Integration of Volumetric and Material Balance Analyses Using a Bayesian Framework To Estimate OHIP and Quantify Uncertainty
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ABSTRACTEstimating original hydrocarbons in place (OHIP) in a reservoir is fundamentally important in estimating reserves and potential profitability. Two traditional methods for estimating OHIP are volumetric and material balance methods. Probabilistic estimates of OHIP are commonly generated prior to significant production from a reservoir by combining volumetric analysis with Monte Carlo methods. Material balance is routinely used to analyze reservoir performance and estimate OHIP. Although material balance has uncertainties due to errors in pressure and other parameters, probabilistic estimates are seldom generated.In this paper we use a Bayesian formulation to integrate volumetric and material balance analyses and to quantify uncertainty in the combined OHIP estimates. Specifically, we apply Bayes rule to the Havlena and Odeh material balance equation to estimate original oil in place, N, and relative gas-cap size, m, for a gas-cap drive oil reservoir. We consider 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 the posterior distribution allows quantification of uncertainty in the estimates of N and m resulting from the combined volumetric and material balance analyses.Our investigations show that material balance data reduce the uncertainty in the volumetric estimate, and the volumetric data reduce the considerable non-uniqueness of the material balance solution, resulting in more accurate OHIP estimates than from the separate analyses. One of the advantages over reservoir simulation is that, with the smaller number of parameters in this approach, we can easily sample the entire posterior distribution, resulting in more complete quantification of uncertainty.
