1
0 1000 2000 3000 4000 -2 0 2 4 6 8 Time (sec) Confining stress (C ) (red) and Pore pressure (Pp) (blue) (MPa) 0 1 2 3 4 5 3 4 5 6 7 Pore pressure (MPa) Confining stress (MPa) Unloading path Loading path σ c P p Fig. 4. Frio sandstone multi-stage triaxial testing at confining stress 500 psi, 1000 psi and 1500 psi: (left) Axial strain and radial strains measured for a single core plug, (right) Failure line at the onset of shear dilation. A Comprehensive Case Study of the Frio CO 2 Sequestration Pilot Test for Safe and Effective Carbon Storage Including Compositional Flow and Geomechanics Hojung Jung, D. Nicolas Espinoza, Gurpreet Singh and Mary F. Wheeler 2016 Mastering the Subsurface through Technology Innovation and Collaboration: Carbon Storage and Oil and Natural Gas Technologies Review Meeting Introduction Carbon dioxide (CO 2 ) geological sequestration is a direct method to reduce carbon emission to the atmosphere by injecting CO 2 into deep geological structures. Deep geological structures include depleted oil and gas reservoirs and saline aquifers. In-depth understanding of the long-term fate of stored CO 2 requires study and analysis of the reservoir formation, the caprock formation, and the adjacent faults. This poster shows an example of a combination of carefully conceived laboratory experiments, upscaling, and numerical simulation of long-term storage of CO 2 in the Frio injection site. Objective This research investigates long term effects of CO 2 injection regarding secure and permanent CO 2 storage by conducting experiments, analyzing well logs and performing numerical reservoir simulation. The experiments include measurement of petrophysical and geomechanical properties of Frio rocks subjected to CO 2 and CO 2 -acidified water at in-situ stress condition. These measurements seek to characterize the relative magnitude of chemical couplings with geomechanics as well as typical flow properties. Finally, the measured parameters are used in a computational geomechanical screening tool that considers the risk associated with CO 2 sequestration. Acknowledgements The authors would like to thank DOE grant DE-FE0023314. The authors would like to express appreciation to Dr. Hovorka and BEG for sharing field data. The calculated porosity for each sample is reported in Table 2. References Experiments with rock specimens of different size (up to 4”) to capture the effect of reservoir heterogeneity in effective properties. Measurement of high pressure and high temperature (HPHT) mechanical properties with CO 2 -specific loadings. The schematic diagram of experiment apparatus is in Figure 3. History matching of the bottom hole pressure field data by correcting pressure boundary condition. Large CO 2 injection reservoir simulation including poro-elasticity. Hovorka, S.D., C. Doughty, S.M. Benson, and others, (2006). Measuring permanence of CO 2 storage in saline formations: The Frio experiment, Environ. Geosci., 13(2): 105121. Hovorka, S.D. (2009) Frio Brine Pilot: the First US Sequestration Test. Bouteca, M., Sarda, J.P., Vincke, O., & Longuemare, P. (1999). Thoughts about the micro-mechanical origin of the evolution of the Biot coefficient of argilites during mechanical load. Scientific days, ANDRA 1999 Summary of conferences and poster communications, (p. 258). France Kong, X., Delshad, M., & Wheeler, M. F. (2015). History Matching Heterogeneous Coreflood of CO 2 /Brine by Use of Compositional Reservoir Simulator and Geostatistical Approach. Society of Petroleum Engineers. doi:10.2118/163625-PA Future work Table 5. Simulation input for compositional fluid flow simulation Fig. 1. Schematic of a Frio formation geological strata (Hovorka, GCCC) (6) Frio C Sand Frio formation is a saline aquifer in East Texas in which two pilot tests of CO 2 sequestration were conducted (Hovorka et al., 2006). Figure 1 shows the geological strata of Frio formation, and it is composed of sands with highly bedded shale layers. Frio sandstone cores are retrieved from the pilot test site and are available from the Houston Research Center (Figure 2, BEG The University of Texas, Austin). Fig. 2. Frio sandstone cores provided by (BEG-UT Austin) Summary of accomplishments to date Elastic and inelastic mechanical properties are accurately measured by multistage triaxial loading test and Biot coefficient loading test. The results show typical behavior of unconsolidated sand, and the analyzed mechanical properties are applied to calibrate well logs analysis. Basic and advanced petrophysical properties are evaluated under the reservoir stress condition. The measured properties are carefully matched with the well logging analysis results. Finally, all the calculated petrophysical properties are implemented into a compositional reservoir simulator, and the simulation results show reasonable pressure transient. Mechanical properties Elastic moduli from triaxial testing Static elastic moduli were measured using the multistage-triaxial loading test attained by increasing deviatoric stress under three different constant confining pressures (500 psi, 1000 psi, and 1500 psi). The static elastic moduli can be calculated with the following relationships: radial radial axial ; radial axial axial E Confining pressure (psi) Deviatoric stress, (psi) E static (GPa) 500 Loading 91.5 - 276.2 0.82 0.21 Loading 365 - 529 1.10 0.25 Unloading 1025 - 809.7 7.21 0.35 1000 Loading 107.3 - 882.5 2.77 0.19 Loading 1057 - 1506 2.74 0.18 Unloading 2966 - 2364 8.47 0.42 1500 Loading 116.2 - 612.4 3.67 0.20 Loading 1068 - 1904 5.46 0.29 Unloading 4294 - 3839 8.04 0.33 Table 1. Static elastic moduli with different stress states Failure parameters from laboratory From the onset of Figure 4 (right), the friction angle is about 38º and the cohesive strength is zero (this is unconsolidated sand). Elastic moduli from well log analysis Dynamic moduli (Young’s modulus (E dynamic ) and Poisson’s ratio ( dynamic ) were calculated with the Frio injection well logging data for Frio C sandstone interval (Raw data courtesy of the Gulf Carbon Center). Figure 7 shows the calculated values and measured logging data, which are required for the calculation. 