Abstract Liners in horizontal thermal wells do occasionally have production inflow problems and fail. Published literature exists on the risks and design issues related to the effects of thermal expansion on slotted liners in horizontal wells. This paper investigates two areas of liner behaviour that seem to have been somewhat overlooked. It examines: (1) the potential effects of thermal expansion or contraction on screened liners and (2) the effects of thermal contraction on slotted and screened liners. Upon injection of steam, horizontal liners will expand or contract and be subject to compressive or tensile axial stresses. Whether the stress is compressive or tensile depends on when the formation closes in on the liner. If it closes in before the well is steamed, the stress will be compressive; if it closes in after steaming the stress will be tensile. This paper examines the effects of shear force from the formation on the screens of liners both in expansion and contraction. It would appear that to some extent the shear or tearing forces on screens are selflimiting making them more resistant to tearing than might be expected. The paper also examines effects on liners of tensile forces caused by contraction and cooling. Tensile forces on liners can approach and exceed yield under common operating conditions. The liners are then susceptible to slot closure and collapse. Limits on operating conditions are presented to reduce the risk of such failures. Suggestions for further RD on the subject are also made.
CSUG/SPE 136871 The Potential for Slot Closure, Screen Damage, and Collapse of Liners in Thermal Horizontal Wells J.C O'Rourke, SPE, Exor Scientific Ltd Copyright 2010, Society of Petroleum Engineers This paper was prepared for presentation at the Canadian Unconventional Resources & International Petroleum Conference held in Calgary, Alberta, Canada, 19–21 October 2010 This paper was selected for presentation by a CSUG/SPE program committee following review of information contained in an abstract submitted by the author(s) Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s) The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied The abstract must contain conspicuous acknowledgment of SPE copyright Abstract Liners in horizontal thermal wells occasionally have production inflow problems and fail Published literature exists on the risks and design issues related to the effects of thermal expansion on slotted liners in horizontal wells This paper investigates two areas of liner behaviour that seem to have been somewhat overlooked It examines: (1) the potential effects of thermal expansion or contraction on screened liners and (2) the effects of thermal contraction on slotted and screened liners Upon injection of steam, horizontal liners will expand or contract and be subject to compressive or tensile axial stresses Whether the stress is compressive or tensile depends on when the formation closes in on the liner If it closes in before the well is steamed, the stress will be compressive; if it closes in after steaming the stress will be tensile This paper examines the effects of shear force from the formation on the screens of liners both in expansion and contraction It would appear that to some extent the shear or tearing forces on screens are self-limiting making them more resistant to tearing than might be expected The paper also examines effects on liners of tensile forces caused by contraction and cooling Tensile forces on liners can approach and exceed yield under common operating conditions The liners are then susceptible to slot closure and collapse Limits on operating conditions are presented to reduce the risk of such failures Suggestions for further R&D on the subject are also made Introduction About five years ago, the author noticed that J55 screened liners had been run in a SAGD well pair At the time, it was normal to run L80 screened liners The author was told that the reasons for running the J55 were to save money and that sufficient L80 liner was not in stock In the author‟s experience, approximately 10% of liners in thermal horizontal wells had failed Other engineers elsewhere had informally reported much higher numbers This led the author to explore whether or not the J55 was okay This led to identifying a wider range of horizontal well liner issues that seemed important and didn‟t appear to be discussed much in any publications This led the author to CSUG/SPE 136871 conduct his own investigation The author presented a half hour discussion of these issues at an annual Slugging-itout Conference on 26 March 2007 in Calgary Alberta organized by the Canadian Heavy Oil Association (CHOA) The title of the presentation was “Why would anyone still use screened liners?” Presentations at these conferences are informal, strictly audio-visual with no handouts, and are not published This paper presents a more formal and in-depth discussion of the issues touched on in that presentation The issues discussed in this paper are: Liner material: What type of liner material should be used? This paper looks at L80 and K55 Tensile stress effects: Can thermal liners be subjected to tensile stresses? If so, then there could be serious effects on liners There are several references discussing the design of liners to handle post yield compressive stresses (Slack 2000; Dall'Acqua 2005; Kaiser 2005) Slack 2000 gives a detailed discussion of earth forces on the liner and the compressive and tensile stresses and failure modes they may cause However their paper mainly discusses a method to handle the compressive forces with a corrugated pup joint placed between liner joints Current thinking, as discussed in Dall'Acqua 2005, states that these post yield compressive forces can be tolerated with proper selection of liner material such as K55 which has stiffer post yield characteristics than L80 This paper focuses on the effects of tensile stress in liners Some of the potential effects of these tensile stresses are: Liner collapse: According to design tables for casing (Bradley 1992) the collapse resistance of casing drops significantly as the tensile axial stress is increased Under this weakened state, earth pressures could be enough to collapse the liner Slot closure: The radial earth pressures on the horizontal liner could cause the slots to close Shear forces on screens: Earth forces acting on screened liners will result in shear forces parallel to the axis of the liner as the liner expands or contracts due to heating or cooling The possibility of these shear forces tearing the screens on the base pipe is examined Design & Operating criteria: Operating temperatures and liner materials are discussed with a view to reducing the potential for damage to liners caused by the issues given above Further investigations: Suggestions are made on what further investigations should be undertaken in the areas of earth forces, thermal behaviour of liners in both compression and tension, and how to mitigate somewhat the stress on liners To examine these issues one should have some knowledge of soil mechanics and mechanics of materials The author referred to texts on these subjects (e.g Sowers 1979; Boresi 2003) and several papers mentioned in the References Typical Liner Types Screened and slotted liners are the most popular thermal horizontal well liner types in use today Other liner types have been and are being developed Screened liners were used in all but one of the SAGD wellpairs at the Underground Test Facility where SAGD was first developed (O‟Rourke et al 2007) Liners in SAGD wells are typically in the order of 700 m (2300 ft) long with a 177.8mm (7 in.) OD Screened liners are also used in vertical CSS wells by thermal operators such as Husky (Wong et al, 2003) Many liners are made of L80 grade steel but some operators prefer K55 because of its post yield (plastic) properties Illustrations of screened and slotted liners are shown in Figs to Many current SAGD operators have gone to slotted liners There are arguments for using either screens or slots but the pendulum has swung in favour of slots A typical screened liner consists of a base pipe with 12.7 mm (½ inch) holes spaced in a diagonal grid 35.8 mm (1.41 inches) apart (Fig & 4) The screen portion is constructed separately from the base pipe and slid over it It consists of a continuous wire that is wrapped and electronically welded onto ribs that run along the axis of the pipe (Fig 2) The wire is spaced with a specified opening between the wires of anywhere from 178 to 635 or more microns (0.007 to 0.025 inches) depending on the grain size and cohesion of the reservoir sand The wire can be tapered with the narrow side of the opening on the outside This reduces sand plugging The screen ends and midsection are welded to the base pipe (Fig 3) Typically the base pipe is 13.3 m long with the screen covering 11.3 m of it A typical slotted liner consists of a similar base pipe but with slots in it instead of holes (Fig 4) Typical slots are cut into the base pipe and then rolled on the outside surface to give them a taper with the narrow end facing out from the liner Slot widths are similar to those in wire wrap screens A type slot used in this paper is 56 mm (2.2 in.) long with a 20 mm (0.79 in.) hoop between them See Table for type slot and screen hole dimensions CSUG/SPE 136871 Screened liners are heavier and have a bit larger OD than an equivalent slotted liner with the same ID This is because the screen is wrapped on the outside of a base pipe with holes in it The slotted liner consists only of a base pipe with slots in it This would tend to make slotted liners easier to install in long horizontal wells, although operators that choose screened liners seem to have no problem installing them