CASING DESIGN.pdf

.....  CASING DESIGN PRINCIPLES 5 Factors Influencing Casing Design TOC Previous Next Table 5.1 Sources of Data Data Source 1. Formation pressure, psi...

.....  CASING DESIGN PRINCIPLES 5 Factors Influencing Casing Design TOC Previous Next Table 5.1 Sources of Data Data Source 1. Formation pressure, psi Offset wells well logs, log analyst 2. Casing setting depths, ft Offset wells, kick tolerance calculations 3. Fracture gradient (psi/ft) or fracture pressure (ppg or Offset wells, well logs, calculation of psi) at casing seat fracture gradient 4. Mud density, ppg As above 5. Mean sea water level, ft 6. Available casing grades and weights Stock status report 7. Strength properties (burst, collapse, yield) API or manufacturer‘s catalogues 8. Geothermal temperatures Offset wells 2.0...... F..ACTORS.........I.NFLUENCING............. C..ASING.......D..ESIGN................................... Casing design involves the determination of factors which influence the failure of casing and the selection of the most suitable casing grades and weights for a specific operation, both safely and economically. The casing programme should also reflect the completion and production requirements. A good knowledge of stress analysis and the ability to apply it are necessary for the design of casing strings. The end product of such a design is a 'pressure vessel' capable of withstanding the expected internal and external pressures and axial loading. Hole irregularities further subject the casing to bending forces which must be considered during the selection of casing grades. 144 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... Factors Influencing Casing Design TOC Previous Next........... A safety margin is always included in casing design, to allow for future deterioration of the casing and for other unknown forces which may be encountered, including corrosion, wear and thermal effects. Table 5.2 Essential Data Casing O.D. inches 18 5/8” (or 20 “) 13 3/8” 9.5/8” 7” Casing setting depth ft (TVD) Casing grade and weight (lb/ft) I.D, in Drift diameter, in Coupling type Collapse strength, psi Burst strength, psi Body yield strength (lbf x 1000) Connection parting load (lbf x 1000) Mud density to drill hole for this casing, ppg Mud density used to drill next hole, ppg Expected formation pressure at next TD, psi Fracture gradient at casing seat, psi/ft Mudline depth, ft Geothermal gradient F /100 ft Casing design is also influenced by: (a) loading conditions during drilling and production; (b) the strength properties of the casing seat (i.e. formation strength at casing shoe); Well Engineering & Construction 145  CASING DESIGN PRINCIPLES 5 Design Criteria TOC Previous Next (c) the degree of deterioration the pipe will be subjected to during the entire life of the well; and (d) the availability of casing. In general, the cost of a given casing grade is proportional to its weight, the heaviest weight being the most expensive. Since the cost of casing in a given well constitutes a high percentage of the total cost of drilling and completion (in some cases up to 40%), the designer should ensure that the lowest grades and lightest weights, consistent with safety, are chosen as these provide the cheapest casing. A casing string incorrectly designed can result in disastrous consequences, placing human lives at risk and causing damage and loss of expensive equipment. The entire oil reservoir may be placed at risk if the casing cannot contain a kick which may develop into a blowout resulting in a large financial loss to the operating company and a large depletion of the reservoir’s potential. 3.0...... D.. ESIGN.......C..RITERIA............................................................ There are three basic forces which the casing is subjected to: collapse, burst and tension. These are the actual forces that exist in the wellbore. They must first be calculated and must be maintained below the casing strength properties. In other words, the collapse pressure must be less than the collapse strength of the casing and so on. Casing should initially be designed for collapse, burst and tension. Refinements to the selected grades and weights should only be attempted after the initial selection is made. The suitability of selected casing depends on the accuracy of data collected in Table 5.2. For directional wells a correct well profile is required to determine the true vertical depth (TVD). All wellbore pressures and tensile forces should be calculated using true vertical depth only. The casing lengths are first calculated as if the well is a vertical well and then these t lengths are corrected for the appropriate hole angle. 146 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... Collapse Criterion TOC Previous Next........... 4.0...... C.. OLLAPSE..........C..RITERION......................................................... Collapse pressure originates from the column of mud used to drill the hole, and acts on the outside of the casing. Since the hydrostatic pressure of a column of mud increases with depth, collapse pressure is highest at the bottom and zero at the top, see Figure 5.1a. This is a simplified assumption and does not consider the effects of internal pressure. For practical purposes, collapse pressure should be calculated as follows: Collapse pressure = External pressure – Internal pressure (5.1) The actual calculations involved in evaluating collapse and burst pressures are usually straight forward. However, knowing which factors to use for calculating external and internal pressures is not easy and requires knowledge of current and future operations in the wellbore. Until recently, the following simplified procedure was used for collapse design: (1) Casing is assumed empty due Figure 5.1 Collapse Criterion to lost circulation at casing setting depth (CSD) or at TD of Pressure Pressure next hole, see Figure 5.1. (2) Internal pressure inside casing is zero (3) External pressure is caused by CSD mud in which casing was run in Next (4) No cement outside casing hole TD section Hence using the above Origin of collapse Effects of next hole on assumptions and applying pressure current casing Equation (5.1), only the external pressure need to be evaluated. Well Engineering & Construction 147  CASING DESIGN PRINCIPLES 5 Lost Circulation TOC Previous Next Therefore: Collapse pressure (C)= mud density x depth x acceleration due to gravity C = 0.052 x x CSD….psi (5.2) where is in ppg and CSD is in ft The above assumptions are very severe and only occur in special cases. The following sections will provide details on practical situations that can be encountered in field operations. 4.1 LOST CIRCULATION If collapse calculations are based on 100% evacuation then the internal pressure (or back-up load) is to zero. The 100% evacuation condition can only occur when: the casing is run empty there is complete loss of fluid into a thief zone (say into a cavernous formation), and there is complete loss of fluid due to a gas blowout which subsequently subsides None of these conditions should be allowed to occur in practice with the exception of encountering cavernous formations, see Chapter 5 for details. During lost circulation, the mud level in the well drops to a height such that the remaining hydrostatic pressure of mud is equal to the formation pressure of the thief zone. In this case the mud pressure exactly balances the formation pressure of the thief zone and fluid loss into the formation will cease. If the formation pressure of the thief is not known, it is usual to assume the pressure of the thief zone to be equal to 0.465 psi/ft. As discussed in Chapter One, this is the pore pressure of a normally pressured zones where the pressure is hydrostatic.Normally pressured zones are assumed to be connected to the sea or to a large aquifer with normal pressure. 