor [/ yr] CF = capacity factor [] myear = CO2 mass flow delivered to injection site per year [ tonnes/ year] Calculation of Pipeline Diameter The equation for calculating pipeline capital cost ( shown in the next section) is not a function of diameter. Nevertheless, when conducting a techno economic analysis, it may be useful to estimate the diameter size for other reasons. Thus, the methodology for calculating pipeline diameter is shown here. Since the calculation of pipeline diameter is an iterative process, one must first guess a value for diameter ( D). A reasonable first approximation is D = 10 inches. The process also requires knowledge of the CO2 temperature ( T) and pressure ( Pinter) in the pipeline. Pinter is based on the pipeline inlet pressure ( Pin, i. e. the pressure of CO2 leaving the power plant or energy complex) and the pipeline outlet pressure ( Pout, i. e. the pressure of CO2 at the end of the pipeline— the injection site). Pinter = ( Pin + Pout) / 2 Furthermore, an estimation of the density ( ρ) and viscosity ( μ) of CO2 in the pipeline ( approximated at T and Pinter) is also required. Since CO2 exhibits unusual trends in its properties 10 over the range of temperatures and pressures that would be experienced in pipeline transport, it is difficult to provide just one value for either density or viscosity here. Therefore, the reader is referred to one of two CO2 property websites, [ 5] and [ 6], or to the set of correlation equations of McCollum [ 7]. Each of these references provide an easy way of obtaining CO2 density and viscosity if one knows only two basic parameters— temperature and pressure. The Reynold’s number ( Re) and Fanning friction factor ( Ff) for CO2 fluid flow in the pipeline are calculated by the following equations from [ 8]: Re = ( 4* 1000/ 24/ 3600/ 0.0254)* m / ( π* μ* D) 1.11 2 10 3.7 12( / ) Re 4 1.8 log 6.91 1 ⎥ ⎥⎦ ⎤ ⎢ ⎢⎣ ⎡ ⎪⎭ ⎪⎬ ⎫ ⎪⎩ ⎪⎨ ⎧ ⎟⎠ ⎞ ⎜⎝ − + ⎛ = D F f ε ( where ε = 0.00015 ft is assumed by [ 8]) The pipeline diameter ( D) is calculated by the following equation, which is adapted from [ 8]: D = ( 1/ 0.0254) * [ ( 32* Ff* m2)*( 1000/ 24/ 3600) 2 / ( π2* ρ*( ΔP/ L)* 106/ 1000) ]( 1/ 5) Finally, since the process for calculating pipeline diameter is iterative, one needs to compare the calculated diameter from this last equation with the value that was initially guessed at the beginning of the process. If there is much difference between the two, then the process must be repeated over and over again until the difference between iterations is satisfactorily small. Capital, O& M, and Levelized Costs of CO2 Transport *** All costs are expressed in year 2005 US$ The equations for estimating onshore pipeline capital cost are given by McCollum [ 9]. Ccap = 9970 * ( m0.35) * ( L0.13) Ctotal = FL * FT * L * Ccap Notice that the capital cost is scaled up by a location factor ( FL) and a terrain factor ( FL). A full list of these factors is provided in [ 1]. A short list is reproduced here: FL: USA/ Canada= 1.0, Europe= 1.0, UK= 1.2, Japan= 1.0, Australia= 1.0. FT: cultivated land= 1.10, grassland= 1.00, wooded= 1.05, jungle= 1.10, stony desert= 1.10, < 20% mountainous= 1.30, > 50% mountainous= 1.50 11 The capital cost can be annualized by applying a capital recovery factor ( CRF) of 0.15. Cannual = Ctotal * CRF ( where CRF = 0.15/ yr) The O& M costs are calculated as 2.5% of the total capital cost. This value is approximately the average O& M factor from a handful of studies on CO2 pipeline transport [ 1], [ 8], [ 10], [ 11], [ 12]. To be precise, [ 1] and [ 8] do not use an O& M factor for estimating O& M costs; rather, they use a per mile cost and an equation, respectively. Their estimates, however, are close to 2.5% of the total capital cost over the range of CO2 flow rates and pipeline lengths considered here. O& Mannual = Ctotal * O& Mfactor ( where O& Mfactor = 0.025) The total annual costs are thus: Total Annual Cost [$/ yr] = Cannual + O& Mannual The total amount of CO2 that must be transported every year is found by applying a capacity factor ( CF) of 0.80. myear = m * 365 * CF ( where CF = 0.80) And the levelized cost of CO2 transport is given by: Levelized Cost [$/ tonne CO2] = ( Total Annual Cost) / myear The following figures show the onshore pipeline capital cost ( Ccap) and levelized cost, as calculated by the above equations, over a range of CO2 mass flow rates and pipeline lengths. From these figures, it is easy to see that for capital cost there is a stronger dependence on flow rate than on length. This is to be expected since, in the equation for Ccap, the exponent on the flow rate term, ‘ m’, is larger than the exponent on the length term, ‘ L’ ( 0.35 vs. 0.13). 12 Pipeline Capital Cost as a Function of CO2 Mass Flow Rate and Pipeline Length 200,000 300,000 400,000 500,000 600,000 700,000 0 5,000 10,000 15,000 20,000 CO2 Mass Flow Rate [ tonnes/ day] Pipeline Capital Cost [$/ km] L = 500 km L = 400 km L = 300 km L = 200 km L = 100 km Figure 6: Pipeline Capital Cost as a Function of CO2 Mass Flow Rate and Pipeline Length Pipeline Capital Cost as a Function of Pipeline Length and CO2 Mass Flow Rate 200,000 300,000 400,000 500,000 600,000 700,000 50 150 250 350 450 550 Pipeline Length [ km] Pipeline Capital Cost [$/ km] m = 20,000 tonnes/ day m = 15,000 tonnes/ day m = 10,000 tonnes/ day m = 5,000 tonnes/ day m = 1,000 tonnes/ day Figure 7: Pipeline Capital Cost as a Function of Pipeline Length and CO2 Mass Flow Rate 13 Levelized Cost of CO2 Transport as a Function of CO2 Mass Flow Rate and Pipeline Length 0 20 40 60 80 100 0 5,000 10,000 15,000 20,000 CO2 Mass Flow Rate [ tonnes/ day] Levelized Cost [$/ tonne CO2] L = 500 km L = 400 km L = 300 km L = 200 km L = 100 km Figure 8: Levelized Cost of CO2 Transport as a Function of CO2 Mass Flow Rate and Pipeline Length ( FL = 1.0 assumed; and FT = 1.20 assumed as an approximate average of all terrains) 14 PART III: CO2 INJECTION & STORAGE Nomenclature m = CO2 mass flow delivered to injection site per day [ tonnes/ day] myear = CO2 mass flow delivered to injection site per year [ tonnes/ year] CF = capacity factor [] Psur = surface pressure of CO2 at the top of the injection well [ MPa] Pres = pressure in the reservoir [ MPa] Pdown = downhole injection pressure of CO2 ( i. e., pressure at bottom of injection well) [ MPa] Pinter = average between reservoir pressure ( Pres) and downhole injection pressure ( Pdown) [ MPa] ΔPdown = downhole pressure difference = Pdown – Pres [ MPa] Tsur = surface temperature of CO2 at the top of the injection well [ oC] Gg = geothermal gradient [ oC/ km] Tres = temperature in the reservoir [ oC] d = reservoir depth [ m] h = reservoir thickness [ m] ka = absolute permeability of reservoir [ millidarcy ( md)] kv = vertical permeability of reservoir [ millidarcy ( md)] kh = horizontal permeability of reservoir [ millidarcy ( md)] μinter = CO2 viscosity at intermediate pressure ( Pinter) [ mPa s] μsur = CO2 viscosity at surface temperature ( Tsur) [ Pa s] ρsur = CO2 density at surface temperature ( Tsur) and surface pressure ( Psur) [ kg/ m3] CO2 mobility = absolute permeability ( ka) divided by CO2 viscosity ( μinter) [ md/ mPa s] CO2 injectivity = mass flow rate of CO2 that can be injected per unit of reservoir thickness ( h) and per unit of downhole pressure difference ( Pdown – Pres) [ tonnes/ day/ m/ MPa] g = gravitational constant [ m/ s2] Pgrav = gravity head of CO2 column in injection well [ MPa] Dpipe = injection pipe diameter [ m] Re = Reynold’s number [] ε = injection pipe roughness factor [ ft] Ff = Fanning friction factor [] vpipe = CO2 velocity in injection pipe [ m/ s] ΔPpipe = frictional pressure loss in injection pipe [ MPa] QCO2/ well = CO2 injection rate per well [ tonnes/ day/ well] Ncalc = calculated number of injection wells [] Nwell = actual number of injection wells ( i. e., rounded up to nearest integer) [] Csite = capital cost of site screening and evaluation [$] Cequip = capital cost of injection equipment [$] Cdrill = capital cost for drilling of the injection well [$] Ctotal = total capital cost of injection wells [$] Cannual = annualized capital cost of injection wells [$/ yr] CRF = Capital Recovery factor [/ yr] O& Mdaily = O& M costs due to normal daily expenses [$/ yr] O& Mcons = O& M costs due to consumables [$/ yr] O& Msur = O& M costs due to surface maintenance [$/ yr] 15 O& Msubsur = O& M costs due to subsurface maintenance [$/ yr] O& Mtotal = total O& M costs [$/ yr] Injection Well Number Calculation The number of CO2 injection wells that are required is strongly dependent on the properties of the particular geological reservoir that is being used to store the CO2. Every reservoir is unique, however, and reservoir properties are quite varied. MIT [ 8] has done some statistical analysis on properties of actual reservoirs in the U. S., and they subsequently use the ranges in the following tables for their study on CO2 storage in saline aquifers and in gas and oil reservoirs. The properties shown are reservoir pressure ( Pres), thickness ( h), depth ( d), and horizontal permeability ( kh). Table 1: Representative Range of Saline Aquifer Reservoir Properties [ 8] Table 2: Representative Range of Oil Reservoir Properties [ 8] Table 3: Representative Range of Gas Reservoir Properties [ 8] The reservoir properties corresponding to “ High Cost Case” in the preceding tables can be taken as the values that will lead to the maximum number of injection wells and, thus, maximum costs. Similarly, the “ Low Cost Case” values will lead to the minimum costs. The “ Base Case” values can be taken as statistically representative of any one reservoir. By assuming a surface temperature of 15 oC ( i. e., at the top of the injection well) and a geothermal gradient of 25 oC/ km [ 8], and taking reservoir depth ( d) from the above tables, the reservoir temperature can be approximated. 16 Tres = Tsur + d*( Gg / 1000) ( where Tsur = 15 oC and Gg = 25 oC/ km) The procedure for calculating the number of CO2 injection wells is iterative. To begin, one must assume a value for the downhole injection pressure ( Pdown), which is the CO2 pressure at the bottom of the injection well. A reasonable first approximation for Pdown is 17 MPa. The intermediate pressure of CO2 in the reservoir ( Pinter) is the average between the downhole injection pressure ( Pdown) and the reservoir pressure far from the injection well ( Pres), which is taken from the above tables. Pinter = ( Pdown + Pres) / 2 Based on Pinter, the CO2 viscosity in the reservoir near the bottom of the injection well ( μinter) can be approximated. As stated in the previous section, since CO2 exhibits unusual trends in its properties over the range of temperatures and pressures that would be experienced with injection and storage, it is difficult to provide a single value for viscosity here. Therefore, the reader is referred to either of two CO2 property websites, [ 5] and [ 6], or to the set of correlation equations of McCollum [ 7]. Each of these references provide an easy way of obtaining CO2 density and viscosity if one knows only two basic parameters— temperature and pressure. The absolute permeability of the reservoir ( ka) is found by an equation from [ 13]. ka = ( kh * kv) 0.5 = ( kh * 0.3kh) 0.5 ( where kh is taken from the above tables) The mobility of CO2 in the reservoir is thus [ 8]: CO2 mobility = ka / μinter The injectivity of CO2 is then found by [ 13]: CO2 injectivity = 0.0208 * CO2 mobility And the CO2 injection rate per well is calculated by the following equation [ 8]. QCO2/ well = ( CO2 injectivity) * h * ΔPdown = ( CO2 injectivity) * h * ( Pdown – Pres) ( where h is taken from the above tables) The number of injection wells is based on the flow rate of CO2 that is delivered to the injection site and the injection rate per well [ 8]. Ncalc = m / QCO2/ well This is the calculated number of injection wells, not the actual number. The actual number of wells must, of course, be an integer value and will be determined in the final step. As stated previously, the calculation of well number is iterative, due to the downhole injection pressure ( Pdown) initially being unknown. Pdown is simply the pressure increase due to the gravity head of the CO2 column in the injection well ( Pgrav), accounting for the fact that there is some pressure drop due to friction in the injection pipe ( ΔPpipe) [ 8]. 17 Pdown = Psur + Pgrav  ΔPpipe The gravity head is a function of the gravitational constant ( g) and the density of CO2 ( ρsur) at the surface temperature ( Tsur) and surface pressure ( Psur). Once again, for estimating CO2 density the reader is referred to either of two CO2 property websites, [ 5] and [ 6], or to the set of correlation equations of McCollum [ 7]. Pgrav = ( ρsur * g * d) / 106 ( where g = 9.81 m/ s2) The frictional pressure loss in the injection pipe is found in much the same way as the pipeline diameter was calculated in a previous section of this report. The Reynold’s number ( Re) is first found by the following equation, adapted from [ 8]: Re = 4 * ( m* 1000/ 24/ 3600/ Ncalc) / π / μsur / Dpipe ( where 1000, 24, and 3600 are unit conversion factors) The CO2 viscosity ( μsur) at the surface temperature ( Tsur) can be approximated by [ 5], [ 6], or [ 7]. The injection pipe diameter ( Dpipe) is assumed to be one of the following values, based on MIT’s report [ 8]:  0.059 m (~ 2.3 in) for all cases except the aquifer base case and aquifer low cost case;  0.1 m (~ 3.9 in) for the aquifer base case;  0.5 m ( 19.7 in) for the aquifer low cost case ( Though, the MIT report mentions that an injection pipe of this size is too large to be used in practice. Therefore, a diameter of 0.12 m (~ 4.7 in) is assumed to be a reasonable upper limit.) The Fanning friction factor ( Ff) for flow in the injection pipe is calculated by the following equation from [ 14]: 1.11 2 10 3.7 0.3048 ( / ) Re 4 1.8 log 6.91 1 ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎪⎭ ⎪⎬ ⎫ ⎪⎩ ⎪⎨ ⎧ ⎟ ⎟⎠ ⎞ ⎜ ⎜⎝ ⎛ − + = pipe f D F ε ( where ε = 0.00015 ft is assumed by [ 8]) The frictional pressure drop is then calculated based on the CO2 velocity in the injection pipe ( vpipe) [ 14]. vpipe = ( m* 1000/ 24/ 3600/ Ncalc) / ( ρsur * π * ( Dpipe/ 2) 2) ΔPpipe = ( ρsur* g* Ff* d* vpipe 2) / ( Dpipe* 2* g) / 106 Once again, the downhole injection pressure ( Pdown) is calculated by: 18 Pdown = Psur + Pgrav  ΔPpipe This calculated value for Pdown can now be used to begin another iteration. The iterative process for calculating Pdown should be carried out over and over again until there is very little difference ( i. e., < 1%) between iterations. Once Pdown is known, the actual number of injection wells ( Nwell) can be found by rounding the calculated number of wells ( Ncalc)— from the final iteration— up to the nearest integer. Nwell = ROUND_ UP ( Ncalc) Capital, O& M, and Levelized Costs of CO2 Injection & Storage *** All costs are expressed in year 2005 US$ The capital cost of site screening and evaluation ( Csite) has been scaled up into year 2005$ based on an estimate by Smith [ 15]. Csite = 1,857,773 Equations for estimating the capital cost of injection equipment were developed by the MIT report [ 8] based on actual injection well costs given by the Energy Information Administration ( EIA) in their annual “ Costs and Indices for Domestic Oil and Gas Field Equipment and Production Operations” report. Injection equipment costs include supply wells, plants, distribution lines, headers, and electrical services [ 16]. The equations of [ 8] have been scaled up into year 2005$. Cequip = Nwell * { 49,433 * [ m / ( 280* Nwell)] 0.5} MIT also developed an equation for estimating the drilling cost of an onshore injection well based on data from the “ 1998 Joint American Survey ( JAS) on Drilling Costs” report. The equations of [ 8] have been scaled up into year 2005$. Cdrill = Nwell * 106 * 0.1063e0.0008* d Therefore, the total capital cost is given by: Ctotal = Csite + Cequip + Cdrill The capital cost can be annualized by applying a capital recovery factor ( CRF) of 0.15. Cannual = Ctotal * CRF ( where CRF = 0.15/ yr) 19 O& M costs were also developed from the EIA “ Costs and Indices for Domestic Oil and Gas Field Equipment and Production Operations” report. They can be grouped into the following four categories: Normal Daily Expenses ( O& Mdaily), Consumables ( O& Mcons), Surface Maintenance ( O& Msur), and Subsurface Maintenance ( O& Msubsur). Costs have been scaled up into 2005$. O& Mdaily = Nwell * 7,596 O& Mcons = Nwell * 20,295 O& Msur = Nwell * { 15,420 * [ m / ( 280* Nwell)] 0.5} O& Msubsur = Nwell * { 5669 * ( d / 1219)} O& Mtotal = O& Mdaily + O& Mcons + O& Msur + O& Msubsur The total annual costs are thus: Total Annual Cost [$/ yr] = Cannual + O& Mtotal The total amount of CO2 that must be injected and stored every year is found by applying a capacity factor ( CF) of 0.80. myear = m * 365 * CF ( where CF = 0.80) Finally, the levelized cost of CO2 injection and storage is given by: Levelized Cost [$/ tonne CO2] = ( Total Annual Cost) / myear The following graphs show the sensitivity of both the levelized costs and number of injection wells to a few of the parameters that could vary between CO2 storage reservoirs. To be sure, carbon capture and sequestration is highly site specific, and the properties of different reservoirs may be wildly different. In the following graphs, for consistency we have used a common set of parameters, and depending on the particular graph, some parameters are held constant while one or two of the others are varied. The common parameters, for the most part, correspond to the Aquifer Base Case values highlighted above A few things are worth mentioning with regard to the graphs. For starters, as one would expect, the levelized cost of CO2 storage decreases as the amount of CO2 to be sequestered increases— i. e., economies of scale are present. Conversely, more injection wells are required at higher flow rates. In addition, as the diameter of the injection pipe gets smaller, the number of injection wells must be increased to compensate, which translates into higher levelized costs at smaller diameters. Moreover, as the reservoir gets thicker and is more permeable, fewer injection wells are needed to do the same job. Note that reservoir depth and pressure were also examined in this sensitivity analysis, but it was found that the number of injection wells is not as 20 dependent on these two parameters as it is for reservoir thickness and permeability. Thus, they have not been shown here. Common Design Bases CO2 flow rate to injection field 1,000 to 20,000 tonnes/ day Plant Capacity Factor 0.80 Surface pressure ( pipeline outlet) 10.3 MPa Surface temperature 15.0 C Reservoir temperature 46.0 C Reservoir depth 1239 m Reservoir thickness 10 to 1000 m Reservoir permeability ( horizontal) 0.1 to 500 md Reservoir pressure 8.4 MPa Injection Pipe Diameter 0.059, 0.1, 0.15, or 0.2 m Common Economic Bases Reference Year for Dollar 2005 Project Lifetime 20 years Discount Rate 0.10 Table 4: Common Set of Parameters Used in Sensitivity Analysis Levelized Cost of CO2 Storage as a Function of Total CO2 Mass Flow Rate Delivered to Injection Site 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1,000 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 20,000 tonnes/ day $/ tonne CO2 Injection Pipe Diameter = 0.059 m Injection Pipe Diameter = 0.1 m Injection Pipe Diameter = 0.15 m Injection Pipe Diameter = 0.2 m Figure 9: Levelized Cost of CO2 Storage as a Function of Total CO2 Mass Flow Rate Delivered to Injection Site 21 Number of Injection Wells as a Function of Total CO2 Mass Flow Rate Delivered to Injection Site 0 1 2 3 4 5 6 7 8 1,000 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 20,000 tonnes/ day Number of Wells Injection Pipe Diameter = 0.059 m Injection Pipe Diameter = 0.1 m Injection Pipe Diameter = 0.15 m Injection Pipe Diameter = 0.2 m Figure 10: Number of Injection Wells as a Function of Total CO2 Mass Flow Rate Delivered to Injection Site Number of Wells at Injection Site as a Function of Reservoir Permeability ( CO2 Mass Flow Rate = 5000 tonnes/ day, Injection Pipe Diameter = 0.1 m, Reservoir Thickness = 171 m) 104 11 2 1 1 1 0 20 40 60 80 100 120 0 1 10 50 100 500 millidarcies Number of Wells Figure 11: Number of Injection Wells as a Function of Reservoir Permeability 22 Number of Wells at Injection Site as a Function of Reservoir Thickness ( CO2 Mass Flow Rate = 5000 tonnes/ day, Injection Pipe Diameter = 0.1 m, Reservoir Permeability = 22 md) 9 4 2 1 1 1 1 1 0 1 2 3 4 5 6 7 8 9 10 10 25 50 100 250 500 750 1,000 meters Number of Wells Figure 12: Number of Injection Wells as a Function of Reservoir Thickness 23 REFERENCES [ 1] IEA Greenhouse Gas R& D Programme, “ Transmission of CO2 and Energy,” Report no. PH4/ 6 ( March 2002). [ 2] Mohitpour, M., H. Golshan, and A. Murray, “ Pipeline Design & Construction: A Practical Approach, The American Society of Mechanical Engineers, New York ( 2000). [ 3] “ Practical Aspects of CO2 Flooding”, Society of Petroleum Engineers ( SPE) Monograph, Vol. 22, Appendix F, ( 2002). [ 4] Hendriks, C., W. Graus, and F. van Bergen, “ Global Carbon Dioxide Storage Potential and Costs”, Ecofys report no. EEP 02001 ( 2004). [ 5] NatCarb, US Department of Energy National Energy Technology Laboratory, http:// www. natcarb. org/ Calculators/ co2_ prop. html ( Accessed on February 11, 2006). [ 6] National Institute of Standards and Technology, http:// webbook. nist. gov/ chemistry/ fluid/ ( Accessed on February 11, 2006). [ 7] McCollum, D. L., “ Simple Correlations for Estimating Carbon Dioxide Density and Viscosity as a Function of Temperature and Pressure”, Institute of Transportation Studies, University of California Davis ( 2006). [ 8] Herzog, Heddle, and Klett, “ The Economics of CO2 Storage”, MIT Laboratory for Energy and the Environment, Pub. # LFEE 2003 003 RP ( August 2003). [ 9] McCollum, D. L., “ Comparing Techno Economic Models for Pipeline Transport of Carbon Dioxide”, Institute of Transportation Studies, University of California Davis ( 2006). [ 10] Hendriks, N., T. Wildenborg, P. Feron, W. Graus, R. Brandsma, “ EC Case Carbon Dioxide Sequestration,” M70066, Ecofys ( December 2003). [ 11] IEA Greenhouse Gas R& D Programme, “ Building the Cost Curves for CO2 Storage: European Sector,” Report no. 2005/ 2 ( February 2005). [ 12] IEA Greenhouse Gas R& D Programme, “ Building the Cost Curves for CO2 Storage: North America,” Report no. 2005/ 3 ( February 2005). [ 13] Law, D. and S. Bachu, “ Hydrogeological and numerical analysis of CO2 disposal in deep aquifers in the Alberta sedimentary basin,” Energy Conversion Mgmt., 37: 6 8, pp. 1167 1174 ( 1996). [ 14] Herzog, Howard, personal e mail communication ( February 2006). 