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C O M P U T E R C A L C U L A T I O N O F T H E T H E R M A LI N S U L A T I O N O F T E C H N O L O G I C A L P I P E L I N E S

A. M. Arkha rov , A . Z . Mi rk in ,a n d T . V . K u z n e t s o v a

UDC 621.643:536.21.001.24

In the design of energy plants, chemi cal, petro leum, and other technological units a larg e amouof work is spent on the calcula tion and design of the the rm al insu lation of pipel ines. Most widely usedare calculations of the the rma l insulation based on perm iss ible heat or cold los ses, on the tem per atu rperm itte d on the surf ace of the insulation lay er, or on the given change in tem per atu re of the productpassing through the pipeline. The optimum insulation thickness 5i. opt must provide the technologicalreg ime r equir ed at a minimum of loss es due to insulation Cref:

ere f = C a ~ - E K = ,nin, (1)where Ce are exploitation costs including the costs for the creation of heat or cold, amortization de-ductions, and costs for maintenance~ E is the norm coefficient of efficiency of capital investment~ Kare capital costs for the insulation and the cover layer including the installation costs.

The capital costs inc rea se with the thickness of the insulation while the costs for t he creation ofthe heat or cold dec rea se which rep res ent the main part of the exploitation costs (Fig. 1). The mini-mum of the sum of re fe rr ed costs det ermi nes the optimum insulation thickness and the correspondi ngheat los ses . To simplify the engineering calculat ions, heat loss norms have been established bymeans of Eq. (1) which ar e ap plicab le to the the rma l insulation designs most widely used in the indus-try . The heat loss norms and consequently the insulation thick ness, other conditions being equal, itis a function of the averag e temp er at ur e of the surrounding medium, of the para met ers of the substancin the pipeline, of the geographical region , and of the heat (or cold) source .

The IZ-1 p rog ram for the calculation of the ther mal insulation of pipelines allows the calculationof the thickness, volume, and surface a rea of a sing le-la yer and two-layer insulat ion from the per missible or given tem pe rat ur e on the sur face of the ilJsulation lay er, and from the tem per atu re drop in thproduct tra nsp ort ed. This approach impro ves the design quality and reduces the labor requ ired. Thecalculated thickness of the insulation is rounded off in the prog ram to the standard thick ness, takinginto account packing of the ma ter ial .

_Single -Layer Insulat ion. The external diameter of the insulat ion for given or permis sible no r-reed heat or cold losses is obtained from the equation

9 D i n . - ~ - Q - ~1 1 De l__ m~e-V 1 ,l - - t ~ q"L't ~"~-~~ p l n ' ~ i - t - ; t 2 t , i(2)

where t and t o is the te mpe ra tur e of the product and the surrounding medium, resp ect ivel y, ~ ql ar ethe heat losses, kcal /m-h~ ai and ae is the heat t ransf er f rom the product to the inner surface of thepipe and from the su rfac e of the insulation to the surroundin g ai r, resp ect ive ly, kca l/m 2. h. dog | Di,De are the internal and exter nal diam ete rs of the pipeline, m~ Din is the external dia mete r of the in-striation, m~ Xp and hi are the ther mal conductivit ies of the pipe mate rial and the insulation, re spe c-t ively, kcal /m 9h 9deg.

Tran slat ed from Khimicheskoe i Neftyanoe Mashin ostroen ie, No. 4, pp. 8-10, April , 1979.

0009-2355/79/1504-0265S07.50 9 Plenum Publishing Corpora tion 265

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Cmf, "Ce,EK

II

6i, opt 5~

F i g . 1 . C o s t p a r a m e t e r s C r e f , C e ,a n d E K o f t h e t h e r m a l i n s u l a ti o n a sf u n c t i o n o f i t s t h i c k n e s s 6 i .

I n E q . ( 2) , t h e p l u s s i g n i n d i c a t e s h e a t l o s s e s , t h e m i n u s s i g n i n d i c a t e s c o l d l o s s e s . T h e h e a t a n d c o l dl o s s n o r m s a r e d e t e r m i n e d i n t h e p r o g r a m b y i n t e r p o l a t io n o f t a b u l a te d d a t a [ 1] .

