Insulation of any hot or cold system plays an important role in energy saving. Insulation can reduce by at least 90 % the unwanted heat trans- fer,that is distribution losses occurring with a bare surface.
To better understand the economic criteria for the thickness of pipeline and insulation, the basic concepts of heat transfer are briefly reviewed below.
The same concepts can be applied to any problem concerning heat transfer and thermal energy balance.
Thermal energy is transferred in three main modes: conduction, radiation, and convection.
Conduction: heat is transferred through both fluids (gas and liquid) and solids when the two sides of a volume of these materials are at different temperatures. The thermal power transfer is proportional to the temperature gradient through a proportionality factork, called thermal conductivity, and the surface.
Thermal conductivity (or k-value in insulation technology) is the measure of the capability of a material to transmit heat. Substances with high values of thermal conductivity, such as copper, are good thermal conductors, and those with low conductivity, such as polystyrene foam or cork, are good insulators.
Thermal conductivity is expressed as the quantity of heat that will be conducted through unit area of a layer of material of unit thickness with unity difference of temperature between the faces in unit time. The Si unit is W/mK; the English unit commonly used is: (Btu/hftF).
The expression of the thermal conduction power transferQthrough a surface A(Fourier’s Law) is as follows:
Q¼kAΔtx ð Þ, Btu=hW ð Þ
whereΔtxis the temperature gradient between the two surfaces (K/m;C/m;F/ft).
The sign of Q, minus in accordance with the laws of thermodynamics, is omitted here.
8.3 Basic Principles of Pipeline Losses and Insulation 127
Thermal conductivities of various materials at room temperature or higher are reported in Table8.1. If the temperature rises, thermal conductivity decreases with homogeneous metals and it increases in composite materials almost linearly in an interval range of 323–373 K (50–100C; 122–212F). With insulating materials, because of the composite or multilayer structure where also air can be present, the kcoefficient must take into account the presence of all the heat transfer basic modes and its value is assessed on empirical bases. For detailed evaluations, manufacturer specifications should be consulted.
Radiation: heat is transferred as radiant energy and does not require any medium of diffusion. Radiation can take place even in a vacuum. Solid surfaces, gases, and liquids all emit, absorb, and transmit thermal radiation in varying degrees.
The rate at which energy is emitted from a system with a surface Asituated inside a large space is quantified by the basic relationship:
Q¼εσAT4sT4o
ð ÞW
whereTsandToare the surface and output surrounding absolute temperatures (K),ε (0<ε<1) is an adimensional quantity that indicates how effectively the surface radiates (ε¼1 for the black body or the perfect emitter), and σ is the Stefan–
Boltzmann constant equal to 5.67108 W/(m2K4). As thermal radiation is associated with the fourth power of surface absolute temperature, the importance of this mode of heat transfer increases rapidly with the temperature.
Values of ε for different operating conditions (materials, different states of surfaces) are shown in Table8.2. As with the conduction energy transfer, different units are commonly used alternatively to the SI units.
Table 8.1 Average values of thermal conductivity of different materials at room temperature Material
Thermal conductivitykin the temperature range 273.15–373.15 K 0–100C 32–212F
Pure aluminum W/mK (a) 228
Btu/hftF (b)¼(a)/1.731 132
Btuin/ft2Fh (c)¼(b)12 1,581
Cast iron W/mK 48
Btu/hftF 28
Btuin/ft2Fh 333
Fiber glass W/mK 0.058
Btu/hftF 0.034
Btuin/ft2Fh 0.402
Ceramic fiber W/mK 0.055
Btu/hftF 0.032
Btuin/ft2Fh 0.381
Cellular polyurethane W/mK 0.025
Btu/hftF 0.014
Btuin/ft2Fh 0.173
The abovementioned relationship is valid if some basic assumptions are respected such as transparent medium, surface with particular spectrum emission behavior, etc. For pipelines and tanks in industrial applications, these hypotheses are widely accepted and the relationship can be used with a proper choice of parameters.
Convection: heat is transferred from a solid surface at one temperature to an adjacent fluid, liquid or gas, at another temperature, when motion occurs. The thermal power transfer from the system with a flatAsurface is expressed as follows:
Q¼hAðtstfÞ ð ÞW
where ts and tf are the surface and fluid temperatures and h is an empirical parameter, depending on operating conditions and surface geometry, called the heat transfer coefficient. The SI unit is W/m2K; the English unit commonly used is: (Btu/hft2F).