24 [ 15] Smith, L. A. et al., “ Engineering and Economic Assessment of Carbon Dioxide Sequestration in Saline Formations,” presented at the First National Conference on Carbon Sequestration, Washington D. C. ( May 14 17, 2001). [ 16] “ Costs and Indices for Domestic Oil and Gas Field Equipment and Production Operations” report, Energy Information Administration ( June 2005). [ 17] Kreutz, T., R. Williams, S. Consonni, and P. Chiesa, “ Co production of hydrogen, electricity and CO2 from coal with commercially ready technology. Part B: Economic Analysis”, International Journal of Hydrogen Energy, 30, pp. 769 784 ( 2005). SECTION II: Simple Correlations for Estimating Carbon Dioxide Density and Viscosity as a Function of Temperature and Pressure David L. McCollum dlmccollum@ ucdavis. edu Institute of Transportation Studies University of California One Shields Avenue Davis, CA 95616 ABSTRACT Recent years have seen an increased interest in carbon capture and sequestration ( CCS)— the idea of capturing carbon dioxide ( CO2) from the exhaust gases of power plants and industrial complexes, compressing the CO2 for pipeline transport, and finally injecting it underground in natural reservoirs, for example, saline aquifers and oil and gas wells. Engineers and researchers need to be able to estimate accurately the properties of CO2, a substance that exhibits unusual behavior in its properties. A number of equation of state correlations for estimating CO2’ s properties already exist, but these are often written in complex computer codes and are functions of a number of specific parameters that an inexperienced user might have trouble dealing with. This paper describes a set of simple correlations for estimating the density and viscosity of CO2 within the range of operating temperatures and pressures that might be encountered in CCS. The correlations are functions of only two input parameters: temperature and pressure. And since the correlation equations are based on experimentally measured data, their agreement with reality, as well as with other correlations, is remarkable. Keywords: carbon dioxide, CO2, CO2, sequestration, pipeline, correlation, density, viscosity 1 DESCRIPTION OF CORRELATIONS We have used experimentally measured carbon dioxide ( CO2) property data to develop a set of correlations for estimating the density and viscosity of CO2 over the range of operating temperatures and pressures that might be encountered in carbon capture and sequestration ( CCS) applications. Specifically, we have limited our correlations to a temperature range of  1.1 to 82.2 oC ( 30 to 180 oF) and a pressure range of 7.6 to 24.8 MPa ( 1100 to 3600 psia), corresponding to the post capture conditions of CO2 used in pipeline transport and underground injection. We obtain our experimental data from Kinder Morgan, a leading CO2 transporter in the United States [ 1]. We believe this data to be quite reliable, and apparently, so does the US Department of Energy National Energy Technology Laboratory’s national carbon sequestration program, NatCarb, who also use the Kinder Morgan property data for their online CO2 property calculator [ 2]. The Kinder Morgan data gives a number of CO2’ s properties as functions of temperature and pressure; some examples include: density, viscosity, compressibility factor, heat capacity, enthalpy, entropy, phase, and so on. With this data, we simply plotted the density/ viscosity vs. pressure for a given temperature and generated a sixth order polynomial regression equation to best fit the data. We then repeated this procedure at all of the other temperature values that we had access to. Some example graphs are shown below. CO2 Density as a Function of Pressure ( at  1.1 oC) y =  3.12829E 07x6 + 3.24752E 05x5  1.43858E 03x4 + 3.67519E 02x3  6.57241E 01x2 + 1.20531E+ 01x + 8.98834E+ 02 R2 = 9.99996E 01 960 970 980 990 1000 1010 1020 1030 1040 1050 7 9 11 13 15 17 19 21 23 25 Pressure ( MPa) Density ( kg/ m3) CO2 Density Regression Figure 1: CO2 density as a function of pressure at  1.1 oC 2 CO2 Density as a Function of Pressure ( at 32.2 oC) y =  1.10256E 03x6 + 1.13457E 01x5  4.76665E+ 00x4 + 1.04530E+ 02x3  1.26111E+ 03x2 + 7.94772E+ 03x  1.97102E+ 04 R2 = 9.86587E 01 400 500 600 700 800 900 1000 7 9 11 13 15 17 19 21 23 25 Pressure ( MPa) Density ( kg/ m3) CO2 Density Regression Figure 2: CO2 density as a function of pressure at 32.2 oC CO2 Viscosity as a Function of Pressure ( at 10.0 oC) y =  1.80098E 13x6 + 1.96869E 11x5  9.09904E 10x4 + 2.33381E 08x3  3.70759E 07x2 + 5.35319E 06x + 7.07073E 05 R2 = 1.00000E+ 00 8.0E 05 9.0E 05 1.0E 04 1.1E 04 1.2E 04 1.3E 04 1.4E 04 7 9 11 13 15 17 19 21 23 25 Pressure ( MPa) Viscosity ( Pa s) CO2 Viscosity Regression Figure 3: CO2 viscosity as a function of pressure at 10.0 oC 3 CO2 Viscosity as a Function of Pressure ( at 32.2 oC) y = 2.27771E 10x6  2.27111E 08x5 + 9.15360E 07x4  1.89857E 05x3 + 2.12163E 04x2  1.19673E 03x + 2.68350E 03 R2 = 9.83381E 01 0.0E+ 00 2.0E 05 4.0E 05 6.0E 05 8.0E 05 1.0E 04 1.2E 04 7 9 11 13 15 17 19 21 23 25 Pressure ( MPa) Viscosity ( Pa s) CO2 Viscosity Regression Figure 4: CO2 viscosity as a function of pressure at 32.2 oC In total, we generated 32 graphs similar to the ones seen above ( 16 density graphs and 16 viscosity graphs for each of the 16 temperatures that we had access to). These particular four graphs are shown because they are representative of all of the others. On each of the graphs, the sixth order polynomial regression equation and R2 correlation coefficient are shown. The ‘ x’ value in the regressions represents pressure ( in MPa) and the ‘ y’ value represents either density ( in kg/ m3) or viscosity ( in Pa s). In general, the R2 coefficient for all of the regressions, both density and viscosity, is greater than 0.995, showing excellent fit, except at temperatures just slightly above the critical temperature of CO2, 31.0 oC. ( Note that all of pressure values considered here are above the critical pressure of CO2, 7.38 MPa.) But even at temperatures just slightly above the critical temperature, e. g. 32.2 oC, the R2 coefficients for both density and viscosity are still greater than 0.983 ( see Figures 2 and 4). After generating all of the regression equations for density and viscosity at each of the given temperatures, we organized the regression equation coefficients into tabular form. In other words, for every temperature value there is a unique regression equation that relates pressure to either density or viscosity. Since each of these equations is unique, it has its own set of unique regression equation coefficients— i. e., the constants that precede the x6, x5, x4, x3, x2, and x terms and the final constant term in the equations shown on the graphs above. These coefficients are shown for both density and viscosity in the tables below. 4 CO2 Density Dependence of regression equation coefficients on temperature Temperature ( oC) a ( x6) b ( x5) c ( x4) d ( x3) e ( x2) f ( x) g  1.1  3.12829E 07 3.24752E 05  1.43858E 03 3.67519E 02  6.57241E 01 1.20531E+ 01 8.98834E+ 02 4.4  9.54845E 08 1.97920E 05  1.41421E 03 5.06981E 02  1.07669E+ 00 1.77109E+ 01 8.42753E+ 02 10.0  6.99274E 07 8.56082E 05  4.41249E 03 1.25510E 01  2.19938E+ 00 2.81960E+ 01 7.68647E+ 02 15.6  2.92964E 07 6.57269E 05  4.75451E 03 1.67603E 01  3.31969E+ 00 4.21135E+ 01 6.70554E+ 02 21.1  7.86428E 06 8.72837E 04  4.02787E 02 9.97669E 01  1.42859E+ 01 1.21788E+ 02 3.84188E+ 02 26.7  4.14913E 05 4.43672E 03  1.95389E 01 4.55038E+ 00  5.96084E+ 01 4.30173E+ 02  5.36390E+ 02 32.2  1.10256E 03 1.13457E 01  4.76665E+ 00 1.04530E+ 02  1.26111E+ 03 7.94772E+ 03  1.97102E+ 04 37.8  5.42882E 04 5.98138E 02  2.70792E+ 00 6.44535E+ 01  8.50922E+ 02 5.92597E+ 03  1.63183E+ 04 43.3 9.60943E 04  9.44447E 02 3.73493E+ 00  7.54076E+ 01 8.07616E+ 02  4.21227E+ 03 8.42194E+ 03 48.9 1.02964E 03  1.05231E 01 4.36150E+ 00  9.33059E+ 01 1.07660E+ 03  6.23329E+ 03 1.42664E+ 04 54.4 4.91938E 04  5.30672E 02 2.32907E+ 00  5.29027E+ 01 6.48716E+ 02  3.97202E+ 03 9.61309E+ 03 60.0 1.78281E 05  5.25573E 03 3.79601E 01  1.19952E+ 01 1.86161E+ 02  1.32231E+ 03 3.60656E+ 03 65.6  2.01381E 04 1.79337E 02  6.14241E 01 9.95370E+ 00  7.50237E+ 01 2.48324E+ 02  1.20531E+ 02 71.1  2.27250E 04 2.17674E 02  8.25519E 01 1.56315E+ 01  1.53782E+ 02 7.78805E+ 02  1.49200E+ 03 76.7  1.72335E 04 1.71075E 02  6.76015E 01 1.34315E+ 01  1.39949E+ 02 7.57756E+ 02  1.56388E+ 03 82.2  1.04002E 04 1.07058E 02  4.38694E 01 9.02417E+ 00  9.70390E+ 01 5.47454E+ 02  1.15792E+ 03 Regression Equation Coefficient CO2 Viscosity Dependence of regression equation coefficients on temperature Temperature ( oC) a ( x6) b ( x5) c ( x4) d ( x3) e ( x2) f ( x) g  1.1  3.76516E 14 4.42744E 12  2.21897E 10 6.35275E 09  1.20061E 07 3.21247E 06 9.69913E 05 4.4  4.13198E 14 5.05771E 12  2.67210E 10 8.10161E 09  1.59689E 07 3.68596E 06 8.53395E 05 10.0  1.80098E 13 1.96869E 11  9.09904E 10 2.33381E 08  3.70759E 07 5.35319E 06 7.07073E 05 15.6  3.83675E 13 4.25032E 11  1.97443E 09 4.99914E 08  7.54380E 07 8.42586E 06 5.17798E 05 21.1  9.83505E 13 1.08507E 10  4.97927E 09 1.22724E 07  1.75059E 06 1.58647E 05 2.01512E 05 26.7  4.04273E 12 4.32435E 10  1.90732E 08 4.45698E 07  5.87710E 06 4.39583E 05  6.75597E 05 32.2 2.27771E 10  2.27111E 08 9.15360E 07  1.89857E 05 2.12163E 04  1.19673E 03 2.68350E 03 37.8 9.44539E 11  9.37386E 09 3.75251E 07  7.70019E 06 8.44425E 05  4.57587E 04 9.69405E 04 43.3 4.61459E 11  4.64533E 09 1.89478E 07  3.98321E 06 4.49854E 05  2.50385E 04 5.50761E 04 48.9 2.17356E 11  2.27268E 09 9.72054E 08  2.16667E 06 2.62433E 05  1.57279E 04 3.81014E 04 54.4 1.75118E 11  1.83939E 09 7.90905E 08  1.77644E 06 2.17839E 05  1.32903E 04 3.32020E 04 60.0 1.59447E 11  1.66290E 09 7.09018E 08  1.57981E 06 1.92861E 05  1.17925E 04 2.99069E 04 65.6 1.33132E 11  1.38244E 09 5.86429E 08  1.30108E 06 1.58745E 05  9.74570E 05 2.52370E 04 71.1 9.59612E 12  9.94594E 10 4.21212E 08  9.35052E 07 1.14752E 05  7.09785E 05 1.90487E 04 76.7 4.94000E 12  5.14144E 10 2.19389E 08  4.94382E 07 6.23334E 06  3.93456E 05 1.15441E 04 82.2 8.35493E 13  9.23510E 11 4.29135E 09  1.10162E 07 1.66420E 06  1.16755E 05 4.94127E 05 Regression Equation Coefficient Table 1: Regression equation coefficients for CO2 density Table 2: Regression equation coefficients for CO2 viscosity With the above regression equation coefficients, the density and viscosity of CO2 at any temperature and pressure in the above ranges ( 1.1 to 82.2 oC and 7.6 to 24.8 MPa) can easily and reliably be calculated. One word of caution, however, is not to use the coefficients to try and 5 extrapolate beyond the above ranges, as this will surely generate inaccurate output. The calculation is outlined below in a series of steps. 1) Specify the operating temperature, Top ( in oC). 2) In the above regression coefficient tables for both density and viscosity, find the range of temperatures ( Thigh and Tlow) that the operating temperature ( Top) is between. 3) In the above regression coefficient tables for both density and viscosity, find the regression equation coefficients that correspond to Thigh and Tlow— a, b, c, d, e, f, and g. 4) Specify the operating pressure, Pop ( in MPa). 5) With Pop calculate the density at Thigh and at Tlow and the viscosity at Thigh and at Tlow. The following generic equation can be used to calculate ρhigh, ρlow, μhigh, and μlow: ρ or μ = a* Pop 6 + b* Pop 5 + c* Pop 4 + d* Pop 3 + e* Pop 2 + f* Pop + g 6) Interpolate for ρop and μop by the following equations. ρop = {( ρhigh – ρlow) * ( Top – Tlow) / ( Thigh – Tlow)} + ρlow μop = {( μhigh – μlow) * ( Top – Tlow) / ( Thigh – Tlow)} + μlow *** A simple example should serve to illustrate this calculation procedure. 1) Assume Top = 47.0 oC 2) From the regression coefficient tables, we find that Top = 47.0 oC is between Thigh = 48.9 oC and Tlow = 43.3 oC. 3) From the density and viscosity tables, the regression equation coefficients are: Density ( ρ): Thigh: a = 1.02964E 03, b =  1.05231E 01, c = 4.36150E+ 00, d =  9.33059E+ 01, e = 1.07660E+ 03, f =  6.23329E+ 03, g = 1.42664E+ 04 Tlow: a = 9.60943E 04, b =  9.44447E 02, c = 3.73493E+ 00, d =  7.54076E+ 01, e = 8.07616E+ 02, f =  4.21227E+ 03, g = 8.42194E+ 03 Viscosity ( μ): Thigh: a = 2.17356E 11, b =  2.27268E 09, c = 9.72054E 08, d =  2.16667E 06, e = 2.62433E 05, f =  1.57279E 04, g = 3.81014E 04 Tlow: a = 4.61459E 11, b =  4.64533E 09, c = 1.89478E 07, d =  3.98321E 06, e = 4.49854E 05, f =  2.50385E 04, g = 5.50761E 04 6 4) Assume Pop = 10 MPa. 5) Calculate ρhigh, ρlow, μhigh, and μlow: ρhigh = 1.02964E 03* Pop 6 +  1.05231E 01* Pop 5 + 4.36150E+ 00* Pop 4 +  9.33059E+ 01* Pop 3 + 1.07660E+ 03* Pop 2 +  6.23329E+ 03* Pop + 1.42664E+ 04 = 409.1 kg/ m3 ρlow = 9.60943E 04* Pop 6 +  9.44447E 02* Pop 5 + 3.73493E+ 00* Pop 4 +  7.54076E+ 01* Pop 3 + 8.07616E+ 02* Pop 2 +  4.21227E+ 03* Pop + 8.42194E+ 03 = 519.0 kg/ m3 μhigh = 2.17356E 11* Pop 6 +  2.27268E 09* Pop 5 + 9.72054E 08* Pop 4 +  2.16667E 06* Pop 3 + 2.62433E 05* Pop 2 +  1.57279E 04* Pop + 3.81014E 04 = 3.24E 05 Pa s μlow = 4.61459E 11* Pop 6 +  4.64533E 09* Pop 5 + 1.89478E 07* Pop 4 +  3.98321E 06* Pop 3 + 4.49854E 05* Pop 2 +  2.50385E 04* Pop + 5.50761E 04 = 3.86E 05 Pa s 6) Interpolate for ρop and μop. ρop = {( 409.1 – 519.0) * ( 47.0 – 43.3) / ( 48.9 – 43.3)} + 519.0 = 446.4 kg/ m3 μop = {( 3.24E 05 – 3.86E 05) * ( 47.0 – 43.3) / ( 48.9 – 43.3)} + 3.86E 05 = 3.45E 05 Pa s 7 COMPARISON WITH OTHER CORRELATIONS We have compared our CO2 correlations to other, more complex equation of state correlations and find that ours are in agreement. Garcia [ 3] does a nice job of explaining equation of state CO2 property correlations and then comparing densities calculated by various correlations over a small range of temperatures and pressures. He provides the following comparison table: Table 3: CO2 density ( kg/ m3) at 320 K ( 47.0 oC) as a function of temperature and pressure by various correlations Note that all of the densities in the above table are for 320 K ( i. e., ~ 47.0 oC). Now, look at the row of CO2 densities that correspond to 100 bar ( i. e., 10 MPa). By design, these are exactly the operating conditions that we used in the example above to illustrate our methods and equations. At these conditions, our correlations estimate the CO2 density to be 446.4 kg/ m3, which is well within the range of values ( 446.78 – 505.36 kg/ m3) calculated by other, more complex correlations, as shown in Garcia’s table. In addition, our correlations match well with online CO2 property calculators like those of NatCarb and the National Institute of Standards and Technology [ 2, 4]. As previously mentioned, the NatCarb calculator uses the same Kinder Morgan property data that we use. The NIST calculator on the other hand uses the correlations of Span and Wagner [ 5], which Garcia references in his table above. Density and viscosity values ( both experimentally measured and those calculated by our regression equations) are shown in the appendices for all of the temperature and pressure 8 operating points that we had data for. Also in the appendix, we show the percent differences between the calculated and experimentally measured values for both density and viscosity. In almost all cases, the percent difference is less than 1%, and much of the time it is less than 0.1%. The greatest differences occur near the critical point of CO2, with differences as high as 13.8% for density and 18.1% for viscosity. Therefore, if one is interested in designing a system where the temperature and pressure are near the critical point of CO2 ( 31.0 oC and 7.38 MPa) for much of the time, then perhaps a more complex equation of state CO2 property correlation should be used. But at virtually any other operating conditions ( at least in the range of conditions studied here), our correlations provide very reliable results. 9 CONCLUSION We have used experimentally measured CO2 property data to create sixth order polynomial correlation equations for estimating the density and viscosity of CO2. Our correlations are functions of only two parameters— temperature and pressure— and can be used in the range of  1.1 to 82.2 oC ( 30 to 180 oF) and 7.6 to 24.8 MPa ( 1100 to 3600 psia). In the case of carbon capture and sequestration, these operating ranges correspond to the postcapture/ post compression conditions of CO2 used in pipeline transport and underground injection. Our correlations provide a simple alternative to the more complex equation of state correlations that are often used. While these more complex correlations may provide slightly more accurate density and viscosity estimates near the critical point of CO2, for the vast majority of operating temperatures and pressures in the ranges mentioned above, our correlations are just as accurate and reliable and should be used with confidence. We believe that simple correlations of this kind will be demanded more and more in the future, as CCS continues to gain interest, especially among those engineers and researchers with little background in the field and who would prefer to use simple correlations to obtain accurate results. * Note: Any parties interested in obtaining a copy of the Microsoft Excel file of the CO2 property correlations described in this report, should feel free to contact the author at dlmccollum@ ucdavis. edu. 10 REFERENCES [ 1] “ Practical Aspects of CO2 Flooding”, Society of Petroleum Engineers ( SPE) Monograph, Vol. 22, Appendix F, ( 2002). [ 2] NatCarb, US Department of Energy National Energy Technology Laboratory, http:// www. natcarb. org/ Calculators/ co2_ prop. html, Accessed on February 11, 2006. [ 3] García, J. E., “ Fluid Dynamics of Carbon Dioxide Disposal Into Saline Aquifers”, PhD dissertation, University of California at Berkeley, Berkeley, California ( December 2003). [ 4] National Institute of Standards and Technology ( NIST), http:// webbook. nist. gov/ chemistry/ fluid/, Accessed on February 11, 2006. [ 5] Span, R. and W. Wagner, “ A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple Point Temperature to 1100 K at Pressures up to 800 MPa”, J. Phys. Chem. Ref. Data, 25, 6, 1509 1596 ( 1996). APPENDIX Appendix 1: Regression equation coefficients for CO2 density Appendix 2: Regression equation coefficients for CO2 viscosity Appendix 3: CO2 density as a function of temperature and pressure ( experimentally measured values from the Kinder Morgan property data) Appendix 4: CO2 density as a function of temperature and pressure ( calculated values from the regression equations) Appendix 5: Percent difference between the calculated and experimentally measured density values at each of the temperature and pressure operating points Appendix 6: CO2 viscosity as a function of temperature and pressure ( experimentallymeasured values from the Kinder Morgan property data) Appendix 7: CO2 viscosity as a function of temperature and pressure ( calculated values from the regression equations) Appendix 8: Percent difference between the calculated and experimentally measured viscosity values at each of the temperature and pressure operating points i Appendix 1 CO2 Density Dependence of regression equation coefficients on temperature Temperature ( oC) a ( x6) b ( x 5 ) c ( x 4 ) d ( x 3 ) e ( x 2 ) f ( x) g  1.1  3.12829E 07 3.24752E 05  1.43858E 03 3.67519E 02  6.57241E 01 1.20531E+ 01 8.98834E+ 02 4.4  9.54845E 08 1.97920E 05  1.41421E 03 5.06981E 02  1.07669E+ 00 1.77109E+ 01 8.42753E+ 02 10.0  6.99274E 07 8.56082E 05  4.41249E 03 1.25510E 01  2.19938E+ 00 2.81960E+ 01 7.68647E+ 02 15.6  2.92964E 07 6.57269E 05  4.75451E 03 1.67603E 01  3.31969E+ 00 4.21135E+ 01 6.70554E+ 02 21.1  7.86428E 06 8.72837E 04  4.02787E 02 9.97669E 01  1.42859E+ 01 1.21788E+ 02 3.84188E+ 02 26.7  4.14913E 05 4.43672E 03  1.95389E 01 4.55038E+ 00  5.96084E+ 01 4.30173E+ 02  5.36390E+ 02 32.2  1.10256E 03 1.13457E 01  4.76665E+ 00 1.04530E+ 02  1.26111E+ 03 7.94772E+ 03  1.97102E+ 04 37.8  5.42882E 04 5.98138E 02  2.70792E+ 00 6.44535E+ 01  8.50922E+ 02 5.92597E+ 03  1.63183E+ 04 43.3 9.60943E 04  9.44447E 02 3.73493E+ 00  7.54076E+ 01 8.07616E+ 02  4.21227E+ 03 8.42194E+ 03 48.9 1.02964E 03  1.05231E 01 4.36150E+ 00  9.33059E+ 01 1.07660E+ 03  6.23329E+ 03 1.42664E+ 04 54.4 4.91938E 04  5.30672E 02 2.32907E+ 00  5.29027E+ 01 6.48716E+ 02  3.97202E+ 03 9.61309E+ 03 60.0 1.78281E 05  5.25573E 03 3.79601E 01  1.19952E+ 01 1.86161E+ 02  1.32231E+ 03 3.60656E+ 03 65.6  2.01381E 04 1.79337E 02  6.14241E 01 9.95370E+ 00  7.50237E+ 01 2.48324E+ 02  1.20531E+ 02 71.1  2.27250E 04 2.17674E 02  8.25519E 01 1.56315E+ 01  1.53782E+ 02 7.78805E+ 02  1.49200E+ 03 76.7  1.72335E 04 1.71075E 02  6.76015E 01 1.34315E+ 01  1.39949E+ 02 7.57756E+ 02  1.56388E+ 03 82.2  1.04002E 04 1.07058E 02  4.38694E 01 9.02417E+ 00  9.70390E+ 01 5.47454E+ 02  1.15792E+ 03 Regression Equation Coefficient ii Appendix 2 CO2 Viscosity Dependence of regression equation coefficients on temperature Temperature ( oC) a ( x6) b ( x 5 ) c ( x 4 ) d ( x 3 ) e ( x 2 ) f ( x) g  1.1  3.76516E 14 4.42744E 12  2.21897E 10 6.35275E 09  1.20061E 07 3.21247E 06 9.69913E 05 4.4  4.13198E 14 5.05771E 12  2.67210E 10 8.10161E 09  1.59689E 07 3.68596E 06 8.53395E 05 10.0  1.80098E 13 1.96869E 11  9.09904E 10 2.33381E 08  3.70759E 07 5.35319E 06 7.07073E 05 15.6  3.83675E 13 4.25032E 11  1.97443E 09 4.99914E 08  7.54380E 07 8.42586E 06 5.17798E 05 21.1  9.83505E 13 1.08507E 10  4.97927E 09 1.22724E 07  1.75059E 06 1.58647E 05 2.01512E 05 26.7  4.04273E 12 4.32435E 10  1.90732E 08 4.45698E 07  5.87710E 06 4.39583E 05  6.75597E 05 32.2 2.27771E 10  2.27111E 08 9.15360E 07  1.89857E 05 2.12163E 04  1.19673E 03 2.68350E 03 37.8 9.44539E 11  9.37386E 09 3.75251E 07  7.70019E 06 8.44425E 05  4.57587E 04 9.69405E 04 43.3 4.61459E 11  4.64533E 09 1.89478E 07  3.98321E 06 4.49854E 05  2.50385E 04 5.50761E 04 48.9 2.17356E 11  2.27268E 09 9.72054E 08  2.16667E 06 2.62433E 05  1.57279E 04 3.81014E 04 54.4 1.75118E 11  1.83939E 09 7.90905E 08  1.77644E 06 2.17839E 05  1.32903E 04 3.32020E 04 60.0 1.59447E 11  1.66290E 09 7.09018E 08  1.57981E 06 1.92861E 05  1.17925E 04 2.99069E 04 65.6 1.33132E 11  1.38244E 09 5.86429E 08  1.30108E 06 1.58745E 05  9.74570E 05 2.52370E 04 71.1 9.59612E 12  9.94594E 10 4.21212E 08  9.35052E 07 1.14752E 05  7.09785E 05 1.90487E 04 76.7 4.94000E 12  5.14144E 10 2.19389E 08  4.94382E 07 6.23334E 06  3.93456E 05 1.15441E 04 82.2 8.35493E 13  9.23510E 11 4.29135E 09  1.10162E 07 1.66420E 06  1.16755E 05 4.94127E 05 Regression Equation Coefficient iii CO2 Density ( kg/ m3) as a Function of Temperature ( oC) and Pressure ( MPa) ( actual values from Kinder Morgan) Pressure ( MPa)  1.1 4.4 10.0 15.6 21.1 26.7 32.2 37.8 43.3 48.9 54.4 60.0 65.6 71.1 76.7 82.2 7.6 964.5 933.1 898.2 858.0 808.5 739.1 473.8 254.4 220.9 200.9 186.8 175.7 166.8 159.2 152.7 146.9 8.3 968.8 938.4 904.9 866.9 821.6 763.3 669.6 371.3 274.7 239.6 218.0 202.6 190.5 180.7 172.4 165.3 9.0 973.0 943.5 911.1 874.9 833.0 781.4 710.4 577.0 361.7 290.3 255.7 233.4 217.1 204.2 193.7 184.9 9.7 977.0 948.3 917.1 882.5 843.1 796.3 736.5 648.4 489.7 359.8 302.1 269.1 246.8 230.0 216.7 205.8 10.3 980.8 952.9 922.7 889.5 852.2 808.9 756.2 686.7 582.9 447.9 359.5 311.1 280.5 258.5 241.7 228.1 11.0 984.7 957.3 928.0 895.9 860.4 820.0 772.4 713.1 634.2 528.0 425.6 359.6 318.3 289.9 268.8 252.1 11.7 988.2 961.4 932.9 902.0 868.0 829.9 786.0 733.6 668.1 584.5 490.0 412.5 359.9 324.1 297.8 277.6 12.4 991.7 965.6 937.7 907.8 875.1 838.9 798.0 750.5 693.6 624.1 543.2 465.0 404.1 360.6 328.7 304.5 13.1 995.2 969.4 942.2 913.2 881.7 847.1 808.6 764.7 713.8 653.7 584.4 511.8 447.9 398.4 361.1 332.7 13.8 998.4 973.3 946.7 918.3 887.9 854.7 818.2 777.4 730.8 677.4 616.6 551.2 488.6 435.7 394.2 361.7 14.5 1001.6 977.0 950.9 923.3 893.7 861.8 827.0 788.6 745.5 697.0 642.5 583.6 524.6 471.3 426.7 391.0 15.2 1004.8 980.5 955.0 928.0 899.3 868.5 835.2 798.7 758.3 713.6 664.1 610.6 555.8 503.8 458.1 420.0 15.9 1007.9 983.9 958.9 932.6 904.6 874.8 842.7 808.0 769.8 728.2 682.5 633.5 582.8 532.9 487.4 447.9 16.5 1010.8 987.2 962.7 936.9 909.7 880.7 849.8 816.5 780.4 741.2 698.7 653.2 606.0 558.9 514.4 474.3 17.2 1013.8 990.6 966.4 941.1 914.5 886.5 856.5 824.5 790.0 752.9 713.0 670.5 626.3 581.8 538.7 499.1 17.9 1016.5 993.8 969.9 945.1 919.1 891.7 862.8 831.8 798.8 763.6 725.8 685.9 644.3 602.1 560.8 521.9 18.6 1019.4 996.8 973.4 949.1 923.6 896.9 868.7 838.9 807.2 773.4 737.5 699.7 660.4 620.4 580.8 543.0 19.3 1022.1 999.9 976.8 952.9 928.0 901.8 874.4 845.5 814.9 782.3 748.2 712.2 674.9 636.9 598.9 562.2 20.0 1024.7 1002.8 980.0 956.6 932.1 906.6 879.7 851.7 822.1 790.8 758.0 723.7 688.2 651.8 615.4 580.0 20.7 1027.3 1005.6 983.2 960.1 936.1 911.1 885.0 857.6 829.0 798.8 767.3 734.3 700.3 665.6 630.6 596.4 21.4 1029.8 1008.5 986.4 963.7 940.0 915.5 890.0 863.2 835.4 806.2 775.8 744.1 711.4 678.1 644.6 611.4 22.1 1032.4 1011.2 989.5 967.0 943.8 919.8 894.8 868.7 841.6 813.3 783.8 753.4 721.8 689.8 657.4 625.4 22.8 1034.8 1014.0 992.3 970.2 947.5 923.8 899.4 874.0 847.5 820.0 791.5 761.8 731.6 700.5 669.4 638.3 23.4 1037.2 1016.5 995.4 973.4 951.0 927.8 903.8 878.9 853.1 826.4 798.5 770.0 740.5 710.7 680.5 650.4 24.1 1039.6 1019.1 998.1 976.6 954.5 931.6 908.1 883.7 858.4 832.3 805.4 777.7 749.2 720.2 690.9 661.7 24.8 1041.8 1021.7 1001.0 979.7 957.9 935.5 912.3 888.4 863.7 838.2 811.8 784.9 757.2 729.2 700.6 672.3 Temperature ( oC) Appendix 3 iv CO2 Density ( kg/ m3) as a Function of Temperature ( oC) and Pressure ( MPa) ( calculated values from regression equations) Pressure ( MPa)  1.1 4.4 10.0 15.6 21.1 26.7 32.2 37.8 43.3 48.9 54.4 60.0 65.6 71.1 7.6 964.5 933.1 898.2 858.0 808.5 739.5 494.7 236.0 203.5 199.6 192.1 180.5 169.1 159.9 8.3 968.8 938.4 904.9 866.8 821.5 762.6 629.9 422.4 295.4 234.5 208.9 196.7 188.2 180.5 9.0 973.0 943.5 911.2 875.0 832.9 781.2 708.3 548.7 390.0 296.8 251.0 228.0 214.1 203.3 9.7 977.0 948.3 917.1 882.5 843.1 796.5 750.3 632.0 478.5 370.9 307.0 269.4 245.8 229.3 10.3 980.8 952.9 922.6 889.5 852.2 809.3 771.0 685.5 555.6 445.9 368.5 316.5 282.2 258.6 11.0 984.6 957.3 927.9 895.9 860.4 820.3 780.7 719.3 618.6 514.9 429.6 366.2 321.8 291.0 11.7 988.2 961.5 932.9 902.0 868.0 830.0 786.5 740.8 667.3 573.8 486.5 415.7 363.2 325.7 12.4 991.7 965.6 937.7 907.8 875.1 838.8 792.3 755.4 702.7 621.4 537.0 463.0 405.1 361.9 13.1 995.1 969.5 942.3 913.2 881.6 846.9 799.9 766.5 726.9 657.7 579.9 506.8 446.1 398.6 13.8 998.5 973.3 946.7 918.4 887.8 854.5 809.8 776.2 742.8 684.4 615.5 546.2 485.1 434.8 14.5 1001.7 976.9 950.9 923.3 893.7 861.7 821.3 785.8 752.9 703.4 644.2 580.8 521.3 469.7 15.2 1004.8 980.5 955.0 928.0 899.3 868.4 833.5 795.7 760.1 717.0 667.2 610.4 554.0 502.4 15.9 1007.9 983.9 958.9 932.5 904.6 874.8 845.1 805.7 766.3 727.5 685.6 635.5 582.8 532.4 16.5 1010.8 987.3 962.7 936.9 909.7 880.9 855.0 815.6 773.3 736.8 700.7 656.3 607.8 559.4 17.2 1013.8 990.5 966.4 941.1 914.5 886.6 862.7 824.9 782.0 746.2 713.6 673.6 629.0 583.2 17.9 1016.6 993.7 969.9 945.2 919.2 892.0 868.0 833.4 792.5 756.5 725.2 688.0 646.8 604.0 18.6 1019.4 996.8 973.4 949.1 923.6 897.1 871.2 840.8 804.4 767.7 736.3 700.4 662.0 622.0 19.3 1022.1 999.9 976.8 952.9 927.9 901.9 873.0 847.2 816.7 779.6 747.1 711.5 675.1 637.8 20.0 1024.7 1002.8 980.1 956.6 932.1 906.5 874.7 852.8 828.2 791.1 757.6 721.9 686.9 651.8 20.7 1027.3 1005.7 983.3 960.2 936.1 911.0 877.5 857.8 837.5 801.2 767.8 732.1 698.1 664.8 21.4 1029.9 1008.5 986.4 963.6 940.0 915.4 882.4 862.8 843.6 808.9 777.2 742.4 709.3 677.2 22.1 1032.4 1011.2 989.4 967.0 943.8 919.7 889.7 868.1 846.3 813.7 785.7 752.8 720.7 689.4 22.8 1034.8 1013.9 992.4 970.3 947.5 923.9 898.9 873.9 846.5 816.1 792.9 763.0 732.1 701.3 23.4 1037.2 1016.6 995.3 973.5 951.1 928.0 907.7 880.0 847.0 817.9 799.3 772.2 742.8 712.7 24.1 1039.6 1019.1 998.2 976.6 954.5 931.9 911.3 885.6 853.1 823.2 805.5 779.5 751.3 722.5 24.8 1041.9 1021.6 1001.0 979.7 957.9 935.4 902.2 888.9 873.2 838.9 813.4 783.1 755.1 728.8 Temperature ( oC) Appendix 4 v Percent difference (%) between calculated and actual CO2 density values ( 100% * [ ( calculated  actual ) / actual ] ) Pressure ( MPa)  1.1 4.4 10.0 15.6 21.1 26.7 32.2 37.8 43.3 48.9 54.4 60.0 65.6 71.1 7.6 0.00 0.00 0.00 0.00 0.01 0.06 4.40  7.20  7.86  0.64 2.85 2.72 1.41 0.41 8.3 0.00 0.00 0.00  0.01  0.01  0.09  5.92 13.75 7.51  2.16  4.16  2.93  1.19  0.13 9.0 0.00 0.00 0.00 0.01 0.00  0.02  0.30  4.90 7.83 2.26  1.82  2.31  1.37  0.46 9.7 0.00 0.00 0.00 0.00 0.00 0.02 1.87  2.53  2.27 3.11 1.62 0.09  0.43  0.32 10.3 0.00  0.01 0.00  0.01 0.00 0.04 1.95  0.17  4.69  0.43 2.52 1.76 0.60 0.03 11.0  0.01 0.00 0.00 0.00 0.01 0.03 1.08 0.87  2.45  2.48 0.94 1.83 1.10 0.35 11.7 0.00 0.01 0.00 0.00 0.00 0.01 0.06 0.98  0.13  1.83  0.71 0.77 0.92 0.50 12.4 0.00 0.00 0.00 0.00 0.00  0.01  0.72 0.66 1.31  0.44  1.15  0.43 0.24 0.36 13.1  0.01 0.00 0.01 0.00 0.00  0.02  1.08 0.23 1.84 0.62  0.75  0.97  0.40 0.05 13.8 0.00 0.00 0.00 0.00  0.01  0.03  1.04  0.15 1.64 1.03  0.17  0.91  0.70  0.20 14.5 0.00 0.00 0.00 0.00 0.00  0.02  0.69  0.35 1.00 0.92 0.27  0.48  0.63  0.34 15.2 0.00 