Abstract

This paper set up a mathematical model of three-dimensional transient flow to describe the pressure behavior for horizontal well with wellbore storage and skin effect in naturally fractured infinite and box-shape-bounded reservoirs. On the basis of obtaining solutions of mathematical model, we study practical algorithms of the pressure response, and use methods of numerical integrating and numerical inversion of Laplace transforms to compute typical curves for recognizing flow regimes and ape curve well test analysis. Based on these, this paper further gives expression equation of dimension pressure in all flow regimes for horizontal well percolation, and analyzes mainly effect factor of the occurrence of the flow regimes. At the same time, this paper presents analysis methods of conventional well test and procedures of type curve analysis. These methods are used to interpret practical well testing data of a example horizontal well in Xinjiang of P.R. China, defined by Warren and Root10. The interporosity flow is modeled with the pseudo-steady state flow equation. The external boundary are both infinite and box-shape bounded reservoirs. Applying the superposition theorem includes fracture permeability, skin factor, wellbore storage coefficient. Storativity ratio, interporosity flow coefficients are obtained. Analysis methods of well test presented in this paper are reliable and applicable.

Introduction

Many papers1–6 had published for well test analysis methods of homogenous reservoirs. Recently several years, well test analysis methods of horizontal well in dual-porosity reservoirs had been reported. R. de S. Carvalho et al7 presented well test analysis method of dual-porosity infinite reservoir, R. Aguilera et al8 presented analytical solution for pressure drawdown and buildup analysis of horizontal well in anisotropic reservoirs with natural fractures, but wellbore storage was not considered. Kui-Fu Du et al9 presented transient pressure response of horizontal well in layered and naturally fractured reservoirs with dual-porosity behavior.

In this paper, we consider the dual-porosity model as Wellbore storage and skin effects. On the basis of obtaining solution of mathematical model, we present practical algorithms of the pressure response, and used methods of numerical integration and H. Stefest11 algorithm to compute pressure derivative typical curves for recognizing flow regimes and type curve for well test analysis.

Methods presented in this paper are used to interpret well testing data of a example horizontal well in Xinjiang of P. R. China, we obtained fracture permeability, skin factor, wellbore storage coefficient, Storativity ratio, interporosity flow coefficient.

Physical Model

We applies the dual-porosity model introduced by Warren and Root10. Fig.1 shows a schematic picture of horizontal well. To set up mathematical model of horizontal well transient flow, we establish the following additional hypotheses:

1. The reservoir is horizontal with constant fracture and matrix permeability (kf and km). It has uniform thickness(h), constant fracture and matrix porosity (•f and •m), the initial pressure is equal to constant (Pi).

2. The external boundary of reservoir is divided two cases, first case is infinite lateral extension, i.e. infinite reservoir, second case is box-shape bounded, i.e. rectangular reservoir, its length is "a" and width is "b".

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