Comprehensive Wellbore Stability Analysis Utilizing Quantitative Risk Assessment

Comprehensive Wellbore Stability Analysis Utilizing Quantitative Risk Assessment Daniel Moos 1 Pavel Peska 1 Thomas Finkbeiner 1 Mark Zoback 2 1 GeoMechanics International, Palo Alto, CA 94303 2 Stanford University, Stanford, CA 94305 Abstract Utilization of a comprehensive approach to wellbore stability requires knowledge of rock strength, pore pressure and the magnitude and orientation of the three principal stresses. These parameters are often uncertain making confidence in deterministic predictions of the risks associated with instabilities during drilling and production difficult to assess. This paper demonstrates the use of Quantitative Risk Assessment (QRA) to formally account for the uncertainty in each input parameter to assess the probability of achieving a desired degree of wellbore stability at a given mud weight. We also utilize QRA to assess how the uncertainty in each parameter affects the mud weight calculated to maintain stability. In one case study, we illustrate how this approach allows us to compute optimal mud weight windows and casing set points at a deep water site. In another case study, we demonstrate how utilizing a comprehensive stability analysis and QRA allow us to assess the feasibility of underbalanced drilling and openhole completion of horizontal wells. I. Introduction Mechanical failure of a wellbore is a result of the interplay between in situ stress, rock strength, and engineering practice. While a number of techniques have been developed to predict optimal operational parameters such as mud weights or drilling trajectories, these techniques have been limited to deterministic analyses that are based on the assumption that in situ conditions and rock properties are precisely known. In reality, geomechanical parameters are never known precisely, due to insufficient data and the need to extrapolate available information over a depth range for which any given parameter may vary as a function of depth. An additional problem relates to the intrinsic uncertainty or error associated with each measurement. To quantify the effects of these uncertainties on wellbore stability predictions it is necessary to utilize probabilistic methods. Although probabilistic methods have frequently been used in the oil industry, e.g. to evaluate the expected value of a project, their application to wellbore stability is quite recent. Ottesen et al. (1999) presented a new statistical approach based on Quantitative Risk Analysis (QRA) that provides a means to assess uncertainties in input data and defines the results in terms of the probability to achieve a desired degree of stability as a function of mud weight, utilizing 3D constitutive based on linear elasticity. McLellan and Hawkes (1998) applied a similar approach to sand production prediction, utilizing poro-elastic constitutive models. 1

