سیستم های فازی، احتمال ترکیبی برای تجزیه و تحلیل ریسک در چشم انداز اکتشاف نفت

Petroleum exploration is an economical activity where many billions of dollars are invested every year. Despite these enormous investments, it is still considered a classical example of decision-making under uncertainty. In this paper, a new hybrid fuzzy-probabilistic methodology is proposed and the implementation of a software tool for assessing the risk of petroleum prospects is described. The methodology is based in a fuzzy-probabilistic representation of uncertain geological knowledge where the risk can be seen as a stochastic variable whose probability distribution counts on a codified geological argumentation. The risk of each geological factor is calculated as a fuzzy set through a fuzzy system and then associated with a probability interval. Then the risk of the whole prospect is calculated using simulation and fitted to a beta probability distribution. Finally, historical and direct hydrocarbon indicators data are incorporated in the model. The methodology is implemented in a prototype software tool called RCSUEX (“Certainty Representation of the Exploratory Success”). The results show that the method can be applied in systematizing the arguing and measuring the probability of success of a petroleum accumulation discovery.

Petroleum exploration is an economic activity plenty of decision problems involving risk and uncertainty. As economical and technological resources are limited, managers of petroleum companies frequently face important decisions regarding the best allocation these scarce resources among exploratory ventures that are characterized by substantial financial risk and geological uncertainty. Few years ago, many petroleum companies improved their exploration performance by using principles of risk analysis and portfolio management. According to Rose (2001), in present days, the adoption of standardized risk analysis methods are essential to portfolio management, in order to optimize the allocation of exploration capital. There are a lot of activities involved in modern petroleum exploration business. Tasks range from modeling geologic theories and data acquisition to econometrics simulations and selection of reservoir, drilling and completion technologies. In this work, we focus our attention to the problem of estimating the chance of success of finding hydrocarbon on a given prospect. That is once an appropriate geological model has been established and an exploration area has been selected, the next step in petroleum exploration is the identification of drilling prospect by geoscientists. This process is critical and requires geotechnical expertise and creativity. After the prospect has been identified, estimating the chance that a producible hydrocarbon accumulation is present, is one of the most important tasks in order to determine the prospect’s value. For many decades of petroleum exploration ventures has been dealt with probability theory as the formal tool to handle and represent uncertainty quantities (da Silva, 2000). Such representation are usually expressed as a probability value, known as “probability of success” (geological or economical), found by the combination of other probabilities that represent, the assessment of geological factors as source rock, trap, reservoir and seal, considered individually and combined by traditional and numerical methods as Monte Carlo Simulation (Behrenbruch et al., 1985, Newendorp and Schuyler, 2000 and Rose, 1992). Despite the great progress in economical risk analysis and portfolio management, the “probability of geological success”, i.e., the discovery of a hydrocarbon accumulation in a given exploratory prospect, is still a new and very hard area of research. Uncertainty is intrinsically involved in all petroleum venture predictions, and particularly in chance of discovery (Rose, 2001). The problem is how to express the technical uncertainties realistically, and in a form that can be used in economic equations in order to estimate the economical risk (Rose, 2001). Geologist suffer in trying to reduce very complex and uncertain knowledge in just a single few numbers that represent the exploratory chance of success. There are extensive attempts in systematizing the process of correctly estimate chance of success of finding hydrocarbon on a given prospect (MacKay, 1996, Newendorp and Schuyler, 2000, Otis and Schneidermann, 1997 and Rose, 2001). But, as this process is done by different geoscientists, in different geologic areas and under a very competitive scenario, it frequently leads to optimistic or pessimistic bias in the prospectors estimative (Rose, 2001). The bias is a very important problem in prospect risk assessment. If the prospect chance of discovery or economic value are contaminated with biased estimates, the exploration company’s decision investments will lead to suboptimal economic performance (Rose, 2001). The more relevant type of bias that affect judgment under uncertainty are Overconfidence – predictive ranges are too narrow, indicating that estimators are much less accurate than they think they are; Overoptimism – prospectors exaggerate magnitude of reserves or chance of success in order to sell the deal; and Representativeness – analog based on small sample size may not be statistically significant (Rose, 2001). The fuzzy set theory has been used to represent and solve problems of petroleum evaluation. Chen and Fang (1993), Chen et al., 2002 and Tounsi, 2005 use fuzzy logic and approximate reasoning to asses petroleum field in different regions. In most of these studies, the geological factors are coupled with multiple-criteria decision-making theory. However, this approach has some inconveniences: the incorporation of a posteriori knowledge as historical and direct hydrocarbon indicators data cannot be easily incorporated in the system, and the difficulty to incorporate qualitative expressions like “excellent”, “fair” or “poor” in the economical evaluation formulas. In this paper, we present a new fuzzy-probabilistic methodology capable to represent uncertain geological knowledge and the prototype software tool called RCSUEX (”Certainty Representation of the Exploratory Success”) that implements the methodology (Schoeninger, 2003). The main purpose of this work is to provide a method to deal with the problem of systematizing the process of correctly estimate chance of success of find hydrocarbon on a given prospect and to facilitate and to standardize the geologist argumentation task. This fuzzy-probabilistic methodology is founded in the following assumptions: risk can be qualified by set of questions and answers concerning the decision problem (Hardman & Ayton, 1997); when expressions like “moderate” and “severe” are significant for the domain expert, then fuzzy sets are more suitable for knowledge representation than “classical” or crisp sets (Terano, Asai, & Sugeno, 1994); fuzzy logic is adequate to represent uncertainty in petroleum geology (Chen and Fang, 1993 and Fang and Chen, 1990); the beta probability distribution is pertinent to represent the certainty of success of a random variable in a Bayesian approach (Groot, 1970). The paper is organized as follows: in Section 2, describes how risk analysis can be applied in the petroleum exploration process focusing in the elements of the hydrocarbon system and estimating the chance that a subsurface trap exist and if it is capable to store and accumulate hydrocarbons. Section 3 presents how fuzzy reasoning can be used as a very efficient mechanism to deal with incomplete and imprecise data, and knowledge expressed in vague and linguistic terms that characterize the petroleum risk evaluation problem. In this section, fuzzification, rule evaluation and defuzzification are described separately and particularities specific for the problem are discussed. Section 4 describes the process performed in our system (RCSUEX) to map from a subjective fuzzy domain to a objective probabilistic domain. Section 5 explains the importance and the methodology to incorporate historical data and Direct Hydrocarbon indicators in order to improve risk assessment. This section proposes a mathematical model that put together the objective perspective with the subjective one. Section 6 shows the application of the proposed method for a simple prospect risk assessment. Section 7 gives conclusions and brief discussion on the proposed methodology.

