Optimal number of Monte-Carlo simulations for hydrocarbon resources probabilistic estimation

Abstract

Background: Probabilistic resource estimation allows to assess the potential of oil and gas prospect, which is used for decision-making in the industry. The main result of the estimation is resource potential, expressed in probability distribution function of geological or recoverable hydrocarbon resources. Monte Carlo simulation commonly used for these purposes. It simulates the numerical value of the objective function.
 Aim: The aim of the work is to find the optimal number of Monte-Carlo simulations in the probabilistic resource estimation.
 Methods: Monte Carlo simulation is based on repeated calculation of the function describing the process using a random number generator. The function variable defined by statistical distributions is calculated using random number. Further, mathematical operations are performed on all variables of the function according to the mathematical model. Summarizing the obtained set of results, the statistical distribution describing the desired function is approximately estimated.
 Results: The accuracy of distribution function estimation increases with an increase of the number of simulations. However, this tend to increase the computation time. Thus, there is a choice between the speed and accuracy of the solution.
 The Latin hypercube reduces the influence of the random number generator imperfection, but intermediate calculations with Latin hypercube attenuate the decrease in the number of simulations compared to random sampling.
 Conclusion: Based on the results of the work, a logarithmic dependence of the calculation accuracy on the number of Monte Carlo simulations was obtained. In most cases, 10000 simulations with accuracy about 1% will be sufficient.