148 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... Lost Circulation TOC Previous Next........... Figure 5.2 Mud level Inside casing After Loss Circulation The length of the mud column remaining inside the casing can be calculated as follows (refer to Figure 5.2) Assuming that the thief zone is at the casing seat, then during lost circulation: Pressure in thief zone =CSD x 0.465 (5.3) Internal pressure at shoe=L x pm1 x 0.052 (5.4) where m1 = mud density used to drill next hole (ppg) Pf = formation pore pressure of thief zone, (psi/ft) (or ppg) (assume = 0.465 psi/ft for most designs) L = length of mud column inside the casing CSD = casing setting depth (TVD) of the casing string being designed, ft Well Engineering & Construction 149  CASING DESIGN PRINCIPLES 5 Lost Circulation TOC Previous Next Combining Equation (5.3) and Equation (5.4) gives (L), the length of mud column remaining inside casing: L = CSDx0.465 ----------------------------- (5.5) 0.052x m1 Depth to top of mud column = CSD - L (5.6) [Note another method of calculating the internal pressure during lost circulation is to use the formation pressure (Pf) and depth of the loss zone (Dlz) in the calculation. The depth of the loss zone can be any where between the casing setting depth and the TD of next hole. The depth to top of mud (h) inside casing after loss circulation is given by: m1 – f h = -------------------- - xDlz (5.7) m1 The internal pressure is then calculated from the mud column (L) remaining inside casing: L = (CSD –h)] Example 5.1 : Col lapse Calc ulat ion s Calculate the collapse pressure for the following casing string assuming lost circulation at the casing shoe: Current mud = 15 ppg Casing was run in = 11 ppg CSD = 10,000 ft Solu ti on First find the length of mud column remaining inside the casing: L=CSD x 0.465 = (10,000 x 0.465) / 0.052 x 15 = 5962 ft 0.052 x pm1 150 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... Collapse Calculations For Individual Casing Strings TOC Previous Next........... Then reference to figure Figure 5.2, three points need to be considered for collapse calculations. (1) At surface (Point A in Figure 5.2) Both the external and internal pressures are zero. Hence the effective collapse at surface is zero. At point A C1= Zero (2) At Point B The internal pressure is zero.This is where the new level of mud starts. Hence collapse pressure is equal to the external pressure only. C2= 0.052 (CSD-L) pm C2 =0.052 x 11 x (10,000 –5962) = 2310 psi (3) At Point C Now both external and internal pressures must be calculated. The external pressure is caused by the mud column in which casing was run. The internal pressure (back-up load) is caused by the length of mud column (L) remaining after lost circulation. C3 = 0.052 CSD x pm - 0.052 L x pm1 = 0.052 x 10,000x 11 – 0.52 x 5962x 15 = 1070 psi 4.2 COLLAPSE CALCULATIONS FOR INDIVIDUAL CASING STRINGS In order the make the calculations more practical, it will be necessary to present the collapse equations for each casing type. Obviously, the given procedures may be modified to suit local conditions. The reader must always take advantage of previous experience in the area, for example, complete lost circulation can be found in a very few areas below the 13 3/8" Well Engineering & Construction 151  CASING DESIGN PRINCIPLES 5 Collapse Calculations For Individual Casing Strings TOC Previous Next casing. If selecting casing in such areas of complete loss circulation, then the 13 3/8" must be designed for external pressure only. Normally, as will be seen later, the 13 3/8" casing is designed for partial loss circulation. 4.2.1 CONDUCTOR The conductor is usually set at a shallow depth ranging from 100 ft to 1500 ft. Assume complete evacuation so that the internal pressure inside the casing is zero. The external pressure is caused by the mud in which the casing was run. For offshore operations, the external pressure is made up of two components: Collapse pressure at mud line=external pressure due to a column of seawater from sea level to mud line =(0.45 psi/ft) x mudline depth = C1 psi Collapse pressure at casing seat =C1 + 0.052 x pm x CSD (5.8) 4.2.2 SURFACE CASING If surface casing is set at a shallow depth, then it is possible to empty out the casing of a large volume of mud if a loss of circulation is encountered in the open hole below. Some designers assume the surface casing to be completely empty when designing for collapse, irrespective of its setting depth, to provide an in-built design factor in the design. Other designs in industry assume a 40% evacuation level. Both approaches have no scientific basis and can result in overdesigns. This overdesign can be significantly reduced if partial loss circulation is assumed and the pressure of the reduced level of mud inside the casing is subtracted from the external pressure to give the effective collapse pressure. The internal pressure is calculated using Equation (5.4). 152 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... Collapse Calculations For Individual Casing Strings TOC Previous Next........... 4.2.3 INTERMEDIATE CASING Complete evacuation in intermediate casing is virtually impossible. This is because during lost circulation, the fluid column inside the casing will drop to a height such that the remaining fluid inside the casing just balances the formation pressure of the thief zone, irrespective of the magnitude of pore pressure of the thief zone (see Figure 5.2). Three collapse points will have to be calculated using the general form: Collapse pressure, C=external pressure - internal pressure (1)Point A: At Surface C1= Zero (5.9) (2)Point B: At depth (CSD-L) = 0.052 (CSD-L) x m -0 C2 = 0.052 (CSD-L) m (5.10) (3)Point C: At depth CSD C3=0.052 CSD x m- 0.052 L x m1 (5.11) where mis the mud weight in which casing was run in. 4.2.4 PRODUCTION CASING For production casing the assumption of complete evacuation is justified in the following situations: 1. if perforations are likely to be plugged during production as in gas wells. In this case surface pressure may be bled to zero and hence give little pressure support inside the casing. 2. in artificial lift operations. In such operations gas is injected from the surface to reduce the hydrostatic column of liquid against the formation to help production. If Well Engineering & Construction 153  CASING DESIGN PRINCIPLES 5 Collapse Design Across Salt Sections TOC Previous Next the well pressure were bled to zero at surface, a situation of complete evacuation could exist. 3. in air/gas drilling all casing strings should be designed for complete evacuation. 4. another situation which results in complete evacuation is a blowout which unloads the entire hole. If none of the above situations are likely in a production casing then partial evacuation should be used for collapse design and equations Equation (5.9) to Equation (5.11) should be used. 4.3 COLLAPSE DESIGN ACROSS SALT SECTIONS There are several areas around the world where casing strings have to be set across salt sections. Salt is a sedimentary rock belonging to the evaporite group which is characterised by having no porosity and no permeability. In most cases, salt is immobile and causes no problems while drilling or production. There are several types of evaporites: Halite NaCl Gypsum CaSO4 2H2O Anhydrite CaSO4 Sylvite KCl Carnalite KMgCl3 6H2O When a salt section is made up entirely of sylvite or carnalite, then the salt section becomes mobile and behaves like a super-viscous fluid. The mobile salt continues to move during drilling operations, in some cases, at the rate of one inch an hour causing the pipe to be stuck. Salt movement also continues after the casing is set and in some cases results in casing collapse. 154 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... Burst Criterion TOC Previous Next........... Salt induced casing collapse occurs in many part of the world; Southern North Sea, Red Sea and Offshore Qatar are a few examples. Casing collapse failure caused by salt movement is a catastrophic failure, almost always requiring sidetracking or redrilling of the well. Currently, there is no accepted analytical method for designing for collapse loads resulting from salt movement.The accepted method is to use an external pressure of 1 psi/ft across the salt section. The reason behind this is that in mobile salts, all the earth stresses become equal to 1 psi/ft. Hence when designing across mobile salt sections, determine the depth of the salt section, say X, ft, then: External pressure at depth X = 1 psi/ft x X (5.12) Internal pressure = pressure resulting from partial loss circulation 5.0...... B..URST......C..RITERION............................................................. In oil well casings, burst occurs when the effective internal pressure inside the casing (internal pressure minus external pressure) exceeds the casing burst strength. Like collapse, the burst calculations are straightforward. The difficulty arises when one attempts to determine realistic values for internal and external pressures. In development wells, where pressures are well known the task is straight forward. In exploration wells, there are many problems when one attempts to estimate the actual formation pressure including: the exact depth of the zone (formation pressure increases with depth) type of fluid (oil or gas) porosity, permeability temperature The above factors determine the severity of the kick in terms of pressure and ease of detection. Well Engineering & Construction 155  CASING DESIGN PRINCIPLES 5 Burst Calculations TOC Previous Next Clearly, one must design exploration wells for a greater degree of uncertainty than development wells. Indeed, some operators manuals detail separate design methods for development and exploration wells. In this book, a general design method will be presented and guidelines for its application will be given. 