quantifying uncertainty in modelling reservoir containment of …iea-eor.ptrc.ca/2012/assets/s4/3 -...

The IEAEOR 33rd Annual Symposium, August 26 to 30, 2012, Regina,The IEAEOR 33rd Annual Symposium, August 26 to 30, 2012, Regina,The IEAEOR 33rd Annual Symposium, August 26 to 30, 2012, Regina,The IEAEOR 33rd Annual Symposium, August 26 to 30, 2012, Regina, Saskatchewan, CanadaSaskatchewan, CanadaSaskatchewan, CanadaSaskatchewan, Canada

Quantifying Uncertainty in Modeling Reservoir Quantifying Uncertainty in Modeling Reservoir Quantifying Uncertainty in Modeling Reservoir Quantifying Uncertainty in Modeling Reservoir Containment of Injected COContainment of Injected COContainment of Injected COContainment of Injected CO2222

Kenny K. NielsenKenny K. NielsenKenny K. NielsenKenny K. Nielsen1111, Laurids Andersen, Laurids Andersen, Laurids Andersen, Laurids Andersen1111, Yngve Borgan, Yngve Borgan, Yngve Borgan, Yngve Borgan2222, Erling H. Stenby, Erling H. Stenby, Erling H. Stenby, Erling H. Stenby3,43,43,43,4, Wei Yan, Wei Yan, Wei Yan, Wei Yan4444, and , and , and , and KristianKristianKristianKristianJessenJessenJessenJessen3,53,53,53,5

1111LloydLloydLloydLloyd’’’’s Register ODS, Denmarks Register ODS, Denmarks Register ODS, Denmarks Register ODS, Denmark

2222LloydLloydLloydLloyd’’’’s Register Scandpower, Norways Register Scandpower, Norways Register Scandpower, Norways Register Scandpower, Norway

3333Tie Tie Tie Tie ---- Line Technology, DenmarkLine Technology, DenmarkLine Technology, DenmarkLine Technology, Denmark

4444CERE CERE CERE CERE ---- DTU Chemistry, Technical University of DenmarkDTU Chemistry, Technical University of DenmarkDTU Chemistry, Technical University of DenmarkDTU Chemistry, Technical University of Denmark

5555University of Southern California, USA University of Southern California, USA University of Southern California, USA University of Southern California, USA


Project Brief

Assessment of Assessment of Assessment of Assessment of reservoir modelling tool limitations in the context of risk analreservoir modelling tool limitations in the context of risk analreservoir modelling tool limitations in the context of risk analreservoir modelling tool limitations in the context of risk analysis uncertainties.ysis uncertainties.ysis uncertainties.ysis uncertainties.

• When and where do we need to be aware of reservoir modelling tool limitations and what are the end effect on the risk assessment

• Investigation of the range of results with the variation of the property models in the simulator for CO2

Main uncertainty in reservoir engineeringMain uncertainty in reservoir engineeringMain uncertainty in reservoir engineeringMain uncertainty in reservoir engineering

• The lack of information about distributed reservoir properties such as porosity, permeability, faults etc.

• On-going project “Propagation of Uncertainty in Geophysical Analysis”


Simulators and their limitations

Benchmark study - Class et al. (2009) “A benchmark study on problems related to CO2 storage in geologic formations”

[2].

• Substantial agreement between results from different simulators

• The disagreement:

• space and time discretization

• difference in fluid property descriptionfluid property descriptionfluid property descriptionfluid property description.

Limitations of reservoir models Limitations of reservoir models Limitations of reservoir models Limitations of reservoir models

• Most simulators are originally developed for optimization of hydrocarbon production in gas and oil reservoirs.

• Coupling between fluid and rock properties

• Complex flow phenomenon

• Fluid property description.


Reservoir Model - COSI

COSI (Compositional Reservoir Simulator)

• 3-dimensional fully implicit compositional three phase isothermal reservoir simulator, owned by Tie-Line Technology.

