Uncertainty Modelling in Multi-Layered Reserve Estimation Using Monte Carlo Simulation

Abstract Risk and uncertainty are important aspects in petroleum engineering, which must be analysed and considered in reserve estimation. The petrophysical parameters such as porosity, permeability, saturation, net thickness and acreage that are pertinent to volumetric reserve estimate are measured with some degree of uncertainty and error. Data sources and means of acquiring data may also result in uncertainties in reserve estimation and forecasting reserve. However, oil and gas companies are indeed concerned with accurate oil and gas reserves and original hydrocarbon in place. In addition, they are interested in recoverable reserve and the time for the recovery process with certain degree of certainty and accuracy. These estimates are rarely accurate or the level of uncertainty sometimes make oil and gas project not economically profitable. The two established volumetric methods of reserve estimation are deterministic and stochastic. In both approaches, mathematical formulae are used to estimate volumes of hydrocarbon. However, the deterministic approach uses single value input parameters that are considered representative of the reservoir. Thus, the corresponding volumetric value obtained is a single best-estimate. On the other hand, stochastic reserve estimation considers the fact that each parameter cannot be represented with a single value due to the uncertainty and heterogeneities associated with these parameters, but it should be included in an interval and model using appropriate normal, lognormal, or triangular distributions. In this study, uncertainty in multi- layered volumetric reserve estimate was quantified using Monte Carlo simulation for all the uncertain parameters, and the total recoverable oil obtained from deterministic method subjected to the Oracle Crystal Ball software for sensitivity analysis. Pessimistic, most likely and optimistic reserve values were obtained with their respective certainty for all the simulation scenarios. Error parameters such as Standard deviation, mean, variance, skewness, kurtosis, and mean standard error were quantified. Very low value of 0.00241 as coefficient of variation indicated that there was a high level of confidence in this estimation based on the modelling of input parameters; and this resulted to 90%, 50% and 10% probabilities of the oil in place calculation as (130.22MMSTB), (88.31MMSTB) and (58.13MMSTB) respectively. Therefore, use of Monte Carlo simulation to modelled risk and uncertainty would increase investors' confidence, and reduce the risk and uncertainty associated with reserve estimates in general terms.