2 s 2ρV (1 ); dynamic E Biot coefficient Petrophysical properties Porosity Sample number V1 V3 H1 Average Porosity 0.376 0.355 0.357 0.363 Table 2. Calculated porosity of Frio samples Capillary pressure and relative permeability Capillary pressure was measured with the air-brine porous-plate method and with mercury injection capillary pressure (MICP) method (Figure 9). CO 2 -water capillary pressure at in-situ conditions are expected to be about one-third of the N 2 -water capillary pressure measured in these tests. Relative permeability is calculated by fitting Brooks-Corey model into MICP measurement. The parameters for Brooks-Corey model are in Table 4. Fig. 9. Fitted MICP experiment result with Brookes-Corey model and (b) relative permeability curves of Frio C sandstone Computational simulation results Frio pilot test Wells 1 injection well and 1 observation well Injection well (1)-(6) Production (Observation) well (1)-(3) Volume Injection rate specified Pressure specified rate ( 2190 psi) Total simulation time 100 days Number of grids (non-uniform grid size) 1.17E+5 grids (50*37*63) Initial porosity (measured value from cored sample) 0.363 Initial reservoir pressure at the perforation depth 2190 psi Rock compressibility 1.0E-6 (1/psi) Fig. 7. Acoustic velocities and density measured by logging and calculated dynamic moduli of Frio C in injection well. 2 2.5 3 3.5 4 4.5 5 0.033 0.0335 0.034 0.0345 0.035 Effective stress (MPa) Ev (-) Permeability Sample number k (mD) k g at breakthrough (mD) k w at S gr (mD) V1 470 184 263 0 100 200 300 400 1 1.5 2 2.5 3 3.5 4 Time (sec) Pressure (atm) 0 0.2 0.4 0.6 0.8 1 400 450 500 550 600 1/Pavg (1/atm) kg (mD) σ m,effective = ( + ) 5050 5055 5060 5065 5070 5075 5080 5085 0 0.1 0.2 0.3 0.4 Depth (ft) Porosity (-) 5050 5055 5060 5065 5070 5075 5080 5085 0 1000 2000 3000 Depth (ft) Permeability (mD) Porosity and permeability from well log analysis Fig. 10. Calculated porosity and permeability from well log analysis of Frio injection well before CO 2 injection. Since the Frio complex is highly laminated in sequences of sand and shaly sand, we used a linear correlation between sandstone and shale properties to correct shaliness and estimate porosity and permeability (Fig. 10). Water and gas (N 2 ) permeabilities were measured at reservoir in-situ stress condition. The applied stress conditions are closely adjusted according to the core depth and in-situ lateral stresses. Table 3. Measured permeability at reservoir stress condtion Fig. 8. Measured gas absolute permeability Bulk Biot coefficient is measured by controlling confining stress and pore pressure step by step according to the procedure proposed by Bouteca et al. (1999) (Fig. 5.). The triaxial loading cell (Fig. 3.) is used to maintain stress condition and regulate pore pressure. The results show that the Biot coefficient for Frio sand is 0.97 (Fig. 6.). Fig. 6. Volumetric strain change as a function of Biot effective stress Fig. 5. Loading and unloading of confining stress (σ c ) and pore pressure (Pp) Fig. 12. Injection schedule of Frio “C” Triaxial loading cell and fluid injection system Control panel Upstream and downstream pipes Downstream cylinder ISCO pump Pressure intensifier Upstream cylinder Pressure booster 0 2 4 6 8 10 12 14 16 18 20 2100 2120 2140 2160 2180 2200 Pressure (psi) Time (days) 0 2 4 6 8 10 12 14 16 18 20 0 20 40 60 80 100 injection rate (gpm) NAME TC (Rº) Critical Pressure (psi) Critical Z Accentric factor (lbM/cu-ft) Molecular weight Parachor Vshift CP CV CO 2 547.56 1070.38 0.3023 0.224 44.01 49 -0.19 14.89 12.91 BRINE 1165.23 3203.88 0.2298 0.244 19.35 52 0.095 17.82 15.83 Compositional fluid flow with fine scale reservoir setup With the properties measured with experiments and well log analysis, a detailed Frio reservoir model is developed in our in-house reservoir simulator IPARs (Integrated Parallel Accurate Reservoir Simulator) to perform history matching for the pilot test. We located the injection and observation well at the right locations and inputted the correct injection schedule. The fine 2ft-scale permeability and porosity are assigned to the simulation (Figure 13). Capillary pressure and relative permeability are also assigned. The fluid properties are fine-tuned according to the Kong et al. (2015). Figure 13 shows the CO 2 saturation along the reservoir after 30 days of the injection. The injection schedule and bottom hole pressure response are shown in Figure 14. The extra fine-tuned history matching will be performed. Approximately, 1,800 tons of CO 2 was injected for 10 days, and breakthrough occurred after 5 days of injection (Hovorka et al., 2006). Table 6. Simulation input for compositional fluid flow simulation 0 1 2 3 4 5 6 7 8 9 10 1900 2000 2100 2200 2300 2400 2500 Pressure (psi) Time (days) 0 1 2 3 4 5 6 7 8 9 10 0 20 40 60 80 100 120 injection rate (gpm) Fig. 3. High-pressure triaxial loading cell and connected fluid flow upstream and downstream system 2 2 P s 2 2 P s V 2V , 2V 2V dynamic Fig. 13. Simulation input 2 ft-scale permeability (left) and CO 2 saturation in the middle of simulation (right) Fig. 14. Simulation results of bottom hope pressure (blue) and injection rate (red) at the injection well 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 Capillayr pressure (MPa) Sw Calculated Pc Air-brine converted MICP 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.5 1 Relatvie permeability Sw Krw krnw λ lnP e P e K r_nw S m 4.741584 0.4595 1.583282 0.82 0.95 Table 4. Brookes-Corey model parameters for Frio C sandstone = 1− = ∗ ( ) (− 1 ) ; No-flow boundary condition results in the increased bottom hole pressure; it will be corrected by locating multiple pressure specified production well.

