Well Test Analysis of Data Dominated by Storage and Skin: Non-Newtonian Power-Law Fluids

Abstract

Summary. We examine pressure falloff behavior dominated by storage and skin subsequent to the injection of a non-Newtonian power-law fluid. New solutions to analyze falloff tests are presented in a form suitable for analyzing field data. The effective wellbore concept is used to combine the wellbore storage constant and skin factor. This phase of our work required extensions to the effective wellbore radius concept (for power-law fluids) given in the literature. To improve analysis procedures, we examine the use of the pressure-derivative technique. We discuss the advantages of this method for the problem under consideration. Introduction We examine pressure falloff behavior dominated by storage and skin subsequent to the injection of a non-Newtonian power-law fluid. This problem was considered in 1980 by Ikoku and Ramey as an extension of their earlier work, which had neglected the influence of wellbore storage effects. New procedures to analyze pressure falloff data discussed in Ref. 2 are also presented by Odeh and Yang. Ikoku and Ramey, as well as Odeh and Yang, obtained approximate closed-form (analytic) solutions by linearizing the nonlinear partial-differential equation that governs the flow of power-law fluids through porous media. Recently, we showed that power-law fluids through porous media. Recently, we showed that Odeh and Yang's results were more appropriate for the analysis of injection data. We also showed that corrections are necessary if the linearized solutions are used to analyze pressure falloff data. These corrections are necessary because the assumption used to linearize the partial-differential equation is not valid during a fall-off period. In this work, we re-examine falloff data in light of the results presented in Ref. 4 and show that corrections are needed if the presented in Ref. 4 and show that corrections are needed if the linearized solutions are used to analyze pressure falloff data influenced by storage and skin. Perhaps more important, we combine the variables of interest and present solution,- that are more convenient for analyzing field data. We use methods similar to that proposed by Earlougher and Kersch to combine the wellbore storage constant and the skin factor. This phase of our work required extensions to the effective wellbore radius concept (for power-law fluids) given by Ikoku and Ramey. We demonstrate that for certain combinations of skin factor and power-law index. the effective wellbore radius vanishes this observation may explain poor injectivity in many polymer floods. To improve analysis procedures, we examine the use of the pressure-derivative technique and discuss the advantages of this Method in analyzing pressure falloff data for the problem of interest. problem of interest. Mathematical Model and Definitions The mathematical model considered here is similar to that examined in Ref. 1. We examine the flow of a slightly compressible fluid in a uniform porous medium of constant thickness. Gravitational effects are assumed to be negligible. The viscosity of the fluid is assumed to obey the Ostwald-de Waele power-law model. In this study, we consider a non-Newtonian pseudoplastic fluid. The well is assumed to penetrate the reservoir completely: fluid is injected at a constant surface rate. We incorporate the skin region by assuming that the skin zone extends over a finite radius from the sandface and that the permeability of the skin region is different from the formation permeability. Wellbore storage effects are considered. Falloff responses are simulated by closing the well (at the surface) and then noting the change in pressure with time. Unless explicitly stated, the influence of the outer boundary, is assumed to be negligible. If we consider the influence of the outer boundary, then we assume that the outer boundary is at constant pressure. (For the problem under consideration, this is the appropriate outer boundary condition.) All results presented here were obtained by a finite-difference model. Details of the model and the verification procedures used are discussed in detail in Ref. 4. Additional details are given in Appendix A. For purposes of generality, results are presented in dimensionless form. The dimensionless wellbore pressure, PwD, is defined by the following equation: (1) when k = formation permeability, h = formation thickness, q = injection rate (assumed to be positive), pi = initial reservoir pressure, Pwf= flowing wellbore pressure, B = FVF, and u* = characteristic viscosity given by (2) Here, rw, is the well radius and Ff is the bed factor defined by (3) where K = Ostwald-de Waele power-law coefficient, n = Ostwald-de Waele power-law index (n less than 1 for a pseudoplastic fluid), and o = porosity of the porous medium. Dimensionless time, tD, is defined by the following relationship: (4) where t = injection time and ct = system compressibility. SPEFE P. 1007