Uncertainty Analysis in Simulation for Reservoir Management: Case Study from Niger Delta
Uncertainty analysis of flow performance predictions involves identifying significant reservoir parameters impacting the flow response. Uncertainty analysis often requires conducting large number of reservoir simulation runs. In this work, experimental design theory (DoE), Response Surface Methodology (RSM) and numerical simulation were integrated to reduce the number of simulations and simplify the optimization process. Various investigators have applied DoE/RSM to approximate a complex process with regression polynomials within a certain well defined region. The application of these DoE/RSM methods is more often based on the experimenter’s discretions or company practices with no attention paid to the risks involved. Hence, in this work, it is necessary to examine the basis for the various DoE/RSM methods for the purpose of developing guidelines for the construction of valid response surfaces. First, three families of linear experimental design methodologies, the Placket-Burman, Fractional and Relative variation, are evaluated for uncertainty screening by computing sensitivity coefficients of all identified uncertainty relative to system parameters. This procedure has useful applications in simulation for the optimization of production and management of a petroleum asset. Second, probable reservoir proxies were developed based on linear sensitivity analysis. Three-level experimental design algorithms, i.e., Box-Behnken, Central Composite, D-Optima and Full Factorial designs, and Adaptive neuro-Fuzzy Inference System were rigorously examined. The methods were analyzed for their capabilities to reproduce actual production forecasts. The best method was selected from the case study and recommendations were made on how to select best DoE methods for similar applications. Uncertainty quantification was performed using the selected response surface model. Although the use of regular Monte Carlo simulations (MCS) has gained tremendous attention, the fundamental assumption of variables being independent and identically distributed is often not valid in petroleum reservoir problems. Methods based on Markov Chains simulations offer reasonable solution to this problem. Mathematical foundation showing the differences between regular MCS and Markov Chains methods was demonstrated in this work using a second case study from the Niger Delta involving the placement of infill wells in a reservoir. In the second case study, the selection of optimum number, type and locations of the infill wells in the reservoir was uncertain. The objective was to optimize infill well selection and placement and quantify the associated uncertainty. To accomplish this objective, the reservoir was delineated into four sub-regions (A, B, C and D). To drain each region, a set of only vertical wells, only horizontal and combination of vertical and horizontal wells were drilled. Reservoir heterogeneity at the infill well locations, number and type of infill wells, horizontal well lengths, perforation intervals and inter-well spacing were considered as uncertainty parameters affecting cumulative oil recovery, water cut and water breakthrough time. Uncertainty quantification was performed using both the regular MCS and Markov Chains simulations. The results of this study are useful for identification and selection of effective tools in uncertainty quantification in the oil industry. The proposed uncertainty analysis methodology in both case studies saves considerable time; and is very useful when limited data is available and can serve as practical guides for effective reservoir management.