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

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WRITE (*, 140)

FORMAT (80(IH-55

DO 10 I=I,NUM

WRITE (*, 150) I,F(I),ALPHA(I),PERD(I),MD(I),PERB(I),MB(I)

FORMAT(3X,I2,7X,F9.4,3X,F9.4,3X,F9.4,2X,F9.4,3X,F9.4,2X,F9.4)

CONTINUE

WRITE (*, 1605

FORMAT (80(IH-))

WRITE (*, 170) K1

FORMAT(3X,'THE HEAVY KEY COMPONENT NUMBER IS:',T60,I2)

WRITE (*, 180) RECLK

FORMAT(3X,'PERCENTAGE RECOVERY OF THE LIGHT KEY COMPONENT',/,

* 3X,'IN THE DISTILLATE IS (%):',T60,F7.2)

WRITE (*, 190) RECHK

FORMAT(3X,'PERCENTAGE RECOVERY OF THE HEAVY KEY COMPONENT',/,

3X,'IN THE BOTTOMS IS (%):',T60,F7.25

WRITE (*, 200) AMIN

FORMAT(3X,'MINIMUM NUMBER OF STAGES IS:',T60,F9.1)

WRITE (*, 210) SUM1, SUM2

FORMAT(~X,'TOTAL MOLES IN THE DISTILLATE IS:',T60,F9.4,/,

3X,'TOTAL MOLES IN THE BOTTOMS IS:',T60,F9.45

WRITE (*, 2205 THETA

FORMAT(3X,'UNDERWOOD CONSTANT:',T60,F9.4)

WRITE (*, 230) MREF

FORMAT(3X,'MINIMUM REFLUX RATIO:',T60,F9.45

WRITE (*, 240) REF

FORMAT(3X,'ACTUAL REFLUX RATIO:',T60,F9.4)

WRITE (*, 250) NUM1

FORMAT(3X,'NUMBER OF THEORETICAL PLATES IN THE COLUMN:',T60,F9.1)

WRITE (*, 2605 FEED

FORMAT(3X,'THE POSITION OF THE FEED PLATE IS:',T60,F4.1)

WRITE (*, 270)

FORMAT (IH ,80(IH-))

OPEN (UNIT=l, FILE='LPTI')

CALL PAPER (NUM,F,ALPHA,PERD,MD,PERB,MB,KI,RECLK,RECHK,AMIN,

* SUMI,SUM2,MREF,REF,NUMI)

CLOSE (i)

RETURN

END

*************************************************************

THIS PROGRAM PRINTS THE RESULTS ONTO A PRINTER

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SUBROUTINE PAPER(NUM,F,ALPHA,PERD,MD,PERB,MB,K1,RECLK,RECHK,

* AMIN,SUM1,SUM2,MREF,REF,NUM1)

DIMENSION F(20), ALPHA(20), PERD(20), PERB(20)

REAL MD(20), MB(20), MREF, NUMI

COMMON/DATA2/THETA, FEED

WRITE (1, 280)

FORMAT (///,25X,'MULTICOMPONENT SYSTEM FRACTIONATION',/,1H ,

* 80(1H*))

WRITE (I, 290)

FORMAT (/, 1X,'COMPONENT',7X,'FEED',5X,'REL VOLATILITY', 3X,

* 'DISTILLATE ', 8X, 'BOTTOMS ')

WRITE (1, 300)

FORMAT (1X,'NUMBER',9X,'MOLES',7X,'ALPHA',IOX,'%',8X,'MOLES',8X,

* '%',6X,'MOLES')

WRITE (1, 310)

FORMAT (80(1H-))

DO i0 1 = i ,NUM

WRITE (I, 320) I, F(I), ALPHA(I), PERD(I), MD(I), PERB(I), MB(I)

FORMAT (3X,I2,7X,F9.4,3X,F9.4,3X,F9.4,2X,F9.4,3X,F9.4,2X,F9.4)

CONTINUE

WRITE (i, 330)

FORMAT (80(IH-))

WRITE (i, 340) K1

FORMAT (3X,'THE HEAVY KEY COMPONENT NUMBER:', T60, I2)

WRITE (i, 350) RECLK

FORMAT (3X,'PERCENTAGE RECOVERY OF THE LIGHT KEY COMPONENT',/,

* 3X,'IN THE DISTILLATE (%):', T60, F7.2)

