Numerical Simulation of Pressure Behavior In a Fractured Reservoir

Abstract

Abstract A simulation model of a reservoir with a symmetrical-horizontal fracture extending from the wellbore to the midpoint of the drainage radius was constructed. The mathematical equation was developed for the case of single-phase unsteady state fluid flow. A solution for an infinite reservoir was obtained numerically and used for pressure drawdown and buildup analysis. The pressure drawdown and buildup analysis. The numerical results shows that: 1. On pressure drawdown and buildup curves, two straight lines are obtained; the first straight line with lower slope yields the effective permeability of the matrix and fracture, and the second straight line with greater slope yields the permeability of matrix. 2. The time of bend between the straight lines increases with increase in fracture radius. As the fracture radius approaches infinity, only one straight line of the Odeh type is obtained. 3. Extrapolation of the first straight line portion of the buildup curve may lead to an incorrect value of the static reservoir pressure. Introduction Analysis of pressure buildup and drawdown data is recognized as a powerful tool by the production and reservoir engineer seeking to production and reservoir engineer seeking to characterize the reservoir. Most pressure analysis techniques have assumed homogeneous reservoirs, i.e. the porosity and permeability are constant. However, some prolific wells produce from fractured reservoirs. These produce from fractured reservoirs. These reservoirs contain two distinct types of porosity and permeability, namely fracture porosity and permeability, namely fracture and matrix. Since the fractured region has higher permeability, reservoir-engineering analysis based on a homogeneous reservoir may lead to erroneous results. The purpose of this study is to develop a mathematical model which will simulate the pressure drawdown and buildup curves that would be obtained from a reservoir with a symmetrical-horizontal fracture around the wellbore. The mathematical model is developed by assuming a cylindrical reservoir of drainage area of uniform thickness is penetrated by a single production well at its center. The two -dimensional diffusivity equation for single phase flow was used to obtain pressure buildup phase flow was used to obtain pressure buildup and drawdown curves. It was necessary to obtain a constant rate solution to the equation because of the mathematical complexities introduced by the fractured reservoir geometry.