Ab st rac t This paper reviews the state-of-the-art in casing/tubing structural reliability analysis, and the knowledge gained from it to date. Results are presented to show that, as previously suspected, burst design based on casing full of gas is overconservative for non-critical wells. However, the risk-calibrated design criteria are strongly dependent on the design philosophy for underground blowout loads. It is demonstrated that well control is the largest single factor in reducing risk; gaps in current knowledge are identified, and recommendations made for future work. Introduction Quantitative risk analysis (QRA) of well casing/tubing systems has undergone rapid development in recent years. The more notable projects have included a risk comparison of steel and 1 corrosion-resistant alloy completions ; methodology and software development, including a pilot study 2; a design code 3,4 calibration using working stress design ; application of QRA 5 methods to casing seat selection ; development of reliability based design design criteria criteria for for HPHT wells wells6; a design code calibration using load and resistance factor design (LRFD) 7,8; and preparation preparation of improved improved design equations equations for for casing casing collap collapse se9. The first stage of development of the subject is largely complete, in that the analysis models and software tools are now reasonably mature, and initial results are available. A review of these results shows that QRA has, as hoped, given answers to many of the important questions remaining in the subject, such as cost-benefit and the appropriate selection of design criteria. Equally, however, it has raised other questions that should have been asked at the beginning. This paper is written from the fortunate position of being, at long last, wise with hindsight. It reviews: 1. The state-of-the-art in well system QRA modelling. 2. The knowledge gained from it to date. 3. The questions which still need to be addressed. 4. The development required to gain this knowledge. The authors emphasise that, while a consensus is developing in many areas of the subject, the views expressed are theirs alone. They are largely based on in-house work carried out at WS Atkins during 1995-7.

Well System QRA QRA Models: t he State of the Ar t Risk Analysis and Structural Reliability. “Quantitative risk analysis” has been used with different meanings by past authors, and it may be helpful to define exactly what is meant. Safety engineering (or risk analysis) answers the question “what is the total risk in the operation of the facility?” As such, it generally considers all the possible risks to the asset and its personnel (e.g., travel to and from the platform, equipment failure, operational errors, etc.), as determined by a hazard identification exercise. The traditional approach is for the risk to be calculated using historical incidence data for each risk type, suitably adjusted for the given facility (e.g., number of wells, frequency of helicopter landings). The various risks, and the consequences of each risk event, are then combined to establish the total potential risk to life, risk to the asset, and so on. This process is called quantified risk assessment . Note this technique generally will not consider the effect of changes in design criteria, because it uses historical failure rate data. Structural reliability can either answer the question “what should the design criteria be?”, or establish the probability of failure of an existing design. It therefore only considers the risk of structural failure, which is usually a very small part of the whole. The risk is calculated by mapping the probability distribution functions (PDFs) of the various load and resistance variables to the predicted failure probability, using the ultimate limit state equations and mathematical techniques such as FORM/SORM (First/Second Order Reliability Method) or advanced Monte Carlo. A description of these techniques is beyond the scope of this paper, and the interested reader is referred to the literature10-12. While the term QRA has been used to describe either technique, in this paper it primarily refers to structural reliability. However, recent work in structural reliability has highlighted the importance of mechanical reliability and human error risks13, which are traditionally the preserve of safety engineers; and it is hoped that future work will address these wider issues. Analysis Methods. This section describes the various steps in a casing/tubing QRA. A consensus is developing in many areas, such as in the use of either FORM/SORM or advanced