WRITE (i, 360) RECHK

FORMAT (3X,'PERCENTAGE RECOVERY OF THE HEAVY KEY COMPONENT',/,

* 3X,'IN THE BOTTOMS (%):', T60, F7.2)

WRITE (I, 370) AMIN

FORMAT (3X,'MINIMUM NUMBER OF STAGES:', T60, F9.1)

WRITE (I, 380) SUM1, SUM2

FORMAT (3X,'TOTAL MOLES IN THE DISTILLATE:', T60, F9.4,/,

* 3X,'TOTAL MOLES IN THE BOTTOMS:', T60, F9.4)

WRITE (i, 3907 THETA

FORMAT (3X,'UNDERWOOD CONSTANT:', T60, F9.4)

WRITE (i, 400) MREF

FORMAT (3X,'MINIMUM REFLUX RATIO:', T60, F9.4)

WRITE (1, 410) REF

588

410 FORMAT (3X,'ACTUAL REFLUX RATIO:', T60, F9.4)

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WRITE (i, 420) NUMI

FORMAT (3X,'NUMBER OF THEORETICAL PLATES IN THE COLUMN:'

F9.1)

WRITE (1, 430) FEED

FORMAT (3X,'THE POSITION OF THE FEED PLATE:', T60, F9.1)

WRITE (I, 440)

FORMAT ( 80 ( IH- ) )

FORM FEED THE PRINTING PAPER TOTHE TOP OF NEXT PAGE.

WRITE (i, *) CHAR(12)

RETURN

END

, T60,

589

CHAPTER 8

Heat Transfer

INTRODUCTION

The increasing cost of energy in recent years has resulted in increased

attention to conservation and efficient energy management. Other types

of technology, for example, pinch technology, have been employed in

the energy integration of process plants and of heat exchangers in par-

ticular. This has often resulted in an improved performance of the plants

at reduced operational costs. Various types of forced convective heat

transfer equipment are used in the chemical process industries. These

range from the simple shell and tube exchangers, double pipe, finned

tube and tubular air cooled exchangers to the plate types, spiral and

compact heat exchangers. Table 8-1 lists the major types of heat

exchanger [ 1 ].

BASIC THEORY

Heat is transferred from points of high temperature to points of lower

temperature by direct contact of particles of matter or the emission and

absorption of radiant energy. The three classifications of heat transfer are:

Conduction.

The transfer of heat from one body to another by physi-

cal contact. The rate of heat flow by conduction is proportional to the

area available for the heat transfer and the temperature gradient in the

direction of the heat flow path. The rate of heat flow in a given direction

can be expressed as:

dQ = -kA dT (8-1)

dO dx

590

Table 8-1

Summary of Types of Heat Exchangers

Type

Major Characteristics

Application

Shell and tube

Air cooled

heat exchanger

Double pipe

Extended

surface

Brazed plate

fin

Spiral wound

Bundle of tubes encased

in a cylindrical shell.

Rectangular tube bundles

mounted on frame, with air

used as the cooling medium

Pipe within a pipe; inner

pipe may be finned or plain.

Externally finned tube.

Series of plates separated

by corrugated fins.

Spirally wound tube coils

within a shell

Always the first type

exchanger to consider.

Economic where cost of

cooling water is high.

For small units.

Services where the outside

tube resistance is appreciably

greater than the inside

resistance. Also used in

debottlenecking existing units.

Cryogenic services: all fluids

must be clean.

Cryogenic services: fluids

must be clean.

Scrapped

surface

Bayonet tube

Falling film

coolers

Pipe within a pipe, with

rotating blades scraping the

inside walls of the inner pipe.

Tube element consists of

an outer and inner tube.

Vertical units using a thin

film of water in tubes.

Crystallization cooling

applications.

Useful for high temperature

difference between shell and

tube fluids.

Special cooling applications.

Barometric

condenser

Cascade

coolers

Impervious

graphite

Direct contact of water

and vapor.

Cooling water flows over

series of tubes.

Constructed of graphite

for corrosion protection.

Where mutual solubilities of

water and process fluid permit.

Special cooling applications for

very corrosive process fluids.

Used in very highly corrosive

heat exchange services.