5.1 BURST CALCULATIONS Burst Pressure, B is give by: B = internal pressure – external pressure Figure 5.3 Burst Design Internal Pressure Burst pressures occur when formation fluids enter the casing while drilling or producing next hole. Internal Pressure Reference to Figure 5.3, shows that in most cases the maximum formation pressure will be encountered when reaching the TD of the next hole section. For the burst criterion, two cases can be designed for: CSD 1. Unlimited kick New Hole 2.Limited kick Pf TD 5.2 UNLIMITED KICK The use of unlimited kick (or gas to surface) used to be the main design criterion in burst calculations. Simply stated, the design is based on unlimited kick, usually gas. The kick is assumed to enter the well, displace the entire mud and then the well is shut-in the moment the last mud drop leaves the well. Clearly, this is an unrealistic situation especially in today’s technology where kicks as small as 10 bbls can be detected even on semi-submersible rigs. However, there is one practical situation when this criterion is actually valid. In gas wells, the production tubing is in fact subjected to controlled unlimited kick all the time. Because 156 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... Limited Kick Design: Kick Tolerance TOC Previous Next........... production occurs under controlled conditions, the flow of gas poses no problems to the surrounding casing. If however, gas leaked from tubing to casing, then the casing will see the full impact of gas during production. This idea will be explored further in this section. Hence reference to Figure 5.3, and assuming a gas kick of pressure Pf from next TD, and the gas fills the entire well then the internal pressures at surface and casing shoe are given by: Internal pressure at surface = Pf - G x TD (5.13) Internal pressure at shoe = Pf - G x (TD - CSD) (5.14) where G is the gradient of gas (typically 0.1 psi/ft). When a gas kick is assumed, two points must be considered: 1. The casing seat should be selected so that gas pressure at the casing shoe is less than the formation breakdown pressure at the shoe. 2. The gas pressure must be available from reservoirs in the open hole section. In exploration wells where reservoir pressures are not known, formation pressure at TD of the next open hole section is calculated from the maximum anticipated mud weight at that depth. A gas pressure equal to this value is used for the calculation of internal pressures. In development areas, reservoir pressures are normally determined by use of wireline logs, drill stem testing or production testing. These pressure values should be used in casing design. 5.3 LIMITED KICK DESIGN: KICK TOLERANCE This method is by far the most widely used and represents realistic conditions for most casings and most wells. The main problem with this method is knowing what realistic values for kick size to use for each hole size and how to distinguish between exploration and development wells. In 1987, detailed limited kick calculations were first presented in a design methodology by Rabia 1. Well Engineering & Construction 157  CASING DESIGN PRINCIPLES 5 External Pressure For Burst Design TOC Previous Next The calculations involved in this method were given in detail in Chapter 3: Kick Tolerance. To apply this method, assume a realistic kick size and calculate the internal pressures at surface and at shoe assuming the kick is being circulated out of hole using the driller’s method of well control. The method can be easily programmed into an Excel sheet. Further, one can add several scenarios to each casing size including type of kick, swabbed kick or overpressured kick with kick margin, effects of temperature and gas compressibility, type of well etc. Whatever volume of kick is used, a realistic value of formation pressure must be used as this is the variable that affects the calculations most. 5.4 EXTERNAL PRESSURE FOR BURST DESIGN The external pressure (or back-up load) is one of the most ambiguous variables to determine. It is largely determined by the type of casing being designed, mud type and cement density, height of cement column and formation pressures in the vicinity of the casing. In practice, although casings are cemented (partially or totally to surface), the external pressure is not based on the cement column. At first glance, this seems strange that we go into a great deal of effort and expense to cement casing and not use the cement as a back-up load. The main reasons for not using the cement column are: 1. it is impossible to ensure a continuous cement sheet around the casing 2. any mud trapped within the cement can subject the casing to the original hydrostatic pressure of the cement 3. the cement sheath is usually highly porous but with little permeability and when it is in contact with the formation, it can theoretically transmit the formation pressure to the casing Because of the above, the exact degree of back-up provided by cement is difficult to determine. The following methods are used by a number of oil companies for calculating external pressure for burst calculations: 1. Regardless of whether the casing is cemented or not, the back-up load is provided by a column of salt saturated water. Hence the external pressure = 0.465 psi/ft x CSD (ft) (5.15) 158 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... Burst Calculations For Individual Casing Strings TOC Previous Next........... The above method is the simplest and is used by many people in the industry. It assumes all muds and cements behind casing degrade with time to a density equivalent to salt-saturated mud having a density of 0.465 psi/ft. In fact, this assumption is used by some commercial casing design software. The author suggests using this method for all casings likely to be in the ground for more than five years. 2. If casing is cemented along its entire length and the casing is in contact with a porous formation via a cement sheath, then with time the cement sheath will degrade and the casing will be subjected to the pore pressure of the open formation. Hence External pressure = maximum expected pore pressure (5.16) In practice only conductor and shallow surface casings are cemented to surface. Hence the maximum pore pressure is likely to be that of a normally pressure zone of around 0.465 psi/ft. 3. For uncemented casings: in the open hole, use a column of mud to balance the lowest pore pressure in the open hole section inside another casing, use mud down to TOC and then from TOC to casing shoe use a column of mud to balance the lowest pore pressure in the open hole section This scenario usually applies to intermediate and production casings. In fact, the author used the above to design high pressure/high temperature wells in the North Sea. Without this realistic assumption, casing of unnecessarily higher grade or weight would be required. 5.5 BURST CALCULATIONS FOR INDIVIDUAL CASING STRINGS At the top of the hole, the external pressure is zero and the internal pressure must be supported entirely by he casing body. Therefore, burst pressure is highest at the top and lowest at the casing shoe where internal pressures are resisted by the external pressure Well Engineering & Construction 159  CASING DESIGN PRINCIPLES 5 Burst Calculations For Individual Casing Strings TOC Previous Next originating from fluids outside the casing. As will be shown later, in production casing the burst pressure at shoe can be higher than the burst pressure at surface in situations where the production tubing leaks gas into the casing. Conductor There is no burst design for conductors. Surface and Intermediate Casings For gas to surface (unlimited kick size), calculate burst pressures as follows: Calculate the internal pressures (Pi) using the maximum formation pressure at next hole TD, assuming the hole is full of gas, (see Figure 5.3). Burst at surface = Internal pressure (Pi) (Equation (5.13)– external pressure Burst pressure at surface (B1) = Pf - G x TD (5.17) (note external pressure at surface is zero) Burst pressure at casing shoe (B2) = internal pressure (Equation (5.14)- backup load = Pi - 0.465 x CSD B2 = Pf - G x (TD - CSD) - 0.465 x CSD (5.18) The back-up load is assumed to be provided by mud which has deteriorated to salt-saturated water with a gradient of 0.465 psi/ft. For the limited kick size, use the appropriate kick size (see Chapter 3) to calculate the maximum internal pressures at surface and at shoe when circulating out the kick. Calculate the corresponding values for B1 and B2 as above. 