Use of orthogonal arrays, quasi-Monte Carlo sampling and kriging response models for reservoir simulation with many varying factors

Asset development teams may adjust simulation model parameters using experimental design to reveal which factors have the greatest impact on the reservoir performance. Response surfaces and experimental design make sensitivity analysis less expensive and more accurate, helping to optimize recovery under geological and economical uncertainties. In this thesis, experimental designs including orthogonal arrays, factorial designs, Latin hypercubes and Hammersley sequences are compared and analyzed. These methods are demonstrated for a gas well with water coning problem to illustrate the efficiency of orthogonal arrays. Eleven geologic factors are varied while optimizing three engineering factors (total of fourteen factors). The objective is to optimize completion length, tubing head pressure, and tubing diameter for a partially penetrating well with uncertain reservoir properties. A nearly orthogonal array was specified with three levels for eight factors and four levels for the remaining six geologic and engineering factors. This design requires only 36 simulations compared to (26,873,856) runs for a full factorial design. Hyperkriging surfaces are an alternative model form for large numbers. Hyperkriging uses the maximum likelihood variogram model parameters to minimize prediction errors. Kriging is compared to conventional polynomial response models. The robustness of the response surfaces generated by kriging and polynomial regression are compared using jackknifing and bootstrapping. Sensitivity analysis and uncertainty analysis can be performed inexpensively and efficiently using response surfaces. The proposed design approach requires fewer simulations and provides accurate response models, efficient optimization, and flexible sensitivity and uncertainty assessment