We consider a non-isothermal compositional gas liquid model for the simulation of well operations in geothermal processes. The model accounts for phase transitions assumed to be at thermodynamical equilibrium and is based on a hydrodynamical Drift Flux Model (DFM) combined with a No Pressure Wave approximation of the momentum equation. The focus of this work is on the design of a robust discretization accounting for slanted and multibranch wells with the ability to simulate both transient behavior such as well opening as well as coupled simulations at the time scale of the reservoir. It is based on a staggered finite volume scheme in space combined with a fully implicit Euler time integration. The construction of consistent and stable numerical fluxes is a key feature for a robust numerical method. This is achieved by combining a monotone flux approximation for the phase superficial velocities with an upwind approximation of the phase molar fractions, density and enthalpy. In order to facilitate the coupling of the well and reservoir models, the Newton linearization accounts for the elimination of the hydrodynamical unknowns leading to Jacobian systems using the same primary unknowns than those of the reservoir model. The efficiency of our approach is investigated on both stand alone well test cases without and with cross flow, and on a fully coupled well-reservoir simulation.
Keywords: thermal well model, drift flux model, liquid gas compositional model, geothermal system, multi-segmented well, finite volume scheme, staggered finite volume, monotone flux, Coats formulation.
Daniel Castanon Quiroz 1; Laurent Jeannin 2; Simon Lopez 3; Roland Masson 4
CC-BY 4.0
@article{SMAI-JCM_2025__11__203_0,
author = {Daniel Castanon Quiroz and Laurent Jeannin and Simon Lopez and Roland Masson},
title = {Multi-segmented non-isothermal compositional liquid gas well model for geothermal processes},
journal = {The SMAI Journal of computational mathematics},
pages = {203--231},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {11},
year = {2025},
doi = {10.5802/smai-jcm.123},
language = {en},
url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.123/}
}
TY - JOUR AU - Daniel Castanon Quiroz AU - Laurent Jeannin AU - Simon Lopez AU - Roland Masson TI - Multi-segmented non-isothermal compositional liquid gas well model for geothermal processes JO - The SMAI Journal of computational mathematics PY - 2025 SP - 203 EP - 231 VL - 11 PB - Société de Mathématiques Appliquées et Industrielles UR - https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.123/ DO - 10.5802/smai-jcm.123 LA - en ID - SMAI-JCM_2025__11__203_0 ER -
%0 Journal Article %A Daniel Castanon Quiroz %A Laurent Jeannin %A Simon Lopez %A Roland Masson %T Multi-segmented non-isothermal compositional liquid gas well model for geothermal processes %J The SMAI Journal of computational mathematics %D 2025 %P 203-231 %V 11 %I Société de Mathématiques Appliquées et Industrielles %U https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.123/ %R 10.5802/smai-jcm.123 %G en %F SMAI-JCM_2025__11__203_0
Daniel Castanon Quiroz; Laurent Jeannin; Simon Lopez; Roland Masson. Multi-segmented non-isothermal compositional liquid gas well model for geothermal processes. The SMAI Journal of computational mathematics, Volume 11 (2025), pp. 203-231. doi : 10.5802/smai-jcm.123. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.123/
[1] Two-phase geothermal model with fracture network and multi-branch wells, SMAI J. Comput. Math., Volume 9 (2023), pp. 121-149 | DOI | MR | Zbl
[2] Wellbore Models GWELL, GWNACL, and HOLA, user’s guide, 1991 http://www.osti.gov/scitech/servlets/purl/5785189 (Earth Sciences Division, Lawrence Berkeley National Laboratory, University of California. Issue: LBL-31428 Volume: LBL-31428)
[3] Modeling of coupled wellbore-reservoir flow in steam-like supercritical geothermal systems, Geothermics, Volume 86 (2020), 101793 https://linkinghub.elsevier.com/retrieve/pii/s0375650519302652 (Accessed 2023-10-15) | DOI
[4] Parallel Geothermal Numerical Model with Fractures and Multi-Branch Wells, ESAIM: ProcS, Volume 63 (2018), pp. 109-134 | DOI | Zbl
[5] Non-isothermal compositional liquid gas Darcy flow: formulation, soil-atmosphere boundary condition and application to high-energy geothermal simulations, Comput. Geosci., Volume 23 (2019) no. 3, pp. 443-470 | DOI | MR | Zbl
