PETR 4303-PRODUCTION METHODS TUBING MOVEMENT
Marshall C. Watson, Ph.D., PE Petroleum Petr oleum Engineering Texas Tech University Fall 2015
TUBING MOVEMENT
Changing the mode of a well (producer, (producer, injector, injector, shut-in, or treating) causes changes in temperature and pressure press ure inside and outside the tubing. This can create length and force changes in the tubing t ubing string that can potentially affect the packer and downhole tools. With a packer permitting free motion of tubing, pressure and temperature effects can elongate or shorten the tubing. If the packer does not permit free motion of the tubing, induced tensile and compressive forces can cause permanent deformation of the string.
TUBING MOVEMENT
Changing the mode of a well (producer, (producer, injector, injector, shut-in, or treating) causes changes in temperature and pressure press ure inside and outside the tubing. This can create length and force changes in the tubing t ubing string that can potentially affect the packer and downhole tools. With a packer permitting free motion of tubing, pressure and temperature effects can elongate or shorten the tubing. If the packer does not permit free motion of the tubing, induced tensile and compressive forces can cause permanent deformation of the string.
IMPACT OF TUBING LENGTH AND FORCE CHANGES After the packer is installed and the t he tubing landed, any operational mode change will cause a change in length or force in the tubing string. The resultant impact on the packer and tubing string is dependent on: 1. How the tubing is connected to the packer 2. The type of packer 3. How the packer is set 4. Tubing compression or tension left on the packer. The length and force changes can be considerable and can cause tremendous stresses on the tubing string, as well as on the packer under certain conditions. The net result could reduce the effectiveness of the downhole tools and/or damage the tubing, casing, or even the formations open to the well.
IMPACT OF TUBING LENGTH AND FORCE CHANGES Failure to consider length and force changes may result in costly failures of such operations as:
Squeeze cementing
Acidizing
Fracturing
Other remedial operations.
CALCULATION OF TUBING MOVEMENT There are four factors that tend t end to cause a change c hange in the length or force in the tubing string: 1. Temperature effect , which is directly influenced by a change in the average
temperature of the string 2. Piston effect, caused by a change in the pressure in the th e tubing or annulus above
the packer acting on a specific affected area 3. Ballooning effect , caused by a change in average pressure inside or outside the
tubing string 4. Buckling effect , which occurs when internal tubing pressure is higher than the
annulus pressure.
LENGTH AND FORCE CHANGES
Buckling will shorten the tubing string; however, the other effects may tend to lengthen or shorten the string depending on the application of the factors. As long as the tubing is allowed to move in the packer bore, the temperature and ballooning effects will only have an impact on tubing-length c hanges, but, if movement is prevented (or restrained) at the packer, these two factors would then create a force. It is important to remember that a string of tubing landed in any packer is initially in a neutral condition, except for any subsequent mechanical strain or compression loads applied by the rig operator. After the tubing is landed, the factors that cause changes in length or force are always the result of a change in temperature and pressure.
PISTON EFFECT Pressure = Force / Unit Area, i.e. Force = Pressure * Area, i.e. No
∗
PISTON EFFECT
PISTON EFFECT The length change or force induced by the piston effect is caused by pressure changes inside the annulus and tubing at the packer, acting on different areas. The length and force changes can be calculated as follows:
=
and
Forces Up
Forces Down
= Δp Δpo
NOMENCLATURE Δ = length change because of the piston effect = force change because of the piston effect = tubing length = modulus of elasticity ( 30×10 psi for steel)
REVIEW OF SOLIDS =
Slope =
=
Δ
NOMENCLATURE CONT’D = cross-sectional area of the tubing wall = area of the packer bore = area of the tubing ID = area of the tubing OD Δ = change in tubing pressure at the packer Δ = change in annulus pressure at the packer.
COUNTERACTING PISTON EFFECT It is possible to eliminate the length changes from forces generated on the tubing string by the piston effect by anchoring (latching) the seals in the packer bore. In a string that is restrained at the packer from movement in either direction, the length change from the piston effect on the tubing string is zero. However, all the forces are now being absorbed or contained completely within the packer.
BUCKLING
Straight Tubing
Buckled Tubing
CORKSCREWING Buckled tubing is tubing that is bowed from its original straight up and down condition In a buckling condition, the tubing will continue to bow out until it contacts the casing wall. When this contact is made, the tubing will begin to coil. This coiling of the tubing is referred to as "corkscrewing" the tubing.
