(CSUGSPE 136871) The Potential for Slot Closure, Screen Damage, and Collapse of Liners in Thermal Horizontal Wells

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

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 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

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

conduct his own investigation The author presented a half hour discussion of these issues at an annual

Slugging-it-out 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 1 to 4 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 1 & 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

mid-section 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 2 for type slot and screen hole dimensions

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 andσe) 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 do 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 5 to 25% of the full earth stress σe If there is water in

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 1 presents basic reservoir data used in this paper An active earth pressure coefficient (Sowers 1997) is used to

estimate the horizontal stress as a function of the vertical 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 1 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 2

cm makes a significant difference in the total displacement of the liner In this paper λf is treated as both zero and 2

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 4

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 5 and 6

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 iszero 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 = 0 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 7 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:

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 = 0 This eq applies only from x = 0 to Xo where λ = 0

In most cases discussed here, we will have λ = 0 and dλ/dl = 0 at Xo = 0 At this point we calculate from eq 7a:

The results for both exponential and constant shear are presented in Table 4 For the special case of no shear, σn = 0 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 = 0 because λ = 0 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 6 gives:

This is the formula used to calculate ΔTy shown in Table 3 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 2 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 2 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 1 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 1 at four times the hole radius Averaging this

linearized Fs over the inter-hole axial distance results in :

CSUG/SPE 136871 5

These formulas were used to compute the stress concentration factors given in Table 2

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 6 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 = 0 because λa = 0 we see from eq 6 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:

σ1 = Fs1σn σ2 = σn σa = Fsaσn (13a, b, c) 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 1 (the web) to be:

(

) Where:

The yield ∆T for region 2 (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 = 0

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

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 1 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 1 (the web) E is the normal elastic modulus for zone 2 (the hoop) which has not reached yield

The graph of Fig 5 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 3 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 3 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 5 and the theory is presented below

We have:

and

( ) ( ) Combining eq 18 and 20 gives:

( ) 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 CSUG/SPE 136871 7

smaller which would result in F being larger

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 3 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 2 were used for the results given in Table 3 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 3 are defined

by the following:

The ultimate strains in Table 3 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 5 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 6 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 3 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 3 will be discussed in the section on collapse

The lower portion of Table 3 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

are less at 84% and 73 % of yield for K55 and L80 grades The graph of Fig 5 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 6 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 6 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 5 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 2 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 3 and values are given in Table 4 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 7 presents a sample case with the same 700 m screened liner used in Fig 6 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 = 0 in eq 3 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 = 2 cm It can be seen that the liner contraction λa at the free end is only 30

to 50 mm (1.2 to 2 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 4 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 CSUG/SPE 136871 9

is somewhere in between

The left side of Table 4 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 5 to 10 cm (2 to 4 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 4 presents cases for start-ups at 5 MPa and 3 MPa for the open hole These cases with just

the liner weight acting only reach 7 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 σc is calculated by: And knowing that the hoop circumferential stress we see obtain:

Values for Fse are given in Table 2 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 9 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 σe

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

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 inter-

hole 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 2 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 1

The collapse earth pressures are the effective vertical stresses on the liner The corresponding horizontal earth

pressures are smaller per eq 2 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:

1 It gives reasonable operational values for ∆T (see table 5)

2 It has a useful depth range (~ 300 to 600 m) for slotted liners

3 The screen web is just at yield and the slotted liner web is 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, 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 5 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

CSUG/SPE 136871 11

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 5 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 1 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 5

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 5 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 6 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 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 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

Nevertheless it is not recommended that the screen web be allowed to exceed tensile yield The post-yield tensile

failure force of 210 kN