0.00  0.01 0.01 0.00  0.01  0.21  0.38 0.23 0.47 0.46  0.03  0.34  0.27 15.9 0.00 0.01 0.00  0.01 0.00 0.01 0.27  0.28  0.46  0.10 0.44 0.31 0.01  0.09 16.5 0.01 0.01 0.00 0.00 0.00 0.02 0.62  0.11  0.91  0.60 0.28 0.47 0.29 0.10 17.2  0.01 0.00 0.00 0.00 0.00 0.01 0.73 0.05  1.02  0.89 0.08 0.45 0.42 0.25 17.9 0.01  0.01 0.00 0.01 0.00 0.03 0.61 0.19  0.80  0.94  0.08 0.31 0.40 0.31 18.6  0.01 0.00 0.00 0.00 0.00 0.02 0.29 0.23  0.35  0.73  0.16 0.11 0.23 0.26 19.3  0.01 0.00 0.00 0.00 0.00 0.01  0.16 0.21 0.22  0.35  0.16  0.09 0.03 0.14 20.0 0.00 0.00 0.01 0.00 0.00  0.01  0.57 0.13 0.74 0.03  0.05  0.25  0.19 0.01 20.7 0.01 0.00 0.00 0.00 0.00  0.01  0.85 0.02 1.03 0.29 0.06  0.30  0.32  0.12 21.4 0.00 0.00 0.00 0.00 0.00  0.01  0.86  0.05 0.99 0.33 0.19  0.22  0.29  0.13 22.1 0.00 0.00 0.00 0.00 0.00  0.01  0.57  0.07 0.56 0.05 0.24  0.07  0.16  0.06 22.8 0.00 0.00 0.01 0.00 0.00 0.01  0.06  0.01  0.12  0.48 0.19 0.15 0.07 0.12 23.4 0.00 0.00  0.01 0.00 0.00 0.03 0.43 0.12  0.72  1.03 0.10 0.29 0.30 0.28 24.1 0.00 0.00 0.01 0.00 0.00 0.03 0.35 0.21  0.62  1.09 0.02 0.23 0.28 0.32 24.8 0.00 0.00 0.00 0.00 0.00  0.01  1.10 0.05 1.10 0.08 0.20  0.23  0.28  0.05 Temperature ( oC) Appendix 5 vi CO2 Viscosity ( Pa s) as a Function of Temperature ( oC) and Pressure ( MPa) ( actual values from Kinder Morgan) Pressure ( MPa)  1.1 4.4 10.0 15.6 21.1 26.7 32.2 37.8 43.3 48.9 54.4 60.0 65.6 71.1 7.6 1.17E 04 1.07E 04 9.76E 05 8.86E 05 7.94E 05 6.92E 05 3.42E 05 2.26E 05 2.14E 05 2.15E 05 2.10E 05 2.07E 05 2.05E 05 2.05E 05 8.3 1.18E 04 1.08E 04 9.93E 05 9.04E 05 8.17E 05 7.24E 05 2.93E 05 2.68E 05 2.48E 05 2.33E 05 2.25E 05 2.19E 05 2.15E 05 2.13E 05 9.0 1.20E 04 1.10E 04 1.01E 04 9.22E 05 8.37E 05 7.51E 05 3.89E 05 3.35E 05 2.93E 05 2.62E 05 2.46E 05 2.35E 05 2.27E 05 2.22E 05 9.7 1.21E 04 1.11E 04 1.02E 04 9.39E 05 8.56E 05 7.74E 05 5.35E 05 4.35E 05 3.58E 05 3.02E 05 2.76E 05 2.58E 05 2.44E 05 2.35E 05 10.3 1.22E 04 1.13E 04 1.04E 04 9.55E 05 8.74E 05 7.95E 05 6.74E 05 5.34E 05 4.25E 05 3.47E 05 3.11E 05 2.86E 05 2.66E 05 2.53E 05 11.0 1.24E 04 1.14E 04 1.05E 04 9.71E 05 8.91E 05 8.14E 05 7.21E 05 5.80E 05 4.68E 05 3.87E 05 3.47E 05 3.17E 05 2.92E 05 2.74E 05 11.7 1.25E 04 1.16E 04 1.07E 04 9.85E 05 9.07E 05 8.31E 05 7.51E 05 6.15E 05 5.07E 05 4.25E 05 3.80E 05 3.44E 05 3.16E 05 2.93E 05 12.4 1.26E 04 1.17E 04 1.08E 04 1.00E 04 9.22E 05 8.48E 05 7.65E 05 6.41E 05 5.40E 05 4.61E 05 4.10E 05 3.70E 05 3.37E 05 3.12E 05 13.1 1.28E 04 1.18E 04 1.10E 04 1.01E 04 9.37E 05 8.64E 05 7.76E 05 6.63E 05 5.68E 05 4.92E 05 4.38E 05 3.94E 05 3.58E 05 3.30E 05 13.8 1.29E 04 1.20E 04 1.11E 04 1.03E 04 9.51E 05 8.79E 05 7.95E 05 6.85E 05 5.92E 05 5.17E 05 4.63E 05 4.18E 05 3.81E 05 3.50E 05 14.5 1.30E 04 1.21E 04 1.12E 04 1.04E 04 9.65E 05 8.94E 05 8.06E 05 7.04E 05 6.16E 05 5.43E 05 4.88E 05 4.42E 05 4.02E 05 3.70E 05 15.2 1.32E 04 1.22E 04 1.14E 04 1.05E 04 9.79E 05 9.08E 05 8.05E 05 7.18E 05 6.40E 05 5.72E 05 5.14E 05 4.65E 05 4.23E 05 3.88E 05 15.9 1.33E 04 1.23E 04 1.15E 04 1.07E 04 9.92E 05 9.22E 05 8.09E 05 7.33E 05 6.62E 05 5.98E 05 5.39E 05 4.87E 05 4.43E 05 4.07E 05 16.5 1.34E 04 1.25E 04 1.16E 04 1.08E 04 1.00E 04 9.35E 05 8.15E 05 7.47E 05 6.83E 05 6.21E 05 5.61E 05 5.08E 05 4.62E 05 4.25E 05 17.2 1.35E 04 1.26E 04 1.17E 04 1.09E 04 1.02E 04 9.48E 05 8.23E 05 7.62E 05 7.01E 05 6.42E 05 5.82E 05 5.28E 05 4.82E 05 4.43E 05 17.9 1.37E 04 1.27E 04 1.18E 04 1.10E 04 1.03E 04 9.61E 05 8.33E 05 7.76E 05 7.18E 05 6.61E 05 6.01E 05 5.47E 05 5.01E 05 4.61E 05 18.6 1.38E 04 1.28E 04 1.20E 04 1.12E 04 1.04E 04 9.73E 05 8.45E 05 7.89E 05 7.33E 05 6.78E 05 6.19E 05 5.66E 05 5.19E 05 4.79E 05 19.3 1.39E 04 1.30E 04 1.21E 04 1.13E 04 1.05E 04 9.85E 05 8.58E 05 8.02E 05 7.47E 05 6.92E 05 6.35E 05 5.83E 05 5.37E 05 4.97E 05 20.0 1.40E 04 1.31E 04 1.22E 04 1.14E 04 1.07E 04 9.97E 05 8.74E 05 8.15E 05 7.58E 05 7.04E 05 6.50E 05 6.00E 05 5.55E 05 5.15E 05 20.7 1.41E 04 1.32E 04 1.23E 04 1.15E 04 1.08E 04 1.01E 04 8.85E 05 8.28E 05 7.73E 05 7.19E 05 6.65E 05 6.16E 05 5.71E 05 5.31E 05 21.4 1.43E 04 1.33E 04 1.24E 04 1.16E 04 1.09E 04 1.02E 04 8.95E 05 8.41E 05 7.87E 05 7.34E 05 6.81E 05 6.31E 05 5.86E 05 5.46E 05 22.1 1.44E 04 1.34E 04 1.26E 04 1.17E 04 1.10E 04 1.03E 04 9.06E 05 8.53E 05 8.00E 05 7.48E 05 6.95E 05 6.45E 05 6.00E 05 5.60E 05 22.8 1.45E 04 1.35E 04 1.27E 04 1.19E 04 1.11E 04 1.04E 04 9.18E 05 8.65E 05 8.13E 05 7.61E 05 7.08E 05 6.59E 05 6.14E 05 5.74E 05 23.4 1.46E 04 1.37E 04 1.28E 04 1.20E 04 1.12E 04 1.05E 04 9.29E 05 8.77E 05 8.25E 05 7.73E 05 7.20E 05 6.71E 05 6.27E 05 5.87E 05 24.1 1.47E 04 1.38E 04 1.29E 04 1.21E 04 1.13E 04 1.06E 04 9.41E 05 8.88E 05 8.36E 05 7.85E 05 7.32E 05 6.83E 05 6.39E 05 5.99E 05 24.8 1.49E 04 1.39E 04 1.30E 04 1.22E 04 1.14E 04 1.08E 04 9.53E 05 8.99E 05 8.47E 05 7.95E 05 7.43E 05 6.94E 05 6.50E 05 6.11E 05 Temperature ( oC) Appendix 6 vii CO2 Viscosity ( Pa s) as a Function of Temperature ( oC) and Pressure ( MPa) ( calculated values from regression equations) Pressure ( MPa)  1.1 4.4 10.0 15.6 21.1 26.7 32.2 37.8 43.3 48.9 54.4 60.0 65.6 71.1 7.6 1.17E 04 1.07E 04 9.76E 05 8.86E 05 7.94E 05 6.92E 05 3.05E 05 2.13E 05 2.08E 05 2.12E 05 2.10E 05 2.07E 05 2.06E 05 2.05E 05 8.3 1.18E 04 1.08E 04 9.93E 05 9.04E 05 8.16E 05 7.23E 05 3.45E 05 2.80E 05 2.52E 05 2.34E 05 2.24E 05 2.17E 05 2.13E 05 2.11E 05 9.0 1.20E 04 1.10E 04 1.01E 04 9.22E 05 8.37E 05 7.50E 05 4.27E 05 3.58E 05 3.04E 05 2.66E 05 2.48E 05 2.36E 05 2.27E 05 2.22E 05 9.7 1.21E 04 1.11E 04 1.02E 04 9.39E 05 8.56E 05 7.74E 05 5.23E 05 4.35E 05 3.59E 05 3.04E 05 2.78E 05 2.60E 05 2.46E 05 2.37E 05 10.3 1.22E 04 1.13E 04 1.04E 04 9.55E 05 8.74E 05 7.95E 05 6.15E 05 5.05E 05 4.12E 05 3.44E 05 3.11E 05 2.86E 05 2.68E 05 2.54E 05 11.0 1.24E 04 1.14E 04 1.05E 04 9.71E 05 8.91E 05 8.14E 05 6.92E 05 5.65E 05 4.61E 05 3.84E 05 3.44E 05 3.14E 05 2.91E 05 2.73E 05 11.7 1.25E 04 1.16E 04 1.07E 04 9.85E 05 9.07E 05 8.32E 05 7.49E 05 6.13E 05 5.04E 05 4.22E 05 3.77E 05 3.42E 05 3.14E 05 2.92E 05 12.4 1.26E 04 1.17E 04 1.08E 04 1.00E 04 9.22E 05 8.48E 05 7.87E 05 6.49E 05 5.41E 05 4.58E 05 4.08E 05 3.69E 05 3.37E 05 3.12E 05 13.1 1.28E 04 1.18E 04 1.10E 04 1.01E 04 9.37E 05 8.64E 05 8.07E 05 6.76E 05 5.72E 05 4.92E 05 4.38E 05 3.95E 05 3.59E 05 3.31E 05 13.8 1.29E 04 1.20E 04 1.11E 04 1.03E 04 9.51E 05 8.79E 05 8.14E 05 6.95E 05 5.99E 05 5.22E 05 4.66E 05 4.19E 05 3.81E 05 3.50E 05 14.5 1.30E 04 1.21E 04 1.12E 04 1.04E 04 9.65E 05 8.94E 05 8.12E 05 7.09E 05 6.22E 05 5.49E 05 4.92E 05 4.43E 05 4.02E 05 3.69E 05 15.2 1.32E 04 1.22E 04 1.13E 04 1.05E 04 9.79E 05 9.08E 05 8.07E 05 7.20E 05 6.43E 05 5.74E 05 5.16E 05 4.65E 05 4.23E 05 3.88E 05 15.9 1.33E 04 1.23E 04 1.15E 04 1.07E 04 9.92E 05 9.22E 05 8.02E 05 7.30E 05 6.61E 05 5.97E 05 5.38E 05 4.86E 05 4.43E 05 4.07E 05 16.5 1.34E 04 1.25E 04 1.16E 04 1.08E 04 1.00E 04 9.35E 05 8.02E 05 7.41E 05 6.79E 05 6.19E 05 5.60E 05 5.07E 05 4.62E 05 4.25E 05 17.2 1.35E 04 1.26E 04 1.17E 04 1.09E 04 1.02E 04 9.48E 05 8.08E 05 7.54E 05 6.96E 05 6.39E 05 5.80E 05 5.27E 05 4.82E 05 4.44E 05 17.9 1.37E 04 1.27E 04 1.18E 04 1.10E 04 1.03E 04 9.61E 05 8.21E 05 7.69E 05 7.13E 05 6.57E 05 5.99E 05 5.46E 05 5.01E 05 4.62E 05 18.6 1.38E 04 1.28E 04 1.20E 04 1.12E 04 1.04E 04 9.73E 05 8.38E 05 7.86E 05 7.30E 05 6.75E 05 6.18E 05 5.65E 05 5.19E 05 4.80E 05 19.3 1.39E 04 1.30E 04 1.21E 04 1.13E 04 1.05E 04 9.85E 05 8.59E 05 8.03E 05 7.47E 05 6.92E 05 6.35E 05 5.83E 05 5.37E 05 4.97E 05 20.0 1.40E 04 1.31E 04 1.22E 04 1.14E 04 1.07E 04 9.97E 05 8.79E 05 8.20E 05 7.63E 05 7.07E 05 6.52E 05 6.00E 05 5.55E 05 5.14E 05 20.7 1.41E 04 1.32E 04 1.23E 04 1.15E 04 1.08E 04 1.01E 04 8.96E 05 8.35E 05 7.77E 05 7.22E 05 6.67E 05 6.16E 05 5.71E 05 5.30E 05 21.4 1.43E 04 1.33E 04 1.24E 04 1.16E 04 1.09E 04 1.02E 04 9.07E 05 8.47E 05 7.90E 05 7.36E 05 6.82E 05 6.31E 05 5.87E 05 5.46E 05 22.1 1.44E 04 1.34E 04 1.26E 04 1.17E 04 1.10E 04 1.03E 04 9.12E 05 8.57E 05 8.02E 05 7.48E 05 6.95E 05 6.45E 05 6.01E 05 5.60E 05 22.8 1.45E 04 1.35E 04 1.27E 04 1.19E 04 1.11E 04 1.04E 04 9.11E 05 8.63E 05 8.11E 05 7.60E 05 7.08E 05 6.58E 05 6.14E 05 5.74E 05 23.4 1.46E 04 1.37E 04 1.28E 04 1.20E 04 1.12E 04 1.05E 04 9.11E 05 8.70E 05 8.21E 05 7.71E 05 7.19E 05 6.70E 05 6.27E 05 5.86E 05 24.1 1.47E 04 1.38E 04 1.29E 04 1.21E 04 1.13E 04 1.06E 04 9.22E 05 8.82E 05 8.33E 05 7.83E 05 7.31E 05 6.81E 05 6.39E 05 5.99E 05 24.8 1.49E 04 1.39E 04 1.30E 04 1.22E 04 1.14E 04 1.08E 04 9.63E 05 9.07E 05 8.51E 05 7.97E 05 7.44E 05 6.94E 05 6.51E 05 6.11E 05 Temperature ( oC) Appendix 7 viii Percent difference (%) between calculated and actual CO2 viscosity values ( 100% * [ ( calculated  actual ) / actual ] ) Pressure ( MPa)  1.1 4.4 10.0 15.6 21.1 26.7 32.2 37.8 43.3 48.9 54.4 60.0 65.6 71.1 7.6 0.00 0.00 0.00 0.00 0.01 0.05  10.75  5.75  2.75  1.08  0.33 0.09 0.38 0.47 8.3 0.00 0.00 0.00 0.00  0.01  0.09 18.05 4.83 1.82 0.53  0.33  0.83  1.00  0.95 9.0 0.00 0.00 0.00 0.00  0.01  0.03 9.81 6.85 4.03 1.69 0.98 0.50 0.19  0.07 9.7 0.00 0.00 0.00  0.01 0.00 0.02  2.16 0.05 0.49 0.64 0.78 0.82 0.79 0.59 10.3 0.00 0.00 0.00 0.00 0.01 0.04  8.71  5.27  2.94  0.91  0.17 0.17 0.47 0.52 11.0 0.00 0.00 0.00 0.00 0.00 0.03  4.06  2.51  1.58  0.85  0.74  0.72  0.55  0.36 11.7 0.00 0.00 0.00 0.00 0.01 0.02  0.20  0.41  0.57  0.70  0.70  0.70  0.52  0.35 12.4 0.00 0.00 0.00 0.00 0.00  0.01 2.88 1.26 0.24  0.49  0.45  0.35  0.14  0.03 13.1 0.00 0.00 0.00 0.00 0.00  0.02 4.04 1.93 0.71  0.10 0.04 0.22 0.42 0.40 13.8 0.00 0.00 0.00 0.00 0.00  0.03 2.33 1.41 1.14 0.96 0.67 0.37 0.18  0.04 14.5 0.00 0.00 0.00 0.00 0.00  0.02 0.67 0.72 1.05 1.22 0.81 0.29  0.03  0.30 15.2 0.00 0.00 0.00 0.00 0.00  0.01 0.22 0.27 0.36 0.39 0.29 0.09 0.05  0.06 15.9 0.00 0.00 0.00 0.00 0.00 0.00  0.81  0.35  0.18  0.06  0.02  0.08 0.03 0.00 16.5 0.00 0.00 0.00 0.00 0.00 0.01  1.56  0.80  0.57  0.40  0.24  0.19 0.02 0.07 17.2 0.00 0.00 0.00 0.00 0.01 0.02  1.79  0.96  0.73  0.57  0.36  0.24 0.02 0.10 17.9 0.00 0.00 0.00 0.00 0.01 0.01  1.48  0.81  0.67  0.57  0.35  0.24 0.01 0.09 18.6 0.00 0.00 0.00 0.00 0.00 0.01  0.77  0.42  0.39  0.36  0.23  0.20 0.03 0.06 19.3 0.00 0.00 0.00 0.00 0.00 0.00 0.03 0.10 0.05 0.01 0.01  0.11 0.00  0.03 20.0 0.00 0.00 0.00 0.00 0.00  0.01 0.58 0.58 0.59 0.57 0.35  0.01  0.06  0.21 20.7 0.00 0.00 0.00 0.00 0.00  0.02 1.31 0.85 0.60 0.42 0.29 0.04 0.05  0.08 21.4 0.00 0.00 0.00 0.00 0.00  0.02 1.35 0.80 0.47 0.24 0.19 0.02 0.13 0.02 22.1 0.00 0.00 0.00 0.00 0.00  0.01 0.60 0.43 0.19 0.04 0.07  0.04 0.12 0.06 22.8 0.00 0.00 0.00 0.00 0.00 0.00  0.72  0.16  0.15  0.15  0.06  0.14 0.08 0.04 23.4 0.00 0.00 0.00 0.00 0.00 0.01  1.99  0.71  0.41  0.25  0.15  0.23 0.00  0.02 24.1 0.00 0.00 0.00 0.00 0.01 0.01  2.03  0.65  0.33  0.19  0.10  0.25  0.03  0.06 24.8 0.00 0.00 0.00 0.00  0.01  0.02 1.05 0.85 0.50 0.26 0.20  0.03 0.12  0.01 Temperature ( oC) Appendix 8 SECTION III: Comparing Techno Economic Models for Pipeline Transport of Carbon Dioxide David L. McCollum dlmccollum@ ucdavis. edu Institute of Transportation Studies University of California One Shields Avenue Davis, CA 95616 ABSTRACT Due to a heightened interest in technologies to mitigate global climate change, research in the field of carbon capture and storage ( CCS) has increased in recent years, with the goal of answering the many questions that still remain in this uncertain field. At the top of the list of key issues are CCS costs: costs of carbon dioxide ( CO2) capture, compression, transport, storage, and so on. This paper focuses on costs of CO2 pipeline transport. Several recent technoeconomic models for estimating pipeline sizes and costs are compared on an “ apples to apples” basis by applying the same set of input assumptions across all models. We find that there is a large degree of variability between the output of the different models, particularly among the cost estimates, that stems from the differing approaches that each model employs. By averaging the cost estimates of the models over a wide range of CO2 mass flow rates and pipeline lengths, we have created a new CO2 pipeline capital cost model that is a function only of CO2 mass flow rate and pipeline length. This removes the need to calculate the pipeline diameter in advance of calculating costs. We feel that this equation is a reliable estimator of mid range costs, given that it has been derived from a number of recent, reliable studies on CCS. Keywords: carbon dioxide, CO2, CO2, CCS, pipeline, transport, sequestration, techno economic, cost model, climate change, greenhouse gas 1 EXECUTIVE SUMMARY Due to a heightened interest in technologies to mitigate global climate change, research in the field of carbon capture and storage ( CCS) has increased in recent years, with the goal of answering the many questions that still remain in this uncertain field. At the top of the list of key questions are CCS costs: costs of carbon dioxide ( CO2) capture, costs of transport, costs of storage, and so on. Although the practice of transporting and storing CO2 underground has been around for a few decades, as it is used in the oil and gas industry for enhanced oil recovery ( EOR), predicting the economics is still uncertain. In light of this, several studies have developed CCS models to try and predict costs, particularly for transport and storage. These models, however, differ in many ways, namely in their cost and flow equations, assumptions for operating conditions, and the reference years that their costs are expressed in. Thus, the models’ output— e. g., pipeline diameter, capital cost, O& M costs, levelized CO2 costs, etc.— comes out differently, making it difficult to compare the models’ predicted costs on an “ apples to apples” basis. By replicating the models and applying some of the same key assumptions across all models, comparisons can be made, similarities/ differences can be noted, and new models can be generated that are essentially a combination of all models. We have carried out this procedure for a few of the more recent CO2 transport models. The scope of this study was limited to onshore pipelines, since they are likely to be the most cost effective and realistic means for transporting CO2 in the future, at least in the United States. The transport models that were compared came from the following studies: Ogden, MIT, Ecofys, IEA GHG PH4/ 6, IEA GHG 2005/ 2, IEA GHG 2005/ 3, and Parker. Each of these studies was carried out within the last four years; and except for the models of Parker, which use natural gas pipeline costs to predict the costs of hydrogen pipelines, all of the models are geared specifically towards CO2 pipelines. In this paper, the basic concepts, equations, and assumptions of the above models are discussed; though, the reader is encouraged to consult the original reports for a more thorough description. The key similarities and differences between the models are then highlighted. And ultimately, a set of common basis assumptions is decided upon, with new models being created that are essentially a combination of all seven of the original models. The wide variability in the costs that each of the models estimates is easily seen in the following graph: 2 Model Comparison: Pipeline Capital Cost vs. CO2 Mass Flow Rate ( Pipeline Length = 100 km) 0 200,000 400,000 600,000 800,000 1,000,000 1,200,000 0 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 20,000 CO2 Mass Flow Rate ( tonnes/ day) Pipeline Capital Cost ($/ km) Ogden MIT Ecofys IEA GHG PH4/ 6 IEA GHG 2005/ 3 IEA GHG 2005/ 2 Parker Average By averaging the estimated capital costs of all models over a range of flow rates and pipeline lengths, we have created the following equation to model pipeline capital cost: Pipeline Capital Cost [$/ km] = ( 9970 * m0.35) * L0.13 ( where m = CO2 mass flow rate [ tonnes/ day], and L = pipeline length [ km]) Costs are given in year 2005 US dollars. This equation provides a method of estimating the pipeline capital cost per unit length based on two quantities that are typically known— CO2 mass flow rate and pipeline length. By approaching the capital cost in this way, one can avoid the calculation of pipeline diameter in advance, which can be advantageous. The above equation is a reliable method for calculating pipeline capital cost since it is essentially derived from seven other pipeline models, all of which are recent and reliable. The upper and lower bounds for the pipeline capital cost are found to be given by the following equations: Pipeline Capital Cost ( Low) [$/ km] = ( 8500 * m0.35) * L0.06 Pipeline Capital Cost ( High) [$/ km] = ( 4100 * m0.50) * L0.13 ( where m = CO2 mass flow rate [ tonnes/ day], and L = pipeline length [ km]) The estimates for average pipeline capital cost, along with the upper and lower bounds are shown together in the following graph. 3 Average Pipeline Capital Cost along with High and Low Values from Other Studies ( Pipeline Length = 100 km) 0 200,000 400,000 600,000 800,000 1,000,000 1,200,000 0 5,000 10,000 15,000 20,000 CO2 Mass Flow Rate ( tonnes/ day) Pipeline Capital Cost ($/ km) High Average Low One can feel comfortable in knowing that while the uncertainty of CO2 pipeline capital cost may be great, it will very likely be within these upper and lower bounds, and probably close to the average. 4 INTRODUCTION Due to a heightened interest in technologies to mitigate global climate change, research in the field of carbon capture and storage ( CCS) has increased in recent years, with the goal of answering the many questions that still remain in this uncertain field. At the top of the list of key questions are CCS costs: costs of carbon dioxide ( CO2) capture, costs of transport, costs of storage, and so on. Although the practice of transporting and storing CO2 underground has been around for a few decades, as it is used in the oil and gas industry for enhanced oil recovery ( EOR), predicting the economics is still uncertain. In light of this, several studies have developed CCS models to try and predict costs, particularly for transport and storage. These models, however, differ in many ways, namely in their cost and flow equations, assumptions for operating conditions, and the reference years that their costs are expressed in. Thus, the models’ output— e. g., pipeline diameter, capital cost, O& M costs, levelized CO2 costs, etc.— comes out differently, making it difficult to compare the models’ predicted costs on an “ apples to apples” basis. By replicating the models and applying some of the same key assumptions across all models, comparisons can be made, similarities/ differences can be noted, and new models can be generated that are essentially a combination of all models. We have carried out this procedure for a few of the more recent CO2 transport models. The scope of this study was limited to onshore pipelines, since they are likely to be the most cost effective and realistic means for transporting CO2 in the future, at least in the United States. The transport models that were compared came from the following studies: Ogden [ 1], MIT [ 2], Ecofys [ 3], IEA GHG PH4/ 6 [ 4], IEA GHG 2005/ 2 [ 5], IEA GHG 2005/ 3 [ 6], and Parker [ 7]. Each of these studies was carried out within the last four years; and except for the models of Parker, which use natural gas pipeline costs to predict the costs of hydrogen pipelines, all of the models are geared specifically towards CO2 pipelines. In this paper, the basic concepts, equations, and assumptions of the above models are discussed; though, the reader is encouraged to consult the original reports for a more thorough description. The key similarities and differences between the models are then highlighted. And ultimately, a set of common basis assumptions is decided upon, with new models being created that are essentially a combination of all seven of the original models. 5 DESCRIPTION OF MODELS The Ogden Models The CO2 transport models used in Ogden’s report ( or rather, those described in detail in Appendix C of the full report) were created to model a hydrogen production and distribution infrastructure that makes use of CCS. Although the publication date of the report is 2004 ( i. e., later than some of the other models that will also be described here), work on the report began much earlier in 2002 and for this reason did not build upon models that have come out more recently. For starters, Ogden’s models use a complex equation for calculating the volumetric flow rate ( Q) of CO2, which was adapted from Farris [ 8]: Q = C1 √( 1/ f) [( Pinpipe 2 – Poutpipe 2 – C2{ GΔhP2 avg / Zavg Tavg}) / ( G Tavg Zavg L)] 0.5 D2.5 E ( where Q = CO2 flow rate [ Nm3/ s], C1 = 18.921, f = friction factor, Pinpipe = pipeline inlet pressure [ kPa], Poutpipe = pipeline outlet pressure [ kPa], C2 = 0.06836, G = CO2 specific gravity = 1.519, Δh = change in elevation [ m], Pavg = average pipeline pressure, Zavg = CO2 compressibility at Pavg, Tavg = average temperature [ K], L = pipeline length [ km], D = pipeline diameter [ m], E = pipeline efficiency) Oftentimes, however, one already knows the CO2 mass flow rate ( e. g., in tonnes/ day), which can be converted to volumetric flow rate, thus enabling the back calculation of pipeline diameter. When using the above equation to solve for diameter, we assumed that some of the variables had the following constant values: change in elevation, Δh= 0; CO2 compressibility, Zavg= 0.25; pipeline efficiency, E= 1.0. The calculated diameter seems to be sensitive to compressibility and, especially, efficiency. We have done a simple sensitivity analysis for both at a given set of operating conditions. Ogden suggests that compressibility will be in the range of 0.17 0.30 for pure CO2 at average pipeline pressures of 8.8 12.0 MPa and temperatures from less than 20 oC up to 40 oC. By our calculations, at a representative CO2 mass flow rate of 10,000 tonnes/ day, inlet and outlet pressures of 15.2 and 10.3 MPa, respectively, and a temperature of 25 oC, a 76% increase in compressibility ( from 0.17 to 0.30) will lead to a calculated pipeline diameter increase of only 11% ( from 10.6 to 11.8 inches). Thus, when replicating Ogden’s models, we assume that Zavg= 0.25, which according to Ogden is a reasonable estimate at the temperature and average pipeline pressure that we will generally consider— 25 oC and 12.75 MPa, respectively. Similarly, we calculate that, at the same operating conditions mentioned above, a decrease in pipeline efficiency of 25 percentage points ( from 100% to 75%) will lead to a calculated pipeline diameter increase of 11% ( from 11.4 to 12.7 inches). The dependence of calculated diameter on pipeline efficiency gets much stronger, however, as efficiency gets lower and lower; for example, the next 25% percentage point decrease in pipeline efficiency ( from 75% to 50%) will lead to a calculated pipeline diameter increase of 17% ( from 12.7 to 14.9 inches). Ogden does not suggest any values for pipeline efficiency in her report, so we simply assume E= 1.0 when replicating her models; this assumption may not reflect real world pipelines but seems reasonable here, since none of the other models under study in this report consider pipeline efficiency. Thus, we are essentially canceling out the effect that pipeline efficiency may have so that the pipeline diameter calculated by Ogden’s models can be more directly compared to that calculated from other models. 6 Notice also that Ogden calculates the friction factor ( f) by the Nikuradse equation; this factor is similar in magnitude to the Fanning friction factor in that it is four times smaller than friction factors used in some of the other models described later in this report. Yet, even after accounting for the factor of four difference, the Nikuradse equation calculates friction factors that are consistently smaller than those assumed in the other models, which affects the size of the calculated pipeline diameter, as will be shown later. Furthermore, a word of caution that might be helpful to others when using the above mentioned flow rate equation is to multiply the length term, L, in the equation by 1000. Although not explicitly stated in the description of the equation, this causes the units to work out and helps calculate a flow rate ( or alternately, a pipeline diameter) that is on the correct order of magnitude. To estimate pipeline capital costs, the Ogden models use capital cost estimates from Skovholt’s 1993 study [ 9]. These estimates give capital costs ( in $/ m) for four different sizes of pipeline diameter ( 16, 30, 40, and 64 inches). With these four data points, an equation is generated that scales up the capital cost as the diameter gets larger. And finally, the capital cost ( in $/ m) is multiplied by the pipeline length ( L) to calculate the total capital cost. These two equations are shown below: Capital Cost ($/ m) = $ 700/ m x ( D / 16 in) 1.2 ( where D = pipeline diameter [ inches]) Total Capital Cost ($) = Capital Cost ($/ m) x L ( m) ( where L = pipeline length [ m]) Ogden prefers, however, to use capital cost equations that are functions directly of CO2 flow rate ( Q) and pipeline length ( L), rather than diameter ( D), thus making it possible to calculate the pipeline capital costs without having to solve for D directly. However, the cost equations are indirectly functions of diameter, since it has simply been parameterized away using other variables. The equation is: Capital Cost ($/ m) = $ 700/ m x ( Q / 16,000 tonnes/ day) 0.48 x ( L / 100 km) 0.24 ( where Q = CO2 mass flow rate [ tonnes/ day], and L = pipeline length [ kilometers]) Total Capital Cost ($) = Capital Cost ($/ m) x L ( m) When replicating and comparing models in this report, we use Ogden’s latter capital cost models, making them the only models ( of those that are compared) that do not use pipeline diameter to calculate costs. Ogden uses the following equation to calculate the levelized cost of CO2 transport: Levelized Cost ($/ tonne CO2) = ( CRF + O& M) x Total Capital Cost / [ Q ( Nm3/ s) x 3.17 x 107 sec/ year x ( 1.965 kg CO2/ Nm3) / ( 1000 kg/ tonne)] ( where CRF = capital recovery factor = 0.15, and O& M = O& M cost factor = 0.04) Finally, note that all of Ogden’s costs are expressed in year 2001 US$. 