T h e p r o g r a m e n v i s a g e s t h e a u t o m a t i c d e t e r m i n a t i o n o f h e a t a n d c o l d l o s s e s i n a c c o r d a n c e w i t h t h en o r m s f o r p e r m i s s i b l e h e a t l o s s e s , t h e t h e r m a l c o n d u c t i v i ty of t h e p i p e m a t e r i a l a n d t h e i n s u l a t i o n , t h e h e a tt r a n s f e r f r o m t h e s u r f a c e o f t h e in s u l a t i o n t o t h e s u r r o u n d i n g a i r , a n d t h e p e r m i t t e d t e m p e r a t u r e o n t h e s u r -f a c e o f t h e i n s u l a t i o n .

T h e t h e r m a l c o n d u c t i v i t y o f t h e i n s u la t i o n i s c a l c u l a t e d a s f u n c t io n o f t h e a v e r a g e t e m p e r a t u r e o f t h ei n s u l a t i o n , u s i n g t h e f o l lo w i n g e q u a t i o n

,~,. =A + Bray,1w h e r e A a n d B a r e e m p i r i c a l c o e f f i c i e n t s f o r g i v e n t y p e s o f i n s u la t i o n a n d t a v i s t h e a v e r a g e t e m p e r a t u r e o ft h e i n s u l a t io n , o b t a i n e d f r o m t h e e m p i r i c a l r e l a t i o n s h i p

t av=3,5+O,533(to--i).I n t h e c a s e o f p i p e s w i t h n e g a t i v e t e m p e r a t u r e s , t h e e f fe c t o f h y g r o s c o p i c w a t e r o n t h e t h e r m a l c o n d u c -

t i v it y i s t a k e n i n t o a c c o u n t . T h e t h e r m a l r e s i s t a n c e o f t h e c o v e r l a y e r i s in s i g n i f ic a n t a n d i s n o t t a k e n i n toa c c o u n t i n t h e c a l c u l a t i o n o f t h e t h e r m a l i n s u l a t i o n .

T h e h e a t t r a n s f e r c o e f f i c i e n t a i f r o m t h e p r o d u c t to t h e in n e r s u r f a c e o f t h e p ip e c a n b e g i v e n , w h e nn e c e s s a r y , i n t h e i n it i a l d a t a , w h i le th e h e a t t r a n s f e r f r o m t h e s u r f a c e o f t h e i n su l a t io n t o t h e s u r r o u n d i n ga i r a e i s c a l c u l a t e d in t h e p r o g r a m f r o m t h e d a t a o f S . V . K h i z h n y a k o v :

a e = ac + a r,w h e r e a c a nd a r a r e t h e h e a t t r a n s f e r c o e f f i c ie n t s o f c o n v e c t i o n a n d r a d i a t i o n , k c a l / m 2. h . d e g .

I n a n e n c l o s e d s p a c e w e h a v e f o r h o r i z o n t a l p i p e l i n e s :3 . . . .ac = 1 ,43 ] f~ -w he n A Din > 9 ,8 9 10 2

4and ac =- 1.18 V A /D in when 9,8 9 l0 -2 > A D~n> 6,5 9 10-6;3f o r v e r t i c a l p i p e l in e s a c = 1 . 5 6 4 A t : I n t h e s e e q u a t i o n s A t = t 0 - t i n w h e r e t in i s t h e t e m p e r a t u r e o n t h e s u r -

f a c e o f t h e i n s u l a t i o n .I n t h e c a s e o f p i p e l i n e s l o c a t e d i n t h e o p e n a i r , a c = 3 . 4 w ~ ~ w h e r e w i s t h e w i n d v e l o c i t y , m / s e c .T h e c o e f f i c i e n t o f r a d i a t i o n h e a t t r a n s f e r i s g i v e n b y t h e e q u a t i o n

( t o + 2 7 3 ' I 'C'L \ 100 ] - - \ lo0 / ]tin-- to

w h e r e C 1 i s th e r a d i a t i o n c o e f f i c ie n t d e t e r m i n e d i n t h e p r o g r a m a s f u n c t i o n o f t h e t y p e o f c o v e r l a y e r , k c a l /m 2 . h - d e g 4 .

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r of formal parameters wllh actual j|f

y , , . , ; 7 ; , ]

$;tO 4;S ~ j][ h2 ;J;';,;, "7 r ;';O;'J S p e c i f i e n t i e n d a e a n d c a l . ] | |eu2atien of D from a given

- J ~ e c f f i c a ~ e n ~ l ] SP .e ~ . c a ~ o _ n o i~ e a ~ , c a l" ]

iSpev2flcation of ao and so lu -~ffon of system o f egtuatiom ,D withrespec~tODinlandDln~ IIvolume, and aa-far area ~ /l e f l m u l a t ~ o n ~ - - ~ I I

L_ ~, mulati on layer . . - Jt o t h e m a ~e r im ~r a m ~ - ~" "

Fig. 2. Enlarg ed blo cks che me of the RR4A module for the calculat ion of the heatinsulation of pipelines.