This paper outlines an interactive approach to QRA that consists of four basic steps: (1) Quantifying uncertainties in input parameters, (2) calculating response surfaces for critical mud pressures, (3) performing Monte Carlo simulations, and (4) plotting probability of success as a function of mud window that prevents the well from both collapsing and losing circulation. In contrast to previous methods such as that presented by Ottesen et al. (1999), this approach analyzes both the collapse pressure and the lost circulation pressure to derive a mud window, it utilizes a Monte Carlo approach which allows sampling of data uncertainties from the actual distributions of the measured parameters (as well as from functional forms for these distributions such as normal or lognormal distributions) and it provides a means to identify the critical parameters which contribute the most to the uncertainties in the results. By determining which data have uncertainties that are large enough to affect the analysis and which data have small enough uncertainties that it is not necessary to refine their values, it is possible to prioritize data collection efforts by determining what new data need to be collected in order to increase the confidence in the stability analysis results. After reviewing the approach, we present two case studies of its application. The first case evaluates the likelihood that a conservative casing program proposed for a vertical well drilled in deep water can be modified to eliminate one casing string. The analysis predicts both the likelihood of success and reveals the data required to reduce uncertainties to acceptable levels, to provide both an assessment of the costs and of the benefits of additional data acquisition. Here the uncertainties are the result of lack of pre-drill data on rock strength and the magnitude of the greatest horizontal stress. The second example illustrates the application of QRA to assess the risks associated with underbalanced drilling and with open-hole completion of horizontal wells drilled through complex geology. Here most of the uncertainty is caused by real variations in physical properties along the horizontal well path, as although most of the reservoir is quite strong in this case, weak zones occur with sufficient frequency as to pose a considerable threat to aggressive drilling and completion strategies. 2. QRA Approach to Stability Analysis The range of safe mud weights to maintain wellbore stability lies between the wellbore collapse pressure and the lost circulation pressure. Wellbore collapse pressure (Pc) is the mud pressure below which the entire wellbore wall becomes unstable, which occurs when zones of compressive wellbore failure (wellbore breakouts) reach a critical width above which there is not enough remaining intact rock keep the well from collapsing. Increasing the mud weight decreases the width of breakouts. However, higher mud weights also increase the risk of lost circulation. The lost circulation pressure is the pressure at which a significant amount of mud is lost into the formation as a result of the initiation and propagation of hydraulic fractures. Both the wellbore collapse pressure and the lost circulation pressure are controlled by the in situ stress orientations and magnitudes, the pore pressure, the rock strength, and the wellbore orientation (e.g., Ito et al., in press). A number of data sources can provide information about the in situ stresses, the pore pressure, and the rock strength. The vertical stress (Sv) can be computed by integrating the weight of the overburden determined from density logs. The pore pressure (Pp) can be measured in sands, and although there are considerable uncertainties in the physical models used in the analyses, Pp trends in shales can be estimated using seismic velocity and can be refined using velocity or resistivity logs (see summary in Huffman, 2001). The minimum horizontal stress (Shmin) can be constrained by leakoff pressures measured using leakoff tests, but a more accurate determination requires measurement of shut-in or closure pressure, or through choked flow-back (Raaen, 2001). The uniaxial rock strength (Co) can be estimated from velocity data or other petrophysical data (e.g., Horsrud, 2001). The remaining parameter, the maximum horizontal stress (SHmax), cannot be measured directly but can only be 2

constrained using information on the occurrence and orientations of tensile wall fractures and the orientations and widths of breakouts (e.g., Moos and Zoback, 1990; Peska and Zoback, 1995). Figure 1 shows a typical example of the application of QRA, where the input parameter uncertainties are given by probability distribution functions (curves limiting the shaded shaded areas in the figure) that can be conveniently specified by means of the minimum, the maximum, and the most likely values of each parameter (Table I; Figure 1a). The probability distribution functions shown here are either normal or log-normal curves depending on whether the minimum and maximum values are symmetrical (e.g., Sv, SHmax, Shmin, and Pp) or asymmetrical (e.g., Co) with respect to the most likely value. In either case, the functional form of the distribution is defined by the assumption that 99% of the possible values lie between the maximum and minimum input values. (a) (b) Figure 1. (A) Probability density functions (smooth, shaded curves) and the sampled values used in the QRA analysis (jagged lines) as defined by the minimum, most likely, and maximum values of the stresses, the pore pressure, and the rock strength listed in Table I. These quantify the uncertainties in the input parameters needed to compute the mud weights limits necessary to avoid wellbore instabilities. (B) Resulting minimum (quantified in terms of the likelihood of preventing breakouts wider than a defined collapse threshold) and maximum (to avoid lost circulation) bounds on mud weights at this depth. The horizontal bar spans the range of mud weights that ensure a greater than 90% likelihood of avoiding either outcome resulting in a minimum mud weight of 12.4 ppg and a mud window of 0.75 ppg. 3