7 The MIT Models The Massachusetts Institute of Technology’s Laboratory for Energy and the Environment published a study on the economics of CO2 storage in 2003. Chapter 2 of their report outlines a methodology for calculating CO2 pipeline diameter and costs; this process is iterative. First, one has to guess a value for the pipeline diameter ( D). Second, the Reynold’s number ( Re) is calculated by the following equation: Re = 4 m / ( π μ D) ( where m = CO2 mass flow rate, D = pipeline diameter, and μ = CO2 viscosity) With the calculated Reynold’s number and the MIT study’s assumed pipeline roughness factor ( ε) of 0.00015 feet, the Fanning friction factor ( f) is found by using a Moody chart. This method, however, would require a manual look up for each iteration, so MIT uses an empirical relation based on the Moody chart [ 10]. 1.11 2 10 3.7 12( / ) Re 4 1.8 log 6.91 1 ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎪⎭ ⎪⎬ ⎫ ⎪⎩ ⎪⎨ ⎧ ⎟⎠ ⎞ ⎜⎝ − + ⎛ = D f ε ( f = friction factor, Re = Reynold’s number, ε = roughness factor [ ft], and D = pipeline diameter [ in]) Next, the diameter is calculated by the following equation: D5 = ( 32 f m2)/ ( π2 ρ ( ΔP/ ΔL)) ( where ΔP = inlet pressure – outlet pressure, and ΔL = pipeline length) The diameter calculated by this equation is then compared to the previously guessed value of diameter. If the calculated diameter is much different from the guessed value, then the calculated value is used to re calculate a new Reynold’s number, friction factor, and diameter. This process is repeated until the calculated diameter is the same as the one used at the start of the iteration. It should also be noted that MIT assumes a CO2 density and viscosity of 884 kg/ m3 and 6.06 x 10 5 N s/ m2, respectively, for their pipeline transport models. To calculate CO2 pipeline costs, the MIT study uses historical cost data for natural gas pipeline construction, as reported in the Oil & Gas Journal. From this data, they conclude that, on average, construction costs for CO2 pipelines would be $ 20,989/ in/ km. Furthermore, based on estimates by Fox [ 11], they suggest that O& M costs, other than pumping, would be $ 3,100/ km/ year, independent of pipeline diameter. Thus, the total annual cost and levelized cost are calculated by the following equations: Total Annual Cost ($/ yr) = {($ 20,989/ in/ km) x D x L x CRF} + {($ 3,100/ km/ yr) x L} ( where D = pipeline diameter [ in], L = pipeline length [ km], and CRF = Capital Recovery Factor = 0.15/ yr) Levelized Cost ($/ tonne CO2) = Total Annual Cost ($/ yr) / { m x CF x 365 } ( where m = CO2 mass flow rate [ tonnes/ day], CF = Plant Capacity Factor = 0.80, and 365 = days per year) 8 Finally, since the MIT study does not state the reference year that they express costs in, we assume that they use year 1998 dollars, owing to the fact that 1998 is the most recent year for which they obtained natural gas pipeline cost data from the Oil & Gas Journal. 9 The Ecofys Models The Ecofys models for CO2 transport are part of a larger report to the European Commision on the potential of CCS as a cost effective strategy to meet Kyoto Protocol targets for emissions reduction in the European Union. The technical and cost aspects of CO2 transport are given in Appendix 3 of the report. First, the equation for back calculating the pipeline diameter is: ΔP = λ * ( L/ D) * ( 1/ 2) * ρ * v2 ( where ΔP = pressure drop [ Pa], λ = friction factor, L = pipeline length [ m], D = pipeline diameter [ m], ρ = CO2 density [ kg/ m3], v = average flow velocity [ m/ s]) In the above flow equation, the velocity term, v, is a function of the mass flow rate and the crosssectional area ( i. e., diameter) of the pipeline. Thus, the equation can be rearranged to form the following equation: D5 = ( 8 λ m2)/ ( π2 ρ ( ΔP/ L)) ( where m = CO2 mass flow rate) Note how similar this equation is to the analogous diameter equation that MIT uses. There are only two main differences: ( 1) The lead constant in the Ecofys equation is 8 versus 32 in the MIT equation— four times smaller because ( 2) The friction factor in the Ecofys equation ( λ) is four times larger than the Fanning friction factor ( f) in the MIT equation. In other words, the Ecofys and MIT equations for calculating pipeline diameter are essentially the same. The only other difference is that the Ecofys study assumes a constant friction factor, whereas MIT uses an equation to calculate the friction factor, as it is a function of Reynold’s number. Ecofys suggests that their friction factor would be less than 1.5 x 10 2 for perfectly smooth pipeline walls and 2.0 x 10 2 for new untreated steel. ( Actually, in the report Ecofys states that the friction factor for new untreated steel would be 2.0 x 102, i. e. the negative sign in the exponent is missing. Though, we believe this to be a typographical error, since using a friction factor of this magnitude would lead to an unusually large pipeline diameter.) The equation used to calculate total pipeline capital cost is given by: Total Capital Cost (€) = ( 1100 €/ m2) * FT * D * L ( where FT = correction factor for terrain = 1 for most common terrain, D = pipeline diameter [ m], L = pipeline length [ m]) The total capital cost is annualized with a 10% discount rate over a 25 year operational lifetime by the following equation: n n i i i Annual Capital Cost euros yr Total Capital Cost euros ( 1 ) ( 1 ) 1 ( / ) ( ) + + − = ( where n = operational lifetime [ years], and i = discount rate) The annual O& M costs are calculated as 2.1% of the total capital cost. And the total annual cost is found by summing the annual capital and O& M costs. 1 0 Annual O& M Costs (€/ yr) = ( O& M factor) * Total Capital Cost ( where O& M factor = 2.1%) Total Annual Cost (€/ yr) = Annual Capital Cost + Annual O& M Costs The Ecofys study does not discuss the method used for calculating levelized cost of CO2 transport, but one can assume that it is similar to that used in other studies, for example, the MIT study’s equation, which is shown below. Levelized Cost (€/ tonne CO2) = Total Annual Cost ($/ yr) / { m * CF * 365 } ( where m = CO2 mass flow rate [ tonnes/ day], CF = Plant Capacity Factor, and 365 = days per year) Finally, since the Ecofys study does not state the reference year that they express costs in, we assume that they use year 2003 euros since that is the year that their report was published. 1 1 The IEA GHG PH4/ 6 Models In 2002, Woodhill Engineering Consultants of the United Kingdom studied the transmission of CO2 and energy for the IEA Greenhouse Gas R& D Programme. They wrote a report on the subject, as well as created a spreadsheet based computer model for estimating the costs and performance of CO2 transport. To calculate CO2 pipeline diameter, the IEA GHG PH4/ 6 study uses the following equation [ 12]: 5 2 2.252 D P f L Q ρ Δ = ( where ΔP = pressure drop [ bar], f = friction factor, L = pipeline length [ km], ρ = CO2 density [ kg/ m3], Q = CO2 flow rate [ liter/ min], and D = pipeline internal diameter [ mm]) A friction factor ( f) of 0.015 is assumed in the model. Further, the report states that a friction factor of this value is “ relatively conservative in that it is likely to slightly oversize a liquid line rather than undersize it” [ 4, p. 3.26]. ( Note that this friction factor is four times larger than the Fanning friction factor used in other studies.) With the internal diameter of the pipeline, the spreadsheet model uses a look up table to find the closest nominal pipe size. We, however, did not have access to the look up table, so when replicating the models of the IEA GHG PH4/ 6 study, we simply use the internal pipeline diameter throughout ( e. g., in the pipeline cost calculations). Woodhill Engineering developed several pipeline cost equations for the IEA GHG PH4/ 6 study based on in house estimates. For onshore pipelines, they give three equations, one for each of three different ANSI piping classes: 600# ( P < 90 bar), 900# ( P < 140 bar), and 1500# ( P < 225 bar). At the higher pressures likely required for CO2 transport, the ANSI Class 1500# pipe would be used. The capital cost equation for ANSI Class 1500# pipe is given as: Pipeline Capital Cost ($) = FL * FT * 106 * [ ( 0.057 * L + 1.8663) + ( 0.00129 * L) * D + ( 0.000486 * L + 0.000007) * D2 ] ( where FL = location factor, FT = terrain factor, L = pipeline length [ km], and D = pipeline diameter [ in]) Location factors ( FL) for a few world regions are reproduced here: USA/ Canada= 1.0, Europe= 1.0, UK= 1.2, Japan= 1.0, Australia= 1.0. ( A full list of location factors for all world regions can be found in the original IEA GHG PH4/ 6 report.) Terrain factors ( FT) are as follows: cultivated land= 1.10, grassland= 1.00, wooded= 1.05, jungle= 1.10, stony desert= 1.10, < 20% mountainous= 1.30, > 50% mountainous= 1.50. Booster stations for raising the CO2 pressure during pipeline transport are also considered in the IEA GHG PH4/ 6 models. In fact, the user of the spreadsheet model has the choice of whether or not to include booster stations. If booster stations are included, their capital costs can be calculated by the following equation: Booster Station Capital Cost ($) = NB * FL * ( 7.82 * Power + 0.46) * $ 1,000,000 ( where NB = number of booster stations, FL = location factor, and Power = pump power [ MW]) ‘ Power’ is calculated by the following equation given in [ 13]: Power ( MW) = ( Q * ΔP) / ( 36,000 * η) 1 2 ( where Q = CO2 flow rate [ m3/ hr], ΔP = pressure increase through booster [ bar], η = pump efficiency = 0.75) The total capital cost is given by: Total Capital Cost ($) = Pipeline Capital Cost + Booster Station Capital Cost Equations for O& M costs were also developed for the IEA GHG PH4/ 6 study. The O& M cost equation for liquid CO2 onshore pipelines is given by: Annual Pipeline O& M Costs ($/ yr) = 120,000 + 0.61( 23,213 * D + 899 * L – 259,269) + 0.7( 39,305 * D + 1694 * L – 351,355) + 24,000 ( where D = pipeline diameter [ in], and L = pipeline length [ km]) Similarly, booster station O& M costs ( both fixed and variable) are also calculated. For fixed O& M costs, a look up table is used. This table provides fixed O& M costs as a function of pump power ( from 0 to 2 MW). To avoid the look up table, we have created a second order regression equation that fits the fixed O& M cost vs. pump power with an R2 value of 0.93. ( Be advised that this equation should only be used in the range of 0 2 MW, since the second order equation is parabolic and will eventually begin predicting increasingly lower costs as the pump power increases.) The equation for booster station fixed O& M costs is given below: Annual Booster Station Fixed O& M Costs ($/ yr) = NB * [ 179,864 * Power2 + 671,665 * Power + 159,292] ( where NB = number of booster stations, and Power = pump power [ MW]) The booster station variable O& M costs are calculated by the following equation: Booster Station Variable O& M Costs ($/ yr) = NB * COE * Power * CF * ( 1000 kW/ MW) * ( 24 hr/ day) * ( 365 days/ yr) ( where NB = number of booster stations, COE = cost of electricity [$/ kWh], Power = pump power [ MW], CF = plant capacity factor) The total annual O& M costs are then: Total Annual O& M Costs ($/ yr) = Annual Pipeline O& M Costs + Annual Booster Station Fixed O& M Costs + Annual Booster Station Variable O& M Costs And finally, the total annual cost and levelized cost are calculated by the following equations: Total Annual Cost ($/ yr) = ( Total Capital Cost * CRF) + Total Annual O& M Costs ( where CRF = Capital Recovery Factor) Levelized Cost ($/ tonne CO2) = Total Annual Cost ($/ yr) / { m * CF * 365 } ( where m = CO2 mass flow rate [ tonnes/ day], CF = plant capacity factor, and 365 = days per year) The IEA GHG PH4/ 6 study reports all cost figures in year 2000 US dollars. 1 3 The IEA GHG 2005/ 2 Models In 2005, the IEA Greenhouse Gas R& D Programme released two additional, related reports ( one for Europe and another for North America) in which the costs and potential of CO2 transport and storage for each of the respective regions were studied. The IEA GHG 2005/ 2 study focused on Europe. ( The study on North America will be discussed later in this report.) Work was carried out by the The Netherlands Geological Survey ( TNO NITG), the geological surveys of Britain ( BGS) and Denmark/ Greenland ( GEUS), and Ecofys. The equation used for calculating pipeline diameter is: D = [ m / ( 0.25 π ρ v ) ] 0.5 / 0.0254 ( where D = pipeline diameter [ in], m = CO2 mass flow rate [ kg/ s], ρ = CO2 density [ kg/ m3], v = flow velocity [ m/ s]) In this equation, the study assumes that the flow velocity ( v) is a constant 2.0 m/ s. The equation used for calculating onshore pipeline capital costs in the IEA GHG 2005/ 2 study is taken almost directly from the IEA GHG PH4/ 6 study for ANSI Class 1500# pipe— the only differences being the following: ( 1) costs are expressed in euros (€) in the IEA GHG 2005/ 2 study; ( 2) a change of sign on the final constant ( from + 0.000007 to  0.000007), which makes virtually no difference in calculated cost; and ( 3) an omission of the location factor term, FL, presumably because in the IEA GHG PH4/ 6 study FL = 1.0 for Europe, the only region considered in the IEA GHG 2005/ 2 study. The equation is shown below: Pipeline Capital Cost (€) = FT * 106 * [ ( 0.057 * L + 1.8663) + ( 0.00129 * L) * D + ( 0.000486 * L  0.000007) * D2 ] ( where FT = terrain factor, L = pipeline length [ km], and D = pipeline diameter [ in]) As with the IEA GHG PH4/ 6 study, terrain factors ( FT) are as follows: cultivated land= 1.10, grassland= 1.00, wooded= 1.05, jungle= 1.10, stony desert= 1.10, < 20% mountainous= 1.30, > 50% mountainous= 1.50. But for the IEA GHG 2005/ 2 study, an average value of 1.20 is taken for FT. For booster stations, capital costs are assumed to be for the most part independent of CO2 mass flow rate, and are instead expressed on a per kilometer basis. The capital cost equation for onshore booster stations is: Booster Station Capital Cost (€) = ( 35,000 €/ km) * L ( where L = pipeline length [ km]) Hence, the total capital cost is given by: Total Capital Cost (€) = Pipeline Capital Cost + Booster Station Capital Cost It appears that in the IEA GHG 2005/ 2 report the capital cost of booster stations is always included in the total capital cost, regardless of the presence or absence of a booster station. A short pipeline ( e. g., 100 km), however, may not require booster stations. Therefore, when replicating the IEA GHG 2005/ 2 models, we assume that booster stations are unnecessary if the pipeline length is less than 200 km, which means that the booster station capital cost is not included in the total capital cost. This assumption for a minimum distance of 200 km is consistent with IEA GHG 2005/ 2 study’s own assumption of 200 km for the average distance between two booster stations, which they use for determination of booster station power use. 1 4 The equation for booster station pumping power use is: Pp = [( 1/ ρ) * ( ΔP/ ηp)] / DistBS ( where Pp = pump power use [ J/ km/ kg CO2], ρ = CO2 density [ kg/ m3], ΔP = pressure increase [ Pa], ηp = pump efficiency, and DistBS = average distance between two booster stations [ km]) In the IEA GHG 2005/ 2 study, the following values are assumed for the above equation: ρ = 800 kg/ m3, ΔP = 4 x 106 Pa, ηp = 0.75, and DistBS = 200 km. The total capital cost is annualized with a 10% discount rate over a 20 year operational lifetime by the following equation: n n i i i Annual Capital Cost euros yr Total Capital Cost euros ( 1 ) ( 1 ) 1 ( / ) ( ) + + − = ( where n = operational lifetime [ years], and i = discount rate) The annual O& M costs of the pipeline are calculated as 3% of the pipeline capital cost. And the annual O& M costs of the booster station are calculated as 5% of the booster station capital cost. Annual Pipeline O& M Costs (€/ yr) = ( Pipeline O& M factor) * Pipeline Capital Cost ( where Pipeline O& M factor = 3%) Annual Booster Station O& M Costs (€/ yr) = ( Booster Station O& M factor) * Booster Station Capital Cost ( where Booster Station O& M factor = 5%) The total annual cost is found by summing the annual capital and O& M costs. Total Annual Cost (€/ yr) = Annual Capital Cost + Annual Pipeline O& M Costs + Annual Booster Station O& M Costs Finally the levelized cost of CO2 transport is calculated as a combination of the total annual costs and the booster station power required for pumping. Levelized Cost (€/ tonne CO2) = 1000 * { [ Total Annual Cost / ( m * ( 31,536,000) * CF)] + [ COE * Pp * L / ( 3.6 * 106)] } ( where 1000 = kg/ tonne, m = CO2 mass flow rate [ kg/ s], 31,536,000 = seconds per year, CF = plant capacity factor, COE = cost of electricity [€/ kWh], Pp = pump power use [ J/ km/ kg CO2], L = pipeline length [ km], and 3.6 x 106 = J/ kWh) An electricity cost of 0.04 €/ kWh is assumed in the original study. Finally, the IEA GHG 2005/ 2 study reports all costs in year 2000 euros. 1 5 The IEA GHG 2005/ 3 Models As mentioned previously, the IEA GHG 2005/ 3 study was published in 2005 and focuses on the costs and potential of CO2 transport and storage in North America ( onshore USA and Canada). Yet, although the goals of this study were the same as those of the European study ( IEA GHG 2005/ 2), some of the approaches, assumptions, models, and, thus, results differ in marked ways. Work on the North American study was carried out by Battelle and the Alberta Energy and Utilities Board. To calculate the pipeline diameter, the IEA GHG 2005/ 3 study cites a rule of thumb in [ 14] that says the CO2 volumetric flow rate should be 0.65 x 106 scf/ day/ in2 of pipe area. In different units, this rule of thumb can be expressed as ( 18.41 ρ) tonnes/ day/ in2 ( where ρ is the CO2 density under standard conditions). The pipeline diameter can then be found by: 1/ 2 18.41 4 m ⎥⎦ ⎤ ⎢⎣ ⎡ = ρ π N D ( where D = pipeline diameter [ in], m = CO2 mass flow rate [ tonnes/ day], and ρ = CO2 density [ kg/ Nm3]) To calculate CO2 pipeline costs, this study takes a similar approach to the MIT study by using historical cost data for natural gas pipeline construction, as reported in the Oil & Gas Journal. From this data, they conclude that, on average, construction costs for CO2 pipelines would be $ 41,681/ in/ mile ($ 25,889/ in/ km). ( For comparison, the MIT study concludes that the pipeline cost would $ 20,989/ in/ km, as mentioned previously.) In terms of CO2 mass flow rate, the pipeline capital cost is calculated by: Pipeline Capital Cost ($/ mile) = 39,409 * ( m / 24) 0.5 ( where m = CO2 mass flow rate [ tonnes/ day], and 24 = hours/ day) Annualizing the pipeline capital cost with a 10% discount rate over a 25 year operational lifetime yields the following equation: Annual Pipeline Capital Cost ($/ mile/ yr) = 4,335 * ( m / 24) 0.5 ( where m = CO2 mass flow rate [ tonnes/ day], and 24 = hours/ day) By assuming the annual O& M costs are 2% of the pipeline capital cost and dividing the total annual capital and O& M costs by the annual CO2 mass flow rate, the total levelized capital and O& M cost equation is given by: Total Levelized Capital and O& M Cost ($/ mile/ tonne CO2) = 5123 * ( m / 24) 0.5 / ( m * CF * 365) ( where m = CO2 mass flow rate [ tonnes/ day], 24 = hours/ day, CF = plant capacity factor, 365 = days/ year) The levelized costs of CO2 transport is given by: Levelized Cost ($/ tonne CO2) = ( L + 10) x 1.17 * ( Total Levelized Capital and O& M Cost) ( where L = pipeline length [ miles], 10 = extra pipeline distance at injection site [ miles], 1.17 = straight line distance adjustment factor) 1 6 Finally, since the IEA GHG 2005/ 3 study does not state the reference year that they express costs in, we assume that they use year 2002 dollars, owing to the fact that 2002 is the year for which they obtained natural gas pipeline cost data from the Oil & Gas Journal. 1 7 The Parker Models Like the MIT and IEA GHG 2005/ 3 studies, Parker uses natural gas pipeline costs, as reported in the Oil & Gas Journal for the years 1991 2003. Parker goes further than the other studies, however. Instead of simply reporting one cost ( e. g., $/ in/ km), he fits second order equations to the cost data and develops equations that predict the costs for each of the four different cost categories— materials, labor, miscellaneous, and right of way. The equations are functions of pipeline diameter and length. And although Parker’s pipeline cost equations were developed with the intent of predicting costs for hydrogen pipelines, they can still be used for CO2 pipelines, as is done in the MIT and IEA GHG 2005/ 3 studies. The pipeline capital cost equations of Parker are shown below: Materials Cost ($) = [ 330.5 * D2 + 687 * D + 26,960] * L + 35,000 Labor Cost ($) = [ 343 * D2 + 2,074 * D + 170,013] * L + 185,000 Miscellaneous Cost ($) = [ 8,417 * D + 7,324] * L + 95,000 Right of Way Cost ($) = [ 577 * D + 29,788] * L + 40,000 Total Capital Cost ($) = Materials Cost + Labor Cost + Miscellaneous Cost + Right of Way Cost = [ 673.5 * D2 + 11,755 * D + 234,085] * L + 355,000 ( where D = pipeline diameter [ in], and L = pipeline length [ miles]) Two of the above equations have been slightly adapted. First, consider the equation for ‘ Right of Way Cost’. On page 17 of his report, Parker states that the diameter term in ‘ 577 * D’ should be squared, ‘ 577 * D2’, however, we believe this to be a typographical error, since the regression equation on Figure 18 of the same page shows the term to be ‘ 576.78 * D’ ( i. e., without the squared exponent). Furthermore, the ‘ 577 * D’ term ( unsquared) is evidently the one that is used when adding up the four individual equations to generate the ‘ Total Capital Cost’ equation. Correcting for this error has large implications on the calculated right of way cost, potentially increasing it by a factor of ten for large diameter pipelines. Second, consider the ‘ Total Capital Cost’ equation. Our equation is nearly identical to that of Parker, aside from the final term and some small rounding differences on the first and second terms. We have added up the final terms from each of the four individual equations ( 35,000 + 185,000 + 95,000 + 40,000) to get 355,000, which we use in our equation for total capital cost, as compared to the 405,000 term that Parker uses. These latter differences are, of course, much smaller in importance than those in the equation for right of way costs. Recent discussions with Parker have confirmed the presence of the typographical errors. Our adaptation of his methodology is, therefore, justified. Parker reports all costs in year 2000 dollars. 1 8 SUMMARY AND COMPARISON OF MODELS The above descriptions of the various CO2 transport models show that each study takes a somewhat unique approach in sizing the pipeline and estimating the associated costs. Further, each of the various studies is built upon differing assumptions and input, which in turn leads to dissimilar output. The main differences in the studies are highlighted in the following table. ( Note that the Parker study is unique in that it does not deal strictly with CO2 transport and sequestration and, thus, cannot be compared to the other studies on many accounts.) Ogden MIT Ecofys IEA GHG PH4/ 6 IEA GHG 2005/ 2 IEA GHG 2005/ 3 Parker Reference Cost Year 2001 1998 2003 2000 2000 2002 2000 Capital Recovery Factor [%/ yr] 15 15  ' user specified'    Discount Rate [%]   10  10 10  Operational Lifetime [ years]   25  20 25  O& M Factor 4.0%/ year of total capital cost $ 3,100/ km/ year 2.1%/ year of total capital cost ' by equation' 3%/ yr of pipeline capital + 5%/ yr of booster capital 2.0%/ year of total capital cost  Plant Capacity Factor [%]  80 ' not reported' ' user specified' 90 ' not reported'  Electricity Cost [ / kWh]    ' user specified' 0.04 €   Booster Stations Included? No No No Yes / No ( user specified) Yes No  Pipeline Inlet Pressure [ MPa] 15 15.2 12 ' user specified'    Pipeline Outlet Pressure [ MPa] 10 10.3 8 ' user specified'    Friction Factor, f ~ 0.0021 ( by equation) ~ 0.0033 ( by Moody chart) 0.015  0.020 (= 4 x f) 0.015 (= 4 x f) 
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Title  Technoeconomic models for carbon dioxide compression, transport, and storage & Correlations for estimating carbon dioxide density and viscosity 
Subject  Carbon dioxideTransportationMathematical models.; Carbon dioxideStorageMathematical models.; Carbon dioxideViscosityMathematical models.; Carbon dioxideDensityMathematical models. 
Description  Text document in PDF format.; Title from PDF title page (viewed on August 30, 2009).; "October 2006."; Thesis (Ph.D.)University of California, Davis, 2006.; Includes bibliographical references. 
Creator  McCollum, David L. 
Publisher  Institute of Transportation Studies, University of California, Davis 
Contributors  Ogden, Joan M.; University of California, Davis. Institute of Transportation Studies. 
Type  Text 
Language  eng 
Relation  http://worldcat.org/oclc/434728164/viewonline; http://pubs.its.ucdavis.edu/publication_detail.php?id=1047 
TitleAlternative  Technoeconomic models for carbon dioxide compression, transport, and storage; Correlations for estimating carbon dioxide density and viscosity; Technoeconomic models for CO₂ compression, transport, and storage; Correlations for estimating CO₂ density and viscosity 
DateIssued  [2006] 
FormatExtent  1 v. (various pagings) : digital, PDF file (1.01 MB) with col. charts. 
RelationRequires  Mode of access: World Wide Web. 
RelationIs Part Of  Research report ; UCDITSRR0614; Research report (University of California, Davis. Institute of Transportation Studies) ; UCDITSRR0614. 
