The Effect of Water Injection on Sustained Combustion in a Porous Medium
Authors: Beckers H.L. , Harmsen G.J. 
Published: December 2007

Abstract
This paper gives a theoretical description of the various semisteady states that may develop if in an in-situ combustion process water is injected together with the air. The investigation bas been restricted to cases of one-dimensional flow without heat losses, such as would occur in a narrow, perfectly insulated tube. perfectly insulated tube. Different types of behavior can be distinguished for specific ranges of the water/air injection ratio. At low values of this ratio the injected water evaporates before it reaches the combustion zone, while at high values it passes through the combustion zone without being completely evaporated, but without extinguishing combustion. At intermediate values and at sufficiently high fuel in which all water entering the combustion zone evaporates before leaving it. Formulas are presented that give the combustion zone velocity as a function of water/air injection ratio for each of the possible situations.

Introduction
In-situ combustion of part of the oil in an oil-bearing formation has become an established thermal-recovery technique, even though its economic prospects are limited by inherent technical drawbacks. The process has been extensively investigated both in the laboratory and in the field, while theoretical studies have also been made. The latter studies showed how performance was affected by various physical and chemical phenomena, such as conduction and convection of phenomena, such as conduction and convection of heat, reaction rate and phase changes. The degree of simplification determined whether these studies were of an analytical or a numerical nature. Recently an improvement of the process has been proposed. This modification involves the proposed. This modification involves the injection of water together with the air. The water serves to recuperate the heat stored in the burned-out sand, which would otherwise be wasted. This heat is now used to evaporate water. The steam thus formed condenses downstream of the combustion zone, where it displaces oil. At sufficiently high water-injection rates unevaporated water is bound to enter the combustion zone because more heat is required for complete evaporation than is available in the hot sand. Experiments showed that even under these conditions combustion is maintained. The improvement consists in a lower oxygen consumption per barrel of oil displaced and lower combustion-zone temperatures. This paper gives a theoretical description of this so-called wet-combustion process as described by Dietz and Weijdema. The prime object is to answer the basic question whether at any water/air injection ratio this process can be steady so that combustion does not die out. This objective justifies a number of assumptions that do not entirely correspond to physical reality, but that owe necessary for a physical reality, but that owe necessary for a tractable analytical treatment. This treatment is limited to the following idealized conditions.The process occurs in a perfectly insulated cylinder of unit cross-sectional area and infinite length.The Hudds are homogeneously distributed over the cross-section of the cylinder.Exchange of heat between the fluid phases and between fluids and matrix is instantaneous, so that in any cross-section the fluid phases are in equilibrium and the temperatures of fluids and porous matrix are the same. porous matrix are the same.Pressure chops over distances of interest are small compared with the pressure itself. (Pressure is taken to be constant.)Injection rates are constant, and a steady state has already been obtained. The second assumption implies that no segregation of liquid and gas occurs. Experimentally this might be achieved by using small-diameter tubes, where segregation is largely compensated by capillarity.
SPEJ
P. 145