The condensation of vapour from gas-vapour mixtures

chemical

Rllgim~

sdeme, 196% vol. !a, pp. la7

The condensation

to 188 Paouaon PressLtd.

of vapour

from gas-vapour

mixtures

R. C. CAIRNS School of Chemmal Engmeermg, New South Waks Umversrty of Technology, Broadway, Sydney, Au&alla (Rewed

28 DGcmrbrr1952)

Summary-The accepted methods for the desrgn of condensers to handle gas-vapour mixtures are revrewed and a smgk vertmle tube condenser is descrrbed from which data are obtamed for the systems chloroform and air, and steam and sir. The method of COL.BUEN and HOUGEN [4] BSapplied to 8 run on each of the systems and the calculated area compared w&h the expected area. The approxnnate method of Comunw [3] is also apphed to the same runs and the area obtained again compared wrth the expected area. The area required to cool a saturated mrxture of chloroform and air from 120 2’F to 94 0°F calculated by the CHOLBUEN and HOWEN[O]method is found to be m good agreement with the expected area, being withm 20,6 of it. The method applied to the cooling of a saturated mixture ofsteam and srrfrom 16Mi”F to 129 B’F grves an area whmh also agrees well, being within 5% of that expected. The mod&atmn of the Co~~uruv and HOWEN[4] methodsuggestedby Srrrn [lo] is found unnecessary in the cases studied. The approxmmte design procedure proposed by COLSU~N[a], apphed to the same conditions, 4 is found to give an area approximately 40% greater than expected for both systems. R&urn&-L’auteur passe en revue ks methodes classiques de calcul pour les condensema trartant des melanges de gas et vapeurs. 11 d&it un condenseur g tube vertmal umque utili& pour IVtude des syst&mes air-chloroforme et an-vapeur d’eau : Led nisultats exp&imentaux sont compares avec ceux pr&bts par les m&.hodes ekssiques. Dam le cas de CHCls-arr, (condensatron entre 120 2’F et @4+‘F), Is n&hode de COLSIJ~NHOUQEN[4] concorde B 20% p&s. Dana le cas HsO-mr (condensation entre 168 8°F et 129 S’F) la copcorehmu3 atteint environ 5%. La modification apportee par Swr~a [lo] B la methode pr&Gdente n’est pas n&ssaire dans les deux cas &udr&s. La methode de cakul approxunatif nroposee par COLBUSN[a] pr6vort ks muf&oes en exc& de 40%, dans les deux cas &.ulii. - INTRODUCTION

unit time per unit cross-sectional area through the resistances of the condensate layer, the metal wall, scale and cooling water flhn is made equal to the heat flow through the gas flm. The heat flow through the gas flhn is made up of sensible heat lost by the mixture and latent heat transferred as the vapour diffuses through the gas fibn and condenses in the condensate film. The total heat flow is represented by an overall coefficient U, multiphed by the temperature drop from the mixture to the water. These conditions are represented by :

When a gas-vapour mixture is exposed to a surface at a lower temperature than the dew point of the mixture, condensation of the vapour occurs. A gas flhn is formed at the surface, which contains a higher gas concentration than the main stream. COLBURN and HOUGEN[4] have shown that the diffusion of the vapour moIecules through the gas film plays an important part in the transfer of heat from the gas-vapour rmxture. They presented a design procedure for estimating the surface area re uired for a cooler-condenser, to cool a satura J gas-vapour mixture, along the 4 (t&J- 4) + g xl h @v - PC) = ho 0. - t,) = UAt (1) saturation line. In their treatment, at any particular point in or in words, the heat flow to the condensate the condenser, the quantity of heat flowing per surface is equal to the heat flow from the

R. C. CAIRNS: The condensation of vapour from gas-vapour nuxturea

condensate surface and these are each equal tc UAt. At any value of fs in the condenser, all the variables in equation (1) are known or can be calculated, except t,, p, and U. The value d p, follows if t, IS known and the value of Uhl ia obtamed by a trial and error substitution d several values of t, until the desired equahty is obtained. By choosing six or more temperatures for td and applying this procedure the point values d UAt can be evaluated and graphical integration of equation (2) is possible, since values of UAt are known for increments of the total heat transferred.