Slotted liners are also somewhat less expensive A typical design of a screened liner would have roughly 7% open area compared to 1.3 % for slotted liners in the screened and slotted portions of the liners This would tend to make screened liners less susceptible to depositional plugging in that it should take longer to plug them Theoretical calculations indicate that the 1.3 % opening of slotted liners is sufficient and does not result in large pressure differentials across the liner when fluid flows through them (Kaiser et al 2000) Radial Earth Forces Acting on Liners The total and effective vertical earth stresses (σet and σe) at depth z is estimated by the equations σet = γz and σe = σet – u 1a, 1b where γ is the unit weight of the earth and u is the liquid pore pressure The effective stress is the net stress on the liner or sand grains and is the stress used to calculate the vertical, horizontal and shear forces on the liner The pore pressure u is equalized inside and outside of the liner so the effective pressure is the net pressure on the liner The horizontal stress is a fraction of this depending on whether the soil is at rest or collapsing These stresses are all in a radial direction relative to the axis of the well liner This paper is concerned with how much of this radial stress is transferred to a horizontal liner that has been inserted into a hole drilled in mostly cohesionless sand Liners are pushed into open holes that are drilled slightly larger than the liner OD For example a 177.8mm (7 in.) liner might be run into a 222mm (8 ¾ in.) or larger hole The OD of a screened liner would be in the order of 192 mm due to the screen wrapped on top of the 177.8 mm base pipe Drillers have techniques to keep the hole open while inserting long (> 1,000 m, 3289 ft.) liners into a well without damaging the liner In this paper it is assumed that the drill hole stays open while the well is being steamed during start-up for a SAGD type operation or a cyclic steam stimulation (CSS) It is assumed that the formation closes in on the liner after the initial steaming How reasonable are these assumptions? Kooijman et al 1996 examined the issue of bore hole closure through laboratory and theoretical work Their work indicated that the sand will gradually slough into the annular space in a „failed zone‟ around the liner The failure occurred at σe > 6.9 MPa (1000 psi) They developed an analytical model that indicated that the vertical stress σv on a liner in this failed zone should be roughly 5% to 25% of the undisturbed earth stress, σe The presence of a small water cut with the oil significantly facilitated the collapse of the hole They explained that the water caused the breakdown of capillary cohesion in the sand If the sand in the failed zone was somehow swept away, the drill hole continued to collapse and resulted in the full earth pressure being exerted on the liner causing it to collapse It would seem that steam would tend to destroy any capillary cohesion although it has been reported that large volumes of steam can create chemical cohesion in the sand It would be a good idea to a little more experimental work in this area with steam There would definitely be condensed steam and connate water produced back into the well after steaming has stopped in a production well This would indicate that a failed sand zone should form around a liner and remain loosely packed (at 5% of σe) as long as there was no sand production However the vertical stress on the liner could increase and approach σe under certain conditions after liquid production starts Some possible conditions are: if sand were produced through large openings in the liner or if bore hole enlargements were created during drilling Large openings in the liner could be caused by too large slots or screen gaps, or screens torn back by shear stresses during installation or thermal expansion/contraction Washouts could occur when drilling stalls or if there were geotechnical property variations in the reservoir These conditions would likely occur at localized points along the liner rather than continuously along the entire length It is known that localized liner collapse does occur in a small but significant number of wells Based on this work, it seems quite possible that a liner could be steamed and that it could expand without much compressive stresses exerted on it It is only after steaming and during the start of production that the sand might fail and result in a partial vertical stress σv on the liner which is to 25% of the full earth stress σe If there is water in CSUG/SPE 136871 the production, and there would be, the drill hole might collapse at some locations where sand can be swept away resulting in the full earth stress σe being exerted on the liner If the liner temperature subsequently dropped, large tensile stresses would occur in the liner Shear stress on the liner Table presents basic reservoir data used in this paper An active earth pressure coefficient (Sowers 1997) is used to as a function of the vertical stress estimate the horizontal stress An average of the vertical and horizontal earth stresses would result in a frictional shear stress τf parallel to the axis of the liner if the liner moved We obtain: μs is the coefficient of friction of the liner with the sand μs would be larger for screened liners than for slotted liners as shown in Table Values for µ were taken from Sowers 1979 for piles against rough concrete and rusty steel respectively The liner would have to move a small distance to mobilize the full dynamic shear stress In this paper this is represented by ( ) λf is a small distance over which shear is mobilized If we assumed a constant shear, λf would be zero which would simplify the math and would not detract from the message in this paper But a seemingly small λf in the order of cm makes a significant difference in the total displacement of the liner In this paper λf is treated as both zero and cm because its actual value was unknown It seems reasonable to expect that it might take some small movement of the liner to mobilize the full shear The basic differential equations governing the stresses on and movement of the liner are given below The sign conventions for the key variables are illustrated in Fig The shear stress on the liner is related to the axial stress σn in the liner by where S is the wall thickness of the liner and is assumed small relative to the liner diameter D l is the axial distance from the fixed end of the liner The fixed end is where the liner is anchored at the heel, or at the midpoint of the liner if both ends were free to move τ is positive in the expansion mode and opposite to the direction of l σn acts in the same direction as τ and is positive for compression and negative for tension The liner displacement λ is positive in the l direction and is related to axial stress and thermal strain ϵt = αΔT by Net eternal strain equals thermal strain minus internal mechanical strain E is the modulus of elasticity of steel ΔT is the temperature change and is positive for an increase in T α is the coefficient of expansion of steel Eqs and can be combined to give: The end of the liner at l = L is assumed to be unrestrained in the axial direction This gives the boundary condition that the axial stress σn is zero at the free end Another boundary condition is that the liner displacement λ will be zero at the fixed end, or midpoint of the liner if both ends are free For most of the discussion in this paper both λ and dλ/dl = because λ reaches zero well before reaching the fixed end The only case where this doesn‟t apply is in the zero earth stress case Eq was solved for exponential shear (eq 4) using the fourth-order Runge-Kutta numerical method It also was solved analytically assuming constant shear giving the following results: CSUG/SPE 136871 Where x = L – l and is the distance from the free end B = τf/(SE) and λo is the extension at the end of the liner where x = This eq applies only from x = to Xo where λ = In most cases discussed here, we will have λ = and dλ/dl = at Xo = At this point we calculate from eq 7a: The results for both exponential and constant shear are presented in Table For the special case of no shear, σn = and the total extension at the free end is given by Another special case is where the liner is totally restrained liner and dλ/dx = because λ = As will be seen, in most cases after start-up the liner is totally restrained except for a short distance Xo near the free end In this case equation gives: This is the formula used to calculate ΔTy shown in Table for the appropriate yield strengths on bare pipe However liners are not bare pipes They have slots or circular holes in them as discussed above This leads to a concentration of stress and strain in the vicinity of the holes Liner stress & strain concentrations Table gives sample dimensions of the holes in slotted and screened liner base pipes The axial stress in the pipe near these holes (in the web) increases above what it would be without the holes This is modeled analytically using a stress concentration factor Fs The stress concentration in the axial direction would be at a maximum where the holes are at their widest An estimate of stress concentration at this location is made using the cross section dimensions Fs1 = 1.41 for a 12.7 mm (1/2 in.) circular hole in a 177.8 mm (7 in.) screened base pipe as shown in Table This means the axial stress σ1 on the web cross-section is 41 % higher than it would be for a bare pipe which would have an Fs of This analysis assumes that the grid lines of holes on a screened liner are parallel to the axis The holes are spaced 50 mm (2 in.) apart on the axial and circumferential directions but 36 mm (1.41 in.) apart in a diagonal