Advanced Techniques for Closed-Loop Reservoir Optimization under Uncertainty

Advisors

Louis Durlofsky, primary advisor
Tapan Mukerji, advisor
Oleg Volkov, advisor

Abstract

In this work, we introduce and apply several new techniques for oil/gas reservoir optimization under uncertainty. As the first contribution, we develop a general methodology for optimal closed-loop field development (CLFD) under geological uncertainty. CLFD involves three major steps: optimizing the field development plan based on current geological knowledge, drilling new wells and collecting hard (well) data and production data, and updating multiple geological models based on all of the available data. In the optimization step, the number, type, locations and controls for new wells (and future controls for existing wells) are optimized using a hybrid Particle Swarm Optimization -- Mesh Adaptive Direct Search algorithm. The objective in the examples presented is to maximize expected (over multiple realizations) net present value (NPV) of the overall project. History matching is accomplished using an adjoint-gradient-based randomized maximum likelihood (RML) procedure. Different treatments are presented for history matching Gaussian and channelized models. Because the CLFD history matching component is fast relative to the optimization component, we generate a relatively large number of history matched models. Optimization is then performed using a representative subset of these realizations. We introduce a systematic optimization with sample validation (OSV) procedure, in which the number of realizations used for optimization is increased if a validation criterion is not satisfied. The CLFD methodology is applied to two- and three-dimensional example cases. Results show that the use of CLFD increases the NPV for the `true' (synthetic) model by 10% --70% relative to that achieved by optimizing over a large number of prior realizations. The CLFD framework includes several components, and different approaches for history matching, optimization, model selection and economic evaluation can be applied. In our second contribution, we address the problem of selecting a subset of representative geological realizations from a large set. Towards this goal, we introduce a general framework, based on clustering, for selecting a representative subset of realizations for use in simulations involving `new' sets of decision parameters. Prior to clustering, each realization is represented by a low-dimensional feature vector that contains a combination of permeability-based and flow-based quantities. Calculation of flow-based features requires the specification of a (base) flow problem and simulation over the full set of realizations. Permeability information is captured concisely through use of principal component analysis. By computing the difference between the flow response for the subset and the full set, we quantify the performance of various realization-selection methods. The impact of different weightings for flow and permeability information in the cluster-based selection procedure is assessed for a range of examples involving different types of decision parameters. These decision parameters are generated either randomly, in a manner that is consistent with the solutions proposed in global stochastic optimization procedures such as GA and PSO, or through perturbation around a base case, consistent with the solutions considered in pattern search optimization. We find that flow-based clustering is preferable for problems involving new well settings (e.g., time-varying well bottom-hole pressures) or small changes in well configuration, while both permeability-based and flow-based clustering provide similar results for (new) random multiwell configurations. We also investigate the use of efficient tracer-type simulations for obtaining flow-based features, and demonstrate that this treatment performs nearly as well as full-physics simulations for the cases considered. The various procedures are applied to select realizations for use in production optimization under uncertainty, which greatly accelerates the optimization computations. Optimization performance is shown to be consistent with the realization-selection results for cases involving new decision parameters. In the third contribution, we introduce a methodology for the joint optimization of economic project life and well controls. We present a nested formulation for this joint optimization problem where we maximize NPV, subject to the constraint that the rate of return of operations is greater than the minimum attractive rate of return (MARR) or hurdle rate. The methodology provides the optimal project life and the optimal well controls such that the maximum NPV is obtained at the end of the project life, and the rate of return of the project is essentially equal to MARR. Application of this procedure, enables avoiding situations where NPV increases slowly in time, but the benefit relative to the capital employed is extremely low. We demonstrate the successful application of this treatment for production optimization for two- and three-dimensional reservoir models.