Rate Decline Analysis of Horizontal Wells with Multiple Variable Conductivity and Uneven Distributed Fractures

Abstract

In this paper, a new rate decline analysis model of horizontal wells with variable conductivity and uneven distribution of multiple fractures is proposed. By Laplace transformation, point source integration, and superposition principle, solutions of multiple infinite conductivity fractures in closed reservoirs are obtained. By coupling Fredholm integral equation of variable conductivity, linear equations of variable conductivity fractures in Laplace space are obtained. Gauss-Newton iteration, Duhamel convolution, and Stehfest numerical inversion method are used to obtain the bottom hole production solution. The accuracy of the results is verified by comparing with Eclipse software simulation. Then, the influence of some important reservoir and fracture parameters on the production is analyzed. The calculative results show that the smaller the fracture spacing is, the earlier the fracture begins to decline, the more the production will decrease; the change of different fracture length with the total fracture length unchanged has almost no effect on the production; the angle between fracture and $x$ -axis has an important effect on the production; the smaller the angle between fracture and $x$ -axis is, the stronger the interference between fractures is, the higher the production; the initial fracture conductivity affects the early production behavior, and the higher the initial fracture conductivity, the higher the production; the larger the fracture declines index, the lower the production, but the decreasing range gradually decreases with the increase of the decline index; the larger the reservoir drainage radius, the later the energy depletion stage, the higher the production. At last, a good fitting effect is obtained by fitting an example of oil field. The model proposed in this paper enriches the model base of rate decline analysis of fractured horizontal wells and lays a theoretical foundation for efficient development and practice of tight reservoirs.