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Monte Carlo to perform the probabilistic mappings. Where no consensus exists, the authors have described best current practice. While the treatment has been kept as simple as possible, some technical detail is unavoidable, and the reader interested primarily in the lessons learned may prefer to move directly to the next section. Input Variables. Field or test data is collected for each input variable, and the PDF type determined by plotting the raw frequency distributions onto probability scales 10,12. The PDF parameters are then calculated 14, including sampling uncertainty if required 15,16. Load and Resistance ULS Equations. The equations for the load and resistance ultimate limit states (‘ULS equations’) are chosen by comparison of predictions from the various candidate equations against field or full-scale test data (as applicable), for a statistically significant number of cases. In general, even the best predictive equation suffers from either mean point bias or underestimation of the output COV, or both. This is usually accounted for by treating the model uncertainty as a post-multiplicative random variable, whose PDF type and parameters are calculated during ULS equation selection10,12. Choice of Analysis. The next step is to determine whether a component or system reliability model is required to accurately characterise the probability response. A component reliability model is one which considers failure of one component (or location) only, whereas a system reliability model considers failure of more than one component or location. For casing/tubing systems, the resistance properties vary along the joint length, which would suggest the need to check the significance of system behaviour. System reliability modelling is more expensive than component reliability, and it is helpful to have some way of assessing the significance of system behaviour without having to do the f ull analysis. For linear systems such as casings, this can conveniently be done by superimposing the required number of component reliability models onto the mean load gradient. Each component model is treated as an independent realisation of 10,12 the resistance variables, using Monte Carlo simulation . The number of component models required is determined by the correlation length of the relevant resistance properties, that is, the length beyond which their realisations can effectively be treated as independent. The probability of failure (P f ) for each component model is calculated, and the system P f obtained as the survival probability of all components. The analysis is then repeated many times, to compensate for the sampling uncertainty of the resistance realisations, and the mean system P f taken. This is then compared against the predicted P f for a component reliability model situated at the highest stressed point (strictly, the point with the lowest margin between the mean load and mean r esistance). Three outcomes are possible, as follows. 1. For high mean load gradients, the component model is usually conservative.

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2. For moderate mean load gradients, the system reliability model gives slightly higher results, and the difference between the two models can be applied as a weighting factor. 3. For low mean load gradients, a system reliability model may be needed. For casing/tubing systems, most load cases fall into the first two categories. Model Implementation and Validation. The chosen ULS mappings are then implemented within a structural reliability program (e.g., STRUREL17), and the combined code validated. This is best done by comparison against the results of single-variable test problems for each load and resistance input. Design Code Calibration. The data space (or design space) is chosen by reference to the physically possible range of each deterministic parameter (e.g., bit depth, pore pressure, fracture gradient, etc). The most important parameters are identified by sensitivity studies, and if possible combined into dimensionless groups to reduce the number of data space variables. Separate data spaces may be required for each structural class (e.g., HPHT and non-critical wells). For casing/tubing systems, the above process usually results in two dominant data space variables. A range of values of each variable is taken, giving a 2D grid of possible designs. The tubular sizings for each grid point are obtained from the design equations, and the probability of failure calculated using the structural reliability program. The process is repeated for a range of design load levels, and the results plotted as graphs of risk versus design load (Figure 1). The graphs can be used to select the appropriate design criteria for a given tolerable risk level. The technique can be applied using either working stress design (single design factor) or load and resistance factor design (multiple or partial design factors). If the latter, then the partial factors are optimised so as to obtain the flattest possible reliability response across the data space (i.e., uniform risk). Techniques exist to determine a starting set of partial factors10, and thereafter the optimisation is done iteratively. Gas Kick Load Case. The description above is general for all load cases, and it may be helpful briefly to describe the analysis procedure for the gas kick load case. The failure probabilities were calculated using ADCOM, a program written for one of the first casing QRA studies 2, and further developed for subsequent work 3,4,6,9. It uses a multi-string 18 finite element casing/tubing analysis program (ADHOC) implemented within the STRUREL code for FORM/SORM analysis17. The kick circulation calculations use a single-bubble model with a constant influx pressure. The model uncertainty was obtained from field data and from calibration runs against distributed-bubble programs. The underground blowout loads are based on a gas column from the fracture strength at the casing shoe.

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ON THE CALIBRATION OF CASING/TUBING DESIGN CRITERIA USING STRUCTURAL RELIABILITY TECHNIQUES

The casing ultimate burst resistance employs the equation of Stewart et al. 199319, with the strain hardening terms set to unity: physically, this suggests that the behaviour of API carbon steels falls somewhere between that predicted by the Tresca and Von Mises failure models 19,20. The model uncertainty was obtained from full-scale test data. A component reliability model was used, as an initial system reliability analysis showed that the influence of system effects was small. The computer program was validated by comparison against single-variable test cases for each load and resistance variable. The agreement was very good, typically better than one part in a thousand throughout. The load variables taken as random are generally kick volume, kick intensity, formation fracture pressure, and model uncertainty. The resistance variables are local OD, minimum wall thickness, ultimate tensile strength (UTS), temperature degradation of UTS, and model uncertainty. Note that casing wear does not appear in the above list. This is because at present, there is insufficient field data to develop a reliable wear PDF. Therefore, existing results only strictly apply to vertical wells, in which wear is not usually significant; however, initial analysis suggests that it has only a small effect on failure risk. Similarly, current QRA models are for pipe body strength only. It is hoped that future work will include consideration of both wear and connection strength. The probability of failure is calculated by summing the risks for all possible outcome events, as shown in Figure 2. This requires three separate program runs, as follows: 1. Kick circulation (formation fracture). 2. Kick circulation (casing failure). 3. Underground blowout, resulting in casing full of gas (casing failure). Kick influx volume has a dual population of ‘normal’ and ‘escalated’ kicks, as described in the next section; so the kick circulation cases require separate mappings for each PDF, with the overall failure probabilities obtained pro-rata from the relative occurrence frequencies for each kick type. The total probability of casing failure is obtained from (Figure 2): Pf = ocfr ( Pfrac Puf Pu