Transcript  Institute of Transportation Studies ◊ University of California, Davis One Shields Avenue ◊ Davis, California 95616 PHONE: ( 530) 752 6548 ◊ FAX: ( 530) 752 6572 WEB: http:// its. ucdavis. edu/ Year 2006 UCD— ITS— RR— 06 14 Techno Economic Models for Carbon Dioxide Compression, Transport, and Storage & Correlations for Estimating Carbon Dioxide Density and Viscosity David L. McCollum Joan M. Ogden Techno Economic Models for Carbon Dioxide Compression, Transport, and Storage & Correlations for Estimating Carbon Dioxide Density and Viscosity David L. McCollum* Joan M. Ogden Institute of Transportation Studies University of California, Davis One Shields Avenue Davis, CA 95616 * Corresponding Author E mail: dlmccollum@ ucdavis. edu October 2006 ABSTRACT Due to a heightened interest in technologies to mitigate global climate change, research in the field of carbon capture and storage ( CCS) has attracted greater attention in recent years, with the goal of answering the many questions that still remain in this uncertain field. At the top of the list of key issues are CCS costs: costs of carbon dioxide ( CO2) capture, compression, transport, storage, and so on. This research report touches upon several of these cost components. It also provides some technical models for determining the engineering and infrastructure requirements of CCS, and describes some correlations for estimating CO2 density and viscosity, both of which are often essential properties for modeling CCS. This report is actually a compilation of three separate research reports and is, therefore, divided into three separate sections. But although each could be considered as a stand alone research report, they are, in fact, very much related to one other. Section I builds upon some of the knowledge from the latter sections, and Sections II & III can be considered as supplementary to Section I. * Section I: Techno Economic Models for Carbon Dioxide Compression, Transport, and Storage – This section provides models for estimating the engineering requirements and costs of CCS infrastructure. Some of the models have been adapted from other studies, while others have been expressly developed in this study. * Section II: Simple Correlations for Estimating Carbon Dioxide Density and Viscosity as a Function of Temperature and Pressure – This section describes a set of simple correlations for estimating the density and viscosity of CO2 within the range of operating temperatures and pressures that might be encountered in CCS applications. The correlations are functions of only two input parameters— temperature and pressure— which makes them different from the more complex equation of state computer code based correlations that sometimes require more detailed knowledge of CO2 properties and operating conditions. * Section III: Comparing Techno Economic Models for Pipeline Transport of Carbon Dioxide – This section illustrates an approach that was used to compare several recent techno economic models for estimating CO2 pipeline sizes and costs. A common set of input assumptions was applied to all of the models so that they could be compared on an “ apples to apples” basis. Then, by averaging the cost estimates of the models over a wide range of CO2 mass flow rates and pipeline lengths, a new CO2 pipeline capital cost model was created that is a function only of flow rate and pipeline length. Keywords: carbon dioxide, CO2, CO2, CCS, pipeline, transport, compression, injection, storage, sequestration, techno economic, cost model, climate change, greenhouse gas, correlation, density, viscosity SECTION I: Techno Economic Models for Carbon Dioxide Compression, Transport, and Storage David L. McCollum dlmccollum@ ucdavis. edu Institute of Transportation Studies University of California One Shields Avenue Davis, CA 95616 ABSTRACT This report provides techno economic model equations for estimating the equipment sizes and costs of compression, pipeline transport, and injection and storage of carbon dioxide ( CO2). Models of this type are becoming increasingly important due to the recent heightened interest in carbon capture and storage ( CCS) as a climate change mitigation strategy. The models described here are based on a combination of several CCS studies that have been carried out over the past few years. Because the models are laid out step by step, the reader should be able to understand the methodology and replicate the models on his or her own. Keywords: carbon dioxide, CO2, CO2, CCS, pipeline, transport, compression, injection, storage, sequestration, techno economic, cost model, climate change, greenhouse gas 1 PART I: CO2 COMPRESSION Nomenclature m = CO2 mass flow rate to be transported to injection site [ tonnes/ day] Pinitial = initial pressure of CO2 directly from capture system [ MPa] Pfinal = final pressure of CO2 for pipeline transport [ MPa] Pcut off = pressure at which compression switches to pumping [ MPa] Nstage = number of compressor stages [] CR = compression ratio of each stage [] Ws, i = compression power requirement for each individual stage [ kW] Zs = average CO2 compressibility for each individual stage [] R = gas constant [ kJ/ kmol K] Tin = CO2 temperature at compressor inlet [ K] M = molecular weight of CO2 [ kg/ kmol] ηis = isentropic efficiency of compressor [] ks = ( Cp/ Cv) = average ratio of specific heats of CO2 for each individual stage [] Ws total = total combined compression power requirement for all stages [ kW] ( Ws) 1 = compression power requirement for stage 1 [ kW] ( Ws) 2 = compression power requirement for stage 2 [ kW] ( Ws) 3 = compression power requirement for stage 3 [ kW] ( Ws) 4 = compression power requirement for stage 4 [ kW] ( Ws) 5 = compression power requirement for stage 5 [ kW] Ntrain = number of parallel compressor trains [] Wp = pumping power requirement [ kW] ρ = density of CO2 during pumping [ kg/ m3] ηp = efficiency of pump [] myear = CO2 mass flow to be transported and stored per year [ tonnes/ yr] CF = capacity factor [] mtrain = CO2 mass flow rate through each compressor train [ kg/ s] Ccomp = capital cost of compressor( s) [$] Cpump = capital cost of pump [$] Ctotal = total capital cost of compressor( s) and pump [$] Cannual = annualized capital cost of compressor( s) and pump [$/ yr] CRF = capital recovery factor [/ yr] Clev = levelized capital costs of compressor( s) and pump [$/ tonne CO2] O& Mannual = annual O& M costs [$/ yr] O& Mfactor = O& M cost factor [/ yr] O& Mlev = levelized O& M costs [$/ tonne CO2] Ecomp = electric power costs of compressor [$/ yr] pe = price of electricity [$/ kWh] Epump = electric power costs of pump [$/ yr] Eannual = total annual electric power costs of compressor and pump [$/ yr] Elev = levelized O& M costs [$/ tonne CO2] 2 Calculation of Compressor & Pump Power Requirements After CO2 is separated from the flue gases of a power plant or energy complex ( i. e., captured), it must be compressed from atmospheric pressure ( Pinitial = 0.1 MPa), at which point it exists as a gas, up to a pressure suitable for pipeline transport ( Pfinal = 15 MPa), at which point it is in either the liquid or ‘ dense phase’ regions, depending on its temperature. Therefore, CO2 undergoes a phase transition somewhere between these initial and final pressures. When CO2 is in the gas phase, a compressor is required for compression, but when CO2 is in the liquid/ dense phase, a pump can be used to boost the pressure. It can be assumed that the ‘ cut off’ pressure ( Pcut off) for switching from a compressor to a pump is the critical pressure of CO2, which is 7.38 MPa. Hence, a compressor will be used from 0.1 to 7.38 MPa, and then a pump will be used from 7.38 to 15 MPa ( or to whatever final pressure is desired). This line of reasoning has been adapted from [ 1]. Pinitial = 0.1 MPa Pfinal = 15 MPa Pcut off = 7.38 MPa The number of compressor stages is assumed to be 5 (= Nstage), and the equation for the optimal compression ratio ( CR) for each stage is given by Mohitpour [ 2]: CR = ( Pcut off / Pinitial)^( 1/ Nstage) ( where Nstage = 5) The compression power requirement for each stage ( Ws, i) is given by the following equation, which is adapted from [ 1] and [ 2]. ( ) ⎥⎦ ⎤ ⎢⎣ ⎡ − ⎟ ⎟⎠ ⎞ ⎜ ⎜⎝ ⎛ − ⎟ ⎟⎠ ⎞ ⎜ ⎜⎝ ⎛ ⎟⎠ ⎞ ⎜⎝ ⎛ ∗ = − 1 24 3600 1 1000 1 , s s k k s s is s in s i CR k k M W mZ RT η Based on some assumptions and CO2 property data from the Kinder Morgan company [ 3], the following values can be used in the above equation:  For all stages:  R = 8.314 kJ/ kmol K  M = 44.01 kg/ kmol  Tin = 313.15 K ( i. e., 40 oC)  ηis = 0.75  1000 = # of kilograms per tonne  24 = # of hours per day  3600 = # of seconds per hour  For stage 1:  Z s = 0.995  k s = 1.277  These values correspond to a pressure range of 0.1 0.24 MPa and an average temperature of 356 K in the compressor. 3  For stage 2:  Z s = 0.985  k s = 1.286  These values correspond to a pressure range of 0.24 0.56 MPa and an average temperature of 356 K in the compressor.  For stage 3:  Z s = 0.970  k s = 1.309  These values correspond to a pressure range of 0.56 1.32 MPa and an average temperature of 356 K in the compressor.  For stage 4:  Z s = 0.935  k s = 1.379  These values correspond to a pressure range of 1.32 3.12 MPa and an average temperature of 356 K in the compressor.  For stage 5:  Z s = 0.845  k s = 1.704  These values correspond to a pressure range of 3.12 7.38 MPa and an average temperature of 356 K in the compressor. Thus, the calculation for compressor power requirement must be conducted five times, since this is the number of stages that have been assumed. Although, this procedure may seem a bit more tedious than simply assuming average values for Zs and ks over the pressure range and using the equation only once, it is prudent to break up the calculation by stage due to the unusual behavior of CO2’ s properties, which are different at each stage. The compressor power requirements for each of the individual stages should then be added together to get the total power requirement of the compressor. Ws total = ( Ws) 1 + ( Ws) 2 + ( Ws) 3 + ( Ws) 4 + ( Ws) 5 According to the IEA GHG PH4/ 6 report [ 1], the maximum size of one compressor train, based on current technology, is 40,000 kW. So if the total compression power requirement ( Wstotal) is greater than 40,000 kW, then the CO2 flow rate and total power requirement must be split into Ntrain parallel compressor trains, each operating at 100/ Ntrain % of the flow/ power. Of course, the number of parallel compressor trains must be an integer value. Ntrain = ROUND_ UP ( Ws total / 40,000) To calculate the pumping power requirement for boosting the CO2 pressure from Pcut off ( 7.38 MPa) to Pfinal ( 15 MPa), the following equation has been adapted from [ 1]: ( ) ⎥ ⎥⎦ ⎤ ⎢ ⎢⎣ ⎡ − ⎟⎠ ⎞ ⎜⎝ ⎛ ∗ = − p final cut off p m P P W 24 36 ρη 1000 * 10 4 ( where ‘ m’ is the CO2 mass flow rate [ tonnes/ day], and the following values can be assumed: ρ = 630 kg/ m3, ηp = 0.75, 1000 = # of kilograms per tonne, 24 = # of hours per day, 10 = # of bar per MPa, 36 = # of m3* bar/ hr per kW) The following figure shows the total power requirement for the compressor( s) and pump over a range of flow rates. Notice that the dependence of compression power on flow rate, ‘ m’, is linear, as would be expected from the equation for Ws. Also, notice how small pumping power is relative to compression power. This is because the compressor raises the CO2 pressure from 0.1 to 7.38 MPa— a total compression ratio of 73.8— whereas the pump raises the pressure from 7.38 to 15 MPa— a total compression ratio of only 2.0. Power Requirement of Compressors and Pumps 0 20,000 40,000 60,000 80,000 100,000 120,000 0 5,000 10,000 15,000 20,000 25,000 CO2 Mass Flow Rate [ tonnes/ day] Power [ kW] Compressor Power ( W_ s) Pump Power ( W_ p) Figure 1: Power Requirement of Compressors and Pumps as a Function of CO2 Mass Flow Rate Capital, O& M, and Levelized Costs of CO2 Compression/ Pumping *** All costs are expressed in year 2005 US$ The CO2 mass flow rate through each compressor train ( mtrain) in units of ‘ kg/ s’ is given by: mtrain = ( 1000 * m) / ( 24 * 3600 * Ntrain) The capital cost of the compressor can then be calculated based on the following equation, which has been slightly adapted from Hendriks [ 4] and scaled up into year 2005$. 5 ( )( ) ( )( ) ⎥⎦ ⎤ ⎢⎣ ⎡ ⎟ ⎟⎠ ⎞ ⎜ ⎜⎝ ⎛ = × − + × − − initial cut off comp train train train train P P C m N 0.13 106 m 0.71 1.40 106 m 0.60 ln The units on the constant terms ( 0.13 x 106 and 1.40 x 106) are ‘$/( kg/ s)’. Therefore, the compressor capital cost ( Ccomp) is given in ‘$’. The capital cost of the pump can be calculated based on the following equation, which has been slightly adapted from [ 1] and scaled up into year 2005$. Cpump = {( 1.11 x 106) * ( Wp / 1000)} + 0.07 x 106 The following graph shows the capital costs of both the compressors and pumps in term of [$/ kW]. As one would expect, at the higher CO2 mass flow rates the values fall in the $ 1000 2000/ kW range, which is consistent with other studies. Note the cost curve for compressors is not entirely smooth. This has something to do with the fact that at a certain level of compression power demand, another compressor train is added, which adds to the capital costs, but not significantly to the power demand. No such restriction is placed on pumps, so the cost curve for pumps is smooth. Capital Costs of Compressors and Pumps 0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 1,000 2,500 5,000 10,000 15,000 20,000 25,000 CO2 Mass Flow Rate [ tonnes/ day] Compressor [$/ kW] 0 200 400 600 800 1,000 1,200 1,400 1,600 Pump [$/ kW] Compressor Pump Figure 2: Capital Costs of Compressors and Pumps as a Function of CO2 Mass Flow Rate The total capital costs are thus: 6 Ctotal = Ccomp + Cpump The capital cost can be annualized by applying a capital recovery factor ( CRF) of 0.15. Cannual = Ctotal * CRF ( where CRF = 0.15/ yr) The total amount of CO2 that must be compressed every year is found by applying a capacity factor ( CF) of 0.80. myear = m * 365 * CF ( where CF = 0.80) The levelized capital costs ( Clev) are thus: Clev = Cannual / myear The annual operation and maintenance costs ( O& Mannual) can be found by applying an O& M factor ( O& Mfactor) of 0.04 to the total capital cost. O& Mannual = Ctotal * O& Mfactor ( where O& Mfactor = 0.04) The levelized O& M costs ( O& Mlev) are thus: O& Mlev = O& Mannual / myear The total electric power costs of the compressor ( Ecomp) and pump ( Epump) are calculated by multiplying the total power requirement by the capacity factor ( CF) of 0.80 and price of electricity ( pe). It can be assumed that the electricity price is $ 0.065/ kWh, based on estimates by Kreutz et al. [ 17] for a coal to hydrogen plant that employs CO2 capture. Eannual = Ecomp + Epump = pe * ( Ws total + Wp) * ( CF * 24 * 365) ( where pe = $ 0.065/ kWh, and CF = 0.80) The levelized power costs ( Elev) are thus: Elev = Eannual / myear Finally, the total annual and levelized costs of CO2 compression/ pumping are: Total Annual Cost [$/ yr] = Cannual + O& Mannual + Eannual Total Levelized Cost [$/ tonne CO2] = Clev + O& Mlev + Elev The following two figures show the contribution of capital, O& M, and power to the total levelized cost of CO2 compression/ pumping. The reason for the cost curves not being smooth is because of the maximum power constraint of 40,000 kW per compressor train. In other words, as the flow rate of CO2 increases, the compression power reaches a threshold point where a new 7 compressor train is needed. This new compressor train causes a spike in the capital cost ( and thus, O& M and total costs). The total power requirements and cost, however, are unaffected by the number of compressor trains that are required. Furthermore, the figures show that there are economies of scale associated with CO2 compression/ pumping— i. e., the capital cost becomes a smaller percentage of total cost as the CO2 flow rate increases. The last figure shows the dependence of levelized power cost and, thus, total levelized cost on the price of electricity. Since electric power is so important to the process of CO2 compression/ pumping, it makes up an increasingly larger share of total costs as electricity becomes more expensive. Levelized Cost of CO2 Compression/ Pumping 0 4 8 12 16 20 0 5,000 10,000 15,000 20,000 25,000 CO2 Mass Flow Rate [ tonnes/ day] $/ tonne CO2 Total Levelized Cost Levelized Power ( E_ lev) Levelized Capital ( C_ lev) Levelized O& M ( O& M_ lev) Figure 3: Levelized Cost of CO2 Compression/ Pumping as a Function of CO2 Mass Flow Rate 8 Component Contribution to Total Levelized Cost of CO2 Compression/ Pumping 8.52 4.95 3.30 3.29 2.60 2.78 2.45 2.27 1.32 0.88 0.88 0.69 0.74 0.65 6.81 6.81 6.81 6.81 6.81 6.81 6.81 0 2 4 6 8 10 12 14 16 18 20 1,000 2,500 5,000 10,000 15,000 20,000 25,000 CO2 Mass Flow Rate [ tonnes/ day] $/ tonne CO2 Levelized Power ( E_ lev) Levelized O& M ( O& M_ lev) Levelized Capital ( C_ lev) Figure 4: Contribution of Capital, O& M, and Power to Total Levelized Cost of CO2 Compression/ Pumping ( Dependence on CO2 Mass Flow Rate) Component Contribution to Total Levelized Cost of CO2 Compression/ Pumping 3.30 3.30 3.30 3.30 3.30 3.30 0.88 0.88 0.88 0.88 0.88 0.88 4.19 6.29 8.39 10.48 12.58 14.68 0 2 4 6 8 10 12 14 16 18 20 0.04 0.06 0.08 0.10 0.12 0.14 Electricity Price, pe [$/ kWh] $/ tonne CO2 Levelized Power ( E_ lev) Levelized O& M ( O& M_ lev) Levelized Capital ( C_ lev) m = 5,000 tonnes/ day Figure 5: Contribution of Capital, O& M, and Power to Total Levelized Cost of CO2 Compression/ Pumping ( Dependence on Electricity Price) 9 PART II: CO2 TRANSPORT Nomenclature D = pipeline diameter [ in] m = CO2 mass flow rate in pipeline [ tonnes/ day] Pin = inlet pipeline pressure [ MPa] Pout = outlet pipeline pressure [ MPa] Pinter = intermediate pipeline pressure [ MPa] ΔP = pressure drop in pipeline = Pin  Pout [ MPa] T = CO2 temperature in pipeline [ oC] μ = CO2 viscosity in pipeline [ Pa s] ρ = CO2 density in pipeline [ kg/ m3] ε = pipeline roughness factor [ ft] Re = Reynold’s number [] Ff = Fanning friction factor [] L = pipeline length [ km] Ccap = pipeline capital cost [$/ km] Ctotal = total pipeline capital cost [$] FL = location factor [] FT = terrain factor [] CRF = capital recovery factor [/ yr] Cannual = annualized pipeline capital cost [$/ yr] O& Mannual = annual O& M costs [$/ yr] O& Mfactor = O& M cost factor [/ yr] CF = capacity factor [] myear = CO2 mass flow delivered to injection site per year [ tonnes/ year] Calculation of Pipeline Diameter The equation for calculating pipeline capital cost ( shown in the next section) is not a function of diameter. Nevertheless, when conducting a techno economic analysis, it may be useful to estimate the diameter size for other reasons. Thus, the methodology for calculating pipeline diameter is shown here. Since the calculation of pipeline diameter is an iterative process, one must first guess a value for diameter ( D). A reasonable first approximation is D = 10 inches. The process also requires knowledge of the CO2 temperature ( T) and pressure ( Pinter) in the pipeline. Pinter is based on the pipeline inlet pressure ( Pin, i. e. the pressure of CO2 leaving the power plant or energy complex) and the pipeline outlet pressure ( Pout, i. e. the pressure of CO2 at the end of the pipeline— the injection site). Pinter = ( Pin + Pout) / 2 Furthermore, an estimation of the density ( ρ) and viscosity ( μ) of CO2 in the pipeline ( approximated at T and Pinter) is also required. Since CO2 exhibits unusual trends in its properties 10 over the range of temperatures and pressures that would be experienced in pipeline transport, it is difficult to provide just one value for either density or viscosity here. Therefore, the reader is referred to one of two CO2 property websites, [ 5] and [ 6], or to the set of correlation equations of McCollum [ 7]. Each of these references provide an easy way of obtaining CO2 density and viscosity if one knows only two basic parameters— temperature and pressure. The Reynold’s number ( Re) and Fanning friction factor ( Ff) for CO2 fluid flow in the pipeline are calculated by the following equations from [ 8]: Re = ( 4* 1000/ 24/ 3600/ 0.0254)* m / ( π* μ* D) 1.11 2 10 3.7 12( / ) Re 4 1.8 log 6.91 1 ⎥ ⎥⎦ ⎤ ⎢ ⎢⎣ ⎡ ⎪⎭ ⎪⎬ ⎫ ⎪⎩ ⎪⎨ ⎧ ⎟⎠ ⎞ ⎜⎝ − + ⎛ = D F f ε ( where ε = 0.00015 ft is assumed by [ 8]) The pipeline diameter ( D) is calculated by the following equation, which is adapted from [ 8]: D = ( 1/ 0.0254) * [ ( 32* Ff* m2)*( 1000/ 24/ 3600) 2 / ( π2* ρ*( ΔP/ L)* 106/ 1000) ]( 1/ 5) Finally, since the process for calculating pipeline diameter is iterative, one needs to compare the calculated diameter from this last equation with the value that was initially guessed at the beginning of the process. If there is much difference between the two, then the process must be repeated over and over again until the difference between iterations is satisfactorily small. Capital, O& M, and Levelized Costs of CO2 Transport *** All costs are expressed in year 2005 US$ The equations for estimating onshore pipeline capital cost are given by McCollum [ 9]. Ccap = 9970 * ( m0.35) * ( L0.13) Ctotal = FL * FT * L * Ccap Notice that the capital cost is scaled up by a location factor ( FL) and a terrain factor ( FL). A full list of these factors is provided in [ 1]. A short list is reproduced here: FL: USA/ Canada= 1.0, Europe= 1.0, UK= 1.2, Japan= 1.0, Australia= 1.0. FT: cultivated land= 1.10, grassland= 1.00, wooded= 1.05, jungle= 1.10, stony desert= 1.10, < 20% mountainous= 1.30, > 50% mountainous= 1.50 11 The capital cost can be annualized by applying a capital recovery factor ( CRF) of 0.15. Cannual = Ctotal * CRF ( where CRF = 0.15/ yr) The O& M costs are calculated as 2.5% of the total capital cost. This value is approximately the average O& M factor from a handful of studies on CO2 pipeline transport [ 1], [ 8], [ 10], [ 11], [ 12]. To be precise, [ 1] and [ 8] do not use an O& M factor for estimating O& M costs; rather, they use a per mile cost and an equation, respectively. Their estimates, however, are close to 2.5% of the total capital cost over the range of CO2 flow rates and pipeline lengths considered here. O& Mannual = Ctotal * O& Mfactor ( where O& Mfactor = 0.025) The total annual costs are thus: Total Annual Cost [$/ yr] = Cannual + O& Mannual The total amount of CO2 that must be transported every year is found by applying a capacity factor ( CF) of 0.80. myear = m * 365 * CF ( where CF = 0.80) And the levelized cost of CO2 transport is given by: Levelized Cost [$/ tonne CO2] = ( Total Annual Cost) / myear The following figures show the onshore pipeline capital cost ( Ccap) and levelized cost, as calculated by the above equations, over a range of CO2 mass flow rates and pipeline lengths. From these figures, it is easy to see that for capital cost there is a stronger dependence on flow rate than on length. This is to be expected since, in the equation for Ccap, the exponent on the flow rate term, ‘ m’, is larger than the exponent on the length term, ‘ L’ ( 0.35 vs. 0.13). 12 Pipeline Capital Cost as a Function of CO2 Mass Flow Rate and Pipeline Length 200,000 300,000 400,000 500,000 600,000 700,000 0 5,000 10,000 15,000 20,000 CO2 Mass Flow Rate [ tonnes/ day] Pipeline Capital Cost [$/ km] L = 500 km L = 400 km L = 300 km L = 200 km L = 100 km Figure 6: Pipeline Capital Cost as a Function of CO2 Mass Flow Rate and Pipeline Length Pipeline Capital Cost as a Function of Pipeline Length and CO2 Mass Flow Rate 200,000 300,000 400,000 500,000 600,000 700,000 50 150 250 350 450 550 Pipeline Length [ km] Pipeline Capital Cost [$/ km] m = 20,000 tonnes/ day m = 15,000 tonnes/ day m = 10,000 tonnes/ day m = 5,000 tonnes/ day m = 1,000 tonnes/ day Figure 7: Pipeline Capital Cost as a Function of Pipeline Length and CO2 Mass Flow Rate 13 Levelized Cost of CO2 Transport as a Function of CO2 Mass Flow Rate and Pipeline Length 0 20 40 60 80 100 0 5,000 10,000 15,000 20,000 CO2 Mass Flow Rate [ tonnes/ day] Levelized Cost [$/ tonne CO2] L = 500 km L = 400 km L = 300 km L = 200 km L = 100 km Figure 8: Levelized Cost of CO2 Transport as a Function of CO2 Mass Flow Rate and Pipeline Length ( FL = 1.0 assumed; and FT = 1.20 assumed as an approximate average of all terrains) 14 PART III: CO2 INJECTION & STORAGE Nomenclature m = CO2 mass flow delivered to injection site per day [ tonnes/ day] myear = CO2 mass flow delivered to injection site per year [ tonnes/ year] CF = capacity factor [] Psur = surface pressure of CO2 at the top of the injection well [ MPa] Pres = pressure in the reservoir [ MPa] Pdown = downhole injection pressure of CO2 ( i. e., pressure at bottom of injection well) [ MPa] Pinter = average between reservoir pressure ( Pres) and downhole injection pressure ( Pdown) [ MPa] ΔPdown = downhole pressure difference = Pdown – Pres [ MPa] Tsur = surface temperature of CO2 at the top of the injection well [ oC] Gg = geothermal gradient [ oC/ km] Tres = temperature in the reservoir [ oC] d = reservoir depth [ m] h = reservoir thickness [ m] ka = absolute permeability of reservoir [ millidarcy ( md)] kv = vertical permeability of reservoir [ millidarcy ( md)] kh = horizontal permeability of reservoir [ millidarcy ( md)] μinter = CO2 viscosity at intermediate pressure ( Pinter) [ mPa s] μsur = CO2 viscosity at surface temperature ( Tsur) [ Pa s] ρsur = CO2 density at surface temperature ( Tsur) and surface pressure ( Psur) [ kg/ m3] CO2 mobility = absolute permeability ( ka) divided by CO2 viscosity ( μinter) [ md/ mPa s] CO2 injectivity = mass flow rate of CO2 that can be injected per unit of reservoir thickness ( h) and per unit of downhole pressure difference ( Pdown – Pres) [ tonnes/ day/ m/ MPa] g = gravitational constant [ m/ s2] Pgrav = gravity head of CO2 column in injection well [ MPa] Dpipe = injection pipe diameter [ m] Re = Reynold’s number [] ε = injection pipe roughness factor [ ft] Ff = Fanning friction factor [] vpipe = CO2 velocity in injection pipe [ m/ s] ΔPpipe = frictional pressure loss in injection pipe [ MPa] QCO2/ well = CO2 injection rate per well [ tonnes/ day/ well] Ncalc = calculated number of injection wells [] Nwell = actual number of injection wells ( i. e., rounded up to nearest integer) [] Csite = capital cost of site screening and evaluation [$] Cequip = capital cost of injection equipment [$] Cdrill = capital cost for drilling of the injection well [$] Ctotal = total capital cost of injection wells [$] Cannual = annualized capital cost of injection wells [$/ yr] CRF = Capital Recovery factor [/ yr] O& Mdaily = O& M costs due to normal daily expenses [$/ yr] O& Mcons = O& M costs due to consumables [$/ yr] O& Msur = O& M costs due to surface maintenance [$/ yr] 15 O& Msubsur = O& M costs due to subsurface maintenance [$/ yr] O& Mtotal = total O& M costs [$/ yr] Injection Well Number Calculation The number of CO2 injection wells that are required is strongly dependent on the properties of the particular geological reservoir that is being used to store the CO2. Every reservoir is unique, however, and reservoir properties are quite varied. MIT [ 8] has done some statistical analysis on properties of actual reservoirs in the U. S., and they subsequently use the ranges in the following tables for their study on CO2 storage in saline aquifers and in gas and oil reservoirs. The properties shown are reservoir pressure ( Pres), thickness ( h), depth ( d), and horizontal permeability ( kh). Table 1: Representative Range of Saline Aquifer Reservoir Properties [ 8] Table 2: Representative Range of Oil Reservoir Properties [ 8] Table 3: Representative Range of Gas Reservoir Properties [ 8] The reservoir properties corresponding to “ High Cost Case” in the preceding tables can be taken as the values that will lead to the maximum number of injection wells and, thus, maximum costs. Similarly, the “ Low Cost Case” values will lead to the minimum costs. The “ Base Case” values can be taken as statistically representative of any one reservoir. By assuming a surface temperature of 15 oC ( i. e., at the top of the injection well) and a geothermal gradient of 25 oC/ km [ 8], and taking reservoir depth ( d) from the above tables, the reservoir temperature can be approximated. 16 Tres = Tsur + d*( Gg / 1000) ( where Tsur = 15 oC and Gg = 25 oC/ km) The procedure for calculating the number of CO2 injection wells is iterative. To begin, one must assume a value for the downhole injection pressure ( Pdown), which is the CO2 pressure at the bottom of the injection well. A reasonable first approximation for Pdown is 17 MPa. The intermediate pressure of CO2 in the reservoir ( Pinter) is the average between the downhole injection pressure ( Pdown) and the reservoir pressure far from the injection well ( Pres), which is taken from the above tables. Pinter = ( Pdown + Pres) / 2 Based on Pinter, the CO2 viscosity in the reservoir near the bottom of the injection well ( μinter) can be approximated. As stated in the previous section, since CO2 exhibits unusual trends in its properties over the range of temperatures and pressures that would be experienced with injection and storage, it is difficult to provide a single value for viscosity here. Therefore, the reader is referred to either of two CO2 property websites, [ 5] and [ 6], or to the set of correlation equations of McCollum [ 7]. Each of these references provide an easy way of obtaining CO2 density and viscosity if one knows only two basic parameters— temperature and pressure. The absolute permeability of the reservoir ( ka) is found by an equation from [ 13]. ka = ( kh * kv) 0.5 = ( kh * 0.3kh) 0.5 ( where kh is taken from the above tables) The mobility of CO2 in the reservoir is thus [ 8]: CO2 mobility = ka / μinter The injectivity of CO2 is then found by [ 13]: CO2 injectivity = 0.0208 * CO2 mobility And the CO2 injection rate per well is calculated by the following equation [ 8]. QCO2/ well = ( CO2 injectivity) * h * ΔPdown = ( CO2 injectivity) * h * ( Pdown – Pres) ( where h is taken from the above tables) The number of injection wells is based on the flow rate of CO2 that is delivered to the injection site and the injection rate per well [ 8]. Ncalc = m / QCO2/ well This is the calculated number of injection wells, not the actual number. The actual number of wells must, of course, be an integer value and will be determined in the final step. As stated previously, the calculation of well number is iterative, due to the downhole injection pressure ( Pdown) initially being unknown. Pdown is simply the pressure increase due to the gravity head of the CO2 column in the injection well ( Pgrav), accounting for the fact that there is some pressure drop due to friction in the injection pipe ( ΔPpipe) [ 8]. 