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2 PTQ Q4 2012 www.digitalrening.com/article/1000653

Nusselt number for the hori -zontal pipe of diameter D isgiven by Churchill and Chu 5 asfollows:

Where RaD = g.β.ρ.cp(∆t)D3/( ν.k f ) = Rayleigh number.

The overall Nusselt numberNu is computed using j = 4 andδ = 0.3. Once the Nusseltnumber is computed, the heattransfer coef cient external tothe pipe is computed as:

h = NuD. k f / D

The radiation heat transfercoef cient outside the pipe iscomputed using the StefanBoltzmann Law:

with ε = 0.95

The overall outside heattransfer coef cient will be:

ho = h + h r

Neglecting the heat transferresistance of the pipe anddifference of pipe inside andoutside diameters, the overallheat transfer coef cient “U”

from gas to air is given by:

1/U = 1/h i + 1/h o

The heat transferred out ofare gas and the pipe metal to

ambient can be computed as:

Q = U x A x (Tgas - Tambient)

The heat transferred to the

stagnant gases in the areheaders can be subjected tovolume shrinkage due to cool -ing. The factors in uencingshrinkage are:• Temperature of gas in theheader after stoppage of aring• Ambient temperature• Wind speed• Flare pipe surface area• Heat capacity of are pipemetal• Thermal conductivity, viscos -ity and density of gas.

MethodHeat transfer from the hot aregases to ambient is by thefollowing means:• Inside the pipe: by naturalconvection (gases inside thepipe are considered stagnantwhen not aring)• Across the pipe wall: byconduction• Outside the pipe: by natural

convection, forced convectionand radiation.Theoretical analysis of natu -

ral convection heat transferinside enclosed surfaces isprovided in the Nusseltequation: 4

NNu = a (NGr NPr )m

where

NNu = hiL/k = Nusselt numberNGr = L3ρ2Gβ∆t/ µ2 = GrashofnumberNPr = cµ/k = Prandtl number.

The factors “a” and “m” forhorizontal cylinders are givenin the reference. Using these, h i ,the heat transfer coef cient fornatural convection inside thepipe, is computed.

When a heated are pipesurface is exposed to owingair, the convective heat transferoutside the pipe is a combina -tion of forced and freeconvection. For this mixedconvection condition, Churchillrecommends the followingequation for computing theheat transfer coef cient h: 5

(Nu - δ) j = (Nuf - δ) j + (Nun - δ) j

The forced convectionNusselt number for the hori -zontal pipe of diameter D is

given by Incropera and Dewitt 5 as follows:

Where ReD = VD/ ν = Reynoldsnumber.

The natural convection

Figure 1 Temperature gradients from aring condition to ambient temperature

] +×

+

×+=

5/48/5

4/13/2

3/12/1

, 282000Re

1Pr)/4.0(1

Pr Re62.03.0 D D D f Nu

]1/4

]

2

27/816/9

6/1

,Pr)/559.0(1

387.006.0

+

×+= D

Dn

Ra Nu

8/27

]

0

40

4

T T

T T r h

s

s

−−

=σε

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due to the ambient coolingeffect. The minimum quantityto maintain safe conditions inthe headers can be estimatedaccording to the method shownin this article. The equivalentcooling rates (see Figure 5) for

different temperature aregases for the case describedhave been found to be slightlylower than Simpson’s rates. 1

Sweeping gas ow systemscan be either continuous orintermittent. Intermittentsystems can provide economyin gas consumption over thecontinuous systems; theirhigher capital cost becomes justi able in large networksand/or high-temperature aresystems.

Ack owledgeme tsThe author wishes to thank Bechtel (India)Pvt Ltd for their support in completingthis study.

Refere ces1 CCPS/AIChE Guideline for Pressure Reliefand Ef uent Handling Systems , Ch 5.2 Bader A, Baukal C E, Jr, Bussman W, Selecting the Proper Flare Systems , CEP Jul2011.3 Pressure-relieving and Depressuring Systems, API Standard 521 (ISO 23251),5th ed.4 Perry’s Handbook, 7th ed, Ch 5, Heatand Mass Transfer.5 ASTM C680-10, Standard Practice for

www.digitalrening.com/article/1000653 PTQ Q4 2012 5

σ Stefan-Boltzmann constant ν Kinematic viscosity

Satish Mathur is a Supervising Engineer inthe Process Department of Bechtel IndiaPvt Ltd. He has over 36 years’ experience inthe oil, gas, petrochemicals and synthetic

bre industry, from conceptual designthrough to commissioning. He holds aBTech degree in chemical engineeringfrom Indian Institute of Technology, NewDelhi, India.Email: sxmathur@bechtel.com

Estimate of the Heat Gain or Loss and theSurface Temperatures of Insulated Flat,Cylindrical, and Spherical Systems by Useof Computer Programs.6 Kern, D Q, Process Heat Transfer.

KeyT, t TemperaturePr Prandtl number U Overall heat transfer coef cientD Diameter V VolumeA Areak Thermal conductivityg Acceleration due to gravityβ Volumetric coef cient of thermalexpansionρ Densityε Effective surface emittance betweenoutside surface and the ambientsurroundings

100

150

50

0 100 200 300

R a

t e o

f t e m p

e r a

t u r e c

h a n g e ,

° C / h r

Temperature, °C

0

1 ft

3 ft

1.5 ft

2 ft

Figure 5 Cooling rates for different temperature are gases

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