Report on application of Probability in Risk Analysis in Oil and Gas Industry


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1 Report on application of Probability in Risk Analysis in Oil and Gas Industry Abstract Risk Analysis in Oil and Gas Industry Global demand for energy is rising around the world. Meanwhile, managing oil and gas projects are becoming more challenging and riskier than ever before. The well drilled may turnout to be oil bearing or dry, which brings in the uncertainty. The average cost of a dry hole is in excess of $20 million. Other uncertainties are thickness of reservoir parameter, oil intervals. Therefore, risk analysis and development of strategies to manage risk are crucial to the reduction of potential future delays and cost overruns in oil and gas projects. This report focuses on risks involved in the estimation of Oil and Gas reserves using Volumetric Estimation (which depends on Porosity, area and thickness of the reservoir) and Monte Carlo simulation which lets you see all the possible outcomes of your decisions and assess the impact of risk, allowing for better decision making under uncertainty. Estimating Porosity and Water Saturation using distributions Porosity and water saturation are parameters often thought to be negatively correlated. These variables are among the data generally available for individual completion intervals as well as reservoirs. This example examines a process of estimating porosity and water saturation from electric well logs. The purpose is twofold. We compare the effects of using uniform versus triangular distributions to generate the estimates. Given estimates of bulk density and true formation resistivity from logs, we want to estimate formation porosity and water saturation. This problem can focus on either an interval in a given wellbore or on a reservoir with several well penetrations where we hope to describe average formation properties throughout the reservoir. Distribution functions to each of several parameters, including the bulk density, formation resistivity, and others, and then deduces corresponding distributions for porosity, formation factor, and water saturation  the outputs. Each uncertain input is represented by a Uniform distribution. For contrast, we also examine a parallel case, using Triangular distributions for each of the uncertain parameters. Then run simulation and step through the output ranges. We can compare the results of Uniform input parameters to Triangular input parameters. The overall result is quite plausible: using Triangular distributions for each of the input variables causes a much steeper CDF. This behaviour would be more obvious for models where the output variables were either sums or products of the inputs. The model involves exponential functions, roots, and rational functions. Nevertheless, it should seem reasonable that when we assign more probability to values of the input variables close to their means, which is what happens with the Triangular distribution compared to
2 the Uniform, the output variables reflect the same pattern. To put it differently, when the inputs have less uncertainty (as measured by the variance), so do the outputs. Triangular p.d.f.  use a triangular distribution if you know very little about the distribution. The Triangular Distribution Function can be completely defined by knowing the absolute minimum value, the most likely value, and the absolute maximum value. It can also be easily skewed to match reality. When people estimate "most likely" values of parameters they tend to favour the answers they want. In other words, most people will underestimate cost projections and overestimate income projections. Therefore, the absolute minimums and maximums should be skewed to compensate for this "natural" bias. What is Monte Carlo simulation? Monte Carlo simulation is a computerized mathematical technique that allows people to account for risk in quantitative analysis and decision making. Monte Carlo simulation furnishes the decisionmaker with a range of possible outcomes and the probabilities they will occur for any choice of action. It shows the extreme possibilitiesthe outcomes of going for broke and for the most conservative decision  along with all possible consequences for middleoftheroad decisions. How Monte Carlo simulation works Monte Carlo simulation performs risk analysis by building models of possible results by substituting a range of values  a probability distribution  for any factor that has inherent uncertainty. It then calculates results over and over, each time using a different set of random values from the probability functions. Depending upon the number of uncertainties and the ranges specified for them, a Monte Carlo simulation could involve thousands or tens of thousands of recalculations before it is complete. Monte Carlo simulation produces distributions of possible outcome values. By using probability distributions, variables can have different probabilities of different outcomes occurring. Probability distributions are a much more realistic way of describing uncertainty in variables of a risk analysis. Common probability distributions include: Normal Or bell curve. The user simply defines the mean or expected value and a standard deviation to describe the variation about the mean. Values in the middle near the mean are most likely to occur. An example of variable described by normal distributions