A Mathematical Model of Thermal Oil Recovery in Linear Systems

Abstract

A generalized mathematical model is presented, which describes the thermal recovery of oil in linear systems with convective external heat loss. Three-phase fluid flow, conduction-convection heat transfer, chemical reaction between oxygen and oil and aqueous phase change are included, making the model applicable to a variety of thermal recovery processes.The complexity of the model requires that numerical solutions be obtained with a digital computer. T he numerical approximations of the partial differential equations are presented and the algorithm is discussed in detail.The analysis is applied to the detailed simulation of a forward-combustion laboratory tube experiment. The results of the simulation exhibit with reasonable accuracy all of the principal thermal and hydrodynamic characteristics observed in the laboratory (i.e., the propagation of a combustion zone, a steam plateau, and oil and water banks). Numerical variations in the parameters appearing in the external heat-loss term, the aqueous phasechange term, and the Arrhenius combustion term are examined, and their effects on the predicted temperature profiles, oil and water production histories, and the air-oil ratio are presented.In spite of an oversimplification in the chemical reaction mechanism and the considerable computer time required to obtain solutions, the model represents a major advance in the ability to simulate the phenomena observed in thermal recovery experiments.

Non-Adiabatic Effects on Combustion Front Propagation in Porous Media: Multiplicity of Steady States

“…This is as expected, as higher rates of heat transfer and/or thinner formations lead to larger heat losses. We remark that the lowest value of heat transfer coefficient used in Figure 12 is about double the value used by Gottfried [9] in his investigation. Figure 14 illustrates the effect of the injected oxygen concentration on the front temperature.…”

“…Baily and Larkin [8] provided simple heat transfer models in linear and radial geometries in the presence of a combustion zone of finite thickness. Gottfried [9] treated the combustion front as a discontinuity involving a point heat source, but without exploring the combustion zone structure. Beckers and Harmsen [lo] detailed the propagation of various regimes in in situ combustion and its variants, e.g.…”

Feasibility Study of In-Situ Combustion in Naturally Fractured Heavy Oil Reservoirs

“…This produced steam plateau consistant with experimental observation. Gottfried 26 developed an in-situ combustion numerical simulator accounting for most of the major phenomena occurring in the process such as three phase fluid flow, conduction and convection heat flow, aqueous phase change, reaction between oxygen and oil, and external heat losses.…”

Modeling and simulation of combustion fronts in porous media

“…In particular, for combustion processes in oil recovery, models and results of numerical simulations have been presented. One of the first models of combustion in a petroleum reservoir was formulated by Gottfried [1]. The model consists of a system of six partial differential equations describing the flow of oil, water, and gas through the porous medium, together with a chemical reaction between oxygen and oil.…”