160 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... Burst Calculations For Individual Casing Strings TOC Previous Next........... Production Casing The worst case occurs when gas leaks from the top of the production tubing to the casing. The gas pressure will be transmitted through the packer fluid from the surface to the casing shoe (see Figure 5.4). Figure 5.4 Burst Design For Production Casing Burst values are calculated as follows: Burst pressure= Internal pressure - External pressure Burst at surface (B1) =Pf - G x CSD (or the maximum anticipated surfacepressure, whichever is the greatest) Burst at shoe (B2)= B1 + 0.052 p x CSD - CSD x 0.465 (5.19) where G =gradient of gas, usually 0.1 psi/ft Well Engineering & Construction 161  CASING DESIGN PRINCIPLES 5 Burst Calculations For Individual Casing Strings TOC Previous Next Pf =formation pressure at production casing seat, psi p =density of completion (or packer) fluid, ppg 0.465 =the density of backup fluid outside the casing to represent the worst case, psi/ft. Note that if a production packer is set above the casing shoe depth, then the packer depth should be used in the above calculation rather than CSD. The casing below the packer will not be subjected to burst loading (see Figure 5.4) as it is perforated. Example 5.2 : Produ c t ion C asin g Calc ula tion s Calculate burst pressures for the following well: CSD = 15000 ft Pf = 8500 psi Packer fluid = 15 ppg Solu ti on Burst at surface (B1) = Pf - G x CSD =8500 – 0.1 x 15000 = 7000 psi Burst at shoe (B2)= B1 + 0.052 pp x CSD - CSD x 0.465 = 7000 + 0.052 x 15 x 15000 - 15000 x 0.465 = 11,725 psi 162 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... Design & Safety Factors TOC Previous Next........... 5.6 DESIGN & SAFETY FACTORS Casings are never designed to their yield strength or tensile strength limits. Instead, a factor is used to derate the casing strength to ensure that the casing is never loaded to failure. The difference between design and safety factors are given below. 5.6.1 SAFETY FACTOR Safety factor uses a rating based on catastrophic failure of the casing. Safety Factor = Failure Load Actual Applied Load When the actual applied load equals the failure load, then the safety factor =1 and failure is imminent. Failure will occur if the actual load is greater than the failure load and in this case the safety factor < 1.0. For the above reasons, safety factors are always kept at values greater than 1. In casing design, neither the actual applied load or failure loads are known exactly, hence design factors are used to evaluate the integrity of casing. 5.6.2 DESIGN FACTOR Design factor uses a rating based on the minimum yield strength of casing. In the oil industry, safety factors are never intentionally used to design tubulars as they imply prior knowledge of the actual failure load and designing to failure or below failure. Design factors are usually used for designing tubulars and are based on comparing the maximum service load relative to the API minimum yield strength.Recall that the casing does not actually fail at the the minimum yield strength and, moreover, the minimum yield strength is an average value of several measurements. Hence, the design factor provides a greater scope for safety than safety factor. Design Factor = Rating of the pipe Maximum Expected Service Load Well Engineering & Construction 163  CASING DESIGN PRINCIPLES 5 Design & Safety Factors TOC Previous Next A Design Factor is usually equal to or greater than 1.The design factor should always allow for forces which are difficult to calculate such as shock loads. The burst design factor (DF-B) is given by: DF-B = Burst Strength Burst Pressure (B) Similarly, the collapse design factor is given by: DF-C = Collapse Strength Collapse Pressure (C) 5.6.3 RECOMMENDED DESIGN FACTORS Collapse = 1. 0 Burst = 1.1 Tension = 1.6 –1. 8 Compression = 1.0 Triaxial Design = 1. 1 Industry Range from various operators Collapse = 1.0 – 1. 1 Burst = 1.1 – 1. 25 Tension = 1.3 –1. 8 Compression = 1.0 Triaxial Design = 1. 1- 1.2 164 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... Casing Selection- Burst And Collapse TOC Previous Next........... Example 5.3 : De sign Fa ctor If the burst strength (Minimum Internal Yield Strength) of casing is 6300 psi. What is the maximum burst pressure that this casing should be subjected to in service? Recommended DF = 1.1 Solu ti on Design burst strength = 6300 = 5727 psi 1.1 5.7 CASING SELECTION- BURST AND COLLAPSE It is customary in casing design to define the load case for which the casing is designed for. There are several load cases which arise due to drilling and production operations and will be discussed in “Load Cases” on page 172. However before a load case is applied, the casing grades/weights should initially be selected on the basis of burst and collpase pressures, then load cases should be applied.If only one grade or one weight of casing is available, then the task of selecting casing is easy. The strength properties of the casings available are compared with the collapse and burst pressures in the wellbore. If the design factors in collapse and burst are acceptable then all that remains is to check the casing for tension. For deep wells or where more than one grade and weight are used, a graphical method of selecting casing is used as follows: 1. Plot a graph of pressure against depth, as shown in Figure 5.5, starting the depth and pressure scales at zero. Mark the CSD on this graph. 2. Collapse Line: Mark point C1 at zero depth and point C2 at CSD. Draw a straight line through points C1 and C2. Well Engineering & Construction 165  CASING DESIGN PRINCIPLES 5 Casing Selection- Burst And Collapse TOC Previous Next 3. For partial loss circulation, there will be three collapse points. Mark C1 at zero depth, C2 at depth (CSD-L) and C3 at CSD. Draw two straight lines through these points. 4. Burst Line:Plot point Figure 5.5 Collpase And Burst Lines B1 at zero depth and 1 2 B1 point B2 at CSD. 0 Pressure Draw a straight line 1 Collapse through point B1 and 2 Line Burst B2 (see Figure 5.5). Line Depth For production casing, the highest pressure Casing Setting Depth will be at casing shoe. B2 C2 5. Plot the collapse and burst strength of the available casing, as shown in Figure 5.6. In this figure, two grades, N80 and K55 are plotted to represent the available casing. Select a casing string that satisfies both collapse and burst. Figure 5.6 provides the initial selection and in many cases this selection differs very little from the final selection. Hence, great care must be exercised when producing Figure 5.6. 166 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... Combination Strings TOC Previous Next........... Figure 5.6 Selection Based On Burst And Collapse Selection Based on Burst and Pressure Collapse 0 B1 Collapse Burst K55 N80 Burst Collapse Strength Line Burst N80 N80 Line Depth K55 K55 K55 K55 N80 Collapse Strength Casing Setting Depth B2 C2 6.0...... C.. OMBINATION..............S. TRINGS...................................................... In a casing string, maximum tension occurs at the uppermost joint and the tension criterion requires a high grade or a heavy casing at this joint. Burst pressures are most severe at the top and, again, casing must be strong enough on top to resist failure in burst. In collapse calculations, however, the worst conditions occur at the bottom and heavy casing must, therefore, be chosen for the bottom part to resist collapse failure. Hence, the requirements for burst and tension are different from the requirements for collapse and a compromise must be reached in casing design. This compromise is achieved in the form of a combination string. In other words, casings of various grades and of differing weights are used at different depths of hole, each grade of casing being capable of Well Engineering & Construction 167  CASING DESIGN PRINCIPLES 5 Tension Criterion TOC Previous Next withstanding the imposed loading conditions at that depth. Strong and heavy casing is used at the surface, light yet strong casing is used in the middle section, and heavy casing may be required at the bottom to withstand the high collapsing pressure. Example 5.6 shows how a combination string is selected. The combination string method represents the most economical way of selecting casing consistent with safety. Although as many grades as possible could be used for a string of casing, practical experience has shown that the logistics of using more than two grades (or two weights) create problems for rig crews. 