(8)

From this t, is found and the total heat transferred from inlet to outlet, is calculated, using t, as the condensate temperature, not ts. A plot of the terminal values of t, and 1, versus q is made and for a calculated value of t,, the estimated true t, is obtained by interpolation on this The corrected heat transferred and graph. corrected t, are then found and this new value of t, used in equation (1) to solve for t, by tnal and error as before. SILVER [9] gives approximate methods for different types of cooler condensers for estimating the gas film sensible heat transfer coefficient (21 and the mean overall heat transfer coefficient. The calculations necessitate knowing the area The method presented by COLJXJ~CNand of an existing condenser and its operating terminal HOUGEN is accepted by all texts at the present conditions. Conversely the methods are applicable time, but it 1s often pointed out that the method to the estimation of the surface area if the gas There also film sensible heat transfer coefficients are known. as applied is extremely tedious. The methods are based on the assumption appears to be no expenmental evidence m the that h, is constant throughout the coohng process literature to support the design procedure. SMITH [iO], however, does state that considerably hqher and that the ratio of the sensible heat transfer heat transfer rates than expected were obtained coefficient to the total gas film heat transfer coefficient is equal to the rat.10 of the sensible on equipment designed by this method. SMITH attnbutes this to the method of cal- heat capacity change to the total heat capacity culatmg the heat transferred between points. change. However the calculation of the area required This is made up of the heat of condensation and the heat transferred by the cooling of the gas, for a given set of conditions does not appear the uncondensed vapour and the condensate. To possible where the values of h, are not known For various equipment under different operating calculate the latter of these it is assumed that the condensate is at the same temperature as the conditions, or where it is not possible to assume main stream, which is not stnctly true. Heat is b8 is constant. This may occur where there is P large velocity change of the gas-vapour mixture removed by the eooling water as the condensate in the equipment caused by the removal of flows past the cooling surface and the condensate vapour from high concentrations of the vapour must be at a lower temperature than the mixture. Where the latent heat of vaporisatlon IS small, in the murture. COLBURN[8] recently has presented an approxiSMITH suggests that the heat transferred by the nate design method which involves only the coolmg of the condensate is no longer negligible, as It IS m the example worked out by COLBURN terminal condltlons of the condenser and elimiand HOUOEN, and for organic vapour and gas lates the need for point to point heat balances md the tnal and error calculation m order to mixtures some allowance must be made. In this method the overall driving SMITHgives a modlficatlon of the COLBURNand obtain Uht. HOUGENmethod whereby an estimate 1s made of !orce from mixture to cooling water IS expressed the final condensate temperature from the LS an enthalpy difference (ig - i:), and the zonductance of heat 1s expressed as an overall emplncal equation : 128

coefficient per unit enthalyy difference that : dq/dA =

COtBURX

finds

u, c from equation (5) : a (0

‘p&)=‘p/J +1/(%2)w and he evaluates 122, for the purposes of calculation at i#. Assummg becomes :

u, constant, then equation % (0

(4)

A=U

W

(

’ 8 c b%, 0 ,

:.

.

u* however is known to (0 % vary and the ar&hmetlc average of the top and

yi~-mNNtwoNmn .