+

[ Pfrac ( 1 − Puf ) + ( 1 − Pfrac ) ] Pc )

where: Pfrac

Pc

=

=

ocfr n ocfr

ocfr n ocfr

⋅

⋅

Pfrac n

Pc n

+

+

ocfr e ocfr

ocfr e ocfr

⋅

Pfrac e

Current Knowl edge Kick Loads. Figure 3 shows a typical joint distribution of kick volume and intensity 1 21. The horizontal axes are shut-in kick influx volume and kick intensity, and the vertical scale gives the number of kicks occurring in each volume-intensity ‘bin’. The kicks fall into three main groups, as described below. 1. Normal kicks, with low volumes (up to 60 bbl) and potentially high intensities (up to 8 ppg). These make up the great majority of kick events (80-90%, depending on well type). 2. Escalated kicks, with high volumes (80-400 bbl) but low intensities (0-2 ppg). These are much less frequent, and make up 10-20% of the whole depending on well type. It is thought that they are caused by difficulties in the well control process. 3. A small group of kicks with both high volume and high intensity (60-200 bbl, 6-8 ppg). While very infrequent, they are by far the most severe kick type. Unlike the first two categories, they occur solely in HPHT wells, and are caused by inadvertently drilling into the overpressured zone while still in the mud weight for the normally pressured zones above it. Note that they generally occur in the 12¼” hole section, and are therefore only an issue for intermediate casing design. This suggests two important conclusions. First, HPHT wells suffer a new and severe class of kick not seen in noncritical wells. QRA studies show that while intermediate casings can be sized to give safe designs for normal and escalated kicks, even the most onerous design criteria cannot give adequate safety levels for circulating the new kick class. This would suggest that risk management via well control procedures is more than usually important for HPHT wells. Procedures should focus on avoiding such kicks; also, procedures should be developed safely to deal with any kicks which do nevertheless occur. Secondly, escalated kicks are likely to dominate the circulation failure risk for non-critical wells. Risk analysis confirms that this is indeed the case, with a predicted failure probability 4-6 orders of magnitude higher than for normal kicks. For all practical purposes, therefore, one could base the 2 QRA on the escalated kicks alone, and neglect normal kicks . Design Criteria. A previous section has described how QRA can be used to calculate plots of notional risk versus design load (e.g., Figure 1). These curves are then used to determine the required design load for a given tolerable risk level (TRL); for example, for the well case used to p repare Figure 1, a TRL 1

⋅

Pc e

Pfrac, Pu and Pc are all calculated using the reliability program, and ocfr and Puf are based on historical data.

3

To protect confidentiality, the figure has been prepared by reducing the field data to PDF parameters, and synthesising the occurrences using random realisations. 2 At least for casing failure risks, where the failure point is down in the low-frequency tail. For formation fracture, where the failure probability is much higher, the failure point is in the parent distribution and the two kick types contribute more or less equally to the total risk.

