Application of Fractional Calculus in Reservoir Characterization From Pressure Transient Data in Fractal Reservoir With Phase Redistribution

Abstract

The present paper describes the use of pressure derivative and second derivative of integral of pressure in a fractal reservoir with matrix participation with phase redistribution in a geological environment that are not possible by conventional techniques. The analysis of this type of data in reservoir characterization is known as “inverse problem” and one can obtain information about interwell and vertical permeability distribution in a reservoir. The fractal geometry in a dynamic pressure transient tests data plays a very vital role for heterogeneity characterization. The pressure transient response is analyzed for flow in a connected fracture network and fracture with matrix participation. The computer aided matching technique for both pressure and its derivative by nonlinear regression techniques are used in estimating the reservoir properties from measured drawdown/buildup and falloff pressure data of heterogeneous reservoir. In the present paper the fractional calculus approach has been utilized to solve the diffusivity equation with phase redistribution in fractal reservoir. The pressure solution of the diffusivity is in terms of Laplace space and its analytical inversion is not possible. We have obtained numerically inversion of the problem and the pressure, pressure derivative, integral of pressure and its first and second derivative has been calculated. The permeability estimated from pressure transient test data of a well are in good agreement with the identified the geological model.