Well Test Simulation for Dual Porosity-Dual Permeability Using Orthogonal Collocation

Abstract

Abstract This paper presents a new way to numerically simulate flow in Dual Porosity - Dual Permeability system which is solved rigorously with wellbore storage and skin. This paper shows that the use of Orthogonal Collocation method is feasible and that, in many cases, it results in solutions that are more realistic than those resulted from numerical inversion of Laplace transform. There are, however, certain disadvantages. For example, oscillation of the pressure derivative which can be overcome by using Orthogonal Collocation on Finite Element (OCFE) in which programming effort are usually in excess of that required by a finite- difference or numerical Laplace inversion scheme. Even so, it is felt that the potential of the technique is sufficient justification for this work and for a continuing effort to apply it to well test simulation problems. Dual Porosity - Dual Permeability well testing problem is described by a complex set of nonlinear partial differential equations. Their solution is normally achieved analytically using Laplace transform or numerically through the use of numerical inverting methods of the Laplcace transform like Stehfest and Crump. This paper is an extension to the paper SPE 120668 that introduced the method for the basic well test problem. The primary objective of this paper is to investigate the feasibility of using Orthogonal Collocation on well test in Dual Porosity - Dual Permeability system. Since this work was primarily concerned with the feasibility of Orthogonal Collocation simulation, no attempt was made to study a wide spectrum of cases of well test problems. However, a few typical applications are presented and some of the results are compared with those derived from analytical and numerical inversion.