# A General Framework Model for Fully Coupled Thermal-Hydraulic-Mechanical Simulation of CO2 EOR Operations

- Authors
- Shihao Wang (Colorado School of Mines) | Yuan Di (Peking University) | Yu-Shu Wu (Colorado School of Mines) | Philip Winterfeld (Colorado School of Mines)
- DOI
- https://doi.org/10.2118/193879-MS
- Document ID
- SPE-193879-MS
- Publisher
- Society of Petroleum Engineers
- Source
- SPE Reservoir Simulation Conference, 10-11 April, Galveston, Texas, USA
- Publication Date
- 2019

- Document Type
- Conference Paper
- Language
- English
- ISBN
- 978-1-61399-634-8
- Copyright
- 2019. Society of Petroleum Engineers
- Disciplines
- 5.4 Improved and Enhanced Recovery, 5.2.1 Phase Behavior and PVT Measurements, 5 Reservoir Desciption & Dynamics, 5.4 Improved and Enhanced Recovery, 5.5 Reservoir Simulation, 5.2 Fluid Characterization, 0.2.2 Geomechanics, 0.2 Wellbore Design
- Keywords
- CO2 EOR, fully coupled simulation, proxy flash calculation
- Downloads
- 17 in the last 30 days
- 152 since 2007

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In this work, we present the development of a comprehensive mathematical formulation and reservoir simulator for thermal-hydraulic-mechanical simulation of CO_{2}-EOR processes

We adopt the integral finite difference method to simulate coupled thermal-hydraulic-mechanical processes during CO2-EOR in conventional and unconventional reservoirs. In our method, the governing equations of the multiphysical processes are solved fully coupled on the same unstructured grid. A multiscale algebraic linear solver is adopted to speed up the non-isothermal flow calculation. Inspired by the meshless method, the algebraic solver eliminates the low-frequency terms through smoothing on a coarse grid. In order to simulate the phase behavior of a three-phase system, a three-phase flash calculation module, based on direct minimization of Gibbs energy, is implemented in the simulator.

We have investigated the impact of cold CO_{2} injection on injectivity as well as on phase behavior. We conclude that cold injection is an effective way to increase injectivity in tight-oil reservoirs. We have observed and studied the temperature decreasing phenomena near the production well, known as the Joule-Thomson effect, induced by expansion of in-situ fluids.

The novelty of this work lies in the fully coupled simulation scheme, including non-isothermal effects on CO2-EOR processes and recoveries, which has been ignored in almost all modeling studies of CO2-EOR. The multiscale solution strategy and the unique phenomena of non-isothermal compositional modeling coupled with geomechanics are captured by our simulator.

File Size | 1 MB | Number of Pages | 24 |

### Supporting information

- SUPPLEMENTARY/SPE-193879-SUP.pdf

Al-Marhoun, M. A., & Osman, E. A. (2002). Using Artificial Neural Networks to Develop New PVT Correlations for Saudi Crude Oils. In Abu Dhabi International Petroleum Exhibition and Conference. Society of Petroleum Engineers. 10.2118/78592-MS

Ballard, A. L. (2002). A non-ideal hydrate solid solution model for a multi-phase equilibria program. Colorado School of Mines. Retrieved from https://dspace.library.colostate.edu/bitstream/handle/11124/78793/T05590.pdf

Ballard, A. L., & Sloan, E. D. (2004). The next generation of hydrate prediction: Part III. Gibbs energy minimization formalism. Fluid Phase Equilibria, 218(1), 15-31. 10.1016/J.FLUID.2003.08.005

Bhargava, V., Fateen, S. E. K., & Bonilla-Petriciolet, A. (2013). Cuckoo Search: A new nature-inspired optimization method for phase equilibrium calculations. Fluid Phase Equilibria, 337, 191-200. 10.1016/J.FLUID.2012.09.018

Bonilla-Petriciolet, A., & Segovia-Hernández, J. G. (2010). A comparative study of particle swarm optimization and its variants for phase stability and equilibrium calculations in multicomponent reactive and non-reactive systems. Fluid Phase Equilibria, 289(2), 110-121. 10.1016/J.FLUID.2009.11.008

Bromley, L. A. (1973). Thermodynamic properties of strong electrolytes in aqueous solutions. AIChE Journal, 19(2), 313-320. 10.1002/aic.690190216

Cheung, A., Adjiman, C. S., Kolar, P., & Ishikawa, T. (2002). Global optimization for clusters of flexible molecules—solvent-solute interaction energy calculations. Fluid Phase Equilibria, 194-197, 169-183. 10.1016/S0378-3812(01)00780-4

Computer Modelling Group LTD. (2010). CMG | Software Solutions. Retrieved from https://www.cmgl.ca/software

Delshad, M., & Pope, G. (1989). Comparison of the three-phase oil relative permeability models. Transport in Porous Media, 4(1), 59-83. 10.1007/BF00134742