17 Pdown = Psur + Pgrav  ΔPpipe The gravity head is a function of the gravitational constant ( g) and the density of CO2 ( ρsur) at the surface temperature ( Tsur) and surface pressure ( Psur). Once again, for estimating CO2 density the reader is referred to either of two CO2 property websites, [ 5] and [ 6], or to the set of correlation equations of McCollum [ 7]. Pgrav = ( ρsur * g * d) / 106 ( where g = 9.81 m/ s2) The frictional pressure loss in the injection pipe is found in much the same way as the pipeline diameter was calculated in a previous section of this report. The Reynold’s number ( Re) is first found by the following equation, adapted from [ 8]: Re = 4 * ( m* 1000/ 24/ 3600/ Ncalc) / π / μsur / Dpipe ( where 1000, 24, and 3600 are unit conversion factors) The CO2 viscosity ( μsur) at the surface temperature ( Tsur) can be approximated by [ 5], [ 6], or [ 7]. The injection pipe diameter ( Dpipe) is assumed to be one of the following values, based on MIT’s report [ 8]:  0.059 m (~ 2.3 in) for all cases except the aquifer base case and aquifer low cost case;  0.1 m (~ 3.9 in) for the aquifer base case;  0.5 m ( 19.7 in) for the aquifer low cost case ( Though, the MIT report mentions that an injection pipe of this size is too large to be used in practice. Therefore, a diameter of 0.12 m (~ 4.7 in) is assumed to be a reasonable upper limit.) The Fanning friction factor ( Ff) for flow in the injection pipe is calculated by the following equation from [ 14]: 1.11 2 10 3.7 0.3048 ( / ) Re 4 1.8 log 6.91 1 ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎪⎭ ⎪⎬ ⎫ ⎪⎩ ⎪⎨ ⎧ ⎟ ⎟⎠ ⎞ ⎜ ⎜⎝ ⎛ − + = pipe f D F ε ( where ε = 0.00015 ft is assumed by [ 8]) The frictional pressure drop is then calculated based on the CO2 velocity in the injection pipe ( vpipe) [ 14]. vpipe = ( m* 1000/ 24/ 3600/ Ncalc) / ( ρsur * π * ( Dpipe/ 2) 2) ΔPpipe = ( ρsur* g* Ff* d* vpipe 2) / ( Dpipe* 2* g) / 106 Once again, the downhole injection pressure ( Pdown) is calculated by: 18 Pdown = Psur + Pgrav  ΔPpipe This calculated value for Pdown can now be used to begin another iteration. The iterative process for calculating Pdown should be carried out over and over again until there is very little difference ( i. e., < 1%) between iterations. Once Pdown is known, the actual number of injection wells ( Nwell) can be found by rounding the calculated number of wells ( Ncalc)— from the final iteration— up to the nearest integer. Nwell = ROUND_ UP ( Ncalc) Capital, O& M, and Levelized Costs of CO2 Injection & Storage *** All costs are expressed in year 2005 US$ The capital cost of site screening and evaluation ( Csite) has been scaled up into year 2005$ based on an estimate by Smith [ 15]. Csite = 1,857,773 Equations for estimating the capital cost of injection equipment were developed by the MIT report [ 8] based on actual injection well costs given by the Energy Information Administration ( EIA) in their annual “ Costs and Indices for Domestic Oil and Gas Field Equipment and Production Operations” report. Injection equipment costs include supply wells, plants, distribution lines, headers, and electrical services [ 16]. The equations of [ 8] have been scaled up into year 2005$. Cequip = Nwell * { 49,433 * [ m / ( 280* Nwell)] 0.5} MIT also developed an equation for estimating the drilling cost of an onshore injection well based on data from the “ 1998 Joint American Survey ( JAS) on Drilling Costs” report. The equations of [ 8] have been scaled up into year 2005$. Cdrill = Nwell * 106 * 0.1063e0.0008* d Therefore, the total capital cost is given by: Ctotal = Csite + Cequip + Cdrill The capital cost can be annualized by applying a capital recovery factor ( CRF) of 0.15. Cannual = Ctotal * CRF ( where CRF = 0.15/ yr) 19 O& M costs were also developed from the EIA “ Costs and Indices for Domestic Oil and Gas Field Equipment and Production Operations” report. They can be grouped into the following four categories: Normal Daily Expenses ( O& Mdaily), Consumables ( O& Mcons), Surface Maintenance ( O& Msur), and Subsurface Maintenance ( O& Msubsur). Costs have been scaled up into 2005$. O& Mdaily = Nwell * 7,596 O& Mcons = Nwell * 20,295 O& Msur = Nwell * { 15,420 * [ m / ( 280* Nwell)] 0.5} O& Msubsur = Nwell * { 5669 * ( d / 1219)} O& Mtotal = O& Mdaily + O& Mcons + O& Msur + O& Msubsur The total annual costs are thus: Total Annual Cost [$/ yr] = Cannual + O& Mtotal The total amount of CO2 that must be injected and stored every year is found by applying a capacity factor ( CF) of 0.80. myear = m * 365 * CF ( where CF = 0.80) Finally, the levelized cost of CO2 injection and storage is given by: Levelized Cost [$/ tonne CO2] = ( Total Annual Cost) / myear The following graphs show the sensitivity of both the levelized costs and number of injection wells to a few of the parameters that could vary between CO2 storage reservoirs. To be sure, carbon capture and sequestration is highly site specific, and the properties of different reservoirs may be wildly different. In the following graphs, for consistency we have used a common set of parameters, and depending on the particular graph, some parameters are held constant while one or two of the others are varied. The common parameters, for the most part, correspond to the Aquifer Base Case values highlighted above A few things are worth mentioning with regard to the graphs. For starters, as one would expect, the levelized cost of CO2 storage decreases as the amount of CO2 to be sequestered increases— i. e., economies of scale are present. Conversely, more injection wells are required at higher flow rates. In addition, as the diameter of the injection pipe gets smaller, the number of injection wells must be increased to compensate, which translates into higher levelized costs at smaller diameters. Moreover, as the reservoir gets thicker and is more permeable, fewer injection wells are needed to do the same job. Note that reservoir depth and pressure were also examined in this sensitivity analysis, but it was found that the number of injection wells is not as 20 dependent on these two parameters as it is for reservoir thickness and permeability. Thus, they have not been shown here. Common Design Bases CO2 flow rate to injection field 1,000 to 20,000 tonnes/ day Plant Capacity Factor 0.80 Surface pressure ( pipeline outlet) 10.3 MPa Surface temperature 15.0 C Reservoir temperature 46.0 C Reservoir depth 1239 m Reservoir thickness 10 to 1000 m Reservoir permeability ( horizontal) 0.1 to 500 md Reservoir pressure 8.4 MPa Injection Pipe Diameter 0.059, 0.1, 0.15, or 0.2 m Common Economic Bases Reference Year for Dollar 2005 Project Lifetime 20 years Discount Rate 0.10 Table 4: Common Set of Parameters Used in Sensitivity Analysis Levelized Cost of CO2 Storage as a Function of Total CO2 Mass Flow Rate Delivered to Injection Site 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1,000 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 20,000 tonnes/ day $/ tonne CO2 Injection Pipe Diameter = 0.059 m Injection Pipe Diameter = 0.1 m Injection Pipe Diameter = 0.15 m Injection Pipe Diameter = 0.2 m Figure 9: Levelized Cost of CO2 Storage as a Function of Total CO2 Mass Flow Rate Delivered to Injection Site 21 Number of Injection Wells as a Function of Total CO2 Mass Flow Rate Delivered to Injection Site 0 1 2 3 4 5 6 7 8 1,000 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 20,000 tonnes/ day Number of Wells Injection Pipe Diameter = 0.059 m Injection Pipe Diameter = 0.1 m Injection Pipe Diameter = 0.15 m Injection Pipe Diameter = 0.2 m Figure 10: Number of Injection Wells as a Function of Total CO2 Mass Flow Rate Delivered to Injection Site Number of Wells at Injection Site as a Function of Reservoir Permeability ( CO2 Mass Flow Rate = 5000 tonnes/ day, Injection Pipe Diameter = 0.1 m, Reservoir Thickness = 171 m) 104 11 2 1 1 1 0 20 40 60 80 100 120 0 1 10 50 100 500 millidarcies Number of Wells Figure 11: Number of Injection Wells as a Function of Reservoir Permeability 22 Number of Wells at Injection Site as a Function of Reservoir Thickness ( CO2 Mass Flow Rate = 5000 tonnes/ day, Injection Pipe Diameter = 0.1 m, Reservoir Permeability = 22 md) 9 4 2 1 1 1 1 1 0 1 2 3 4 5 6 7 8 9 10 10 25 50 100 250 500 750 1,000 meters Number of Wells Figure 12: Number of Injection Wells as a Function of Reservoir Thickness 23 REFERENCES [ 1] IEA Greenhouse Gas R& D Programme, “ Transmission of CO2 and Energy,” Report no. PH4/ 6 ( March 2002). [ 2] Mohitpour, M., H. Golshan, and A. Murray, “ Pipeline Design & Construction: A Practical Approach, The American Society of Mechanical Engineers, New York ( 2000). [ 3] “ Practical Aspects of CO2 Flooding”, Society of Petroleum Engineers ( SPE) Monograph, Vol. 22, Appendix F, ( 2002). [ 4] Hendriks, C., W. Graus, and F. van Bergen, “ Global Carbon Dioxide Storage Potential and Costs”, Ecofys report no. EEP 02001 ( 2004). [ 5] NatCarb, US Department of Energy National Energy Technology Laboratory, http:// www. natcarb. org/ Calculators/ co2_ prop. html ( Accessed on February 11, 2006). [ 6] National Institute of Standards and Technology, http:// webbook. nist. gov/ chemistry/ fluid/ ( Accessed on February 11, 2006). [ 7] McCollum, D. L., “ Simple Correlations for Estimating Carbon Dioxide Density and Viscosity as a Function of Temperature and Pressure”, Institute of Transportation Studies, University of California Davis ( 2006). [ 8] Herzog, Heddle, and Klett, “ The Economics of CO2 Storage”, MIT Laboratory for Energy and the Environment, Pub. # LFEE 2003 003 RP ( August 2003). [ 9] McCollum, D. L., “ Comparing Techno Economic Models for Pipeline Transport of Carbon Dioxide”, Institute of Transportation Studies, University of California Davis ( 2006). [ 10] Hendriks, N., T. Wildenborg, P. Feron, W. Graus, R. Brandsma, “ EC Case Carbon Dioxide Sequestration,” M70066, Ecofys ( December 2003). [ 11] IEA Greenhouse Gas R& D Programme, “ Building the Cost Curves for CO2 Storage: European Sector,” Report no. 2005/ 2 ( February 2005). [ 12] IEA Greenhouse Gas R& D Programme, “ Building the Cost Curves for CO2 Storage: North America,” Report no. 2005/ 3 ( February 2005). [ 13] Law, D. and S. Bachu, “ Hydrogeological and numerical analysis of CO2 disposal in deep aquifers in the Alberta sedimentary basin,” Energy Conversion Mgmt., 37: 6 8, pp. 1167 1174 ( 1996). [ 14] Herzog, Howard, personal e mail communication ( February 2006). 24 [ 15] Smith, L. A. et al., “ Engineering and Economic Assessment of Carbon Dioxide Sequestration in Saline Formations,” presented at the First National Conference on Carbon Sequestration, Washington D. C. ( May 14 17, 2001). [ 16] “ Costs and Indices for Domestic Oil and Gas Field Equipment and Production Operations” report, Energy Information Administration ( June 2005). [ 17] Kreutz, T., R. Williams, S. Consonni, and P. Chiesa, “ Co production of hydrogen, electricity and CO2 from coal with commercially ready technology. Part B: Economic Analysis”, International Journal of Hydrogen Energy, 30, pp. 769 784 ( 2005). SECTION II: Simple Correlations for Estimating Carbon Dioxide Density and Viscosity as a Function of Temperature and Pressure David L. McCollum dlmccollum@ ucdavis. edu Institute of Transportation Studies University of California One Shields Avenue Davis, CA 95616 ABSTRACT Recent years have seen an increased interest in carbon capture and sequestration ( CCS)— the idea of capturing carbon dioxide ( CO2) from the exhaust gases of power plants and industrial complexes, compressing the CO2 for pipeline transport, and finally injecting it underground in natural reservoirs, for example, saline aquifers and oil and gas wells. Engineers and researchers need to be able to estimate accurately the properties of CO2, a substance that exhibits unusual behavior in its properties. A number of equation of state correlations for estimating CO2’ s properties already exist, but these are often written in complex computer codes and are functions of a number of specific parameters that an inexperienced user might have trouble dealing with. This paper describes a set of simple correlations for estimating the density and viscosity of CO2 within the range of operating temperatures and pressures that might be encountered in CCS. The correlations are functions of only two input parameters: temperature and pressure. And since the correlation equations are based on experimentally measured data, their agreement with reality, as well as with other correlations, is remarkable. Keywords: carbon dioxide, CO2, CO2, sequestration, pipeline, correlation, density, viscosity 1 DESCRIPTION OF CORRELATIONS We have used experimentally measured carbon dioxide ( CO2) property data to develop a set of correlations for estimating the density and viscosity of CO2 over the range of operating temperatures and pressures that might be encountered in carbon capture and sequestration ( CCS) applications. Specifically, we have limited our correlations to a temperature range of  1.1 to 82.2 oC ( 30 to 180 oF) and a pressure range of 7.6 to 24.8 MPa ( 1100 to 3600 psia), corresponding to the post capture conditions of CO2 used in pipeline transport and underground injection. We obtain our experimental data from Kinder Morgan, a leading CO2 transporter in the United States [ 1]. We believe this data to be quite reliable, and apparently, so does the US Department of Energy National Energy Technology Laboratory’s national carbon sequestration program, NatCarb, who also use the Kinder Morgan property data for their online CO2 property calculator [ 2]. The Kinder Morgan data gives a number of CO2’ s properties as functions of temperature and pressure; some examples include: density, viscosity, compressibility factor, heat capacity, enthalpy, entropy, phase, and so on. With this data, we simply plotted the density/ viscosity vs. pressure for a given temperature and generated a sixth order polynomial regression equation to best fit the data. We then repeated this procedure at all of the other temperature values that we had access to. Some example graphs are shown below. CO2 Density as a Function of Pressure ( at  1.1 oC) y =  3.12829E 07x6 + 3.24752E 05x5  1.43858E 03x4 + 3.67519E 02x3  6.57241E 01x2 + 1.20531E+ 01x + 8.98834E+ 02 R2 = 9.99996E 01 960 970 980 990 1000 1010 1020 1030 1040 1050 7 9 11 13 15 17 19 21 23 25 Pressure ( MPa) Density ( kg/ m3) CO2 Density Regression Figure 1: CO2 density as a function of pressure at  1.1 oC 2 CO2 Density as a Function of Pressure ( at 32.2 oC) y =  1.10256E 03x6 + 1.13457E 01x5  4.76665E+ 00x4 + 1.04530E+ 02x3  1.26111E+ 03x2 + 7.94772E+ 03x  1.97102E+ 04 R2 = 9.86587E 01 400 500 600 700 800 900 1000 7 9 11 13 15 17 19 21 23 25 Pressure ( MPa) Density ( kg/ m3) CO2 Density Regression Figure 2: CO2 density as a function of pressure at 32.2 oC CO2 Viscosity as a Function of Pressure ( at 10.0 oC) y =  1.80098E 13x6 + 1.96869E 11x5  9.09904E 10x4 + 2.33381E 08x3  3.70759E 07x2 + 5.35319E 06x + 7.07073E 05 R2 = 1.00000E+ 00 8.0E 05 9.0E 05 1.0E 04 1.1E 04 1.2E 04 1.3E 04 1.4E 04 7 9 11 13 15 17 19 21 23 25 Pressure ( MPa) Viscosity ( Pa s) CO2 Viscosity Regression Figure 3: CO2 viscosity as a function of pressure at 10.0 oC 3 CO2 Viscosity as a Function of Pressure ( at 32.2 oC) y = 2.27771E 10x6  2.27111E 08x5 + 9.15360E 07x4  1.89857E 05x3 + 2.12163E 04x2  1.19673E 03x + 2.68350E 03 R2 = 9.83381E 01 0.0E+ 00 2.0E 05 4.0E 05 6.0E 05 8.0E 05 1.0E 04 1.2E 04 7 9 11 13 15 17 19 21 23 25 Pressure ( MPa) Viscosity ( Pa s) CO2 Viscosity Regression Figure 4: CO2 viscosity as a function of pressure at 32.2 oC In total, we generated 32 graphs similar to the ones seen above ( 16 density graphs and 16 viscosity graphs for each of the 16 temperatures that we had access to). These particular four graphs are shown because they are representative of all of the others. On each of the graphs, the sixth order polynomial regression equation and R2 correlation coefficient are shown. The ‘ x’ value in the regressions represents pressure ( in MPa) and the ‘ y’ value represents either density ( in kg/ m3) or viscosity ( in Pa s). In general, the R2 coefficient for all of the regressions, both density and viscosity, is greater than 0.995, showing excellent fit, except at temperatures just slightly above the critical temperature of CO2, 31.0 oC. ( Note that all of pressure values considered here are above the critical pressure of CO2, 7.38 MPa.) But even at temperatures just slightly above the critical temperature, e. g. 32.2 oC, the R2 coefficients for both density and viscosity are still greater than 0.983 ( see Figures 2 and 4). After generating all of the regression equations for density and viscosity at each of the given temperatures, we organized the regression equation coefficients into tabular form. In other words, for every temperature value there is a unique regression equation that relates pressure to either density or viscosity. Since each of these equations is unique, it has its own set of unique regression equation coefficients— i. e., the constants that precede the x6, x5, x4, x3, x2, and x terms and the final constant term in the equations shown on the graphs above. These coefficients are shown for both density and viscosity in the tables below. 4 CO2 Density Dependence of regression equation coefficients on temperature Temperature ( oC) a ( x6) b ( x5) c ( x4) d ( x3) e ( x2) f ( x) g  1.1  3.12829E 07 3.24752E 05  1.43858E 03 3.67519E 02  6.57241E 01 1.20531E+ 01 8.98834E+ 02 4.4  9.54845E 08 1.97920E 05  1.41421E 03 5.06981E 02  1.07669E+ 00 1.77109E+ 01 8.42753E+ 02 10.0  6.99274E 07 8.56082E 05  4.41249E 03 1.25510E 01  2.19938E+ 00 2.81960E+ 01 7.68647E+ 02 15.6  2.92964E 07 6.57269E 05  4.75451E 03 1.67603E 01  3.31969E+ 00 4.21135E+ 01 6.70554E+ 02 21.1  7.86428E 06 8.72837E 04  4.02787E 02 9.97669E 01  1.42859E+ 01 1.21788E+ 02 3.84188E+ 02 26.7  4.14913E 05 4.43672E 03  1.95389E 01 4.55038E+ 00  5.96084E+ 01 4.30173E+ 02  5.36390E+ 02 32.2  1.10256E 03 1.13457E 01  4.76665E+ 00 1.04530E+ 02  1.26111E+ 03 7.94772E+ 03  1.97102E+ 04 37.8  5.42882E 04 5.98138E 02  2.70792E+ 00 6.44535E+ 01  8.50922E+ 02 5.92597E+ 03  1.63183E+ 04 43.3 9.60943E 04  9.44447E 02 3.73493E+ 00  7.54076E+ 01 8.07616E+ 02  4.21227E+ 03 8.42194E+ 03 48.9 1.02964E 03  1.05231E 01 4.36150E+ 00  9.33059E+ 01 1.07660E+ 03  6.23329E+ 03 1.42664E+ 04 54.4 4.91938E 04  5.30672E 02 2.32907E+ 00  5.29027E+ 01 6.48716E+ 02  3.97202E+ 03 9.61309E+ 03 60.0 1.78281E 05  5.25573E 03 3.79601E 01  1.19952E+ 01 1.86161E+ 02  1.32231E+ 03 3.60656E+ 03 65.6  2.01381E 04 1.79337E 02  6.14241E 01 9.95370E+ 00  7.50237E+ 01 2.48324E+ 02  1.20531E+ 02 71.1  2.27250E 04 2.17674E 02  8.25519E 01 1.56315E+ 01  1.53782E+ 02 7.78805E+ 02  1.49200E+ 03 76.7  1.72335E 04 1.71075E 02  6.76015E 01 1.34315E+ 01  1.39949E+ 02 7.57756E+ 02  1.56388E+ 03 82.2  1.04002E 04 1.07058E 02  4.38694E 01 9.02417E+ 00  9.70390E+ 01 5.47454E+ 02  1.15792E+ 03 Regression Equation Coefficient CO2 Viscosity Dependence of regression equation coefficients on temperature Temperature ( oC) a ( x6) b ( x5) c ( x4) d ( x3) e ( x2) f ( x) g  1.1  3.76516E 14 4.42744E 12  2.21897E 10 6.35275E 09  1.20061E 07 3.21247E 06 9.69913E 05 4.4  4.13198E 14 5.05771E 12  2.67210E 10 8.10161E 09  1.59689E 07 3.68596E 06 8.53395E 05 10.0  1.80098E 13 1.96869E 11  9.09904E 10 2.33381E 08  3.70759E 07 5.35319E 06 7.07073E 05 15.6  3.83675E 13 4.25032E 11  1.97443E 09 4.99914E 08  7.54380E 07 8.42586E 06 5.17798E 05 21.1  9.83505E 13 1.08507E 10  4.97927E 09 1.22724E 07  1.75059E 06 1.58647E 05 2.01512E 05 26.7  4.04273E 12 4.32435E 10  1.90732E 08 4.45698E 07  5.87710E 06 4.39583E 05  6.75597E 05 32.2 2.27771E 10  2.27111E 08 9.15360E 07  1.89857E 05 2.12163E 04  1.19673E 03 2.68350E 03 37.8 9.44539E 11  9.37386E 09 3.75251E 07  7.70019E 06 8.44425E 05  4.57587E 04 9.69405E 04 43.3 4.61459E 11  4.64533E 09 1.89478E 07  3.98321E 06 4.49854E 05  2.50385E 04 5.50761E 04 48.9 2.17356E 11  2.27268E 09 9.72054E 08  2.16667E 06 2.62433E 05  1.57279E 04 3.81014E 04 54.4 1.75118E 11  1.83939E 09 7.90905E 08  1.77644E 06 2.17839E 05  1.32903E 04 3.32020E 04 60.0 1.59447E 11  1.66290E 09 7.09018E 08  1.57981E 06 1.92861E 05  1.17925E 04 2.99069E 04 65.6 1.33132E 11  1.38244E 09 5.86429E 08  1.30108E 06 1.58745E 05  9.74570E 05 2.52370E 04 71.1 9.59612E 12  9.94594E 10 4.21212E 08  9.35052E 07 1.14752E 05  7.09785E 05 1.90487E 04 76.7 4.94000E 12  5.14144E 10 2.19389E 08  4.94382E 07 6.23334E 06  3.93456E 05 1.15441E 04 82.2 8.35493E 13  9.23510E 11 4.29135E 09  1.10162E 07 1.66420E 06  1.16755E 05 4.94127E 05 Regression Equation Coefficient Table 1: Regression equation coefficients for CO2 density Table 2: Regression equation coefficients for CO2 viscosity With the above regression equation coefficients, the density and viscosity of CO2 at any temperature and pressure in the above ranges ( 1.1 to 82.2 oC and 7.6 to 24.8 MPa) can easily and reliably be calculated. One word of caution, however, is not to use the coefficients to try and 5 extrapolate beyond the above ranges, as this will surely generate inaccurate output. The calculation is outlined below in a series of steps. 1) Specify the operating temperature, Top ( in oC). 2) In the above regression coefficient tables for both density and viscosity, find the range of temperatures ( Thigh and Tlow) that the operating temperature ( Top) is between. 3) In the above regression coefficient tables for both density and viscosity, find the regression equation coefficients that correspond to Thigh and Tlow— a, b, c, d, e, f, and g. 4) Specify the operating pressure, Pop ( in MPa). 5) With Pop calculate the density at Thigh and at Tlow and the viscosity at Thigh and at Tlow. The following generic equation can be used to calculate ρhigh, ρlow, μhigh, and μlow: ρ or μ = a* Pop 6 + b* Pop 5 + c* Pop 4 + d* Pop 3 + e* Pop 2 + f* Pop + g 6) Interpolate for ρop and μop by the following equations. ρop = {( ρhigh – ρlow) * ( Top – Tlow) / ( Thigh – Tlow)} + ρlow μop = {( μhigh – μlow) * ( Top – Tlow) / ( Thigh – Tlow)} + μlow *** A simple example should serve to illustrate this calculation procedure. 1) Assume Top = 47.0 oC 2) From the regression coefficient tables, we find that Top = 47.0 oC is between Thigh = 48.9 oC and Tlow = 43.3 oC. 3) From the density and viscosity tables, the regression equation coefficients are: Density ( ρ): Thigh: a = 1.02964E 03, b =  1.05231E 01, c = 4.36150E+ 00, d =  9.33059E+ 01, e = 1.07660E+ 03, f =  6.23329E+ 03, g = 1.42664E+ 04 Tlow: a = 9.60943E 04, b =  9.44447E 02, c = 3.73493E+ 00, d =  7.54076E+ 01, e = 8.07616E+ 02, f =  4.21227E+ 03, g = 8.42194E+ 03 Viscosity ( μ): Thigh: a = 2.17356E 11, b =  2.27268E 09, c = 9.72054E 08, d =  2.16667E 06, e = 2.62433E 05, f =  1.57279E 04, g = 3.81014E 04 Tlow: a = 4.61459E 11, b =  4.64533E 09, c = 1.89478E 07, d =  3.98321E 06, e = 4.49854E 05, f =  2.50385E 04, g = 5.50761E 04 6 4) Assume Pop = 10 MPa. 5) Calculate ρhigh, ρlow, μhigh, and μlow: ρhigh = 1.02964E 03* Pop 6 +  1.05231E 01* Pop 5 + 4.36150E+ 00* Pop 4 +  9.33059E+ 01* Pop 3 + 1.07660E+ 03* Pop 2 +  6.23329E+ 03* Pop + 1.42664E+ 04 = 409.1 kg/ m3 ρlow = 9.60943E 04* Pop 6 +  9.44447E 02* Pop 5 + 3.73493E+ 00* Pop 4 +  7.54076E+ 01* Pop 3 + 8.07616E+ 02* Pop 2 +  4.21227E+ 03* Pop + 8.42194E+ 03 = 519.0 kg/ m3 μhigh = 2.17356E 11* Pop 6 +  2.27268E 09* Pop 5 + 9.72054E 08* Pop 4 +  2.16667E 06* Pop 3 + 2.62433E 05* Pop 2 +  1.57279E 04* Pop + 3.81014E 04 = 3.24E 05 Pa s μlow = 4.61459E 11* Pop 6 +  4.64533E 09* Pop 5 + 1.89478E 07* Pop 4 +  3.98321E 06* Pop 3 + 4.49854E 05* Pop 2 +  2.50385E 04* Pop + 5.50761E 04 = 3.86E 05 Pa s 6) Interpolate for ρop and μop. ρop = {( 409.1 – 519.0) * ( 47.0 – 43.3) / ( 48.9 – 43.3)} + 519.0 = 446.4 kg/ m3 μop = {( 3.24E 05 – 3.86E 05) * ( 47.0 – 43.3) / ( 48.9 – 43.3)} + 3.86E 05 = 3.45E 05 Pa s 7 COMPARISON WITH OTHER CORRELATIONS We have compared our CO2 correlations to other, more complex equation of state correlations and find that ours are in agreement. Garcia [ 3] does a nice job of explaining equation of state CO2 property correlations and then comparing densities calculated by various correlations over a small range of temperatures and pressures. He provides the following comparison table: Table 3: CO2 density ( kg/ m3) at 320 K ( 47.0 oC) as a function of temperature and pressure by various correlations Note that all of the densities in the above table are for 320 K ( i. e., ~ 47.0 oC). Now, look at the row of CO2 densities that correspond to 100 bar ( i. e., 10 MPa). By design, these are exactly the operating conditions that we used in the example above to illustrate our methods and equations. At these conditions, our correlations estimate the CO2 density to be 446.4 kg/ m3, which is well within the range of values ( 446.78 – 505.36 kg/ m3) calculated by other, more complex correlations, as shown in Garcia’s table. In addition, our correlations match well with online CO2 property calculators like those of NatCarb and the National Institute of Standards and Technology [ 2, 4]. As previously mentioned, the NatCarb calculator uses the same Kinder Morgan property data that we use. The NIST calculator on the other hand uses the correlations of Span and Wagner [ 5], which Garcia references in his table above. Density and viscosity values ( both experimentally measured and those calculated by our regression equations) are shown in the appendices for all of the temperature and pressure 8 operating points that we had data for. Also in the appendix, we show the percent differences between the calculated and experimentally measured values for both density and viscosity. In almost all cases, the percent difference is less than 1%, and much of the time it is less than 0.1%. The greatest differences occur near the critical point of CO2, with differences as high as 13.8% for density and 18.1% for viscosity. Therefore, if one is interested in designing a system where the temperature and pressure are near the critical point of CO2 ( 31.0 oC and 7.38 MPa) for much of the time, then perhaps a more complex equation of state CO2 property correlation should be used. But at virtually any other operating conditions ( at least in the range of conditions studied here), our correlations provide very reliable results. 