Pressure Transient Behavior in Horizontal Wells and Hydraulically Fractured Vertical Wells With Non-Newtonian Fluid Flow in Porus Media: Non-Composite and Composite Reservoirs

Abstract

Two fluid regions are usually created during either water or polymer injection into an oil reservoir for enhanced oil recovery. The two fluid regions create a composite reservoir system that requires analytical solution that can be used to evaluate the injection performance. This study present a 2D solution for non-Newtonian fluid in the inner Zone coupled with infinite boundary in the outer Zone; using power law model. The outer Zone fluid can either be Newtonian or non-Newtonian. Moreover, the mathematical model is formulated such that either Zone can be with non-Newtonian power law fluid or Newtonian fluid. The infinite conductivity fractured solution obtained was compared with the ones obtained using the radial line source solution that had already been developed in the literatures and a perfect match was obtained. An application was made to three examples that have been presented in a previous work and satisfactory results were obtained. The dimensionless pressure drops during the early linear flow regime for all values of flow indices are the same, but with deviation during radial flow regime. Moreover, the existing work is limited to radial model in a vertical well, infinite conductivity hydraulic fracture, software simulation model and numerical model. Up to date, there has been no analytical work presented for horizontal well using power law model. Power law model best characterizes non-Newtonian rheological properties and the fluid flow in porous media. Today, horizontal well is widely being used in the exploitation of oil and gas in the industry; either as a producer or an injector. A reservoir where the flow of injected polymer solution during enhanced oil recovery and high viscosity crude oil exhibit non-Newtonian behavior, is better characterized with pressure transient with power law model. This fact has been established. This study also presents a 3-D power law model for analyzing pressure transient behavior in a reservoir with fluid flow that exhibits non-Newtonian behavior. The solution provided is semi-analytical and numerically inverted using Stehfest Algorithm. A step-by-step analytical procedure for analyzing each flow regime is developed. In order to validate the 3-D model, type curves were developed and matched with data provided from simulator in previous work. The step-by-step procedure was used to analyze an eclipse simulated data. There was consistency in the results that validated the analytical mathematical model. The 3-D analytical model developed is also applicable to composite reservoir with two distinct zones due to fluid and rock properties. The flow behavior index in both zones can either be 1.0 or less than 1.0. This is unique to this study. Furthermore, finite conductivity hydraulic fracture mathematically gives the general solution for transient pressure behavior in a fractured well. This study presents a semi-analytical solution and a numerical method which can be used to evaluate the performance of an injection operation in a finite conductivity fracture either in a homogeneous reservoir or a naturally fractured reservoir. The solution obtained was subjected to a validation process by comparing the estimated dimensionless wellbore pressure obtained with that of a previous work where numerical method was used. A good match was obtained. An application was also made to field examples that have been presented in a previous work and satisfactory results were obtained.