2 Effective Carbon Storage Including Compositional Flow and … · 2016-08-31 · Hojung Jung, D. Nicolas Espinoza, Gurpreet Singh and Mary F. Wheeler 2016 Mastering the Subsurface

  • Upload
    others

  • View
    1

  • Download
    0

Embed Size (px)

Citation preview

Page 1: 2 Effective Carbon Storage Including Compositional Flow and … · 2016-08-31 · Hojung Jung, D. Nicolas Espinoza, Gurpreet Singh and Mary F. Wheeler 2016 Mastering the Subsurface

0 1000 2000 3000 4000-2

0

2

4

6

8

Time (sec)

Confinin

g s

tress (

C )

(re

d)

and

Pore

pre

ssure

(P

p)

(blu

e)

(MP

a)

0 1 2 3 4 53

4

5

6

7

8

Pore pressure (MPa)

Confinin

g s

tress (

MP

a)

0 1 2 3 4 50.033

0.0335

0.034

0.0345

0.035

0.0355

Pp (MPa)

Ev

3 4 5 6 7 80.033

0.0335

0.034

0.0345

0.035

0.0355

Pc (MPa)

Ev

Loading

Unloading

Loading

Unloading

Unloading path

Loading pathσc

Pp

Fig. 4. Frio sandstone multi-stage triaxial testing at confining stress 500 psi, 1000 psi and

1500 psi: (left) Axial strain and radial strains measured for a single core plug, (right) Failure

line at the onset of shear dilation.

