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.
Abstract 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 that integrates the Distributed Gauss-Newton (DGN) method with the RML method to generate multiple realizations conditioned to production data synchronously. RML generates samples from an approximate posterior by finding a large ensemble of maximum posteriori points, from a distribution function in which the data and prior mean values have been perturbed with Gaussian noise. Rather than performing these optimizations 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 optimizations whenever these results are helping to converge a specific optimization. In order to improve sharing of results, we relax the accuracy of the finite difference approximations for the gradients, by using more widely spaced simulation results. To avoid trapping in local optima, a novel global search algorithm integrated with DGN and RML is applied. In this way we can significantly increase the number of conditional realizations that sample the approximate posterior, while reducing the total number of simulations needed to converge the optimization processes needed to obtain these realizations. The proposed workflow has been applied to field examples on liquid rich shale or tight oil reservoirs developed with hydraulically fractured horizontal wells. The uncertain parameters include stimulated rock volume (SRV) and matrix properties, such as permeability and porosity, and hydraulic-fracture properties, such as conductivity, height, and half length. The case studies involve a sensitivity analysis to identify key parameters, a history matching study to generate history-matched realizations with the proposed method, and an uncertainty quantification of production forecasting based on those conditioned models. The new approach is able to enhance the confidence level of the Estimated Ultimate Recovery (EUR) assessment by accounting for production forecasting results generated from all history-matched realizations. Numerical results indicate that the new method is very efficient compared with traditional methods. Hundreds of history-matched, or rather data-conditioned, realizations can be generated in parallel within 20-40 iterations. The computational cost (CPU usage) is reduced by a factor of 10 to 25 when compared to the traditional RML approach.
Abstract Well test analysis in turbidite reservoirs is complicated by the intricate stratigraphy prevailing in this depositional environment. Because of this complexity, important reservoir architectural parameters driving flow behavior (e.g., shale drape coverage, object dimensions) cannot be estimated using simple analytical reservoir models employed in conventional well test analysis techniques. Alternatively, simulation-based well test analysis offers the advantage of being able to capture stratigraphic complexity. However, it requires a very large number of models and simulations to identify multiple solutions to such a highly non-unique inversion problem. In this work, we have developed a novel well test analysis workflow by constructing a large library of build-up type curves derived by appropriately scaling a comprehensive set of reference drawdown simulations. This set is used to rapidly identify a variety of stratigraphic scenarios matching a given well test. Key stratigraphic parameters are then estimated through statistical analysis of the results. The proposed well test analysis technique has been applied to synthetic and field examples. For the tested cases, stratigraphic interpretations derived from well tests are found to be consistent with those obtained from other data sources.
Abstract Fault modeling has become an integral element of reservoir simulation for structurally complex reservoirs. Modeling of faults in general has major implications for the simulation grid. In turn, the grid quality control is very important in order to attain accurate simulation results. We investigate the dynamic effects of using stair-step grid (SSG) and corner-point grid (CPG) approaches for fault modeling from the perspective of dynamic reservoir performance forecasting. We have performed a number of grid convergence and grid-type sensitivity studies for a variety of simple, yet intuitive faulted flow simulation problems with gradually increasing complexity. We have also explored the added value of the multipoint flux approximation (MPFA) method over the conventional two-point flux approximation (TPFA) to increase the accuracy of reservoir simulation results obtained on CPGs. Effects of fault seal modeling on grid-resolution convergence and grid-type sensitivity have also been briefly examined. For simple geometries, both SSG and CPG can be used for fault modeling with similar accuracy in conjunction with the pillar-grid approach. This is evidenced by the fact that simulation results from SSG and CPG converge to identical solutions. SSG and CPG yield different results for more complex geometries. Simulation results approach to a converged solution for relatively fine SSGs. However, a SSG only provides an approximation to the fault geometry and reservoir volumes when the grid is coarse. On the other hand, non-orthogonality errors are increasingly evident in relatively more complex faulted models on CPGs and such errors cannot be addressed by grid refinement. It has been observed that MPFA partially addresses the discretization errors on non-orthogonal grids but only from the total flux accuracy perspective. However, transport related errors are still evident. Grid convergence behaviors and grid effects are quite similar with or without fault seal modeling (i.e., dedicated fault-zone modeling by use of scaled-up seal factors) for simple geometries. However, in more complex test cases, we have observed that it is more difficult to achieve converged results in conjunction with fault seal modeling due to increased heterogeneity of the underlying problem.
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