Solution and Type Curve Analysis of Fluid Flow Model for Fractal Reservoir

Abstract

Conventional pressure-transient models have been developed under the assumption of homogeneous reservoir. However, core, log and outcrop data indicate this assumption is not realistic in most cases. But in many cases, the homogeneous models are still applied to obtain an effective permeability corresponding to fictitious homogeneous reservoirs. This approach seems reasonable if the permeability variation is sufficiently small. In this paper, fractal dimension and fractal index are introduced into the seepage flow mechanism to establish the fluid flow models in fractal reservoir under three outer-boundary conditions. Exact dimensionless solutions are obtained by using the Laplace transformation assuming the well is producing at a constant rate. Combining the Stehfest’s inversion with the Vongvuthipornchai’s method, the new type curves are obtained. The sensitivities of the curve shape to fractal dimension (θ) and fractal index (d) are analyzed; the curves don’t change too much when θ is a constant and d change. For a closed reservoir, the up-curving has little to do with θ when d is a constant; but when θ is a constant, the slope of the up-curving section almost remains the same, only the pressure at the starting point decreases with the increase of d; and when d = 2 and θ = 0, the solutions and curves become those of the conventional reservoirs, the application of this solution has also been introduced at the end of this paper.