Efficient Design of Reservoir Simulation Studies for Development and Optimization

Abstract

Summary Development studies examine geologic, engineering, and economic factors to formulate and optimize production plans. If there are many factors, these studies are prohibitively expensive unless simulation runs are chosen efficiently. Experimental design and response models improve study efficiency and have been widely applied in reservoir engineering. To approximate nonlinear oil and gas reservoir responses, designs must consider factors at more than two levels—not just high and low values. However, multilevel designs require many simulations, especially if many factors are being considered. Partial factorial and mixed designs are more efficient than full factorials, but multilevel partial factorial designs are difficult to formulate. Alternatively, orthogonal arrays (OAs) and nearly-orthogonal arrays (NOAs) provide the required design properties and can handle many factors. These designs span the factor space with fewer runs, can be manipulated easily, and are appropriate for computer experiments. The proposed methods were used to model a gas well with water coning. Eleven geologic factors were varied while optimizing three engineering factors. An NOA was specified with three levels for eight factors and four levels for the remaining six factors. The proposed design required 36 simulations compared to 26,873,856 runs for a full factorial design. Kriged response surfaces are compared to polynomial regression surfaces. Polynomial-response models are used to optimize completion length, tubinghead pressure, and tubing diameter for a partially penetrating well in a gas reservoir with uncertain properties. OAs, Hammersley sequences (HSs), and response models offer a flexible, efficient framework for reservoir simulation studies.