A Comprehensive Case Study of the Frio CO2 Sequestration Pilot Test for Safe and Effective Carbon Storage Including Compositional Flow and Geomechanics

Hojung Jung, D. Nicolas Espinoza, Gurpreet Singh and Mary F. Wheeler

2016 Mastering the Subsurface through Technology Innovation and Collaboration: Carbon Storage and Oil and Natural Gas Technologies Review Meeting

Introduction

Carbon dioxide (CO2) geological sequestration is a direct method to reduce

carbon emission to the atmosphere by injecting CO2 into deep geological

structures. Deep geological structures include depleted oil and gas reservoirs

and saline aquifers. In-depth understanding of the long-term fate of stored CO2

requires study and analysis of the reservoir formation, the caprock formation,

and the adjacent faults. This poster shows an example of a combination of

carefully conceived laboratory experiments, upscaling, and numerical

simulation of long-term storage of CO2 in the Frio injection site.

Objective

This research investigates long term effects of CO2 injection regarding secure

and permanent CO2 storage by conducting experiments, analyzing well logs and

performing numerical reservoir simulation. The experiments include

measurement of petrophysical and geomechanical properties of Frio rocks

subjected to CO2 and CO2-acidified water at in-situ stress condition. These

measurements seek to characterize the relative magnitude of chemical

couplings with geomechanics as well as typical flow properties. Finally, the

measured parameters are used in a computational geomechanical screening

tool that considers the risk associated with CO2 sequestration.

Acknowledgements

The authors would like to thank DOE grant DE-FE0023314. The authors would like to express appreciation to Dr. Hovorka and BEG for sharing field data.

The calculated porosity for each sample is reported in Table 2.

References

• Experiments with rock specimens of different size (up to 4”) to capture the

effect of reservoir heterogeneity in effective properties.

• Measurement of high pressure and high temperature (HPHT) mechanical

properties with CO2-specific loadings. The schematic diagram of experiment

apparatus is in Figure 3.

• History matching of the bottom hole pressure field data by correcting

pressure boundary condition.

• Large CO2 injection reservoir simulation including poro-elasticity.

• Hovorka, S.D., C. Doughty, S.M. Benson, and others, (2006). Measuring permanence

of CO2 storage in saline formations: The Frio experiment, Environ. Geosci., 13(2):

105–121.

• Hovorka, S.D. (2009) – Frio Brine Pilot: the First US Sequestration Test.

• Bouteca, M., Sarda, J.P., Vincke, O., & Longuemare, P. (1999). Thoughts about the

micro-mechanical origin of the evolution of the Biot coefficient of argilites during

mechanical load. Scientific days, ANDRA 1999 Summary of conferences and poster

communications, (p. 258). France

• Kong, X., Delshad, M., & Wheeler, M. F. (2015). History Matching Heterogeneous

Coreflood of CO2/Brine by Use of Compositional Reservoir Simulator and

Geostatistical Approach. Society of Petroleum Engineers. doi:10.2118/163625-PA

Future work

Table 5. Simulation input for compositional fluid flow simulation

Fig. 1. Schematic of a Frio formation

geological strata (Hovorka, GCCC)

(6)

Frio C Sand

Frio formation is a saline aquifer in East

Texas in which two pilot tests of CO2

sequestration were conducted (Hovorka et

al., 2006). Figure 1 shows the geological

strata of Frio formation, and it is

composed of sands with highly bedded

shale layers. Frio sandstone cores are

retrieved from the pilot test site and are

available from the Houston Research

Center (Figure 2, BEG – The University of

Texas, Austin).

Fig. 2. Frio sandstone cores provided by (BEG-UT

Austin)

Summary of accomplishments to date

• Elastic and inelastic mechanical properties are accurately measured by

multistage triaxial loading test and Biot coefficient loading test. The results

show typical behavior of unconsolidated sand, and the analyzed mechanical

properties are applied to calibrate well logs analysis.