square To simplify the analysis, these dimensions were averaged to become a square grid parallel to the axis with 43.3 mm (1.71 in.) sides A 50 mm square would have made the pipe too strong and a 41 mm square too weak There are multiple rows of holes along the length of the pipe An average stress concentration factor Fsa is used to represent the average Fs over the center to center distance La between the holes For the slotted liner, the hole width Dc is small compared to the axial inter hole distance La (Table 2) A simple dimensional relation is used for determining and average Fs slotted liners: ( ) Boresi 2003 indicates that the axial stress influence around a hole in an infinite sheet becomes small at a distance of four times the hole radius For circular holes in a screen liner base pipe it is assumed that the hole stress concentration Fs extends linearly from Fs at the center of the hole to at four times the hole radius Averaging this linearized Fs over the inter-hole axial distance results in : CSUG/SPE 136871 These formulas were used to compute the stress concentration factors given in Table The average stress concentration factor results in an average axial stress σa on the liner such that This σa is used in place of σn in eq to compute an average extension λa These are averages over the inter-hole axial distance La They account for the weakness in the pipe caused by the holes Also for the special case of a totally restrained liner where dλa/dx = because λa = we see from eq that The normal liner stress σn is: P is the total compressive axial force on the liner, Do and Di are the liner OD and ID and S is the thin wall thickness This stress is multiplied by the stress concentration factor Fs to obtain strain near the holes We have the following relations: σ2 = σn σa = Fsaσn (13a, b, c) σ1 = Fs1σn where σ2 is the stress on the plain pipe between holes (hoop), σ1 is the stress at the holes (web), and σa is the average stress along the length of the pipe from hole center to hole center From these equations we get the yield ΔT for region (the web) to be: ( ) Where: The yield ∆T for region (the hoop) is discussed in the post yield section below Strain will be concentrated where the stress is concentrated and will be proportional to the stress concentration There is also stress concentration in the circumferential direction This becomes important when considering collapse stress and slot closure caused by the earth stress σe The stress concentrations for screened liners are the same in both the circumferential and axial dimensions because the symmetry of the holes However the slotted liner will have a high circumferential stress concentration because the slots are long relative to the hoop width The circumferential stress concentration factor Fsc for the slotted liner is based on the slot geometry This is the stress concentration in the hoop that could cause the slots to close This will be discussed later in the section on slot closure As shown in Table 2, the Fsc for the slotted liner is 3.75 This is 2.6 times the Fsc for the screened liner On a theoretical note, the portions of the stressed liner where λa is zero, there would still be a small λ1 and λ2 occurring in the web and hoop over each distance La They would cancel out over the distance La resulting in λa = Post yield strain concentration After the web area reaches yield the analysis becomes strain based, rather than stress based as it was in the elastic mode The stress concentrations are still valid but eq 11b is not The web area at the holes, region 1, will reach yield before the hoop area between holes, region 2, due to the stress concentration at the holes Once this happens most of the incremental strain beyond yield will occur in the web Once the liner is restrained by the formation, the total axial force P in the pipe will be the same in the web as in the hoop The normal liner stress σn is given by eq 12 This stress is multiplied by the stress concentration factor Fs1 to obtain the web stress 7 CSUG/SPE 136871 Think of a separate problem where we have a liner with two moduli of elasticity Let the region over a length L1 in the web have stress σ1, strain ϵ1, extension λ1 and a linear modulus Ep Similarly, over a length L2, the hoop region, we have stress σ2, strain ϵ2, extension λ2 and modulus E Now we have: From which we get: Also we see that: Relating this to our current situation in the post yield realm, we can think of these as variables as applying after region at the holes has reached yield We denote them with a prime as in λ1′ and λ2′ We can think of Ep as a plastic modulus for zone (the web) E is the normal elastic modulus for zone (the hoop) which has not reached yield The graph of Fig shows a linearized version of the elastic and plastic stress-strain curves for casing grades K55 and L80 ΔT is used to represent the thermal strain αΔT The maximum ∆T is 325 C which corresponds to a 15 MPa start-up pressure from an ambient T of 20 °C A linearized plastic modulus Ep for each material was estimated using the difference between the minimum yield and the minimum ultimate stress which occurs at 4% strain in the graph in IRP 2002 These plastic moduli are given in Table The range of the total thermal strain ϵt is fairly small and has a value of 0.41% at a ΔT of 325 C After the axial web stress σ1 exceeds yield, the axial web strain ϵ′1 is amplified by a strain concentration factor Fn1 The strain ϵ2 in the hoop region remains almost constant after the web reaches yield because most of the strain is concentrated in the web and the hoop stress is almost constant (Fig 5) Values of λ1′/λ2′ are given in Table The liner is in the fully restrained mode so the extensions λ are virtual in that they are what would be required push the liner back into the pre ∆T position The amplified strain in the web is shown in the graph of Fig and the theory is presented below We have: and ( ( ) ) Combining eq 18 and 20 gives: ( ( ) ) We let Fn1 denote a plastic axial strain concentration factor for the web where: ( ) The stresses in the plastic zone are given by: The web length L1 used to calculate Fn1 was taken to be 0.79 * Da This is the length of the axial side of a rectangle with the other side of length Dc and the same area as the hole of diameter Da It is entirely possible that L1 could be smaller which would result in Fn1 being larger 8 CSUG/SPE 136871 Using the above relationships, an expression can be derived for ∆Ty2, the ∆T at which the hoop reaches axial yield Values of ∆Ty2 are given in Table These calculated values assume there is no circumferential stress on the liner They are outside the range of ∆T‟s that are normally used in SAGD operations However for a 15 MPa cyclic steam process the pure axial (i.e no circumferential) hoop stress for a K55 slotted liner could reach yield Of course there will be vertical hence circumferential stress on the liner which, as will be seen below, can cause the hoop to go into yield at normal operating temperatures Stresses & Strains on the liner – analytical results and discussion If the liner is restrained and the ΔT values are positive, the liner will go into compression If the ΔT values are negative the liner will go into tension The effects of compression on a slotted liner are discussed quite thoroughly by other authors as mentioned in the introduction This paper focuses on the tensile effects The typical liner parameters that are given in Table were used for the results given in Table which are discussed in more detail below Yield and ultimate stresses and corresponding strains for plain pipe are given for K55 and L80 grade casings Plain pipe is pipe without holes in it The hoop region between holes is plain pipe The yield strains in Table are defined by the following: The ultimate strains in Table are estimated from the typical stress–strain graphs given in IRP 2002 As stated below, the thermally induced strain is expected to be well below these values for initial steam pressures up to 15 MPa The plastic moduli were introduced in a previous section The axial yield ΔT‟s on plain pipe are computed from eq 15 using the yield stress Fig shows graphs of the web strains ϵ1 versus ∆T for the case of a slotted liner using both K55 and L80 grades of steel It can be seen that the maximum strain ϵ1 for a 325 C (15 MPa startup) thermal strain is in the order of 1.2 % at the post yield area around the holes (webs) These strains are well under the ultimate tensile strains which are in the order of to 10 % As mentioned above, ϵ1 could be higher if the value for L1 is less than 0.79*Da Best to not exceed web yield until future experimental work proves otherwise However there will be a radial earth stress on the web which would cause it to bend This is more significant for the slotted liner which has a relatively long web By modeling the web as a cantilevered beam at both ends with a uniform vertical load and an axial tensile stress, it can be shown that the maximum tensile stress will occur at the top of the web where it joins the hoop It can also be shown that the ΔT required for the outside web stress at the hoop to reach yield is greater than the collapse ∆T criteria of the hoop (discussed below) and less than the tensile yield ∆T of the entire web So the hoop ∆T collapse criteria will more than cover these web yield concerns in the slotted liner The mid part of Table presents results for pipe with holes in it and makes use of the stress concentration factors discussed above The yield ∆Ty1‟s for the webs of the liners were calculated with eq 14 ∆T‟s should be kept below these values if one wishes to avoid going into tensile yield The stresses and strains for the hoop regions, assuming the webs are at yield, are given next The hoop stresses