7.0...... T..ENSION........C..RITERION........................................................... Most axial tension arises from the weight of the casing itself. Other tension loadings can arise due to: bending, drag, shock loading and during pressure testing of casing. In casing design, the uppermost joint of the string is considered the weakest in tension, as it has to carry the total weight of the casing string. Selection is based on a design factor of 1.6 to 1.8 for the top joint. Tensile forces are determined as follows: 1. calculate weight of casing in air (positive value) using true vertical depth; 2. calculate buoyancy force (negative value); 3. calculate bending force in deviated wells (positive value); 4. calculate drag force in deviated wells (this force is only applicable if casing is pulled out of hole); 5. calculate shock loads due to arresting casing in slips; and 6. calculate pressure testing forces Forces (1) to (3) always exist, whether the pipe is static or in motion. Forces (4) and (5) exist only when the pipe is in motion. The total surface tensile load (sometimes referred to as installation load) must be determined accurately and must always be less than the yield 168 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... Tension calculations TOC Previous Next........... strength of the top joint of the casing. Also, the installation load must be less than the rated derrick load capacity so that the casing can be run in or pulled out of hole without causing damage to the derrick. In the initial selection of casing, check that the casing can carry its own weight in mud and when the casing is finally chosen, calculate the total tensile loads and compare them with the joint or pipe body yield values, using the lower of the two values. A design factor (= coupling or pipe body yield strength divided by total tensile loads) in tension of 1.6 to 1.8 should be used. 7.1 TENSION CALCULATIONS The selected grades/ weights in Figure 5.6 provide the basis for checking for tension. The following forces must be considered: Buoyant Weight Of Casing (Positive Force) The buoyant weight is determined as the difference between casing air weight and buoyancy force. Casing air weight = casing weight (lb/ft) x hole TVD (5.20) For open-ended casing, see Figure 5.7. Buoyancy force = Pe (Ae – Ai) (5.21) For closed casing, see Figure 5.7 Figure 5.7 Buoyancy Force Buoyancy force = Pe Ae – Pi Ai (5.22) Ae where Pe = external hydrostatic pressure, psi Ae Pi = internal hydrostatic pressure, psi Ai Ae and Ai are external and internal areas Ai of the casing Pi Pi Pi Pe Open-ended Casing Closed Casing Well Engineering & Construction 169  CASING DESIGN PRINCIPLES 5 Tension calculations TOC Previous Next Since the mud inside and outside the casing is invariably the same, the buoyancy force is almost always given by Equation (5.23): Buoyancy force = Pe (Ae – Ai) (5.23) If a tapered casing string is used then the buoyancy force at TD is calculated as above. At a cross-sectional change, the buoyancy force is calculated as follows: Buoyancy force = Pe2 (Ae2 – Ae1) – Pi2 (Ai2- Ai1) (5.24) Figure 5.8 Buoyancy Force For A tapere String For most applications, the author recommends Ae2 calculating the buoyant weight as follows: Buoyant weight = air weight x buoyancy Section 2 Ai2 factor (5.25) Pi2 Pi2 Depth X One can easily prove that there is very little of Ai1 Section 1 accuracy using the above equation except for tapered strings or when the bottom of the casing is Pi1 landed in compression. Pe2 Ae2 2. Bending Force The bending force is given by: Bending force = 63 Wn x OD x (5.26) where Wn = weight of casing lb/ft (positive force) = dogleg severity, degrees/100 ft 3. Shock Load Shock loading in casing operations results when: Sudden decelerations are applied Casing is picked off the slips 170 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... Tension calculations TOC Previous Next........... Slips are kicked in while pipe is moving Casing hits a bridge or jumps off an edge downhole Shock loading is a dynamic force with a very short duration: approximately one second.It can be shown that the shock is given by 1: Fshock = 1780 V As (5.27) where As = cross-sectional area V = pipe running velocity in ft/s, usually taken as the instantaneous velocity (some operators use V = 5 ft/s as the instantaneous velocity) The main difficulty with using Equation (5.27) is knowing which value to use for casing running speed when shock loading occurs. The author found that the equation below gives satisfactory results 1: Shock load (max)= 1500 x Wn (5.28) 4. Drag Force This force is usually of the order of 100,000 lbf (positive force). Because the calculation of drag force is complex and requires an accurate knowledge of the friction factor between the casing and hole, shock load calculations will in most cases suffice.The effect of the drag force lasts for the duration of running a joint of casing; shock loading lasts for only 1 second or so. Hence shock loading and drag forces can not exist simultaneously. In most cases the magnitude of shock and drag forces are approximately the same. Hence calculating one force will be sufficient in most cases. Both shock and drag forces are only applicable when the casing is run in hole. In fact, drag forces reduce the casing forces when running in hole and increase them when pulling out. However, despite the fact that the casing operation is a one-way job (running in), there are many occasions when a need arises for moving casing uphole, e.g. to reciprocate casing or to Well Engineering & Construction 171  CASING DESIGN PRINCIPLES 5 Pressure Testing Issues TOC Previous Next pull out of hole due to tight hole. Hence, the extreme case should always be considered for casing selection. 5. Pressure Testing The casing should be tested to the maximum pressure which it sees during drilling and production operations (together with a suitable rounding margin). 2 ID F t = ----------------- x test pressure (5.29) 4 where Ft = pressure test force, lb ID = inside diameter of casing, in 7.2 PRESSURE TESTING ISSUES When deciding on a pressure test value, the resulting force must not be allowed to exceed: 80% of the rated burst strength the connection pressure rating 75% of the connection tensile rating triaxial stress rating of the casing 7.3 LOAD CASES There are three load cases for which the total tensile force should be calculated for: running conditions, pressure testing and static conditions. These load cases are sometimes described as Installation Load cases. Other load cases will be discussed later. Load Case 1:Running Conditions This applies to the case when the casing is run in hole and prior to pumping cement: Total tensile force = buoyant weight + shock load +bending force 172 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... Load Cases TOC Previous Next........... Load Case 2: Pressure Testing Conditions This condition applies when the casing is run to TD, the cement is displaced behind the casing and mud is used to apply pressure on the top plug. This is usually the best time to test the casing while the cement is still wet. In the past, some operators tested casing after the cement was set. This practice created micro channels between the casing and the cement and allowed pressure communication between various zones through these open channels. Total tensile force = buoyant weight + pressure testing force +bending force Load Case 3: Static Conditions This condition applies when the casing is in the ground, cemented and the wellhead installed. The casing is now effectively a pressure vessel fixed at top and bottom.One can argue that other forces should be considered for this case such as production forces, injection forces, temperature induced forces etc. However, for the sake of clarity these forces will be discussed later in this chapter and also separately in Chapter 15. Total tensile force = buoyant weight + bending force + (miscellaneous forces) It is usually sufficient to calculate the total force at the top joint, but it may be necessary to calculate this force at other joints with marginal safety factors in tension. Once again, ensure that the design factor in tension during pressure testing is greater than 1.6, i.e. DF-T = Yield Strength Total tensile forces during pressure testing Example 5.4: Te nsile F or ce s Calculate the tensile forces for the following casing string: 20 "casing, ID = 18.71 inch, 133 lb/ft CSD = 2800 ft Well Engineering & Construction 173  CASING DESIGN PRINCIPLES 5 Load Cases TOC Previous Next Mud =10 ppg Test Pressure =2500 psi Dogleg = 0.75 deg/100 ft Solu ti on F1 =Buoyant weight of casing (in 10 ppg mud) = 2800 x 133 x 0.847 = 315,423 lbf F2 =Shock load = 1500x 133 = 199,500 lbf F3 =Bending force = 63 casing weight x OD x DLS = 63x133x20x0.75 = 125,685 lbf F4 = Pressure test force = (casing ID)2 x test pressure 4 = (18.71)2 x 2500 = 687,349 lbf 4 The following table may be constructed: Running conditions Pressure Testing Condi- Static Conditions tions F1: Buoyant Weight 315,423 315,423 315,423 F2: Shock Load 199,500 0 0 F3: Bending Force 125,685 125,685 125,685 F4: Pressure Testing 0 687,349 0 Force Total Force (lbf) 530,608 1,128457 441,108 174 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... Service Loads During Drilling And Production Operations TOC Previous Next........... From the above table, it can be seen the maximum force that the top casing joint sees is in fact during pressure testing. Casing pressure testing is usually carried out for approximately 15 minutes. Despite the fact that this force acts for a short duration, it must be used in the final selection as the casing could fail if it is subjected to similar pressures during kicks, production, injection, leaks etc. 8.0...... S..ERVICE........L..OADS......D. URING....... D.. RILLING......... A..ND... P..RODUCTION.............O. PERATIONS............. Once the casing is landed and cemented, it will be subjected to additional forces if drilling is continued beyond this casing or if this casing is used as a production casing. These service loads represent extra set of load cases which must be checked before the casing is selected. To calculate the tensile load on the casing, the base load must first be calculated: Fbase