Rate Dependence of Bilinear Flow in Unconventional Gas Reservoirs

Abstract

Summary Unconventional fractured gas wells occasionally exhibit bilinear flow during early production. When this flow regime is observed, important fracture properties can be estimated such as conductivity and/or spacing. However, the application of present-day rate-transient-analysis (RTA) methods to bilinear flow results in up to 18% error. This error is rate-dependent, and occurs because of nonlinearities in the gas-diffusivity equation. This paper presents a new correction factor that handles the rate dependency of bilinear flow, and enables more-accurate reservoir characterization. The diffusivity equation of gas in porous media has some nonlinearities that cannot be addressed by only using the real-gas pseudopressure. Even though neglecting these nonlinearities results in a model that is sufficiently accurate for the radial-flow case, errors arise in the boundary-dominated-flow (BDF) (Fraim and Wattenbarger 1987), the linear-flow (Ibrahim and Wattenbarger 2006; Nobakht and Clarkson 2012), and, as shown in this article, the bilinear-flow cases. Currently, no research studies provide an accurate bilinear-flow analytical model for gas reservoirs. To bridge this gap and to provide rate-transient analysts with a practical tool, this work presents a correction factor that can be incorporated into the existing bilinear-flow models. The correction factor was developed following an approach similar to that of Ibrahim and Wattenbarger (2006). The first step was to simulate a number of reservoir and well conditions. Second, fracture properties were back calculated with the current bilinear-flow models. Finally, errors between the back calculated and the simulated properties were correlated to dimensionless drawdown. After these steps, a correction factor was obtained that applied to various bilinear-flow cases. The obtained numerical results indicate that errors in bilinear-flow models are correlated with rate, or more precisely, dimensionless drawdown [a similar behavior is observed in the analytical model of linear flow, as demonstrated by Ibrahim and Wattenbarger (2006)]. This correlation can be used to reduce error to less than ±3%. Because the simulated cases cover an extensive range of unconventional-reservoir conditions, the empirical correction is robust and applicable to a wide variety of reservoir conditions. Most importantly, the correction is practical and can be readily incorporated into existing bilinear-flow models. The application of the new correction is demonstrated in this article with synthetic and field examples.