Source: Cheremisinoff [1]

591

592

Fortran Programs for Chemical Process Design

where Q = amount of heat transferred in time O hr, Btu

k = the thermal conductivity, or proportionality constant,

B tu/(hr) (ft2)( ~ F/ft)

A = area of heat transfer perpendicular to direction of heat

flOW, ft 2

T = temperature, ~

x = length of conduction path in direction of heat flow, ft

Convection. The transfer of heat by the mixing or movements of

fluids or fluids with a solid. Mixing may occur as a result of density

difference alone, as in natural convection. Alternatively, mechanically

induced agitation may produce forced convection, as in turbulent flow

in a heat exchanger tube, or to the heat transfer fluid in the jacket of an

agitated vessel. The rate of heat transfer is:

= hAAt (8-2)

where h = the heat transfer coefficient or the proportionality constant,

which is a function of the type of agitation, the degree of

turbulence, and the nature of the fluid. For the steady state

condition, Equation 8-2 becomes

q- hAAt (8-3)

Radiation. The transfer of heat by the absorption of radiant energy,

transformed into heat in surrounding bodies. The rate at which radiant

heat energy is emitted from a source is:

= (ysAT 4 (8-4)

where (s- Stefan-Boltzmann constant

= 0.1713 x 10 -8 B tu/hrftZ(~

- emissivity of surface

A - exposed surface area of heat transfer, ft 2

T- absolute temperature, ~

The most common applications of heat transfer are a combination of

one or more of these classifications. Also in many processes where a

phase change occurs, that is, condensation, boiling, and evaporation,

other physical phenomena play an important role in limiting the achiev-

able heat transfer rate. However, only the most common, forced

Heat Transfer 593

convective heat transfer, is considered here as well as an illustration of

conductive heat transfer.

The procedures for the design of heat exchangers vary with the type

of problem, but are often repetitive and tedious. An increasing number

of software packages have been developed, for example, Heat Transfer

and Fluid Flow Services (HTFS) and Heat Transfer Research Inc.

(HTRI). These programs are available to the member companies. Two

procedures are used in the design of heat exchangers. They are the rat-

ing method and the optimization design method.

The Rating Method

In the rating method, the designer assumes the form of an exchanger

and then develops computations to determine whether the exchanger

could handle the process requirements under known conditions. If the

exchanger does not satisfy the requirements, a different exchanger is

assumed, and the calculations repeated until a satisfactory design is

obtained. For an example, for any given set of process requirements,

the designer could assume an exchanger constructed of specific materi-

als and having a known tube size, number of tubes, tube spacing, and

passes, a shell size, baffling and number of passes (other more detailed

assumptions such as removable bundle and floating head arrangements

and end constructions). In addition, there are six process variables:

9 inlet temperature of hot stream

9 outlet temperature of hot stream

9 inlet temperature of cold stream

9 outlet temperature of hot stream

9 flow rate of hot stream

9 flow rate of cold stream

The designer will proceed by checking whether the energy balance cal-

culations between the fluids are consistent. If there is a large deviation

(for example 10%), the hot fluid duty is used for the design calcula-

tions. Further calculations could be the required heat transfer area,

lengths, pressure drops on either side (AP), and an overall heat transfer

coefficient. Repeated trials may be required to achieve an accurate overall

heat transfer coefficient. If the results of the final design show that

(allowing for any accumulations of scale during service between clean-

ing) the assumed exchanger is of reasonable dimensions, of a low cost,

and will create acceptable pressure drops, the equipment is considered

adequate for the duty.

594

Fortran Programs for Chemical Process Design

Optimization Design Method

This approach is based upon optimum economic conditions. By choos-

ing various conditions, the designer can arrive at a final design giving

the least total cost for fixed charges and operation. Any increase in the

fluid velocity on either side may result in a larger heat transfer coeffi-

cient, and consequently require a smaller heat transfer area and exchanger

cost for a given rate of heat transfer. However, increased fluid velocity

will result in a greater pressure drop and pumping costs. The optimum

economic design occurs at the conditions where the total cost is at a

minimum. This method minimizes the sum of the variable annual costs

for the exchanger and its operation.

In general, the design of a heat exchanger involves the following steps:

1. Determine the flow rates and the rate of heat transfer required for

given conditions.

2. Decide on the type of heat exchanger (e.g., 1:1, 1:2 type, or 2:4

type) to be used. Assume permissible scale factors and show the

basic equipment specifications.