The value of

u. is used to evaluate A. ( 0 c. Although the mechanism of the condensation of a vapour from a non-condensing gas is well understood, little appears to have been done to check expenmentally the methods lust described.. It was felt that an expenmental mvestlgatlon on the validity of the design methods was most desirable. It is the purpose of this paper to present cxpenmental data, obtamed from a simple apparatus, to which design calculations can be apphed and to compare the accuracy of the design methods with the known surface area used m the expenmental work. Air mixtures with pure chloroform and with water vapour were chosen for the experimental work because of the differences in properties of these two vapours ; notably the latent heat of vaponzation.

bottom values of

and the internal dlmenslons are 10 rn. x 10 m. x 16 in. The boiler 1s cadnuum plated and 19 fitted with a gauge glass and safety lute. A $ m. filling cock 1s provided and the exit vapour line leaves from an approximately 1 in. I.D. copper tube m the centre of the cover plate. A 8,000watt Helicoil A.G.E., twm element immersion heater is sealed mto the side of the boiler. The power input to the boiler 1s controlled by a 9 amps 280 volt Vanac on each element and 1s recorded on an Ez~ershed artd Vzgnoles Recording Watt Meter. The vapour lines from the boiler are approxlmately 1 in. I.D. and lead to the gas-vapour mixer which is also m glass. One foot before the nuxer the air IS introduced through a ) m, glass line pomtmg in the dlrectlon of the vapour flow and the gas plus vapour enter the mixer tangentially. The nuxer IS constructed on the lines of a cyclone separator, the mixture of gas and APPARATUS AND PROCEDURE vapour leaving from the top of the mixer. The The apparatus, as shown in Fig. 1 consists princi- mixed gas and vapour then pass to the condenser pally of a boiler, a gas-vapour mixer, a verticle in approximately 1 in. glass lines ; a three feet tube condenser, a condensate separator and an calming section is provided before the condenser. auxiliary condenser. The condenser consists of a vertlcle double-pipe The boiler is made from l/l6 in. steel sheet, exchanger, with the gas-vapour mixture flowing 149

R. C. CA~RNU : The condensationof vapeur from gfts-vapourmixtures downwards mside the centrc tube and cooling water flowmg countercurrent to this m the annulus. The centre tube IS of standard 12 gauge copper and is 1282 m. O.D., 1081 m. I.D. and the length of tube exposed to cooling water is six feet (or 1 70 sq. ft. internal area). The join between glass calmmg section and copper tube is a simple butt lomt, both surfaces being first ground flat. The internal diameter of the glass at the join is the same as that of the copper tube. The two sections are held together by means of a bored rubber bung which fits mto the annulus between the two metal tubes. The external tube forming the water Jacket is standard 8 gauge black iron pipe 2.055 m. I.D. A 1 m. I.D., glass line which is six inches long leads from the bottom of the condenser and 1s fitted to the condenser in a similar manner to the calming section. The condensate formed is separated from the exit gas-vapour mixture m the condensate separator. This IS attached to the glass hne which IS flared at its end. Another glass line fittmg under this takes off the exit gas-vapour mixture. The condensate rate is dctermmed directly from the volume collected m a known time. For the chloroform and air runs, an auxiliary condenser was used to remove as much chloroform vapour aa possible before dischargmg to the atmosphere. A nine feet condenser with tnchlor-

ethylene cooled by dry-we as the coolant, was used for this purpose. The maximum cooling water-rate available was pumped by a gear pump and metered through a rotameter. Standard thermometers are located at the top of the calming section, at the condensate outlet of the separator, m the exit gas-vapour line and m the mlet water hne. Beckmann thermometers are used at the mlet and outlet of the cooling water to determine the water temperature rise. No correction was found necessary, at the waterrate used, to allow for flmd friction. For the system, chloroform and air, where the ratio of vapour to air is very high, the air was pumped by an Edwards Type IV Compressor (4 hp 1 kg/sq. cm., 75 htres/mm.) and measured through a calibrated constnction meter before entermg the system. For the steam and au runs a Beecoz Rotary Air Bump, O-10 c.f.m., was used for the higher air rates needed m this case. The air was first filtered and metered through a prcv~ously checked i m. x & m. Venturi. For this system also the air was electrically heated before entering the vapour hne. / The boiler was cahbrated for power mput versus rate of evaporation for both water and chloroform. This cahbration was obtamcd by setting the eqmpment for total condensation without air flow and after allowmg sufficient time

Table 1 Coolwag Gas-Vapowr temperature ‘C water rate Inlet outkt &i

101

Exptl.

Cakd

2010

51 8

400

Rxptl --a618

2010

510

490

a68

2010

514

490

a64

2010

518

400

a68

249

--102 255 --10.0 25 5 ---100 25 2

180

Water an&t tqp

Cakd 34.4 -a50 -a44 -a44

la7 150 149 147

of vapour fhin gd-vapour mixtures

R. C. CAIRNS : The condensation

for the eqmhbrmm the condensate rate was measured. A voltage regulator was found necessary to reduce the effects of mains voltage fluctuation. The boiler ISlagged with a 1 m. asbestos sheetmg and the condenser is lagged with ljb m. asbestos rope. All glass hnes and the gas-vapour mixer is lagged with 3 m. of slag wool. The chloroform used was fractionated from B.P. chloroform to remove the added alcohol and then dried. The water used was taken directly from the mains. In making a run the water was turned on and the boiler set at the required vaporisation rate. Sufficient time was allowed for the vaporisation from the boiler to become steady and the an was mtroduced mto the vapour line. The apparatus was allowed to come to eqmhbrmm and before readings were taken the mixer was dramed. The amount of condensate m the mixer after a run was found to be neghgible. The time required to make a run was approximately two hours. The results for both systems are listed m Table 1 together with the calculated saturation temperatures at mlet and outlet and the ratio of heat in to heat out, obtamed by an enthalpy balance applied to the experimental results. APPLIED CALCULATIONS The design method of COLBURN and HOUGEN [4] and also that of COL~URN [8] were applied to one set of experimental results from each system. Run numbers 4 m each case were chosen for the calculations. In applymg the design methods the inlet temperature at saturation correspondmg to the humidity of the mlet mixture was used for the purpose of the calculation and the outlet saturation temperature correspondmg to the calculated humidity of the outlet mixture was also used. This was necessitated by the fact that the expenmental temperatures did not correspond exactly to the temperature at saturation for the humidity mvolved, and that the COLIWRN and Houce~ method assumes coohng along the saturation line. In view of the fact that the actual temperatures did not differ greatly from 181

the theoretical temperatures as seen m Table 1, this procedure 1s justifiable. The calculations for both systems have been carried through simultaneously and for the sake of clarity sample calculations are given : CoZburn ami Hougen

Method

Table 2 lists the conditions known for each system Tablr 2

----

--

An rate lb moles/hour Inlet temperature “F Outlet temperature “F Coohug water rate lbs/hour Inlet water temperature “C Pressure atm Inlet con&tlons : Vapour pressure atm Gas partial pressure ntm Outlet conditions Vapour pressure atm Gas part& pressure atm lb moles vapour entermg per hou lb moles vapour leavmg per hour lb moles vapour condensed per hour

:idorofmw

Sicnm

am-lnar

nnd aar

0 20 1202 94-O 2010 14 7 1

0 369 1933 129 9 ?Olrl 19 1 1

0*994 O*339

0 391 0609

OcM2 om0 0 395 O-124

O-151 0349 0 553 0.153

0 271

0403

and the results of the overall mass balances. The inlet and outlet vapour pressures are obtained at the mlet and outlet temperatures respectively. Throughout the calculations the followmg properties were taken as constant : c for au c for water vapour c for chloroform vapour c for water c for chloroform hclmd Molecuhr weight of au Moleculrrr weight of chloroform Molecuhu we@t of water

0.24 B.T.U /(lb) 9 45 B.T U./(lb) 9 14 B.T.U./(lb) 1 0 B T U /(lb) 0 23 B.T.U./(lb) 29

(“F) (“h’) (“P) (“U) (“F)

119 4 18

The physical properties of the gas-vapour mixtures are given m Table 8 and were evaluated at the pomt temperatures chosen. The viscosities of the mixtures were calculated usmg the method of BROMLEY and WILKE [l] while the molecular weights, densities and specific heats were cab culated by standard methods. The diffusirities

