NOMENCLATURE
a/ = thermal diffusivity of formation.
A{ — area corresponding to internal area, in.2
Ajp — area under last perfect thread, in.2
Atowl — internal area of the lower section of the pipe at depth /Здд,. in.2.
A0 = area corresponding to external area, in.2
As = pipe cross-sectional area, in.2
Asc = area steel in coupling, in.2
Asp — As — area of steel in pipe body, in.2
ASJ: — cross-sectional area of the pipe at depth x. in.2
AUpi — internal area of the upper section of pipe at depth D^a.* in.2
BF — buoyancy factor, lbf.
с = radial clearance, in.
С = cost, USS.
Cc = clinging constant.
Cpn = accumulated total return, minimal cost of n
sections of casing for each load. Fn. USS.
Cs(l) — correction factor for contact surface between
pipe and borehole.
Cjn = return function, total cost of n unit
sections of casing, USS. dbox = internal diameter of the joint under the last
perfect thread, in.
(iToot — diameter at the root of the coupling thread
of the pipe in the powertight position for API Round thread casing and tubing, in. dco — outside diameter of coupling, in.
doc = outside diameter of the coupling, in.
di — internal diameter, in.
djt — internal diameter of the joint, in.
external diameter of the joint, in. outside diameter, in.
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d; = Jo d„ = |
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du. D Dn Di Ds Ddop Deo в Deod Drop Dj- Dtoc Da a. E F Er Et f fb № Ea Fab F |
external diameter of the pin under the last perfect thread, in. diameter of the wellbore. in. vertical depth, ft.
depth where normal pressure zone ends. ft. setting depth of intermediate rasing, ft. setting depth of surface casing, ft. true vertical depth of dropoff point, ft. true vertical depth of end of build, ft. true vertical depth of end of dropoff, ft. true vertical depth of kickoff point, ft. true vertical total depth, ft. depth of the top of cement, ft.
depth of change in pipe cross-section.4^ of the pipe. ft. modulus of elasticity. .40 x 10b psi.
Young’s Modulus of cement sheath, psi. reduced modulus, psi.
tangent modulus — localised slope of stress-strain curve in
the elastoplastic transition range of material, psi.
flow friction factor.
borehole friction factor.
transient heat conduction factor.
axial force, lbf.
total tensile failure load with bending 0. lbf.
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O-homo F = 1 0-part F = 1 ae — E*J = Eair = F = ■* ap Fas = Fau = P = 1 a — p Fau.■ = F, = Fa2 = Fb = Fbu = Fbuv = Fbuc = Fuccr — |
axial force — homogeneous solution, lbf.
axial force — particular solution, lbf.
total effective axial force, lbf.
tensional force for joint failure, lbf.
weight of string in air. lbf.
piston force, lbf.
force applied at surface, lbf.
total tensile load at fracture, lbf.
axial force arising from a change in temperature, lbf.
weight of casing string carried by the joint above the TOC. lbf.
axial force at Qj — equivalent to F„Ql. lbf.
axial force at a2 — equivalent to Faa2. lbf.
bending force, lbf.
buoyant force acting at the casing shoe. lbf. vertical projected buoyant weight of pipe. lbf. buckling force, lbf. critical buckling force, lbf.
vertical component of bouyant force, lbf.
drag force, lbf.
hook load, lbf.
normal force, lbf.
radial force, lbf.
radial and tangential force at any depth x, lbf.
shock load, lbf.
peak shock load, lbf.
tangential force, lbf.
hydrodynamic viscous drag force, lbf.
force exerted by the borehole wall at the couplings, lbf.
gravity force, ft/s2.
r2 ‘ _
pressure gradient of cement slurry, psi/ft. formation fluid gradient at depth psi/ft. pressure gradient of gas, psi/ft. pressure gradient of fluid in the casing, psi/ft. pressure gradient of mud, psi/ft. pressure gradient of fluid in the annulus at r02, psi/ft.
distance between top of fluid and surface (Collapse), ft. gas interval between bottom of fluid and formation fracture, ft.
gas interval between casing seat and top of gas column, ft.
distance between shoe and fluid top (Collapse), ft.
distance between fluid top and formation
fracture (Collapse), ft.
enthalpy of steam, Btu/lbm.
enthalpy of water, Btu/lbm.
moment of inertia, in.4
distance between the end of the pipe and center of the coupling in the power tight position, in. thermal conductivity of casing, Btu/hr ft °F. thermal conductivity of the formation, Btu/hr ft °F. thermal conductivity of insulating material, Btu/hr ft °F. thermal conductivity of ‘j’th completion element, Btu/hr ft °F. thermal conductivity of tubing, Btu/hr ft °F.
Power Law parameter, buildup constant, collapse coefficient (Sturm), dropoff constant, reinforcement factor.
