Fully implicit and fully coupled numerical scheme for discrete fracture modeling of shale gas flow in deformable rock

Du, Xin; Li, Qingyu; Xian, Yuxi; Lu, Detang

doi:10.1016/j.petrol.2021.108848

Cited by 13 publications

(6 citation statements)

References 36 publications

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“…where the fluid free energy F(S w , S n ) and chemical potentials 𝜇 𝛼 are given in ( 8)- (10). It is deduced from (37) that the model ( 41) obeys the following energy dissipation law…”

Section: Model Formulationmentioning

confidence: 99%

“…The rock compressibility caused by the pore fluid pressure has been recognized as another important factor influencing many subsurface processes including oil/gas production and geological stability. 1,2,[9][10][11][12] The isothermal rock compressibility refers to the change of the pore volume with respect to the pore fluid pressure. This phenomenon often occurs in the geological engineering and special oil reservoirs where the solid/rock particles have relatively loose structures and the rearrangement and movement of particles caused by the pore pressure may lead to the large change in the pore volume.…”

Section: Introductionmentioning

confidence: 99%

“…The classical models for two‐phase flow in porous media 3‐8 generally depend on multiple physical quantities including phase saturations, phase pressures, relative permeabilities and capillary pressure in addition to the absolute permeability and fluid viscosities. The rock compressibility caused by the pore fluid pressure has been recognized as another important factor influencing many subsurface processes including oil/gas production and geological stability 1,2,9‐12 . The isothermal rock compressibility refers to the change of the pore volume with respect to the pore fluid pressure.…”

Section: Introductionmentioning

confidence: 99%

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An energy stable, conservative and bounds‐preserving numerical method for thermodynamically consistent modeling of incompressible two‐phase flow in porous media with rock compressibility

Kou

Wang

Chen

et al. 2023

Numerical Meth Engineering

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Summary In this paper, we consider modeling and numerical simulation of incompressible and immiscible two‐phase flow in porous media with rock compressibility. Using the second law of thermodynamics, we rigorously derive a thermodynamically consistent mathematical model, which characterizes the two‐phase capillarity and rock compressibility through free energies, thereby following an energy dissipation law. We also derive a general and thermodynamically consistent formulation for the effective pore fluid pressure acting on rocks, which is a fundamental problem for two‐phase flow with rock compressibility. To solve the model effectively, we propose an energy stable numerical method, which can preserve multiple physical properties, including the energy dissipation law, full conservation law for both fluids and pore volumes, and positivity of porosity and saturations. Benefiting from the newly‐developed energy factorization approach and careful treatments for the effective pressure and porosity, the proposed scheme can inherit the energy dissipation law at the discrete level. The fully discrete scheme is constructed using a locally conservative cell‐centered finite difference method. The implicit strategy is applied to treat the upwind phase mobilities and porosity in the phase mass conservation equations and the porosity equation so as to conserve the mass of each phase as well as pore volumes. The positivity of porosity and saturations is proved without any restrictions on time step and mesh sizes. An efficient sequential iterative method is also developed to solve the nonlinear system resulting from the scheme. Finally, numerical results are given to verify the features of the proposed method.

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Section: Model Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An energy stable, conservative and bounds‐preserving numerical method for thermodynamically consistent modeling of incompressible two‐phase flow in porous media with rock compressibility

Kou

Wang

Chen

et al. 2023

Numerical Meth Engineering

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“…The public domain simulator Black Oil Applied Simulationn Tool (BOAST) (Fanchi, 1997) is used, which solves the non‐linear system of differential equations by finite differences with an IMPES (Implicit in Pressure, Explicit in Saturation) algorithm. Although the IMPES formulation has stability restrictions, its computational cost is lower than that of the fully implicit options (Du et al., 2021). It is worth highlighting the use of a free simulator that, with slight modifications, can model fracking and production in unconventional fields.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of fracking and gas production in shale gas reservoirs

