Abstract
In the current paper, an iterative algorithm is developed to simulate the problem of two-phase flow with heat transfer in porous media. The convective body force caused by heat transfer is described by Boussinesq approximation throughout with the governing equations, namely, pressure, saturation, and energy. The two coupled equations of pressure and saturation are solved using the implicit pressure-explicit saturation (IMPES) scheme, while the energy equation is treated implicitly, and the scheme is called iterative implicit pressure, explicit saturation, implicit temperature (I-IMPES-IMT). In order to calculate the pressure implicitly, the equations of pressure and saturation are coupled by linearizing the capillary pressure which is a function of saturation. After that, the equation of saturation is solved explicitly. Then, the velocity is computed which is used in the energy equation to calculate the temperature implicitly. The cell-centered finite difference (CCFD) method is utilized for spatial discretization. Furthermore, a relaxation factor along is used with the Courant–Friedrichs–Lewy (CFL) condition. Finally, in order to illustrate the efficiency of the developed algorithm, error estimates for saturation and temperature for different values of time steps and number of iterations are presented. Moreover, numerical examples of different physical scenarios of heterogamous media are presented.
Highlights
In the reservoir simulation, there are two numerical methods for solving the governing equations, namely, implicit pressure, explicit saturation (IMPES) method, and the fully implicit method
We develop an iterative implicit pressure, explicit saturation, implicit temperature (I-IMPES-IMT) scheme to simulate the problem of non-isothermal two-phase flow in porous media
This paper dealt with the issue of non-isothermal two-phase flow in porous media
Summary
There are two numerical methods for solving the governing equations, namely, implicit pressure, explicit saturation (IMPES) method, and the fully implicit method. The model of two-phase flow in porous media can be solved numerically using a fully implicit scheme [1,2,3], or using an implicit-explicit (IMEX) one [4,5]. In [14], an iterative implicit pressure, explicit saturation, implicit concentration scheme was developed to solve the model of nanoparticle transport with two-phase flow in porous media.The linearized capillary pressure function was used to couple the implicit saturation and pressure equations, while the concentration equations were treated implicitly. We develop an iterative implicit pressure, explicit saturation, implicit temperature (I-IMPES-IMT) scheme to simulate the problem of non-isothermal two-phase flow in porous media.
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