Di, Y., Zhang, Y., & Wu;Yu-Shu. (2015). Gibbs ?????????????-?-??????.. Acta Petrolei Sinica, 36(5), 593-599. Retrieved from http://www.cqvip.com/qk/95667x/201505/665024208.html

Eslami, M., Hetnarski, R., Ignaczak, J., Noda, N., & Sumi, N. (2013). Theory of elasticity and thermal stresses. New York: Springer. Retrieved from http://link.springer.com/content/pdf/10.1007/978-94-007-6356-2.pdf

Gaganis, V., & Varotsis, N. (2012). Machine Learning Methods to Speed up Compositional Reservoir Simulation. In SPE Europec/EAGE Annual Conference. Society of Petroleum Engineers. 10.2118/154505-MS

Gharbi, R. B., & Elsharkawy, A. M. (1997). Neural Network Model for Estimating The PVT Properties of Middle East Crude Oils. In Middle East Oil Show and Conference. Society of Petroleum Engineers. 10.2118/37695-MS

Grigg, R. B., & Schechter, D. S. (1997). State of the Industry in CO2 Floods. In SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers. 10.2118/38849-MS

Hajibeygi, H., & Jenny, P. (2009). Multiscale finite-volume method for parabolic problems arising from compressible multiphase flow in porous media. Journal of Computational Physics, 228(14), 5129-5147. 10.1016/J.JCP.2009.04.017

Hoffman, E. J. (1968). Flash calculations for petroleum fractions. Chemical Engineering Science, 23(9), 957-964. 10.1016/0009-2509(68)87081-2

Jager, M. D., Ballard, A. L., & Sloan, E. D. (2003). The next generation of hydrate prediction: II. Dedicated aqueous phase fugacity model for hydrate prediction. Fluid Phase Equilibria, 211(1), 85-107. 10.1016/S0378-3812(03)00155-9

Kaya, E., Zarrouk, S. J., & O'Sullivan, M. J. (2011). Reinjection in geothermal fields: A review of worldwide experience. Renewable and Sustainable Energy Reviews, 15(1), 47-68. 10.1016/j.rser.2010.07.032

Kruczek, B. (2014). Carman-Kozeny Equation. In Encyclopedia of Membranes (pp. 1-3). Berlin, Heidelberg: Springer Berlin Heidelberg. 10.1007/978-3-642-40872-4_1995-1

LeCun, Y., Bengio, Y., & Hinton, G. (2015). Deep learning. Nature, 521(7553), 436-444. 10.1038/nature14539

Leibovici, C. F., & Neoschil, J. (1995). A solution of Rachford-Rice equations for multiphase systems. Fluid Phase Equilibria, 112(2), 217-221. 10.1016/0378-3812(95)02797-I

Leverett, M. C. (1941). Capillary Behavior in Porous Solids. Transactions of the AIME, 142(01), 152-169. 10.2118/941152-G

Manrique, E. J., Thomas, C. P., Ravikiran, R., Izadi Kamouei, M., Lantz, M., Romero, J. L., & Alvarado, V. (2010). EOR: Current Status and Opportunities. In SPE Improved Oil Recovery Symposium. Society of Petroleum Engineers. 10.2118/130113-MS

McTigue, D. F. (1986). Thermoelastic response of fluid-saturated porous rock. Journal of Geophysical Research, 91(B9), 9533. 10.1029/JB091iB09p09533

Michelsen, M. L. (1982a). The isothermal flash problem. Part I. Stability. Fluid Phase Equilibria, 9(1), 119. 10.1016/0378-3812(82)85001-2

Michelsen, M. L. (1982b). The isothermal flash problem. Part II. Phase-split calculation. Fluid Phase Equilibria, 9(1), 21-40. 10.1016/0378-3812(82)85002-4

Narasimhan, T. N., & Witherspoon, P. A. (1976a). An integrated finite difference method for analyzing fluid flow in porous media. Water Resources Research, 12(1), 57-64. 10.1029/WR012i001p00057

Narasimhan, T. N., & Witherspoon, P. A. (1976b). An integrated finite difference method for analyzing fluid flow in porous media. Water Resources Research, 12(1), 57-64. 10.1029/WR012i001p00057

Nichita, D. V., Gomez, S., & Luna, E. (2002). Multiphase equilibria calculation by direct minimization of Gibbs free energy with a global optimization method. Computers & Chemical Engineering, 26(12), 1703-1724. 10.1016/S0098-1354(02)00144-8

Norris, A. (1992). On the correspondence between poroelasticity and thermoelasticity. Journal of Applied Physics, 71(3), 1138. 10.1063/1.351278

Okuno, R., Johns, R., & Sepehrnoori, K. (2010a). A New Algorithm for Rachford-Rice for Multiphase Compositional Simulation. SPE Journal, 15(02), 313-325. 10.2118/117752-PA

Okuno, R., Johns, R., & Sepehrnoori, K. (2010b). A New Algorithm for Rachford-Rice for Multiphase Compositional Simulation. SPE Journal, 15(02), 313-325. 10.2118/117752-PA

