Convolution integral for fractional diffusion equation

A modified version of the classical diffusion equation, called the fractional diffusion equation (FDE), has been developed to describe anomalous fluid flow through porous media. Since the FDE does not contain the rate as the input of the well-reservoir system, in this paper, we re-develop the FDE containing both rate (input) and pressure (output). Based on the new FDE, we show that the conventional convolution integral can still be used to relate the rate and pressure in reservoirs with anomalous behavior. A prac-tical application of the convolution integral and how to use it in practice is presented using a synthetic example. (c) 2021 Elsevier Ltd. All rights reserved.