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К к К 2 |
= |
constants in the Lame equations. |
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I |
= |
length of pipe, ft. |
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h |
= |
length of joint, ft. |
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he |
= |
length of casing with coupling, ft. |
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e |
= |
measured depth, ft. |
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CDOP |
measured depth of dropoff point, ft. |
|
|
LEOB |
= |
measured depth of end of build, ft. |
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£eod |
= |
measured depth of end of dropoff, ft. |
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(KOP |
= |
measured depth of kickoff point, ft. |
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tT |
= |
measured total depth, ft. |
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L |
= |
length of the test specimen, in. |
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Let |
length of engaged thread, in. |
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Lc |
= |
coupling length, in. |
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Li |
= |
make-up loss, in. |
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m |
= |
mass of pipe of length Vjft, lbm. |
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m |
=r |
mass flow rate of the fluids (steam к water), lbm/s. |
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M |
= |
bending moment, ft-lbf. |
|
MPo |
— |
bending moment at any section of ring caused by external pressure p0. ft-lbf. |
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n |
= |
Power Law parameter. |
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NRe |
Reynolds number. |
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Nw |
=: |
number of different casings of unit weight. |
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Pb |
= |
burst pressure rating of material (Barlow), psi. |
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Pbr |
= |
burst pressure rating of material defined by the API. psi |
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Pe |
— |
collapse pressure for stresses above the elastic limit (Sturm), psi. |
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Pcb |
— |
burst pressure rating corrected for biaxial or triaxial stress, psi. |
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Pee |
= |
collapse pressure rating for biaxial stress (API Bui. 5C3. 1989), psi. |
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Pee |
= |
collapse pressure in the elastic range (Bresse). psi. |
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Peep |
collapse resistance of the composite pipe body, psi. |
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Per |
— |
critical value for external pressure for collapse of ring, psi. |
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Pet, |
— |
critical external pressure for collapse in the transition range based on E,. the tangent modulus, psi. |
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Pctr |
= |
critical external pressure for collapse in the transition range based on Er. the reduced modulus, psi. |
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Peyi |
= |
critical collapse pressure for onset of internal yield in ideally plastic material (Lame), psi. |
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Pe У2 |
— |
critical collapse pressure for onset of internal yield in casing (Barlow), psi. |
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Pc, |
= |
collapse resistance of the inside pipe. psi. |
collapse resistance of the outside pipe, psi.
internal pressure at depth /)дл., psi.
collapse pressure in the elastic range for E = 30 xlO6 psi
and v = 0.3 (API), psi.
collapse pressure in the upper elastic range
(API) from Clinedinst. psi.
internal pressure, psi.
internal pressure at r,,, psi.
internal pressure of 2nd string (composite casing) at r!2, psi.
kick-imposed pressure at depth Z), psi. external pressure, psi. external pressure equivalent, psi. external pressure at r0], psi.
external pressure of 2nd string (composite casing) at r0,. average collapse strength in plastic range (API), psi. minimum plastic collapse strength (API), psi. change in surface pressure inside pipe, psi. change in surface pressure outside pipe. psi. transition collapse pressure (API), psi. collapse pressure in the yield range (API), psi. distributed price, USS/100ft. potential energy.
distributed price of the VUre/„ of casing. USS/lOOft. distributed price of the cheapest casing within m. USS/100 ft. steam quality, heat flow, Btu/hr.
heat transfer coefficient (natural convection and conduction), Btu/hr.
heat transfer coefficient (radiation), Btu/hr.
radius of ring prior to deformation.
radial clearance between hole and casing, in.
internal radius of casing, in.
internal radius of innermost string, in.
internal radius of 2nd or outer string in composite
casing = outside radius of cement, in.
external radius of casing, in.
external radius of innermost casing = internal radius of cement in composite casing, in.
outside radius of 2nd or outer string of composite casing, in. inside radius of tubing, in. outside radius of tubing, in. radius of curvature, ft.
R(l) = hole curvature after drilling, ft.
SF = safety factor.
SM = safety margin.
t = wall thickness, in.
Tt, = bottom hole temperature, °F.
TCt = temperature of inside of casing, °F.
Тстп<, = temperature at outer surface of cement sheath, °F
Te = undisturbed temeprature of the formation, °F.
Th = temperature at the cement-formation interface, °F.
Тг = temperature at internal surface, °F.
T0 = temeprature at external surface, °F.
Ts = surface temperature, °F.
Tst — temperature of flowing fluid (steam) inside tubing, °F. Ttb, — temperature at the inside surface of the tubing, °F.
Ttb0 = temperature at the outside surface of the tubing, °F.
Tj = initial temperature, °F.
T2 — final temperature, °F.
Utot = overall heat tranfer coefficient, Btu/hr sq ft °F.
v = velocity of the two-phase mixture, ft/s.
vav = equivalent displacement velocity, ft/s.
