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.
Complexity of Reservoir Studies
Reservoir studies require integration of geologic properties, drilling and production strategies, and economic parameters. Integration is complex because parameters such as permeability, gas price, and fluid saturations are uncertain.
In exploration and production decisions, alternatives such as well placement, artificial lift, and capital investment must be evaluated. Development studies examine these alternatives, as well as geologic, engineering, and economic factors to formulate and optimize production plans (Narayanan et al. 2003). Reservoir studies may require many simulations to evaluate the many factor effects on reservoir performance measures, such as net present value (NPV) and breakthrough time.
Despite the exponential growth of computer memory and speed, computing accurate sensitivities and optimizing production performance is still expensive, to the point that it may not be feasible to consider all alternative models. Thus, simulation runs should be chosen as efficiently as possible. Experimental design addresses this problem statistically, and along with response models, it has been applied in engineering science (White et al. 2001; Peng and Gupta 2004; Peake et al. 2005; Sacks et al. 1989a) toMinimize computational costs by choosing a small but statistically representative set of simulation runs for predicting responses (e.g., recovery)Decrease expected error compared with nonoptimal simulation designs (i.e., sets of sample points)Evaluate sensitivity of responses to varying factorsTranslate uncertainty in input factors to uncertainty in predicted performance (i.e., uncertainty analysis)Estimate value of information to focus resources on reducing uncertainty in factors that have the most significant effect on response uncertainty to help optimize engineering factors.
Space-filling designs for computer experiments: A review
