- HUMPHREYS & GLASGOW LTD. A p p r o x i mate Si zing of Air Cooled Heat Exchangers M-06-701/1 Page 1 of 12 March 1970 APPROXIMATE SIZING OF AIR COOLED :BAT EXCHANGaS (Simplified Method) i. Scope The method outlined below gives reasonable approximations to the surface area and H.?, requirements of an air cooled exchanger given certain known process conditions and properties. It is not a complete design analysis of an air cooler and is not intended to be so, but simply gives within about 15% accuracy, surface area, plot size, H.P.'s and costs, for use on proposals, or evaluating against water cooled systems. Information required to be known To be calculated Q = Seat load to be dissipated t2 = Air outlet temp. OF Bthu ' s/hr 0 T = Process fluid inlet temp. F U = Overall heat trans er coef- 1 5 ficient. 8thufs/ft hrO~ 0 T2 = ?rocess.fluid outlet temp. F F = Air temp. rise correction factor = 9esign ambient a i r temp. '8 7 = Lm correction factor 5 -m h, = Inside tube heat transf r - .,. coefficient. Bthufs/ft hr F HP = Motor horsepower f = Inside tube fouling factor. 17, = !4ir approach velocity ~t/rnin Bthu ' s/f t2 hr OF i\ 0 = T, - t, A = bare tube A o surface area T~ - sa. ft. 2. Contents Page - 3 Inside Tube Heat Transfer Coefficients 4 Details of Method 5. Worked Example 6. Table 1 - Typical Inside Tube Coefficients & Fouling Factors Fig. 1 - vs Inside Coefficient h. with V as parameter 1 A Fig. 2 - V vs Inside Coefficient h. with overall A Coefficient U and a i r temp: rise factor F. Fig. 3 - V v s Power A Fig. 4 & 5- Temperature Conversion Factors 9 T Fig. 6 - LMTD Graph Fig. 7 - Cost of FinnedSurface vs Area Made by : M. W. ~reweek/~.~.G. Distribution: Issued by: E. w.Owen/P.~.~. 1306 Heat Transfer D.N. (50) Spares held bx: B. Douglas/~.~.G. 1200 Process h g s ' D.M. (90) 9800 Estimating D.M. (35)
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APPROXIMATE SIZING OF AIR COOLED :BAT EXCHANGaS
( S i m p l i f i e d Method)
i. Scope
The method o u t l i n e d below g i v e s reasonable approximations t o t h e s u r f a c e a r e a and H.?, requi rements of a n a i r cooled exchanger g iven c e r t a i n known p rocess cond i t ions and p r o p e r t i e s . I t i s n o t a complete d e s i g n a n a l y s i s of a n a i r c o o l e r and i s n o t in tended t o be so, b u t s imply g i v e s w i t h i n about 15% accuracy, s u r f a c e a r e a , p l o t s i z e , H . P . ' s and c o s t s , f o r use on p roposa l s , o r e v a l u a t i n g a g a i n s t water cooled systems.
Informat ion r e q u i r e d t o be known To be c a l c u l a t e d
Q = S e a t l o a d t o be d i s s i p a t e d t2
= A i r o u t l e t temp. OF Bthu ' s / h r
0 T = Process f l u i d i n l e t temp. F U = Overa l l h e a t t r a n s e r coef - 1 5
f i c i e n t . 8 t h u f s / f t h r O ~ 0 T2 = ? r o c e s s . f l u i d o u t l e t temp. F F = Air temp. r i s e c o r r e c t i o n
f a c t o r = 9es ign ambient a i r temp. '8 7 = L m c o r r e c t i o n f a c t o r
5 - m h, = I n s i d e tube h e a t t r a n s f r - .,. c o e f f i c i e n t . B t h u f s / f t h r F HP = Motor horsepower
f = I n s i d e tube f o u l i n g f a c t o r . 17, = !4ir approach v e l o c i t y ~ t / r n i n Bthu ' s / f t2 h r OF
i\
0 = T, - t, A = bare tube A o s u r f a c e a r e a
T~ - s a . f t .
