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 ( Ws-total)
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 post-capture/
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 ( experimentally-measured
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 techno-economic
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 cross-sectional
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.
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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.
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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)
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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.
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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.
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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) --