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The Effects of Linearization on Solutions of Reservoir Engineering Problems

Abstract The natural processes are nonlinear. Each property is affected by the variation of other properties existing in a process. However, it is necessary to impose some simplification and linearization in order to obtain numerical description for the majority of the problems in applied sciences. The simplification may take place in mathematical formulation and/or during numerical evaluation of a problem. This article investigates the effects of nonlinearity in the flow equation of a petroleum reservoir. The petroleum industry is well known for its intense use of computer models that employ various levels of linearization. Because the computational operation is repeated numerous times for billions of discrete grid blocks, any systematic error induced by linearization can have profound impact on predicted results. In this article, the dependency of the fluid and formation properties on the variation of the reservoir pressure is evaluated during the solution of the flow equation using the engineering approach. The continuous functions and piecewise functions are applied to approximate the variation of viscosity, fluid formation volume factor, and permeability. The computational results are compared with the linearized approximation for the variation of these properties. The approximation that imposes linearization on the mathematical formulation is also evaluated. The continuous nonlinear functions are not appropriate to approximate the variation of a process property. The best approximation may be obtained using the piecewise function such as a spline function of different orders.