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A.J. ADAMS AND T. HODGSON

-4

of 10 on total risk for a non-critical exploration well requires a design pressure of 0.77 times the casing full of gas pressure. For an HPHT exploration well, however, the same TRL requires a design pressure of 0.91 times casing full of gas: or equally, for a given design pressure, HPHT wells have a failure risk about an order of magnitude higher than that for non-critical wells. It is emphasised that the design pressures above are case-specific, and do not provide a basis for general well design. If we repeat the QRA for a range of shoe depths, and read off the required design loads for a given TRL, we obtain the bold line of Figure 4. Shallow wells require the highest design loads; or equivalently, for a constant design load, shallow wells have a higher failure risk than deep wells. The reason for this is simple. The historical kick data suggests a constant mean escalated kick volume with well depth; and shallow wells are therefore closer to the casing full of gas condition than deep wells. Note, however, that shallow wells are more likely to have oversized casings, because the steps in strength between available weights and grades are a larger proportion of the design load than for deep wells. This compensates in part for the higher risk on the load side. Returning to Figure 4, we see that it contains not one but two curves, which deserves a little explanation. Referring to the event tree in Figure 2, we see that event E1 is the risk due to casing full of gas (CFOG) loads after formation fracture and an unsuccessful dynamic kill. While underground blowouts are quite rare (the historical occurrence frequency for the North Sea is around 1 in 3000), we still want to have a reasonable safety level if one does occur; so there is a strong argument for setting a TRL on the conditional3 probability P u (the risk of casing failure after CFOG), as well as on the total probability Pf . This is the basis for the second curve of Figure 4 (dotted line), which was prepared by setting a separate (and higher 4) TRL on Pu only. The design is limited by the underground blowout risk Pu rather than the total risk P f ; and this is true not only for this well case, but for most cases for the intermediate and production casings. For the surface casing, the design is usually limited by the total risk P f . For cases governed by Pu, the limiting design load is almost constant with well depth (Figure 4), and we will investigate the reasons for this in the next section. For the moment, it is sufficient to note that if we choose to set a TRL on Pu, we get very good risk control (i.e., nearly uniform reliability) by using working stress design and a very simple design equation; and therefore, for the gas kick load case at least, more complex design methods such as load and 3

Conditional probability = probability of failure if the event occurs. Total probability = event occurrence frequency × conditional probability. 4 It is customary to set rather higher TRLs for conditional than for total probabilities, because the event itself has a low occurrence frequency.

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resistance factor design (LRFD) give only limited additional benefit. However, it proves that other load cases, such as tubing leak, do require LRFD to obtain uniform risk. Finally, we note that both curves lie below the traditional design basis for gas kick, namely the CFOG pressure; for the case chosen, a design pressure of 0.82 times CFOG would satisfy both TRLs. For all well cases, the range of design pressures for a TRL of 10-2 on Pu is 0.79 to 0.95, depending on well type, casing size, and shoe depth; and for a TRL of 10 -3, the similar values are 0.84 to 1.05. This confirms the longstanding suspicion that CFOG is over-conservative for the less severe well types, and that reduced design loads would still give acceptable safety levels. This raises the question of whether tubing leak will now govern the production casing design for non-critical wells. 4 Early QRA results for tubing leak suggest that design savings can likewise be obtained for this load case; and hence it should be possible to achieve cost savings for the production casing once a more detailed tubing leak QRA has been undertaken. Design Methods. The next question is therefore how best to implement the new design criteria. The expectation of most workers was that this would be done via limited-kick design (i.e., design for a given influx volume, with the wellhead pressure calculated from a single-bubble gas kick model); or more technically, that the design equations would have a volume basis. However, this supposition proved to be incorrect. The reason for this lies in the relationship between the design equations and the ultimate limit state (ULS) equations, on the load side. To achieve uniform risk, the design and ultimate loads should have a near-constant ratio across the data space; and we would therefore prefer the design and ULS equations to be based on the same physical effect, as this is most likely to achieve constant scaling. Now, tolerable risk levels (TRLs) have been applied both to P f , the total risk, and to P u, the risk of casing failure during CFOG. If the design is governed by the TRL on P u, then we will only achieve linear scaling by basing the design equations on a proportion of the CFOG pressure, rather than on the influx volume. Figure 4 shows that pressure-based design does indeed give near-uniform reliability for the underground blowout case; and as this case governs for the majority of wells, pressure-based design gives better risk control than volume-based design. This also explains why, for cases governed by the TRL on Pu, the design load is almost constant with well depth. The design equation is based on the CFOG pressure, multiplied by a factor to obtain the required safety level (Figure 4). For designs limited by P u, the ULS load equation is also based on the CFOG pressure, so there is an almost constant ratio between the design and ULS loads, regardless of influx depth. The only difference is in the two influx pressures: the design influx pressure is based on the pore pressure only, whereas the ULS influx pressure is a function of pore pressure plus kick

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ON THE CALIBRATION OF CASING/TUBING DESIGN CRITERIA USING STRUCTURAL RELIABILITY TECHNIQUES

intensity. The ULS gas column is therefore slightly denser, which causes the minor variation in design pressure seen in Figure 4. Table 1 compares the quality of risk control for pressureand volume-based design. Note that where the design is governed by the TRL on Pf , neither method gives particularly good risk control (as witness Figure 4, in which the required design load varies by nearly 30% with shoe depth); and therefore there may be merit in applying both a volume-based check to control circulation risks, and a pressure-based check to control underground blowout risks. This is, however, only an issue for a small minority of cases, such as shallow HPHT wells. Further work is required to determine the best design format for these cases. Well Control. In the preceding sections, we have seen that CFOG loads result in much higher risks than circulation loads, as one might expect. This suggests that calculation of the probability of developing CFOG (P cfog) is likely to be an important part of the risk analysis process. In the present method, it is obtained as (Figure 2): Pcfog