load = Air weight – Buoyancy force + bending force + pressure testing force + landing force (if applied) (5.30) The additional forces that must be added include ballooning force and temperature force. Ballooning force = 2 (Ai Pi - Ae Pe) (5.31) where = Poisson’s ratio Pi = change in internal pressure inside the casing Pe = change in external pressure outside the casing Force due to temperature change = - 207 As T (5.32) where T = temperature change, F As = cross-sectional area, in2 To use Equation (5.31), the engineer therefore must define all possible changes in internal and external pressures to calculate the ballooning force. For the majority of conventional wells, the base load case in Equation (5.30) provides most of the forces the casing is likely to see in its service life. Well Engineering & Construction 175  CASING DESIGN PRINCIPLES 5 Compression Loads TOC Previous Next Other loadings that may develop in the casing include: (a) bending with tongs during make- up; (b) pull-out of the joint and slip crushing; (c) corrosion and fatigue failure, both of the body and of' the threads; (d) pipe wear due to running wire line tools and drillstring assembly which can be extremely detrimental to casing in deviated and dog-legged holes; and (e) additional loadings arising from treatment operations. The latter operations include acidising, cementing and hydrofracturing operations. As a design rule, it usually accepted that casings which are subjected to a great deal of wear as a result of drilling and wireline operations should be upgraded to the next weight up. In other words if the design shows that 43.5 lb/ft,95/8" casing satisfy collapse, burst and tension, then it should be upgraded to 47 lb/ft if this casing is expected to see a great deal of wear. 9.0...... C.. OMPRESSION..............L. OADS...................................................... Compression loading arises in casings that carry inner strings where the weight of inner strings is transferred to the larger supporting casing. Production casings do not carry inner casing strings and are used, amongst other things, to suspend production tubings which are very light in comparison with casing. Consequently, production casings are not designed for compression loading. The integrity of surface casing in compression should be checked by adding the buoyant weight of all subsequent strings.This weight is then compared with the compressive strength of casing (assumed equal to the minimum yield strength) to obtain a minimum design factor of 1.1. 10.0 BIAXIAL EFFECTS............................................................................. The combination of stresses due to the weight of the casing and external pressures are referred to as 'biaxial stresses 1. Biaxial stresses reduce the collapse resistance of the casing and must be accounted for in designing for deep wells or combination strings. The determination of the collapse resistance under tensile load was presented in detail in Chapter 4. The procedure for allowing for biaxial effects is as follows: 176 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... Biaxial Effects TOC Previous Next........... 1. Select grade/weight based on burst/collapse calculations 2. Check the grade/weight satisfy the tension criterion 3. Determine the tension at critical points within the well 4. Apply the procedure in Chapter 4 to calculate the reduced collapse strength 5. Re-calculate the new design factor in collapse Example 5.5 : De t ai le d Casi ng De sig n - 20" C asing Given the following well data: Setting depth = 2200 ft RKB Mud weight used to drill 26" hole = WM mud 9 ppg Fracture gradient at 20" shoe depth= 0.78 psi/ft = 16.35 ppg TD of next section = 7980 ft Max pore pressure in next section = 9 ppg (3735 psi) Average cement density =13.5 ppg Casing to be cemented to seabed Temperature gradient = 0.01 F /ft From offset wells, a thief zone could occur any where below the casing setting depth of 2200 ft with severe loss circulation. You are required to: 1. Calculate collapse and burst pressures 2. Kick tolerance for the well 3. Ascertain if Grade X52, 129.33#, ID = 18.75 in, can be utilised and if not suggest another grade or weight 4. Carry out detailed tension calculations assuming a dogleg of 1deg/100 ft Well Engineering & Construction 177  CASING DESIGN PRINCIPLES 5 Biaxial Effects TOC Previous Next Figure 5.9 Example 5.5 20” Casing Rotary Table 60 ft Sea Level 80 ft Seabed 2060 ft 2200 ft Gas RKB 17.5” hole Next TD = 7980 ft Pf = 3735 psi Solu ti on First, the well data can be converted to a sketch as shown in Figure 5.9 Collapse Loading (i) Partial Evacuation – Since the 20" casing is set 2200 ft it likely that 100% evacuation could occur during lost circulation. Collapse pressure at surface = 0 psi Collapse pressure at shoe = external pressure – internal pressure = 0.052x9x2200 – 0 = 1030 psi 178 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... Biaxial Effects TOC Previous Next........... During cementation External pressure at shoe due to cement and water = (2200 – 140) x 13.5 x.052 + 80x.45 = 1482 psi Internal pressure at shoe = 0.052x 9x 2200 = 1030 psi Effective collapse pressure at shoe during cementation = 1482 – 1030 = 452 psi (b) Kick Tolerance Formation fracture pressure at 20" shoe = 1716 psi The height of a tolerable kick (H) is given by: H = 0.052 x Pm (TD - CSD) + (FG x CSD x 0.052) - Pf (0.052 x m) - G H = 0.052 x 9.5 x (7980-2200) + (15 x 2200 x 0.052) - 3735 (0.052 x 9.5) - 0.1 = 2123 ft Hole capacity between 5" DP and 17.5" hole = 1.534 cu ft = 0.273 bbl/ft V1= volume of kick at shoe = 0.273 x 2123 =579.6 bbls At the 20" shoe and bottom hole conditions, using P1V1 = P2V2, we obtain: V2 =579.6 x (15 x 0.052 x 2200) = 266 bbls 3735 (c) Burst Loading (i) Gas to surface Well Engineering & Construction 179  CASING DESIGN PRINCIPLES 5 Biaxial Effects TOC Previous Next Internal Pressure at surface= Pore pressure at next TD - gas to surface = 0.052x9x7980 - 0.1 x 7980 = 2937 psi Burst Pressure at surface = internal pressure – external pressure (back-up load) = 2937 – 0 = 2937 psi Burst Pressure at casing shoe = internal pressure – back-up load Internal Pressure= Pore pressure - gas gradient to the shoe = 3735 – (7980 –2200) x 0.1 = 3157 psi Back-up load= 2200 x 0.465 = 1023 psi Burst Pressure at casing shoe= 2134 psi (ii) Shoe Fracture Consideration Gas pressure just below the 20" shoe = Pore pressure - gas gradient to the shoe = 3175 psi Fracture gradient at the 20" shoe = 0.78x 2200 = 1716 psi The formation is therefore unable to support a full column of gas to the surface. The maximum allowable surface pressure that can be applied at the wellhead prior to the shoe breaking down with the well evacuated to gas and a seawater backup = Fracture gradient at shoe - gas gradient - backup load at surface = (0.78 x2200) - (0.1 x 2200) - 0 = 1496 psi Maximum surface pressure to breakdown shoe = 1496 psi 180 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... Biaxial Effects TOC Previous Next........... The above calculations are shown for illustration only as a maximum allowable surface pressure of 1496 psi implicitly indicates that a kick is being circulated out of the hole and its pressure is reduced when the top of the bubble reaches the surface. In other words control over the kick pressure within the well should be exercised. With today’s technology, control can also be made on much a kick volume can be safely taken before the well is shut-in. (iii) Burst Based on Circulating out a 150 bbls gas kick In this example we will use a 150 bbl kick for burst calculations. Formation pressure at the next TD of 7980 ft = 0.052 x 9 x7980= 3735 psi The burst design will be based on the ability to circulate a 150 bbl kick from 7980 ft. The Drillers method should be used to establish the annular pressures associated with this kick while circulating with the original mud weight (9 ppg). The annulus pressure at the casing shoe is given by (Refer to Chapter 3 for details): The internal pressure at any point: P at any depth = ½ [A + (A2 + 4.Pf.M.N.yf. m) 0.5] where A =Pf - pm (TD - X) - Pg Pf = 3735 psi TD = 7980 ft CSD = 2200 ft pm = 9.5 x 0.052= 0.494 psi/ft For a 150 bbl kick V1 150 bbl yf 2 2 549. 6 ft V2 (17. 5 5 ) 1 x bbl / ft 4 144 x 5. 