Vp — velocity at which pipe is running into hole, ft/s.
Vs = velocity of induced stress wave in casing, ft/s.
W = WnBF
= weight of unit section, lb/ft.
Wa — weight of string in air, lb/ft.
Wb — buoyancy force acting on the pipe, lb/ft.
Wb(l) = unit buoyant weight projection on the binormal
direction, lb/ft.
Wd(l) = Wd(l, fb)
— unit drag or rate of drag change, lb/ft.
We = effective weight of the pipe, lb/ft.
Wmn = distributed weight of the casing within m, lb/ft.
Wn = nominal weight per unit length, lb/ft.
Wit(1) — buoyant weight projection on the
principal normal direction, lb/ft.
Wp(l) — unit buoyant weight projection on the
principal normal direction, lb/ft.
Wpc = plain end weight per unit length, lb/ft.
WPn — distributed weight of casing lighter or equal to
VFre/„, lb/ft.
Wrejn = distributed weight of the cheapest casing at
stage n, lb/ft.
Wtc = threaded and coupled weight per unit length, lb/ft.
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wu(l) |
— |
unit buoyant weight projection on the tangential direction, lb/ft. |
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Ур |
= |
yield strength, psi. |
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Ypa |
= |
yield strength of axial stress equivalent grade, psi. |
|
= |
(Ty for cra = 0 |
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a |
= |
angle of inclination to the vertical, deg. |
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Ct |
= |
rate of change of inclination, deg. |
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a i |
— |
angle of inclination between the vertical and the slant section, deg. |
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d |
= |
buildup rate, ° /100 ft. |
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a2 |
= |
angle of inclination between the vertical and the end of of the dropoff, deg. |
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a2 |
= |
dropoff rate, 0 /100 ft. |
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fi |
= |
overall angle change, radians. |
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1cm |
= |
specific weight of cement slurry, lb/gal. |
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If |
= |
specific weight of formation fluid, lb/gal. |
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1m |
specific weight of drilling fluid, lb/gal. |
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1 mn |
= |
new specific weight of drilling fluid, lb/gal. |
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ъ |
= |
specific weight of steel. 489.5 lb/ft3. |
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AT i-w max |
= |
refer to Fig. 4.27 on page 225. |
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AT, |
= |
refer to Fig. 4.27 on page 225. |
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ft. Е-Г <1 |
= |
temperature at which yield point is reached, °F. |
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Де2 |
= |
deformation of outside surface of pipe. |
|
= |
deformation in the x-axis. |
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Zy |
deformation in the y-axis. |
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ea |
= |
deformation in the z-axis. |
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в |
= |
bearing angle change, rad. |
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0 |
= |
degrees per 100 feet of pipe, ‘dogleg severity". |
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A |
contact angle, rad. |
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i/ |
Poisson’s ratio. |
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Vcm |
= |
Poisson’s ratio for cement sheath. |
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z |
= |
ratio of Young’s modulus to the tangent modulus at the yield point, <jy. |
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<TS |
= |
stress resulting from slip action, psi. |
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va |
= |
axial stress, psi. |
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Vabui |
— |
change in axial stress due to the effect of change in fluid specific weight on buoyant weight, psi. |
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Vabu2 |
— |
change in axial stress due to the effect of change in surface pressure on buoyant weight, psi. |
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Vap |
= |
axial stress due to piston effect, psi. |
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Vapi |
vap 4“ Асгдр, psi. |
|
|
A^ap |
— |
change in piston effect due to effect of changing in fluid densities and surface pressures, psi. |
additional axial stress due to a change in temperature, axial stress due to pipe weight, psi.
&aw ~"f" i PSI.
Gabui “t" &abu2
critical stress for buckling, psi.
compressive strength of cement, psi.
collapse resistance of the cement sheath
under the external pressure рсЛ. psi.
effective yield strength under combined load. psi.
limit of elasticity, psi.
maximum total stress, psi.
average nominal stress, psi.
residual axial stress present prior to heating body, psi. tangential stress due to external pressure p0. psi. reduced yield strength due to axial loading, psi. stress resulting from the action of slips, psi. tangential stress due to internal pressure, psi. minimum ultimate yield strength of the material, psi. minimum ultimate yield strength of the coupling, psi. minimum ultimate yield strength of the pipe. psi. average tangential stress for a particular value of ET, psi.
maximum tangential stress, psi. minimum yield strength, psi.
yield stress corrected for temperature (hot yield stress), psi. joint yield stress (cold yield stress).
<7a = axial stress, psi.
tensile stress required to produce a total elongation of
0. 2% of the gauge length of the test specimen, psi. coefficient of thermal expansion, contact surface angle, rad.
angle of internal friction calculated from Mohr’s circle. Fa/EI = definition.
1 + ((?’*)3p0)/£/ = definition, time, second.