Equation predicts non-Darcy flow coefficient

Abstract

An equation has been derived for obtaining a non-Darcy flow coefficient that facilitates gas well remedial treatment calculations and production performance evaluations. For high-capacity gas wells, pressure drop near the well bore cannot be estimated from the Darcy equation in which the pressure gradient is proportional to the flow velocity (laminar flow). To describe the additional pressure drop in the transition of the laminar-turbulent flow regime, Forchheimer proposed an equation in which the non-Darcy term is proportional to the flow velocity squared. To determine the coefficient of proportionality, the non-Darcy flow coefficient, [beta], empirical data or semitheoretical equations are used. As a result of non-Darcy flow, estimates of the coefficient from build-up pressure test values of the apparent skin become rate dependent. For this reason, the nature of the skin, formation (true) skin or rate dependent skin, is important for designing remedial treatments or for evaluating the productivity of a perforated gas well. A semitheoretical equation is proposed in this article for relating the non-Darcy flow coefficient, [beta] (cm[sup [minus]1]), to effective gas permeability, k[sub g] (Darcies), porosity, [phi], and irreducible water saturation, S[sub w].