Content of PetroWiki is intended for personal use only and to supplement, not replace, engineering judgment. SPE disclaims any and all liability for your use of such content. The oil and gas industry invests significant money and other resources in projects with highly uncertain outcomes. We drill complex wells and build gas plants, refineries, platforms, and pipelines where costly problems can occur and where associated revenues might be disappointing. We may lose our investment; we may make a handsome profit.

We are in a risky business. Assessing the outcomes, assigning probabilities of occurrence and associated values, is how we analyze and prepare to manage risk. Risk and decision analysis software is as diverse as the analysis methods themselves.

Risk and decision analysis -

There are programs to do Monte Carlo simulation and decision tree analysis. Analytic models to do economics can be linked to both Monte Carlo simulation and decision trees. Closely related are optimization, sensitivity analysis, and influence diagrams. Extending further, we encounter forecasting, expert systems, and fuzzy logic.

Any description of Monte Carlo simulation and decision trees must devote some time to the underpinnings of statistics and probability. Undergraduate engineering programs sometimes include one course in statistics, and graduate programs often require one. Unfortunately, what engineers take away from those classes does not always prepare them to deal with uncertainty analysis.

For whatever reason, engineers do not gain a level of comfort with the language nor see immediate use for it in their jobs.

Statistical concepts in risk analysis introduces the concepts of:. Correlation and regression, especially the former, serve to describe the relationship between two parameters. We use Excel to illustrate these descriptive statistics. This section clarifies what it means to fit historical data.

The premise is that we usually have a small sample taken from a huge population, which we wish to describe. The process begins by constructing a histogram from the data and then seeking a density function that resembles the histogram.

This statistical tool contrasts sharply with the well-known linear regression, in spite of the fact that their metrics to judge the goodness of fit appear similar. Three common distribution types—normal, log-normal, and binomial—are discussed at length to assist users in choosing an appropriate type when building a model. The central limit theorem establishes guidelines about sums and products of distributions. Monte Carlo simulation and decision trees are defined and illustrated, compared and contrasted.

Some problems yield to one or the other of these tools. Occasionally, both methods can serve a useful purpose. Decision trees are visual. Their impact diminishes as the model becomes larger and more complex.

Decision trees rely on expected value, but decision makers do not always do the same, which brings about the notion of utility functions. Decision trees have their unique form of sensitivity analysis, limited to tweaking one or two variables at a time.

Solutions to decision trees consist of a recommended path or choice of action and an associated expected value. Monte Carlo models do not result in a recommended course of action. Rather they make estimates, providing ranges rather than single values like deterministic models.

These models and the subsequent analysis and presentation show the wide range of possible outcomes and the probability of each. Additional tools such as optimization and options may also be useful.

A proper start in risk analysis requires investing time in the design of a model. Design of uncertainty models steps through the principal components of a Monte Carlo model:. Uncertainty analysis evolved during the latter half of the 20th century. Its underpinnings in statistics and probability were in place by Problem solving, especially in industrial engineering and operations research, was introduced in midcentury, following how to buy nasdaq shares in india theoretical modeling in physics, chemistry, and mathematics in the early s.

The computer revolution, and in particular the availability of desktop computers and spreadsheet programs in the s and s, supplied the final ingredient.

Of course, there had to be motivation and hard problems to solve. Numerical simulation methods such as reservoir and geostatistical models became established tools, making it easier to argue for Monte Carlo and decision tree tools. Risk analysis did not simply spring forth in full bloom in the midth century. Among its progenitors were the 17th- and 18th- century origins of probability theory in the context cash burn cash earnings. Although some notable contributions to probability and statistics appeared much earlier Cardano, Galileo, Gauss, Fermat, the Bernoulis, De Moivre, Bayesit was waitrose altrincham opening hours new years eve until the end of the 19th century that statistics became formalized with pioneers like:.

During the early and midth century, statistics focused on population. Statistics was a mature science by the early 20th century, though the field has advanced mightily since then. Gossett introduced the t-distribution in Fisher made several advances, including:. The roots of Monte Carlo simulation [the name of which was coined by researchers at Los Alamos National Laboratory US ] were in theoretical statistics, but its application of fuzzy theory to binomial option pricing model to a spectrum of practical problems accounts for its popularity.

The term Monte Carlo, as applied to uncertainty analysis, was introduced by von Neumann, Metropolis, and Ulam at Los Alamos National Laboratory around Hertz published application of fuzzy theory to binomial option pricing model classic article [3] in Ten years later there was commercial software available to do Monte Carlo simulation.