[6] A multi-feedzone geothermal wellbore simulator (1987) https://www.osti.gov/biblio/6569407 (Technical report) | DOI
[7] Well flow models for various numerical methods, Int. J. Numer. Anal. Model., Volume 6 (2009), pp. 375-388 | MR | Zbl
[8] Transient Multiphase Flow: Past, Present, and Future with Flow Assurance Perspective, Energy Fuels, Volume 26 (2012) no. 7, pp. 4137-4144 (Accessed 2023-10-11) | DOI
[9] Thermohydraulique des réacteurs nucléaires, Génie atomique, EDP Sciences, 2008 | DOI
[10] On some upstream weighting schemes for oil recovery simulation, Les Annales de l’Enit, Volume 4 (1990) no. 2
[11] The Wellbore Simulator FloWell - Model Enhancement and Verification, World Geothermal Congress 2015 (2015)
[12] Implicit Hybrid Upwind scheme for coupled multiphase flow and transport with buoyancy, Comput. Methods Appl. Mech. Eng., Volume 311 (2016), pp. 599-624 | DOI | MR | Zbl
[13] Prediction of Multiphase Flow in Pipelines: Literature Review, Ingenieria y Ciencia, Volume 11 (2015) no. 22, pp. 213-233 (Accessed 2023-10-11) | DOI
[14] Numerical study of the effects of CO gas in geothermal water on the fluid-flow characteristics in production wells, Eng. Appl. Comput. Fluid Mech., Volume 15 (2021) no. 1, pp. 111-129 (Accessed 2023-10-10) | DOI
[15] Advanced well model for superhot and saline geothermal reservoirs, Geothermics, Volume 105 (2022), 102529 | DOI
[16] A fully-coupled thermal multiphase wellbore flow model for use in reservoir simulation, J. Petroleum Sci. Eng., Volume 71 (2010) no. 3, pp. 138-146 (Fourth International Symposium on Hydrocarbons and Chemistry) | DOI
[17] 40 years of Dogger aquifer management in Ile-de-France, Paris Basin, France, Geothermics, Volume 39 (2010) no. 4, pp. 339-356 | DOI
[18] Transient simulation of two-phase flows in pipes, Int. J. Multiphase Flow, Volume 24 (1998) no. 5, pp. 739-755 | DOI | Zbl
[19] T2Well-An integrated wellbore-reservoir simulator, Comput. Geosci., Volume 65 (2014), pp. 46-55 | DOI
[20] Interpretation of Well-Block Pressures in Numerical, SPE J., Volume 18 (1978) no. 03, pp. 183-194 | DOI
[21] Interpretation of Well-Block Pressures in Numerical Reservoir Simulation with Nonsquare Grid Blocks and Anisotropic Permeability, SPE J., Volume 23 (1983) no. 03, pp. 531-543 | DOI
[22] Exsolving two-phase flow in oil wells, Geophys. Astrophys. Fluid Dyn., Volume 114 (2020) no. 3, pp. 283-305 (Accessed 2023-10-15) | DOI | MR | Zbl
[23] The effect of calcite deposition on geothermal well in flow performance, Geothermics, Volume 28 (1999) no. 3, pp. 425-444 | DOI
[24] Drift-Flux Modeling of Two-Phase Flow in Wellbores, SPE J., Volume 10 (2005) no. 01, pp. 24-33 | DOI
[25] Steady-state Multiphase Flow: Past, Present, and Future with Flow Assurance Perspective, Energy Fuels, Volume 26 (2012) no. 7, pp. 4145-4157 (Accessed 2023-10-11) | DOI
[26] Simulation of complex transient flows in geothermal wells, Geothermics, Volume 108 (2023), 102631 | DOI
[27] A transient geothermal wellbore simulator, Geothermics, Volume 110 (2023), 102653 | DOI
[28] A review of mathematical models for geothermal wellbore simulation, Geothermics, Volume 97 (2021), 102255 | DOI
[29] The No Pressure Wave (NPW) Model: Application to Oil and Gas Transport, Third International Symposium on Finite Volume for Complex Applications Porquerolles France (2002) | Zbl
[30] One-dimensional two-phase flow, McGraw-Hill, 1969
[31] Parallel numerical modeling of hybrid-dimensional compositional non-isothermal Darcy flows in fractured porous media, J. Comput. Phys., Volume 345 (2017), pp. 637-664 | DOI | MR | Zbl
[32] A rigorous approach to scale formation and deposition modelling in geothermal wellbores, Geothermics, Volume 87 (2020), 101841 https://linkinghub.elsevier.com/retrieve/pii/s0375650519303554 (Accessed 2023-08-23) | DOI
[33] Average Volumetric Concentration in Two-Phase Flow Systems, J. Heat Transfer, Volume 87 (1965) no. 4, pp. 453-468 https://asmedigitalcollection.asme.org/heattransfer/article/87/4/453/429617/average-volumetric-concentration-in-twophase-flow (Accessed 2023-10-15) | DOI
[34] Average volumetric concentration in two-phase flow systems, J. Heat Transfer, Volume 87 (1965), pp. 453-458 | DOI
Cited by Sources: