CAD of a Multi-ComponentCondenser

Computer Aided Design (CAD) of a Multi-component Condenser

S. Bandyopadhyay, M. S. Alam, V. K. Agrawal, and K. L. Wasewar*Chemical Engineering Department, Indian Institute of Technology,Roorkee – 247667 India, Tel.: +91-1332-285347, Fax: +91-1332-276535,Email: [email protected], [email protected]

In the case of multi-component condensation the ‘condensing vapour contains amixture of components having different boiling points, which condense over a wide tem-perature range, either in presence of or absence of non-condensing material. In this work,a design algorithm for the condensation of a multi-component vapour mixture in shellside of a shell and tube vertical condenser has been developed using Bell and Ghaly’smethod. Based on this algorithm, an in-house computer code has been developed. Thiscode was used for the design of the condenser for the condensation of a hydrocarbonvapour mixture containing propane, butane, hexane, heptane and octane in the molecomposition of 0.15, 0.25, 0.05, 0.30 and 0.25, respectively. A code was also developedfor the Kern’s method for the condenser design. It was found that Kern’s method pro-vides a lesser heat transfer area because Kern’s method does not consider the mass trans-fer resistance, nor does it take care of handling the sensible heat transfer during conden-sation. These facts have been incorporated in Bell and Ghaly’s method by taking theone-phase heat transfer coefficient during vapour sensible heat transfer. The effects ofoperating variables viz. vapour flow rate, coolant flow rate, vapour inlet temperature,and coolant inlet temperature on the overall heat transfer coefficient, and shell side pres-sure drop have been studied for the wide range of parameters. The results are useful forthe design of multi-component condensation.

Key words:CAD, multi-component condensation, design

Introduction

A condenser is a device in which the heat re-moved in the process of converting a vapour to liq-uid is transferred to a coolant. An indirect or sur-face condenser has a thin wall separating the cool-ant from the vapour and its condensate; the heatpasses through this wall. The surface used in indi-rect condensers may be plates or tubes and thesesurfaces can be plain, extended with fins, enhancedby passive or active augmentation techniques. Thephysical arrangement of the surfaces can take manyforms and affects the two-phase flow patterns of thevapour-condensate mixture and the flow pattern ofthe coolant, thus influencing the heat transfer rates.The shell side condensation plays an important rolein a variety of engineering applications includingelectric power, refrigeration, and chemical processindustries. Nowadays, significant insight has beengained into the two-phase flow pattern and heattransfer phenomenon that occurs on the shell sideof a surface condenser.

In the case of multi-component condensation,the ‘condensing vapour’ contains a mixture of com-ponents having different boiling points, which con-

dense over a wide temperature range, either in pres-ence or absence of non-condensing material. Thethree words ‘multi-component vapour mixture’cover a wide range of situations. One limit of thisrange is one in which all components have boilingpoints above maximum coolant temperature; in thiscase the mixture can be totally condensed. Theother limit is a mixture in which at least one com-ponent in the initial vapour stream has a boilingpoint lower than the minimum coolant temperatureand, also is negligibly soluble in the liquid conden-sate formed from the other components and hencecannot be condensed at all. An intermediate case istypified by a mixture of light hydrocarbons in whichthe lightest members often cannot be condensed aspure components at the temperature encountered inthe condenser, but instead will dissolve in theheavier components. In each of these cases, thevapour mixture may form partially or completelyimmiscible condensate.

Existing methods for designing heat exchangersto condense multi-component mixtures can broadlybe classified into two basic methods: equilibriummethods, such as those proposed by Kern,1 and Belland Ghaly2 and the differential or non-equilibriummethods that have been developed following thework of Colburn and Drew.3 Colburn and Hougen4

S. BANDYOPADHYAY et al., Computer Aided Design (CAD) of a Multi-component …, Chem. Biochem. Eng. Q. 21 (2) 97–103 (2007) 97

*Corresponding author

Original scientific paperReceived: June 6, 2006

Accepted: November 27, 2006

and later Colburn and Edison5 formulated in fairlyrigorous form the equations and design procedurefor condensation of a pure component from a com-pletely insoluble gas in either co-current or coun-ter-current flow.

Kern1 proposed a general-purpose designmethod based on the equilibrium model. He sug-gested how to employ the nonlinear condensationtemperature curve instead of the log mean tempera-ture difference but did not discuss how to handlea multipass coolant quantitatively. Bell and Ghaly2

proposed an approximate generalized designmethod based on the equilibrium method formulti-component partial condensers. They compen-sated the error introduced by neglecting the masstransfer resistance by overestimating the heat trans-fer resistance. After Bell and Ghaly2 a little workhas been done on the equilibrium model. To designa condenser using film theory methods requires cal-culations of the local heat and mass transfer ratesand integrating these local rates over the condenserlength using differential mass and energy balances.This was proposed by Krishna and Panchal.6

In this paper, an in-house CAD algorithm of amulti-component condenser based on the equilib-rium model has been developed to investigate theeffects of operating variables viz. vapour flow rate,coolant flow rate, vapour inlet temperature andcoolant inlet temperature on the weighted meantemperature difference, the heat transfer area, over-all heat transfer coefficient, and shell side pressuredrop of condenser.

Multi-component condenser design

To design a multi-component condenser, onerequires a suitable method to evaluate the overallheat transfer coefficient, which is useful for deter-mining the heat transfer area. Evaluation of theoverall heat transfer coefficient needs suitable equa-tions to predict the heat transfer rates i. e. heattransfer coefficients. In this paper, the equilibriummethod proposed by Bell and Ghaly2 was consid-ered for predicting the surface area required for heattransfer because of its robustness, speed, and reli-ability. Condensation at shell side, in a vertical shelland tube heat exchanger was considered because ofits large industrial practices and suitability towardsthe equilibrium method. For the tube arrangement,square, triangular and rotated square layouts wereconsidered. Multi-component condensation takesplace over a wide temperature range – from dew tobubble point. Therefore, it is necessary to determinethe dew and bubble points before starting designcalculations.

Assumptions

The design method is based on the followingassumptions:

1. The liquid and vapour compositions are inequilibrium at the vapour bulk temperature.

2. Liquid and vapour enthalpies are those ofthe equilibrium phases at the vapour bulk tempera-ture.

3. The sensible heat of the vapour is transferredfrom the bulk vapour to the vapour-liquid interfaceby a convective heat transfer process. The heattransfer coefficient is calculated from a correlationfor the geometry involved, assuming only thevapour phase is present and using physical proper-ties of vapour and local vapour flow rate.

4. The total latent heat of condensation andsensible heat of the cooling condensate are trans-ferred through the entire thickness of the liquidfilm.

Dew and bubble point temperature

The dew point of vapour corresponds with theonset of condensation and the bubble point will cor-respond with total condensation. At any tempera-ture intermediate to the dew and bubble point, thecompositions of the equilibrium liquid xi and yi canbe determined by vapour liquid equilibrium consid-eration.

At dew point

x ii

n

�

� �1

1 (1)

At bubble point

y ii

n

�

� �1

1 (2)

At any intermediate temperature, the vapourfraction must satisfy the following equation:

Z y xi i iF, ( )� � �1 � (3)

where ZF,I is the vapour feed composition.From eq. (3) the following equations are ob-

tained for calculating the vapour and liquid mix-ture’s composition.

xZ

Kii

i

��

F,

( )1 1�(4)

and

xK Z

Kii i

i

��

F,

( )1 1�(5)

98 S. BANDYOPADHYAY et al., Computer Aided Design (CAD) of a Multi-component …, Chem. Biochem. Eng. Q. 21 (2) 97–103 (2007)

The shell-side heat-transfer coefficient was ob-tained from the correlation taken from the HeatExchanger Design Handbook7 while the pressuredrop was obtained from the Martinelli equation.8

The tube-side heat-transfer coefficient was obtainedfrom the correlation given by Kutaleladze andBorishanskii9 and pressure drop from the correla-tion taken from Coulson and Richardson.10

Heat transfer area

The basic equation for calculation of the heattransfer area is

� �T m o m�U A T (6)

where, Um is the mean overall heat transfer coeffi-cient, Ao is the total heat exchanger area, and �Tm isthe mean temperature difference between the hotand the cold fluid stream.

The nature of the heat release curve inmulti-component condensation is not linear. There-fore, it is unrealistic to take the mean temperaturedifference and mean overall heat-transfer coeffi-cient over the whole exchanger. Here, the calcula-tion was carried out at each point and then the re-sults were integrated to obtain the total exchangerarea. During condensation, there are three types ofheat loads to be accounted for total heat load. Theseare latent heat load, liquid sensible heat load, andvapour sensible heat load.

d

d

d d

dT

o

sv p

om p c

� � �

A AU T T�

�� ( ) (7)

where,

UA

h AR

A

A

x

k AR

hi

mo

i idi

o w

w ido

o

d

d

d

d d

��

11

where subscript ‘i’ and ‘o’ stand for the inside andoutside of the tube, respectively.

The heat flux for the sensible heat removalfrom the vapour to the vapour-liquid interface isgiven as follows:

d

dsw

osw v l

�

Ah T T� �( ) (8)

Substitution of Tl from eq. (8) into eq. (7)gives:

d dT

m v c

o

m

m

�

U T T

AZU

h( )�

��1

(9)

where, Z�d

dsv

T

�

�

Integration yields the following equation:

d do

m

sv

m vT

o T

A

ZU

h

U T T

A

0 0

1

� ��

�

�

��

�

��

( )

�

� (10)

The overall heat transfer coefficient formulti-component condensation Umc is calculated bythe following equation:

1 1

U U

Z

hmc m sv

� � (11)

If the assumptions are taken that Um and hsv de-pend only upon the local vapour side condition, thegeneralized design equation for the multipass canbe written as follows

A

ZU

h

U T T T To

m

sv

m v m

T d�

�

�

��

�

��

��

1

0 ( ) ( )

� �(12)

where, TT

Nk

N

mck

tp

tp

��

�1

The term ( )T T� m within the integration limitis the mean temperature between the hot vapour andthe coolant at any position. The integration is car-ried out numerically and the zones are insufficientlysmall, hence the logarithmic temperature differenceat each interval was taken.

Results and discussion

The upper and lower limits of the operatingvariables used are given in Tab. 1. The value of a setof operating and geometrical variables and outputvariables are given in Tab. 2. A logical structure andflow chart based on the algorithm used for the designof the condenser are shown in Fig. 1(a) and 1(b).

The surface area of the condenser calculated forvarious cumulative heat load for condensation of hy-drocarbon vapours using Kern’s and Bell and Ghay’s


T a b l e 1 – Range of variables

VariableVapourflow rateqm/kg s–1

Vapour inlettemperatureTi/K

Coolantflow rateqm/kg s–1

Coolant inlettemperatureTc/K

range 8 – 18 430 – 480 150 – 600 287 – 308

methods are shown in Fig. 2. Fig. 2 reveals thatKern’s method under design the multi-componentcondenser. Both the methods give the same area forsuperheating and subcooling zone but differ duringcondensation. This is because during multi-compo-nent condensation not only is there heat transfer


T a b l e 2 – Set values of operating, geometrical, and outputvariables for the condensation of hydrocarbonvapour mixture

Variable Value

Operating variables:coolant flow rate, qma/kg s–1 12.00vapour inlet temperature, Ti,v/K 430.00vapour outlet temperature, To,v/K 320.00coolant inlet temperature, Tc/K 293.00coolant flow rate, qmc/kg s–1 298.00pressure, p/kPa 506.66

Geometrical variables:tube outer diameter, do/mm 25.4tube inside diameter, di/mm 19.86length of tube, l/m 2.348

pitch arrangementEquilateral

triangular pitchpitch 1.25donumber of tubes, N 2

baffle type25% cut

Segmental bafflebaffle spacing, m Ds/5tube sheet thickness, �/mm 54tube roughness, mm 0.0016thermal conductivity of tube wall material,h/W m–2 K–1 16.30

fouling resistance, R/m2 K W–1 0.0004

Output variables:dew point of the vapour mixture, Td/K 429.72bubble point of the vapour mixture, k 330.28total heat load, �l/kW 5885.05weighted mean temperature difference, �T/K 77.0overall heat transfer coefficient, U/W m–2 K–1 546.10heat transfer surface area, A/m2 139.82total number of tubes, Nt 752tube side pressure drop, �p/Pa 0.1677 × 105

shell side pressure drop, �p/Pa 0.1123 × 104

F i g . 1 b – Flow chart for the design of multi-component con-denser

F i g . 1 a – Basic logical structure for process design of con-denser

from both the liquid and vapour phases to the cool-ant but also transfer of vapour molecules from thevapour phase to the liquid phase. Therefore, there isdiffusional mass transfer resistance along with heattransfer resistance during multi-component conden-sation. In Kern’s method, the effect of mass transferis not considered. Hence, Bell and Ghay’s method ismore reliable and used for the design.

Effect of the vapour flow rate

Fig. 3 shows the variation of the overall heattransfer coefficient with the vapour flow rate for sin-gle and two tube pass condensers. As it can be seenfrom Fig. 3, the overall heat transfer coefficient de-creases with the increase in vapour flow rate, irrespec-tive of the tube pass. Typically, if the flow increases,the heat transfer coefficient also increases due tohigher turbulence. However, in this investigation thecase is different. In the case of a vertical condensa-tion, the heat-transfer coefficient decreases with theincrease in Reynolds number up to 2000, and then in-creases with the Reynolds number.10 Reynolds num-ber in this investigation was calculated in every possi-ble combination of temperatures and condensate flowrates, and the values of Reynolds numbers were wellbelow 2000. This justifies the results obtained by the

model. Also, the higher the vapour flow rate, thehigher the heat load of the condenser, thereby thehigher the required surface area. Therefore, the overallheat transfer coefficient decreases. For any given flowrate, the two-tube pass condenser gives a higher over-all heat transfer coefficient.

Fig. 4 represents the variation of the shell-sidepressure drop with the vapour flow rate for a singleand two-tube pass condenser. A close examinationof Fig. 4 depicts that the shell-side pressure drop in-creases with the increase in vapour flow rate, irre-spective of the tube pass arrangement. Besides, fora given value of vapour flow rate the two-tube passcondenser gives a lesser pressure drop than the sin-gle-tube pass. The above features are obvious be-cause the increase in flow rate increases the pres-sure drop. In any given geometry, to obtain moreflow through a restriction (condenser is a restrictionto vapour flow), one must have more pressure up-stream of the restriction, i. e. pressure drop in thecondenser increases.

Effect of vapour inlet temperature

Fig. 5 shows the variation in the overall heattransfer coefficient for a single and two-tube passcondenser. A close examination reveals that increasein vapour inlet temperature decreases the overall heat


F i g . 2 – Heat-transfer surface area for various cumulativehead loads for condensation of hydrocarbon va-pours

F i g . 3 – Effect of vapour flow rate on overall heat transfercoefficient for single and two-tube pass con-densers

F i g . 4 – Effect of vapour flow rate on shell-side pressuredrop for single and two-tube pass condensers

F i g . 5 – Effect of vapour inlet temperature on overall heattransfer coefficient for single and two-tube passcondensers

transfer coefficient, irrespective of the number oftube passes. Also, for a given vapour inlet tempera-ture, the two-tube pass condenser provides a higheroverall heat transfer coefficient. In general, the con-densation overall heat transfer coefficient dependsupon factors such as condenser type, layout, surfacegeometry, heat load and thermo-physical propertiesof the condensing vapour. Since the change in inletvapour temperature alters the thermo-physical prop-erties of vapour, as we know the behaviour of vapourdensity and vapour dynamic viscosity with change intemperature from the fundamentals of intermolecularforces and collision phenomenon. With an increasein vapour temperature, the density of vapour de-creases and dynamic viscosity increases. With aclose examination of Nusselt model equation, it isclear that an increase in inlet vapour will adverselyaffect the heat transfer coefficient.10 Also, the abovefeatures can be explained by the fact that an increasein vapour inlet temperature increases the de-super-heat zone heat load, therefore decreases the overallheat transfer coefficient.

Fig. 6 depicts a plot between the tube-side pres-sure drop for a single and two-tube pass condenser.This figure reveals that an increase in vapour inlettemperature decreases the tube-side pressure drop.This is because the increase in vapour inlet tempera-ture increases the heat-transfer surface area, andthereby the tube-side pressure drop.

Effect of the coolant flow rate

Fig. 7 shows the variation of the overall heattransfer coefficient with the coolant flow rate for asingle and two-tube pass condenser. It can be seenfrom the figure that the increase in coolant flow rateenhances the overall heat transfer coefficient irre-spective of tube pass arrangement. Also, for a givencoolant flow rate, the two-tube pass condenser offershigher overall heat transfer coefficients. The abovefeatures are due to the fact that the increase in flow

rate decreases the heat transfer area and thereby in-creases the overall heat transfer coefficient.

Fig. 8 is a plot between the heat transfer areafor the coolant flow rate for single and two-tubepass condensers. This figure reveals that the in-crease in coolant flow rate decreases the heat-trans-fer surface area irrespective of tube pass arrange-ment. This is due to the fact that the increase incoolant flow rate decreases the heat transfer coeffi-cient and thereby the surface area of the condenser.

Effect of coolant inlet temperature

Fig. 9 shows the variation of the overall heattransfer coefficient with the coolant inlet temperaturefor single and two-tube pass condensers. This figureshows that the increase in coolant inlet temperaturedecreases the overall transfer coefficient irrespectiveof the tube pass. This is because the increase in cool-ant inlet temperature reduces the weighted meantemperature difference and increases the heat transferarea, thereby reducing the overall heat transfer coef-ficient. The condensation overall heat-transfer coeffi-cient depends upon factors such as condenser type,layout, surface geometry, heat load and thermo-phys-ical properties of the condensing vapour. The changein coolant inlet temperature will change the vapour


F i g . 6 – Effect of vapour inlet temperature on tube-sidepressure drop for single and two-tube pass con-densers

F i g . 7 – Effect of coolant flow rate on overall heat transfercoefficient for single and two-tube pass con-densers

F i g . 8 – Effect of coolant flow rate on heat-transfer sur-face area for single and two-tube pass condensers

temperature, which alters the thermo-physical prop-erties of vapour. Hence, it is clear that an increase ininlet coolant temperature will adversely affect theheat transfer coefficient.

