Probabilistic and Fuzzy Models to Evaluate Uncertainties and Risks Related to HC Reserves Estimation

About the authors:

Alexander Ye. Altunin, Cand. Sci. (Tech.), Senior Expert, Tyumen Petroleum Research Center; aealtunin@rosneft.ru

Mikhail V. Semukhin, Dr. Sci. (Tech.), Chief Specialist, Tyumen Petroleum Research Center; mvsemukhin@rosneft.ru

Olga A. Yadryshnikova, Cand. Sci. (Tech.), Chief Manager, Algorithmization Department, Tyumen Petroleum Research Center; oayadrishnikova@tnnc.rosneft.ru

Abstract:

The methods for evaluating the error in the estimation of reserves and resources are becoming increasingly relevant. First, this is a requirement of international reserves classifications, and second, the knowledge of the reserves errors (or distribution function) ensures a correct geological and economic assessment of the reliability and risks for the recoverable reserves.

The paper analyzes the comparative potential of probabilistic and statistical methods (a robust Monte Carlo method, stratified samples from Latin hypercubes, use of discrete quantities), and Fuzzy Set Theory methods for evaluating uncertainties in the volumetric estimation of hydrocarbon reserves. Particular attention is paid to the analysis of the methods convergence rate and the stability of statistical estimates.

The robust Monte Carlo method, which is widely used for probabilistic estimation of hydrocarbon reserves, can be improved in terms of convergence and stability of results using a Latin-hypercube-based stratified sample. Alternatively, numerical operations on discrete random quantities (or histogram variables) using step-by-step condensation of probability distributions can be used.

The proposed numerical method allows solving large-scale problems, since it involves a linear, rather than an exponential, function of the problem order growth. It ensures high efficiency of solving large-scale problems due to the reduction of computational operations on modeling the initial probability distributions for each test. There is no bias in the evaluation results in repeated runs and sensitivity to program sensors of pseudo-random numbers. There is a possibility to update the model run results within the interval covering the point of interest.

Fuzziness and randomness, being qualitatively different types of uncertainty, are not mutually exclusive, but, on the contrary, are interrelated and complement each other in the analysis of the same events. This paper describes a method for finding the resultant reserves membership function using a direct method similar to the method of probability distributions condensation.

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