for the screened and slotted liners are 71% and 95% of yield respectively for both the K55 and L80 grades So the entire slotted liner is close to yield when the webs are at yield It will be seen later that the 95% in slotted liner is too high to be safe from collapse The 71 % hoop stress for the screens seems to be a reasonably safe maximum hoop stress The collapse depths in Table will be discussed in the section on collapse The lower portion of Table gives results for the maximum case where the ∆T is 325 C corresponding to a 15 MPa steam pressure at start up This represents the maximum expected downhole pressure to be used in field operations If the liner is restrained, as assumed in all these examples, the web would go into the post yield (plastic) mode Most of the post yield extension would be taken up by the web as indicated by the λ′1/λ′2 ratios We see that the slotted liner hoop stresses are 100 & 96 % of yield for K55 and L80 grades respectively The screened liner hoop stresses CSUG/SPE 136871 are less at 84% and 73 % of yield for K55 and L80 grades The graph of Fig also shows some of the post-yield relations Eq 23 was used to calculate the web strains in the post-yield region It is important to note that the strains are well under the ultimate tensile strains which are in the order of to 10 % This means the liner is unlikely to part due to this axial stress alone But it could collapse, as will be discussed later, and collapse could result in the liner parting These numbers are from linearized stress-strain relationships and from step-like stress and strain concentrations In reality the material will behave more smoothly with more gradual transitions In particular the strain concentrations might be higher therefore so could the strains Because of this uncertainty in the strain concentration, it would be preferable to avoid letting the web go into yield Experimental work is advisable Also successive thermal cycles should be considered but are not discussed in this paper Liner extension, results Fig presents a graph showing the amount of liner extension expected for a screened liner with a ΔT of 244 C with only the weight of the liner on the open drill hole producing shear τ on the liner This ΔT corresponds to a MPa start-up steam pressure with an ambient reservoir temperature of 20 °C Two cases are shown, one for a 700 m liner and the other for a 350 m long liner The liner parameters are as given in Table however the screened liner weight at 47.6 kg/m (32 lb/ft.) is heavier than the bare pipe because an extra assumed weight was added to account for the wrapped on screen The liners were assumed fixed at one end The graph shows that the free ends of the liners will extend by 1.06 and 2.07 m for the 350 and 700 m lengths respectively The maximum axial stresses in the pipe are 19 and 38 MPa (2.8 and 5.5 ksi) which are well below the yield stresses of the pipe The 350 m case could be taken to represent what the extension and stress would be if the 700 m liner were free at both ends It would be free to move but stationary in the middle This applies only in the case where there is no earth pressure on the liner Next we examine how far a liner will extend if acted on by earth forces The axial shear stress on a liner is calculated from eq and values are given in Table Effective stresses (eq 1.b) were used The pore pressure was assumed to be 70% of the hydrostatic gradient The horizontal stresses were estimated by using an active earth pressure coefficient Ka of 0.36 It is assumed that production has begun According to Kooijman et al the sand would fail and the annulus between the hole and liner would fill with loose sand The vertical pressure on the liner would be roughly 5% of the ambient effective earth pressure At locations where the sand somehow gets swept away, the drill hole would completely collapse and the liner would be exposed to the full σe resulting in a shear force 20 times higher (full earth stress) Next we discuss the liner extensions expected for the partial and full earth pressure cases Fig presents a sample case with the same 700 m screened liner used in Fig but with stresses that would occur at 500m depth It is assumed that the liner is fixed at one end and has expanded without significant compressive stress The drill hole partially fails with the start of production Sand is packed in around the liner but has not been swept away This represents the partial earth pressure case The effective ambient vertical earth stress σe would be 7.4 MPa (1080 psi) The vertical stress on the liner would be 5% of σe or 372 kPa (54 psi) The shear stress τf would be 134 kPa (19.5 psi ) where the liner experiences movement It is assumed that the liner is then cooled by 192 C, which is the ΔT required to reach axial yield in the web of an L80 screened liner The liner would be in tension The graph shows two cases In the constant shear case, the full shear stress τf is mobilized by any movement of the liner We let λf = in eq or use eqs 7a, b, and c In the exponential shear case, some liner movement is required to mobilize the shear stress We assume λf = cm It can be seen that the liner contraction λa at the free end is only 30 to 50 mm (1.2 to in.) The liner reaches a maximum axial stress σa (tensile) of 483 MPa (70 ksi) within 25 to 52 m (82 to 171 ft.) of the free end This is the average tensile stress σa in the liner The maximum stress σ1 occurs at the holes and is equal to (Fs1/Fsa) * σa or 552 MPa (80 ksi) This is the yield strength of the steel in the liner The shear stress τ is at a maximum of 134 kPa (19.5 psi) at the free end and drops to almost zero within 25 to 52 m (82 to 171 ft.) of the free end along with λa Tables presents a summary of several more cases giving key results for each case The cases are for both L80 and K55 grade liners and for screened and slotted liners Cases are presented for 500m and 200m depths; and for zero, partial, and full earth pressures Both exponential and constant shear cases are shown assuming that the correct value is somewhere in between 10 CSUG/SPE 136871 The left side of Table looks at liner expansion / contraction using ∆T‟s required to put the web into yield The key observations to make here are: (1) for the partial earth pressure cases the maximum liner contraction is in the order of to 10 cm (2 to in.) and, (2) the shear stress on the liners drops to less than 60 kPa within about 25 m of the free end The one full earth pressure case would occur if the sand is somehow swept away The liner free end move less than a centimeter The right side of Table presents cases for start-ups at MPa and MPa for the open hole These cases with just the liner weight acting only reach to 10% of yield at the holes The open hole case would occur if start-up began shortly after completing the well There wouldn‟t be any earth pressure on the liner We assume this is the startup case for the remainder of this paper This subsequently allows for the creation of maximum tension in the liner when the drillhole closes just after the start of production The potential for slot closure As the axial tension in the liner increases, the compressive yield stress in the circumferential direction decreases We express this using the von Mises yield criterion (Boresi 2003 or Bradley 1992): [ ( ) ] ( ) σ2cy is the compressive yield stress in the circumferential direction in the hoop The other variables have been defined previously Almost all the circumferential stress is concentrated in the hoop We use the vertical earth pressure σv for slot closure The side slots will start to close before the top slots since the earth stress is greater in the vertical than the horizontal direction By geometric reasoning (see Fig 8) we also see that the circumferential stress And knowing that the hoop circumferential stress we see obtain: σc is calculated by: Values for Fse are given in Table Using the plastic stress-strain relation: ( ) and eq 28 we come up with a relationship between σv and slot closure λc as shown in the graph of Fig It shows the ΔT cases for L80 and K55 slotted liners that would have minimal slot closure at full earth pressures at 200 and 500 m depth We see that the L80 liner meets this criterion at ∆T‟s of 195 and 127 C at the respective depths The K55 liner meets this criterion for 200 m and 500 m depth at ΔT‟s of 122 and 36 C respectively The graph is for slots only because screened liners are not vulnerable to hole closure due to their circular hole shape The partial and full effective earth stresses at 500 m depth are shown in the graph It can be seen that slot closure should not be a problem for either L80 or K55 slotted liners at the partial earth pressure However if the drill hole does collapse more, the slots could partially close as the earth pressure builds For example, from the graph it can be seen that the slots of an L80 liner at a ΔT of 195 C would close by 0.25 mm (0.010 in.) at a vertical earth pressure of 4.8 MPa, equivalent to a depth of 305 m at full σ e Slot closure starts just after the hoop reaches yield As we will soon see, the liner collapse occurs as the combined axial and earth stresses cause the hoop to approach yield So slot closure would likely occur with or slightly after liner collapse begins Liner Collapse Liner collapse in most thermal operation depths will only happen if the liner is in tension As with circumferential yield strength, the collapse strength of the liner diminishes as the axial tension increases The ΔT‟s in this analysis are all negative since the liner is cooling The liners are assumed to start cooling from a zero axial stress state This is possible if the liners expanded with little or no earth pressure acting on them as discussed earlier in this paper CSUG/SPE 136871 We