• Basic and advanced petrophysical properties are evaluated under the

reservoir stress condition. The measured properties are carefully matched

with the well logging analysis results.

• Finally, all the calculated petrophysical properties are implemented into a

compositional reservoir simulator, and the simulation results show

reasonable pressure transient.

Mechanical properties

Elastic moduli from triaxial testing

Static elastic moduli were measured using the multistage-triaxial loading test

attained by increasing deviatoric stress under three different constant confining

pressures (500 psi, 1000 psi, and 1500 psi). The static elastic moduli can be

calculated with the following relationships:

radial

radial

axial

;

radial

axial

axial

E

Confining pressure (psi) Deviatoric stress, (psi) Estatic (GPa) 𝜈

500 Loading 91.5 - 276.2 0.82 0.21

Loading 365 - 529 1.10 0.25

Unloading 1025 - 809.7 7.21 0.35

1000 Loading 107.3 - 882.5 2.77 0.19

Loading 1057 - 1506 2.74 0.18

Unloading 2966 - 2364 8.47 0.42

1500 Loading 116.2 - 612.4 3.67 0.20

Loading 1068 - 1904 5.46 0.29

Unloading 4294 - 3839 8.04 0.33

Table 1. Static elastic moduli with different stress states

Failure parameters from laboratory

From the onset of Figure 4 (right), the friction angle is about 38º and the

cohesive strength is zero (this is unconsolidated sand).

Elastic moduli from well log analysis

Dynamic moduli (Young’s modulus (Edynamic) and Poisson’s ratio (𝜈dynamic) were

calculated with the Frio injection well logging data for Frio C sandstone interval

(Raw data courtesy of the Gulf Carbon Center). Figure 7 shows the calculated

values and measured logging data, which are required for the calculation.

2

s2ρV (1 );dynamicE

Biot coefficient

Petrophysical properties

Porosity

Sample number V1 V3 H1 Average

Porosity 0.376 0.355 0.357 0.363

Table 2. Calculated porosity of Frio samples

Capillary pressure and relative permeability

Capillary pressure was measured with the air-brine porous-plate method and

with mercury injection capillary pressure (MICP) method (Figure 9). CO2-water

capillary pressure at in-situ conditions are expected to be about one-third of the

N2-water capillary pressure measured in these tests. Relative permeability is

calculated by fitting Brooks-Corey model into MICP measurement. The

parameters for Brooks-Corey model are in Table 4.

Fig. 9. Fitted MICP experiment result with Brookes-Corey model and (b) relative permeability

curves of Frio C sandstone

Computational simulation results

Frio pilot test

Wells 1 injection well and 1 observation well

Injection well (1)-(6)

Production (Observation) well (1)-(3)

Volume Injection rate specified

Pressure specified rate ( 2190 psi)

Total simulation time 100 days

Number of grids (non-uniform grid size) 1.17E+5 grids (50*37*63)

Initial porosity (measured value from cored sample) 0.363

Initial reservoir pressure at the perforation depth 2190 psi

Rock compressibility 1.0E-6 (1/psi)

Fig. 7. Acoustic velocities and density measured by logging

and calculated dynamic moduli of Frio C in injection well.

2

2.5

3

3.5

4

4.5

5

0.033 0.0335 0.034 0.0345 0.035

Effe

ctiv

e st

ress

(M

Pa)

Ev (-)

Permeability

Sample number k (mD) kg at breakthrough (mD) kw at Sgr (mD)

V1 470 184 263

0 100 200 300 4001

1.5

2

2.5

3

3.5

4

Time (sec)

Pre

ssure

(atm

)

Cycle1, kl=469.1(mD), b=0.065601

0 0.2 0.4 0.6 0.8 1400

450

500

550

600

1/Pavg (1/atm)

kg (

mD

)

σm,effective = (𝜎𝑚 + 𝛼𝑃𝑝)

5050

5055

5060

5065

5070

5075

5080

5085

0 0.1 0.2 0.3 0.4

Dep

th (

ft)

Porosity (-)

5050

5055

5060

5065

5070

5075

5080

5085

0 1000 2000 3000

Dep

th (

ft)

Permeability (mD)

Porosity and permeability from well log analysis

Fig. 10. Calculated porosity and permeability from well log analysis of Frio injection well before

CO2 injection.