In this paper, we have presented a new fuzzy-probabilistic representation of uncertain geological knowledge where the risk can be seen as a stochastic variable whose probability distribution counts on a codified geological argumentation. The risk of each geological factor is calculated as a fuzzy set through a fuzzy system and then associated with a probability interval. Then the risk of the whole prospect is calculated using simulation and fitted to a beta probability distribution. Finally, historical and direct hydrocarbon indicators data are incorporated in the model. The hybrid fuzzy-probabilistic approach provides a strong modeling framework for a consistent and systematic utilization in argumentation of prospect appraisal. The fuzzy approach can deal with incomplete data and imprecise information typical in the exploratory domain. Observed frequencies of success coming from historical observations and direct hydrocarbon indicators are incorporated in the model. The application of the theory of fuzzy sets to model the exploratory reasoning using linguistic terms allows to better understand the decisions and uncertainty concerned with the prediction of hydrocarbon accumulations. The process of definition of input variables and elaboration of rules permits knowledge and expertise aggregation by many company specialists and favors the treatment of more critical uncertainties. We proposed that considering the fuzzy expert system output as favorability risk for each geological factor and associating it with probability intervals allows the connection between the fuzzy geologic interpretation and the probabilistic approach. With favorability of success now in the probabilistic domain, we showed how to use Bayesian probability theory in order to put together the objective perspective with the subjective one using the Bayesian model of Bernoulli distribution conjugated with Beta distribution, so it can be calibrated by comparisons with portfolio outcomes. The system was applied in a simple hypothetical prospect example in order to evaluate the application of methodology. The proposed system is geologically sound and first results agreed with expected probability assessed by company experts. As chance is expressed numerically it can be directly used by corporate systems into economic analysis of exploration ventures. In the future we expect to apply the system on real petroleum prospects.,