assume that the hoops provide the total resistance to liner collapse This is reasonable for slotted liners because the hoop widths (La – Da) are small relative to the slot length (Da) which would result in the web taking on a lot of the radial earth stress but little of the circumferential stress This is a bit of a conservative consumption for screened liners because the holes behave somewhat like a hole in a plate and their radius of influence is about half the interhole distance Collapse formulas in Bradley 1992 were used to construct the graph shown in Fig 10 These collapse formulas use the von Mises yield criteria (Boresi 2003) API Bulletin 5C3 gives a detailed discussion of these collapse equations The collapse formulas give the minimum collapse stress with a 95% probability that the collapse strength will exceed the value calculated These formulas are based on test data The collapse curves in Fig 10 are for a K55 grade liner The values for an L80 liner are approximately 20% higher The full pipe case is for a pipe without holes The screen and slot stresses are calculated by dividing the full pipe stress by the circumferential stress concentration factors Fsc given in Table The partial and full vertical effective earth pressures are shown for 500 m depth Full effective earth pressure at 700 m and 200 m are also shown The markers along the horizontal axis are the axial hoop stress to yield ratios (σ2/σy) for various liner case ∆T‟s as identified in the legend The collapse earth stress for slotted or screened liner cases can be read off the appropriate curve These earth stresses can be converted to depths by dividing by the effective earth pressure gradient give in Table The collapse earth pressures are the effective vertical stresses on the liner The corresponding horizontal earth pressures are smaller per eq This might actually make the liner more vulnerable to collapse This should be investigated further It can be seen from Fig 10 that the collapse strength of liners drops toward zero as the axial hoop stress approaches yield Liners subject to partial (5%) earth pressure shouldn‟t collapse if the hoop axial stress is below yield However if the full earth pressure at 500 m depth is imposed on a slotted liner, it is at risk of collapse even if the axial hoop stress is low Slotted liners at σ2/σy = 0.71 (vertical red dashed line) would be safe at approximately 200 m depth If the start-up steam pressure reaches 10 MPa, the K55 hoop could reach axial yield and collapse at any earth pressure if allowed to cool back to ambient T (triangular marker at 1.0 on the axis of Fig 11) This might only happen in an aborted start-up situation The case where the slotted liner webs are allowed to reach yield (the square marker on the horizontal axis at σ2/σy = 0.95) is a bit less likely to collapse because the slotted liner collapse pressure is higher than the partial earth pressure But they would collapse if the full earth pressure was imposed The screened liner at web yield has a relatively high collapse strength as shown by the diamond marker and vertical line at σ2/σy = 0.71 The author selected the value of 0.71 as the maximum recommended hoop axial stress This was done for the following reasons: It gives reasonable operational values for ∆T (see table 5) It has a useful depth range (~ 300 to 600 m) for slotted liners The screen web is just at yield and the slotted liner web is well below yield In the bottom part of Table collapse depths are given for the 325 C ∆T case The webs in all liners are above yield The axial hoop stresses all exceed the 71% criterion mentioned above The screen hoop axial stress is still only at 73 to 84 % of yield while the slot hoop stress is at 96 to 100 % This results in the collapse depths for the screened liners being in the, still useful, 400 to 700 m range where the slotted liners are in the, not very useful, zero to 100 m range The collapse equations are not valid at these high values of slot hoop stress (API Bulletin), so we estimated the collapse strength to be 70 % of the depth required to put the hoop into yield This behaviour can be explained as follows The screen web goes into yield at the relatively low hoop stress value of 71% of yield compared to the slotted value of 95% of yield After the web goes into yield the axial web stress increases with T at a much lower rate as shown in the graph of Fig Since σ2 = σ1/Fs1, the axial hoop stress also increases slowly with T In other words, the ∆T required to incrementally increase the axial hoop stress becomes larger than it was before the web went into yield 11 12 CSUG/SPE 136871 Nevertheless it is not recommended that the screen web be allowed to exceed tensile yield The post-yield tensile strain concentration could be larger than assumed in this paper and the web strain in the screen could approach its tensile strength value (6 – 10 %) and part the liner Lab testing is recommended This analysis implies that: (1) L80 liners are less susceptible to collapse than K55 liners, and (2) slotted liners are quite a bit more vulnerable to collapse than screened liners Table gives values of ΔT for various liner types for σ2/σy = 0.71 and for web yield The collapse strengths for this hoop stress were converted into depths using the effective earth pressure gradient given in Table The liner approaches collapse as the hoop approaches yield under the combined thermal axial (σ2) stress and earth imposed circumferential (σ2c) stress The depths at which the liner hoop reaches combined yield are also given in Table These depths are 10% to 30% greater than the collapse depths for the same ∆T This is likely attributable to both the collapse occurring before the hoop reaches yield; and to a built-in safety factor because the collapse equations are for the minimum collapse strength Since the slots will only start to close after the hoop reaches this combined yield stress, the collapse process might tend to occur just prior to slot closure If the slots close before the liner collapses completely, the collapse strength would increase to that of a blank liner But this is just conjecture and shouldn‟t be considered in the operating criteria This would be something to study in the lab It can be seen from Table that slotted liners meet the collapse criteria only up to 278 m depth for our standard 178 mm L80 (34.2 kg/m) liner The maximum depth increases to 635 m for the heaviest L80 slotted liner K55 liners in Bradley 1992 did not go to this heaviest weight Screened liners meet the collapse criteria up to 763 m depth (1757 m for the heaviest) L80 liner Note that these depths will vary depending on the effective earth pressure gradient Risk Collapse and slot closure depend on the liner being subject to the maximum possible tensile stress for a given ΔT However this max tensile stress may not actually occur often because a perfect storm of concurrent events are needed for this to happen The liner would have to expand on first steam without compressive stress There is likely to be some compression on expansion The full weight of the formation would have to be on the liner This would happen only where there was a drillhole wash out or somehow sand was produced into or around the liner The ΔT would have to be large enough and occur over a short time period if there was any stress relaxation in the sand This is likely why there haven‟t been more liner failures than have actually occurred Nevertheless it would be prudent to design liners and operating procedures as if this max tensile stress could occur Adding blank joints The effect of adding blank joints was looked into as a bit of a side issue Sometimes liners are alternated with blank joints to cut costs or blanks are inserted to block off parts of the formation The stress & strain formulas given above will apply with L2 representing the blank lengths The results are presented in Table In a nutshell, it shows that one or two blanks can be added between screen or slot joints if the operating ΔT‟s are kept within the collapse criteria values given in Table The hoop stress should be kept in the 70 to 75 % range The web axial strain and hoop stress both increase as blank joints are added If more blank joints are added the ∆T‟s should be decreased The potential for tearing a screened liner If the base pipe of the screened liner moved due to thermal strain and there was some earth stress on it, one could imagine the possibility of the screen tearing from the base pipe It turns out that this shouldn‟t be a problem unless there are flaws in the screen ribs or the weld that attaches the screen to the liner base pipe The shear τf of the sand on the screen is opposed by the shear τp of the screen to the pipe These shears are equal to the average earth stress σe times their respective coefficients of friction µf and μp Summing the axial forces, we get the net shear force W on the weld holding the screen ) ( Ls is the length of the screen between welds It is 5.65 m for an average 13.3 m (43.6 ft.) joint where the screen is welded in the middle We use values of 0.53 and 0.3 for μs and μp The maximum allowable W to prevent screen failure is calculated using the ultimate tensile stress for steel on the ribs and this value is in the order of 210 kN (47,000 lb) It is assumed there are 48 ribs around the diameter of the pipe and they have a cross-sectional area of 6.69 mm2 Using eq 31 we calculate a maximum earth stress of 0.29 MPa (42 psi) that is required to generate the failure force of 210 kN CSUG/SPE 136871 From Table we see that the distance Xo to zero shear in the constant shear model is close to the value for X at 50% shear in the exponential shear case We use the constant shear value of Xo to represent the location of minimal shear and liner