Okuno, R., Johns, R. T., & Sepehrnoori, K. (2010c). Three-Phase Flash in Compositional Simulation Using a Reduced Method. SPE Journal, 15(03), 689-703. 10.2118/125226-PA

Pan, L., & Oldenburg, C. M. (2016). TOGA: A TOUGH code for modeling three-phase, multicomponent, and non-isothermal processes involved in CO2-based Enhanced Oil Recovery. Berkeley, CA (United States). 10.2172/1332134

Pruess, K. (1985). A Practical Method for Modeling Fluid and Heat Flow in Fractured Porous Media. Society of Petroleum Engineers Journal, 25(01), 14-26. 10.2118/10509-PA

Rao, D. (2001). Gas Injection EOR- A New Meaning in the New Millennium. Journal of Canadian Petroleum Technology, 40(02). 10.2118/01-02-DAS

Rossi, C. C. R. S., Cardozo-Filho, L., & Guirardello, R. (2009). Gibbs free energy minimization for the calculation of chemical and phase equilibrium using linear programming. Fluid Phase Equilibria, 278(1-2), 117-128. 10.1016/J.FLUID.2009.01.007

Rutqvist, J., Wu, Y.-S., Tsang, C.-F., & Bodvarsson, G. (2002). A modeling approach for analysis of coupled multiphase fluid flow, heat transfer, and deformation in fractured porous rock. International Journal of Rock Mechanics and Mining Sciences, 39(4), 429-442. 10.1016/S1365-1609(02)00022-9

Shock, E. L., & Helgeson, H. C. (1988). Calculation of the thermodynamic and transport properties of aqueous species at high pressures and temperatures: Correlation algorithms for ionic species and equation of state predictions to 5 kb and 1000°C. Geochimica et Cosmochimica Acta, 52(8), 2009-2036. 10.1016/0016-7037(88)90181-0

Stefansson, V.-dur. (1997). Geothermal reinjection experience. Geothermics, 26(1), 99-139. 10.1016/S0375-6505(96)00035-1

Taron, J., Elsworth, D., & Min, K.-B. (2009). Numerical simulation of thermal-hydrologic-mechanical- chemical processes in deformable, fractured porous media. International Journal of Rock Mechanics and Mining Sciences, 46(5), 842-854. 10.1016/j.ijrmms.2009.01.008

Walton, S., Hassan, O., Morgan, K., & Brown, M. R. (2011). Modified cuckoo search: A new gradient free optimisation algorithm. Chaos, Solitons & Fractals, 44(9), 710-718. 10.1016/J.CHAOS.2011.06.004

Wang, L., Tian, Y., Yu, X., Wang, C., Yao, B., Wang, S., ... Wu, Y.-S. (2017). Advances in improved/enhanced oil recovery technologies for tight and shale reservoirs. Fuel, 210, 425-445. 10.1016/J.FUEL.2017.08.095

Wang, L., Wang, S., Zhang, R., Wang, C., Xiong, Y., Zheng, X., . Rui, Z. (2017). Review of multi-scale and multi-physical simulation technologies for shale and tight gas reservoirs. Journal of Natural Gas Science and Engineering, 37, 560-578. 10.1016/j.jngse.2016.11.051

Wang, S., Huang, Z., Wu, Y.-S., Winterfeld, P. H., & Zerpa, L. E. (2016). A semi-analytical correlation of thermal-hydraulic-mechanical behavior of fractures and its application to modeling reservoir scale cold water injection problems in enhanced geothermal reservoirs. Geothermics, 64, 81-95. 10.1016/j.geothermics.2016.04.005

Wang, S., Lukyanov, A. A., & Wu, Y.-S. (2019). Second-order gas slippage model for the Klinkenberg effect of multicomponent gas at finite Knudsen numbers up to 1. Fuel, 235, 1275-1286. 10.1016/J.FUEL.2018.08.113

Wang, S., Winterfeld, P. H., & Wu, Y.-S. (2015). An Efficient Adaptive Nonlinearity Elimination Preconditioned Inexact Newton Method for Parallel Simulation of Thermal-Hydraulic-Mechanical Processes in Fractured Reservoirs. In SPE Reservoir Simulation Symposium. Society of Petroleum Engineers. 10.2118/173227-MS

YARBOROUGH, L. (1972). Vapor-Liquid Equilibrium Data for Multicomponent Mixtures Containing Hydrocarbon and Nonhydrocarbon Components. Journal of Chemical and Engineering Data, 17(2), 129-133. Retrieved from https://pubs.acs.org/doi/pdf/10.1021/je60053a027

Zhong, H., Wu, K., Ji, D., & Chen, Z. (2017). Using Least Square Support Vector Machines to Approximate Single Phase Flow. In SPE Europec featured at 79th EAGE Conference and Exhibition. Society of Petroleum Engineers. 10.2118/185881-MS