=

Pfrac Puf

Pfrac is obtained using the reliability program, and P uf is determined from historical data. As P uf is a measure of the effectiveness of the well control process, we can investigate the sensitivity of the total risk to well control by varying P uf about the historical average, as shown in Figure 5. The historical value of P uf is given by the central curve, and the likely upper and lower bounds by the curves marked ‘Puf = 0.1’ and ‘Puf = 0.001’ respectively. The variation in failure risk is around an order of magnitude; and while this analysis is only approximate, we can safely conclude that the total risk is likely to be sensitive to well control. The modelling issues are discussed in more detail in the next section.

Remaining Questions Escalation of Underground Flow to CFOG. Probably the most important remaining question concerns the treatment of Puf , the probability of underground flow escalating to CFOG. Currently, Puf is modelled as an occurrence frequency based on historical data, with the implicit assumptions that it is uniform over the load data space, and has a similar value for all well types. Both assumptions are open to question; and in order to understand why, we must briefly review well control methods. If the formation fractures during kick circulation, underground flow will generally result, with a further ingress of kick fluid at the influx point, and egress at the fracture point. There are two main approaches to dealing with this. The first is dynamic well kill (DWK) 22-24, in which heavy weight mud is pumped rapidly down the drillpipe to ‘dilute’ the kick as it travels to the fracture point, with slow flow down

5

the annulus to prevent its evacuation to gas. The second involves setting a cement, “gunk” or settling plug above the influx zone to block the f low path. This may not be successful if flow continues as the plug is being set. The most appropriate method varies from well to well. If the well control capacity (measured as available mud weight and volume, pump pressure and flow rate) is sufficient, then the well will eventually be brought to a s tatic full-of-killmud condition for DWK, or (if conditions are right) a plugged annulus for plug setting. If the capacity is insufficient, or the plug does not set, then continued flow will escalate into CFOG5, if bridging does not occur (see below). For any given combination of influx volume, kick intensity and kick tolerance, we can calculate whether the well can be dynamically killed; and the question of whether control can be regained is therefore more deterministic, as a function of the data space variables, than probabilistic in the sense of being uncertain of prediction. In practice, the more severe kicks (that is, those of high volume, high intensity or both) will result in underground flows which are very difficult to control, and which are likely to escalate to CFOG, whereas the less severe events can be dynamically killed or plugged. The CFOG load mapping will thus probably be concentrated in one corner of the data space; and the present assumption of a uniform P uf may therefore be oversimplistic. There remains one final question, namely whether CFOG will necessarily occur even if dynamic well control fails. In some underground blowouts, formation collapse in open hole leads to plugging of the flow path (often called bridging), and isolation of the casing. This should likewise be included in the QRA, if reliable historical data can be obtained; at present, it is conservatively assumed that bridging never occurs. Effect of Well Control Capability on Design Criteria. Sensitivity analysis on P uf (Figure 5) suggests that the ability to perform a successful dynamic kill, and hence to prevent the escalation of underground flow to CFOG, is probably the largest single factor in reducing the overall risk. However, as discussed above, this ability varies widely with available well control capability, reckoned as available mud weight and volume, pump pressure and flow rate. It is therefore quite possible that the level of well control capability may have a significant effect on the casing design criteria: or equivalently, that the design criteria by well type may need to be premised upon a certain capability level. Unfortunately, this question cannot be investigated with current QRA models, because they cannot explicitly model

5

Most of the papers on dynamic kill deal with the system capacity required to kill an existing blowout. However, the method 23 can also model the growth of initial underground flow into an uncontrolled blowout, or alternatively its containment; and it is this process which appears to dominate the overall risk.

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A.J. ADAMS AND T. HODGSON

dynamic well control. Effect of Kick Influx Behaviour. In present QRA models, the kick volume PDF is based on historical data for each well type (HPHT/non-critical, exploration/development, etc.); and this again supposes that all wells in each class behave similarly. This premise is likewise open to question, because shut-in volume is a function of formation permeability, hole diameter, rate of penetration, and reaction time; and at least some of these will vary from well to well. Whilst it can be argued that part of this variation is reflected in the distribution of recorded kick volumes, it would be well worth checking the risk sensitivity to formation permeability. This would require the inclusion of a kick influx model (as distinct from the current kick circulation model) within the reliability program.

