Fractional flow equations. A model for pressure deficit in an oil well

TL;DR

This paper introduces a fractional flow model for pressure deficits in complex oil reservoirs, incorporating anomalous fluid behavior and memory effects to improve accuracy in pressure prediction.

Contribution

It develops a novel fractional flow equation system that models pressure deficits considering reservoir heterogeneity and anomalous flow phenomena using fractional calculus.

Findings

Semi-analytical solutions obtained in Laplace space.

Model captures anomalous flow behavior in non-conventional reservoirs.

Enhanced pressure deficit modeling accuracy.

Abstract

This article presents a novel system of flow equations that models the pressure deficit of a reservoir considered as a triple continuous medium formed by the rock matrix, vugular medium and fracture. In non-conventional reservoirs, the velocity of the fluid particles is altered due to physical and chemical phenomena caused by the interaction of the fluid with the medium, this behavior is defined as anomalous. A more exact model can be obtained with the inclusion of the memory formalism concept that can be expressed through the use of fractional derivatives. Using Laplace transform of the Caputo fractional derivative and Bessel functions, a semi-analytical solution is reached in the Laplace space.