3. Calculate the fluid velocities of the film coefficients and the over-

all heat transfer coefficient.

4. Calculate the mean temperature difference driving force.

5. Determine the required area of heat transfer and the exchanger

dimensions.

6. Evaluate the results to see that all dimensions, costs, APs, and

other design parameters are satisfactory.

7. If the results in Step 6 show that the exchanger is not satisfactory,

the specifications given in Step 2 are inadequate. Choose new

specifications and repeat Steps 3 through 7 until a satisfactory

design is achieved.

This chapter presents rating calculations for the shell and tube heat

exchanger, procedures for the design of double pipe or longitudinal finned

tube heat exchanger, air cooler, heat tracer requirements for pipelines,

and heat transfer in batch reactors.

LMTD IN SHELL AND TUBE HEAT EXCHANGERS

In a shell and tube heat exchanger, the rate of heat transfer from the

hot to the cold fluid is directly proportional to the temperature differ-

ence between the two fluids. For the rating of heat exchangers, it is

Heat Transfer 595

important to determine the mean temperature difference based on the

hot and cold fluids' inlet and outlet temperatures. The heat transfer pro-

cess is generally more efficient where there is countercurrent flow com-

pared to co-current flow. The relative direction of the fluids affects the

value of the log mean temperature difference (LMTD). A further

advantage of approaching countercurrent flow, except where one fluid

is isothermal (that is, constant temperature) is that in co-current flow,

the hot fluid cannot be cooled below the cold fluid outlet temperature,

so the ability to recover heat is limited. There are a few cases where

co-current flow is preferred. For example, when cooling a viscous fluid,

a higher heat transfer coefficient may be obtained by a rapid initial

reduction in viscosity. Co-current may also be favorable if the tempera-

ture of the warmer fluid could otherwise be reduced to its freezing point.

In the majority of industrial operations, higher velocities, shorter tubes,

and a more economical exchanger can be achieved with a multipass

flow design as shown in Figure 8-1. The flow pattern is however part

countercurrent and part co-current. Therefore, the mean temperature

difference lies between the countercurrent and co-current log mean tem-

perature differences (LMTD). The mean temperature differences for the

Shell inlet

7"1

....... s "1

.... ~.="

1',,

7"2 Tube inlet

Figure 8-1. Flow patterns in a multipass exchanger (1:2 floating head as shown).

596

Fortran Programs for Chemical Process Design

various types of crossflow exchanger are also less than for countercur-

rent flow designs, but greater than for co-current flow. In addition, the

relationships between terminal temperatures and mean temperature dif-

ference restrict the performance of each type of exchanger. A correction

factor, F, is defined to convert the LMTD to the corrected mean tem-

perature difference (CMTD). For true countercurrent flow, F = 1, and as

more co-current flow is introduced, the factor is reduced and the effi-

ciency of the exchanger drops. A low value of F requires a large surface

requirement for a given heat load. Performance can be enhanced by

using several shells in series or by increasing the number of passes in

the same shell. The lower limit of practical efficiency is in the range

F = 0.75 to 0.8. The lowest F value is for one shell when rating shell and

tube exchangers in series. This value is raised as the number of shells

increases, and the flow more nearly resembles countercurrent flow.

For the design of shell and tube exchangers, the minimum number of

shells that will raise the F value above the chosen minimum of 0.75 to

0.8 is calculated.

Here, a computer program is written by setting the minimum correc-

tion factor to 0.75. The program automatically increases the number of

shells until the value of F exceeds 0.75 or some other preset value.

Bowman

et al.

[2] simplified the calculations required to determine

the mean temperature difference in a shell and tube exchanger. Figure

8-2 shows some of the major types of the shell and tube heat exchanger

construction, and Figures 8-3 to 8-6 illustrate correction factor plots for

various shell and tube exchangers. The equations given by Bowman

et al.

[2] are used to determine the corrected LMTD.

Heat Exchanger Design

The thermal rating of heat exchanger equipment requires the compu-

tation of the LMTD between the shell and tube fluids' temperatures.

This is defined by

LMTD - At~ - At 2 (8-5)

In(

Atj

where for countercurrent flow

Atl = the larger terminal temperature difference, T 1

- t 2

(text continued on page 602)