In most cases, heat is transferred by a combination of the abovementioned basic modes through composite or multilayer systems, and the evaluation is generally made by means of empirical parameters and linearization of the heat transfer relationships. A simplified approach based on a monodimensional scheme is gen- erally introduced in industrial applications. As a rule, radiation is included in the heat transfer coefficient in a wide range of temperature values.
Values ofhfor different operating situations with surface exposed to the air are given in Table8.3.
Values ofhfor fluid flowing in pipelines depend on many factors (temperature, speed, state of pipe, etc.) and must be calculated by using special formulae. They are greater than those for air and they range between hundreds and thousands W/m2K (see also Chap.15).
Table 8.2 Total emissivity average
values (e) Surface
Temperature range
C F ε Aluminum
Commercial sheet 200–600 400–1,100 0.09 Heavily oxidized 100–550 200–1,000 0.3 Iron
Steel polished 40–250 100–500 0.085
Steel oxidized 250 500 0.8
Brick
Red 40 100 0.93
White refractory 1,100 2,000 0.29
Concrete 40 100 0.94
Glass 40 100 0.94
8.3 Basic Principles of Pipeline Losses and Insulation 129
Table 8.3 Typical values of heat transfer coefficient (h)
(a) W/m2 ⫻ K (b) Btu/ h ⫻ft2⫻ °F (b)=(a)⫻ 0.1761
Surface Emittance
Wind
velocity Heat transfer from a hot solid surface to air (h)
km/h Operating -C 100 200 300 400 –550
temperature °F 212 392 572 752 –1022
1.0 0 (a) 9.31 11.13 12.34 13.52
(b) 1.64 1.96 2.17 2.38
3 11.83 13.85 15.35 16.22
2.08 2.44 2.70 2.86
6 13.85 16.70 18.32 19.58
2.44 2.94 3.23 3.45
0.6 0 7.28 9.01 9.96 10.32
1.28 1.59 1.75 1.82
3 10.32 12.62 13.85 14.20
1.82 2.22 2.44 2.50
6 12.62 14.94 16.22 16.70
2.22 2.63 2.86 2.94
0.2 0 5.56 7.14 7.69 8.33
0.98 1.26 1.35 1.47
3 8.48 10.32 11.13 11.59
1.49 1.82 1.96 2.04
6 10.32 12.91 14.20 14.94
1.82 2.27 2.50 2.63
For low temperature service, values are lower. For higher wind velocity, values are higher
Heat transfer from liquid or gas to a solid surface (h)
From steam to a solid surface (a) 4000–3000 W/m2 ⫻K (b)704 –528 Btu/h⫻ft2⫻ °F From water to a solid surface (a) 400 – 200 W/m2 ⫻K (b) 70 –35 Btu/ h⫻ ft2⫻ °F From heavy organic liquid to a solid surface (a) 100 – 50 W/m
2 ⫻K (b) 18 – 9 Btu/ h⫻ft2⫻°F
In a multilayer system,heat is transferred from one fluid(fluid inside i)at higher temperature (ti) through an n-layer slab to another fluid (fluid outside o)at lower temperature(to).
The fundamental equation for the heat transfer calculation is:
Heat flow through unit area¼fluid temperature difference overall thermal resistance ¼tito
Rth
¼ðtitoÞU W m2
Btu hft2
where
ti¼inside fluid temperature(K), (C) (F), to¼outside fluid temperature(K), (C)(F), Rth¼overall thermal resistance m2WK
¼m2WC
hft2F Btu
U¼1/Rth¼overall heat transfer coefficient(see Chap.15) Note that:
• For homogeneous materials, thermal resistance is the reciprocal of the system thermal conductance which represents the quantity of heat that will be conducted through unit area of a layer of material of a defined thickness with unity difference of temperature between the two fluids in unit time;
• Forn-layer systems thermal resistanceRthis the reciprocal of the system thermal conductance which represents the quantity of heat conducted through unit area of an-layer material of defined thicknesses with unity difference of temperature between the two fluids in contact with the end faces in unit time;
• The above given relationship is based on the assumption that the radiation heat transfer is negligible or that its effect is introduced into theRthby linearizing the radiation law. In the same way, all heat transfer models are linearized;
• At thermal steady state, the same amount of heat flows through each layer of the system. Thus, the temperature of each layer can be calculated.
Specialized handbooks on this subject should be consulted for more detailed evaluations.
Examples are given below of flat-surface and of pipeline multilayer systems with bare surfaces and with insulation.
