Due to scarcity of data and/or prior knowledge of subsurface, uncertainty is always present in oil &gas exploration and production. Therefore, risk analysis is essential to the efficient field development.
In this study, in order to improve the quality of a risk analysis under a certain field development plan, a method for history matching and quantification of uncertainty of production forecasts using the Hamiltonian Monte Carlo (HMC) algorithm is proposed. The HMC algorithm is a Markov chain Monte Carlo (MCMC) technique that combines the characteristics of Hamiltonian dynamics and Metropolis algorithm to sample complex distributions.
The workflow basically consisted of the development of a program using HMC as a sampling algorithm and of the combination of this program with a commercial simulation software. The program was constructed and combined with the CMG commercial simulator. Then the effectiveness of the proposed methodology was examined fora realistic benchmark reservoir (PUNQ-S3), comparing the results by this program with those by other techniques.
It was confirmed that this program was effective for sampling parameter distributions and was successfully used to perform both history matching and quantification of uncertainty. The comparisons of the HMC with other algorithms were made by analyzing their performances for completing history matched models and for quantifying uncertainties. HMC and the other algorithms (Random Brute Force, Differential Evolution and CMG Designed Exploration & Controlled Evolution) presented the similar results for history matching, which reveals the effectiveness of the proposed algorithm for history matching. As far as the quantification of uncertainty, HMC was faster and showed a wider sampling distribution than Monte Carlo simulation. The results obtained in this study suggest that HMC is promising and can be used in the oil & gas industry.