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Abstract The chief use of probabilistic methods is to assess risk and opportunity, making them most applicable to situations of significant uncertainty. Hence, the cardinal sin unique to probabilistic analysis is to underestimate the range of outcomes. Unfortunately, the situations of the greatest uncertainty are also the ones where poor judgment is most likely to create unreliable results and dangerous decisions. The best judgment in probabilistic analysis is that which recognizes the full range of uncertainty by carefully framing the problem and by avoiding pitfalls which artificially reduce the range of results. Introduction Probabilistic analysis has become an essential tool of the practicing reservoir engineer and reserve evaluator because its benefits are undisputed and well-documented. They include the following:Probabilistic analysis forces the practitioner to think more completely, thoroughly, and thus clearly about the issues at hand. Probabilistic analysis can reveal the drivers of value or risk more clearly, making it possible to focus on risk mitigation efforts, data acquisition, further analysis and upside potentials. The results of a probabilistic study give a decision-maker more information about upside and downside uncertainty to inform his business decisions, future plans and portfolio analysis. Probabilistic analysis communicates the uncertainty unambiguously (to those conversant in the terms of statistics). The first two uses add the greatest value. It is only in the framing, interrogation and audit of the model that the user obtains these advantages. Moreover, those benefits must be actively pursued in the process in order to obtain a meaningful quantitative result. Without judicious implementation of the model, the quantified results may mislead and endanger the decision-maker with unmerited confidence. Much effort has been spent on discussion of input distributions to the probabilistic analysis, i.e., the form and range of the uncertain variables. Unfortunately, these considerations are dwarfed in importance by the architecture of the model. Model architecture represents the way the model is set up, e.g., the type of calculation, the number of parts, the correlation of parts, and the rules in the model. The discussion below deals first with issues related to model architecture and second with issues related to the input distributions. In designing the architecture of a probabilistic model, it is essential to identify those drivers with the greatest impact on uncertainty, to consider all possible sources of uncertainty, to select an appropriate calculation methodology and level of detail. Input distributions are defined by range and form. Definition of these two parameters, however, is predicated upon proper understanding of biases and types of uncertainty. All of these are discussed below. Poor model-building causes an excessively narrow distribution of results and higher estimates of "reasonably certain" values. For example, the three most commonly cited pitfalls of implementation (aggregation, correlation, and range of input variables) all tend to reduce the range of outcomes. Ironically, though the high confidence end of the distribution is used to define Proved reserves, the extremes of a resultant distribution of outcomes are more poorly defined and subject to change than central estimates. Identifying the judgment calls which impact the range of results makes it possible to appreciate the limitations and subjectivity of probabilistic analysis. Model Architecture The single most important factor in the construction of a probabilistic model is the conceptual framework. This consideration more than any other affects the predicted range of outcomes.
Distinguished Author Series articles are general, descriptive representations that summarize the state of the art in an area of technology by describing recent developments for readers who are not specialists in the topics discussed. Written by individuals recognized as experts in the area, these articles provide key references to more definitive work and present specific details only to illustrate the technology. Purpose: to inform the general readership of recent advances in various areas of petroleum engineering. Introduction Monte Carlo simulation is a statistics-based analysis tool that yields probability-vs.-value relationships for key parameters, including oil and gas reserves, capital exposure, and various economic yardsticks, such as net present value (NPV) and return on investment (ROI). These probability relationships help the user answer such questions as "What is the probability that the NPV of this prospect will exceed the target of $1,500,000?" or "How likely is it that the reserves added from this year's exploration program will fall short of our planned production? "Monte Carlo simulation is a part of risk analysis and is sometimes performed in conjunction with or as an alternative to decision [tree] analysis. Putting aside for the moment a description of Monte Carlo simulation, the method has attracted its share of critics over the years. Their comments include "I did this in FORTRAN in 1964, It just never caught on. "; "Why not just add or subtract 10% to the base case?" ; "The answer is whatever you want it to be. "; "The answer depends on who is doing the simulation. "; "Garbage in, garbage out. "; "You never have enough data" ; "A black box, hocus-pocus, that's all it is, "; and "It takes too long to run enough cases. "To some degree, the critics have been silenced by the evolution of virtually universal spreadsheet programs, much faster computers, and relatively simple software to run simulation and process data. Nonetheless, we will address some of the underlying concerns, but it is necessary to lay some foundation first. Our objectives are (1) to define Monte Carlo simulation in a more general context of risk and decision analysis; (2) to provide some specific applications, which can be interrelated; (3) to respond to some of the criticisms; (4) to offer some cautions about abuses of the method and recommend how to avoid the pitfalls; and (5) to predict what the future has in store. What Is Risk Analysis? Although the word "risk" occurs with great regularity these days in the petroleum literature, it has not always been fashionable. In its 60-pageSubject Index, the 1989 printing of the 1,727-page Petroleum Engineering Handbook contains just one reference to "risk [factor]" in an article about property evaluation. Among the numerous words and phrases associated with risk analysis are decision analysis, risk assessment, risk management, portfolio management and optimization, and strategic planning. In some contexts, these words are used only in a qualitative sense, but our focus is quantitative. Decision analysis, in its broadest form, includes problem identification, specification of objectives and constraints, modeling, uncertainty analysis, sensitivity analysis, and rules that lead to a decision. Generally speaking, risk analysis and assessment refer to the quantification of uncertainty, almost always in the context of possible investments. In the oil and gas business, although much of the analysis might pertain to reserve size, capital cost, production forecasting, and the like, the bottom line universally is monetary value. Risk management connotes a second stage, where the investors seek protection from unfavorable situations; i.e., they work to mitigate the risks. Thus, turnkey contracts, guarantees, insurance, locked-in prices, and hedges are instruments of risk management. A portfolio is an aggregation of investments. Portfolio managers mix their prospects to reduce collective risk and enhance ROI. Optimization is often taken as maximizing some measure of reward, such as NPV or profit-to-investment ratio, subject to constraints on risk. Strategic planning involves portfolio management but may include more intangible aspects of investments, such as the advantage of having a presence in a country.
