Markov Chain Monte Carlo Methods for Reserves Estimation

Abstract Monte Carlo methods are used to integrate the data pertinent to reserves estimation including material balance, production decline, reservoir volumetrics, and petrophysics. Many of these techniques produce independent estimates of reserves and hydrocarbons initially in place (HCIIP): for example, material balance and volumetric methods independently estimate HCIIP. Similarly, independent estimates for recovery factors are obtained from production decline, analogue reservoir studies and simulation. Traditional Monte Carlo methods are unable to combine such independent estimates in a natural way. Markov chain Monte Carlo methods, on the other hand, enable all such data to be integrated leading to robust, unbiased and accurate estimates of HCIIP and reserves. The algorithms for achieving this are presented and illustrated using field examples. Introduction Monte Carlo simulation for the estimation of hydrocarbon reserves and fluids in place is a well established technique in the oil and gas industry. Traditionally, Monte Carlo estimation of hydrocarbons initially in place (HCIIP) and reserves uses samples from prior distributions of reservoir parameters, such as gross rock volume, porosity, with these samples being used to calculate the distribution of HCIIP or reserves directly. Generally, apart from the range constraints implicit in the prior distributions, no other constraints are applied to either the calculated output distributions or input variables. It is likely, however, that additional quantitative information is available which imposes constraints or dependencies between variables or constraints on the likelihood of the calculated HCIIP or reserves. For example, reserves estimates should be consistent with material balance, volumetrics, decline curves and analogue or expert opinion. This paper shows how the Markov chain Monte Carlo (MCMC) method can combine such information, and prior parameter distributions, to produce consistent estimates of HCIIP and reserves. The MCMC approach is similar to the acceptance-rejection method of Stoltz et al who used filtered Monte Carlo simulation.