movement If we assume a constant shear τf We calculate (eq 7b) that the distance Xo from the free end to zero movement and zero shear is: This is plotted in Fig 11 The max earth stress to tear the liner is also shown If the earth stress is greater than this max stress the liner movement will stop within one joint (13.3m) of the free end If the earth stress is less than this max amount the movement could extent up to three or four joints but the screen should not tear because the stress on it is below the amount required for it to fail Placing one or two blank (no screen or holes) joints at the free end should prevent the screen from tearing due to thermal expansion or contraction Conclusions Earth pressures and drill hole closure a Drillholes could stay open until production starts This is why liners are able to be installed after drilling by simply pushing them in It also means the liners could expand upon steaming with little compressive stress b Once production of oil and water starts the drill hole is expected to close to a partial pressure of roughly % of full effective earth pressure c The liner will be subject to full earth pressure if and where sand is swept from the drill hole This could occur at specific locations along the liner where the drill hole has been washed out during drilling, or where the liner is damaged or slots are too large and allow sand into it Stresses and strains in liners a Once production inflow starts the drill hole will partially fail and the liner will be griped by the formation If production operations cool to below start up steam temperatures, and they usually do, the liner could be subject to tensile strains in proportion to the amount of cooling The liner could actually cool to its initial T if start up were aborted for some reason b These tensile stresses and strains in the liner could exceed yield but are unlikely to reach ultimate or rupture tensile strains This means these tensile stresses alone wouldn‟t tear the liner apart However a combination of axial and circumferential stresses can lead to collapse and parting of the liner c Startup T‟s would be 234 to 264 °C for steam pressures of to MPa If the liners subsequently cooled they could reach tensile yield at T‟s anywhere from 18 to 132 °C depending on whether it was slotted or screened, K55 or L80 grade Specific minimum T values can be calculated from the ΔT values given in Table L80 screens are strongest having the highest ΔT‟s to reach yield K55 screens are the weakest having the lowest ΔT‟s to reach yields d Liners go into yield first at the webs, the steel areas in the circumferential directions between the holes Hoops are the part of the base pipe that are in between the holes and form close to a continuous circle around the circumference of the pipe The hoops not reach pure axial yield for startup pressures of up to 10 MPa are used Hoops will go into yield as earth pressure is added to the thermal stress This can cause the liner to collapse e After the webs reach yield, most of the incremental thermal extension in the liner is concentrated in the webs at anywhere from 13 to 380 times the hoop incremental extension Even so, the maximum strain in the webs at a high ∆T of 292 C (10 MPa steam pressure) is estimated to be 1.2% or less (Table and Fig 5) Ultimate tensile strains are in the order of - 10 % and rupture strains at greater than 15% So the liners should not rupture at the webs in one T cycle If subsequent temperature cycles are experienced, these strains would be different but are not covered in this paper Liner expansion a As liners are heated or cooled they expand or contract This expansion is limited by the earth stress on the liners In an open hole, the free end of a 700 m (2300 ft.) liner can expand by up to m (6.6 ft.) at a startup pressure of MPa (725 psi) (see Fig and Table 4) 13 CSUG/SPE 136871 14 b At partial earth pressures the free end expansions are in the order of to 10 cm (1.5 to in.) for ΔT‟s in the order of 200 C This expansion occurs over a relatively short distance Xo from the free end of the liner Xo is in the order of 20 m to 50 m for depths of 500 to 200 m respectively The shear stress on the surface of the liner is in the order of 140 kPa at the free end and declines to zero at distances in the order of Xo from the free end (Fig 7, Table 4) c The axial stress in the liner starts at zero at the free end and reaches its maximum value at approximately Xo and remains at that over the remaining liner length This axial stress is highest in the liner webs and can reach yield at normal operating ΔT‟s d At full earth pressures and ΔT‟s of 200 C the liner expansions are in the order of cm (0.4 in.) and the shear stress in the order of 2.6 MPa They both decline to zero within m (6.5 ft.) from the free end Slot closure a Liner slots are long and narrow The relatively narrow steel hoops between the slots will bear most of the earth pressures on the liner This leads to high compressive circumferential stress concentrations in the hoop in the order of 28 times the vertical earth stress (Eq 28 and Fig 8) b This concentrated earth stress could result in the hoop going into the post yield (plastic) domain resulting in large compressive strains The web is not subject to circumferential stress and so does not get compressed This means all the strain in the hoop is taken up by the slot openings getting smaller For example, a 25 mm (0.010 in.) wide slot would close entirely if the hoop circumferential strain was 2.3 % c The risk of slot closure is minimal if subject to only the partial earth pressure of 5% of full earth pressure up to 700 m depth But they could start to close if subjected to a higher fraction of earth pressure As discussed above, these pressures could occur at specific locations where the drill hole has totally collapsed on the liner Based on Kooijman et al 1996, they are unlikely to occur over the entire liner length unless the pressures gradually increase over time d The circumferential yield stress of the hoop is lowered significantly as the liner tensile stress is increased in the axial direction Slots in an L80 liner at 500 m depth will not close at all if the ∆T (cooling) is 127 C or less, however 25 mm slots in the same liner at a ∆T of 195 C would close entirely if subjected to full earth pressures at 500 m depth (Fig 9) e L80 liner slots stay open at higher ∆T‟s than K55 liners because they have higher yield strength For example, at 200 m depth a K55, slots would stay open at a ∆T of 122 C or less, but an L80 slot would stay open at a ∆T of 195 C or less (Fig 9) f The start of slot closure and liner collapse will tend to occur together Therefore the liner will tend to collapse before much slot closure can take place Liner collapse a Liners subject to post start up cooling are likely to be subject to axial tensile stresses These stresses reduce the collapse resistance of the liner As a result, a liner could collapse under some typical operating conditions where specific conditions are met (Fig 10) b Liners are unlikely to collapse under the expected partial earth pressures of 5% of full earth pressure if operated at below web yield ∆T‟s c However, under a „perfect storm‟ of conditions, a liner is subject to collapse These conditions are: i The liner expands with little compressive stress ii The pressure on it is a large fraction of the full earth pressure This could occur at locations where the drill hole has washed out during drilling or production iii The ∆T is large and rapid enough to cause hoop yield There may be stress relaxation in the formation that reduces the stress if it occurs slowly d Almost all of the resistance to the earth pressures is concentrated in the hoop region This results in the collapse resistance of screened liners being about 2.7 times higher than slotted liners (Fig 10) e At a hoop to yield stress ratio (σ2/σy) of 0.71 the collapse resistances are acceptable for K55 and L80 slotted liners at up to 225 and 278 m depth, and screened liners at up to 596 and 763 m depth respectively (Table and Fig 10) This is the collapse criterion used this paper f Increasing the liner wall thickness (liner weight) will significantly increase the collapse resistance (see Table 5) g Adding blank joints in-between screened or slotted joints increases the stress and strain in the web and hoop of the liner, bringing it closer to collapse However if the collapse ∆T criteria are followed, then adding one or two blank joints between regular screened or slotted joints should be acceptable (see Table 6) CSUG/SPE 136871 Screen tearing a A shear stress in the order of 150 kPa (22 psi) on a screened liner would cause the screen ribs to rupture and tear the screen from the liner This shear stress would occur at a vertical effective earth stress of 290 kPa (42 psi) b At 200 m depth the earth stress on the liner is below the rupture stress of 290 kPa so the screen should not tear c As the formation depth increases the earth stress would increase above this rupture stress and could tear at the liner at the free end d However shear stresses that would cause screen tearing will tend to occur within short distances (10 to 20 m) of the free end(s) of the liner (Fig 11) Recommendations More experimental work should be done on the subject of earth pressures to investigate the following: a How long could drill holes stay open prior to production operations? b Kooijman et al 1996 drilled their bore holes in the sand before applying pressure and observed gradual failure as they applied pressure Would the results have been different if the holes were drilled after stress was applied? c What are the effects of steam operations on drillhole closure d Is the partial pressure state stable or does it gradually approach