8.3.1 Flat-Surface Multilayer System (See Fig.8.2)
When a flat surface is heated on one side and cooled on the other, as shown in Fig.8.2, heat flows from the hot side to the cold side.
8.3 Basic Principles of Pipeline Losses and Insulation 131
The flow of heat is defined as follows:
Q¼Atito
Rth
where A¼internal and external surfaces with the same value (m2) (ft2), Rth¼h1iþXn
1
jdkj
jþh1om2WK
¼m2WC
ft2hF Btu
, dj¼thickness of thejlayer (m) (ft),
ti¼inside temperature (K) (C) (F), to¼outside temperature (K) (C) (F), kj¼thermal conductivity of thejlayermWK
¼ mWC
Btu
fthF
, dj/kj¼thermal resistance of thejlayer m2WK
¼m2WC
ft2hF Btu
,
hi¼heat transfer coefficient, radiation included, between the inside fluid and the internal surface of the first layer, m2WK
¼ m2WC
Btu
ft2hF
,
ho¼heat transfer coefficient, radiation included, between the external surface of the last layer and the fluid outside m2WK
¼ m2WC
Btu
ft2hF
If one of the layers is made of insulating material, this layer has the highest thermal resistance (dj/kj) and the heat flow is less than with a bare surface.
Table 8.4 shows heat losses from a composite wall. Notice that heat transfer through the layers is reduced by insulation to roughly 10 %.
Fig. 8.2 Heat transfer through a multilayer wall
Table8.4Heatlossesfromacompositewall(referenceFig.8.2) Thickness of insulation (d2)Overall thermal resistanceHeat losses QEnergy saving mm10-3 ⫻ ftrn2⫻K/Wft2 ⫻h⫻°F/BtuW/m2 Btu/h⫻ft2 W/m2 Btu/h⫻ft2 kgoil/h⫻m2 00.00.1901.079526167000.000 1032.80.3722.11226985257820.026 2065.60.5543.144181573461100.035 3098.40.7354.177136433901240.039 40131.20.9175.209109354171320.042 50164.01.0996.24291294351380.044 60196.91.2817.27478254481420.045 70229.71.4638.30768224581450.046 80262.51.6459.34061194661480.047 90295.31.82610.37255174721490.048 100328.12.00811.40550164771510.048 INPUT DATA wall conductivity k12.500 W/m⫻ K1.444 Btu/h⫻ft⫻ °FBASIC FORMULA fiberglass conductivity k20.055 W/m⫻K0.032 Btu/h⫻ft⫻ °F Q=A⫻ti−to Rthwall thickness d10.100 m0.328 ft heat-transfer coefficient hi20 W/m2 ⫻K3.522 Btu/h⫻ft2 ⫻ °F heat-transfer coefficient ho10 W/m2 K1.761 Btu/h⫻ft2 ⫻ °F Rth=1 hi+d1 k1+d2 k2+1 hoti-to100°C = 100 K180°F saving inkgoil h⫻m2=W m2⫻3,600 η⫻41,860⫻103 ηcombustion assumed 0.85 (LHVas reference) LHV of oil 41,860 kJ/kg ANNUAL ENERGY SAVING 70 mm insulation 5,000 h/year 100 m2surface 23 TOE/year 8.3 Basic Principles of Pipeline Losses and Insulation 133
8.3.2 Cylindrical Surface Multilayer System (See Fig.8.3)
This example is typical of pipelines for steam or other hot fluids. The same approach can also be followed in the case of cold fluids.
The flow of heat is:
Q¼Atito
Rth
whereA¼the outside (2πLro) or the inside (2πLri) surface of the pipeline of length L. Note that theRthexpression will be modified by the choice between the outside and the inside surface,ri¼inside pipe radius,ro¼outside multilayer pipe radius.
Thus:
outside surface
A¼2πLro(outside surface) (m2) (ft2) Rth¼ 1
hiro
riþXn
1jro
kjlnrjþ1
rj þ 1 ho
m2C=W
ft2hF=Btu
inside surface
A¼2πLri(inside surface) (m2) (ft2) Rth ¼1
hi
þXn 1jri
kj
lnrjþ1
rj
þ 1 ho
ri
ro
m2C=W
ft2hF=Btu
Fig. 8.3 Heat transfer through a multilayer pipe
In the case of a bare tube, if the outside surface is taken as reference, the abovementioned relationships (withn¼1) are modified as follows:
Q¼Atito
Rth
wherer2¼ro,A¼2πLro
Rth¼h1irroiþrko1lnrr2
1þh1o¼h1irroiþrko1lnrro
iþh1o
If the thickness (rori) of the pipe is small (rori<0.1ri), this expression can be approximated to the following, as for a flat surface:
Rth¼1 hi
þrori
k1
þ 1 ho
simplified formula
ð Þ
Notice that 1/hiis usually the lowest term in the case of pipelines, because of the moving fluid inside the pipe.