62 Well Engineering & Construction 181  CASING DESIGN PRINCIPLES 5 Biaxial Effects TOC Previous Next Pg =Pressure in the gas bubble = G yf = 0.1 x 549.6 = 54.9 psi At Surface X= 0 ft M = 17.5" hole x 5" DP 20"casing x5" DP ann vol 1.534 = ---------------- =0.8613 1.7811 Assume Zs = Zb =1 (gas compressibility factors at surface (S) and at bottom (b)) Tsurface Ns = –––––––––––– T bottom hole 60 + 460 = ---------------------------------------------------------- = 0.959 60 + 0.01x7980 + 460 A = 3735 – 0.494 x (7980 – 0) –54.9 = - 262 psi 4.Pf.M.N.yf m = 4 x 3735 x 0.8613 x 0.959 x 549 x 0.494 = 3,346,747 psi 2 Psurface= ½[-262+ (-262 2 + 3,346,747)0.5] = 793 psi = Internal Pressure at surface At Shoe X= 2200 ft M =1 Assume Zshoe = Zb =1 (gas compressibility factors at shoe and bottom hole) Tshoe 60 + 0.01x2200 + 460 Ns = –––––––––––– = ---------------------------------------------------------- = 0.904 60 + 0.01x7980 + 460 T bottom hole 182 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... Biaxial Effects TOC Previous Next........... A = 3735 – 0.494 x (7980 - 2200) –54.9 = 825 psi 4.Pf.M.N.yf. m = 4 x 3735 x 1 x 0.904 x 549 x 0.494 = 3,662,843 psi 2 Pshoe= ½[825 + (8252 + 3,662,843)0.5] = 1455 psi = Internal Pressure at casing shoe Summary of Kick Tolerance Calculations Surface pressure for a 150 bbl kick = 793 psi, and The gas kick pressure at the 20" shoe =1455 psi Fracture pressure at the 20" shoe = 1716 psi Therefore the formation will not break down if a kick of 150 bbls is taken. Effective burst pressure at the surface = 793 psi Effective burst pressure at the 20" shoe = 1455 - 0.465 x 2200 = 432 psi (iv) Pressure Testing The 20" casing should be tested to a pressure above the maximum anticipated surface pressure of 793 psi from a 150 bbl gas kick. The test pressure must also confirm the competence of the casing, but must be below 80% of the burst strength. The casing will therefore be tested to 1500 psi. Pressure at casing shoe = Test pressure + MW x shoe depth - Back-up gradient = 1500 + 9 x 0.052 x 2200 - 0.465 x 2200 = 1506 psi The 1500 psi will be used as the maximum burst pressure the casing will see. Well Engineering & Construction 183  CASING DESIGN PRINCIPLES 5 Biaxial Effects TOC Previous Next (d) Casing Selection Grade X52, 129.33# casing has the following strength properties (from API tables or by calculations using equations in Chapter 4). Burst strength =2840 psi Collapse strength=1420 psi Yield Strength=1,978,000 lbf Design Factors Burst (pressure test) = 2840 = 1.9 1500 Collapse (lost circulation) = 1420 = 1.4 1030 (e) Tension F1= Buoyant weight of casing (in 9 ppg mud) = 2200 x 129.33 x 0.862 = 245,261 lbf F2= Shock load =1500 x 129.33 =193,955 lbf F3= Bending force = 63 casing weight x OD x DLS = 63x129.33x20 x1 = 162,955 lbf F4= Pressure test force = (casing ID) 2 x test pressure 4 = (18.75) 2 x 1500 = 414,175 lbf 4 184 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... Triaxial Analysis TOC Previous Next........... A summary of the interaction of the above forces is shown in the following table: Running conditions Pressure Testing Static Conditions Conditions F1 : Buoyant Weight 245,261 245,261 245,261 F2 : Shock Load 193,955 0 0 F3 : Bending Force 162,955 162,955 162,955 F4 : Pressure Testing 0 414,175 0 Force Total Force (Ft) (lbf) 602,171 1,016,346 408,216 Casing Yield Strength 1,978,000 1,978,000 1,978,000 Design Factor = Yield/Ft 3.3 1.7 4.8 Required safety factor 1.6 1.6 1.6 Therefore, grade X52, 129.33# satisfy the burst, collapse and tension criteria. Example 5: P ro duc t ion Ca sin g HPHT Details of this example are given in Chapter 15: HPHT wells. 11.0 TRIAXIAL ANALYSIS............................................................................. In the previous sections, pressure and axial loads were treated separately in what is termed as uniaxial approach. In practice, pressure loads and axial stresses exist simultaneously. For example, in a casing string subjected to collapsing load, the stresses within the string will depend on the magnitude of the external pressure causing the collapse load as well as on the resisting internal pressure and the axial load at the point of interest. The axial force, external and internal pressure generate triaxial stresses within the casing body. These triaxial stresses are more representative of the loading at any point as they consider the effects of all applied stresses at that point. In other words, tension is not Well Engineering & Construction 185  CASING DESIGN PRINCIPLES 5 Points of Interest For Triaxial Checks TOC Previous Next considered separately from burst or collapse. The three generated triaxial stresses are: axial, radial and tangential. To perform triaxial analysis, the axial, radial and tangential stresses need to be calculated at each point of interest, e.g. at surface, top of cement and shoe. These stresses will also need to be calculated at both the internal and the external radii of the casing at critical points. 11.1 POINTS OF INTEREST FOR TRIAXIAL CHECKS The following points should be checked: At surface At top of cement At change in casing weight, grade, ID, or OD (ie in combination strings) At change in external pressure At changes in hole geometry: dogleg severity, washouts etc. 11.2 CONDITIONS FOR CARRYING OUT TRIAXIAL CHECKS Pore pressure is greater than 12000 psi Bottom hole temperature is greater than 250 F For all HPHT intermediate and production casing strings H2S service For casing with OD/t ratio less than 15 11.3 RADIAL AND TANGENTIAL STRESSES The presence of fluids inside and outside the casing generate radial and tangential stresses which are given by: di 2 Pi de 2 P e di 2 de 2 ( Pi P e) r (5.33) de 2 di 2 (de 2 di 2 )r 2 di 2 P i de 2 P e di 2 de 2 ( Pi Pe) t de 2 di 2 (de 2 di 2 )r 2 (5.34) 186 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... Axial Stress TOC Previous Next........... where r = distance at which r and t are measured. Pi = Internal pressure, psi Pe = external pressure di and de = internal and external diameter respectively The magnitude of the radial and tangential stresses depend on the magnitude of external and internal pressures and on the distance r. 11.4 AXIAL STRESS The effective axial stress is given by: a= (air weight / casing cross-sectional area) – buoyancy force …….psi (5.35) 11.5 VON MISES EQUIVALENT STRESS The Von Mises (VM) distortion energy theory is used to predict the onset of yielding in duc- tile materials such as casing. The axial, radial and tangential stresses can be combined into an equivalent triaxial stress ( VM) acting at a particular point, given by: 1 2 0.5 VM a t ( t r )2 ( r a )2 (5.36) 2 The yield criterion is satisfied when the combined VM stress is equal to the material yield stress (YP).In the absence of bending forces, the maximum VM stresses occur at the inner radius, r= di. With bending, the maximum stresses can occur at the inside or outside diameter of the casing. The calculated VM stress is then compared with the yield strength of the casing and a design factor > 1.25 should be obtained: DF = Material Yield Stress VM Well Engineering & Construction 187  CASING DESIGN PRINCIPLES 5 Procedure For Triaxial Analysis TOC Previous Next 11.6 PROCEDURE FOR TRIAXIAL ANALYSIS 1. At a given depth, say at surface, calculate at the inner and outer radii of the casing the three stresses ( a, r, t) Tensile forces a = axial stress = cross sec tional area air we ig ht lb a bu oyanc y forc e ps i (5.37) A s in 2 r, t are given by equations (5.33) and (5.34). 2. Calculate 1 2 2 2 0.5 VM a r r t t a 2 3. Compare VM with YP YP DF 1. 25 VM (Notes: 1. For a , we must add bending and shock loading for running conditions 2. Add bending force for static conditions) Example 5.6 : Ex amp le Carry out a triaxial stress check on the following casing string: Casing OD = 7" casing ID = 6.094 " 188 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... Procedure For Triaxial Analysis TOC Previous Next........... As = 9.3173 in2 Weight = 32 # Formation pressure = 12231 psi Setting Depth = 15880 ft Gas Gradient = 0.184 psi/ft Cement Density = 16 ppg from 12,915 ft to 15,880 ft. Mud weight inside casing and at TOC = 15.6 ppg Solu ti on Investigate the case of gas to surface This case could occur after a new section of hole is drilled when a kick is taken from just underneath the casing shoe. Formation pressure at TD (Pf) = 12231 psi at 15 880 ft Surface pressure = 12331 – 0.184 x 15880 = 9309 psi At surface, internal pressure = 9309 psi, external pressure = 0 Evaluate radial and tangential stresses at r = di 6.094 2 x 9309 0 6.094 2 x 7 2 ( 9309 0) r = - 9309 psi 7 2 6.094 2 (7 2 6.094 2 ) 6.094 2 2 2 2 t = 6.094 x9309 – 0- + --------------------------------------------------- --------------------------------------- 6 x7 x 9309 – 0 - = 67,591 psi 2 2 2 2 2 7 – 6.094 7 – 6.094 x6.094 Axial Stress a= (air weight / casing cross-sectional area) – buoyancy force …….psi = [32x 15880/ 9.3173] – [16x 0.052x(15880-12915) + 0.052x12915x15.6] Well Engineering & Construction 189  CASING DESIGN PRINCIPLES 5 Bending Forces TOC Previous Next = 54,539- 12,943 = 41,596 psi 1 2 0.5 VM a t ( t r )2 ( r a )2 2 1 2 0.5 VM 41,596 67 ,591 ( 67 ,591 9309 ) 2 ( 9309 41,596 ) 2 = 67,922 psi 2 DF = Material Yield Stress VM = 110,000 / 67,922 = 1.6 The above analysis can be repeated at r = de at surface and for other critical points along the casing string such as top of cement or shoe. These calculations are left as an exercise for the reader. The above calculations can also be repeated for the case of a limited gas kick of say 50 bbl. 11.7 BENDING FORCES In the presence of bending and buckling forces, the axial stress equation should be modified to allow for these forces. The axial stress then becomes: a= (air weight / casing cross-sectional area) – buoyancy force b buckling (5.38) Both b and buckling are local stresses and should be calculated and applied at the point of interest, ie at a washout. These stresses should not be applied over the length of the casing string. In the absence of bending, the peak VM occurs always at the ID. In the presence of bend- ing, the peak VM can occur on the inside or outside of the casing. As bending causes com- pression on the inside of the casing and tension on the outside of the casing, four calculations are required in the presence of bending. Two at the inside diameter for minimum a (axial 190 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... Triaxial Load Capacity Diagram TOC Previous Next........... stress less compression) and maximum a (axial stress plus bending). Similarly, two calcu- lations are required for the OD of the casing. 