Handling uncertainty in geomechanical design

This section focuses on handling uncertainity and lack of data in geomechanical design. If few, or no, wells have been drilled in an area, or few measurements exist from earlier wells, developing a reliable geomechanical model will be more challenging.

Geomechanical design with very little data

It is not necessary to have a well-constrained stress state to utilize geomechanical design principals. Sometimes, knowing just the stress regime (normal, strike-slip, or reverse), it is possible to estimate relative risk as a function of wellbore deviation and determine the importance of knowing the stress orientation. If geological analysis provides information about stress orientation as well, it is also possible to determine the relative risk as a function of wellbore azimuth.

Fig. 1 shows relative wellbore stability as a function of wellbore orientation at 5,000 ft in normal, strike-slip, and reverse-faulting regimes. In all cases, S_Hmax is oriented East-West (E-W).

As can be seen, the required mud weights and their variation with azimuth and deviation are quite different. The lowest mud weights are required in a normal faulting environment. Mud weight increases with deviation when both horizontal stresses are low, and there is only a small sensitivity of mud weight to drilling direction. Required mud weights are higher in the strike-slip regime, and there is a larger variation with drilling direction, especially at higher deviations. Vertical wells require the highest mud weight in this case. To drill in a reverse faulting environment, very high mud weights are necessary regardless of well orientation. The highest mud weights are required for vertical wells and for wells deviated to the North or South (the direction of the minimum horizontal stress), regardless of the amount of deviation.

Mud weight decreases with increasing deviation in other directions, and the lowest mud weights are required for wells drilled with high deviations to the east and west. Based on plots similar to Fig. 1, it is possible, given only an indication of the stress regime and its orientation (for example, based on the orientations of currently active faults), to define the relative mud weight required for wells drilled at different orientations. If seismic data are available, and the velocity data can be inverted to constrain pore pressure and rock strength, it is possible to make approximate predictions of required mud weights for wells of all orientations.

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  Fig. 1—Required mud weight to prevent excessive wellbore failure (breakouts) as a function of wellbore orientation at a depth of 5,000 ft, for normal (a), strike-slip (b), and reverse (c) faulting regimes. The gray scales are the same for all three cases.

Handling uncertainty

In cases in which no wells have yet been drilled in a new exploration area, estimates of required mud weight can have considerable uncertainties. It is, however, possible to quantify those uncertainties and also to learn what measurements are required to provide the maximal improvement in prediction accuracy, using quantitative risk assessment (QRA). QRA analyses can be carried out at a single depth, or over the range of depths between casing seats. Fig. 2 is an example of handling uncertainty at a single depth.

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  Fig. 2—This plot shows quantitative risk assessment (QRA) of the cumulative likelihood of avoiding excessive wellbore stability problems (in percent) as a function of mud weight, for the stress state and properties distributions shown in Table 1. A well drilled using a deterministic mud weight recommendation (dotted line) has a 67% likelihood to avoid wellbore instability.

In this example, a well is being drilled at a 30° inclination to the north in the strike-slip stress state used to compute Fig. 1.b. Based on the deterministic recommendation shown in that figure, the minimum mud weight required to drill the well without excessive instability is 14.6 lbm/gal. If at the time of analysis no well had yet been drilled, there would, however, be large uncertainties in the magnitudes of the two horizontal stresses and their orientations. It is also possible that the stress field may be inclined slightly with respect to the vertical. There may also be large uncertainties in the overburden stress, S_v, and in the rock strength and pore pressure, even if these had been estimated from seismic data. The parameter values and their uncertainties are shown in Table 1. Because QRA is carried out using a Monte Carlo approach, it is possible to allow asymmetrical distributions of the inputs, for example, for the rock strength.

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  Table 1-Range of Values For Input Parameters In Wellbore Stability Calculations For A Well That Is Deviated 30° To The North In A Strike-Slip Environment*

The results of the analysis are shown in Fig. 2. This figure plots the cumulative probability of avoiding drilling problems associated with wellbore instability as a function of mud weight. The predicted likelihood of avoiding problems using the mud weight calculated deterministically is only slightly greater than 60%, as shown by the vertical dashed line. To guarantee the well’s success, the mud weight would probably have to be higher.

The sensitivity of the mud weight recommendation to the parameter uncertainties is shown in Fig. 3. It can immediately be seen that the largest uncertainty is associated with the poorly constrained value of C_o. For higher values, the mud weight required to avoid instabilities is considerably reduced. In addition, the large variation in the magnitude of S_Hmax produces a similarly large uncertainty in the recommended mud weight. The pore-pressure uncertainty results in approximately ± 1 lbm/gal uncertainty. Uncertainties in the magnitude of the minimum stress and in the stress inclination contribute very little. Using these results, it is possible to design a data acquisition and analysis program that achieves the greatest reduction in uncertainty at the minimum cost. In this case, the most cost-effective improvement would result from a better constraint on the rock strength.

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  Fig. 3—This series of plots shows the sensitivity of the mud weight recommendations shown in Fig. 1.54 to the uncertain parameters. Plots such as these can be used to identify those parameters for which reduced data uncertainty would result in the biggest reduction in uncertainty in the recommended mud weight.

Even when rock properties and the stress model are well defined, there can be geological uncertainty based on poorly defined or unknown structure. An example of this is shown in Figs. 4 and 5 for a horizontal well drilled through hard sandstones containing an unknown distribution of intermittent shaley intervals. In such cases, the uncertainty is not caused by measurement error, but rather by the natural complexity of the structure being drilled. Fig. 4.a shows the distribution of log-derived strengths within this interval obtained from the pilot hole, which was drilled overbalanced. Fig. 4.b shows the distribution used for the QRA analysis, which has a similar shape. Using this distribution, the QRA analysis of the likelihood of excessive wellbore instability is shown in Fig. 5. It is clear from this figure that there is little risk associated with a balanced well. However, a well drilled with a 1 lbm/gal underbalance has only a 66% likelihood of avoiding excessive wellbore failure. Because the company for which the well was drilled was risk-averse, the decision was made not to attempt underbalanced drilling.

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  Fig. 4—(a) Histogram of log-derived C_o for a reservoir interval proposed for underbalanced drilling and openhole completion. (b) Log-normal probability distribution function for C_o consistent with the variation shown in the histogram in (a). (Reprinted from “Comprehensive Wellbore Stability Analysis Utilizing Quantitative Risk Assessment,” Moos et al., J. of Petroleum Science and Engineering, Vol. 38, pages 97–109, © 2003, with permission from Elsevier.)

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  Fig. 5—This figure shows the cumulative likelihood of successfully drilling a well for which the uncertainty in rock strength is caused by its variability within the reservoir, as shown in Fig. 1.56. In this case, the analysis suggests that there is a 90% likelihood of success for a balanced well, but only a 64% likelihood of success when drilling with a 1 lbm/gal underbalance. (Reprinted from “Comprehensive Wellbore Stability Analysis Utilizing Quantitative Risk Assessment,” Moos et al., J. of Petroleum Science and Engineering, Vol. 38, pages 97–109, © 2003, with permission from Elsevier.)

See also

Building geomechanical models

PEH:Geomechanics_Applied_to_Drilling_Engineering

Page champions

Rene Alcalde

Fersheed Mody, Ph.D., P.E.