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Summary Reservoir model parameters generally have very large uncertainty ranges, and need to be calibrated by history matching (HM) available production data. Properly assessing the uncertainty of production forecasts (e.g., with an ensemble of calibrated models that are conditioned to production data) has a direct impact on business decision making. It requires performing numerous reservoir simulations on a distributed computing environment. Because of the current low-oil-price environment, it is demanding to reduce the computational cost of generating multiple realizations of history-matched models without compromising forecasting quality. To solve this challenge, a novel and more efficient optimization method (referred to as SVR-DGN) is proposed in this paper, by replacing the less accurate linear proxy of the distributed Gauss-Newton (DGN) optimization method (referred to as L-DGN) with a more accurate response-surface model of support vector regression (SVR). Resembling L-DGN, the proposed SVR-DGN optimization method can be applied to find multiple local minima of the objective function in parallel. In each iteration, SVR-DGN proposes an ensemble of search points or reservoir-simulation models, and the flow responses of these reservoir models are simulated on high-performance-computing (HPC) clusters concurrently. All successfully simulated cases are recorded in a training data set. Then, an SVR proxy is constructed for each simulated response using all training data points available in the training data set. Finally, the sensitivity matrix at any point can be calculated analytically by differentiating the SVR models. SVR-DGN computes more-accurate sensitivity matrices, proposes better search points, and converges faster than L-DGN. The quality of the SVR proxy is validated with a toy problem. The proposed method is applied to a real field HM example of a Permian liquid-rich shale reservoir. The uncertain parameters include reservoir static properties, hydraulic-fracture properties, and parameters defining relative permeability curves. The performance of the proposed SVR-DGN optimization method is compared with the L-DGN optimizer and the hybrid Gauss-Newton with a direct-pattern-search (GN-DPS) optimizer, using the same real field example. Our numerical tests indicate that the SVR-DGN optimizer can find better solutions with smaller values of the objective function and with a less computational cost (approximately one-third of L-DGN and 1/30 of GN-DPS). Finally, the proposed method is applied to generate multiple conditional realizations for the uncertainty quantification of production forecasts.

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Summary Although it is possible to apply traditional optimization algorithms together with the randomized-maximum-likelihood (RML) method to generate multiple conditional realizations, the computation cost is high. This paper presents a novel method to enhance the global-search capability of the distributed-Gauss-Newton (DGN) optimization method and integrates it with the RML method to generate multiple realizations conditioned to production data synchronously. RML generates samples from an approximate posterior by minimizing a large ensemble of perturbed objective functions in which the observed data and prior mean values of uncertain model parameters have been perturbed with Gaussian noise. Rather than performing these minimizations in isolation using large sets of simulations to evaluate the finite-difference approximations of the gradients used to optimize each perturbed realization, we use a concurrent implementation in which simulation results are shared among different minimization tasks whenever these results are helping to converge to the global minimum of a specific minimization task. To improve sharing of results, we relax the accuracy of the finite-difference approximations for the gradients with more widely spaced simulation results. To avoid trapping in local optima, a novel method to enhance the global-search capability of the DGN algorithm is developed and integrated seamlessly with the RML formulation. In this way, we can improve the quality of RML conditional realizations that sample the approximate posterior. The proposed work flow is first validated with a toy problem and then applied to a real-field unconventional asset. Numerical results indicate that the new method is very efficient compared with traditional methods. Hundreds of data-conditioned realizations can be generated in parallel within 20 to 40 iterations. The computational cost (central-processing-unit usage) is reduced significantly compared with the traditional RML approach. The real-field case studies involve a history-matching study to generate history-matched realizations with the proposed method and an uncertainty quantification of production forecasting using those conditioned models. All conditioned models generate production forecasts that are consistent with real-production data in both the history-matching period and the blind-test period. Therefore, the new approach can enhance the confidence level of the estimated-ultimate-recovery (EUR) assessment using production-forecasting results generated from all conditional realizations, resulting in significant business impact.

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