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TRANSPORTATION SYSTEMS 11/153
where h i is film coefficient of pipeline inner surface; h o is considered temperature effect on pressure-transient analyses
film coefficient of pipeline outer surface; A i is area of pipe- in well testing. Stone et al. (1989) developed a numerical
line inner surface; A o is area of pipeline outer surface; r m is simulator to couple fluid flow and heat flow in a wellbore
radius of layer m;and k m is thermal conductivity of layer m. and reservoir. More advanced studies on the wellbore heat-
Similar equations exist for transient-heat flow, giving transfer problem were conducted by Hasan and Kabir (1994,
an instantaneous rate for heat flow. Typically required 2002), Hasan et al. (1997, 1998), and Kabir et al. (1996).
insulation performance, in terms of OHTC (U value) of Although multilayers of materials have been considered in
steel pipelines in water, is summarized in Table 11.5. these studies, the external temperature gradient in the longi-
Pipeline insulation comes in two main types: dry insula- tudinal direction has not been systematically taken into ac-
tion and wet insulation. The dry insulations require an count. Traditionally, if the outer temperature changes with
outer barrier to prevent water ingress (PIP). The most length, the pipe must be divided into segments, with assumed
common types of this include the following: constant outer temperature in each segment, and numerical
algorithms are required for heat-transfer computation. The
. Closed-cell polyurethane foam accuracy of the computation depends on the number of
. Open-cell polyurethane foam segments used. Fine segments can be employed to ensure
. Poly-isocyanurate foam accuracy with computing time sacrificed.
. Extruded polystyrene Guo et al. (2006) presented three analytical heat-transfer
. Fiber glass solutions. They are the transient-flow solution for startup
. Mineral wool mode, steady-flow solution for normal operation mode,
. Vacuum-insulation panels and transient-flow solution for flow rate change mode
(shutting down is a special mode in which the flow rate
Under certain conditions, PIP systems may be considered changes to zero).
over conventional single-pipe systems. PIP insulation may
be required to produce fluids from high-pressure/high- Temperature and Heat Transfer for Steady Fluid Flow.
temperature (>150 8C) reservoirs in deepwater (Carmi- The internal temperature profile under steady fluid-flow
chael et al., 1999). The annulus between pipes can be filled conditions is expressed as
with different types of insulation materials such as foam,
granular particles, gel, and inert gas or vacuum. T ¼ 1 b abL ag e a(LþC) , (11:133)
A pipeline-bundled system—a special configuration of a 2
PIP insulation—can be used to group individual flowlines
together to form a bundle (McKelvie, 2000); heat-up lines where the constant groups are defined as
can be included in the bundle, if necessary. The complete 2pRk
bundle may be transported to site and installed with a a ¼ vrC p sA , (11:134)
considerable cost savings relative to other methods. The
extra steel required for the carrier pipe and spacers can
sometimes be justified (Bai, 2001). b ¼ aG cos (u), (11:135)
Wet-pipeline insulations are those materials that do not
need an exterior steel barrier to prevent water ingress, or the g ¼ aT 0 , (11:136)
water ingress is negligible and does not degrade the insulation
properties. The most common types of this are as follows: and
1
2
C ¼ ln (b a T s ag), (11:137)
. Polyurethane a
. Polypropylene where T is temperature inside the pipe, L is longitudinal
. Syntactic polyurethane distance from the fluid entry point, R is inner radius
. Syntactic polypropylene of insulation layer, k is the thermal conductivity of the
. Multilayered insulation material, v is the average flow velocity of fluid in
the pipe, r is fluid density, C p is heat capacity of fluid at
The main materials that have been used for deepwater insu- constant pressure, s is thickness of the insulation layer,
lations have been polyurethane and polypropylene based. A is the inner cross-sectional area of pipe, G is principal
Syntactic versions use plastic or glass matrix to improve thermal-gradient outside the insulation, u is the angle be-
insulation with greater depth capabilities. Insulation coat- tween the principal thermal gradient and pipe orientation,
ings with combinations of the two materials have also been T 0 is temperature of outer medium at the fluid entry
used. Guo et al. (2005) gives the properties of these wet location, and T s is temperature of fluid at the fluid entry
insulations. Because the insulation is buoyant, this effect point.
must be compensated by the steel pipe weight to obtain The rate of heat transfer across the insulation layer over
lateral stability of the deepwater pipeline on the seabed. the whole length of the pipeline is expressed as
2pRk
11.4.2.2.2 Heat Transfer Models Heat transfer across q ¼
the insulation of pipelines presents a unique problem s
affecting flow efficiency. Although sophisticated G cos (u) 2 1 ab 2
computer packages are available for predicting fluid T 0 L 2 L a 2 (b ag)L 2 L
temperatures, their accuracies suffer from numerical
treatments because long pipe segments have to be used to þ 1 e a(LþC) e aC gÞ, (11:138)
save computing time. This is especially true for transient a
fluid-flow analyses in which a very large number of
numerical iterations are performed. where q is the rate of heat transfer (heat loss).
Ramey (1962) was among the first investigators who stud- Transient Temperature During Startup. The internal
ied radial-heat transfer across a well casing with no insula- temperature profile after starting up a fluid flow is
tion. He derived a mathematical heat-transfer model for an expressed as follows:
outer medium that is infinitely large. Miller (1980) analyzed
heat transfer around a geothermal wellbore without ins- T ¼ 1 {b abL ag e a[Lþf (L vt)] }, (11:139)
ulation. Winterfeld (1989) and Almehaideb et al. (1989) a 2