Experimental Design as a Framework for Reservoir Studies

Abstract

Summary Numerical simulation integrates extensive geoscience and engineering data with complex process models to examine reservoir behavior. Reservoir studies commonly consider many scenarios, cases, and realizations. However, reservoir simulation can be expensive. Complexity, combinatorics, and expense motivate improved reservoir study methods. The experimental design framework selects relevant models, records factor settings for models, creates data files, controls execution, gathers summary data, and creates response models. Response surface models facilitate Monte Carlo simulation, uncertainty analysis, optimization, parameter estimation, upscaling, and performance forecasting. A pre development study of a Gulf of Mexico turbidite reservoir uses this framework to examine the sensitivity of oil production predictions to well location, absolute horizontal permeability, pore compressibility, aquifer size, skin, and vertical permeability. Well location is optimized for cases with uncertain parameters. Rationale for Designed Reservoir Simulation Numerical models are widely used in engineering and scientific studies. Experimental design has been used in diverse areas such as aeospace1 and electronics2 for analysis and optimization of complex, nonlinear systems described by computer models.3 Many reservoir engineering studies have used experimental design.4–14 Factors. In an experimental design framework, the parameters that are varied are called factors. Factors can be classified by our knowledge and our ability to change them. Controllable factors can be varied by process implementers; reservoir development programs specify the well location. Observable factors can be measured relatively accurately, but cannot be controlled; the depth to the top of a structure may be considered observable. Uncertain factors can neither be measured accurately nor controlled; permeability far from wells may be uncertain. The factors are explicitly identified and described in the designed approach. Responses. Decisions are based on responses obtained by measurement or modeling. Reservoir studies examine responses that affect project value (e.g., time of water breakthrough, peak oil rate, and cumulative oil recovery). Controllable factors are selected to maximize project value subject to observable factors and over the ranges of uncertain factors. Optimization requires understanding how all factors interact to change project value. The designed approach promotes this understanding. Structure of Reservoir Models. Numerical reservoir models have many large, interacting data elements. Several features of reservoir models affect study design and execution.Data elements are interdependent (e.g., the well specifications depend on the grid).A factor may influence many elements (e.g., absolute permeability changes the permeability array assignment and saturation table selection).Data elements may be large (e.g., corner point grids).Elements may be based on complex algorithms and data sets (e.g., geostatistical models for permeability).There may be many versions of each data element, corresponding to various scenarios, cases and realizations. Scenarios are different process models or development plans, cases have distinct parameter settings (or factor combinations), and realizations differ by stochastic processes commonly based on random number sequences.Many elements must be assembled into models.Numerical simulation may be time-consuming.The number of models increases with the number of scenarios, cases, and realizations. A designed approach helps ensure that the models are correct, consistent, labeled, and archived. Factors. In an experimental design framework, the parameters that are varied are called factors. Factors can be classified by our knowledge and our ability to change them. Controllable factors can be varied by process implementers; reservoir development programs specify the well location. Observable factors can be measured relatively accurately, but cannot be controlled; the depth to the top of a structure may be considered observable. Uncertain factors can neither be measured accurately nor controlled; permeability far from wells may be uncertain. The factors are explicitly identified and described in the designed approach. Responses. Decisions are based on responses obtained by measurement or modeling. Reservoir studies examine responses that affect project value (e.g., time of water breakthrough, peak oil rate, and cumulative oil recovery). Controllable factors are selected to maximize project value subject to observable factors and over the ranges of uncertain factors. Optimization requires understanding how all factors interact to change project value. The designed approach promotes this understanding. Structure of Reservoir Models. Numerical reservoir models have many large, interacting data elements. Several features of reservoir models affect study design and execution.Data elements are interdependent (e.g., the well specifications depend on the grid).A factor may influence many elements (e.g., absolute permeability changes the permeability array assignment and saturation table selection).Data elements may be large (e.g., cornerpoint grids).Elements may be based on complex algorithms and data sets (e.g., geostatistical models for permeability).There may be many versions of each data element, corresponding to various scenarios, cases and realizations. Scenarios are different process models or development plans, cases have distinct parameter settings (or factor combinations), and realizations differ by stochastic processes commonly based on random number sequences.Many elements must be assembled into models.Numerical simulation may be time-consuming.The number of models increases with the number of scenarios, cases, and realizations. A designed approach helps ensure that the models are correct, consistent, labeled, and archived.