Integration and quantification of uncertainty of volumetric and material balance analyses using a Bayesian framework

摘要

Estimating original hydrocarbons in place (OHIP) in a reservoir is fundamentallyimportant to estimating reserves and potential profitability. Quantifying the uncertaintiesin OHIP estimates can improve reservoir development and investment decision-makingfor individual reservoirs and can lead to improved portfolio performance. Twotraditional methods for estimating OHIP are volumetric and material balance methods.Probabilistic estimates of OHIP are commonly generated prior to significant productionfrom a reservoir by combining volumetric analysis with Monte Carlo methods. Materialbalance is routinely used to analyze reservoir performance and estimate OHIP. Althoughmaterial balance has uncertainties due to errors in pressure and other parameters,probabilistic estimates are seldom done.In this thesis I use a Bayesian formulation to integrate volumetric and material balanceanalyses and to quantify uncertainty in the combined OHIP estimates. Specifically, Iapply Bayes?? rule to the Havlena and Odeh material balance equation to estimateoriginal oil in place, N, and relative gas-cap size, m, for a gas-cap drive oil reservoir. Thepaper considers uncertainty and correlation in the volumetric estimates of N and m(reflected in the prior probability distribution), as well as uncertainty in the pressure data(reflected in the likelihood distribution). Approximation of the covariance of theposterior distribution allows quantification of uncertainty in the estimates of N and mresulting from the combined volumetric and material balance analyses. Several example applications to illustrate the value of this integrated approach arepresented. Material balance data reduce the uncertainty in the volumetric estimate, andthe volumetric data reduce the considerable non-uniqueness of the material balancesolution, resulting in more accurate OHIP estimates than from the separate analyses. Oneof the advantages over reservoir simulation is that, with the smaller number ofparameters in this approach, we can easily sample the entire posterior distribution,resulting in more complete quantification of uncertainty. The approach can also detectunderestimation of uncertainty in either volumetric data or material balance data,indicated by insufficient overlap of the prior and likelihood distributions. When thisoccurs, the volumetric and material balance analyses should be revisited and theuncertainties of each reevaluated.