12.0 TRIAXIAL LOAD CAPACITY DIAGRAM............................................................................. The triaxial load capacity diagram is a 2-D representation of the triaxial load capacity of the pipe body, the API load capacity lines and the expected loading modes. The diagram is a rep- resentation of the Von Mises stress intensity of the pipe body, represented in the form of axial force against internal or external pressure. The triaxial load diagram provides on one a page a pictorial view of how close the pipe stresses are to the design limits. Recall from Chapter 4 that collapse failures for OD/t ratios >15 occur mostly from elastic- plastic instability and not due to yield on the ID of the casing. The triaxial load diagram (and ellipse of elasticity) is only applicable for casing OD/t ratios 15. The diagram provides a picture of the triaxial stress operating ellipse. The triaxial load capacity diagram can be constructed as follows: 1. Establish the API load capacity lines 2. Establish the stress ellipse 3. Establish service loads and plot inside the stress ellipse 12.1 API LOAD CAPACITY LINES These lines are the collapse strength, burst strength and yield strength of the pipe body adjusted by a suitable design factor. The area bounded by these lines is the API operating window. Construction Well Engineering & Construction 191  CASING DESIGN PRINCIPLES 5 API Load Capacity Lines TOC Previous Next 1. On a pressure/force graph, mark the upper half of the ordinate as positive and the lower half as negative, see Figure 5.10. 2. Repeat step 1 for the x-axis (F-axis). 3. Plot axial design rating lines using: F = (Yield strength/ design factor) x cross-sectional area 4. Plot an effective burst line on the ordinate using the value: burst strength/design factor 5. Plot an effective collapse line on the ordinate using: collapse strength/design factor 6. Check Chapter 4 for correcting collapse strength for biaxial effects. Then plot the new collapse values under tension, shown as the dotted line, Figure 5.11. 7. For a given loading condition, plot the effective pressure and effective axial force at surface. Plot a second point for the top of cement. Plot a third point representing the shoe,Figure 5.10. 8. For a safe design, the line joining the points above should be inside the rectangle,Figure 5.10. Example 5.7 : T riaxial des ig n Using the data in Example 5.6, trace a triaxial diagram and the points representing gas to surface. Solu ti on F= ( 110 /1.6) x area = ( 110 /1.6) x 9.3173 = 640.564 kips Effective burst strength = 12,458/ 1.1 = 11, 325 psi = 11.325 ksi Effective collapse strength = 10,760 / 1= 10.76 ksi 192 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... API Load Capacity Lines TOC Previous Next........... The above lines are plotted as shown in Figure 5.10. Service load A service load line is constructed using data from biaxial analysis for internal and external pressures and axial load. Usually three points are required for each service line: surface, top of cement and at shoe. Other critical points may be selected. The line representing gas to surface is obtained as follows: Point 1 at Surface: Psurface = internal pressure – external pres- Figure 5.10 API load capacity lines sure = 9309 – 0 = 9.309 ksi effective yield strength Effective tension = (air weight) x buoyancy factor effective burst strength 1 3 = (32x 15880) x 0.7615 = 386.95 kips 2 Point 2: At top of cement at 12915 ft Effective pressure = 12231 – (15880 – effective collapse strength 12915) x 0.184 - 12915x 0.465 = 5680 psi = 5.68 ksi 1 3 2 Effective tension = (air weight) x buoyancy factor = [32x (15880-12915)] x 0.7615 = 72.25 kips Point 3: at shoe Peffective= 12231 – 0.465x 15,880 = 4.85 ksi Buoyancy Force = (total air weight – buoyant weight) Well Engineering & Construction 193  CASING DESIGN PRINCIPLES 5 API Load Capacity Lines TOC Previous Next = 32x 15,880 - 386,950 = 121,210 lbf = 121.21 kips This force is compressive ie = - 121.21 kips The three points are plotted as shown in Figure 5.10. The line joining these points lie within the rectangle indicating the casing is being operated well within the specified safety limits. Figure 5.11 Ellipse of elasticity with API load lines + Ve Burst Strength - Ve + Ve 0 Yield Yield 16. 16. Collapse Reduced collapse strength due to tension - Ve 194 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... Stress Ellipse TOC Previous Next........... 12.2 STRESS ELLIPSE The VM stress ellipse represents the stress level in the Figure 5.12 Stress ellipse for pipe body in terms of axial stress, internal pressure and pipe body external pressure. + The construction API ellipse for pipe body is shown B below,Figure 5.12. T - + 12.3 ELLIPSE CONSTRUCTION C From Von Mises Equation 2 - 2 1 2 2 (5.39)2 Y2 VM a r r a 2 Simplifying 2 a a C 1 Pi C 2 Pe C 3 Pi 2 C 4 Pe 2 C 5 Pi Pe Y2 0 (5.40) In Excel Sheet, calculate: de 2 di 2 C1 1 K, K (5.41) de 2 di 2 C2 1 K C3 K2 K 1 2 C4 K 1 C5 2K 1 The ellipse has two parts. Solving the above quadratic equation for each half of the ellipse gives a total of four roots. a. Upper Part The upper part is constructed by setting the external pressure to zero and the VM to the material yield strength. Using internal pressures, for any value of internal pressure, the axial stress is given by: Well Engineering & Construction 195  CASING DESIGN PRINCIPLES 5 Ellipse Construction TOC Previous Next 2 2 a 0. 5 C 1 Pi 0.5 C 1 Pi 4 C 3 Pi Y 2 (5.42) Above quadratic equation has +Ve and -Ve roots. Calculate as follows: Pi psi a Ve x A s lbf a Ve x A s lbf 0 500 1000 1500 2000 …. And then plot upper half of ellipse b. Lower Part of ellipse The lower part is constructed by setting the internal pressure to zero and the VM to the material yield strength. Hence for any value of external pressure, the axial stress is given by: 2 a 0.5 C 2 P e 0.5 C 2 Pe 4 C 4 Pe 2 Y2 (5.43) Above equation has +Ve and -Ve roots Calculate as follows: 196 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... Ellipse Construction TOC Previous Next........... Pe psi a Ve x A s lbf a Ve x A s lbf 0 - 500 - 1000 - 1500.. And then plot lower half of ellipse c. The two halves will form an ellipse of pipe body Well Engineering & Construction 197  CASING DESIGN PRINCIPLES 5 Learning Milestones TOC Previous Next 13.0 LEARNING MILESTONES............................................................................. In this chapter, you should have learnt to: 1..List the major steps in the casing design process 2. Name the three types of Load Cases used in Detailed Casing Design 3. Understand the use of design factors 4. Carry out design for burst & collapse loads for both drilling and production casings 5..Carry out Tensile (Installation) calculations 6. Carry out detailed casing design calculation for a complete casing string 7. Calculate triaxial stresses 14.0 REFERENCES............................................................................. 1. Rabia H (1987) "Fundamentals of Casing Design". Kluwer Group 2. Klementich, E f and Jellison, MJ (1986). A service model for casing strings. SPE Drilling Engineering, April, pp 141-151 15.0 EXERCISES............................................................................. 1. List the major steps in the casing design process 2. List the three major forces in casing design: 3. Shock loading is most influenced by: Hole angle Casing weight Pipe OD 198 Well Engineering & Construction  CASING DESIGN PRINCIPLES..... Exercises TOC Previous Next........... 4. When designing casing across salt sections, the effective collapse loading is calculated using: External mud pressure External and internal mud pressure 1 psi/ft external pressure and internal pressure due to mud highest casing available on the market (MUST CASING) 5. The casing sees the maximum surface pressure when: Casing is full of gas and the well is then shut-in When a large kick is detected but the casing is immediately shut-in When an underground blowout occurs 80% burst strength 6. What determines the casing test pressure Well Engineering & Construction 199  CASING DESIGN PRINCIPLES 5 Exercises TOC Previous Next 200 Well Engineering & Construction