Abstract

Various geomechanical-modeling approaches, which cover a wide range of techniques and complexity, have been developed to assess the stability of a borehole and/or the integrity of well casing. The ability to confidently use these models can be limited, however, because they generally do not allow the model user to consider the "real-world" variability of the input parameters defined in the models. Often, these geomechanical models do not adequately accommodate the innate variability of the rock properties (mechanical and petrophysical) of the target reservoirs. Consequently, this deterministic approach too often results in uncertainty about the "correct" value of a critical parameter to use and insecurity in the model results. Decisions based on these results can later, not surprisingly, be found to be incorrect. Model users attempting to overcome the limitations noted above have tried various techniques. Subjective estimation, arbitrary "minimums", grading techniques, and stepwise estimation have all been commonly used.

Recently, more powerful techniques such as Monte Carlo simulation and decision analysis have come into popular use. Over the past decade these two techniques have been extensively used in the petroleum industry to evaluate and solve a wide range of analytical problems in reservoir engineering and the geosciences. In this paper, the application of these techniques to a number of generalized geomechanical problems will be illustrated. A Monte Carlo simulation enables the user to identify, measure or estimate, and evaluate uncertainties in the problems being analyzed. The simulation models the random behavior of the input variables much like in a game of chance. That is, the variables have an uncertain value within a known range for any particular time or event. Numerical model and software packages are developed based on the Green's function for a nucleus of strain in the reservoir. The model is coupled with reservoir simulations to evaluate pressure maintenance and reservoir development schedule effect on casing integrity, fault stability via sensitivity studies. The geomechanics solutions would be coupled with both commercial or in-house developed reservoir simulators. The results of multiple simulations, done to determine the most likely outcome of various wellbore solution options, are reported in the current paper.

Risk Analysis and Uncertainty

Uncertainty about numbers is prevalent in all reservoir management decisions. How large are the reserves of a proposed new exploitation project? What will be the average market price for the reservoir produced? What is the optimum production rate for the project? Each of these numbers is an unknown quantity. If the profit or pay out from a proposed project strategy depends on various unknown quantities, then the final answer can not be computed without making some prediction of these unknown quantities.

A common approach to this problem is to make a "good-faith" point estimate for each of these unknown quantities and use these estimates to compute the possible benefit of each proposed project strategy. But there is a serious problem with this method because it completely ignores the inherent uncertainty the project faces. A better approach is to incorporate uncertainty into the analysis, assess the randomness or probability distributions for any variable quantities, and analyze these variables in a spreadsheet model that simulates the project.

When we say that a random variable in a spreadsheet represents some unknown real quantity, we mean that any event for this simulated random variable is just as likely as the same event for the real unknown quantity. For example, if the unknown number of competitive entrants has a probability 0.10 of being 1, then the random variable in the spreadsheet should also have probability 0.10 of being 1 after the next recalculation of the spreadsheet. For any number k, the probability that the random variable will be less than k after the next recalculation should be the same as the probability that the real unknown quantity is less than k.

It should be noted that there have been various geomechanical-modeling techniques developed in the past to assess the stability of a borehole and/or the integrity of well casing. McLellan and Hawkes (1998) have observed that these models cover a wide range of techniques and complexity. The ability to confidently use these models can be limited, however, because they typically do not allow the model user to consider the "real-world" variability of the input parameters defined in the models. Risk and uncertainty are not considerations in the models. It is too common that these geomechanical models do not make adequate allowances for the innate variability of the rock properties (mechanical and petrophysical) of the reservoirs being studied. Too often, this results in uncertainty about the "correct" value of a critical parameter to use and, consequently, insecurity in the model results. Decisions based on these results can later, not surprisingly, be found to be incorrect.

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