Conclusions Design Philosophy 1. The design criteria for the gas kick load case depend principally upon whether it is considered possible for underground flow after formation fracture to escalate into a casing full of gas (CFOG) condition. There are currently two schools of thought on the matter. The first discounts the possibility of near-CFOG loads, on the basis either that modern well control techniques can potentially prevent all well control events from developing into blowouts, or that if a blowout does happen, bridging may isolate the casing from the flow. The second admits the possibility, on the basis that in practice well control capability is limited by human factors and equipment failure, and that bridging will not always occur. 2. For the first position (near-CFOG loads discounted), considerable savings can be made with respect to current design practice, although if such loads do occur, casing failure is almost certain. 3. For the second position (near-CFOG loads considered possible if unlikely), limited savings can be achieved with respect to current design practice. 4. Further work is necessary to determine which of the above views is the more valid. If possible, this should include field measurements of annulus pressure during UGBO events. Design Criteria (premised upon the possibility of near-CFOG loads) 1. For non-critical wells, burst design for casing full of gas is slightly over-conservative, and reduced design loads will still satisfy normal tolerable risk levels. 2. For HPHT wells, the predicted risk is at or slightly above tolerable levels even for CFOG design. Risk analysis for HPHT wells thus appears to be much more a matter of engineering the well design (seen as both tubular design and well control planning) to achieve acceptable saf ety levels, than of investigating possible relaxations in design policy. 3. The design equations should be based on a given

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proportion of the CFOG pressure, rather than on a given influx volume. 4. For the gas kick load case, working stress design gives almost uniform reliability for most well cases, and thus load and resistance factor design (LRFD) offers only limited additional benefit. For other load cases, such as tubing leak, LRFD gives appreciable benefit with respect to current design methods. Recommendations for Further Work 1. Escalated kicks result in much higher risk than normal kicks, and CFOG gives much higher risk than escalated kicks. Well control procedures should therefore consider means for preventing normal kicks from developing into escalated kicks, and escalated kicks from developing into underground blowouts. 2. No intermediate casing design can safely provide for the high-pressure, high-intensity kicks possible in HPHT wells. Procedures should focus on avoiding such kicks: this has already been recognised by the industry, as witness the effort made precisely to identify the geological sections of the transition zone in the Lower Cretaceous and Kimmeridge sections of North Sea HPHT wells. In addition, procedures should be developed to deal safely with any kicks which do nevertheless occur. 3. The effectiveness of well control is the largest single factor in reducing the overall risk, especially for HPHT wells. However, this field is only now becoming better understood and several questions remain to be addressed, including the effect of dynamic well control capability (available mud weight and volume, pump pressure and flow rate); the significance of kick influx behaviour (formation permeability, hole diameter, ROP and response time); and possible high-risk cases such as deep-water horizontal wells, high build rates, and synthetic OBMs. An understanding of these issues should result in improved well safety, and development of this area is strongly recommended.

Nomenclature ocfr = total kick occurrence frequency = ocfr n + ocfr e ocfr n = occurrence frequency for normal kicks ocfr e = occurrence frequency for escalated kicks Pc = total probability of casing failure during kick circulation Pc n = conditional probability of casing failure during circulation of normal kicks Pc e = conditional probability of casing failure during circulation of escalated kicks P f = total probability of casing failure (all outcome events) P frac = total probability of formation fracture during kick circulation P frac n = conditional probability of formation fracture during circulation of normal kicks P frac e = conditional probability of formation fracture during

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ON THE CALIBRATION OF CASING/TUBING DESIGN CRITERIA USING STRUCTURAL RELIABILITY TECHNIQUES

circulation of escalated kicks Pu = conditional probability of casing failure during CFOG Puf = conditional probability of underground flow escalating into CFOG

