Summary Although a large amount of wells has been extensively drilled to develop unconventional reservoirs, uncertainty associated with reservoir and fracture properties can significantly affect the evaluation of an individual well's performance with simulations. From the history-matching point of view, this uncertainty causes nonuniqueness of solutions that should be obtained with a robust probabilistic method without overly exhausting simulation resources. Because of the challenge in this work, a proxy-based history-matching approach can deliver unique advantages of reducing the computational requirement and providing probabilistic interpretation. The work flow presented in this paper is designed to exploit full ranges of proxy-modeling benefits from prioritizing significant reservoir properties, estimating the variation of model responses, and searching multiple history-matching solutions for reliable probabilistic forecasts. A screening process is introduced at the initial stage of the work flow with design of experiment (DOE) and response-surface methodology (RSM), so the dimensions of proxy models can be reduced. In addition, the proxy models progress through the work flow by iterations that aim to improve their accuracy. This iterative work flow efficiently uses simulation resources by use of all the completed runs to provide more information about the model responses for the subsequent iterations. While the work flow is being iterated, multiple proxy models are explored for history-matching solutions by a Markov chain Monte Carlo (MCMC) algorithm. Then, history-matching solutions are used to evaluate the probability distribution of the long-term estimated ultimate recovery (EUR). Finally, an application of the work flow to a horizontal well in the Middle Bakken is presented in this paper.
Summary 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.
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