Correction Factor Model for Transient-Linear Flow in Tight Gas Reservoirs

Abstract

Under a constant wellbore pressure condition during transient-linear flow, gas viscosity-compressibility product is governed by a time-invariant average pressure. Therefore, evaluating this product at either the initial reservoir pressure or flowing wellbore pressure introduces a significant error in the estimation of xFk. Although attempts have been made to address this problem, existing models suffer from at least two limitations. First, they are derived under limited reservoir conditions, despite μgct being strongly dependent on complex interactions among pressure drawdown, gas, water, and formation compressibilities. Second, other existing formulations are based on iterations/graphical techniques, which are difficult to apply in practice. This study presents a new empirically derived correction factor based on a suite of numerical simulation results. A one-dimensional real-gas flow in a multifractured tight reservoir was simulated in a Python environment. The simulation results suggest that the correlation of the correction factor with pressure drawdown yields a family of quadratic curves, each of which is governed by reservoir conditions. In particular, the coefficients of these quadratic equations are governed by the initial pressure and compressibilities of gas, water, and formation, suggesting that a correction-factor model cannot be represented by a fixed-coefficient expression. This finding reveals a limitation of the widely used Ibrahim and Wattenbarger’s correlation, which fixed coefficients render it insensitive to rock and fluid compressibilities. In contrast, the proposed correlation admits pressure drawdown and rock/fluid compressibilities as input parameters, allowing more accurate xFk estimates. The proposed model has been validated against numerical simulation and applied to field data. Results of this study demonstrate that the proposed model improves the correction factor estimation and, thus, reduces errors in xFk calculations. Neglecting the correction factor or applying a fixed-coefficient model can result in an overestimation of xFk.