Abstract
Reservoir simulation is traditionally based on the assumption that water is an inert phase, while hydrocarbon components split into oil and gas phases. This approach is usually reasonable when modeling conventional hydrocarbon recovery, but specific applications may require accounting for mass exchange between the water and hydrocarbon phases. We here present the extension of our Graphics Processing Units (GPUs) compositional reservoir simulator (Esler et al. SPE J. 27(01), 597–612, 2021) to support gas-water equilibrium. Specifically, the Søreide and Whitson equation of state (EoS) (Søreide and Whitson Fluid Phase Equilib. 77, 217–240, 1992) was implemented to compute mutual solubilities of hydrocarbon/brine mixtures. The impact of salinity on phase equilibrium is accounted for, with salt being treated as an active tracer. The simulator uses a mass-variables formulation, meaning that little modifications to the construction of transport equations and Jacobian assembly was required; most of the required code changes are localized in the EoS module for the computation of component fugacities, and phase properties such as partial molar fractions and partial molar volumes. Treating salt as an active tracer instead of defining a further pseudo-component has an important advantage with the Søreide and Whitson EoS. If salinity changes as in water vaporization processes, our choice ensures that flash iterations can still be cast as a Gibbs Minimization problem with salinity being a constant parameter. On the contrary, salinity would change as flash iterations progress, jeopardizing the thermodynamic consistency of the phase equilibria. The overall reservoir simulation system of equations is still accurate to first order in time, at the cost of possibly slight volume imbalances at the end of converged timesteps. In this paper, we focused on CO\(_2\) sequestration in saline aquifers, where solubility trapping is a key mechanism. The accuracy of our implementation with respect to conventional CPU ones is first demonstrated on a synthetic box model. We then select an open-access aquifer model (Gassnova 2016) to illustrate its applicability in an industrial setting. Finally, we show how being able to seamlessly run high resolution models allows for modeling of convective mixing. A key conclusion of this work is that the extreme performance of GPU-based reservoir simulation naturally transfers to new fields of study, which is critical when modeling saline aquifers whose extent is an order of magnitude larger than that of typical oil and gas fields.
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Data supporting the findings of this study are available within the paper; data-sets are available from the corresponding author on reasonable request.
References
Afanasyev, A., Vedeneeva, E.: Compositional modeling of multicomponent gas injection into saline aquifers with the MUFITS simulator. J. Nat. Gas Sci. Eng. 94, 103988 (2021)
Babaei, M.: Integrated carbon sequestration-geothermal heat recovery: performance comparison between open and close systems. Transp. Porous Media 126(1), 249–273 (2019)
Bear, J.: Dynamics of fluids in porous media. Cour, Corp (1988)
Chabab, S., Theveneau, P., Coquelet, C., Corvisier, J., Paricaud, P.: Measurements and predictive models of high-pressure H2 solubility in brine (H2O+ NaCl) for underground hydrogen storage application. Int. J. Hydrog. Energy. 45(56), 32206–32220 (2020)
Chang, Y.B., Coats, B., Nolen, J.: A compositional model for CO2 floods including CO2 solubility in water. SPE Reserv. Eval. Eng. 1(02), 155–160 (1998)
Computer Modelling Group: GEM User Guide (2016)
Ennis-King, J., Paterson, L.: Role of Convective Mixing in the Long-Term Storage of Carbon Dioxide in Deep Saline Formations. SPE J. 10(03), 349–356 (2005)
Equinor, Gassnova: Smeaheia on-line dataset. https://co2datashare.org/dataset/smeaheia-dataset (2022). Accessed 10 May 2022
Esler, K., Gandham, R., Patacchini, L., Garipov, T., Samardzic, A., Panfili, P., Caresani, F., Pizzolato, A., Cominelli, A.: A graphics processing unit-based, industrial grade compositional reservoir simulator. SPE J. 27(01), 597–612 (2022)
Fawad, M., Mondol, N.H.: Geological and geophysical investigation of CO2 storage site Smeaheia in the northern North Sea. In: SEG Technical Program Expanded Abstracts 2019, Society of Exploration Geophysicists, pp. 3285–3289 (2019)
Gandham, R., Esler, K., Mukundakrishnan, K., Zhang, Y., Fang, C., Natoli, V.: GPU acceleration of equation of state calculations in compositional reservoir simulation. In: ECMOR XV-15th European Conference on the Mathematics of Oil Recovery. European Association of Geoscientists & Engineers, Amsterdam, The Netherlands (2016)
Gandham, R., Zhang, Y., Esler, K., Natoli, V.: Improving GPU throughput of reservoir simulations using NVIDIA MPS and MIG. In: Fifth EAGE Workshop on High Performance Computing for Upstream, 2021, 1–5 (2021)
Gassnova, G.: Feasibility study for full-scale CCS in Norway. Minist. Pet. Energy 1–62 (2016)
Gross, H., Mazuyer, A.: GEOSX: A multiphysics, multilevel simulator designed for exascale computing. SPE Reserv. Simul, Conf (2021)
Halliburton: Nexus Technical Reference Guide (2014)