2 . Contents Page - 3 I n s i d e Tube Heat T r a n s f e r C o e f f i c i e n t s
4 D e t a i l s of Method
5. Worked Example
6. Table 1 - Typica l I n s i d e Tube C o e f f i c i e n t s & Foul ing F a c t o r s
F ig . 1 - v s I n s i d e C o e f f i c i e n t h . w i t h V a s parameter 1 A
Fig. 2 - V v s I n s i d e C o e f f i c i e n t h . w i th o v e r a l l A C o e f f i c i e n t U and a i r temp: r i s e f a c t o r F.
F ig . 3 - V v s Power A F ig . 4 & 5- Temperature Conversion F a c t o r s 9
T Fig . 6 - LMTD Graph
F ig . 7 - Cost of F innedSur face vs Area
Made by : M. W. ~ r e w e e k / ~ . ~ . G . D i s t r i b u t i o n : I s s u e d by: E. w . O w e n / P . ~ . ~ . 1306 Heat T r a n s f e r D.N. ( 5 0 ) S p a r e s h e l d bx: B. D o u g l a s / ~ . ~ . G . 1200 Process h g s ' D.M. ( 9 0 )
9800 Es t imat ing D.M. (35)
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A p p r o x i m a t e S i z i n g o f A i r C o o l e d H e a t E x c h a n g e r s
z / . Inside Tube Xeat Transfer Coefficients
The nost important part of the whole ~ethed is tne estimation of :he lnside txbe heat transfer coefficient h:. As nucn inforaazion as ossi5le must be obtained about the F'rocess-2xld, so xhat a coelficiens nay be selected from the suggested rar.ge in tne Tabie Xo. 1 3aXtng due allowance for properties, pressure drop, fouling etc. The figures in this table have been collected as being typical tube side coefficients for the fluids involved, wizhin the limits of fouling indicated and will be r2viewed and revised as new fluids are dealt with or specific information comes to hand. .4 generalised list of this kina can only be of iimited accuracy. If acy more accurate figures are known from "historicaliy" simllar duties then zhese should also be tried.
For condensers xnich involve a desuperheating and cordensing duty its suggested the calculation, as with a shell and tube unit is divided into the
f L-do respective parts, and the surface areas be determined for each zone. Fgr steam coming out of some gases during condensation a bulge is produced In the heat release curve, and advantage may be taken of this when considering the LIWD. Normally, however, for expediency a straight line condensing curve is assumed, unless a known order of improvement is to hand.
Step 1
Calculate the factor fl from the;own temperature conditicns where
Step 2
Select an appropriate heat transfer coefficient from the Table 1 (?age 7 ) Step 3
From Fig. 1 (page 8) read the required air approach velocity V in f t/min . A
Step 4
Using VA go to Fig. 2 (page 9 ) and obtain an overall heat transfer coefficient U and a value for factor F.
Step 5 With the value of F, the air temp. rise and thereby the air outlet
temperature can be determined from the following :
Air rise = t2 - tl = F(T + T1 - 2tl) 2
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4. Deta i l s of Method - cont 'd
Step 6
\ A l l four terminal tenperatures now being known the l og mean temp.
d i f f . ('L\'ITD) can be calcula ted.
This is done i n the normal way, using Fig. 4 or 5 (page 1 0 ) f o r the correct ion f a c t o r s depending on whether the u n i t s have one or more passes on the tube s ide .
A t the proposal s tage the numbers of tube s i de passes a r e not known, the re fore a general r u l e must be used. For near ly a l l l i q u i d coolers a t l e a s t two passes w i l l be i n s t a l l e d , and f o r t he d u t i e s with a l a rge tem- perature range on the product s ide two passes and more w i l l probably be used. However, f o r ' e s t ima t ing purposes the u n i t s w i l l be simply sub-divided i n t o two categor ies , i . e . s i ng l e pass, two pass and inore. Single pass u n i t s x i11 normally be necessary f o r gas cooling du t i e s with low operat ing pressures and pressure drops, ( say approximately 1.5 p s i rnax.) and s imi l a r l y f o r some condensers with condensate coming out of gas with s imi l a r condi t ions t o the above.