includes energy prices. Lognormal Values are positively skewed, not symmetric like a normal distribution. It is used to represent values that don t go below zero but have unlimited positive potential. An example of variable described by lognormal distributions includes oil reserves. Uniform All values have an equal chance of occurring, and the user simply defines the minimum and maximum. An example of variable that could be uniformly distributed includes manufacturing costs. Triangular The user defines the minimum, most likely, and maximum values. Values around the most likely are more likely to occur. An example of variable could be described by a triangular distribution include past sales history per unit of time. During a Monte Carlo simulation, values are sampled at random from the input probability distributions. Each set of samples is called iteration, and the resulting outcome from that sample is recorded. Monte Carlo simulation does this hundreds or thousands of times, and the result is a probability distribution of
3 possible outcomes. In this way, Monte Carlo simulation provides a much more comprehensive view of what may happen. It tells you not only what could happen, but how likely it is to happen. Monte Carlo Methods Measurement Determining the volume of oil that can be recovered from an underground reservoir requires several measurements to be combined. Running 3D seismic surveys may cost $50,000/day and exploratory wells between $1million and $20million, thus an estimate of reserves is based the combination of data elements from a limited number of sample points. For example the porosity determined from the discovery well may not be representative of the field as a whole. Thus whilst a core sample may have porosity of 10%, a geologist with experience of an area may treat this value as a triangular distribution with a minimum value of 2.5%, a modal value of 7.5% and a maximum value of 20%, giving a mean value of 10%. The same principle can be applied to the area of the field, its thickness and recovery factor all of which are combined using the formula: V= A x T x P x R Where: V is the volume of oil which will be recovered from the reservoir A is the area of the reservoir T is the thickness of the reservoir P is the porosity of the reservoir, this is the %age of the reservoir's rock volume which is void space. For example, if a reservoir has a porosity of 10%, the void space in 1 cubic meter of rock which might contain fluid is 0.1 cubic meter. R is the recovery factor. Not all the oil from the reservoir will be recovered; the recovery factor is an estimate of the %age that can be extracted economically from the reservoir. Using the Monte Carlo technique we can derive an estimate of the recoverable reserves in the form of a distribution. The choice of distribution for each parameter depends on the nature of the parameter and the amount of data available to estimate them. In this example, we'll use a triangular distribution for all the independent variables. An alternative would be a lognormal distribution. Parameter Units Minimum Mode Maximum Area KM Thickness M Porosity % Recovery % Evaluating the reserves formula 1 million times and sorting the results so that they can be plotted on a probability density curve, yields the highly left skewed plot shown in Figure 1. Whilst in Figure 2 frequency curves and probability density graphs give a good visual indication of skewness and kurtosis, the cumulative probability curve has the advantage that probabilities can be visually extracted.
4 Figure 1 The spread of reserves of our hypothetical oilfield in cubic meters is: Figure 2 5% 194,000 50% (Median) 839,000 95% 2,286,000 Mode 400,000 Triangular distributions are used in oil and gas exploration where data is expensive to collect and it is almost impossible to model the population being sampled accurately, thus subjectivity plays a greater role than in data rich sectors. The geologist determines the maximum and the minimum value of a particular variable example size of field. The example below shows a subjective assessment of the expected size of discoveries in the United Kingdom's East Midland's Basin: Figure 3 The figures below are the porosity of rock samples from deep bore holes. These are very expensive to collect and only a few are available to the analyst who may be asked to provide input for some form of MonteCarlo evaluation: 10.0%, 13.5%, 15.5%, 20.0% The successive bisection algorithm estimates the mode as 14.5%. The mean value of the observations is 14.75%, using this value together with the min and max into this formula sets the mode as 14.25%: Mode = 3 x mean max  min A subjective estimate of the mode by a cautious analyst might set the mode at 12%.
5 Conclusion We see that the estimation procedure followed in determining the parameters and eventually giving the estimate of oil reserves. But since drilling a well requires a huge investment the estimates are checked by various tools available for example the Palisade Corporation & Brighton Webs Ltd. Statistical and data services for Industry have individual software for performing all these estimation. The risk involved oil reserves estimation is calculated and based on the profit the wells are drilled. References: Monte Carlo Estimation: Brighton Webs Ltd. Statistical and data services for industry Volumetric Estimation: Palisade Corporation
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