Mathematical Description of Detergent Flooding in Oil Reservoirs

Abstract

Abstract This paper presents a mathematical description of detergent flooding of oil reservoirs. With several assumptions, this description reduces to a hyperbolic system of partial differential equations. The method of characteristics proves to be a suitable method of solution, particularly because multiple shock behavior is inherent in the system. Introduction For many years the problem of increasing ultimate recovery of oil from a reservoir has been a subject of interest to the oil industry. At present, a standard secondary recovery technique is to flood the reservoir with water when natural forces of the system are depleted. The permeability characteristics of the rock, together with interfacial forces which exist between the two fluids and porous material, allow only part of the oil in the rock formation to be recovered by water flooding. Laboratory experiments have shown that when detergents are added to the flooding water, flow properties of oil in a porous rock are improved. This improvement results in greater oil recovery. Even though higher recoveries are obtained using detergents, extra cost associated with the method may make it economically unsatisfactory. To establish economic feasibility requires either extensive field trials, or laboratory tests together with a calculation method describing field behavior. Pilot tests with field systems take years to complete; then the results must be interpreted. The interpretation is often no more certain than predictions based on laboratory data. For these reasons we have developed the mathematical representation of detergent flooding discussed here. The mathematical solution can be used with laboratory tests for detergent flood evaluation.