Once the input uncertainties have been specified, response surfaces for the wellbore collapse and the lost circulation pressures can be defined. These response surfaces are assumed to be quadratic polynomial functions of the individual input parameters. Their unknown coefficients in the linear, quadratic and interaction terms are determined by a linear regression technique that is used to fit the surfaces to theoretical values of the wellbore collapse and lost circulation pressures. The theoretical values are calculated for multiple combinations of input values that are selected according to the representative design matrix based on the minimum, maximum and most likely values. The calculations discussed in this paper assume that the rock behaves elastically up to the point of failure. The analysis can be generalized to model poroelastic responses as well as chemical and thermal interactions between the mud and the rock. After the response surfaces have been determined, Monte Carlo simulations can be efficiently performed to establish uncertainties in the wellbore collapse and the lost circulation pressures. Ten thousand random values of each input parameter are generated (red curves in Figure 1a) using a mean and standard deviation identical to that calculated for the appropriate probability density function (shaded curves). The ten thousand random numbers then enter the polynomial response surface functions to provide output values for the collapse and lost circulation pressures. The output values can be displayed either as histograms or as cumulative distribution functions of the likelihood of a given outcome. Table I. Minimum, most likely, and maximum values of the input data used in the QRA analysis shown in Figure 1. Parameter Minimum Value Most Likely Value Maximum Value Sv, ppg 13.22 13.92 14.62 SHmax, ppg 16.24 17.10 17.96 Shmin, ppg 12.84 13.52 14.20 Pp, ppg 10.25 10.79 14.20 UCS, psi 1000 1400 1470 Figure 1b shows the cumulative likelihood of avoiding wellbore collapse (the lower bound curve on the left) and the cumulative likelihood of avoiding lost circulation (the upper bound curve shown on the right) as a function of the mud weight at the depth of interest. The horizontal line illustrates the range of mud weights that will simultaneously provide at least a 90% certainty of avoiding both collapse and lost circulation. This is because there is a greater than 90% certainty of avoiding collapse provided the mud weight is above 12.4 ppg (for example, a mud weight of 12.5 ppg provides a better than 95% certainty of avoiding collapse). At the same time, there is a 90% certainty of avoiding lost circulation provided the mud weight is less than 13.15 ppg (for example, for a mud weight of 13 ppg there is at least a 97% certainty of avoiding lost circulation). The analysis result suggests that optimum stability can be achieved utilizing a static mud weight close to the lower bound value of 12.4 ppg, and indicates that there is little likelihood of lost circulation so long as ECDs are below 13.1 ppg. Figure 2 shows an actual application of QRA to the selection of casing intervals. Figure 2a shows a deterministic analysis of the collapse and lost circulation pressures as a function of depth for a deep-water well. A casing design has been proposed based on this deterministic analysis. The stability of each open-hole section is controlled by the minimum value of the lost circulation pressure within the interval, and by the maximum value of the collapse pressure within the interval. In many cases (but not in all cases) the minimum lost circulation pressure occurs at the top of the interval, and the maximum collapse pressure occurs at the bottom of the interval. The design requires that a 0.5 ppg window must exist between these two values. However, because the input parameters (the stresses, rock strength, and pore pressure) are uncertain to some degree, there is also an inherent uncertainty in the predictions. 4

Wellbore Collapse Lost Circulation (a) (b) Figure 2. (a) Example showing a deterministic analysis of the mud weights required to prevent drilling problems (mud windows for each casing interval are indicated by shaded rectangles), along with recommended casing set points to maintain an adequate mud window between the collapse mud weight and the mud weight above which lost circulation may occur. (b) The cumulative likelihood as a function of mud weight to avoid lost circulation and collapse while drilling the 6 th casing interval. The shape of the upper bound is defined by uncertainties in the fracture gradient at the previous casing shoe. The shape of the lower bound is defined by the collapse gradient at the bottom of the interval. Figure 2b shows the effect of uncertainties in the input parameters for the analysis of the deepest casing interval. The stability of this interval is controlled by the lost circulation pressure at a depth of 9,997 feet (where the fracture gradient is smallest) and by the collapse pressure at a depth of 12,596 feet (where the wellbore collapse pressure is greatest). Once the uncertainties in the input parameters are specified at both critical depths, the response surfaces can be calculated, Monte Carlo simulations can be carried out, and the cumulative distribution functions for the wellbore collapse and the lost circulation pressures can then be plotted. Figure 2b shows the probability of avoiding drilling problems for various mud windows that are limited by wellbore collapse (increasing curve on the left-hand side) and lost circulation (decreasing curve on the right). The horizontal dashed line in Figure 2b indicates that there is at least a 47% chance of avoiding both wellbore collapse and lost circulation for the entire interval spanned by the deepest casing section, provided that the mud weight is kept between 13.90 and 14.30 PPG. 5

