MONTE CARLO SIMULATIONS FOR UNCERTAINTY QUANTIFICATION: MATHEMATICAL FOUNDATION AND IMPLICATION OF UNDERLYING ASSUMPTIONS

Abstract

Many problems in petroleum engineering involve solving multivariable complex integrals and analytic calculation is rarely possible in most practical cases. Numerical approximation appears to be practicable. However, majority of existing numerical solution of a D–dimensional integral with a relative accuracy (ϵ) requires a computation time proportional to ϵ^-D. Hence, the use of Ordinary Monte Carlo simulation (OMCS) in uncertainty quantification has gained tremendous attention. In reality, when historical data is available, variables are not independent and identically distributed (iid). The direct sampling of variable under this condition is not expected to be easy and use of OMCS can be erroneous. Methods based on Markov Chains will offer reasonable solution to this problem. This study evaluates simulation methods for quantifying uncertainty in reservoir forecast. The implications of underlying mathematics and assumptions that characterizes them were covered. The p5-p10–p50–p90-p95 uncertainty envelopes from different methods were presented using a case study from Niger Delta. The result is useful for identification and selection of effective tools in uncertainty quantification in the oil industry.