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

Abstract

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.

Modeling fluid flow in fractured porous media: a comparative analysis between Darcy–Darcy model and Stokes–Brinkman model

“…Different numerical schemes depend on the discretization method for simulating fluid transport in fractured media under the DFM (Formaggia et al 2020). They include the finite volume method (Mehrdoost 2022;Ahmed et al 2015;Gläser et al 2017), mimetic finite difference method (Huang et al 2014), the finite element method (Zhang et al 2013;Alotaibi et al 2022), mixed finite element method (Younes et al 2023;Fu and Yang 2022;He et al 2021a, b) and extended finite element method (Wang et al 2020;Mortazavi et al 2022) etc. Researchers are also looking into reduced-order models and machine-learning methods to speed up DFM simulations while maintaining accuracy (de Hoop et al 2022;He et al 2020;Liu et al 2017;Garipov et al 2016).…”

FEM‐based dual length‐scale simulation of hydrothermal ore‐forming systems involving convective flow in fluid‐saturated porous media

“…It should be pointed out that not only can nonlinearly coupled problems involving multiple physical processes be widely encountered in hydrothermal ore-forming systems, but also they can be broadly found in enhanced geothermal systems. [12][13][14][15][16][17][18][19][20] For example, to computationally simulate an enhanced geothermal system, a nonlinearly coupled problem involving heat transfer (i.e., thermal), pore-fluid flow (i.e., hydraulic) and rock deformation (i.e., mechanical) processes has been extensively considered in recent years. [12][13][14][15][16][17][18][19][20] However, compared with simulating enhanced geothermal systems, chemical reaction processes must be considered in the computational simulations of hydrothermal ore-forming systems.…”

“…[12][13][14][15][16][17][18][19][20] For example, to computationally simulate an enhanced geothermal system, a nonlinearly coupled problem involving heat transfer (i.e., thermal), pore-fluid flow (i.e., hydraulic) and rock deformation (i.e., mechanical) processes has been extensively considered in recent years. [12][13][14][15][16][17][18][19][20] However, compared with simulating enhanced geothermal systems, chemical reaction processes must be considered in the computational simulations of hydrothermal ore-forming systems. Otherwise, an ore deposit cannot be quantitatively evaluated in a hydrothermal ore-forming system.…”

“…It should be pointed out that not only can nonlinearly coupled problems involving multiple physical processes be widely encountered in hydrothermal ore‐forming systems, but also they can be broadly found in enhanced geothermal systems 12–20 . For example, to computationally simulate an enhanced geothermal system, a nonlinearly coupled problem involving heat transfer (i.e., thermal), pore‐fluid flow (i.e., hydraulic) and rock deformation (i.e., mechanical) processes has been extensively considered in recent years 12–20 .…”

A bi‐fidelity model for hydraulic fracturing

“…[8] authors proposed he hybrid FEM approach, in Ref. [9] the extended FEM approach, in Ref. [10] the unstructured mesh algorithm, the isogeometric analysis, 11 and the implicit level set algorithm (ILSA) 4–7,12 …”