A model for moisture and heat flow in fractured unsaturated porous media

Amini

Numerical Meth Engineering

2021

In this article, a computational model is presented for the analysis of coupled thermo-hydro-mechanical process with phase change (evaporation/condensation) in fractured porous media in order to model multiphase fluid flows, heat transfer, and discontinuous deformation by employing the extended finite element method. The ideal gas law and Dalton's law are employed to consider vapor and dry air as miscible gases. To take into account the phase change, latent heat and specific vapor enthalpy are incorporated into the physical model. The set of governing equations consists of linear momentum for the solid-phase, energy balance equation and mass conservation equations of water species (liquid and vapor) and dry air, which are derived within the framework of the generalized Biot's theory. The weak forms are presented in terms of the displacement, water pressure, capillary pressure, and temperature as the primary variables. The spatial and temporal discretizations are carried out applying the extended finite element method and the generalized Newmark scheme, respectively, resulting in the final system of fully coupled nonlinear equations. Finally, several numerical examples are solved to demonstrate not only the robustness of the proposed computational model but also the effect of the crack orientation, intrinsic permeability, and elastic modulus on the fluid flow patterns, relative humidity, and temperature distribution. Moreover, an edge-crack propagation is investigated under mode I fracture due to drying conditions.

Section: Introductionmentioning

confidence: 99%

Modeling non‐isothermal two‐phase fluid flow with phase change in deformable fractured porous media using extended finite element method

Amini

Numerical Meth Engineering

2021

“…In fact, the coupling terms between the thermal partition and the hydraulic partition should be omitted to symmetrize the Jacobian matrix. The symmetrized Jacobian matrix is a common practice in other similar studies 44,49 . The exclusion of these coupling terms results in two decoupled partitions in the Jacobian matrix, which can be solved by the staggered iteration scheme rather than a monolithic solution.…”

Section: Spatial and Temporal Discretizationmentioning

confidence: 99%

“…modeled the thermo‐hydro‐mechanical problems in saturated fractured porous media using the X‐FEM. Varnosfaderani et al 44 . employed the X‐FEM to investigate the propagation of fracture in unsaturated porous media under non‐isothermal conditions.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of cold and hot water injection into naturally fractured porous media using the extended–FEM and an equivalent continuum model

Pirmoradi

Num Anal Meth Geomechanics

2021

In this paper, a computational technique is presented for the isothermal and non‐isothermal water injection into naturally fractured oil reservoirs. A remarkable number of naturally fractured reservoirs contain relatively heavy oils that could not be extracted economically; hence, the thermal recovery methods are extensively used for such reservoirs. In this study, the effectiveness of hot water injection over cold (isothermal) water injection in oil production is quantified. The influence of long and short fractures and their alignments on oil recovery are discussed. To this end, a 2D model for two‐phase fluid flow and heat transfer is presented. The medium is assumed to be partially saturated with water as the wetting phase and oil as the non‐wetting phase. The governing equations consist of the energy balance equation together with the continuity equations of both fluid phases. To take the long (macro) fractures into account, the extended finite element method is employed by considering permeable fracture faces; accordingly, the mass and heat transfer between the fracture and the matrix are captured accurately. In addition, the network of short (micro) fractures is incorporated by an equivalent continuum model. Several numerical examples are presented to demonstrate the influence of injection temperature, initial reservoir temperature, and the long and short fractures on oil production. Furthermore, the simultaneous effect of the macro‐ and micro‐fractures along with the injection temperature are examined. The results show that the proposed computational model is a promising tool that can be used in the cold or hot water injection, and can be employed in the economic feasibility studies of recovery methods in the future.

“…This strategy has been recently applied to various problems, for instance, see Refs. 38 and 47. Hence, the Jacobian matrices can be modified to become symmetric.…”

Section: Discretization Of Equationsmentioning

confidence: 99%

“…The X‐FEM was applied by Khoei et al 37 in THM modeling of saturated porous media with impermeable discontinuities. Varnosfaderani et al 38 proposed the X‐FEM to model the moisture and heat flow in fractured unsaturated porous media, in which the passive‐air‐phase was taken into account together with the phase change due to increase of the temperature. Arzanfudi and Al‐Khoury 39 presented a mixed FEM/X‐FEM model for thermo‐hydrodynamic‐mechanical multiphase flow simulation of CO 2 geo‐sequestration in fracturing porous media, in which the Darcy law was used for the fluid flow in the matrix domain and the Navier‐Stokes equation was utilized for the fracture domain.…”

Section: Introductionmentioning

confidence: 99%

Thermo‐hydro‐mechanical modeling of fracturing porous media with two‐phase fluid flow using X‐FEM technique

Num Anal Meth Geomechanics

2020

In this paper, a fully coupled thermo-hydro-mechanical model is presented for two-phase fluid flow and heat transfer in fractured/fracturing porous media using the extended finite element method. In the fractured porous medium, the traction, heat, and mass transfer between the fracture space and the surrounding media are coupled. The wetting and nonwetting fluid phases are water and gas, which are assumed to be immiscible, and no phase-change is considered. The system of coupled equations consists of the linear momentum balance of solid phase, wetting and nonwetting fluid continuities, and thermal energy conservation. The main variables used to solve the system of equations are solid phase displacement, wetting fluid pressure, capillary pressure, and temperature. The fracture is assumed to impose the strong discontinuity in the displacement field and weak discontinuities in the fluid pressure, capillary pressure, and temperature fields. The mode I fracture propagation is employed using a cohesive fracture model. Finally, several numerical examples are solved to illustrate the capability of the proposed computational algorithm. It is shown that the effect of thermal expansion on the effective stress can influence the rate of fracture propagation and the injection pressure in hydraulic fracturing process. Moreover, the effect of thermal loading is investigated properly on fracture opening and fluids flow in unsaturated porous media, and the convective heat transfer within the fracture is captured successfully. It is shown how the proposed computational model is capable of modeling the fully coupled thermal fracture propagation in unsaturated porous media.