PERMANENTLY CORKSCREWED DEFORMATION As long as the stresses in the tubing produced from buckling do not exceed the yield strength of the tubing, the tubing will return to its original shape when the force causing the buckling is removed. When the stresses due to buckling exceed the yield strength of the tubing, permanent corkscrewing
BUCKLING EFFECTS Tubing strings tend to buckle only when the internal tubing pressure ( ) is greater than the annulus pressure ( ). The result is always a shortening of the tubing string, but the actual force exerted is negligible. The decrease in length occurs because of the tubing string being in a spiral shape rather than straight. The tubing-length change is calculated with the following:
Δ Δ Δ = 8(W W W )
NOMENCLATURE Δ = length change because of the buckling effect .. = radial clearance between tubing OD and casing ID, ..–
= area of the packer bore = area of the tubing ID = area of the tubing OD Δ = change in tubing pressure at the packer
NOMENCLATURE CONT’D Δ = change in annulus pressure at the packer = modulus of elasticity ( 30×10 psi for steel) = moment of inertia of tubing about its diameter [I = π/64 (D 4 – d4, where D is the tubing OD and d is the tubing ID]
= weight of tubing per inch = weight of fluid in tubing per inch = weight of displaced fluid per inch
NEUTRAL POINT Tubing buckling is most severe at the bottom of the tubing where the pressure is the greatest. It lessons further up the hole until, normally, a point is reached where tubing buckling does not occur. This point is known as the neutral point. Notice that the tubing below the neutral point is buckled while the tubing above remains straight. Use this formula to determine length from packer to neutral point:
=
NEUTRAL POINT CONT’D Where
=The distance from packer to Neutral Point, in. =packer valve area, in2 =total tubing pressure at the packer that will exist for the given conditions, psi. = total annulus pressure at the packer that will exist for the given conditions, psi. = weight of tubing per inch = weight of fluid in tubing per inch = weight of displaced fluid per inch
BALLOONING AND REVERSE BALLOONING
BALLOONING AND REVERSE BALLOONING The ballooning effect is caused by the change in average pressure inside or outside the tubing string. Internal pressure swells or "balloons" the tubing and causes it to shorten. Likewise, pressure in the annulus squeezes the tubing, causing it to elongate. This effect is called "reverse ballooning." The ballooning and reverse ballooning length change and force are given by:
2 Δ Δ Δ = 1 and
= 0.6(Δ Δ )
BALLOONING NOMENCLATURE ΔL3
= length change because of ballooning/reverse ballooning
F3 = force change because of ballooning/reverse ballooning L = tubing length
= Poisson’s ratio (0.3 for steel) E = modulus of elasticity ( 30×10 psi for steel) Δpia
= change in average tubing pressure
BALLOONING NOMENCLATURE CONT’D Δpoa
= change in average annulus pressure
Ai= area of the tubing ID Ao = area of the tubing OD R = ratio of tubing OD to ID for common tubing sizes and weights.
The ballooning effect will always result in tubing-length changes, but it does not become a force unless the tubing movement is restrained at the packer.
TEMPERATURE EFFECT
TEMPERATURE EFFECT Thermal expansion or contraction causes the major length c hange in the tubing. Heated metal expands, and cooled metal contracts. In a long string of tubing with a temperature change over its entire length, this contraction or elongation can be considerable. The three operational modes that influence temperature effect are producing, injecting (water, gas, or steam), and treating. The change in tubing length because of temperature effect is calculated as follows:
Δ = Δ
NOMENCLATURE ΔL4
= change in tubing length
L = tubing length
= coefficient of thermal expansion ( 6.9×10− inin℉ for steel) Δt =
change in average temperature.
TEMPERATURE EFFECT If tubing movement is constrained, forces will be introduced as a result of the temperature change. The temperature-induced force is
= 207 Δ F4 = pounds force (tensile or compression, depending on the direction of AS = cross-sectional area of the tubing wall ΔT =
change in average tubing temperature.
