Coker A.K. Fortran Programs for Chemical Process Design, Analysis, and Simulation

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CHANNEL

AND REMOVABLE COVER

"_l

SPECIAL HIGH PRESSURE CLOSURE

FRONT END

STATIONARY HEAD TYPI~

BONNET (Ih"I'EGRAL COVER)

o.= _~1.1C4_

CHANNEL INTEGRAL WITH TUBE-

SHEET AND REMOVABLE COVER

CHANNEL INTEGRAL WITH TUBE-

5J-IEET AND REMOVABLE COVER

SHELL TYPES

ONE PASS SHELL

Two PASS SHELL

WITH LONGITUDINAL BAFFLE

SPLIT FLOW

~1 ~ T

-I~

.k .1_

DOUBLE SPLIT FLOW

DIVIDED

FLOW

KETTLE TYPE REBOILER

•

CROSS FLOW'

RI~R END

HEAD TY PF.S

FIXED TUBESHEET

UKE "A ~ STATIONARY HEAD

FIXED TUBESHEET

LIKE "B" STATIONARY HEAD

f.'•-'l•.l

FIXED TUBESHEET

LIKE *"I,4" STATIONARY HEAD

OUTSIDE PACKED FLOATING HEAD

FLOATING HEAD

WITH BACKING DEVICE

-- .... ~,., o

PULL THROUGH FLOATING HEAD

U.TUBE BUNDLE

. i!

EXTERNALLY SEALED

FLOATING TUBESHEET

Figure 8-2. Tubular Exchanger Manufacturers Association (TEMA) classification and

terminology for heat exchangers. TEMA heat exchanger head types.

597

Figure 8-3. LMTD correction factor 9 1978 Tubular Exchanger Manufacturers Association.

598

Figure 8-4. LMTD correction factor.

599

Figure 8-5. LMTD correction factor.

600

Figure 8-6. LMTD correction factor.

601

602

Fortran Programs for Chemical Process Design

(text continued from page 596)

and

At 2 = the smaller terminal temperature difference,

T 2

-tl

For co-current flow

Atj = T I - t~

and

At 2 =

-t2

The equations used to calculate F are based on the following assumptions:

9 The overall heat transfer coefficient, U, is constant through the heat

exchanger.

9 The rate of flow of each fluid is constant.

9 The specific heat of each fluid is constant.

9 There is no condensation of vapor or boiling of liquid in that part

of the exchanger considered.

9 Heat losses are negligible.

9 There is equal heat transfer surface in each pass.

9 The temperature of the shell side fluid in any shell side pass is

uniform over any cross section.

Figure 8-7 shows typical temperature profiles of two fluids in true coun-

tercurrent flow through a 1-1 exchanger.

= t 2 --

t~ (8-6)

T~ - tj

R - TI - T2 (8-7)

t 2 -

For an exchanger with N shell passes, Bowman

et al.

[2] developed a

general solution for the correction factor,

(

~R 2 + 1)ln<

R-1

(1- Px) }

(1-

RPx)

F - (8-8)

+ +l}

(2/Px)-l-R-~2 +1

Heat Transfer 603

Temperature

Inlet T 1

' 2At 2

Outlet ~ Inlet

Cold Fluid

Tube length

Cold fluid in,

-[tl,.

Hot fluid in,

9 I I

I I

t 2

T 2

Figure

8-7. Counter-current flow in a 1-1 exchanger.

where

1-I RP- 1] ~/N

p = P- 1 (8-9)

R-I RP-P-111'/N

N is the total number of shell passes, that is, the product of shell passes

per shell and the number of units in series. Solving for N by repetitive

trial and error with a minimum desired F, the minimum required num-

ber of shell passes can be determined.

If R = 1, Equation 8-9 becomes indeterminate, which reduces to

P~ = (8-10)

(N- NP + P)

Equation 8-8 then becomes

604

Fortran Programs for Chemical Process Design

F m

Px~/R 2 +1

1 -- Px

ln{(2/P~)- 1- R + ~/R2 +1}

(2/P~)- 1- R- CR 2 +1

(8-11)

The corrected mean temperature difference (CMTD) becomes

CMTD - (F)(LMTD)

(8-12)

Nomenclature

F- correction factor

LMTD - log mean temperature difference,~

N - number of series exchanger shells required

T~ - hot fluid inlet temperature, ~

T 2 - hot fluid outlet temperature, ~

t~ - cold fluid inlet temperature, ~

t 2 - cold fluid outlet temperature, ~

Shell and Tube Heat Exchanger Design

The various designs of heat exchangers are well illustrated in stan-

dard texts and in the literature [3,4,5,6,7,8,9]. Recently, Pooley

et al.

[ 10] developed algorithms for both shell and tube exchangers and com-

pact exchangers. Their algorithms rely on the allowable pressure drops

of both of the streams being contacted.

The rating of an exchanger involves using the equations to calculate

the suitability of an existing exchanger for given process conditions.

The following steps are used for rating a shell and tube exchanger where

there is no phase of change. The process conditions required are

Hot fluid"

T~,

T2, W, C, s, ~

Rd, AP

Cold fluid: t~, t 2, w, c, s, ~ k, R d, AP

The data required are

SHELL SIDE

Baffle space

passes

TUBE SIDE

Number and length

ID, OD, B WG, and pitch

passes

Heat Transfer 605

From the process conditions, the heat load, Q, is

(1) Q - WC(T,

- T2) - wc(t 2 -

t,)

(8-13)

(2) The true temperature difference, At (assuming a number of tube

passes) is"

LMTD - (T, - t 2 )

(T 2 - t I )

Approach factor, F c, is determined from

= t 2 -

t~ (8-6)

- t I

- Tl -- T2

(8-7)

t 2 - t I

and Figures 8-3 to 8-6. Alternatively, F c can be calculated from Equa-

tion 8-8 and Equation 8-11.

(3) At - (LMTD)(F c)

(8-15)

Tube Side

(4) Flow area a t, ft2:

a t ~--

( no. of tubes)( flow area/tube)

no. of pases

N t a'

9 t

144n

ft 2

(8-16)

(5) Mass velocity, G t, is

G~-W( lb )- , (8-17)

a t

ft 2 . hr

(6) Reynolds number, Re t, is

Re t = (ID/12). G t (8-18)

606

Fortran Programs for Chemical Process Design

where

~t-2.42xcP(fl.lb )hr.

(7) Prandtl number, Pq, is

Pr t = clLt (8-19)

(8) The heat transfer coefficient, h~, for viscous flow (Re t < 2100) as

given by Sieder and Tate's correlation [ 11 ]:

/ /'/3/ 'J3/ )0'4

h~.ID = 1.86 ID.G cg ID g

k g --k -L ~-w (8-20)

where Nu = Nusselt number = h~.ID/k

ID = inside tube diameter, ft

Equation 8-20 can be expressed as:

h i . ID

io 033/ / 0.,4

= 1.86 Re~ 33 Pr~ 33 -L- ~ww

(8-21)

For turbulent flow (Re t > 10,000), h i, can be expressed as:

h i . ID

3o.8 )o.33 )o.

- C( ID.~t. Gt ("-k--ClLt (~w~ 14

(8-22)

where C = 0.021 for gases

C = 0.023 for n0n-viscous liquids

C = 0.027 for viscous liquids

For applications in turbulent flow, the viscosity ratio can be omitted,

and Equation 8-22 reduces to:

12)

0.8 prO.33

h~-C.k i-D Re~

(8-23)

for

0.7 < Pr~ < 17,000