• Validated against Class et al. (2009) problem 3 (Johansen formation)

Log(p

erm

, m

D)


MethodReservoir typesReservoir typesReservoir typesReservoir types

Property Reference model Alternative models

CO2

density Span and Wagner Peng-Robinson

CO2

viscosity Fenghour et al. LBC and F-theory

Brine density Rowe and Chow -

Brine viscosity Kestian et al. -

CO2

solubility Spycher et al.Modified Soreide and

Whitson

Leaky well index calc. 100 mD 10 mD

Critical gas in well 0% 15%

Table 2: Classification of aquifer settings after Kopp et al. (2009)

Cases Depth Pressure Temp ρBrine

ρCO2

µBrine

µCO2

- - [m] [bar] [Deg C.] [kg/m3] [kg/m3] [cP] [cP]

Median M 1524 154.7 55.13 1025.5 660.7 0.629 0.053

Warm W 1524 149.5 104.49 994.5 316.8 0.347 0.028

Cold C 1524 155.1 37.43 1031.7 805.5 0.843 0.072

Shallow S 386 40.6 21.58 1032.9 98.3 1.162 0.016

Deep D 3495 353.1 115 995.2 666.1 0.321 0.055

Table 3: Model selection for simulation study

Fluid property and leaky well modelsFluid property and leaky well modelsFluid property and leaky well modelsFluid property and leaky well models

Ref. Density Solubility Well Index Well Sgc

Viscosity A Viscosity B

Median X X X X X X X

Warm X X X X X X X

Cold X X X X X X X

Shallow X X X X X X X

Deep X X X X X X X

Table 4: Case matrix for initial simulation study.

Case matrixCase matrixCase matrixCase matrix


Aquifer model

• Black-Oil simulation

• PUNQ-S3 Reservoir model[3]

• 19x28x5 active cells.

• Thickness of formation 30m, depth varies 150m.

• Injection well (green) 2000m from leaky well (red).

• Open boundary condition at edges, except for top layer which is impermeable.

• Average porosity value of 19.3%.

• Average permeability 150mD.

• Pore volume of 85million cubic meter with target injection rate of 0.4E+06 ton of CO2 per year for a 15 year period, simulation is run additional 25 years.

• 100 % Brine at initialization.

• Initial hydrostatic pressure distribution.

• Hysteresis is included in the imbibition process.

Figure 18: Initial hydrostatic pressure distribution in the medium reference model.

Figure 16: Brine and CO2 relative permeability functions used in all numerical calculations.


Results

Figure 21: Comparison of CO2 viscosity calculated from Fenghour et al. (reference

model), the LBC correlation and F-theory in the pressure range of relevance to the simulation of

fluid flow in the medium aquifer.

Figure 20: Comparison of CO2 density as calculated from Span-Wagner (reference) and the PR EOS in the pressure range of

relevance to the simulation of fluid flow in the medium aquifer.

Medium ReservoirMedium ReservoirMedium ReservoirMedium Reservoir

Figure 7: Leakage from abandoned well in a medium aquifer setting.


Shallow ReservoirShallow ReservoirShallow ReservoirShallow Reservoir

Figure 13: Leakage from abandoned well in a shallow aquifer setting

Figure 14: Left: Comparison of CO2density as calculated from Span-Wagner (reference) and the

PR EOS in the pressure range of relevance to the simulation of fluid flow in the shallow aquifer. Right: Comparison of CO

2viscosity calculated from Fenghour et al. (reference model),

the LBC correlation and F-theory in the pressure range of relevance to the simulation of fluid flow in the shallow aquifer.

Results


Warm ReservoirWarm ReservoirWarm ReservoirWarm Reservoir

Figure 23: Distribution of CO2 in the medium aquifer after 10 years of injection

Figure 24: Distribution of CO2 in the warm aquifer after 10 years of injectionFigure 9: Leakage from abandoned well in a warm aquifer setting

Results


Cold ReservoirCold ReservoirCold ReservoirCold Reservoir

Figure 12: Leakage from abandoned well in a cold aquifer setting Figure 15: Leakage from abandoned well in a deep aquifer setting

Deep ReservoirDeep ReservoirDeep ReservoirDeep ReservoirResults


Summary of results

CasesMobility ratio

Leakage percentageafter 40 yrs

Breakthroughtime [days]

Conclusions

Medium

P = 155 Bar

T = 55 C

11.9 12.2 – 15 % 6000Medium brine viscosity and CO2 density values makes it a medium good choice for

storage.