The tem per atu re in ~ on the surfa ce of the insulation isqt 1 (3)tin= to ~= - - - - .%Din

The externa l dia meter of the insulation at a given tempera ture on the insulation s urface is given by theequation :

,~ I 1 D e 1 a . ~tin-- to

The heat flow throu gh the insulation is det ermi ned in this case f rom Eq. (3).The external diame ter of the insulation for a given tempera ture drop in the product is obtained from the

equationl 1 1 n)'in t b -- t___2o ~a i Di ~eDi (5)

where l is the pipe length, M is the produc t throughput, kg/ h, c is the specific heat of the produc t, kcal /kg.deg, and t b and ten d is the temp era tur e at the beginning and the end of the pipe, ~ res pec tiv ely .

The tem per atu re on the insulation surf ace is equal to

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a t t h e b e g i n n i n g o f t h e p i p eql : b . .t i . b = to + ~a0Di

a t t h e e n d o f t h e p i p eq t e n dt i , a n d =~ o + ~ae, Oi~;

w h e r e q / . b a n d q L e n d a r e t h e h e a t f l o w s a t t h e b e g i n n i n g a n d t h e e n d o f t h e p i p e , r e s p e c t i v e l y , w h i c h a r e g i v e nb y t h e e q u a t io n s

= ( t b - t o )qt b= 1 1 _D_~ . 1a i/ 91 + '~ i I n De % % D i n(tend'to)

q~e~ 1 /~n 1 ", i D i + l ~ l n - -2~ De + aeDinE q u a t i o n s ( 2) , ( 4) , a n d ( 5) a r e s o l v e d w i t h r e s p e c t t o D in b y t h e a p p r o x i m a t i o n m e t h o d o f N e w t o n , t a k i n g

D i n = 1 . 6 D e a s t h e i n i t i a l v a l u e .T w o - L a y e r i n s u la t io n . In t h e c a l c u la t io n o f t w o - l a y e r i n s u la t io n s t h e t e m p e r a t u r e t i . b a t t h e l a y e r

b o u n d a r y m u s t b e g i v e n . A t a g i v e n h e a t o r co l d l o s s th e d i a m e t e r o f t h e f i r s t i n s u l a ti o n l a y e r D i m i s o b t a i n e df r o m t h e e q u a t i o n :

t _ t l ~ + q..A _l 1 1 )9 ~ i + ' ~ i t D e 'a_~D_~ + _ ~ p ln De 1 In Di--nl

a n d t h e d i a m e t e r o f t h e s e c o n d i n s u l a t io n l a y e r D i n 2 f r o m t h e e q u a t io n

w h e r e X il a n d k i2 a r e t h e t h e r m a l c o n d u c t i v i t i e s o f t h e f i r s t a n d s e c o n d i n s u l a ti o n l a y e r .A t a g i v e n t e m p e r a t u r e t i o n t h e s u r f a c e o f t h e s e c o n d i n s u l a t i o n l a y e r t h e d i a m e t e r D i m a n d D i n 2 a r e

o b t a i n e d b y t h e s i m u l t a n e o u s s o l u t io n o f t h e f o ll o w i n g s y s t e m o f e q u a t i o n s :t--tLb_ 2 k i z ( a e _ ~ ~ D etl .b - -t i In Di_._nz + ~ In DZ

Dint+ ;

t l , b - t i = % q . r ~ i n D . . ~ 2t~ -- to 2~i2 D i n ~T h e e n l a r g e d b l o c k s c h e m e o f t h e I Z - I p r o g r a m i s s h o w n i n F i g . 2 .I t i s i n t e n d e d t o u s e t h e p r o g r a m a s a n a u t o n o m o u s p r o g r a m a n d a s a m o d u l e ( R R 4 A ) i n t h e a u t o m a t e d

s y s t e m f o r t h e d e s i g n o f p i p e l i n e s . T h e m o d u l e c o n t a i n s t h e g o v e r n i n g s u b - p r o g r a m a n d t h e s u b - p r o g r a m sf o r t h e c a l c u l a t i o n o f t h e p e r m i t t e d l o s s e s o f h e a t o r c o l d , t h e p e r m i t t e d t e m p e r a t u r e o n t h e s u r f a c e o f t h e i n -s u l a t i o n , t h e c o e f f i c i e n t a e , t h e d i a m e t e r o f t h e i n s u l a t i o n f r o m t h e p e r m i t t e d o r g i v e n h e a t l o s s e s , f r o m t h et e m p e r a t u r e o n t h e i n s u l a t i o n s u r f a c e , a n d f r o m t h e g i v e n t e m p e r a t u r e c h a n g e i n t h e p r o d u c t , a n d f o r t h e c a l -c u l a t i o n o f t h e t h i c k n e s s , v o l u m e , a n d s u r f a c e a r e a o f t h e i n s u l a t i o n .

