A unified numerical framework model for simulating flow, transport, and heat transfer in porous and fractured media

Abstract

A Unified Numerical Framework Model for Simulating Flow, Transport, and Heat Transfer in Porous and Fractured Media Yu-Shu Wu Earth Sciences Division, Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, CA 94720, USA ABSTRACT It has long been recognized that a common ground exists between governing equations used for describing various flow and transport phenomena in porous media. Put another way they are all generally based on the same form of mass and/or energy conservation laws. This implies that there may exist a unified formulation and numerical scheme applicable to modeling all of these physical processes. This paper explores such a possibility and proposes a generalized framework, as well as a mathematical formulation for modeling all known transport phenomena in porous media. Based on this framework, a unified numerical approach is developed and tested using multidimensional, multiphase flow, isothermal and nonisothermal reservoir simulators. In this approach, a spatial domain of interest is discretized with an unstructured grid, then a time discretization is carried out with a backward, first-order, finite-difference method. The final discrete nonlinear equations are handled fully implicitly, using Newton iteration. In addition, the fracture medium is handled using a general dual- continuum concept with continuum or discrete modeling methods. A number of applications are discussed to demonstrate that with this unified approach, modeling a particular porous- medium flow and transport process simply becomes a matter of defining a set of state variables, along with their interrelations or mutual influence. 1. INTRODUCTION Since the late 1950s, significant progress has been made in developing and applying numerical simulation techniques in petroleum engineering [3,1,12,17] and in groundwater literature [9,10]. Because of its generality and effectiveness in handling subsurface multiphase flow and transport problems, the numerical simulation technique has become the major tool used by scientists and engineers in studies of flow and transport processes within a porous medium. Numerical modeling approaches currently used for simulating multiphase flow and transport processes are generally based on methodologies developed for petroleum and geothermal reservoir simulations, as well as groundwater modeling. They involve solving fully coupled formulations describing these processes, using finite-difference or finite-element schemes with a volume-averaging approach. Continual research effort, driven by the need to develop underground natural resources and resolve subsurface contamination problems, has developed and provided many numerical modeling approaches and models for field applications. Mathematical modeling techniques