Warm

P = 150 Bar

T = 105 C

12.3 42 – 45 % 3500 Low Brine viscosity and low CO2 density makes it bad choice for storage.

Cold

P = 155 Bar

T = 37 C

11.7 0.2 – 3.2 % 8000 High CO2 density and high Brine viscosity provide the best choice for storage.

Shallow

P = 41 Bar

T = 22 C

72.6 9 – 55 % 5300Low CO2 density, high mobility ratio and CO2 phase transition makes it a really bad

choice for CO2 storage.

Deep

P = 353 Bar

T = 115 C

5.8 3.2 – 5 % 5100 Low mobility ratio, high CO2 density makes it second best choice for storage.


Conclusion

• There is a large variation in the predicted fraction of leaked CO2 percentage, depending on the reservoir type.

• The effect of the investigated variables strongly depends on the reservoir type.

• The effect of the leaky well permeability is significant in all reservoir types.

• The simulations were performed with the same injection rate of CO2 on a mass or molar basis. This reflects the situation where a given source of CO2 has to be dealt with.

• In this study the effect of each selected variable has been tested individually. It is expected that a combination of these effects will lead to an even larger spread in the results.

• Leakage expressed as leaked CO2 in percent of injected CO2 varies from 2.5% to 45% depending on the reservoir type and the variable settings.


References[1] – Oladyshkin, S., Class, H., Helmig, R., & Nowak, W. (2009). An Integrative Approach to Robust Design and Probabilistic Risk Assessment for CO 2 Storage in Geologic Formations.

[2] – Class, H., Ebigbo, A., Helmig, R., Dahle, H. K., Nordbotten, J. M., Celia, M. a., Audigane, P., et al. (2009). A benchmark study on problems related to CO2 storage in geologic formations. Computational Geosciences, 13(4), 409-434. doi:10.1007/s10596-009-9146-x

[3] – Floris, F.J.T. et al.: Methods for Quantifying the Uncertainty of Production Forecasts: A Comparative Study, Petroleum Geoscience (2001) 7, 87.[4] - Kopp, a., Class, H., & Helmig, R. (2009). Investigations on CO2 storage capacity in saline aquifers—Part 2: Estimation of storage capacity coefficients. International Journal of Greenhouse Gas Control, 3(3), 277-287. doi:10.1016/j.ijggc.2008.10.001

[5] - Kestin, J., Khalifa, H.E., Abe, Y., Grimes, C.E., Sookiazian, H. and Wakeham, W.A. “Effect of Pressure on the Viscosity of Aqueous NaClSolutions in the Temperature Range 20-150 C”, J Chem. Eng. Data, vol 23, no 4, 1978, pp 328-336.

[6] - Fenghour, A., Wakeham, W. A., Vesovic, V., “The Viscosity of Carbon Dioxide,” J. Phys. Chem. Ref. Data, Vol 27, No 1, (1998) pp. 31-44.

[7] - Spycher, N., Pruess, K., “CO2-H2O Mixtures in the Geological Sequestration of CO2. II. Partitioning in Chloride Brines at 12-100 C and up to 600 bar”, Geochimica et Cosmochimica Acta. Vol. 69 No. 13 (2005) pp3309-3320.

For more information, please contact:

Lloyd's Register Group Ltd, its affiliates and subsidiaries and their respective officers, employees or agents are, individually and collectively, referred to in this clause as the 'Lloyd's Register Group of Companies'. The Lloyd's Register Group of Companies assumes no responsibility and shall not be liable to any person for any loss, damage or expense caused by reliance on the information or advice in this document or howsoever provided, unless that person has signed a contract with the relevant Lloyd's Register Group of Companies entity for the provision

of this information or advice and in that case any responsibility or liability is exclusively on the terms and conditions set out in that contract.

Laurids AndersenConsultant, Energy, Fluid Dynamics.

Lloyd’s Register ODSStrandvejen 1042900 HellerupDenmark

T +45 3531 1042E [email protected] www.lr-ods.com

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