Performance-Based Comparison for Hydraulically Fractured Tight and Shale-Gas Reservoirs With and Without Non-Darcy-Flow Effect

Abstract

Summary Reservoir performance of hydraulically fractured tight and shale-gas formations is affected by an extensive range of parameters. Non-Darcy flow is one of these parameters, characterized by a significant effect on near-wellbore pressure drop for horizontal wells and near-fracture tips for hydraulic fractures (HFs). Non-Darcy flow develops in porous media when the velocity of reservoir fluid becomes extremely high because of continuous narrowing in the cross-sectional area of flow and the convergence of flow streamlines. As a result, the inertial forces could be considered the major contributor to the total pressure drop required by fluids to move from the outer drainage area toward the wellbore. Pressure drop, caused by non-Darcy flow, is described by the Forchheimer (1901) equation, wherein the deviation from Darcy's law is proportional to the inertial factor (β), which in turn is a function of porous-media characteristics such as permeability and porosity. This paper investigates the effect of non-Darcy flow, represented by the non-Darcy-flow coefficient (D) and/or the rate-dependent skin factor (DQsc), on pressure profiles, flow regimes, and productivity indices (PIs) of multiple HFs that propagate in tight and shale-gas reservoirs. This paper also introduces a new simplified technique for estimating both DQsc and D by knowing bottomhole flowing pressure and cumulative production at any time. For this purpose, a multilinear-flow-regime model was generated and modified for the existence of non-Darcy flow. A comparison for reservoir performance with and without non-Darcy flow was conducted for different reservoir configurations, including the reservoir-drainage area (2xe and 2ye), fracture conductivities, fracture dimensions, and fracture-propagation ratios. A set of plots has been developed for estimating the rate-dependent skin factor depending on production time with respect to cumulative PI. The outcomes of this study can be summarized as understanding the conditions at which non-Darcy flow could have considerable effects on reservoir performance; estimating the deviation in PI caused by the existence of non-Darcy flow from the cases where Darcy flow is the dominant; and introducing a new technique to estimate DQsc and D. The most interesting points in this study are the ability to estimate these two parameters without the need for experimental studies or use of an empirical model; that all flow regimes expected to develop in the entire life of reservoirs are not affected by non-Darcy flow, unlike pressure behaviors and PI; and that the PI is constant for high values of DQsc at early-time production and sharply declines at later production time.