Ac kn ow led gement s The authors would like to thank WS Atkins Oil and Gas, for allowing publication of this paper; the Health and Safety Executive; BP Exploration, for funding the initial development of ADCOM; the participants of DEA Europe project DEA(E)64 (AGIP, Amerada Hess, Amoco, British Gas, BP, Conoco, Elf, Exxon, the HSE, Mobil, Norsk Hydro, the NPD, Phillips Norway, Ranger, Saga, Shell, Statoil, Texaco, Total and Unocal), for funding the ADCOM enhancements and associated technical development; Tim Harris (Shell), Torfinn Hellstrand (Statoil), Colin Leach (Well Control and Systems Design), Steve Parfitt (BP), and Flemming Stene (Saga), for many helpful conversations on the gas kick load case; and the SPE reviewers, for their constructive comments. References 1. Banon, H., Johnson, D.V. and Hilbert, L.B., “Reliability considerations in design of steel and CRA production tubing strings”, SPE 23483, Proc. 1st International Conf. on Health, Safety and Environment, The Hague, November 1991. 2. Adams, A.J., Parfitt, S.H.L., Reeves, T.B. and Thorogood, J.L., “Casing system risk analysis using structural reliability”, SPE/IADC 25693, Proc. SPE/IADC Drilling Conf., Amsterdam, February 1993. 3. Adams, A.J., “Quantitative risk analysis (QRA) in casing/tubing design”, Proc. 7th Annual Offshore Drilling Technology Conf., Aberdeen, November 1993. 4. Adams, A.J. and Glover, S.B. “An investigation into the application of QRA in casing design”, SPE 48319, Proc. SPE Applied Technology Workshop on Risk Based Design of Well Casing and Tubing, Houston, May 1998. 5. Parfitt, S.H.L. and Thorogood, J.L.T., “Application of QRA methods to casing seat selection”, SPE 28909, Proc. European Petroleum Conf., London, October 1994. 6. Adams, A.J., “QRA for casing/tubing design”, Proc. Seminar of Norwegian HPHT Programme, Stavanger, January 1995. 7. Lewis, D.B. et al., “Load and resistance factor design for oil country tubular goods”, OTC 7936, Proc. 27th Offshore Technology Conf., Houston, May 1995. 8. Brand, P.R., Whitney, W.S. and Lewis, D.B., “Load and resistance factor design case histories”, OTC 7937, Proc. 27th Offshore Technology Conf., Houston, May 1995. 9. Adams, A.J. et al., “On the development of reliability-based design rules for casing collapse”, SPE 48331, Proc. SPE Applied Technology Workshop on Risk Based Design of Well Casing and Tubing, Houston, May 1998. 10. Thoft-Christensen, P. and Baker, M.J., Structural reliability theory and its applications, Springer-Verlag, 1982. 11. Madsen, H.O., Krenk, S., and Lind., N.C., Methods of structural safety, Prentice-Hall, 1986. 12. Ang, A.H-S. and Tang, W.H., Probability concepts in engineering planning and design, Volume II: Decision, risk and reliability, John Wiley, 1984.

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13. Wilson, J.A. and Brown, N.P., “A consideration of human factors when handling kicks”, Proc. IADC Well Control Conf., Milan, June 1995. 14. Mann, N.R., Schafer, R.E. and Singpurwalla, N.D., Methods for statistical analysis of reliability and life data, John Wiley, 1974. 15. Kendall, M.G. and Stuart, A., The advanced theory of statistics, Vol I: Distribution theory, Charles Griffin, 1958. 16. Thoman, D.R. et al., “Inferences on the parameters of the Weibull distribution”, Technometrics, vol. 11, no. 3, August 1969. 17. “STRUREL theoretical manual” and “COMREL and SYSREL users manual”, version 4.20, RCP Consulting GmbH, Munich, November 1995. 18. Adams, A.J., “How to design for annulus fluid heat-up”, SPE 22871, Proc. 66th Annual SPE Conf., Dallas, October 1991. 19. Stewart, G., Klever, F.J. and Ritchie, D., “An analytical model to predict the burst capacity of pipelines”, KSEPL Publication 1200, December 1993. 20. Klever, F.J., Palmer, A.C. and Kyriakides, S., “Limit-state design of high-temperature pipelines”, KSEPL Publication 1196, December 1993. 21. Kick PDF data provided by the Offshore Safety Division of the Health and Safety Executive. 22. Blount, E.M. and Soeiinah, E., “Dynamic kill: controlling wild wells a new way”, World Oil, October 1981. 23. Wessel, M. and Tarr, B.A., “Underground flow well control: the key to drilling low-kick-tolerance wells safely and economically”, SPE Drilling Engineering, December 1991. 24. Kouba, G.E. et al., “Advancements in dynamic-kill calculations for blowout wells”, SPE 22559, Proc. 66th Annual SPE Conf., Dallas, October 1991.