Since the Frio complex is highly laminated in sequences of sand and shaly

sand, we used a linear correlation between sandstone and shale properties to

correct shaliness and estimate porosity and permeability (Fig. 10).

Water and gas (N2) permeabilities were measured at reservoir in-situ stress

condition. The applied stress conditions are closely adjusted according to the

core depth and in-situ lateral stresses.

Table 3. Measured permeability at reservoir stress condtion

Fig. 8. Measured gas absolute permeability

Bulk Biot coefficient is measured by

controlling confining stress and pore

pressure step by step according to the

procedure proposed by Bouteca et al.

(1999) (Fig. 5.). The triaxial loading cell

(Fig. 3.) is used to maintain stress

condition and regulate pore pressure.

The results show that the Biot coefficient

for Frio sand is 0.97 (Fig. 6.).

Fig. 6. Volumetric strain change as a function of Biot effective stress

Fig. 5. Loading and unloading of confining stress (σc) and pore pressure (Pp)

Fig. 12. Injection schedule of Frio “C”

Triaxial loading cell and fluid injection system

Control panel

Upstream and downstream pipes

Downstream cylinder

ISCO pump

Pressure intensifier

Upstream cylinder

Pressure booster

0 2 4 6 8 10 12 14 16 18 202100

2120

2140

2160

2180

2200

Pre

ssu

re (

psi)

Time (days)

0 2 4 6 8 10 12 14 16 18 200

20

40

60

80

100

inje

ctio

n r

ate

(g

pm

)

NAME TC (Rº) Critical

Pressure (psi) Critical Z

Accentric factor (lbM/cu-ft)

Molecular weight

Parachor Vshift CP CV

CO2 547.56 1070.38 0.3023 0.224 44.01 49 -0.19 14.89 12.91

BRINE 1165.23 3203.88 0.2298 0.244 19.35 52 0.095 17.82 15.83

Compositional fluid flow with fine scale reservoir setup

With the properties measured with experiments and well log analysis, a

detailed Frio reservoir model is developed in our in-house reservoir simulator

IPARs (Integrated Parallel Accurate Reservoir Simulator) to perform history

matching for the pilot test. We located the injection and observation well at the

right locations and inputted the correct injection schedule. The fine 2ft-scale

permeability and porosity are assigned to the simulation (Figure 13). Capillary

pressure and relative permeability are also assigned. The fluid properties are

fine-tuned according to the Kong et al. (2015).

Figure 13 shows the CO2 saturation along the reservoir after 30 days of the

injection. The injection schedule and bottom hole pressure response are shown

in Figure 14. The extra fine-tuned history matching will be performed.

Approximately, 1,800 tons of CO2 was injected for 10 days, and breakthrough

occurred after 5 days of injection (Hovorka et al., 2006).

Table 6. Simulation input for compositional fluid flow simulation

0 1 2 3 4 5 6 7 8 9 101900

2000

2100

2200

2300

2400

2500

Pre

ssu

re (

psi)

Time (days)

0 1 2 3 4 5 6 7 8 9 100

20

40

60

80

100

120

inje

ctio

n r

ate

(g

pm

)

Fig. 3. High-pressure triaxial loading cell and connected fluid flow upstream and downstream

system

2 2

P s

2 2

P s

V 2V,

2V 2Vdynamic

Fig. 13. Simulation input 2 ft-scale permeability (left) and CO2 saturation in the

middle of simulation (right)

Fig. 14. Simulation results of bottom hope pressure (blue) and injection rate (red) at

the injection well

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1

Capill

ayr

pre

ssure

(M

Pa)

Sw

Calculated Pc

Air-brine converted MICP

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.5 1

Rela

tvie

perm

eabili

ty

Sw

Krw krnw

λ lnPe Pe Kr_nw Sm

4.741584 0.4595 1.583282 0.82 0.95

Table 4. Brookes-Corey model parameters for Frio C sandstone

𝑆𝑤∗ =

𝑆𝑤 − 𝑆𝑤𝑖𝑟1 − 𝑆𝑤𝑖𝑟

𝑃𝑐 = 𝑃𝑒 ∗ (𝑆𝑤∗ )(−

1

𝜆);

No-flow boundary condition results in the increased bottom hole pressure;

it will be corrected by locating multiple pressure specified production well.

(a) Permeability (mD) (b) CO2 saturation