Δt )
DERIVATION OF Δ = Δ
RELATIONSHIP
(1)
Also, it goes without saying that,
= Where =
=
(2) and = . So
(3)
Δ can be written in terms of temperature change, so
=
(4)
After rearranging this equation, we have
= A Δ
(5)
= (30 × 10 ) × (6.9×10−) = 207. where for steel,
MECHANICALLY APPLIED LENGTH CHANGE Compute the mechanically applied length change if necessary. (Use at the time the weight is slacked off) Δ = 8
, , and
NOMENCLATURE Δ = length change due to mechanically applied load [in] = mechanically applied load [lb] = tubing length [in] Modulus of elasticity [psi] =
= cross-sectional area of the tubing wall = moment of inertia of tubing about its diameter [I = π/64 (D 4 – d4, where D is the tubing OD and d is the tubing ID]
= weight of tubing per inch = weight of fluid in tubing per inch = weight of displaced fluid per inch
COMBINED TEMPERATURE AND PRESSURE EFFECTS The net or overall length change (or force) is the sum of the length changes (or forces) caused by the temperature, piston, and ballooning effects. The direction of the length change for each effect (or action of the force) must be considered when summing them. It follows that for a change in conditions, the motion (or force) created by one effect can be offset, or enhanced, by the motion (or force) developed by some other effect.
= Δ = Δ Δ Δ Δ Δ Mosely presented a method for graphically determining the length and force changes as a result of buckling and ballooning ( L2 , L3, and F3). This method is particularly useful on a fieldwide basis, where wells have the same-size tubing, casing, and packers.
NET RESULTS OF COMBINED EFFECTS When planning the sequential steps of a completion or workover, care should be taken to consider the temperatures and pressures in each step once the tubing and packer systems become involved. By careful selection of the packer bore and use of annulus pressures, one pressure effect (or a combination of pressure effects) could be used to offset the adverse length or force change of another effect.
EXAMPLE PROBLEM FOR RECITATION
PROBLEM STATEMENT 1.
Logs show bottom hole temperature at 9036 feet to be 180ºF. (mean annual temperature is 74ºF).
2.
Hole is full of 9.5 lbs/gal completion fluid.
3.
Set a 3.5” seal bore packer on wireline in 7”, 29 lbs/ft CASING at 9036 feet (straight hole).
4.
Run seal assembly on 2-7/8”, 6.5 lbs/ft, N-80 tubing, sting into packer, and land with 17000 pounds of weight.
5.
Apply a maximum of 1500 psi on the casing annulus.
6.
Frac below the packer with 5000 to 7000 psi on tubing using 93000 gal of 12.2 lbs/gal frac fluid (expect ambient temperature of 60ºF).
7.
Fluid tubing movement of forces.
SOLUTION 1.
Find the appropriate tubing areas, inertia & ratio.
= 6.492 in2 = 4.680 in2 = 1.812 in2 = 1.611 in4 = 1.178 2.
Compute the packer seal bore area ( )
= 9.621 in2
SOLUTION CONT’D 3. Compute the pressure, pressure changes, and average pressure change needed in the analysis. (Changes are final condition minus initial condition; Averages are surface condition plus bottom hole condition divided by 2)
= 0 0.052 × 9.5 × 9036 = 4464 psi = 7000 0.052 × 12.2 × 9036 = 12732 psi Δ = – = 12732– 4464 = 8268 psi + Δ = + – = 7634 psi
SOLUTION CONT’D = = 1500 0.052 × 9.5 × 9036 = 5964 psi Δ = – = 1500 psi Δ = + – + = 1500 psi 4. Compute the average temperature change + Δ = + – = 67℉
PISTON EFFECT Compute the appropriate piston effect
1 =
Δ
Δ
= 9.621 – 6.492 × 1500 9.621– 4.680 × 8268 = 36158 lb × Δ = = − = 72.1 in × .
Click for nomenclature
BUCKLING EFFECT Compute radial clearance and terms for string weight in fluid if buckling effect is to be computed:
=
( )
= . = 0.542
= 0.0034 tbg.I.D. = 0.0034 tbg.O.D.
× 12.2 = 0.247 Final in tubing = 0.0034 × 2.441 × 9.5 = 0.267 Final in annnulus = 0.0034 × 2.875
.−. = c...−... = = 1.655"
BUCKLING EFFECT CONT’D Compute the buckling effect if required:
Δ =
− − +−
. ×. × − = −×× ×.× .+.−. = 57.5 in
Compute the neutral point:
=
− +−
Note that
− = . = 124741 in = 10395 ft .+.−.
