A history matching workflow using proxy-based MCMC applied in tight reservoir simulation studies
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Reservoir simulation for tight reservoirs often requires characterization of hydraulic and natural fracture networks in the reservoir model. Microseismic data reveals approximate boundary of the fracture networks but its direct application of stimulated rock volume (SRV) fails short to capture fracture connectivity and fracture conductivity, which significantly dominate well performance. Embedding discrete fractures in reservoir simulation is thus required to attain more realistic reservoir behavior. However, using local grid refinement (LGR) to model discrete fractures is computationally expensive. Even more challenging is generating multiple realizations of the fracture-embedded reservoir models during history-matching. Not only one simulation but extensive series of simulations are required to deal with complex geometry of fractures as well as other uncertain parameters. However, recent developments in a methodology called Embedded Discrete Fracture Model (EDFM) have overcome the computational complexity using discrete fractures in reservoir simulations. In this thesis, we develop an efficient assisted history matching (AHM) workflow using proxy-based Markov chain Monte Carlo (MCMC) algorithm and integrate the workflow with the EDFM preprocessor. To improve the efficiency, the optimal proxy is studied by comparing the performance of four types of proxies: quadratic polynomial, cubic polynomial, k-nearest neighboring (KNN), and kriging under various contexts such as different measurement errors. The results show that kriging proxy is more accurate than KNN proxy and cubic proxy. The quadratic proxy was the least accurate in our evaluations. However, if larger measurement error is introduced, the distinction between accuracy of the four proxies becomes less clear in spite of their different computational costs. Incorporating these findings, the proxy-based MCMC workflow is developed and implemented in conjunction with the EDFM to history match a shale oil well in Vaca Muerta formation to demonstrate the application of the workflow. The microseismic data are accounted to constrain the uncertain geometries of the fractures. The integrated workflow can successfully and efficiently history match the actual shale-oil well with complex fractures. Not only the uncertainties of reservoir properties are narrowed down but the posterior likelihood of fracture geometry scenario is also attained after history matching. We also compare the proxy-based MCMC workflow with the direct MCMC and a commercial history matching software in terms of accuracy and efficiency. It is found that the direct MCMC cannot find enough solutions to construct the posterior probability density (PPD) in an efficient manner. For the commercial software, it can find solutions faster than the proxy-based MCMC. However, the former is stuck in the local minima, thus resulting in an invalid PPD. Ultimately, the proxy-based MCMC workflow provides the most accurate history matching results with efficient manner for this tight oil reservoir.