A probabilistic model of petroleum discovery

Quantitative Geology and Geostatistics, 2005

There are two major problems in construction of a stochastic model that describes quantitatively the spatial distribution of undiscovered petroleum accumulations: a) available exploration results are biased and b) information associated with the locations of accumulations is incomplete. Studies in the Western Canada Sedimentary Basin (WCSB) and elsewhere indicate that the spatial characteristics of petroleum accumulations are fractal. In this paper we propose the use of these fractal characteristics to calibrate sampling bias, thus deriving an unbiased spatial correlation (covariance function) for the stochastic modeling. The uncertainty in the modeled locations of undiscovered accumulations resulting from insufficient information is captured by equal-probable realizations of the simulation and these are subsequently converted to a probability map of petroleum occurrence. In the example, a pre-1994 exploratory data set for the Rainbow gas play in WCSB was used to derive simulation parameters. A comparison of the simulated results to post-1993 gas discoveries in the same play shows that most of the post-1993 discoveries are located in areas with high predicted probability values.

Mathematical Geology, 2000

An approach is proposed to predict the spatial distributions of undiscovered petroleum resources. Each pool is parameterized as a marked-point. The independence chain of the Hastings algorithm is used to generate an appropriate structure for pool combinations in a play. Petroleum-bearing favorability estimated from geological observations is used to represent the sampling probabilities of pool locations. An objective function measuring

Mathematical Geology, 2000

An approach is proposed to predict the spatial distributions of undiscovered petroleum resources. Each pool is parameterized as a marked-point. The independence chain of the Hastings algorithm is used to generate an appropriate structure for pool combinations in a play. Petroleum-bearing favorability estimated from geological observations is used to represent the sampling probabilities of pool locations. An objective function measuring the distance between characteristics of the realization and constraints is constructed from both the pool size distribution and entropy maximum criterion, in which the entropy criterion places all undiscovered pools in the most favorable positions. The geometrical convergence property of the proposed Hastings algorithm is presented. The method is illustrated by a case study from the Western Canada Sedimentary Basin.

Natural resources research, 1996

Recently, Manly's method has been successfully applied:to hydrocarbon exploration modeling in order to approximate the expected value and the standard deviation of the total amount of hydrocarbons discovered. This method is much faster than running prolonged simulations normally required by the probabilistic model of the hydrocarbon discovery process, and the results axe very accurate. This paper extends the usefulness of the approximation method by developing an approximate analytical model of the whole probability distribution of the total volume of hydrocarbons discovered. The mean and the standard deviation from Manly's approximation are used to help set the parameters of a family of beta distributions, to represent the distributions of the total amount of hydrocarbons discovered from the beginning to the end of the exploration process in an area. Three real datasets-the Nova Scotian Shelf from offshore northeastern Canada, the Bistcho Play, and the Zama Play from northwestern Canada-are chosen to verify the methodology developed. Confidence intervals of the forecast for each number of discovered fields are constructed from the analytical approximation and compared with confidence intervals generated by the simulation. Sensitivity analyses are performed to show that the idea of using a family of beta distributions is a robust approximation.

Mathematical Geology - MATH GEOL, 2002

Undiscovered oil and gas assessments are commonly reported as aggregate estimates of hydrocarbon volumes. Potential commercial value and discovery costs are, however, determined by accumulation size, so engineers, economists, decision makers, and sometimes policy analysts are most interested in projected discovery sizes. The lognormal and Pareto distributions have been used to model exploration target sizes. This note contrasts the outcomes of applying these alternative distributions to the play level assessments of the U.S. Geological Survey's 1995 National Oil and Gas Assessment. Using the same numbers of undiscovered accumulations and the same minimum, medium, and maximum size estimates, substitution of the shifted truncated lognormal distribution for the shifted truncated Pareto distribution reduced assessed undiscovered oil by 16% and gas by 15%. Nearly all of the volume differences resulted because the lognormal had fewer larger fields relative to the Pareto. The lognorma...