full pressure? e How much stress relaxation occurs in the formation? f What is the distance λf over which earth shear stress on the liner is fully mobilized by liner movement? Is the collapse strength of a liner lessened by the fact that the horizontal earth stress is less than the vertical stress? Expand this analysis to cases with liners subjected to repeated temperature cycles Conduct finite element analysis and lab testing on the tensile strength and failures of liners at high temperatures What is the range of ∆T over which thermal strain is a linear function of ∆T? The compressive and tensile failure modes should be examined together This paper considered mainly tensile effects From the tensile viewpoint, it is preferable to choose L80 grade pipe over K55 to minimize the risk of slot closure and liner collapse Based on the calculated results in this paper, the recommended maximum operating ΔT‟s and maximum depths to prevent failure of a liner in collapse (or slot closure) are given in bold font in Table Place one or two blank joints of casing at the free end(s) of a screened liner in order to minimize the risk of tearing the screen from the casing Continue the search for a perfect liner It would combine the shear (tearing) resistance of the slotted liner with the collapse and closure resistance of the screened liner 10 In SAGD the start-up ∆T can be limited to somewhat below hydrostatic pressure by circulating steam using steam and/or gas lift This is more important for the producer as it is usually subject to the largest ∆T‟s 11 It should be possible to reduce the amount of tensile stress in a liner by attempting to generate a prestressed compressive state in the liner before it reaches the maximum start up pressure For example, the liner might be steamed to half the max ∆T and then produced back for a little while to initiate some well bore sand failure Then complete the start up by heating it to the desired max T This should cause the liner be in some compression at max T which would reduce the subsequent tensile stress when the liner is cooled Nomenclature ′ = prime symbolizing post yield conditions ∆Ty1, ∆Ty2, ∆Tyo = ∆T‟s that cause yield at the web, hoop, and for a full pipe, C B = τf/(SE), a constant, 1/m 15 CSUG/SPE 136871 16 C = centigrade degree Da = axial dimension of the hole, mm Dc = circumferential dimension of the hole, mm Do, Di = outside and inside diameters of the pipe, mm E = elastic modulus of steel, Pa Ep = plastic or post yield modulus of steel, Pa Fn1 = web axial strain concentration factor in the post yield mode Fs1 = max axial stress concentration factor in the web adjacent to the liner holes Fsa = average stress concentration over the axial distance La Fsc = circumferential stress concentration factor in the hoop Fse = earth stress concentration factor, concentrates stress from the formation to the hoop Ka = active earth pressure coefficient L = total length of liner from the fixed end, subscripts and mean web and hoop regions, m l = length along the liner from the fixed to the free end, m La = axial distance between holes, mm Lc = circumferential distance between holes, m P = the total compressive axial force on the liner at some distance, N S = pipe wall thickness, mm T, ∆T = temperature and change in temperature, °C and C u = pore pressure in the reservoir, MPa W = total force on the weld holding the screen to the base pipe, N x = distance from the free end of the liner toward the fixed end, m Xo = distance from the end of the liner to the point where λ = in the constant shear model, m α = coefficient of expansion of steel, 1/C ϵ = strain, subscripts 1, 2, and y mean at the web, hoop, and yield λ = liner extension due to changes in temperature, subscripts and refer to web and hoop, cm λf = constant used to represent liner movement over which it takes to mobilize shear, cm λo = liner extension at the free end, cm μ = coefficient of friction, subscripts s and p represent sand on the screen and steel on the pipe σ1 and σ2 = axial compressive stress at holes (web) and between holes (hoop), MPa σa = average compressive stress in liner wall over the over the distance La, MPa σc = circumferential stress in the liner, MPa σe = effective vertical earth stress, MPa σh = horizontal effective pressure on the liner, MPa σn = normal or full pipe compressive stress in liner wall, MPa σv = vertical effective pressure on the liner, MPa σy = yield stress of K55 or L80 grade steel casing, MPa τ f = frictional shear stress on the surface of the liner, MPa Acknowledgements The author would like to thank a few people for useful discussions on this and other subjects over the years These include Don Anderson and Karl Miller of Husky Energy; Simon Gittins of Encana now Cenovus; Trent Kaiser and Dan Dall‟Acqua of Noetic Engineering; Bill and James Neucomb and Darryl Grosse at Variperm Canada Limited These people have not read nor endorsed any of the concepts or content in this paper The author is totally responsible for any errors in concept or content contained in this paper References API Bulletin 5C3 Bulletin on formulas and calculations for casing, tubing, drill pipe, and line pipe properties, sixth ed 1994 Boresi, A.P., and Schmidt, R.J 2003 Advanced mechanics of materials, sixth ed 2003 John Wiley & Sons, Inc Bradley, H.B ed Petroleum Engineering Handbook (SPE) Third printing 1992 Richardson, TX, U.S.A Dall‟Acqua, D., Smith, D.T., and Kaiser, T.M.V 2005 Post-yield thermal design basis for slotted liner SPE 97777 2005 SPE International Thermal Operations and Heavy Oil Symposium, Calgary Alberta Canada, 1-3 Nov 2005 IRP 2002, Fig 2, Appendix E, Industry recommended practice Volume – 2002, Enform.ca Kaiser, T.M.V., Wilson, S., and Venning, L.A 2000 Inflow analysis and optimization of slotted liners SPE 65517 CSUG/SPE 136871 17 SPE/Petroleum Society of CIM International Conference on Horizontal Well Technology, Calgary, Alberta, Canada, – Nov 2000 Kooijman, A.P., van den Hoek, P.J., De Bree, Ph., Kenter, C.J., Zheng, Z., and Khodaverdian, M 1996 Horizontal wellbore stability and sand production in weakly consolidated sandstones SPE 36419 SPE Annual Technical Conference, Denver, 6-9 October 1996 14 pp O‟Rourke, J.C., Begley, A.G., Boyle, H.A., Yee, C.T., Chambers, J.I., and Luhning, R.W 1997 UTF Project Status Update May 1997 Petroleum Society of Canada Annual Technical Meeting, Jun - 11, 1997 , Calgary, Alberta 1997 Slack, M., Roggensack, W.D., Wilson, G., and Lemieux, R.O 2000 Thermal deformation resistant slotted liner design for horizontal wells SPE 65523, 2000 Sowers, G.F., 1979 Introductory soil mechanics and foundations: geotechnical engineering Macmillan Publishing Co Inc Wong, F.Y.F., Anderson, D.B., O'Rourke, J.C., Rea, H.Q, and Scheidt, K.A 2001 Meeting the Challenge to Extend Success at the Pikes Peak Steam Project to Areas with Bottom Water SPE Annual Technical Conference and Exhibition, 30 September-3 October 2001, New Orleans, Louisiana TABLE Reservoir data Earth weight gradient, saturated Pore pressure gradient, assumed Effective pressure gradient Internal friction angle of sand, φ Fraction of earth pressure on liner, loose sand Active earth pressure coeff, Ka Friction coeff between sand and slotted liner, μ Friction coeff between sand and screened liner, μ kPa/m kPa/m kPa/m deg 22.7 6.86 15.8 28 5% 0.36 0.40 0.53 TABLE Screen & slot base pipe dimensions & stress factors OD Unit weight Wall thickness Steel modulus of elasticity, E Coeff of thermal expansion, α Liner geometry 178 mm 34 kg/m 8.05 mm 200E+9 Pa 1.26E-05 1/C screen mm in 12.7 0.5 12.7 0.5 43.3 1.7 7.0 in 23 lb/ft 0.32 in 29.0E+6 psi 7.00E-06 1/F slots mm in 0.51 0.02 55.9 2.2 76.2 Hole or slot width, Dc Hole or slot length, Da *Axial spacing of holes or slots, La *Circumferential spacing of holes / slots, 43.3 1.7 10.9 0.43 Lc Max axial stress concentration factor at holes, Fs1 max 1.41 1.05 Average axial conc factor, Fsa 1.24 1.04 **Circumferential stress concentration factor on the hoop, Fsc 1.41 3.75 earth vertical stress concentration factor, Fse 15.6 41.4 * spacing is center to center distance Screens are avg of & 1.41 in ** the hoop is the steel between the holes in the axial direction CSUG/SPE 136871 18 TABLE Stress & thermal strain data & results K55 Grade L80 σy, yield strength, MPa, (ksi) 379 (55) 552 (80) σu, ultimate strength, MPa (ksi) 655 (95) 655 (95) ϵy, yield strain 0.190% 0.28% ϵu, ultimate strain 10% 8% Ep, pseudo plastic modulus; MPa, ksi 7,506 1,089 3,034 440 ΔTyo, axial yield, plain pipe, C 150 219 Stress & strain with webs at yield screened slotted screened slotted * ΔTy1, axial web yield, C 132 149 192 216 ** σ2, max axial hoop stress, MPa 268 362 390 526 ϵ2, max axial hoop strain 0.13% 0.18% 0.19% 0.26% σ2/σy, axial hoop stress / yield 71% 95% 71% 95% ***collapse depth (m) 596 94 763 136 Stress & strain at ∆T = 325 C, Psat = 15 MPa, 20C ambient λ1'/λ2', web / hoop ext'n ratio, plastic region 11 77 28 190 Fn, axial strain concentration factor, plastic 3.97 1.35 domain * ϵ1, max axial web strain, ΔT = 325 C 1.15% 0.49% σ1/σy, axial web stress (ΔT = 325 C) 1.19 1.06 ϵ2, max axial hoop strain, ΔT = 325 C 0.16% 0.19% σ2/σy, axial hoop stress (ΔT = 325 C) 84% 100% ***collapse depth (m) 405 ΔTy2, hoop at pure axial yield, C 551 294 red or underlined font means over yield * the web is the steel between the holes in the circumferential direction ** the hoop is the steel between the holes in the axial direction *** estimated collapse depth for slots by taking 70% of hoop yield depth 4.17 1.36 0.97% 1.04 0.20% 73% 727 1629 0.46% 1.01 0.27% 96% 109 735 19 CSUG/SPE 136871 Table Liner expansion/contraction results Liner length 700 m temperature mode grade type ΔT, C σ1, max axial web stress, MPa σ2, max axial hoop stress, MPa