Efficient Design of Reservoir Simulation Studies for Development and Optimization

Abstract

Abstract Development studies examine the importance of geologic, engineering, and economic parameters to formulate and optimize production plans. If there are many factors, these studies are prohibitively expensive unless simulation runs are chosen and analyzed efficiently. Experimental design and response models can improve study efficiency, and have been widely applied in reservoir engineering. To approximate nonlinear oil and gas reservoir responses accurately, 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 and have not been used in reservoir engineering. Orthogonal arrays and nearly orthogonal arrays provide the required design properties and can handle many factors. These arrays span the design space with fewer runs, can be manipulated easily, and are appropriate for computer experiments. The proposed methods have been applied to a model of a gas well with water coning. Eleven geologic were varied while optimizing three engineering factors (total of fourteen factors). A nearly orthogonal array was specified with three levels for eight factors and four levels for the remaining six geologic and engineering factors. The proposed design required 36 simulations compared to 46 × 38 = 26,873,856 runs for a full factorial design. Kriged response surfaces can approximate the relationship between the parameters and responses; these are compared to polynomial regression surfaces. Polynomial response surfaces are used to optimize completion length, tubing head pressures, and tubing diameters for a partially penetrating well in a gas reservoir with uncertain properties. Compared with full and partial factorials, the nearly orthogonal array design improves flexibility, requires fewer simulation runs, and yields more accurate response models. Thus, orthogonal arrays allow more efficient optimization and straightforward sensitivity and uncertainty assessment.