*

RC.Culwa:

Thcc?o&ndh

ofvnpourkmlgfls.vapourmixturea Tatlie

j -(1)

120.2

0664

0.6295

89 0

0.210

0 174

O&W

0394

(2)

115.6

0 a00

0.0665

882

0.198

0.186

0.351

0439

chloro(2) --form and air (4)

110.6

0%543

oe810

78.1

0.188

0*166

0*34b

0.473

1039

0489

oaJ17

78 2

6.178

6.191

6.842

0.521

(5)

100.0

0+&O

oaM2

68.7

0.162

0.196

OWY

O*S69

(6)

94.0

0 882

0.0829

635

0 157

oe61

0882

0.681

(1) ---

1683

0 391

06467

2L7

oa89

0QY.a

1.28

0 61

(3)

1660

0322

oa419

255

OQ568

0.808

1*26

O-62

(3)

160~

0*25-b

oa430

96.2

0.0688

Q296

1.17

0.66

(4) -----

1460

0 197

0.6489

26.8

oa612

0.282

1.14

0.66

(5)

1350

w17a

OQ443

27-l

0.9624

0276

1.18

068

(6)

120 9

0.151

oa445

27.8

06684

0.272

1.12

0.69

--

Steam and ok

-

were found from the equation of GILLILAND [5] for chloroform and air but the value for the diffusivity reported by SIIERWOOD [S] for steam

and air was used after correcting for temperature. The Schmidt numbers were calculated but since the variation for steam and air was slight an

Tabk4 IIeal oj

&I~

Points

Heat removed

fm

Heatmnwtd m wpouz B.T.U./how

Hmt r.motwd from oar B.T.U./hour

Total B.T U./hour

B%$EW 1225

18.6

26.1

72

1272

(2)_(B)

868

21.6

19.8

7.0

851

(8)_(J)

611

28.0

15.9

7.0

662

(4)_(5)

444

82.7

18.1

7.0

497

(5)_(6)

433

44.7

124

8.4

499

Totals

8616

140.0

874

86.6

8781

(l)_(2)

2692

217

278

so2

2242

(w4)

Chloroform and air

Steamandair

‘2762

(2)-(8)

PlZO

47.2

240

66.6

(8)-(4)

l!l66

62.1

17 8

60.5

1646

(4)_(S)

584

83.9

78

80.2

6!JS

(5)_(e)

476

87a

64

30.8

s66

Tot.&

7278

261.9

82.8

282.2

779E

1SB

Il.C. CAUWX : The ewrdenuution

of vupour fromgus-vapour mixture8 point and the total water temperature rise to be :alculated. Table 5 gores these values. The mass relocities and Reynolds numbera arc

average value of O-69 was chosen for calculating the mass transfer coeficlent. In Table 4 the results of the point to point heat balances are shown.

TOblC5

e.g. Pointi (a)-(5) Steasc aId dir _-

Heut of condensation

At (1)

18 x 1014 = 58-J B.T.U./hr

=0*869 x

Heat removed from condenscrte(wndensed assumed to leave nt sume temuerature as the mixture) 0 891 =0869x x 5 -0600 0828

(

L

---

Heut removed fron uncondensed vupuur 0172 = =x8 x 0869x18 x 045 x 5

cllloro-

tOlDI

sndarr

66 OB.T.U./hr

7.6 B.T.U./hr

Heat removed fron air Heat

transferred

(4) and (5)

between

-~--_

0

60 3

w-l2)

1272

063

59 7

(2)-W

851

0 42

39 6

(B)-(4)

662

088

(4).(5)

497

0.25

(5)-(6)

499

025

Totals

8782

188

At (1)