9 CONCLUSION We have used experimentally measured CO2 property data to create sixth order polynomial correlation equations for estimating the density and viscosity of CO2. Our correlations are functions of only two parameters— temperature and pressure— and can be used in the range of  1.1 to 82.2 oC ( 30 to 180 oF) and 7.6 to 24.8 MPa ( 1100 to 3600 psia). In the case of carbon capture and sequestration, these operating ranges correspond to the postcapture/ post compression conditions of CO2 used in pipeline transport and underground injection. Our correlations provide a simple alternative to the more complex equation of state correlations that are often used. While these more complex correlations may provide slightly more accurate density and viscosity estimates near the critical point of CO2, for the vast majority of operating temperatures and pressures in the ranges mentioned above, our correlations are just as accurate and reliable and should be used with confidence. We believe that simple correlations of this kind will be demanded more and more in the future, as CCS continues to gain interest, especially among those engineers and researchers with little background in the field and who would prefer to use simple correlations to obtain accurate results. * Note: Any parties interested in obtaining a copy of the Microsoft Excel file of the CO2 property correlations described in this report, should feel free to contact the author at dlmccollum@ ucdavis. edu. 10 REFERENCES [ 1] “ Practical Aspects of CO2 Flooding”, Society of Petroleum Engineers ( SPE) Monograph, Vol. 22, Appendix F, ( 2002). [ 2] NatCarb, US Department of Energy National Energy Technology Laboratory, http:// www. natcarb. org/ Calculators/ co2_ prop. html, Accessed on February 11, 2006. [ 3] García, J. E., “ Fluid Dynamics of Carbon Dioxide Disposal Into Saline Aquifers”, PhD dissertation, University of California at Berkeley, Berkeley, California ( December 2003). [ 4] National Institute of Standards and Technology ( NIST), http:// webbook. nist. gov/ chemistry/ fluid/, Accessed on February 11, 2006. [ 5] Span, R. and W. Wagner, “ A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple Point Temperature to 1100 K at Pressures up to 800 MPa”, J. Phys. Chem. Ref. Data, 25, 6, 1509 1596 ( 1996). APPENDIX Appendix 1: Regression equation coefficients for CO2 density Appendix 2: Regression equation coefficients for CO2 viscosity Appendix 3: CO2 density as a function of temperature and pressure ( experimentally measured values from the Kinder Morgan property data) Appendix 4: CO2 density as a function of temperature and pressure ( calculated values from the regression equations) Appendix 5: Percent difference between the calculated and experimentally measured density values at each of the temperature and pressure operating points Appendix 6: CO2 viscosity as a function of temperature and pressure ( experimentallymeasured values from the Kinder Morgan property data) Appendix 7: CO2 viscosity as a function of temperature and pressure ( calculated values from the regression equations) Appendix 8: Percent difference between the calculated and experimentally measured viscosity values at each of the temperature and pressure operating points i Appendix 1 CO2 Density Dependence of regression equation coefficients on temperature Temperature ( oC) a ( x6) b ( x 5 ) c ( x 4 ) d ( x 3 ) e ( x 2 ) f ( x) g  1.1  3.12829E 07 3.24752E 05  1.43858E 03 3.67519E 02  6.57241E 01 1.20531E+ 01 8.98834E+ 02 4.4  9.54845E 08 1.97920E 05  1.41421E 03 5.06981E 02  1.07669E+ 00 1.77109E+ 01 8.42753E+ 02 10.0  6.99274E 07 8.56082E 05  4.41249E 03 1.25510E 01  2.19938E+ 00 2.81960E+ 01 7.68647E+ 02 15.6  2.92964E 07 6.57269E 05  4.75451E 03 1.67603E 01  3.31969E+ 00 4.21135E+ 01 6.70554E+ 02 21.1  7.86428E 06 8.72837E 04  4.02787E 02 9.97669E 01  1.42859E+ 01 1.21788E+ 02 3.84188E+ 02 26.7  4.14913E 05 4.43672E 03  1.95389E 01 4.55038E+ 00  5.96084E+ 01 4.30173E+ 02  5.36390E+ 02 32.2  1.10256E 03 1.13457E 01  4.76665E+ 00 1.04530E+ 02  1.26111E+ 03 7.94772E+ 03  1.97102E+ 04 37.8  5.42882E 04 5.98138E 02  2.70792E+ 00 6.44535E+ 01  8.50922E+ 02 5.92597E+ 03  1.63183E+ 04 43.3 9.60943E 04  9.44447E 02 3.73493E+ 00  7.54076E+ 01 8.07616E+ 02  4.21227E+ 03 8.42194E+ 03 48.9 1.02964E 03  1.05231E 01 4.36150E+ 00  9.33059E+ 01 1.07660E+ 03  6.23329E+ 03 1.42664E+ 04 54.4 4.91938E 04  5.30672E 02 2.32907E+ 00  5.29027E+ 01 6.48716E+ 02  3.97202E+ 03 9.61309E+ 03 60.0 1.78281E 05  5.25573E 03 3.79601E 01  1.19952E+ 01 1.86161E+ 02  1.32231E+ 03 3.60656E+ 03 65.6  2.01381E 04 1.79337E 02  6.14241E 01 9.95370E+ 00  7.50237E+ 01 2.48324E+ 02  1.20531E+ 02 71.1  2.27250E 04 2.17674E 02  8.25519E 01 1.56315E+ 01  1.53782E+ 02 7.78805E+ 02  1.49200E+ 03 76.7  1.72335E 04 1.71075E 02  6.76015E 01 1.34315E+ 01  1.39949E+ 02 7.57756E+ 02  1.56388E+ 03 82.2  1.04002E 04 1.07058E 02  4.38694E 01 9.02417E+ 00  9.70390E+ 01 5.47454E+ 02  1.15792E+ 03 Regression Equation Coefficient ii Appendix 2 CO2 Viscosity Dependence of regression equation coefficients on temperature Temperature ( oC) a ( x6) b ( x 5 ) c ( x 4 ) d ( x 3 ) e ( x 2 ) f ( x) g  1.1  3.76516E 14 4.42744E 12  2.21897E 10 6.35275E 09  1.20061E 07 3.21247E 06 9.69913E 05 4.4  4.13198E 14 5.05771E 12  2.67210E 10 8.10161E 09  1.59689E 07 3.68596E 06 8.53395E 05 10.0  1.80098E 13 1.96869E 11  9.09904E 10 2.33381E 08  3.70759E 07 5.35319E 06 7.07073E 05 15.6  3.83675E 13 4.25032E 11  1.97443E 09 4.99914E 08  7.54380E 07 8.42586E 06 5.17798E 05 21.1  9.83505E 13 1.08507E 10  4.97927E 09 1.22724E 07  1.75059E 06 1.58647E 05 2.01512E 05 26.7  4.04273E 12 4.32435E 10  1.90732E 08 4.45698E 07  5.87710E 06 4.39583E 05  6.75597E 05 32.2 2.27771E 10  2.27111E 08 9.15360E 07  1.89857E 05 2.12163E 04  1.19673E 03 2.68350E 03 37.8 9.44539E 11  9.37386E 09 3.75251E 07  7.70019E 06 8.44425E 05  4.57587E 04 9.69405E 04 43.3 4.61459E 11  4.64533E 09 1.89478E 07  3.98321E 06 4.49854E 05  2.50385E 04 5.50761E 04 48.9 2.17356E 11  2.27268E 09 9.72054E 08  2.16667E 06 2.62433E 05  1.57279E 04 3.81014E 04 54.4 1.75118E 11  1.83939E 09 7.90905E 08  1.77644E 06 2.17839E 05  1.32903E 04 3.32020E 04 60.0 1.59447E 11  1.66290E 09 7.09018E 08  1.57981E 06 1.92861E 05  1.17925E 04 2.99069E 04 65.6 1.33132E 11  1.38244E 09 5.86429E 08  1.30108E 06 1.58745E 05  9.74570E 05 2.52370E 04 71.1 9.59612E 12  9.94594E 10 4.21212E 08  9.35052E 07 1.14752E 05  7.09785E 05 1.90487E 04 76.7 4.94000E 12  5.14144E 10 2.19389E 08  4.94382E 07 6.23334E 06  3.93456E 05 1.15441E 04 82.2 8.35493E 13  9.23510E 11 4.29135E 09  1.10162E 07 1.66420E 06  1.16755E 05 4.94127E 05 Regression Equation Coefficient iii CO2 Density ( kg/ m3) as a Function of Temperature ( oC) and Pressure ( MPa) ( actual values from Kinder Morgan) Pressure ( MPa)  1.1 4.4 10.0 15.6 21.1 26.7 32.2 37.8 43.3 48.9 54.4 60.0 65.6 71.1 76.7 82.2 7.6 964.5 933.1 898.2 858.0 808.5 739.1 473.8 254.4 220.9 200.9 186.8 175.7 166.8 159.2 152.7 146.9 8.3 968.8 938.4 904.9 866.9 821.6 763.3 669.6 371.3 274.7 239.6 218.0 202.6 190.5 180.7 172.4 165.3 9.0 973.0 943.5 911.1 874.9 833.0 781.4 710.4 577.0 361.7 290.3 255.7 233.4 217.1 204.2 193.7 184.9 9.7 977.0 948.3 917.1 882.5 843.1 796.3 736.5 648.4 489.7 359.8 302.1 269.1 246.8 230.0 216.7 205.8 10.3 980.8 952.9 922.7 889.5 852.2 808.9 756.2 686.7 582.9 447.9 359.5 311.1 280.5 258.5 241.7 228.1 11.0 984.7 957.3 928.0 895.9 860.4 820.0 772.4 713.1 634.2 528.0 425.6 359.6 318.3 289.9 268.8 252.1 11.7 988.2 961.4 932.9 902.0 868.0 829.9 786.0 733.6 668.1 584.5 490.0 412.5 359.9 324.1 297.8 277.6 12.4 991.7 965.6 937.7 907.8 875.1 838.9 798.0 750.5 693.6 624.1 543.2 465.0 404.1 360.6 328.7 304.5 13.1 995.2 969.4 942.2 913.2 881.7 847.1 808.6 764.7 713.8 653.7 584.4 511.8 447.9 398.4 361.1 332.7 13.8 998.4 973.3 946.7 918.3 887.9 854.7 818.2 777.4 730.8 677.4 616.6 551.2 488.6 435.7 394.2 361.7 14.5 1001.6 977.0 950.9 923.3 893.7 861.8 827.0 788.6 745.5 697.0 642.5 583.6 524.6 471.3 426.7 391.0 15.2 1004.8 980.5 955.0 928.0 899.3 868.5 835.2 798.7 758.3 713.6 664.1 610.6 555.8 503.8 458.1 420.0 15.9 1007.9 983.9 958.9 932.6 904.6 874.8 842.7 808.0 769.8 728.2 682.5 633.5 582.8 532.9 487.4 447.9 16.5 1010.8 987.2 962.7 936.9 909.7 880.7 849.8 816.5 780.4 741.2 698.7 653.2 606.0 558.9 514.4 474.3 17.2 1013.8 990.6 966.4 941.1 914.5 886.5 856.5 824.5 790.0 752.9 713.0 670.5 626.3 581.8 538.7 499.1 17.9 1016.5 993.8 969.9 945.1 919.1 891.7 862.8 831.8 798.8 763.6 725.8 685.9 644.3 602.1 560.8 521.9 18.6 1019.4 996.8 973.4 949.1 923.6 896.9 868.7 838.9 807.2 773.4 737.5 699.7 660.4 620.4 580.8 543.0 19.3 1022.1 999.9 976.8 952.9 928.0 901.8 874.4 845.5 814.9 782.3 748.2 712.2 674.9 636.9 598.9 562.2 20.0 1024.7 1002.8 980.0 956.6 932.1 906.6 879.7 851.7 822.1 790.8 758.0 723.7 688.2 651.8 615.4 580.0 20.7 1027.3 1005.6 983.2 960.1 936.1 911.1 885.0 857.6 829.0 798.8 767.3 734.3 700.3 665.6 630.6 596.4 21.4 1029.8 1008.5 986.4 963.7 940.0 915.5 890.0 863.2 835.4 806.2 775.8 744.1 711.4 678.1 644.6 611.4 22.1 1032.4 1011.2 989.5 967.0 943.8 919.8 894.8 868.7 841.6 813.3 783.8 753.4 721.8 689.8 657.4 625.4 22.8 1034.8 1014.0 992.3 970.2 947.5 923.8 899.4 874.0 847.5 820.0 791.5 761.8 731.6 700.5 669.4 638.3 23.4 1037.2 1016.5 995.4 973.4 951.0 927.8 903.8 878.9 853.1 826.4 798.5 770.0 740.5 710.7 680.5 650.4 24.1 1039.6 1019.1 998.1 976.6 954.5 931.6 908.1 883.7 858.4 832.3 805.4 777.7 749.2 720.2 690.9 661.7 24.8 1041.8 1021.7 1001.0 979.7 957.9 935.5 912.3 888.4 863.7 838.2 811.8 784.9 757.2 729.2 700.6 672.3 Temperature ( oC) Appendix 3 iv CO2 Density ( kg/ m3) as a Function of Temperature ( oC) and Pressure ( MPa) ( calculated values from regression equations) Pressure ( MPa)  1.1 4.4 10.0 15.6 21.1 26.7 32.2 37.8 43.3 48.9 54.4 60.0 65.6 71.1 7.6 964.5 933.1 898.2 858.0 808.5 739.5 494.7 236.0 203.5 199.6 192.1 180.5 169.1 159.9 8.3 968.8 938.4 904.9 866.8 821.5 762.6 629.9 422.4 295.4 234.5 208.9 196.7 188.2 180.5 9.0 973.0 943.5 911.2 875.0 832.9 781.2 708.3 548.7 390.0 296.8 251.0 228.0 214.1 203.3 9.7 977.0 948.3 917.1 882.5 843.1 796.5 750.3 632.0 478.5 370.9 307.0 269.4 245.8 229.3 10.3 980.8 952.9 922.6 889.5 852.2 809.3 771.0 685.5 555.6 445.9 368.5 316.5 282.2 258.6 11.0 984.6 957.3 927.9 895.9 860.4 820.3 780.7 719.3 618.6 514.9 429.6 366.2 321.8 291.0 11.7 988.2 961.5 932.9 902.0 868.0 830.0 786.5 740.8 667.3 573.8 486.5 415.7 363.2 325.7 12.4 991.7 965.6 937.7 907.8 875.1 838.8 792.3 755.4 702.7 621.4 537.0 463.0 405.1 361.9 13.1 995.1 969.5 942.3 913.2 881.6 846.9 799.9 766.5 726.9 657.7 579.9 506.8 446.1 398.6 13.8 998.5 973.3 946.7 918.4 887.8 854.5 809.8 776.2 742.8 684.4 615.5 546.2 485.1 434.8 14.5 1001.7 976.9 950.9 923.3 893.7 861.7 821.3 785.8 752.9 703.4 644.2 580.8 521.3 469.7 15.2 1004.8 980.5 955.0 928.0 899.3 868.4 833.5 795.7 760.1 717.0 667.2 610.4 554.0 502.4 15.9 1007.9 983.9 958.9 932.5 904.6 874.8 845.1 805.7 766.3 727.5 685.6 635.5 582.8 532.4 16.5 1010.8 987.3 962.7 936.9 909.7 880.9 855.0 815.6 773.3 736.8 700.7 656.3 607.8 559.4 17.2 1013.8 990.5 966.4 941.1 914.5 886.6 862.7 824.9 782.0 746.2 713.6 673.6 629.0 583.2 17.9 1016.6 993.7 969.9 945.2 919.2 892.0 868.0 833.4 792.5 756.5 725.2 688.0 646.8 604.0 18.6 1019.4 996.8 973.4 949.1 923.6 897.1 871.2 840.8 804.4 767.7 736.3 700.4 662.0 622.0 19.3 1022.1 999.9 976.8 952.9 927.9 901.9 873.0 847.2 816.7 779.6 747.1 711.5 675.1 637.8 20.0 1024.7 1002.8 980.1 956.6 932.1 906.5 874.7 852.8 828.2 791.1 757.6 721.9 686.9 651.8 20.7 1027.3 1005.7 983.3 960.2 936.1 911.0 877.5 857.8 837.5 801.2 767.8 732.1 698.1 664.8 21.4 1029.9 1008.5 986.4 963.6 940.0 915.4 882.4 862.8 843.6 808.9 777.2 742.4 709.3 677.2 22.1 1032.4 1011.2 989.4 967.0 943.8 919.7 889.7 868.1 846.3 813.7 785.7 752.8 720.7 689.4 22.8 1034.8 1013.9 992.4 970.3 947.5 923.9 898.9 873.9 846.5 816.1 792.9 763.0 732.1 701.3 23.4 1037.2 1016.6 995.3 973.5 951.1 928.0 907.7 880.0 847.0 817.9 799.3 772.2 742.8 712.7 24.1 1039.6 1019.1 998.2 976.6 954.5 931.9 911.3 885.6 853.1 823.2 805.5 779.5 751.3 722.5 24.8 1041.9 1021.6 1001.0 979.7 957.9 935.4 902.2 888.9 873.2 838.9 813.4 783.1 755.1 728.8 Temperature ( oC) Appendix 4 v Percent difference (%) between calculated and actual CO2 density values ( 100% * [ ( calculated  actual ) / actual ] ) Pressure ( MPa)  1.1 4.4 10.0 15.6 21.1 26.7 32.2 37.8 43.3 48.9 54.4 60.0 65.6 71.1 7.6 0.00 0.00 0.00 0.00 0.01 0.06 4.40  7.20  7.86  0.64 2.85 2.72 1.41 0.41 8.3 0.00 0.00 0.00  0.01  0.01  0.09  5.92 13.75 7.51  2.16  4.16  2.93  1.19  0.13 9.0 0.00 0.00 0.00 0.01 0.00  0.02  0.30  4.90 7.83 2.26  1.82  2.31  1.37  0.46 9.7 0.00 0.00 0.00 0.00 0.00 0.02 1.87  2.53  2.27 3.11 1.62 0.09  0.43  0.32 10.3 0.00  0.01 0.00  0.01 0.00 0.04 1.95  0.17  4.69  0.43 2.52 1.76 0.60 0.03 11.0  0.01 0.00 0.00 0.00 0.01 0.03 1.08 0.87  2.45  2.48 0.94 1.83 1.10 0.35 11.7 0.00 0.01 0.00 0.00 0.00 0.01 0.06 0.98  0.13  1.83  0.71 0.77 0.92 0.50 12.4 0.00 0.00 0.00 0.00 0.00  0.01  0.72 0.66 1.31  0.44  1.15  0.43 0.24 0.36 13.1  0.01 0.00 0.01 0.00 0.00  0.02  1.08 0.23 1.84 0.62  0.75  0.97  0.40 0.05 13.8 0.00 0.00 0.00 0.00  0.01  0.03  1.04  0.15 1.64 1.03  0.17  0.91  0.70  0.20 14.5 0.00 0.00 0.00 0.00 0.00  0.02  0.69  0.35 1.00 0.92 0.27  0.48  0.63  0.34 15.2 0.00 0.00  0.01 0.01 0.00  0.01  0.21  0.38 0.23 0.47 0.46  0.03  0.34  0.27 15.9 0.00 0.01 0.00  0.01 0.00 0.01 0.27  0.28  0.46  0.10 0.44 0.31 0.01  0.09 16.5 0.01 0.01 0.00 0.00 0.00 0.02 0.62  0.11  0.91  0.60 0.28 0.47 0.29 0.10 17.2  0.01 0.00 0.00 0.00 0.00 0.01 0.73 0.05  1.02  0.89 0.08 0.45 0.42 0.25 17.9 0.01  0.01 0.00 0.01 0.00 0.03 0.61 0.19  0.80  0.94  0.08 0.31 0.40 0.31 18.6  0.01 0.00 0.00 0.00 0.00 0.02 0.29 0.23  0.35  0.73  0.16 0.11 0.23 0.26 19.3  0.01 0.00 0.00 0.00 0.00 0.01  0.16 0.21 0.22  0.35  0.16  0.09 0.03 0.14 20.0 0.00 0.00 0.01 0.00 0.00  0.01  0.57 0.13 0.74 0.03  0.05  0.25  0.19 0.01 20.7 0.01 0.00 0.00 0.00 0.00  0.01  0.85 0.02 1.03 0.29 0.06  0.30  0.32  0.12 21.4 0.00 0.00 0.00 0.00 0.00  0.01  0.86  0.05 0.99 0.33 0.19  0.22  0.29  0.13 22.1 0.00 0.00 0.00 0.00 0.00  0.01  0.57  0.07 0.56 0.05 0.24  0.07  0.16  0.06 22.8 0.00 0.00 0.01 0.00 0.00 0.01  0.06  0.01  0.12  0.48 0.19 0.15 0.07 0.12 23.4 0.00 0.00  0.01 0.00 0.00 0.03 0.43 0.12  0.72  1.03 0.10 0.29 0.30 0.28 24.1 0.00 0.00 0.01 0.00 0.00 0.03 0.35 0.21  0.62  1.09 0.02 0.23 0.28 0.32 24.8 0.00 0.00 0.00 0.00 0.00  0.01  1.10 0.05 1.10 0.08 0.20  0.23  0.28  0.05 Temperature ( oC) Appendix 5 vi CO2 Viscosity ( Pa s) as a Function of Temperature ( oC) and Pressure ( MPa) ( actual values from Kinder Morgan) Pressure ( MPa)  1.1 4.4 10.0 15.6 21.1 26.7 32.2 37.8 43.3 48.9 54.4 60.0 65.6 71.1 7.6 1.17E 04 1.07E 04 9.76E 05 8.86E 05 7.94E 05 6.92E 05 3.42E 05 2.26E 05 2.14E 05 2.15E 05 2.10E 05 2.07E 05 2.05E 05 2.05E 05 8.3 1.18E 04 1.08E 04 9.93E 05 9.04E 05 8.17E 05 7.24E 05 2.93E 05 2.68E 05 2.48E 05 2.33E 05 2.25E 05 2.19E 05 2.15E 05 2.13E 05 9.0 1.20E 04 1.10E 04 1.01E 04 9.22E 05 8.37E 05 7.51E 05 3.89E 05 3.35E 05 2.93E 05 2.62E 05 2.46E 05 2.35E 05 2.27E 05 2.22E 05 9.7 1.21E 04 1.11E 04 1.02E 04 9.39E 05 8.56E 05 7.74E 05 5.35E 05 4.35E 05 3.58E 05 3.02E 05 2.76E 05 2.58E 05 2.44E 05 2.35E 05 10.3 1.22E 04 1.13E 04 1.04E 04 9.55E 05 8.74E 05 7.95E 05 6.74E 05 5.34E 05 4.25E 05 3.47E 05 3.11E 05 2.86E 05 2.66E 05 2.53E 05 11.0 1.24E 04 1.14E 04 1.05E 04 9.71E 05 8.91E 05 8.14E 05 7.21E 05 5.80E 05 4.68E 05 3.87E 05 3.47E 05 3.17E 05 2.92E 05 2.74E 05 11.7 1.25E 04 1.16E 04 1.07E 04 9.85E 05 9.07E 05 8.31E 05 7.51E 05 6.15E 05 5.07E 05 4.25E 05 3.80E 05 3.44E 05 3.16E 05 2.93E 05 12.4 1.26E 04 1.17E 04 1.08E 04 1.00E 04 9.22E 05 8.48E 05 7.65E 05 6.41E 05 5.40E 05 4.61E 05 4.10E 05 3.70E 05 3.37E 05 3.12E 05 13.1 1.28E 04 1.18E 04 1.10E 04 1.01E 04 9.37E 05 8.64E 05 7.76E 05 6.63E 05 5.68E 05 4.92E 05 4.38E 05 3.94E 05 3.58E 05 3.30E 05 13.8 1.29E 04 1.20E 04 1.11E 04 1.03E 04 9.51E 05 8.79E 05 7.95E 05 6.85E 05 5.92E 05 5.17E 05 4.63E 05 4.18E 05 3.81E 05 3.50E 05 14.5 1.30E 04 1.21E 04 1.12E 04 1.04E 04 9.65E 05 8.94E 05 8.06E 05 7.04E 05 6.16E 05 5.43E 05 4.88E 05 4.42E 05 4.02E 05 3.70E 05 15.2 1.32E 04 1.22E 04 1.14E 04 1.05E 04 9.79E 05 9.08E 05 8.05E 05 7.18E 05 6.40E 05 5.72E 05 5.14E 05 4.65E 05 4.23E 05 3.88E 05 15.9 1.33E 04 1.23E 04 1.15E 04 1.07E 04 9.92E 05 9.22E 05 8.09E 05 7.33E 05 6.62E 05 5.98E 05 5.39E 05 4.87E 05 4.43E 05 4.07E 05 16.5 1.34E 04 1.25E 04 1.16E 04 1.08E 04 1.00E 04 9.35E 05 8.15E 05 7.47E 05 6.83E 05 6.21E 05 5.61E 05 5.08E 05 4.62E 05 4.25E 05 17.2 1.35E 04 1.26E 04 1.17E 04 1.09E 04 1.02E 04 9.48E 05 8.23E 05 7.62E 05 7.01E 05 6.42E 05 5.82E 05 5.28E 05 4.82E 05 4.43E 05 17.9 1.37E 04 1.27E 04 1.18E 04 1.10E 04 1.03E 04 9.61E 05 8.33E 05 7.76E 05 7.18E 05 6.61E 05 6.01E 05 5.47E 05 5.01E 05 4.61E 05 18.6 1.38E 04 1.28E 04 1.20E 04 1.12E 04 1.04E 04 9.73E 05 8.45E 05 7.89E 05 7.33E 05 6.78E 05 6.19E 05 5.66E 05 5.19E 05 4.79E 05 19.3 1.39E 04 1.30E 04 1.21E 04 1.13E 04 1.05E 04 9.85E 05 8.58E 05 8.02E 05 7.47E 05 6.92E 05 6.35E 05 5.83E 05 5.37E 05 4.97E 05 20.0 1.40E 04 1.31E 04 1.22E 04 1.14E 04 1.07E 04 9.97E 05 8.74E 05 8.15E 05 7.58E 05 7.04E 05 6.50E 05 6.00E 05 5.55E 05 5.15E 05 20.7 1.41E 04 1.32E 04 1.23E 04 1.15E 04 1.08E 04 1.01E 04 8.85E 05 8.28E 05 7.73E 05 7.19E 05 6.65E 05 6.16E 05 5.71E 05 5.31E 05 21.4 1.43E 04 1.33E 04 1.24E 04 1.16E 04 1.09E 04 1.02E 04 8.95E 05 8.41E 05 7.87E 05 7.34E 05 6.81E 05 6.31E 05 5.86E 05 5.46E 05 22.1 1.44E 04 1.34E 04 1.26E 04 1.17E 04 1.10E 04 1.03E 04 9.06E 05 8.53E 05 8.00E 05 7.48E 05 6.95E 05 6.45E 05 6.00E 05 5.60E 05 22.8 1.45E 04 1.35E 04 1.27E 04 1.19E 04 1.11E 04 1.04E 04 9.18E 05 8.65E 05 8.13E 05 7.61E 05 7.08E 05 6.59E 05 6.14E 05 5.74E 05 23.4 1.46E 04 1.37E 04 1.28E 04 1.20E 04 1.12E 04 1.05E 04 9.29E 05 8.77E 05 8.25E 05 7.73E 05 7.20E 05 6.71E 05 6.27E 05 5.87E 05 24.1 1.47E 04 1.38E 04 1.29E 04 1.21E 04 1.13E 04 1.06E 04 9.41E 05 8.88E 05 8.36E 05 7.85E 05 7.32E 05 6.83E 05 6.39E 05 5.99E 05 24.8 1.49E 04 1.39E 04 1.30E 04 1.22E 04 1.14E 04 1.08E 04 9.53E 05 8.99E 05 8.47E 05 7.95E 05 7.43E 05 6.94E 05 6.50E 05 6.11E 05 Temperature ( oC) Appendix 6 vii CO2 Viscosity ( Pa s) as a Function of Temperature ( oC) and Pressure ( MPa) ( calculated values from regression equations) Pressure ( MPa)  1.1 4.4 10.0 15.6 21.1 26.7 32.2 37.8 43.3 48.9 54.4 60.0 65.6 71.1 7.6 1.17E 04 1.07E 04 9.76E 05 8.86E 05 7.94E 05 6.92E 05 3.05E 05 2.13E 05 2.08E 05 2.12E 05 2.10E 05 2.07E 05 2.06E 05 2.05E 05 8.3 1.18E 04 1.08E 04 9.93E 05 9.04E 05 8.16E 05 7.23E 05 3.45E 05 2.80E 05 2.52E 05 2.34E 05 2.24E 05 2.17E 05 2.13E 05 2.11E 05 9.0 1.20E 04 1.10E 04 1.01E 04 9.22E 05 8.37E 05 7.50E 05 4.27E 05 3.58E 05 3.04E 05 2.66E 05 2.48E 05 2.36E 05 2.27E 05 2.22E 05 9.7 1.21E 04 1.11E 04 1.02E 04 9.39E 05 8.56E 05 7.74E 05 5.23E 05 4.35E 05 3.59E 05 3.04E 05 2.78E 05 2.60E 05 2.46E 05 2.37E 05 10.3 1.22E 04 1.13E 04 1.04E 04 9.55E 05 8.74E 05 7.95E 05 6.15E 05 5.05E 05 4.12E 05 3.44E 05 3.11E 05 2.86E 05 2.68E 05 2.54E 05 11.0 1.24E 04 1.14E 04 1.05E 04 9.71E 05 8.91E 05 8.14E 05 6.92E 05 5.65E 05 4.61E 05 3.84E 05 3.44E 05 3.14E 05 2.91E 05 2.73E 05 11.7 1.25E 04 1.16E 04 1.07E 04 9.85E 05 9.07E 05 8.32E 05 7.49E 05 6.13E 05 5.04E 05 4.22E 05 3.77E 05 3.42E 05 3.14E 05 2.92E 05 12.4 1.26E 04 1.17E 04 1.08E 04 1.00E 04 9.22E 05 8.48E 05 7.87E 05 6.49E 05 5.41E 05 4.58E 05 4.08E 05 3.69E 05 3.37E 05 3.12E 05 13.1 1.28E 04 1.18E 04 1.10E 04 1.01E 04 9.37E 05 8.64E 05 8.07E 05 6.76E 05 5.72E 05 4.92E 05 4.38E 05 3.95E 05 3.59E 05 3.31E 05 13.8 1.29E 04 1.20E 04 1.11E 04 1.03E 04 9.51E 05 8.79E 05 8.14E 05 6.95E 05 5.99E 05 5.22E 05 4.66E 05 4.19E 05 3.81E 05 3.50E 05 14.5 1.30E 04 1.21E 04 1.12E 04 1.04E 04 9.65E 05 8.94E 05 8.12E 05 7.09E 05 6.22E 05 5.49E 05 4.92E 05 4.43E 05 4.02E 05 3.69E 05 15.2 1.32E 04 1.22E 04 1.13E 04 1.05E 04 9.79E 05 9.08E 05 8.07E 05 7.20E 05 6.43E 05 5.74E 05 5.16E 05 4.65E 05 4.23E 05 3.88E 05 15.9 1.33E 04 1.23E 04 1.15E 04 1.07E 04 9.92E 05 9.22E 05 8.02E 05 7.30E 05 6.61E 05 5.97E 05 5.38E 05 4.86E 05 4.43E 05 4.07E 05 16.5 1.34E 04 1.25E 04 1.16E 04 1.08E 04 1.00E 04 9.35E 05 8.02E 05 7.41E 05 6.79E 05 6.19E 05 5.60E 05 5.07E 05 4.62E 05 4.25E 05 17.2 1.35E 04 1.26E 04 1.17E 04 1.09E 04 1.02E 04 9.48E 05 8.08E 05 7.54E 05 6.96E 05 6.39E 05 5.80E 05 5.27E 05 4.82E 05 4.44E 05 17.9 1.37E 04 1.27E 04 1.18E 04 1.10E 04 1.03E 04 9.61E 05 8.21E 05 7.69E 05 7.13E 05 6.57E 05 5.99E 05 5.46E 05 5.01E 05 4.62E 05 18.6 1.38E 04 1.28E 04 1.20E 04 1.12E 04 1.04E 04 9.73E 05 8.38E 05 7.86E 05 7.30E 05 6.75E 05 6.18E 05 5.65E 05 5.19E 05 4.80E 05 19.3 1.39E 04 1.30E 04 1.21E 04 1.13E 04 1.05E 04 9.85E 05 8.59E 05 8.03E 05 7.47E 05 6.92E 05 6.35E 05 5.83E 05 5.37E 05 4.97E 05 20.0 1.40E 04 1.31E 04 1.22E 04 1.14E 04 1.07E 04 9.97E 05 8.79E 05 8.20E 05 7.63E 05 7.07E 05 6.52E 05 6.00E 05 5.55E 05 5.14E 05 20.7 1.41E 04 1.32E 04 1.23E 04 1.15E 04 1.08E 04 1.01E 04 8.96E 05 8.35E 05 7.77E 05 7.22E 05 6.67E 05 6.16E 05 5.71E 05 5.30E 05 21.4 1.43E 04 1.33E 04 1.24E 04 1.16E 04 1.09E 04 1.02E 04 9.07E 05 8.47E 05 7.90E 05 7.36E 05 6.82E 05 6.31E 05 5.87E 05 5.46E 05 22.1 1.44E 04 1.34E 04 1.26E 04 1.17E 04 1.10E 04 1.03E 04 9.12E 05 8.57E 05 8.02E 05 7.48E 05 6.95E 05 6.45E 05 6.01E 05 5.60E 05 22.8 1.45E 04 1.35E 04 1.27E 04 1.19E 04 1.11E 04 1.04E 04 9.11E 05 8.63E 05 8.11E 05 7.60E 05 7.08E 05 6.58E 05 6.14E 05 5.74E 05 23.4 1.46E 04 1.37E 04 1.28E 04 1.20E 04 1.12E 04 1.05E 04 9.11E 05 8.70E 05 8.21E 05 7.71E 05 7.19E 05 6.70E 05 6.27E 05 5.86E 05 24.1 1.47E 04 1.38E 04 1.29E 04 1.21E 04 1.13E 04 1.06E 04 9.22E 05 8.82E 05 8.33E 05 7.83E 05 7.31E 05 6.81E 05 6.39E 05 5.99E 05 24.8 1.49E 04 1.39E 04 1.30E 04 1.22E 04 1.14E 04 1.08E 04 9.63E 05 9.07E 05 8.51E 05 7.97E 05 7.44E 05 6.94E 05 6.51E 05 6.11E 05 Temperature ( oC) Appendix 7 viii Percent difference (%) between calculated and actual CO2 viscosity values ( 100% * [ ( calculated  actual ) / actual ] ) Pressure ( MPa)  1.1 4.4 10.0 15.6 21.1 26.7 32.2 37.8 43.3 48.9 54.4 60.0 65.6 71.1 7.6 0.00 0.00 0.00 0.00 0.01 0.05  10.75  5.75  2.75  1.08  0.33 0.09 0.38 0.47 8.3 0.00 0.00 0.00 0.00  0.01  0.09 18.05 4.83 1.82 0.53  0.33  0.83  1.00  0.95 9.0 0.00 0.00 0.00 0.00  0.01  0.03 9.81 6.85 4.03 1.69 0.98 0.50 0.19  0.07 9.7 0.00 0.00 0.00  0.01 0.00 0.02  2.16 0.05 0.49 0.64 0.78 0.82 0.79 0.59 10.3 0.00 0.00 0.00 0.00 0.01 0.04  8.71  5.27  2.94  0.91  0.17 0.17 0.47 0.52 11.0 0.00 0.00 0.00 0.00 0.00 0.03  4.06  2.51  1.58  0.85  0.74  0.72  0.55  0.36 11.7 0.00 0.00 0.00 0.00 0.01 0.02  0.20  0.41  0.57  0.70  0.70  0.70  0.52  0.35 12.4 0.00 0.00 0.00 0.00 0.00  0.01 2.88 1.26 0.24  0.49  0.45  0.35  0.14  0.03 13.1 0.00 0.00 0.00 0.00 0.00  0.02 4.04 1.93 0.71  0.10 0.04 0.22 0.42 0.40 13.8 0.00 0.00 0.00 0.00 0.00  0.03 2.33 1.41 1.14 0.96 0.67 0.37 0.18  0.04 14.5 0.00 0.00 0.00 0.00 0.00  0.02 0.67 0.72 1.05 1.22 0.81 0.29  0.03  0.30 15.2 0.00 0.00 0.00 0.00 0.00  0.01 0.22 0.27 0.36 0.39 0.29 0.09 0.05  0.06 15.9 0.00 0.00 0.00 0.00 0.00 0.00  0.81  0.35  0.18  0.06  0.02  0.08 0.03 0.00 16.5 0.00 0.00 0.00 0.00 0.00 0.01  1.56  0.80  0.57  0.40  0.24  0.19 0.02 0.07 17.2 0.00 0.00 0.00 0.00 0.01 0.02  1.79  0.96  0.73  0.57  0.36  0.24 0.02 0.10 17.9 0.00 0.00 0.00 0.00 0.01 0.01  1.48  0.81  0.67  0.57  0.35  0.24 0.01 0.09 18.6 0.00 0.00 0.00 0.00 0.00 0.01  0.77  0.42  0.39  0.36  0.23  0.20 0.03 0.06 19.3 0.00 0.00 0.00 0.00 0.00 0.00 0.03 0.10 0.05 0.01 0.01  0.11 0.00  0.03 20.0 0.00 0.00 0.00 0.00 0.00  0.01 0.58 0.58 0.59 0.57 0.35  0.01  0.06  0.21 20.7 0.00 0.00 0.00 0.00 0.00  0.02 1.31 0.85 0.60 0.42 0.29 0.04 0.05  0.08 21.4 0.00 0.00 0.00 0.00 0.00  0.02 1.35 0.80 0.47 0.24 0.19 0.02 0.13 0.02 22.1 0.00 0.00 0.00 0.00 0.00  0.01 0.60 0.43 0.19 0.04 0.07  0.04 0.12 0.06 22.8 0.00 0.00 0.00 0.00 0.00 0.00  0.72  0.16  0.15  0.15  0.06  0.14 0.08 0.04 23.4 0.00 0.00 0.00 0.00 0.00 0.01  1.99  0.71  0.41  0.25  0.15  0.23 0.00  0.02 24.1 0.00 0.00 0.00 0.00 0.01 0.01  2.03  0.65  0.33  0.19  0.10  0.25  0.03  0.06 24.8 0.00 0.00 0.00 0.00  0.01  0.02 1.05 0.85 0.50 0.26 0.20  0.03 0.12  0.01 Temperature ( oC) Appendix 8 SECTION III: Comparing Techno Economic Models for Pipeline Transport of Carbon Dioxide David L. McCollum dlmccollum@ ucdavis. edu Institute of Transportation Studies University of California One Shields Avenue Davis, CA 95616 ABSTRACT Due to a heightened interest in technologies to mitigate global climate change, research in the field of carbon capture and storage ( CCS) has increased in recent years, with the goal of answering the many questions that still remain in this uncertain field. At the top of the list of key issues are CCS costs: costs of carbon dioxide ( CO2) capture, compression, transport, storage, and so on. This paper focuses on costs of CO2 pipeline transport. Several recent technoeconomic models for estimating pipeline sizes and costs are compared on an “ apples to apples” basis by applying the same set of input assumptions across all models. We find that there is a large degree of variability between the output of the different models, particularly among the cost estimates, that stems from the differing approaches that each model employs. By averaging the cost estimates of the models over a wide range of CO2 mass flow rates and pipeline lengths, we have created a new CO2 pipeline capital cost model that is a function only of CO2 mass flow rate and pipeline length. This removes the need to calculate the pipeline diameter in advance of calculating costs. We feel that this equation is a reliable estimator of mid range costs, given that it has been derived from a number of recent, reliable studies on CCS. Keywords: carbon dioxide, CO2, CO2, CCS, pipeline, transport, sequestration, techno economic, cost model, climate change, greenhouse gas 1 EXECUTIVE SUMMARY Due to a heightened interest in technologies to mitigate global climate change, research in the field of carbon capture and storage ( CCS) has increased in recent years, with the goal of answering the many questions that still remain in this uncertain field. At the top of the list of key questions are CCS costs: costs of carbon dioxide ( CO2) capture, costs of transport, costs of storage, and so on. Although the practice of transporting and storing CO2 underground has been around for a few decades, as it is used in the oil and gas industry for enhanced oil recovery ( EOR), predicting the economics is still uncertain. In light of this, several studies have developed CCS models to try and predict costs, particularly for transport and storage. These models, however, differ in many ways, namely in their cost and flow equations, assumptions for operating conditions, and the reference years that their costs are expressed in. Thus, the models’ output— e. g., pipeline diameter, capital cost, O& M costs, levelized CO2 costs, etc.— comes out differently, making it difficult to compare the models’ predicted costs on an “ apples to apples” basis. By replicating the models and applying some of the same key assumptions across all models, comparisons can be made, similarities/ differences can be noted, and new models can be generated that are essentially a combination of all models. We have carried out this procedure for a few of the more recent CO2 transport models. The scope of this study was limited to onshore pipelines, since they are likely to be the most cost effective and realistic means for transporting CO2 in the future, at least in the United States. The transport models that were compared came from the following studies: Ogden, MIT, Ecofys, IEA GHG PH4/ 6, IEA GHG 2005/ 2, IEA GHG 2005/ 3, and Parker. Each of these studies was carried out within the last four years; and except for the models of Parker, which use natural gas pipeline costs to predict the costs of hydrogen pipelines, all of the models are geared specifically towards CO2 pipelines. In this paper, the basic concepts, equations, and assumptions of the above models are discussed; though, the reader is encouraged to consult the original reports for a more thorough description. The key similarities and differences between the models are then highlighted. And ultimately, a set of common basis assumptions is decided upon, with new models being created that are essentially a combination of all seven of the original models. The wide variability in the costs that each of the models estimates is easily seen in the following graph: 2 Model Comparison: Pipeline Capital Cost vs. CO2 Mass Flow Rate ( Pipeline Length = 100 km) 0 200,000 400,000 600,000 800,000 1,000,000 1,200,000 0 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 20,000 CO2 Mass Flow Rate ( tonnes/ day) Pipeline Capital Cost ($/ km) Ogden MIT Ecofys IEA GHG PH4/ 6 IEA GHG 2005/ 3 IEA GHG 2005/ 2 Parker Average By averaging the estimated capital costs of all models over a range of flow rates and pipeline lengths, we have created the following equation to model pipeline capital cost: Pipeline Capital Cost [$/ km] = ( 9970 * m0.35) * L0.13 ( where m = CO2 mass flow rate [ tonnes/ day], and L = pipeline length [ km]) Costs are given in year 2005 US dollars. This equation provides a method of estimating the pipeline capital cost per unit length based on two quantities that are typically known— CO2 mass flow rate and pipeline length. By approaching the capital cost in this way, one can avoid the calculation of pipeline diameter in advance, which can be advantageous. The above equation is a reliable method for calculating pipeline capital cost since it is essentially derived from seven other pipeline models, all of which are recent and reliable. The upper and lower bounds for the pipeline capital cost are found to be given by the following equations: Pipeline Capital Cost ( Low) [$/ km] = ( 8500 * m0.35) * L0.06 Pipeline Capital Cost ( High) [$/ km] = ( 4100 * m0.50) * L0.13 ( where m = CO2 mass flow rate [ tonnes/ day], and L = pipeline length [ km]) The estimates for average pipeline capital cost, along with the upper and lower bounds are shown together in the following graph. 3 Average Pipeline Capital Cost along with High and Low Values from Other Studies ( Pipeline Length = 100 km) 0 200,000 400,000 600,000 800,000 1,000,000 1,200,000 0 5,000 10,000 15,000 20,000 CO2 Mass Flow Rate ( tonnes/ day) Pipeline Capital Cost ($/ km) High Average Low One can feel comfortable in knowing that while the uncertainty of CO2 pipeline capital cost may be great, it will very likely be within these upper and lower bounds, and probably close to the average. 4 INTRODUCTION Due to a heightened interest in technologies to mitigate global climate change, research in the field of carbon capture and storage ( CCS) has increased in recent years, with the goal of answering the many questions that still remain in this uncertain field. At the top of the list of key questions are CCS costs: costs of carbon dioxide ( CO2) capture, costs of transport, costs of storage, and so on. Although the practice of transporting and storing CO2 underground has been around for a few decades, as it is used in the oil and gas industry for enhanced oil recovery ( EOR), predicting the economics is still uncertain. In light of this, several studies have developed CCS models to try and predict costs, particularly for transport and storage. These models, however, differ in many ways, namely in their cost and flow equations, assumptions for operating conditions, and the reference years that their costs are expressed in. Thus, the models’ output— e. g., pipeline diameter, capital cost, O& M costs, levelized CO2 costs, etc.— comes out differently, making it difficult to compare the models’ predicted costs on an “ apples to apples” basis. By replicating the models and applying some of the same key assumptions across all models, comparisons can be made, similarities/ differences can be noted, and new models can be generated that are essentially a combination of all models. We have carried out this procedure for a few of the more recent CO2 transport models. The scope of this study was limited to onshore pipelines, since they are likely to be the most cost effective and realistic means for transporting CO2 in the future, at least in the United States. The transport models that were compared came from the following studies: Ogden [ 1], MIT [ 2], Ecofys [ 3], IEA GHG PH4/ 6 [ 4], IEA GHG 2005/ 2 [ 5], IEA GHG 2005/ 3 [ 6], and Parker [ 7]. Each of these studies was carried out within the last four years; and except for the models of Parker, which use natural gas pipeline costs to predict the costs of hydrogen pipelines, all of the models are geared specifically towards CO2 pipelines. In this paper, the basic concepts, equations, and assumptions of the above models are discussed; though, the reader is encouraged to consult the original reports for a more thorough description. The key similarities and differences between the models are then highlighted. And ultimately, a set of common basis assumptions is decided upon, with new models being created that are essentially a combination of all seven of the original models. 