Conclusions

The mathematical design models have been de-veloped based on the equilibrium method, andthereby a computer aided design algorithm for thedesign of a multi-component condenser has been de-veloped based on Bell and Ghaly’s method. Basedon the algorithm, a computer program has also beendeveloped. This program was tested for a wide rangeof operating variables and found satisfactory in giv-ing expected results. The design algorithm based onBell and Ghaly’s method was compared with Kern’smethod. It has been found that Kern’s methodundersizes the condenser because it omits the masstransfer resistance and does not take enough care tohandle sensible heat transfer during condensation.This fact has been incorporated into Bell andGhaly’s method by taking the vapour phaseheat-transfer coefficient during vapour sensible heattransfer in the hope that it will approximately overes-timate the mass transfer resistance. The undersize ofthe condenser may be severe by Kern’s method if thecondensing range becomes large.

The effects of operating variables viz. vapourflow rate, vapour inlet temperature, coolant flow rateand its inlet temperature on the output variables viz.overall heat transfer coefficient, heat transfer surfacearea were studied for both single and two-tube passcondensers. As a result, the overall heat transfer co-efficient was found to increase with coolant flow rateand decrease with an increase in coolant inlet tem-perature, vapour inlet temperature, and vapour flowrate. Further, the pressure drop in the tube side wasfound to increase with an increase in coolant flowrate, and decrease with an increase in vapour flowrate and coolant inlet temperature. The shell-side

pressure drop was found to increase with vapourflow rate where other variables have nominal effects.

N o m e n c l a t u r e

Ao – heat transfer area based on outside tube area, m2

Ai – heat transfer area based on inside tube area, m2

hi – heat transfer coefficient inside the tube, W m–2 K–1

ho – heat transfer coefficient outside the tube, Wm–2 K–1

hsv – sensible heat transfer coefficient, W m–2 K–1

K – vapour – liquid equilibrium constant�W – thermal conductivity of the wall, W m–1 K–1

N – number of componentsqm – vapor mass flow rate, kg s–1

� – heat load, kW�l – liquid phase heat load, kW�sv – sensible heat load for vapour, kW�T – total heat load, kWRdi – fouling resistance inside the tube, m2 K W–1

Rdo – fouling resistance outside the tube, m2 K W–1

T – temperature, KTl – liquid phase temperature, KTm – mean temperature, K�Tm – mean temperature difference between hot and

cold fluid streams, KTv – vapour phase temperature, KTc – coolant temperature, KUm – mean overall design heat-transfer coefficient,

W m–2 K–1

Umc – overall heat-transfer coefficient for multi-compo-nent condenser, W m–2 K–1

x – mole fraction in liquid phase, 1�W – tube wall thickness, my – mole fraction in vapour phase, 1ZF – feed molar composition� – vapour fraction molar basis

R e f e r e n c e s

1. Kern, D. Q., AIChE J. 17(5) (1971) 1037.2. Bell, K. J., Ghaly, M. A., AIChE Symp. Ser. 131(69)

(1973) 72.3. Colburn, A. P., Drew, T. B., Trans. Am. Inst. Chem.

Engnrs. 33 (1937) 197.4. Colburn, A. P., Hougen, O. A., Ind. Eng. Chem. 26 (1934)

1178.5. Colburn, A. P., Edison, A. G., Hydrocarbon Processing 33

(1941) 457.6. Krishna, R., Panchal, C. B., Chem. Eng. Sci. 32 (1977) 742.7. Heat Exchanger Design Handbook, Hemisphere. 1983,

New York8. Lockhart, Q. W., Martinelli, R. C., Chem. Eng. Prog. 48

(1949) 39.9. Kutaleladze, S. S., Borishanskii, V. M., Concise Encyclo-

pedia of Heat Transfer, Pergamon Press, Oxford, 1966.10. Sinnott, R. K., Coulson & Richardson’s Chemical Engi-

neering Vol. 6, Butterworth-Heinemann, London, 1996.


F i g . 9 – Effect of coolant inlet temperature on overallheat-transfer coefficient for single and two-tubepass condensers

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CAD of a Multi-ComponentCondenser