Depth, H, m MPa start up yield at holes 500 L80 screened 192 552 390 200 slotted 216 500 526 500 K55 screened 132 379 268 500 200 MPa start up L80 or K55 screened 244 214 38 27 na Earth stress partial full partial pipe weight vertical stress on liner, kPa 396 158 7,920 396 158 na max potential shear on liner, τf, kPa 210 84 4,209 210 84 exponential shear, λs = cm λo, max extension at free end, cm 4.9 9.5 0.83 5.3 3.0 5.5 208 181 Xo, Distance from end to λ ~ 0, exp shear, m 52 97 10 38 48 83 700 700 τ max, shear stress, kPa 122 53 913 124 104 50 0.44 0.44 X at 1/2 τmax, m 23 56 2.6 26 17 40 na na constant shear, λs = cm λo, max extension at free end, cm 3.0 7.6 0.2 3.8 1.44 3.6 207.3 181 Xo, Distance from end to λ = 0, m 25 63 1.3 28 17 43 700 Averaged between vertical and horizontal radial stress using the active earth constant Ka This will be the same as max potential shear for const shear It will be a bit less for exponential shear Table Maximum ΔT's & depths to minimize risk of collapse liner thickness (mm) Collapse criteria: hoop axial stress (σ2) = 71% of yield (σy) Assumes maximum effective earth pressure max ΔT (C) * max L80 std 34.2 kg / m 8.05 13.7 maximum depth criteria, m *** hoop collapse collapse yield 763 974 1,757 596 670 1,266 278 368 635 225 253 480 ** collapse web yield grade Screen L80 192 192 K55 132 132 Slot L80 160 216 K55 110 149 * K55 may not go to 13.7 mm thickness ** Bold figures are recommended maximum values *** Combined hoop yield Combines axial plus earth stresses Slot closure starts at this hoop yield CSUG/SPE 136871 20 Table Effect of insertting blank joints Screen Slot Screen Slot grade L80 K55 L80 K55 L80 K55 L80 K55 * ΔT (C) 192 132 160 110 192 132 160 110 # of 13 m blank joints ϵ1, web axial strain 0.26% 0.48% 1.47% 0.18% 0.35% 0.81% 0.21% 0.21% 0.21% 0.14% 0.14% 0.14% σ2/σy, axial hoop stress / yield 71% 72% 76% 71% 74% 80% 71% 72% 73% 71% 72% 73% * ∆T's are collapse criteria values Fig.1 Photo of screened liner base pipe with holes Fig Photo of screen wrap & ribs This is slipped over and welded at the ends to the base pipe CSUG/SPE 136871 Fig Photo of weld of screen wrap to base pipe Fig Schematic diagram of forces on the surface of a liner Cut out A is enlarged to screen hole and slot hole cutouts 21 CSUG/SPE 136871 22 Axial stress and strain at web for a screened liner ∆T up to 325 °C (15 MPa startup) 600 573 500 ϵ1, L80 400 ϵt = αΔT ϵ2, L80 1.0% ϵ2, K55 0.8% 132, 379 300 0.6% strain Stress, MPa 452 σ1, K55 ϵ1, K55 1.4% 1.2% 192, 552 σ1, L80 0.41% 200 0.4% 100 0.2% 0.0% 100 200 ∆T, C 300 Fig Linearized axial stress-thermal strain graph for elastic and plastic ranges at the web on a screened liner base pipe Open hole expansion, screened liner, τf = 0.44 kPa, ΔT = 244 C, pipe weight only, fixed at one end, L = 350 & 700 m 2.5 45 λ, m @ L = 350m extention λ, m 35 30 1.5 25 20 15 axial stress, kPa 40 λ, m @ L = 700m σc, MPa @ L = 350m 10 0.5 0 200 400 σc, MPa @ L = 700m 600 distance x from liner end, m Fig Expansion of liner under its own weight with zero earth force versus distance from the free end 23 CSUG/SPE 136871 Screened liner expansion, exponential & constant shear, partial earth pressure , Depth = 500 m, τf = 143 kPa, ΔT (C) = 192 600 140 λ, mm, const shear 500 120 400 100 80 300 60 200 axial stress σ, MPa extension λ, mm & shear τ, kPa 160 40 100 20 0 20 40 60 80 distance from liner free end, m 100 Fig Screened liner expansion showing constant and exponential shear model results Cross-section of earth forces on a liner σv vertical earth stress S pipe thickness σh horizontal earth stress σh σc circumferential stress σc D liner diameter Fig Schematic diagram showing X-section of half a liner with earth and internal forces λa, mm @ exp shear, λs(cm) = τ, kPa, const shear τ, kPa @ exp shear, λs(cm) = σa, MPa, const shear, λs(mm) = σa, MPa @ exp shear, λs(cm) = CSUG/SPE 136871 24 Vertical earth stress vs incremental slot closure typical slot ~ 0.51mm (0.02 in.) K55 @ ΔT (C) = 36 Vertical earth pressure, MPa 14 L80 @ ΔT (C) = 127 12 11 K55 @ ΔT (C) = 122 10 7.9 L80 @ ΔT (C) = 195 full eff earth P @700 m 3.2 full eff earth P @ 500 m 0.40 full eff earth P @ 200 m 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 λc, slot closure, mm partial eff earth P @ 500 m Fig Graph showing the effects of earth pressure on slot closure L80 and K55 grades are compared at specified ΔTs Slot closure is unlikely where only partial pressures are on the liner Vertical collapse pressures vs axial hoop stress in 23 lb/ft, K55 base pipe, L80 values are about 20 % higher API collapse formula not valid for σ2/σy > ~ 75% full pipe 25 Vertical collapse pressure, M Pa σ2/σy =0.707 screen (L80) 20 screen 15 slot full σe @ 700 m 10 K55 slot at 10 MPa (∆T 292 C) full σe @ 500 m slot web yield full σe @ 200 m 5% σe @ 500 m -0.2 0.2 0.4 0.6 0.8 screen web yield (Table collapse criteria) hoop / yield stress, σ2/σy Fig 10 Graph showing the K55 liner vertical collapse pressure versus hoop yield stress The collapse pressures for an L80 liner have the same shapes but approximately 10% higher Hoop stress ratios and ΔT‟s for key cases are shown on the horizontal axis The red diamond line at 0.707 is a „safe‟ line for all cases 25 CSUG/SPE 136871 distance from free end to zero movement, m Distance Xo to zero screen shear stress vs earth stress - constant shear 50 Xo @ ΔT (C) = 192 Xo @ ΔT (C) = 132 40 screen rupture earth stress, σev max 30 20 10 0.05 0.10 0.20 0.40 0.80 σev, vertical earth stress, MPa 1.60 3.20 Fig 11 Horizontal liner expansion distance vs vertical effective earth stress This shows that screen tearing is unlikely if two blank joints (2*13.3 = 26.6m) are placed as anchors at the free end [...]... a liner in collapse (or slot closure) are given in bold font in Table 5 8 Place one or two blank joints of casing at the free end(s) of a screened liner in order to minimize the risk of tearing the screen from the casing 9 Continue the search for a perfect liner It would combine the shear (tearing) resistance of the slotted liner with the collapse and closure resistance of the screened liner 10 In. .. thermal strain and there was some earth stress on it, one could imagine the possibility of the screen tearing from the base pipe It turns out that this shouldn‟t be a problem unless there are flaws in the screen ribs or the weld that attaches the screen to the liner base pipe The shear τf of the sand on the screen is opposed by the shear τp of the screen to the pipe These shears are equal to the average... or slotted joints increases the stress and strain in the web and hoop of the liner, bringing it closer to collapse However if the collapse ∆T criteria are followed, then adding one or two blank joints between regular screened or slotted joints should be acceptable (see Table 6) CSUG/SPE 136871 6 Screen tearing a A shear stress in the order of 150 kPa (22 psi) on a screened liner would cause the screen. .. between screen or slot joints if the operating ΔT‟s are kept within the collapse criteria values given in Table 5 The hoop stress should be kept in the 70 to 75 % range The web axial strain and hoop stress both increase as blank joints are added If more blank joints are added the ∆T‟s should be decreased The potential for tearing a screened liner If the base pipe of the screened liner moved due to thermal. .. of the liner Xo is in the order of 20 m to 50 m for depths of 500 to 200 m respectively The shear stress on the surface of the liner is in the order of 140 kPa at the free end and declines to zero at distances in the order of Xo from the free end (Fig 7, Table 4) c The axial stress in the liner starts at zero at the free end and reaches its maximum value at approximately Xo and remains at that over the. .. times their respective coefficients of friction µf and μp Summing the axial forces, we get the net shear force W on the weld holding the screen ) ( Ls is the length of the screen between welds It is 5.65 m for an average 13.3 m (43.6 ft.) joint where the screen is welded in the middle We use values of 0.53 and 0.3 for μs and μp The maximum allowable W to prevent screen failure is calculated using the. .. that over the remaining liner length This axial stress is highest in the liner webs and can reach yield at normal operating ΔT‟s d At full earth pressures and ΔT‟s of 200 C the liner expansions are in the order of 1 cm (0.4 in. ) and the shear stress in the order of 2.6 MPa They both decline to zero within 2 m (6.5 ft.) from the free end Slot closure a Liner slots are long and narrow The relatively narrow... (σ2/σy) of 0.71 the collapse resistances are acceptable for K55 and L80 slotted liners at up to 225 and 278 m depth, and screened liners at up to 596 and 763 m depth respectively (Table 5 and Fig 10) This is the collapse criterion used this paper f Increasing the liner wall thickness (liner weight) will significantly increase the collapse resistance (see Table 5) g Adding blank joints in- between screened... (Fig 9) f The start of slot closure and liner collapse will tend to occur together Therefore the liner will tend to collapse before much slot closure can take place Liner collapse a Liners subject to post start up cooling are likely to be subject to axial tensile stresses These stresses reduce the collapse resistance of the liner As a result, a liner could collapse under some typical operating conditions... well below yield In the bottom part of Table 3 collapse depths are given for the 325 C ∆T case The webs in all liners are above yield The axial hoop stresses all exceed the 71% criterion mentioned above The screen hoop axial stress is still only at 73 to 84 % of yield while the slot hoop stress is at 96 to 100 % This results in the collapse depths for the screened liners being in the, still useful,