3. Feasibility for Underbalanced Drilling and Open-hole Completion of a Horizontal Well This case study evaluates the feasibility for underbalanced drilling and open hole completion of a horizontal well drilled into a slightly underpressured (Pp = 8.2 ppg equivalent) sand unit that is divided into an upper and lower unit by a layer of chert, and is cross-cut by a series of imbricate thrust faults. These faults repeatedly juxtaposed various intervals of the reservoir rocks thereby making it difficult to predict with certainty the rock properties along any well path. QRA analysis allowed calculation of a realistic estimate of the likelihood of avoiding collapse for horizontal wells, and also made it possible to assess the benefit of making additional measurements based on the extent to which they could reduce uncertainties in the predictions. Measured depth [feet] Gamma ray 0 50 100 150 x900 x000 x100 x200 x300 x400 Chert Sandstone Shale tc [µsec/ft] Excellent data were available to constrain pore pressure (from MDT tests), in situ stress orientation (from the observation of wellbore breakouts in acoustic wellbore image data), and all three principal in situ stress magnitudes (from extended leak-off tests, density logs, and observations of wellbore failure). We constrained compressive rock strength utilizing available wireline log data from offset pilot wells utilizing a strength model appropriate for these high porosity relatively weak rocks. Figure 3 shows gamma ray, lithology, sonic travel time and computed rock strength as a function of depth within the upper reservoir interval and the chert section. The sonic travel times reveal a significant increase in slowness upon entry into the chert section suggesting heavy fracturing, which is common for this brittle material; strength values are correspondingly reduced. 40 60 80 100 C 0 [psi; Moos et al.] 2000 6000 10000 x500 Figure 3. Gamma ray, lithology (chert in green, sandstones in yellow, and shales in grey), compressionalwave sonic transit time (inverse velocity) and predicted rock strengths calculated from sonic and density data using a relationship from Moos et al. (in press). 6

(a) (b) Figure 4. a) Histogram of predicted strength values for the reservoir interval proposed for underbalanced drilling and open-hole completion. b) Log-normal probability distribution function for rock strength Co consistent with the variation shown in the histogram in (a). Figure 4a shows a histogram of the predicted strength values, which generally range from 3,300 psi to 16,000 psi with a mean of 7,400 psi. Although the strength is lithology dependent, we consider the entire range of strength values to compute a lognormal probability density function for rock strength (Figure 4b) as input for the quantitative risk assessment (QRA). This is necessary primarily because the considerable lithologic complexity of the reservoir precludes predictions prior to drilling of the precise sequence of rock types expected along any one horizontal well section. For the other parameters of the geomechanical model (i.e., SHmax, Shmin and Sv magnitudes and the pore pressure) we assigned a default uncertainty of ±5% which is consistent with our experience when the appropriate data are available. Figure 5 shows the probability distributions of these four parameters, which are assumed in this case to be symmetrical about their mean values. Figure 5. The shaded regions show Gaussian probability density functions that provide a measure of the uncertainties in the values (in ppg) of the parameters comprising the geomechanical model (the rock strength distribution is shown in Figure 6). The jagged lines show the values of these parameters used in the Monte Carlo simulations to predict the likelihood of avoiding wellbore instabilities. 7

