The optimal reservoir configuration for maximum productivity index of gas reservoirs depleted by horizontal wells under Darcy and non-Darcy flow conditions

Abstract

A new approach for estimating productivity index of horizontal wells depleting finite gas reservoirs is introduced in this paper. This approach focuses on using reservoir configurations and anisotropy as well as wellbore length for calculating productivity index at pseudo-steady state conditions when production time is no longer affects reservoir performance. The paper also aims to determine the optimal reservoir configurations that could give the maximum productivity index.For this purpose, new analytical models were developed for productivity index of gas reservoirs depleted by horizontal wells based on the solutions of the flow equation (Diffusivity equation) at pseudo-steady state condition. Gas flow in the porous media was considered obeying both Darcy and non-Darcy flow. These models were modified for bounded gas reservoirs when the pressure drawdown becomes time invariant and gas flow rate is constant. The study investigated the effects of reservoir boundaries, anisotropy, wellbore length, wellbore horizontal penetration ratio with respect to reservoir length, and the asymmetricity of wellbore in the formation on the productivity index.The outcomes of this study can be summarized in: 1) Productivity index of gas reservoirs in pseudo-steady state is affected by the dominant flow type in the reservoirs: Darcy or non-Darcy flow. 2) Wellbore length, reservoir configuration, and anisotropy affect the productivity index as well as wellbore asymmetricity. 3) Productivity index of Darcy flow is greater than non-Darcy flow. 4) Wellbore horizontal penetration ratio with respect to reservoir length may have significant impact on productivity index as well as reservoir width. The most interesting points in this study are: 1) The maximum productivity index could be reached for reservoir length of (xeD=0.55−0.65) regardless reservoir width. 2) The anisotropy may affect productivity index for short and moderate wellbores, however, it does not have significant effects in long wellbores. 3) Productivity index might be affected by wellbore location with respect to reservoir width and length but not wellbore location in the vertical direction. 4) Pseudo-steady state productivity index can be estimated by the proposed models using reservoir configuration and wellbore length with a full consideration to the formation anisotropy and wellbore asymmetricity.