ABSTRACT
The macro scale equations have received attention in recent years and thermo-hydrodynamic theories have been developed including interfacial effects (Hassanizadeh & Gray 1990, Soria & De Lasa 1991, Bousquet-Melou et al. 2002). Since averaged quantities are of engineering interest, one of the main approaches to multiphase flow modeling has been to average (in time, space, over an ensemble or in some combination of these) the original local instantaneous conservation equations. The volume averaging method has been widely used to develop the transport equation for multiphase flow (Gray 1975, Whitaker 1986, Nakayama et al. 2001, Bousquet-Melou et al. 2002, Andrew et al. 2003, Espinosa-Paredes & Cazarez-Candia 2004, Duval et al. 2004), and it can be used to solve an in-situ combustion problem. Predictive models for in-situ combustion have been formulated since early field applications of the process. Depending of their basic approach (analytical, numerical, scaled experimental, empirical, or correlative) and the specific objectives under which they were developed, they vary not only in complexity but also in applicability regarding process mode and parameters. For example, Genrich & Pope (1985) developed a simplified performance predictive model for in-situ combustion processes where they shown the calculations of production oil, gas, and water from forward in-situ combustion processes for given reservoir characteristics and injection rates. The model combines specific descriptions of fractional flow; combustion reactions, phase behavior, and heat transfer. Onyekonwu et al. (1986) discussed the effects of some parameters on in-situ combustion process derived from experimental and simulation studies of laboratory in-situ combustion recovery. On the other hand, Lu &Yortsos (2001) developed a pore-network model for in-situ combustion in porous media. They used dual pore networks (pores and solid sites) for modeling the effect of the microstructure on combustion processes. The model accounts for the transport of the gas phase in the pore space and for the heat transfer by conduction in solid phase. The development of sustained front propagation was studied as a function of various parameters, which include heat losses, instabilities, a correlated pore space and the distribution of fuel.