Journal of Energy Research and Reviews

The chance to discover hydrocarbon volumes of economic quantity diminishes with progressive discovery in explored basins. Given the preponderance of smaller deposits in extensively explored basins and the cost implications of discovering deposits less than the required Minimum Economic Reserves (MER), explorationists and investors in exploration activities need a framework to evaluate the chance of a successful petroleum resources discovery to minimize the risk of unsuccessful exploration. This study develops a new framework to evaluate the chance of discovery of at least a minimum economic reserves volume in an extensively explored basin. It leverages on the postulation for the determination of probability of hydrocarbon economic success as a building block for the new framework. The model combines the concepts of Minimum Economic Reserves, Discovery Efficiency and Probability to derive an explicit analytical function for discovery efficiency and hydrocarbon probability for a comme...

Mathematical Geology, 2006

Stochastic simulation has been proven to be a useful tool for revealing uncertainties in petroleum exploration and exploitation. The application to petroleum resource assessment would result in predicted potential accumulations with geographic locations, a desirable feature for improving both resource management and exploration efficiency. The associated uncertainties with the prediction provide information useful for exploration risk analysis. This attempt has been encumbered by two typical technical difficulties: biased observation data and lack of information with respect to the undiscovered accumulation locations. In this paper we propose a model-based simulation approach, in which models are used to perform unbiased parameter estimation from biased data and to facilitate the location of undiscovered petroleum accumulations based on reasoning of available geological and geophysical observations. The Fourier transform algorithm is chosen for the simulation because the spatial correlation and location-specific features can be studied separately from different data sources and integrated in the simulation in a frequency domain. The proposed approach is illustrated by an example from the Rainbow petroleum play in the West Canadian Sedimentary Basin. In the application example, a pre-1994 exploration history data set was used as input, and the predictions are then checked against the locations of post-1993 exploratory drilling results. The comparison of the predictions from the proposed approach and the traditional conditional simulation shows that the model-based approach captures the essentials of geological controls on the spatial distribution of petroleum accumulation, thus improving the projections of undiscovered petroleum accumulations.

Journal of Petroleum Science and Engineering, 1993

The problem considered in this paper is that of estimating the nature of the size distribution of petroleum reservoirs and their values. The method used consists of a Bayesian technique for parameter estimation. A sampling procedure based on minimizing the mean squared error of the posterior Bayesian estimator is developed using the beta density function to model the prior distribution. This Bayesian approach provides several typical representative distributions which are broad enough in scope, to provide a satisfactory economic analysis. These distributions reflect general patterns of similar regions, and include dry holes, as well as several representative class sizes of discoveries, and of course the probabilities associated with each of these classes. Mathematical expressions are provided for the probability estimates for the three-category case, as well as for the general case ofk samples. This Bayesian method permits a more detailed economic analysis than is possible by the use of binomial distribution, where wells are simply classified as good or bad.

2020

The homophobia of a number of Christian and Jewish denominations can be traced back to two verses in the Hebrew Bible, Leviticus 18:22 and Leviticus 20:13. One generally overlooked characteristic of both these passages is that their normative thrust is gendered. My argument will start from this obvious fact to conduct an inquiry into the way the feminine is constructed in the Holiness Code. The conclusion of my analysis is that the real object of the Biblical prohibition it not sex between men but the erasure of the social difference between man and woman, which poses a formidable threat to the status of the only subject whose existence is acknowledged by the social order of ancient Israelitic culture, the adult human male. And, of course, the very anxiety associated with this possibility is a clue to the fact that in the Holiness Code gender is conceived of not as an essence but as the intrinsically unstable result of relationships, events, and negotiations; in short, as what thous...

Sumario: I. Introducción. II. Juicio de amparo colectivo. III. Interés legítimo. IV. Algunos ejemplos relevantes de amparos colectivos en nuestro sistema jurídico mexicano. V. Conclusiones.