Summary. This paper summarizes the "state of the art" in classifying reserves of oil and gas with the emphasis on (1)worldwide inconsistencies in terminology and (2) problems in reconciling reserves calculated with deterministic methods and those calculated and classified with probabilistic methods. Hypothetical models are developed to investigate possible relationships between reserves calculated with the two methods. These models indicate that the relationship between the reserves calculated from deterministic and probabilistic methods depends on the nature of the statistical distributions of the input variables;chiefly, the skewness of those distributions.
Experienced reservoir engineers know that uncertainty exists in geologic and engineering data and, consequently, in the results of calculations made with these data. The degree of uncertainty in most reservoir engineering calculations, however, usually is not formally quantified. Most reserve calculations in the U.S. industry have been deterministic, with the degree of uncertainty indicated by classifying reserves as proved, probable, or possible (PPP). The addition of status categories-e.g., producing, behind pipe, or undrilled-to each reserve classification conveys additional information about the degree of uncertainty. The assignment of status categories is obvious; the assignment of reserve classifications, however, is rather subjective, despite efforts to develop global standards. In geologic settings and operating areas where the industry has substantial experience, there has been no compelling reason to use stochastic methods for reserve estimation. This is especially true for proved producing reserves, which are generally considered the least uncertain classification and category. However, in new geologic settings (for example, coalbed methane)and new operating areas (for example, the North Sea), the industry has used probabilistic methods to calculate and classify reserves in an attempt to assess the high degree of uncertainty typically associated with these types of ventures. The different approaches to reserve estimation and classification-deterministic vs. stochastic-have contributed to the problem of developing global standards for reserve classification.
Current Industry Practice
Most systems used to classify reserves of minerals are based on concepts first proposed by the U.S. Geological Survey (USGS), which are exemplified by what has come to be known as the "McKelvey box," shown in Fig. 1. This system classifies mineral resources using two attributes: (1) degree of geologic assurance and (2) feasibility of commercial extraction. Although initially proposed to classify "hard" mineral resources like coal, the concepts embodied in this system have been adopted by the oil and gas industry for the classification of reserves of crude oil and natural gas. In this context, "reserves" are the portion of the resource base that has been discovered and has a high feasibility of commercial extraction. As noted by McKelvey, the oil industry terms "proved," "probable," and "possible" have been associated with the terms "measured," "indicated,"and "inferred," as shown in Fig. 1, even though there is not a one-to-one correspondence in the concepts embodied in the two sets of terms. The meaning of the PPP terms varies between the major producing countries of the world and differs between various agencies within many countries. Private industry and governmental and regulatory agencies frequently use slightly different terminology or attribute different meanings to the same terms. Table 1, which shows the terminology in use by various agencies reported by the 1987 World Petroleum Congress, is an example of these inconsistencies. Although the PPP terms are widely used, the terms appear to imply different levels of uncertainty from one country to another. For example, both Austria and The Netherlands define proved as having more than 90% certainty and probable as having more than 50% certainty. The U.K., however, used the qualification "virtually certain" to define proved reserves, with probable reserves having more than 50% certainty. Three systems were reported for Australia. The Bureau of Mineral Resources reported using the PPP system. The Australian Minerals and Energy Council reported using a quantified PPP system, with 93, 60, and 5% certainty required for each of the three classification levels. The Natl. Energy Advisory Committee reported using a modified McKelvey system. Terminology differs between various groups in Canada. Most operators, consulting firms, and banks use the PPP system.
Abstract In oil and natural gas production projects, many investment and development plans are based on oil and gas reserve estimates. There is a large uncertainty in the calculation of hydrocarbon reserves because the input variables always contain uncertainties to some degree that propagate into reserve estimates. From the view point of a field investment, an accurate assessment of uncertainty in reserves is crucial for making decisions that will create value and/or mitigate loss in value. Therefore, to make good decisions, one must be able to accurately assess and manage the uncertainties and risks. In this study, we present an analytical uncertainty propagation method (AUPM) for modeling of uncertainties on volumetric reserve estimations. Analytical uncertainty propagation equations (AUPEs) are derived based on a Taylor-series expansion around the mean values of the input variables. The AUPEs are general in that correlation among the input variables, if it exists, can also be accounted for on the resulting uncertainty. Comparative studies that we have conducted show that the AUPM is as accurate as the Monte Carlo method (MCM). The AUPM provides a fast alternative to Monte Carlo simulation for accurately characterizing uncertainty markers such as variance, P90, P50, and P10. In addition, we present uncertainty percentage coefficient for simulating uncertainty contribution of each parameter and correlated parameter pairs to the total uncertainty in volumetric calculations. We also discuss the problem of probabilistic aggregation of reserves for projects involving more than one reservoir or field. We provide a general analytical formulation for estimating the values of mean, variance, P10, P50 and P90 for aggregated estimates. Probabilistic aggregation requires the knowledge of pair-wise correlation of the fields. In this study, we propose uncertainty sorting method (USM) to determine pair-wise correlation coefficients for multiple resources. The method provides a simple and fast analytical approach based on uncertainty percentage coefficient of individual field parameters. Proposed analytical models can be used as a fast tool eliminating the need for MCM.