I f the correct ion f ac to r , F i s l e s s than 0.7 then i t i s suggested T t h a t the a i r out temp. is adjusted t o lower value i n an at tempt t o improve the cor rec t ion . I f t h i s f a i l s t o give a reasonable f i gu re then the s u i t a b i l - i t y of the duty aga ins t the ava i lab le a i r condit ions must be examined. Whilst on the sub jec t of the a i r condit ions it i s suggested t h a t a minimum approach temp. of 10 deg F between process o u t l e t and ambient a i r design i s worked t o . Approach temperature d i f fe rences below t h i s normally give r i s e t o uneconomical u n i t s and a l s o vunerable ones from the po in t of view of hot a i r r e c i r cu l a t i on which e x i s t s t o some degrees on most a i r coolers , dependicg on loca t ion , s i t e wind condit ions, and a i r temperature r i s e through the cooler .
Step 7
Calculate t he bare tube surface area required.
This i s done using two formulae, one the basic hea t t r a n s f e r equation, the other an empirical one u t i l i s i n g a constant which wi thin t he degree of accuracy required, has been found t o give reasonable r e s u l t s .
A = sq. f t - 0 u x m
- Q A -
0 sq. f t
127 (t2 - t,) Normally, these two equations giveanswerswithin reasonable approx-
imation t o one another, the re fore a simple average of t he two answers is taken.
The equation No. 3 normally gives the higher va1ue;if the two values d i f f e r by more than say 20% a second attempt should be made, changing the a i r temp. r i s e s l i g h t l y and checking t h a t the assumed tube s i de heat t r ans - f e r coe f f i c i en t is bes t poss ible attempt f o r t hebown process f l u i d .
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4. D e t a i l s of Nethod - c o n t ' d
S t e ~ 8 The f inned s u r f a c e a r e a i s a r r i v e d a t by mul t ip ly ing the ba re tube
s u r f a c e A by a f a c t o r of 27. Th i s f a c t o r i s , f o r the most commonly used 0 a i r c o o l e r tube i . e . 1 O/D x 11 f i n s / i n 5" high.
A x 27 = SA ( f i n n e d ) 0
S t e o 9
Ca lcu la t e an approx. p l o t a r e a simply us ing the fo l lowing formula
0 .22 x A = p l o t a r e a sq. f t . 0
For p l o t a r e a s l e s s than 300 - 400 sq. f t . t he tube l e n g t h w i l l be 20 f t . o r l e s s down t o 12 f t . f o r smal l su r face a r e a s . With t h e s e s m a l l e r ilnits cons ide ra t ion must be given t o p u t t i n g them on the same s t r u c t u r e a s ' o t h e r c o o l e r s on t h e job, i n o rde r t h a t motors may be shared, c o s t s kep t down, space conserved.
For the u n i t s of 400 sq . f t . p lus a >Oft. tube l e n g t h i s norna l , and f o r l a r g e r u n i t s a 40 f t . tube can sometimes be u t i l i s e d .
S t e p 1 0
Determine H.P. necessary t o d r i v e u n i t s .
T h i s i s determined by a d i r e c t reading from F i g . 3 . ( p . l O ) . On t h i s c h a r t X.P, i s r e l a t e d t o approach v e l o c i t y VA.
T h i s g i v e s t h e t o t a l absorbed power inc luding l o s s e s e t c . and it needs simply t o be rounded o f f t o t h e n e a r e s t s i z e and number of motors. A s a gene ra l r u l e f a n s can be ob ta ined t o serve up t o a 21 f t . max. width of u n i t i . e . up t o a 800 sq . f t . p l o t s i ze - two motors and f a n s could j u s t 3e used. Normally above t h i s f o u r o r more f ans and motors a r e r e q u i r e d . I f t h e r e f o r e the p l o t width i s d i v i d e d by 21 and rounded up t o t h e n e a r e s t whole number t h i s g i v e s t h e number of motor bays and wi th two motors g e r bay as a minimum t h e number of motors i s obtained.