The cumulative distribution function which indicates the likelihood of avoiding wellbore collapse as a function on the mud weight used to drill the well is shown in Figure 6. Wellbore collapse is defined to occur when breakout widths surpass a critical limit such that the remaining intact section of the wellbore wall can no longer support the surrounding stress concentration and the well continues to enlarge. This successive enlarging of the well eventually leads to complete failure around the wall, hence collapse. We consider two values for the critical breakout width. Figure 6a shows the probability of avoiding breakouts that are larger than 30º, which is conservative for drilling, but is sufficiently small so that even if failure does occur it is likely to stabilize rapidly, limiting sand volume produced to controllable levels. Figure 6b shows the mud weights required to maintain breakouts smaller than 60º, which is safe for drilling, provided hole cleaning is maintained, but may lead to some risk for sand production over the life of the well. The cumulative likelihood of success using the conservative failure criterion (a breakout width of 30º) is 78% for a balanced well, and if the fluid pressure in the well is 1 ppg lower than the reservoir pressure the probability drops to 55%. For the less conservative failure criterion with a breakout width of 60º, the model predicts a success rate of 85% for balanced conditions and a 65% chance of success if the mud weight is 1 ppg lower than the reservoir pressure. Together these results suggest that underbalanced drilling is possible (although a 1 ppg underbalance is likely to be risky), but without further analysis open-hole completion is not recommended. P p P p Probability of success [%] 1 ppg underbalance Probability of success [%] 1 ppg underbalance Mud weight [ppg] Mud weight [ppg] Figure 6. Cumulative probability functions for wellbore collapse for the reservoir section of the well proposed for underbalanced drilling and openhole completion, using a critical breakout width of (a) 30º and (b) 60º. The solid line corresponding to a mud weight of 8.2 ppg indicates the pore pressure in the reservoir. Also shown is a vertical line that indicates a mud weight equivalent to 1 ppg underbalance. Figure 7 shows the QRA response surfaces that reveal the sensitivity of the predicted mud weight to the uncertainty of each input parameter. These response surfaces are quite flat for Sv, SHmax, and Shmin magnitudes and for the pore pressure, suggesting that these parameters are known with sufficient precision not to require additional analysis. However, the predictions are extremely sensitive to the compressive rock strength (Co). For the weakest rocks likely to be encountered (i.e., Co ~ 3,500 psi) a mud weight of 10 ppg is required. The strongest rock, in contrast, will be stable even if the fluid pressure in the well is much lower than the pore pressure in the reservoir. Thus the critical parameter necessary to refine the predictions of the lower bound safe wellbore fluid pressure is the rock strength. 8

Figure 7. Response surfaces for individual geomechanical parameters that illustrate the sensitivity of the mud weight predictions expressed in ppg associated with each parameter s uncertainty. Fortunately, it is possible to acquire the data necessary to measure the rock strength prior to completing the well using LWD and/or wireline log measurements. Because the uncertainties in the predictions are essentially independent of uncertainties in any parameters other than the rock strength, these measurements provide the information necessary to refine the results of QRA (which indicate that safe completion requires sand control measures) after drilling the well but before running casing or screens. Thus in this case the QRA analysis provides both a reasonable constraint on safe mud weights for drilling, and a recommendation for data acquisition to reassess completion decisions that can be implemented in the course of drilling the well. 4. Effect of Uncertainty on Casing Design for a Vertical Well in Deep Water Pre-drill planning incorporating a geomechanical analysis of stress and wellbore failure to minimize stability problems has been demonstrated to be extremely cost-effective for deep-water wells (van Oort, 2001). However, data uncertainties can be quite large due to a number of factors, and thus there are often large uncertainties in the predictions of the safe range of mud weights appropriate to avoid stability problems. By applying QRA analyses it is possible quantify the mud weight uncertainties using reasonable estimates of the uncertainties in the input data, and to establish the benefits of additional measurements to reduce those uncertainties and thereby reduce the risk of later drilling problems. Figure 8a shows an example pre-drill well design for a vertical well in deep water which penetrated a large fault block into which no other wells had been drilled. A smooth pore pressure profile was calculated from seismic velocity data, and the fracture gradient was estimated using offset well leak-off pressures. Because of uncertainties in both estimates, the casing depths and mud weights were selected to provide at least a 1 ppg mud window for all but the first two casings. In order to reach TD given these design constraints, six casings were required. 9

