A Pore-Network Model of In-Situ Combustion in Porous Media

Abstract

Abstract In-situ combustion in porous media find applications in a variety of problems. Existing models to date are based on a continuum description, in which effective porous media are used. In this paper, we consider the use of dual pore networks (pores and solid sites) for modeling the effect of the microstructure on combustion processes in porous media. The model accounts for flow and transport of the gas phase in the porespace, where convection predominates, and for heat transfer by conduction in the solid phase. Gas phase flow in the pores and throats is governed by Darcy's law. Heterogeneous combustion with one-step finite kinetics is assumed at the pore walls. The time-dependent problem is solved numerically using a fully implicit scheme. The validity of the model is tested against existing 1-D solutions, in which three types of combustion patterns arise, depending on the value of a dimensionless parameter related to the ratio of heat capacities. Then, we report on 2-D simulations for forward combustion. The development of sustained front propagation is studied as a function of various parameters, which include heat losses, instabilities, a correlated porespace and the distribution of fuel. Implications of the findings for continuum models are discussed. Introduction In-situ combustion (ISC) is a well-known process for the recovery of heavy oil from oil reservoirs. Extensive reviews of the method and its field applications have been provided in the literature (Prats, 1982). Even though one of the oldest techniques for heavy oil recovery, however, ISC is also one of the most complex. In addition to the common mechanisms it shares with conventional recovery methods, such as waterflooding and steamflooding, ISC involves the additional complexity of the oxidation reactions. These serve to, first, form the fuel in a regime of Low Temperature Oxidation (LTO) and, subsequently, provide the main combustion reaction under conditions of High Temperature Oxidation (HTO). The main goal of ISC is the sustained propagation of combustion fronts, to supply the necessary heat for viscosity reduction and the self-sustaining of the overall process. As a result, issues of front stability, sustained front propagation and possible extinction are of fundamental importance. A large number of studies have been published in the literature on ISC, addressing a wide range of issues, from the detailed kinetics of the reaction processes to mathematical models to field applications. Of specific interest to this study is the modeling of the combustion process. Typically, this is done using conventional continuum models, in which reaction rates, concentrations and temperatures are volume-averaged continuum variables. The solution of such models is then sought in the various applications of interest, including laboratory and field scales. This approach has validity as long as the following conditions hold: that the variables of interest, such as concentrations, temperature and reaction rates, do not involve large gradients in space at the underlying microscale, for volume-averaged quantities to be meaningful; and that the effective parameters used in the continuum models reflect fairly accurately the actual processes. Because of the strong non-linearities involved in reaction kinetics, particularly of the Arrhenius dependence of the true reaction rate on temperature,Equation the volume average of the rate will not have the same dependence, namelyEquation. if the local concentration or temperature vary significantly over the averaging volume.