With t h e l a r g e r u n i t s and t h e r e f o r e l a r g e r t o t a l H . P . ' s manufacturers do n o t normally l i k e t o suspend a motor l a r g e r than 30 H.P. from t h e s t r u c - t u r e occas iona l ly t h i s can be extended t o 40 H.P. Above t h i s motors a r e normally r equ i red t o be mounted on concre te quadropods on t h e ground invo lv ing c o s t e t c . Therefore , a s we l l a s f i n a l i s i n g a number of motors based on a 21 f t . bay width r u l e , as a check d i v i d e the t o t a l H.P. by 30 a s t h i s w i l l sometimes g ive a f i g u r e t-ffo motors more a t l e a s t , over t h e former f i g u r e . Also from t h e p o i n t of view of c o s t and maintenance e t c . , it may be of some advantage on a ba tch of coo le r s t o s t a n d a r d i s e on i d e a l l y one, p o s s i b l y 2 motors s i z e s throughout the p lan t , and t h i s w i l l have some e f f e c t on the Nos. of motors r equ i red . However t h i s l a s t o p t i m i s a t i o n i s normally l e f t t o the Vendor 'at t he c o n t r a c t s t age , t h e f i r s t 2 c r i t e r i o s mentioned being s u f f i c i e n t f o r e s t i m a t i n g and proposal purposes i n r e s p e c t of motor numbers.
Ca lcu la t e t h e c o s t from t h e curves Fig.7 t h e c o s t of t h e u n i t from t h e known f inned s u r f a c e a r e a . The curve f o r t h e purpose; of t h i s method makes no d i s t i n c t i o n between t h e va r ious types of header box des ign , some being a l i t t l e above average o t h e r s below i n terms of c o s t . The curve i s n o t a s t r a i g h t l i n e o r a smooth curve t h i s is because of changes, w i th
- - - - - - - - - A - La. . A + +.,ha 1 a m n + k a+,,
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5 . Worked Example
'< Lean Amine Liquid Cooler
0 Amine so lu t ion cooled from - 177 F t3 1 0 0 2 Fouling f a c t o r - ,002 f t h r F/Btu Pressure drop allowed - 10 p s i Ambient Air Design temp. - 70°3 Heat Load - 5.45 x 10 6 Btu/hr
Step i
Step 2 0
Consider a s Aqueous Sol . with ,002 foul ing f t 2 h r F/Btu 2 hl = 350 Btu/ft h r OF
Step 3 From Fig 1 VA = 595 ft/min
Step 4
Step 5
A i r temp. r i s e = t2 - tl = F(T +T - 2 t l) 2 1
= 0.332 (177+100 - 2 x 70) = 0.332 (137) = 45.5 deg F
Step 6
177 100 LMTD from Fig 6 (page 11) = 44 deg F
-4ssuming a t l e a s t 2 pass tubeside R = 177-100 = 77 115.5-70 45.5
. ' . = FT from Fig. 5 (page 10) = 0.97
. ' . Corrected LNTD = .97 x 44 = 42.7 deg F
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HP = from Pig. 3 (page IO) for V = 595; power factor = 2.2/100 sq. ft. A . ' . HP = 2.2 x 993/100 = 21.8
Say 2 x 1& HP motors or 2 x 15 HP motors if 1& HP difficult to procure
Step 11
From the cost curve at 26800 sq. ft.
Price per sq. ft. 2.8/-
Cost
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M a r c h 1 9 7 0 / 0 . Table 1 - Typical Inside Tube Coefficients and Fouling Factors
Fouling up to
aaximum of:
h inside heat 1 transfer coeff. incluc?i ng fouling
LIQUID COOLERS
Water Aqueous solutions Aqueous solutions L.P.G. Light hydrocarbons C2 to C4 Hydrocarbon Yean viscosity 1 cp
- 5 10
CONDENSERS
Ammonia Me than01 Steam C2 to C4 (total) C2 to C4 (partial) C2 to C4 plus inerts (H2, N2, CH4, C5 (partial) C5 (total) Organic acid/alcohol (total) Organic acid/alcohol (partial) Cooling and condensing steam from gases with morethan 60% H2 100 psi 400 psi
L.P.G. Light hydrocarbon Light naphtha Heavy naphtha Reactor effluent Gasoline Gas Oil
,001 .0005 ,0005 ,001 .001
etc.) ,001 ,001 ,001 I .001
GAS COOLERS
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PIG. 1
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Greater Terminal Temperature Difference
N O T G F o r points not Included on thi9 sheet multiply Greater Terminal Temperature Difference and Lesser Terminal Temperature Difference by any multiple of 10 and divide resulting value of curved lines by same multtol-
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