Transient Flow Behavior of Horizontal Wells, Pressure Drawdown, and Buildup Analysis

Abstract

Summary Four flow periods may occur during the transient behavior of a horizontal well. Drawdown and buildup equations describing the flow behavior of each of the four flow periods are given. Methods for analyzing data obtained from testing the well to determine permeability anisotropy in the drainage volume of the well, as well as the skin factor, are presented. The calculation procedures are illustrated by examples. Introduction Transient pressure analysis of horizontal wells is considerably more complicated than that of vertical wells. This is due to the potential occurrence of four transient flow periods in contrast to the occurrence of essentially one flow period for vertical wells. In the case of a vertical well, the equations describing the transient flow behavior are derived assuming infinite horizontal extension of the reservoir. This assumption has resulted in a valid analysis because of the existence of only the radial flow period. Many authors(1–5) have employed the infinite or semi-infinite extension assumption of the reservoir in the x-y plane to obtain the transient flow behavior of a horizontal well. Because of the effect of the boundaries on the occurrence of the four flow periods, such an assumption could lead to erroneous conclusions. It could result in the occurrence and non-occurrence of two of the four flow periods when actually this may not happen. The transient flow behavior of a horizontal well requires that the actual physical system be unaltered. Thus, the analysis must be made on a drainage volume with closed boundaries, actual anisotropy, and the length and location of the well. In this paper, we provide equations for analyzing drawdown and buildup data obtained on a horizontal well. The equations were derived using a closed drainage volume, with arbitrary anisotropy, location, and length of the well. We also indicate the duration of each of the flow periods, and illustrate the method of analysis by examples. Theoretical Analysis The Physical Model. The physical model was reported in reference 6. It consists of a well of radius rw, and length L. The well is drilled in a box-shaped drainage volume, parallel to the y-direction. The dimensions of the drainage volume are: thickness=h, length (x-direction)=a, and width (y-direction)=b. The well has a length L b, and extends between y1 and y 2 . Its × and z locations are indicated by xo and zo respectively. It produces at a constant rate q (uniform flux). The permeabilities in the x-, y-, and z-directions are respectively kx, ky, and k z. The porosity f is constant, and the fluid is slightly compressible. All the boundaries of the drainage volume are sealed. The pressure in the drainage volume prior to producing the well, i.e., at t=0, is uniform and is equal to pi. At time t=0 +, we start to withdraw a quantity of fluid at the rate q from the well. We want to find the pressure drop ?p=pi-p as a function of time and space for t>0. The Physical Model. The physical model was reported in reference 6. It consists of a well of radius rw, and length L. The well is drilled in a box-shaped drainage volume, parallel to the y-direction. The dimensions of the drainage volume are: thickness=h, length (x-direction)=a, and width (y-direction)=b. The well has a length L b, and extends between y1 and y 2. Its × and z locations are indicated by xo and zo respectively. It produces at a constant rate q (uniform flux). The permeabilities in the x-, y-, and z-directions are respectively kx, ky, and k z. The porosity f is constant, and the fluid is slightly compressible. All the boundaries of the drainage volume are sealed. The pressure in the drainage volume prior to producing the well, i.e., at t=0, is uniform and is equal to pi. At time t=0 +, we start to withdraw a quantity of fluid at the rate q from the well. We want to find the pressure drop ?p=pi-p as a function of time and space for t>0.