> L (=9036 ft).
BALLOONING EFFECT Compute the appropriate ballooning effect:
= 0.6 Δ Δ = 0.6 1500 × 6.492 7634 × 4.68 = 15593 lb . − Δ = −
. . − = = . −
31.0 in
TEMPERATURE EFFECT Compute the appropriate temperature effect:
= 207 Δ = 207 × 1.812 × 67 = 25131 lbs Δ = Δ = 0.0000069 Δ = (108432 in) × 6.9 × 10−
in × (67℉) = 50.1 in in ℉
MECHANICALLY APPLIED EFFECT Compute the mechanically applied length change if necessary. (Use at the time the weight is slacked off) Δ = + −
= ×× × ×.
. ×××.×(.+.−.) =
38.3 in
, , and
TOTAL EFFECT Find the proper total effect:
= = (36158) (15593)(25131)(17000)=59882 lbs Δ = Δ Δ Δ Δ Δ = 72.1 56.5 31.0 50.1 38.3 = 171.4 in
REFERENCES 1. Packer Calculations Handbook. 1992. Baker Oil Tools Div. 2. Lubinski, A., Althouse, W.S., and Logan, J.L. 1962. Helical Buckling of Tubing Sealed in Packers. J. Pet Tech 14 (6): 655-670. SPE-178-PA. http://dx.doi.org/10.2118/178-PA. 3. Moseley, N.F. 1973. Graphic Solutions to Tubing Movement in Deep Wells. Petroleum Engineering Intl: 59.
HOOK LOAD In this type of problem, the calculation is for hook load, or what the weight indicator should read under neutral condition at packer To find this load calculate the weight of steel in the tubing. Then, calculate the pressure pushing either up or down, and the size of the areas acted on, for these will change its weight.
TO figure the hook load to release from a packer having tubing larger than the bore, take the following steps:
ANNULUS: Calculate the pressure in the annulus at the packer. Calculate the area from the OD of tubing to the ID of the packer bore. Multiply the pressure by the amount of area, and since it is an upward force, assign a pounds force up (#↑) sign to it.
Tubing: • Calculate the pressure inside the tubing at the packer depth. Determine the area from the ID of the tubing to the ID of the packer bore. • Multiply the pressure by that amount of area. Since the ID of the tubing is larger than the bore, assign a pounds down (# ↓) sign to it.
HOOK LOAD: Find the weight of the steel by multiplying the weight per foot by the number of feet of tubing, and assign a down force (# ↓)) sign to it. Add this down force to the down force created by the pressure in the tubing. The answer is given by subtracting the up force created in the annulus
EXAMPLE#1 Tubing larger than the bore 9,510 ft. Packer depth 2-3/8” EU 4.7#/ft. tubing 1.96 packer bore 40 API gravity Oil in annulus 9.6#/gal. SW in tubing 71.8#/cu.ft. What will be the hook load to release?
OBSERVATION 1: IN THE ANNULUS Fluid pressure resulting from oil acting on the cross sectional area of the tubing-packer bore connection tends to lift the tubing up. This force is found as follows,
lbs =
×
in × in × 0.052
= (4.43 3.00)(in ) × 3,395(psi) = 4,855(lb)
Δℎ = Distance from surface to packer, [ft].
×
×Δℎ
ft
OBSERVATION 2: INSIDE THE TUBING Inside the tubing, fluid pressure resulting from saltwater acting on the cross sectional area of the tubing-packer bore connection tends to push the tubing down. This force is found as follows,
lbs =
×
in in
× 0.052
= (3.13 3.00)(in ) × 4,745.5(psi) = 616(lb)
×
×Δℎ
ft
HOOK LOAD Tubing weight pushing the packer down is found to be,
lb =
×Δℎ
ft = 4.7
× 9,510 ft = 44,469(lb)
Tubing
Annulus
2-3/8” OD=4.43 in2
2 3/8” ID=3.13 in2
1.96”=
1.96”=
-3.00 in2
0.13 in2
-3.00 in2
1.43 in2
9,510 ft.
9,510 ft.
×.375 psi/ft.
×.499 psi/ft.
=3,395.070 psi =4,745.49 psi =4,746 psi
=3,395.070 psi
× .13 in2
×1.43 in2
=
=
4,854.85#↑
616.98#↓
