Physics-based and empirical rate-time models inherently assume constant bottomhole flowing pressure (BHP) conditions. However, this is a poor assumption for many unconventional wells. Hence, applying these models to unconventional wells might lead to inaccurate: (a) flow regime identification, (b) estimation of the parameters of these models, and (c) estimated ultimate recovery (EUR) and drainage volume predictions. This work evaluates and compares the predictions of rate-time relations omitting and correcting for time-varying BHP conditions for both synthetic and tight-oil wells.
We generate a synthetic example with errors in the time-varying BHP. First, we deconvolve the BHP history to obtain an equivalent rate-the unit-pressure-drop rate-under constant BHP. We apply five inverse schemes to assess their robustness and accuracy: naïve, generalized Tikhonov, truncated generalized singular value decomposition (TGSVD), truncated total least-squares (TTLS) and regularized exponential basis functions. Second, we fit the production with a scaled single-phase slightly compressible physics-based model using: (a) rate-time-pressure data (with the deconvolution procedure), and (b) only rate-time data. Finally, we compare the results in terms of the reservoir properties and EUR predictions. We conclude by illustrating the application of this procedure to tight-oil wells.
For the synthetic case, we observe that the regularized basis exponential functions solution is robust and stable to regenerate the unit-pressure-drop rate and the variable pressure oil rate in the case where measurement errors are present. Furthermore, the fit of the single-phase rate-time model using pressure deconvolution is able to accurately estimate the hydrocarbon pore volume and characteristic time of the system and the EUR. In contrast, the rate-time fit without accounting for variable BHP have considerable errors in both quantities. Regarding the tight-oil well examples, the regularized exponential basis functions deconvolution allows us to clearly and properly identify flow regimes present in the well, which can be difficult to detect by only analyzing rate-time data. For this reason, the fits of single-phase model using only rate-time results in unreasonably large estimates of the characteristic time (time to depletion) and EUR. In contrast, the application of deconvolution naturally regularizes the fits of single-phase rate-time model yielding more realistic estimates of time to depletion and EUR.
This paper illustrates the application of a workflow that accounts for time-varying BHP by incorporating and assessing the performance of different inversion techniques that estimate an equivalent constant unit-pressure-drop rate useful for rate-time analysis. The approach history matches and forecasts production of unconventional reservoirs using rate-time models more accurately than assuming constant BHP.