(a) (b) (c) Figure 8. (a) Proposed casing design for a vertical well in deep water, showing mud weight windows (shaded rectangles) obtained using Pp + 0.5 ppg, and FG 0.5 ppg. (b) Revised mud windows for the original program, which include the wellbore collapse pressure (solid red line). (c) An alternative casing program that honors the collapse and fracture gradient constraints and provides at least a 0.5 ppg mud weight window throughout. The mud window of 1 ppg ensures at least a 0.5 ppg safety margin for the pore pressure and the fracture gradient. While the 0.5 ppg safety margin for the fracture gradient may be justified, it is likely that the 0.5 ppg margin for the minimum mud weight can be reduced based on the recognition that it is required solely due to the necessity to maintain an unknown excess mud weight above the pore pressure to prevent collapse. In order to compute the collapse pressure it is necessary to determine the rock strength and the horizontal stress magnitudes. Fortunately, rock strength can be estimated from seismic velocity. An upper bound for the collapse pressure in a vertical well can then be computed, assuming that the least horizontal stress is equal to the shut-in pressure from previous leak-off tests and that the maximum horizontal stress is close to the vertical stress computed from the weight of the overburden. Because SHmax can vary between Shmin and Sv, the choice of this value for maximum horizontal stress will result in a worst-case deterministic constraint on the lowest safe mud weight. Figure 8b shows the mud window predictions for the original casing program determined using this new constraint. It requires that the lower limit of the mud window must be greater than both the pore pressure and the collapse pressure. At shallow depth, a mud pressure only slightly above the inferred pore pressure appears to be sufficient, but the collapse pressure is considerably higher than the pore pressure in the interval covered by the third and fourth casing strings. This effectively reduces the mud window for these casings to 0.6 ppg and 0.2 ppg, respectively, indicating a substantially greater risk of drilling problems for these intermediate casings. 10

Figure 8c presents an example of a new casing program that was designed by honoring the casing setting depth of the first string, and then requiring that each subsequent interval maintain a 0.5 ppg mud window between the collapse pressure and the fracture gradient. Only five casing strings are required, in comparison to the previous program that required six. To achieve this reduction it is necessary to extend the setting depth of the second casing string. We employ QRA to analyze the impact of uncertainties in the parameters used to evaluate this design on the setting depth for this string. The input parameter variations are listed in Table II. Figure 9 shows the result of the analysis of the required mud weight to maintain stability at the bottom of the second casing string, presented in terms of the cumulative likelihood of keeping breakouts small enough to maintain arch support as a function of mud weight. For a mud weight of approximately 9.3 ppg, which is the lower bound of the mud window for the second casing string predicted using the deterministic analysis shown in Figure 8c, 50% of these simulations predicted a breakout width that was smaller than the required value. Figure 9. Analysis of the probability of avoiding drilling problems, as a function of the mud weight used, while drilling the second casing interval shown in Figure 8c due to the uncertainties in the stresses, pore pressure and rock strength shown in Table II. The left-hand curve shows the cumulative probability of avoiding collapse at the bottom of the interval. The right-hand curve shows the cumulative probability of avoiding lost circulation at the previous casing shoe. The horizontal bar shows the range of mud weights between 9.3 and 9.8 ppg necessary to maintain at least a 50% probability of avoiding both events. 11