T e n t y p e s o f c a l c u l a t i o n s a r e e n v i s a g e d i n t h e p r o g r a m :1 ) f r o m t h e p e r m i t t e d h e a t l o s s e s i n s t e a m p i p e l i n e s ( a c c o r d i n g t o n o r m s ;2 ) f r o m t h e p e r m i t t e d l o s s e s o f h e a t o r c o l d , i n o t h e r p i p e l in e s e x c e p t f o r s t e a m ( a c c o r d in g to n o r m s ) ;3 ) f r o m g i v e n h e a t o r co l d l o s s e s d i f f e r e n t f r o m t h e n o r m s ;4 ) f r o m t h e t e m p e r a t u r e o n t h e i n s u l a t io n s u r f a c e ( fo r " h o t " p ip e l i n e s t i = 5 5 - 60 ~ i n o p e n a i r a n d t i = 4 5~

i n e n c l o s e d s p a c e s ; f o r " c o l d " p i p e l i n e s t i is 5 % a b o v e th e d e w p o i n t ) ;

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5) f r o m t h e t e m p e r a t u r e o n t h e s u r f a c e o f t h e in s u l at io n w h i c h d i f f er s f r o m t h e t e m p e r a t u r e s g i v e ni n 4 ) ;

6) f r o m a g i v e n c h an g e in p r o d u c t t e m p e r a t u r e ;7 ) f r o m p e r m i t t e d h e a t l o s s e s i n s t e a m p i p e l i n e s w i t h v e r i f i c a t i o n o n t h e b a s i s o f t h e t e m p e r a t u r e o n

t h e i n s u l a t i o n s u r f a c e ;8 ) f r o m p e r m i t t e d h e a t o r c o l d l o s s e s i n p i p e l i n e s o t h e r t h a n s t e a m p i p e l i n e s ( a c c o r d i n g to n o r m s ) w i t h

v e r i f i c a t i o n o n t h e b a s i s o f t e m p e r a t u r e o n t h e i n s u la t i o n s u r f a c e ;9) f r o m g i v e n l o s s e s o f h e a t o r c o l d t h a t d i f f e r f r o m t h e n o r m w i t h v e r i f i c a t i o n o n t h e b a s i s o f t h e t e m -

p e r a t u r e o n t h e i n s u l a ti o n s u r f a c e ;1 0) f r o m a g i v e n c h a n g e in p r o d u c t t e m p e r a t u r e w i t h v e r i f i c a t i o n o n t h e b a s i s o f t h e t e m p e r a t u r e o n t h e

i n s u l a t i o n s u r f a c e .T h e i n f o r m a t i o n s t o r e o f t h e p r o g r a m c o n ta i n s n o r m s f o r h e a t a n d c o l d l o s s e s , t e m p e r a t u r e d r o p s (t o

- - t i) f o r l o w - t e m p e r a t u r e p i p e l i n e s , t h e c h a r a c t e r i s t i c s o f t w o t y p e s o f p i p e m a t e r i a l s ( s te e l a n d a l u m i n u m ) ,3 6 t y p e s o f i n s u l a t i o n , a n d 10 t y p e s o f c o v e r l a y e r s . T h e p r o g r a m i s w r i t t e n in F O R T R A N - 4 a n d o c c u p i e s 8 2c b ( oc tu p le ) o f m e m o r y . T h e t i m e r e q u i r e d f o r th e c a l c u l a ti o n o f o n e e x a m p l e o n a n I C L - 4 c o m p u t e r i s l e s st h a n 0 . 1 s e c .

1 .L I T E R A T U R E C I T E D

S . V . K h i z h n y a k o v , P r a c t i c a l C a l c u l a t i o n o f T h e r m a l I n s u l a ti o n [in R u s s i a n ] , l ~ n e r g iy a , M o s c o w ( 19 64 )

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