To appreciate a Monte Carlo model, we must first discuss deterministic and analytical models. It now may seem natural to recognize the uncertainty implicit in so many of the variables we estimate, but the early models from engineering, physics, and mathematics were deterministic: There was no uncertainty.

Thus, any Excel worksheet with at least one cell containing a formula that references other cells in order to calculate a result is a deterministic model. We calculated the time for light to travel from the sun to the Earth 8 minutes 19 seconds at the equinoxes. We used calculus to calculate the optimal order quantity that would minimize total cost—ordering plus storage plus stockout—for inventory models.

We found the regression line that minimized the sum of squared residuals for a crossplot. Introducing uncertainty amounts to replacing one or more input values with a range of possible values, or more properly, a distribution. This leads us to two classes of models, the Monte Carlo models, which are a central topic on this page, and another class called analytical models, which we discuss briefly.

The analytical model can be thought of as lying between deterministic models and numerical simulation.

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In an analytical model, the inputs might be represented as probability distributions, and the outputs are also probability distributions. But, unlike a Monte Carlo simulation, we find the output by a formula. Trading options dvd general, for independent distributions, the sum of the means is the mean of the sum, and the sum of the variances is the variance of the sum.

Things get complicated fast as our models get more complex algebraically, as we include dependence relationships and more exotic distribution types. Nonetheless, some work has been done combining probability distributions with formulas. Decision trees had their roots in business schools. They lie somewhere between deterministic and probabilistic models. They incorporate uncertainty in both estimates of the chance that something will happen and a range more properly a list of consequences.

Thus, they are probabilistic. The solution, however, is a single number and a unique path to follow. Moreover, the sensitivity analysis for decision trees, which adds credibility to the model, is often ignored in papers and presentations and is quite limited in its scope compared to Monte Carlo simulation. Industry courses sponsored by the American Association of Petroleum Geologists AAPG and Society of Petroleum Engineers SPE often emphasized exploration. Oddly, cost models and production forecasting were often given short shrift or treated trivially.

By the early s, however, while Wall Street was hyping hedges and both companies and individuals were wondering about optimizing their portfolios, several companies began marketing probabilistic cash flow models for the petroleum industry. The half dozen or so competing cash flow models in the petroleum industry began including some form of uncertainty analysis as optional features in their software.

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During the late s, SPE began an intensive dialog about probabilistic reserves definitions. Finally, bypioneers were promoting portfolio optimization and real options, both of which acknowledge volatility of prices.

Estimate Reserves by Using Computer Simulation Method.

Risk Analysis in Capital Investments. Harvard Buisness Review 95 1: Planning for Risk and Uncertainty in Oil Exploration. Long Range Planning 26 1: An Introduction to Risk Analysis. Evaluating Uncertainty in Engineering Calculations. J Pet Technol 19 Probability Models for Petroleum Investment Decisions. J Pet Technol 22 5: Probability Estimates for Petroleum Drilling Decisions.

J Pet Technol 26 6: Uncertainty and Risk in Petroleum Exploration and Development: The Expectation Curve Method. Presented at the SPE Asia-Pacific Conference, Sydney, Australia, September An Evaluation of Procedures to Estimate Uncertainty in Hydrocarbon Recovery Predictions.

Presented at the SPE Asia Pacific Conference on Integrated Modelling for Asset Management, Yokohama, Japan, April Comparing Three Methods for Evaluating Oil Projects: Option Pricing, Decision Trees, and Monte Carlo Simulations. Presented at the SPE Hydrocarbon Economics and Evaluation Symposium, Dallas, Texas, March Risk Analysis Of Tarsands Exploitation Projects in Trinidad. The Valhall Waterflood Evaluation: A Decision Analysis Case Study. Presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, October Coupling Probabilistic Methods and Finite Difference Simulation: Stochastic Formulation for Uncertainty Assessment of Two-Phase Flow in Heterogeneous Reservoirs.

Presented at the SPE Reservoir Simulation Symposium, Houston, Texas, February Oil and Gas Economics and Uncertainty. Society of Petroleum Engineers.

List of statistics articles - Wikipedia

Decision Analysis for Petroleum Exploration. Statistical concepts in risk analysis. Application of risk and decision analysis. Cost and time estimates. Resources and reserves models.

Problems with deterministic models. Challenges with probabilistic models. Design of uncertainty models. Join SPE Log in About Help. This page was last modified on 16 Julyat This page has been accessed 19, times.

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