Table II. Minimum, most likely, and maximum values of the input data used in the QRA analysis shown in Figure 9. Parameter 4668 feet 5894 feet Minimum Most Likely Maximum Minimum Value Value Value Value Most Likely Value Maximum Value Sv, ppg 10.28 10.82 11.36 11.72 12.34 12.96 SHmax, ppg 11.73 12.35 12.97 14.90 15.70 16.46 Shmin, ppg 9.28 9.77 10.26 10.60 11.16 11.72 Pp, ppg 8.32 8.76 9.20 8.98 9.45 9.92 UCS, psi N/A N/A N/A 1660 1750 1840 At the same time, Figure 9 also shows the effect of the uncertain input data on the fracture gradient at the previous shoe. Based on the range of results from offset leakoff tests at similar depths, there is a 50% chance that a mud weight of 9.8 ppg will cause circulation losses. The likelihood of losses increases rapidly for higher mud weights, such that there is a 90% chance of exceeding the lost circulation pressure for a 10 ppg mud weight. As discussed above in the context of an analysis of stability at a single depth, this analysis of minimum lost circulation for the entire proposed casing interval, combined with the analysis of greatest required wellbore collapse pressure, can be used to assess the overall likelihood of success in completing the planned casing section. By selecting a particular required likelihood of success, it is possible to establish both the minimum mud weight necessary for safe drilling and the mud window, honoring the data uncertainties. In this case the horizontal bar indicates that a static mud weight of 9.3 ppg provides a 0.5 ppg mud window with a 50% combined likelihood of avoiding drilling problems. A number of variables contribute to the uncertainty in the above analysis. In order to investigate which of these is most important in defining the lower bound of the mud window for this casing interval, Figure 10 presents a sensitivity plot of the required mud weight to prevent collapse as a function of each input parameter. As can be seen, the uncertainty in the vertical stress has no influence on the results. Variation in the vertical stress between 11.72 and 12.96 ppg equivalent results in no change in the 9.28 ppg mud weight required to stabilize the well. The pore pressure has the single largest uncertainty and contributes the most to the uncertainty in the required mud weight (+/- 0.27 ppg). The uncertainty in UCS contributes a relatively small amount, whereas the magnitudes of SHmax and Shmin each contribute approximately +/- 0.15 ppg. Thus, a considerable additional measurement and analysis effort is required to reduce the uncertainty in the collapse pressure. On the other hand, the lost circulation pressure in this interval is controlled only by fairly large uncertainty in the least principal stress at the previous casing shoe. Thus, the best method for reducing the uncertainty in the likelihood of success for this interval is to conduct an extended leakoff test at the previous shoe, to (1) precisely determine the leakoff pressure, and (2) quantify the least principal stress at the top of the interval. This in turn will help to refine estimates of the least stress at the bottom of the interval. Subsequently, an extended leakoff test was conducted at the base of the second casing shoe that previously had not been included in the drilling program that resulted in a lower than expected leakoff pressure which justified the extra expense of the more conservative casing program. 5. Conclusions The above discussion illustrates a new approach to wellbore stability utilizing 12

Quantitative Risk Assessment to predict the required mud weights to avoid stability problems and the uncertainty in those predictions. This approach differs from previous methods in that it allows determination of the uncertainties in both the collapse and the lost circulation pressures, and explicitly analyzes these in terms of all three of the in situ stresses, the pore pressure, and the rock properties. Furthermore, it provides a measure of the effects of uncertainties in each of the input parameters on the output mud weight predictions, thereby revealing the key measurements needed to reduce uncertainties in the most cost-effective way. Finally, the method can be applied over large intervals of open hole, where the lowest mud weight to avoid collapse and the highest mud weight to prevent lost circulation can be calculated independently for the worst case depth in each instance. Figure 10. Sensitivity plots showing the effects of uncertainties in the input stresses, the pore pressure, and the rock strength on the minimum mud weight (vertical axis, in ppg) required to avoid collapse over the second casing interval shown in Figure 8c. With the exception of the vertical stress, large uncertainties in the required mud weight are associated with all of these parameters. Analysis of the degree of risk to a deepwater well associated with extending the depth of a shallow casing seat revealed that uncertainties in the actual width of the relatively narrow mud window for that casing interval could be reduced by conducting an extended leakoff test at the previous casing shoe. The same analysis suggested that it was not likely to be possible to reduce uncertainty in the collapse gradient sufficiently to provide enough of a benefit to justify the effort. Applying the approach to evaluate the risks associated with drilling a horizontal underbalanced well and utilizing an openhole completion strategy revealed that the biggest problem in quantifying the likelihood of success was the uncertain rock strength. While the predictions indicated a reasonable likelihood of success for underbalanced drilling, more stringent stability requirements for open-hole completion made it difficult to establish the likelihood of avoiding excessive sand production. However, the sensitivity analysis provided a recommendation for data acquisition that could be implemented in the course of drilling the well to reduce the uncertainty sufficiently to allow a reassessment of the recommendation not to complete the well without sand control. 13

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