For insulated pipelines with one insulation layer, there follows:
Q¼Atito
Rth
whereA¼2πLri
Rth¼h1iþkr1ilnrr2
1þkri2lnrr3
2þh1orroi,j¼2;r1¼ri;r3¼ro
Ifr1¼riis assumed to be equal tor2(small thickness of the pipe) there follows:
Rth¼ 1 hiþri
k2lnr3
r2þ 1 hori
ro
If the thickness of the insulation layer is small in comparison with the bare pipe radius, that is (r3r2)<0.1r2¼0.1ri and (ri/ro)>0.9 the expression given above can be approximated as follows:
Rth¼1
hiþr3r2
k2 þ 1 hori
ro
Table8.5shows heat losses from a composite metal pipeline to still air.
Notice that insulation reduces heat transfer through the layers to roughly 10 %.
Attention must be paid to surface conditions such as film deposits, surface scaling, and corrosion. A fouling factor can be introduced to take account of these phenomena as an additional term in the overall thermal resistanceRth(see also Chap.15).
8.3 Basic Principles of Pipeline Losses and Insulation 135
Table8.5Heatlossesfromacompositesteelpipelinetostillair(seereferenceFig.8.3) Thickness of insulation (ro–r2)External radius (ro)RthHeat losses QRthsimplifiedEnergy saving mmmm2 ⫻K/WW/m2 W/mm2 ⫻K/WW/m2Btu/h⫻ft2kgoil/h⫻m2 0 10 20 30 40 50 60 70
0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12
0.045 0.187 0.308 0.413 0.506 0.590 0.666 0.735
3308 802 487 363 296 254 225 204
935 227 138 103 84 72 64 58
0.045 0.220 0.396 0.574 0.753 0.932 1.112 1.292
0 2506 2821 2945 3012 3054 3083 3104
0 794 894 933 955 968 977 984
0.000 0.254 0.285 0.298 0.305 0.309 0.312 0.314 INPUT DATA pipe conductivity k150.000 W/m⫻K28.885 Btu/h⫻ft⫻°F fiberglass conductivity k20.055 W/m⫻K0.032 Btu/h⫻ft⫻°F internal radius (ri)0.045 m0.1476 ft pipe thickness0.005 m0.016 ft bare pipe external radius (r2)0.05 m0.164 ft heat-transfer coefficient hi4,000 W/m2 ⫻K704.4 Btu/h⫻ft2 ⫻°F heat-transfer coefficient ho20 W/ m2 ⫻K3.522 Btu/h⫻ft2 ⫻°F ti-to150°C = 150 K270°F
BASIC FORMULA REFERRED TO INSIDE SURFACE Q=A⫻ti−to Rth Rth=1 hi+ri k1⫻lnr2 ri+ri k2⫻lnro r2+1 ho⫻ri ro SIMPLIFIED FORMULA Rth=1 hi+ro−r2 k2+1 ho⫻ri ro saving inkgoil hm2=W m2⫻ ⫻
3,600 η⫻41,860⫻103 ηcombustionassumed 0.85 (LHVas reference) LHVof oil 41,860 kJ/kg ANNUAL ENERGY SAVING 50 mm insulation 5,000 h/year 100 m2 bare surface 154.5 TOE/year
As in the case of bare pipelines, the above expressions are modified if the insulated pipeline outside surface is taken as reference.
In all the foregoing relationships, average values of temperatures must be introduced in the following situations:
• When a fluid enters a pipe at one temperature (tin) and leaves at another (tout) an average temperature must be equal to (tin+tout)/2 at any point along the pipe (see also log-mean temperature in Chap.15);
• When the value of the parameter k for insulation material varies significantly with the temperature, the mean temperature between the two faces of the insulation must be considered. The mean value is calculated as half the sum of the temperatures on either side of the insulation.
Since the same amount of heatQflows through each layer of a multilayer wall or pipeline, the temperature difference between the surfaces of each layer is proportional to the thermal resistance of each layer
ΔtLayer¼QRthLayer
.
8.3.3 Tanks, Other Equipment
In these cases specialized handbooks should be consulted to ascertain the relationships and coefficients related to the shape of the structure to insulate and to the operating temperature.