Fundamentals and Applications of the Monte Carlo Method
- E. Stoian (Oil and Gas Conservation Board)
- Document ID
- Petroleum Society of Canada
- Journal of Canadian Petroleum Technology
- Publication Date
- July 1965
- Document Type
- Journal Paper
- 120 - 129
- 1965.Petroleum Society of Canada
- 5.2 Reservoir Fluid Dynamics, 5.7 Reserves Evaluation, 4.3.4 Scale, 1.6.10 Coring, Fishing, 6.1.5 Human Resources, Competence and Training
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Perhaps no industry is more vitally concerned with risk than the oil and gasindustry, and few professional men other than petroleum engineers are requiredto recommend higher investments on the basis of such uncertain and limitedinformation. In recent years, the number of methods dealing with risk anduncertainty has grown extensively so that the classical approach, usinganalytical procedures and single-valued parameters, has undergone a significanttransformation. The use of stochastic variables, such as those frequentlyencountered in the oil industry, is now economically feasible in the evaluationof an increasing number of problems by the application of Monte Carlotechniques.
This paper defines the Monte Carlo method as a subset of simulationtechniques and a combination of sampling theory and numerical analysis.Briefly, the basic technique of Monte Carlo simulation involves therepresentation of a situation in logical terms so that, when the pertinent dataare inserted, a mathematical solution becomes possible. Using random numbersgenerated by an "automatic penny-tossing machine" and a cumulative frequencydistribution, the behaviour pattern of the particular case can be determined bya process of statistical experimentation. In practical applications, theprobabilistic data expressed in one or several distributions may pertain togeological exploration, discovery processes, oil-in-place evaluations or theproductivity of heterogeneous reservoirs. The great variety of probabilitymodels used to date (e.g., normal, log-normal, skewed log-normal, linear,multi-modal, discontinuous, theoretical, experimental) confirms a broad rangeof experimental computations and a genuine interest in realisticrepresentations of random impacts encountered in practice.
Emphasis in this paper is directed to the salient characteristics of theMonte Carlo method, with particular reference to applications in areas relatedto the oil and gas industry. Attention is focused on reservoir engineeringmodels. Nevertheless. management facets of the oil and gas business areconsidered along with other applications in statistics, mathematics, physicsand engineering. Sample size reducing techniques and the use of digitalcomputers are also discussed.
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