Physics-based and empirical rate-time models inherently assume constant bottomhole flowing pressure (BHP), an assumption that may not hold for many unconventional wells. Hence, applying these models without accounting for BHP variations might lead to inaccurate: (a) flow regime identification, (b) estimation of the parameters of these models, and (c) estimated ultimate recovery (EUR) and drainage volumes. This study evaluates and compares the predictions of rate-time relations including and ignoring corrections for time-varying BHP for both synthetic and shale gas wells.

We generate a real gas synthetic case with errors in the time-varying BHP. First, we convert pressures into pseudopressures. Second, we deconvolve the pseudopressure history by applying the regularized exponential basis function inverse scheme to obtain an equivalent rate—the unit-pseudopressure-drop rate at standard conditions—at constant BHP. Third, we history-match the production using the scaled single-phase compressible fluid physics-based model for three different approaches: (a) using rate-time-pressure data with rate-pseudopressure deconvolution, (b) using rate-time-pressure data using just rate-pressure deconvolution, and (c) using only rate-time data. Finally, we compare the results in terms of their history-matches and estimated reservoir parameters. We conclude by illustrating the application of this procedure to shale gas wells.

For the synthetic case, the fit of the single-phase compressible fluid rate-time model using rate-pseudopressure deconvolution can accurately estimate the original gas-in-place, characteristic time, gas permeability, and fracture half-length. In contrast, considerable errors are noted when either using rate-pressure deconvolution or failing to account for variable BHP. Regarding the shale gas examples, the rate-pseudopressure deconvolution scheme accurately identifies the flow regimes present in the well, which can be difficult to detect by only analyzing rate-time data. For this reason, the fits of the scaled single-phase compressible fluid model using only rate-time results in unreasonably large estimates of the reservoir parameters and EUR. In contrast, the application of rate-pseudopressure deconvolution constrains the fits of single-phase compressible fluid model yielding more realistic estimates of time of end of linear flow, and EUR.

This paper illustrates the application of a workflow that accounts for variable BHP by estimating an equivalent constant unit-pseudopressure-drop gas rate (at standard conditions). We illustrate the workflow for a particular decline-curve model, but the workflow is general and can be applied to any rate-time model. The approach history matches and forecasts the production of unconventional gas reservoirs using rate-time models more accurately than assuming constant BHP.

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