Juanes, R., Spiteri, E., Orr Jr, F., Blunt, M.: Impact of relative permeability hysteresis on geological CO2 storage. Water Resour. Res. 42(12) (2006)
Killough, J., Kossack, C.: Fifth comparative solution project: evaluation of miscible flood simulators. In: SPE Symposium on Reservoir Simulation. OnePetro (1987)
Korrani, A.K.N., Sepehrnoori, K., Delshad, M.: Coupling IPhreeqc with UTCHEM to model reactive flow and transport. Comput. Geosci. 82, 152–169 (2015)
Kumar, A., Ozah, R., Noh, M., Pope, G.A., Bryant, S., Sepehrnoori, K., Lake, L.W.: Reservoir simulation of CO2 storage in deep saline aquifers. Spe J. 10(03), 336–348 (2005)
Li, Y.K., Nghiem, L.X.: Phase equilibria of oil, gas and water/brine mixtures from a cubic equation of state and Henry’s law. Can. J. Chem. Eng. 64(3), 486–496 (1986)
Lorentz, J., Bray, B., Clark, C.: Calculating viscosity of reservoir fluids from their composition. J. Pet. Tech. 1171, 231 (1964)
Michelsen, M., Mollerup, J.: Thermodynamic models: fundamentals and computational aspects. Tie-line Publications, Ronnebarvej, Denmark (2007)
Moortgat, J., Li, Z., Firoozabadi, A.: Three-phase compositional modeling of CO2 injection by higher-order finite element methods with CPA equation of state. In: SPE Reservoir Simulation Symposium. (2011)
Mukundakrishan, K., Rosa, A., Ranjan, S., Panfili, P., Cinquini, F., Cominelli, A., Patacchini, L., Esler, K.: Full-GPU simulation of coupled multi-reservoir models: implementation and field examples. In: SPE Reservoir Characterisation and Simulation Conference and Exhibition (2023)
Oldenburg, C.M.: Joule-Thomson cooling due to CO2 injection into natural gas reservoirs. Energy Convers. Manag. 48(6), 1808–1815 (2007)
Open Porous Media: OPM Flow Reference Manual 2022-04 (2022)
Orsini, P., Ponting, D., Stone, D.: A study of temperature effects in the bunter closure 36, a potential large-scale CO2 Storage Site in UK. In: Proceedings of the 15th Greenhouse Gas Control Technologies Conference, pp. 15–18 (2021)
Pan, L., Spycher, N., Doughty, C., Pruess, K.: ECO2N V2. 0: A TOUGH2 fluid property module for mixtures of water, NaCl, and CO2. Scientific report LBNL-6930E (2015)
Pedersen, K., Fredenslund, A., Thomassen, P.: Properties of oils and natural gases, contributions in petroleum engineering. 5, 199–207 (1989)
Peng, D.Y., Robinson, D.B.: A new two-constant equation of state. Ind. Eng. Chem. Fundam. 15(1), 59–64 (1976)
Petitfrere, M., Patacchini, L., de Loubens, R.: Three-phase EoS-based reservoir simulation with salinity dependent phase-equilibrium calculations. In: ECMOR XV-15th European Conference on the Mathematics of Oil Recovery. European Association of Geoscientists & Engineers, cp–494 (2016)
Riaz, A., Hesse, M., Tchelepi, H., Orr, F.: Onset of convection in a gravitationally unstable diffusive boundary layer in porous media. J. Fluid Mech. 548, 87–111 (2006)
Sandve, T., Rustad, A., Thune, A., Nazarian, B., Gasda, S., Rasmussen, A.: Simulators for the Gigaton Storage Challenge. A Benchmark Study on the Regional Smeaheia Model. In: EAGE GeoTech 2022 Sixth EAGE Workshop on CO2 Geological Storage, 2022. European Association of Geoscientists & Engineers, pp. 1–5 (2022)
Schlumberger: Eclipse 2019.1, Technical Description (2019a)
Schlumberger: Intersect 2019.1, Technical Description (2019b)
Soave, G.: Equilibrium constants from a modified Redlich-Kwong equation of state. Chem. Eng. Sci. 27(6), 1197–1203 (1972)
Søreide, I., Whitson, C.H.: Peng-Robinson predictions for hydrocarbons, CO2, N2, and H2 S with pure water and NaCI brine. Fluid Phase Equilib. 77, 217–240 (1992)
Vidyasagar, A., Patacchini, L., Panfili, P., Caresani, F., Cominelli, A., Gandham, R., Mukundakrishnan, K.: Full-gpu reservoir simulation delivers on its promise for giant carbonate fields. In: Third EAGE WIPIC Workshop: Reservoir Management in Carbonates, 2019. European Association of Geoscientists & Engineers, pp. 1–5 (2019)
Wei, L.: Sequential coupling of geochemical reactions with reservoir simulations for waterflood and EOR studies. SPE J. 17(02), 469–484 (2012)
Whitson, C.H., Brulé, M.R.: Phase behavior, 20. Society of Petroleum Engineers, Henry L. Doherty Memorial Fund of AIME (2000)
Yamamoto, H., Doughty, C.: Investigation of gridding effects for numerical simulations of CO2 geologic sequestration. Int. J. Greenh. Gas Control 5(4), 975–985 (2011)
Yan, W., Huang, S., Stenby, E.H.: Measurement and modeling of CO2 solubility in NaCl brine and CO2-saturated NaCl brine density. Int. J. Greenh. Gas Control 5(6), 1460–1477 (2011)
Yan, W., Michelsen, M.L., Stenby, E.H.: On application of non-cubic EoS to compositional reservoir simulation. In: SPE EUROPEC/EAGE Annual Conference and Exhibition. OnePetro (2011b)
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The results presented in this paper have been achieved in the furtherance of a cooperative development agreement between Stone Ridge Technology and Eni S.p.A.
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Panfili, P., Patacchini, L., Ferrari, A. et al. Implementation of Soreide and Whitson EoS in a GPU-based reservoir simulator. Comput Geosci 28, 341–354 (2024). https://doi.org/10.1007/s10596-023-10257-8
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DOI: https://doi.org/10.1007/s10596-023-10257-8