Arenas Zapata,

Savioli,

Santos

et al. 2024

Geophysical Prospecting

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In this work, different stages of gas production in shale reservoirs are modeled. First, hydraulic fracturing is considered by injecting water at high pressures to crack the formation and increase the flow capacity of the reservoir. During the fluid injection, rock properties are modified and water appears in the stimulated area. Then, these changes can be detected through seismic monitoring. Finally, once the fracking stage is completed, the simulation of gas production begins. The simultaneous gas‐water flow in the injection and production stages is modeled using the Black‐Oil formulation. Furthermore, a fracture criterion is applied under the hypothesis of constant temperature and constant stress field in this first analysis of the problem. The numerical simulations allow us to analyze the propagation of the fracture and the behavior of the pore pressure and water saturation in the stimulated area. The advance of the fracturing fluid is delayed in relation to the breakdown of the rock. Besides, the presence of new fractures is detected by applying a poroviscoelastic wave propagation simulator that considers mesoscopic losses induced by heterogeneities in rock and fluids. After the fracture network is created, the injecton well becomes a producer, allowing the extraction of gas and the flowback of the injected fluid. The simulated gas flow rates are compared with those obtained by a simplified single‐phase analytical solution used for practical applications, achieving optimum matching results.This article is protected by copyright. All rights reserved

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“…7,8 For instance, during the oil/gas recovery, the injected water alters the pore fluid pressure and subsequently destroys the mechanical equilibria between fluids and solid skeletons, thereby leading to the non-negligible changes of solid/rock properties including porosity and permeability. 1,3,[9][10][11][12] The solid/rock compressibility model is one of the traditional models employed to account for the changes of solid/rock properties caused by the pore fluid pressure through the definition of solid/rock compressibility coefficients. [13][14][15] Such a model is simple and easy-to-implement in numerical simulation but limited to the situations with slight solid/rock changes.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamically consistent numerical modeling of immiscible two‐phase flow in poro‐viscoelastic media

Kou,

Salama,

Chen

et al. 2024

Numerical Meth Engineering

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Numerical modeling of immiscible two‐phase flow in deformable porous media has become increasingly significant due to its applications in oil reservoir engineering, geotechnical engineering and many others. The coupling between two‐phase flow and geomechanics gives rise to a major challenge to the development of physically consistent mathematical models and effective numerical methods. In this article, based on the concept of free energies and guided by the second law of thermodynamics, we derive a thermodynamically consistent mathematical model for immiscible two‐phase flow in poro‐viscoelastic media. The model uses the fluid and solid free energies to characterize the fluid capillarity and solid skeleton elasticity, so that it rigorously follows an energy dissipation law. The thermodynamically consistent formulation of the pore fluid pressure is naturally derived for the solid mechanical equilibrium equation. Additionally, the model ensures the mass conservation law for both fluids and solids. For numerical approximation of the model, we propose an energy stable and mass conservative numerical method. The method herein inherits the energy dissipation law through appropriate energy approaches and subtle treatments for the coupling between two phase saturations, the effective pore pressure and porosity. Using the locally conservative cell‐centered finite difference methods on staggered grids with the upwind strategies for saturations and porosity, we construct the fully discrete scheme, which has the ability to conserve the masses of both fluids and solids as well as preserve the energy dissipation law at the fully discrete level. In particular, the proposed method is an unbiased algorithm, that is, treating the wetting phase, the non‐wetting phase and the solid phase in the same way. Numerical results are also given to validate and verify the features of the proposed model and numerical method.

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Fully implicit and fully coupled numerical scheme for discrete fracture modeling of shale gas flow in deformable rock

Cited by 13 publications

References 36 publications

An energy stable, conservative and bounds‐preserving numerical method for thermodynamically consistent modeling of incompressible two‐phase flow in porous media with rock compressibility

An energy stable, conservative and bounds‐preserving numerical method for thermodynamically consistent modeling of incompressible two‐phase flow in porous media with rock compressibility

Numerical simulation of fracking and gas production in shale gas reservoirs

Thermodynamically consistent numerical modeling of immiscible two‐phase flow in poro‐viscoelastic media

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