An Iterative Response-Surface Methodology by Use of High-Degree-Polynomial Proxy Models for Integrated History Matching and Probabilistic Forecasting Applied to Shale-Gas Reservoirs

作者：Wantawin Marut; Yu Wei^*; Dachanuwattana Silpakorn; Sepehrnoori Kamy

来源：SPE Journal, 2017, 22(6): 2012-2031.

DOI：10.2118/187938-pa

Response-surface methodology (RSM) has been widely used in the petroleum industry as an assistive tool for numerical-reservoir-simulation studies. Instead of generating simulation cases exhaustively to solve history-matching (HM) problems, proxy models that are created by RSM provide useful benefits in terms of simplicity and computational efficiency. However, the capability of proxy models to fully capture uncertainty ranges of HM results and production forecasts might be deficient in complex problems if the simplified proxy models only deliver partial solutions. Hence, to decide whether the uncertainty-assessment process by proxy models is complete, the models should deliver as many HM solutions as required to build probability distribution of production forecasts. Therefore, we developed the work flow to combine both processes into an integrated proxy-based approach that searches for the accepted HM solution while probabilistic forecasts are evaluated simultaneously. In addition, the combined work flow is an iterative approach. It gradually modifies the proxy models dependent on the increasing number of completed simulation runs, which continually update the original proxy model into higher degree of polynomial. The use of higher-degree-polynomial equations appears to have the benefit to provide an expanded set of HM solutions inside the uncertain parameter space compared with the commonly used quadratic form. More solutions found from the iterations could eventually approximate wider uncertainty ranges of probabilistic forecasts, which is consistent with the direct Markov-chain Monte Carlo (MCMC) method but with a significant reduction of simulated cases. Finally, this paper applies the proxy-based approach to a reservoir-simulation model containing a horizontal hydraulic-fractured well in the Marcellus Shale formation. This proxy-based approach helps assess the uncertainty of reservoir and fracture properties of unconventional reservoirs. Also, it is useful for evaluating the ranges of ultimate gas recovery.

• 出版日期2017-12