SI Metric Conversion Factors bbl × 1.589 873 E − 01 = m3 ft × 3.048 E − 01 = m 3 ppg × 1.198 264 E + 02 = kg/m

Adr ian Adam s is a principal engineer at WS Atkins in Aberdeen, where he is team leader for casing/tubing design, conductor/riser design, and associated safety engineering. He has 17 years experience of well and offshore design, 14 with WS Atkins and three with Enertech as technical director. Adams holds a BS degree in civil engineering from Manchester U. Trevor Hodgson, a chief engineer, has worked for WS Atkins for 21 years, and is head of structural analysis in Aberdeen. He has many years experience in offshore structural engineering, and now specialises in FE analysis and software development. Hodgson holds a BS degree in civil engineering from Birmingham U.

TABLE 1 - COMPARISON OF DESIGN BASES Design basis Pressure Volume

8

A.J. ADAMS AND T. HODGSON

Circulation loads Risk-calibrated design criteria constant with well depth? • kick tolerance? • overbalance? •

No No No

CFOG loads Risk-calibrated design criteria constant with well depth? • kick tolerance? • overbalance? •

Very nearly Yes No

INITIATING EVENT (KICK) (ocfr / (1) section)

SPE 36447

FORMATION FRACTURE AT SHOE

(2)

(Pfrac /kick)

Notes

Very nearly Very nearly 1 Yes

1) Historical frequency 2) Calculated using ADCOM

No No No

ocfr Pfrac Y

Control over circulation risk • blowout risk • total risk (TRL on Pf governs) • total risk (TRL on Pu governs) •

2

3

Fair Very good 2 Fair Very good

Good Very poor 2,3 Fair Very poor

UNDERCASING GROUND FAILURE BLOWOUT (UGBO) DEVELOPS (2) (Pc /circ.) (Puf / (1) (2) (Pu /UGBO) fracture)

oc fr Pfrac Puf Pu ocfr Pfrac Puf Y

OUTCOME EVENT

E1 - CASING FAILURE E2 - NO FAILURE

Y ocfr Pfrac (1 - P uf ) Pc Y

ocfr

E3 - CASING FAILURE E4 - NO FAILURE

KICK

ocfr (1 - Pfrac ) Pc Y

E5 - CASING FAILURE E6 - NO FAILURE

1. 2. 3.

Because not applicable Would need depth and overbalance-dependent design criteria May need kick intensity-dependent design criteria

t s r u b g n ) i l s l a e c w f o r e y p t ( i l i b a b o r P

Figure 2 Event tree for the gas kick l oad case

1.0E-01 HPHT

1.0E-02

Normal kicks

exploration w e ll

1.0E-03

Escalated kicks

1.0E-04 Non-critical 1.0E-05

exploration w ell

1.0E-06 0.5

0.6

0.7

0.8

0.9

1.0

Design pressure/ C as i n g f u l l o f g as p r e s s u r e

1. 2.

Intermediate casing (P110), kick tolerance = 100 bbl, Puf = 0.01 The above curves are for a given case only, and do not apply to all possible wells. They should not be used as a basis for general well design. Figure 1 Typical design basis vs. risk cur ve

Figure 3 Typical kick volume vs. intensity scatter plot

SPE 36447

ON THE CALIBRATION OF CASING/TUBING DESIGN CRITERIA USING STRUCTURAL RELIABILITY TECHNIQUES

e r u s / s e e r r u p s s s e a r g p f o n l g l i u s f e g D n i s a C

1.1

0.9

TRL on Pu = 0.01

0.7

TRL on Pf = 0 .0001 0.5 4000

6000

8000

10000

12000

C as i n g s h o e d e p t h ( f t )

1. 2. 3.

Non-critical development well (floater drilled) Intermediate casing (P110), kick tolerance = 100 bbl, Puf = 0.01 The above curves are for a given case only, and do not apply to all possible wells. They should not be used as a basis for general well design. Figure 4 Typical design basis vs. depth curve

t s r u b g n ) i l s l a e c w f o r e y p t ( i l i b a b o r P

1.0E-02 Puf = 0.1

1.0E-03

Puf = 0.01

1.0E-04 1.0E-05 1.0E-06

Puf = 0.001

1.0E-07 0.5

0.6

0.7

0.8

0.9

1.0

De s i g n p r e s s u r e / C as i n g f u l l o f g as p r e s s u r e

1. 2. 3.

Non-critical exploration well, deep shoe Intermediate casing (P110), kick tolerance = 100 bbl The above curves are for a given case only, and do not apply to all possible wells. They should not be used as a basis for general well design. Figure 5 Effect of w ell control

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