Efficient Design of Reservoir Simulation Studies for Development and Optimization

Abstract

Abstract Development studies examine the importance of geologic, engineering, andeconomic parameters to formulate and optimize production plans. If there aremany factors, these studies are prohibitively expensive unless simulation runsare chosen and analyzed efficiently. Experimental design and response models can improve study efficiency, andhave been widely applied in reservoir engineering. To approximate nonlinear oiland gas reservoir responses accurately, designs must consider factors at morethan two levels, not just high and low values. However, multilevel designsrequire 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 havenot been used in reservoir engineering. Orthogonal arrays and nearly orthogonal arrays provide the required designproperties and can handle many factors. These arrays span the design space withfewer runs, can be manipulated easily, and are appropriate for computerexperiments. The proposed methods have been applied to a model of a gas well with waterconing. Eleven geologic were varied while optimizing three engineering factors(total of fourteen factors). A nearly orthogonal array was specified with threelevels for eight factors and four levels for the remaining six geologic andengineering factors. The proposed design required 36 simulations compared to4[6] x 3[8] = 26,873,856 runs for a full factorial design. Kriged response surfaces can approximate the relationship between theparameters and responses; these are compared to polynomial regression surfaces.Polynomial response surfaces are used to optimize completion length, tubinghead pressures, and tubing diameters for a partially penetrating well in a gasreservoir with uncertain properties. Compared with full and partial factorials, the nearly orthogonal arraydesign improves flexibility, requires fewer simulation runs, and yields moreaccurate response models. Thus, orthogonal arrays allow more efficientoptimization and straightforward sensitivity and uncertainty assessment. Complexity of Reservoir Studies Reservoir studies require integration of geological properties of thereservoir, drilling and production strategies, and economic parameters.Integration is complex, because parameters such as permeability, gas price, andfluid saturations are uncertain. Uncertainty in permeability, for example, could be caused by prediction at unknown locations from inexact seismic data.Sparseness of precise well data, imprecise seismic data, and uncertainty inspatial correlation makes the estimation at most reservoir locationsuncertain. In exploration and production decisions, alternatives such as wellplacement, drainage strategies, artificial lift, and capital investment must beevaluated. Development studies examine these alternatives and uncertaingeologic, engineering, and economic parameters to formulate and optimizeproduction plans.[1] As a result, reservoir studies may require manysimulations to evaluate the effects of variables on reservoir performancemeasures such as net present value and breakthrough time. Despite theexponential growth of computational memory and speed, computing accuratesolutions is still expensive, so that it may not be feasible to consider allalternative models.