5 DESCRIPTION OF MODELS The Ogden Models The CO2 transport models used in Ogden’s report ( or rather, those described in detail in Appendix C of the full report) were created to model a hydrogen production and distribution infrastructure that makes use of CCS. Although the publication date of the report is 2004 ( i. e., later than some of the other models that will also be described here), work on the report began much earlier in 2002 and for this reason did not build upon models that have come out more recently. For starters, Ogden’s models use a complex equation for calculating the volumetric flow rate ( Q) of CO2, which was adapted from Farris [ 8]: Q = C1 √( 1/ f) [( Pinpipe 2 – Poutpipe 2 – C2{ GΔhP2 avg / Zavg Tavg}) / ( G Tavg Zavg L)] 0.5 D2.5 E ( where Q = CO2 flow rate [ Nm3/ s], C1 = 18.921, f = friction factor, Pinpipe = pipeline inlet pressure [ kPa], Poutpipe = pipeline outlet pressure [ kPa], C2 = 0.06836, G = CO2 specific gravity = 1.519, Δh = change in elevation [ m], Pavg = average pipeline pressure, Zavg = CO2 compressibility at Pavg, Tavg = average temperature [ K], L = pipeline length [ km], D = pipeline diameter [ m], E = pipeline efficiency) Oftentimes, however, one already knows the CO2 mass flow rate ( e. g., in tonnes/ day), which can be converted to volumetric flow rate, thus enabling the back calculation of pipeline diameter. When using the above equation to solve for diameter, we assumed that some of the variables had the following constant values: change in elevation, Δh= 0; CO2 compressibility, Zavg= 0.25; pipeline efficiency, E= 1.0. The calculated diameter seems to be sensitive to compressibility and, especially, efficiency. We have done a simple sensitivity analysis for both at a given set of operating conditions. Ogden suggests that compressibility will be in the range of 0.17 0.30 for pure CO2 at average pipeline pressures of 8.8 12.0 MPa and temperatures from less than 20 oC up to 40 oC. By our calculations, at a representative CO2 mass flow rate of 10,000 tonnes/ day, inlet and outlet pressures of 15.2 and 10.3 MPa, respectively, and a temperature of 25 oC, a 76% increase in compressibility ( from 0.17 to 0.30) will lead to a calculated pipeline diameter increase of only 11% ( from 10.6 to 11.8 inches). Thus, when replicating Ogden’s models, we assume that Zavg= 0.25, which according to Ogden is a reasonable estimate at the temperature and average pipeline pressure that we will generally consider— 25 oC and 12.75 MPa, respectively. Similarly, we calculate that, at the same operating conditions mentioned above, a decrease in pipeline efficiency of 25 percentage points ( from 100% to 75%) will lead to a calculated pipeline diameter increase of 11% ( from 11.4 to 12.7 inches). The dependence of calculated diameter on pipeline efficiency gets much stronger, however, as efficiency gets lower and lower; for example, the next 25% percentage point decrease in pipeline efficiency ( from 75% to 50%) will lead to a calculated pipeline diameter increase of 17% ( from 12.7 to 14.9 inches). Ogden does not suggest any values for pipeline efficiency in her report, so we simply assume E= 1.0 when replicating her models; this assumption may not reflect real world pipelines but seems reasonable here, since none of the other models under study in this report consider pipeline efficiency. Thus, we are essentially canceling out the effect that pipeline efficiency may have so that the pipeline diameter calculated by Ogden’s models can be more directly compared to that calculated from other models. 6 Notice also that Ogden calculates the friction factor ( f) by the Nikuradse equation; this factor is similar in magnitude to the Fanning friction factor in that it is four times smaller than friction factors used in some of the other models described later in this report. Yet, even after accounting for the factor of four difference, the Nikuradse equation calculates friction factors that are consistently smaller than those assumed in the other models, which affects the size of the calculated pipeline diameter, as will be shown later. Furthermore, a word of caution that might be helpful to others when using the above mentioned flow rate equation is to multiply the length term, L, in the equation by 1000. Although not explicitly stated in the description of the equation, this causes the units to work out and helps calculate a flow rate ( or alternately, a pipeline diameter) that is on the correct order of magnitude. To estimate pipeline capital costs, the Ogden models use capital cost estimates from Skovholt’s 1993 study [ 9]. These estimates give capital costs ( in $/ m) for four different sizes of pipeline diameter ( 16, 30, 40, and 64 inches). With these four data points, an equation is generated that scales up the capital cost as the diameter gets larger. And finally, the capital cost ( in $/ m) is multiplied by the pipeline length ( L) to calculate the total capital cost. These two equations are shown below: Capital Cost ($/ m) = $ 700/ m x ( D / 16 in) 1.2 ( where D = pipeline diameter [ inches]) Total Capital Cost ($) = Capital Cost ($/ m) x L ( m) ( where L = pipeline length [ m]) Ogden prefers, however, to use capital cost equations that are functions directly of CO2 flow rate ( Q) and pipeline length ( L), rather than diameter ( D), thus making it possible to calculate the pipeline capital costs without having to solve for D directly. However, the cost equations are indirectly functions of diameter, since it has simply been parameterized away using other variables. The equation is: Capital Cost ($/ m) = $ 700/ m x ( Q / 16,000 tonnes/ day) 0.48 x ( L / 100 km) 0.24 ( where Q = CO2 mass flow rate [ tonnes/ day], and L = pipeline length [ kilometers]) Total Capital Cost ($) = Capital Cost ($/ m) x L ( m) When replicating and comparing models in this report, we use Ogden’s latter capital cost models, making them the only models ( of those that are compared) that do not use pipeline diameter to calculate costs. Ogden uses the following equation to calculate the levelized cost of CO2 transport: Levelized Cost ($/ tonne CO2) = ( CRF + O& M) x Total Capital Cost / [ Q ( Nm3/ s) x 3.17 x 107 sec/ year x ( 1.965 kg CO2/ Nm3) / ( 1000 kg/ tonne)] ( where CRF = capital recovery factor = 0.15, and O& M = O& M cost factor = 0.04) Finally, note that all of Ogden’s costs are expressed in year 2001 US$. 7 The MIT Models The Massachusetts Institute of Technology’s Laboratory for Energy and the Environment published a study on the economics of CO2 storage in 2003. Chapter 2 of their report outlines a methodology for calculating CO2 pipeline diameter and costs; this process is iterative. First, one has to guess a value for the pipeline diameter ( D). Second, the Reynold’s number ( Re) is calculated by the following equation: Re = 4 m / ( π μ D) ( where m = CO2 mass flow rate, D = pipeline diameter, and μ = CO2 viscosity) With the calculated Reynold’s number and the MIT study’s assumed pipeline roughness factor ( ε) of 0.00015 feet, the Fanning friction factor ( f) is found by using a Moody chart. This method, however, would require a manual look up for each iteration, so MIT uses an empirical relation based on the Moody chart [ 10]. 1.11 2 10 3.7 12( / ) Re 4 1.8 log 6.91 1 ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎪⎭ ⎪⎬ ⎫ ⎪⎩ ⎪⎨ ⎧ ⎟⎠ ⎞ ⎜⎝ − + ⎛ = D f ε ( f = friction factor, Re = Reynold’s number, ε = roughness factor [ ft], and D = pipeline diameter [ in]) Next, the diameter is calculated by the following equation: D5 = ( 32 f m2)/ ( π2 ρ ( ΔP/ ΔL)) ( where ΔP = inlet pressure – outlet pressure, and ΔL = pipeline length) The diameter calculated by this equation is then compared to the previously guessed value of diameter. If the calculated diameter is much different from the guessed value, then the calculated value is used to re calculate a new Reynold’s number, friction factor, and diameter. This process is repeated until the calculated diameter is the same as the one used at the start of the iteration. It should also be noted that MIT assumes a CO2 density and viscosity of 884 kg/ m3 and 6.06 x 10 5 N s/ m2, respectively, for their pipeline transport models. To calculate CO2 pipeline costs, the MIT study uses historical cost data for natural gas pipeline construction, as reported in the Oil & Gas Journal. From this data, they conclude that, on average, construction costs for CO2 pipelines would be $ 20,989/ in/ km. Furthermore, based on estimates by Fox [ 11], they suggest that O& M costs, other than pumping, would be $ 3,100/ km/ year, independent of pipeline diameter. Thus, the total annual cost and levelized cost are calculated by the following equations: Total Annual Cost ($/ yr) = {($ 20,989/ in/ km) x D x L x CRF} + {($ 3,100/ km/ yr) x L} ( where D = pipeline diameter [ in], L = pipeline length [ km], and CRF = Capital Recovery Factor = 0.15/ yr) Levelized Cost ($/ tonne CO2) = Total Annual Cost ($/ yr) / { m x CF x 365 } ( where m = CO2 mass flow rate [ tonnes/ day], CF = Plant Capacity Factor = 0.80, and 365 = days per year) 8 Finally, since the MIT study does not state the reference year that they express costs in, we assume that they use year 1998 dollars, owing to the fact that 1998 is the most recent year for which they obtained natural gas pipeline cost data from the Oil & Gas Journal. 9 The Ecofys Models The Ecofys models for CO2 transport are part of a larger report to the European Commision on the potential of CCS as a cost effective strategy to meet Kyoto Protocol targets for emissions reduction in the European Union. The technical and cost aspects of CO2 transport are given in Appendix 3 of the report. First, the equation for back calculating the pipeline diameter is: ΔP = λ * ( L/ D) * ( 1/ 2) * ρ * v2 ( where ΔP = pressure drop [ Pa], λ = friction factor, L = pipeline length [ m], D = pipeline diameter [ m], ρ = CO2 density [ kg/ m3], v = average flow velocity [ m/ s]) In the above flow equation, the velocity term, v, is a function of the mass flow rate and the crosssectional area ( i. e., diameter) of the pipeline. Thus, the equation can be rearranged to form the following equation: D5 = ( 8 λ m2)/ ( π2 ρ ( ΔP/ L)) ( where m = CO2 mass flow rate) Note how similar this equation is to the analogous diameter equation that MIT uses. There are only two main differences: ( 1) The lead constant in the Ecofys equation is 8 versus 32 in the MIT equation— four times smaller because ( 2) The friction factor in the Ecofys equation ( λ) is four times larger than the Fanning friction factor ( f) in the MIT equation. In other words, the Ecofys and MIT equations for calculating pipeline diameter are essentially the same. The only other difference is that the Ecofys study assumes a constant friction factor, whereas MIT uses an equation to calculate the friction factor, as it is a function of Reynold’s number. Ecofys suggests that their friction factor would be less than 1.5 x 10 2 for perfectly smooth pipeline walls and 2.0 x 10 2 for new untreated steel. ( Actually, in the report Ecofys states that the friction factor for new untreated steel would be 2.0 x 102, i. e. the negative sign in the exponent is missing. Though, we believe this to be a typographical error, since using a friction factor of this magnitude would lead to an unusually large pipeline diameter.) The equation used to calculate total pipeline capital cost is given by: Total Capital Cost (€) = ( 1100 €/ m2) * FT * D * L ( where FT = correction factor for terrain = 1 for most common terrain, D = pipeline diameter [ m], L = pipeline length [ m]) The total capital cost is annualized with a 10% discount rate over a 25 year operational lifetime by the following equation: n n i i i Annual Capital Cost euros yr Total Capital Cost euros ( 1 ) ( 1 ) 1 ( / ) ( ) + + − = ( where n = operational lifetime [ years], and i = discount rate) The annual O& M costs are calculated as 2.1% of the total capital cost. And the total annual cost is found by summing the annual capital and O& M costs. 1 0 Annual O& M Costs (€/ yr) = ( O& M factor) * Total Capital Cost ( where O& M factor = 2.1%) Total Annual Cost (€/ yr) = Annual Capital Cost + Annual O& M Costs The Ecofys study does not discuss the method used for calculating levelized cost of CO2 transport, but one can assume that it is similar to that used in other studies, for example, the MIT study’s equation, which is shown below. Levelized Cost (€/ tonne CO2) = Total Annual Cost ($/ yr) / { m * CF * 365 } ( where m = CO2 mass flow rate [ tonnes/ day], CF = Plant Capacity Factor, and 365 = days per year) Finally, since the Ecofys study does not state the reference year that they express costs in, we assume that they use year 2003 euros since that is the year that their report was published. 1 1 The IEA GHG PH4/ 6 Models In 2002, Woodhill Engineering Consultants of the United Kingdom studied the transmission of CO2 and energy for the IEA Greenhouse Gas R& D Programme. They wrote a report on the subject, as well as created a spreadsheet based computer model for estimating the costs and performance of CO2 transport. To calculate CO2 pipeline diameter, the IEA GHG PH4/ 6 study uses the following equation [ 12]: 5 2 2.252 D P f L Q ρ Δ = ( where ΔP = pressure drop [ bar], f = friction factor, L = pipeline length [ km], ρ = CO2 density [ kg/ m3], Q = CO2 flow rate [ liter/ min], and D = pipeline internal diameter [ mm]) A friction factor ( f) of 0.015 is assumed in the model. Further, the report states that a friction factor of this value is “ relatively conservative in that it is likely to slightly oversize a liquid line rather than undersize it” [ 4, p. 3.26]. ( Note that this friction factor is four times larger than the Fanning friction factor used in other studies.) With the internal diameter of the pipeline, the spreadsheet model uses a look up table to find the closest nominal pipe size. We, however, did not have access to the look up table, so when replicating the models of the IEA GHG PH4/ 6 study, we simply use the internal pipeline diameter throughout ( e. g., in the pipeline cost calculations). Woodhill Engineering developed several pipeline cost equations for the IEA GHG PH4/ 6 study based on in house estimates. For onshore pipelines, they give three equations, one for each of three different ANSI piping classes: 600# ( P < 90 bar), 900# ( P < 140 bar), and 1500# ( P < 225 bar). At the higher pressures likely required for CO2 transport, the ANSI Class 1500# pipe would be used. The capital cost equation for ANSI Class 1500# pipe is given as: Pipeline Capital Cost ($) = FL * FT * 106 * [ ( 0.057 * L + 1.8663) + ( 0.00129 * L) * D + ( 0.000486 * L + 0.000007) * D2 ] ( where FL = location factor, FT = terrain factor, L = pipeline length [ km], and D = pipeline diameter [ in]) Location factors ( FL) for a few world regions are reproduced here: USA/ Canada= 1.0, Europe= 1.0, UK= 1.2, Japan= 1.0, Australia= 1.0. ( A full list of location factors for all world regions can be found in the original IEA GHG PH4/ 6 report.) Terrain factors ( FT) are as follows: cultivated land= 1.10, grassland= 1.00, wooded= 1.05, jungle= 1.10, stony desert= 1.10, < 20% mountainous= 1.30, > 50% mountainous= 1.50. Booster stations for raising the CO2 pressure during pipeline transport are also considered in the IEA GHG PH4/ 6 models. In fact, the user of the spreadsheet model has the choice of whether or not to include booster stations. If booster stations are included, their capital costs can be calculated by the following equation: Booster Station Capital Cost ($) = NB * FL * ( 7.82 * Power + 0.46) * $ 1,000,000 ( where NB = number of booster stations, FL = location factor, and Power = pump power [ MW]) ‘ Power’ is calculated by the following equation given in [ 13]: Power ( MW) = ( Q * ΔP) / ( 36,000 * η) 1 2 ( where Q = CO2 flow rate [ m3/ hr], ΔP = pressure increase through booster [ bar], η = pump efficiency = 0.75) The total capital cost is given by: Total Capital Cost ($) = Pipeline Capital Cost + Booster Station Capital Cost Equations for O& M costs were also developed for the IEA GHG PH4/ 6 study. The O& M cost equation for liquid CO2 onshore pipelines is given by: Annual Pipeline O& M Costs ($/ yr) = 120,000 + 0.61( 23,213 * D + 899 * L – 259,269) + 0.7( 39,305 * D + 1694 * L – 351,355) + 24,000 ( where D = pipeline diameter [ in], and L = pipeline length [ km]) Similarly, booster station O& M costs ( both fixed and variable) are also calculated. For fixed O& M costs, a look up table is used. This table provides fixed O& M costs as a function of pump power ( from 0 to 2 MW). To avoid the look up table, we have created a second order regression equation that fits the fixed O& M cost vs. pump power with an R2 value of 0.93. ( Be advised that this equation should only be used in the range of 0 2 MW, since the second order equation is parabolic and will eventually begin predicting increasingly lower costs as the pump power increases.) The equation for booster station fixed O& M costs is given below: Annual Booster Station Fixed O& M Costs ($/ yr) = NB * [ 179,864 * Power2 + 671,665 * Power + 159,292] ( where NB = number of booster stations, and Power = pump power [ MW]) The booster station variable O& M costs are calculated by the following equation: Booster Station Variable O& M Costs ($/ yr) = NB * COE * Power * CF * ( 1000 kW/ MW) * ( 24 hr/ day) * ( 365 days/ yr) ( where NB = number of booster stations, COE = cost of electricity [$/ kWh], Power = pump power [ MW], CF = plant capacity factor) The total annual O& M costs are then: Total Annual O& M Costs ($/ yr) = Annual Pipeline O& M Costs + Annual Booster Station Fixed O& M Costs + Annual Booster Station Variable O& M Costs And finally, the total annual cost and levelized cost are calculated by the following equations: Total Annual Cost ($/ yr) = ( Total Capital Cost * CRF) + Total Annual O& M Costs ( where CRF = Capital Recovery Factor) Levelized Cost ($/ tonne CO2) = Total Annual Cost ($/ yr) / { m * CF * 365 } ( where m = CO2 mass flow rate [ tonnes/ day], CF = plant capacity factor, and 365 = days per year) The IEA GHG PH4/ 6 study reports all cost figures in year 2000 US dollars. 1 3 The IEA GHG 2005/ 2 Models In 2005, the IEA Greenhouse Gas R& D Programme released two additional, related reports ( one for Europe and another for North America) in which the costs and potential of CO2 transport and storage for each of the respective regions were studied. The IEA GHG 2005/ 2 study focused on Europe. ( The study on North America will be discussed later in this report.) Work was carried out by the The Netherlands Geological Survey ( TNO NITG), the geological surveys of Britain ( BGS) and Denmark/ Greenland ( GEUS), and Ecofys. The equation used for calculating pipeline diameter is: D = [ m / ( 0.25 π ρ v ) ] 0.5 / 0.0254 ( where D = pipeline diameter [ in], m = CO2 mass flow rate [ kg/ s], ρ = CO2 density [ kg/ m3], v = flow velocity [ m/ s]) In this equation, the study assumes that the flow velocity ( v) is a constant 2.0 m/ s. The equation used for calculating onshore pipeline capital costs in the IEA GHG 2005/ 2 study is taken almost directly from the IEA GHG PH4/ 6 study for ANSI Class 1500# pipe— the only differences being the following: ( 1) costs are expressed in euros (€) in the IEA GHG 2005/ 2 study; ( 2) a change of sign on the final constant ( from + 0.000007 to  0.000007), which makes virtually no difference in calculated cost; and ( 3) an omission of the location factor term, FL, presumably because in the IEA GHG PH4/ 6 study FL = 1.0 for Europe, the only region considered in the IEA GHG 2005/ 2 study. The equation is shown below: Pipeline Capital Cost (€) = FT * 106 * [ ( 0.057 * L + 1.8663) + ( 0.00129 * L) * D + ( 0.000486 * L  0.000007) * D2 ] ( where FT = terrain factor, L = pipeline length [ km], and D = pipeline diameter [ in]) As with the IEA GHG PH4/ 6 study, terrain factors ( FT) are as follows: cultivated land= 1.10, grassland= 1.00, wooded= 1.05, jungle= 1.10, stony desert= 1.10, < 20% mountainous= 1.30, > 50% mountainous= 1.50. But for the IEA GHG 2005/ 2 study, an average value of 1.20 is taken for FT. For booster stations, capital costs are assumed to be for the most part independent of CO2 mass flow rate, and are instead expressed on a per kilometer basis. The capital cost equation for onshore booster stations is: Booster Station Capital Cost (€) = ( 35,000 €/ km) * L ( where L = pipeline length [ km]) Hence, the total capital cost is given by: Total Capital Cost (€) = Pipeline Capital Cost + Booster Station Capital Cost It appears that in the IEA GHG 2005/ 2 report the capital cost of booster stations is always included in the total capital cost, regardless of the presence or absence of a booster station. A short pipeline ( e. g., 100 km), however, may not require booster stations. Therefore, when replicating the IEA GHG 2005/ 2 models, we assume that booster stations are unnecessary if the pipeline length is less than 200 km, which means that the booster station capital cost is not included in the total capital cost. This assumption for a minimum distance of 200 km is consistent with IEA GHG 2005/ 2 study’s own assumption of 200 km for the average distance between two booster stations, which they use for determination of booster station power use. 1 4 The equation for booster station pumping power use is: Pp = [( 1/ ρ) * ( ΔP/ ηp)] / DistBS ( where Pp = pump power use [ J/ km/ kg CO2], ρ = CO2 density [ kg/ m3], ΔP = pressure increase [ Pa], ηp = pump efficiency, and DistBS = average distance between two booster stations [ km]) In the IEA GHG 2005/ 2 study, the following values are assumed for the above equation: ρ = 800 kg/ m3, ΔP = 4 x 106 Pa, ηp = 0.75, and DistBS = 200 km. The total capital cost is annualized with a 10% discount rate over a 20 year operational lifetime by the following equation: n n i i i Annual Capital Cost euros yr Total Capital Cost euros ( 1 ) ( 1 ) 1 ( / ) ( ) + + − = ( where n = operational lifetime [ years], and i = discount rate) The annual O& M costs of the pipeline are calculated as 3% of the pipeline capital cost. And the annual O& M costs of the booster station are calculated as 5% of the booster station capital cost. Annual Pipeline O& M Costs (€/ yr) = ( Pipeline O& M factor) * Pipeline Capital Cost ( where Pipeline O& M factor = 3%) Annual Booster Station O& M Costs (€/ yr) = ( Booster Station O& M factor) * Booster Station Capital Cost ( where Booster Station O& M factor = 5%) The total annual cost is found by summing the annual capital and O& M costs. Total Annual Cost (€/ yr) = Annual Capital Cost + Annual Pipeline O& M Costs + Annual Booster Station O& M Costs Finally the levelized cost of CO2 transport is calculated as a combination of the total annual costs and the booster station power required for pumping. Levelized Cost (€/ tonne CO2) = 1000 * { [ Total Annual Cost / ( m * ( 31,536,000) * CF)] + [ COE * Pp * L / ( 3.6 * 106)] } ( where 1000 = kg/ tonne, m = CO2 mass flow rate [ kg/ s], 31,536,000 = seconds per year, CF = plant capacity factor, COE = cost of electricity [€/ kWh], Pp = pump power use [ J/ km/ kg CO2], L = pipeline length [ km], and 3.6 x 106 = J/ kWh) An electricity cost of 0.04 €/ kWh is assumed in the original study. Finally, the IEA GHG 2005/ 2 study reports all costs in year 2000 euros. 1 5 The IEA GHG 2005/ 3 Models As mentioned previously, the IEA GHG 2005/ 3 study was published in 2005 and focuses on the costs and potential of CO2 transport and storage in North America ( onshore USA and Canada). Yet, although the goals of this study were the same as those of the European study ( IEA GHG 2005/ 2), some of the approaches, assumptions, models, and, thus, results differ in marked ways. Work on the North American study was carried out by Battelle and the Alberta Energy and Utilities Board. To calculate the pipeline diameter, the IEA GHG 2005/ 3 study cites a rule of thumb in [ 14] that says the CO2 volumetric flow rate should be 0.65 x 106 scf/ day/ in2 of pipe area. In different units, this rule of thumb can be expressed as ( 18.41 ρ) tonnes/ day/ in2 ( where ρ is the CO2 density under standard conditions). The pipeline diameter can then be found by: 1/ 2 18.41 4 m ⎥⎦ ⎤ ⎢⎣ ⎡ = ρ π N D ( where D = pipeline diameter [ in], m = CO2 mass flow rate [ tonnes/ day], and ρ = CO2 density [ kg/ Nm3]) To calculate CO2 pipeline costs, this study takes a similar approach to the MIT study by using historical cost data for natural gas pipeline construction, as reported in the Oil & Gas Journal. From this data, they conclude that, on average, construction costs for CO2 pipelines would be $ 41,681/ in/ mile ($ 25,889/ in/ km). ( For comparison, the MIT study concludes that the pipeline cost would $ 20,989/ in/ km, as mentioned previously.) In terms of CO2 mass flow rate, the pipeline capital cost is calculated by: Pipeline Capital Cost ($/ mile) = 39,409 * ( m / 24) 0.5 ( where m = CO2 mass flow rate [ tonnes/ day], and 24 = hours/ day) Annualizing the pipeline capital cost with a 10% discount rate over a 25 year operational lifetime yields the following equation: Annual Pipeline Capital Cost ($/ mile/ yr) = 4,335 * ( m / 24) 0.5 ( where m = CO2 mass flow rate [ tonnes/ day], and 24 = hours/ day) By assuming the annual O& M costs are 2% of the pipeline capital cost and dividing the total annual capital and O& M costs by the annual CO2 mass flow rate, the total levelized capital and O& M cost equation is given by: Total Levelized Capital and O& M Cost ($/ mile/ tonne CO2) = 5123 * ( m / 24) 0.5 / ( m * CF * 365) ( where m = CO2 mass flow rate [ tonnes/ day], 24 = hours/ day, CF = plant capacity factor, 365 = days/ year) The levelized costs of CO2 transport is given by: Levelized Cost ($/ tonne CO2) = ( L + 10) x 1.17 * ( Total Levelized Capital and O& M Cost) ( where L = pipeline length [ miles], 10 = extra pipeline distance at injection site [ miles], 1.17 = straight line distance adjustment factor) 1 6 Finally, since the IEA GHG 2005/ 3 study does not state the reference year that they express costs in, we assume that they use year 2002 dollars, owing to the fact that 2002 is the year for which they obtained natural gas pipeline cost data from the Oil & Gas Journal. 1 7 The Parker Models Like the MIT and IEA GHG 2005/ 3 studies, Parker uses natural gas pipeline costs, as reported in the Oil & Gas Journal for the years 1991 2003. Parker goes further than the other studies, however. Instead of simply reporting one cost ( e. g., $/ in/ km), he fits second order equations to the cost data and develops equations that predict the costs for each of the four different cost categories— materials, labor, miscellaneous, and right of way. The equations are functions of pipeline diameter and length. And although Parker’s pipeline cost equations were developed with the intent of predicting costs for hydrogen pipelines, they can still be used for CO2 pipelines, as is done in the MIT and IEA GHG 2005/ 3 studies. The pipeline capital cost equations of Parker are shown below: Materials Cost ($) = [ 330.5 * D2 + 687 * D + 26,960] * L + 35,000 Labor Cost ($) = [ 343 * D2 + 2,074 * D + 170,013] * L + 185,000 Miscellaneous Cost ($) = [ 8,417 * D + 7,324] * L + 95,000 Right of Way Cost ($) = [ 577 * D + 29,788] * L + 40,000 Total Capital Cost ($) = Materials Cost + Labor Cost + Miscellaneous Cost + Right of Way Cost = [ 673.5 * D2 + 11,755 * D + 234,085] * L + 355,000 ( where D = pipeline diameter [ in], and L = pipeline length [ miles]) Two of the above equations have been slightly adapted. First, consider the equation for ‘ Right of Way Cost’. On page 17 of his report, Parker states that the diameter term in ‘ 577 * D’ should be squared, ‘ 577 * D2’, however, we believe this to be a typographical error, since the regression equation on Figure 18 of the same page shows the term to be ‘ 576.78 * D’ ( i. e., without the squared exponent). Furthermore, the ‘ 577 * D’ term ( unsquared) is evidently the one that is used when adding up the four individual equations to generate the ‘ Total Capital Cost’ equation. Correcting for this error has large implications on the calculated right of way cost, potentially increasing it by a factor of ten for large diameter pipelines. Second, consider the ‘ Total Capital Cost’ equation. Our equation is nearly identical to that of Parker, aside from the final term and some small rounding differences on the first and second terms. We have added up the final terms from each of the four individual equations ( 35,000 + 185,000 + 95,000 + 40,000) to get 355,000, which we use in our equation for total capital cost, as compared to the 405,000 term that Parker uses. These latter differences are, of course, much smaller in importance than those in the equation for right of way costs. Recent discussions with Parker have confirmed the presence of the typographical errors. Our adaptation of his methodology is, therefore, justified. Parker reports all costs in year 2000 dollars. 1 8 SUMMARY AND COMPARISON OF MODELS The above descriptions of the various CO2 transport models show that each study takes a somewhat unique approach in sizing the pipeline and estimating the associated costs. Further, each of the various studies is built upon differing assumptions and input, which in turn leads to dissimilar output. The main differences in the studies are highlighted in the following table. ( Note that the Parker study is unique in that it does not deal strictly with CO2 transport and sequestration and, thus, cannot be compared to the other studies on many accounts.) Ogden MIT Ecofys IEA GHG PH4/ 6 IEA GHG 2005/ 2 IEA GHG 2005/ 3 Parker Reference Cost Year 2001 1998 2003 2000 2000 2002 2000 Capital Recovery Factor [%/ yr] 15 15  ' user specified'    Discount Rate [%]   10  10 10  Operational Lifetime [ years]   25  20 25  O& M Factor 4.0%/ year of total capital cost $ 3,100/ km/ year 2.1%/ year of total capital cost ' by equation' 3%/ yr of pipeline capital + 5%/ yr of booster capital 2.0%/ year of total capital cost  Plant Capacity Factor [%]  80 ' not reported' ' user specified' 90 ' not reported'  Electricity Cost [ / kWh]    ' user specified' 0.04 €   Booster Stations Included? No No No Yes / No ( user specified) Yes No  Pipeline Inlet Pressure [ MPa] 15 15.2 12 ' user specified'    Pipeline Outlet Pressure [ MPa] 10 10.3 8 ' user specified'    Friction Factor, f ~ 0.0021 ( by equation) ~ 0.0033 ( by Moody chart) 0.015  0.020 (= 4 x f) 0.015 (= 4 x f)  



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