Rate Dependence of Bilinear Flow in Unconventional Gas Reservoirs
- Mohammed S. Kanfar (University of Calgary) | Christopher R. Clarkson (University of Calgary)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- February 2018
- Document Type
- Journal Paper
- 17 - 30
- 2018.Society of Petroleum Engineers
- Rate Transient Analysis, Correction Factor, Unconventional Gas, Bilinear Flow
- 5 in the last 30 days
- 454 since 2007
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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-transientanalysis (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.
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