0

---

5(10 567 38 5

=

=Oaex2sxOMx5

0

60.2 B.T.U./hr

points 655 B.T.U./hr Weam and air

The total heat transferred between inlet and outlet is thus 8781 B.T.U./hr for the chloroform and air system and 7795 B.T.U./hr for steam and air. This enables the water temperature at each

0

768 _---_ 68 0

(l)-(2)

2702

1 64

(2)_(6)

2242

1.12

67 B--

W(4)

1646

082

67.0

(4) -(a

655

686

66.6

(4).(6)

550

0.27

66.4

Totals

7795

8 88

Tabk6

Chloroform

and air

Steam and air

12,200

oat68

8.18

1.17

1860

11,060

0.0069

7.68

1.08

1860

10,000

OaO40

6 74

191

1660

a.400

0.0040

6 17

0*86s

1660

a.ioo

o*ooM

5@!a

0406

1860

8,900

0.0040

574

0.886

1860

188

H. C. CAIRNS: The condenwtlonof vapour fxwn gus-vnpouratituw

shown in Table 6 for each pomt. evaluated as follows : e.g. Point (2).

These are

Chloroform and Air

Tube dwmeter Cross-scctronal llrcu

= 1 081m. = OaO6378q ft ‘2 G = 0.20(119.4 x of

and

p at

(2)

so iv&

Heat Trarasfe

CoeffficientR ok

than tk

Gu Filr~

The heat that IS transferred to the surface of the condensate film must pass through the resistances of the condensate film, the tube wall, scale and the water film before being removed by the cooling These resistances are calculated as water. + 29) follows :

0 00087 = Q,SQO lb/(hr) (sq ft) = 0 080.5 lb/@) (ft) = 1081 x 0630 = 193Wl 12 x00805

(a) Con4iknsate filnr, h, Values of $ are calculated from the equation of NUSSELT [6],

hc=0.98k

The j factor is read directly from figure (1) of

(9)

reference [2]. The values of the sensible heat transfer coeffl- For chloroform and ar h, was calculated at each clent, h,, and the mass transfer coefficient, K, are point. For steam and air, where the condensing calculated from the equations of CEIILTON and film coefficient 1s much higher, the value at the bottom of the condenser, where the res&ance is COLBURN [2]. greatest, WM taken as constant throughout the jCG h, = (7) condenser. This value was calculated from CP * equation (9) as 1860 B.T.U./(hr) (sq ft) (“F). 3Table 6 also lists the point values of lbC for jG K= (8) chloroform.

0

i

(b) Tube Wall, The value of 0 80 IS assumed for the Prandtl number for chloroform and an- giving

h, =

(Pr)f = 0 833

j = oaw33

air.

G=65SO

ccc* - 0.864 (F1 From eqnatlon(7), h, =00088 x 0180 x 05QO U 862 s 4 50B.T.U./(hr) (sq ft) (OF) AlSo Au,=882 - c rO.MQ c E 0.180

A scale coefficient both systems.

S-

0448

of

1,000 IS allowed

for

hd = 1,066 B.T.U./(hr) (sq ft) (“F) (d) Water Film, h, The film coefficient on the water side was evaluated from COLBURN’S equation for fluids inside tubes in turbulent flow, recommended by PERRY [7] for turbulent flow in an annulus : (2)

(gL-

0 028 &)”

(10)

The value obtained 1s

PD

From equatton(8). OOQ8QXQ58Q R = 88 2 x pr/ x (0 439)3

(sq ft) (“F)

(c) Scale, hd

The calculated values of h, and (K x p,/) are also listed in Table 6. e.g. Poitd (2). Chbrofo~m ad

220 x 12

0 104 = 25,400 B.T.U./(hr)

(Pr)f = 0 862 For steam and air a value of 0.76 is taken for the Prandtl number giving

hp

h,

= 179 B.T.U./(hr)

(sq ft) (“I?)

When these coefliclents are corrected inside area of the condenser tube,

ha = 179 B.T.U./(hr)

pe/

134

(sq ft) (“F)

to the

It. C. CAIRNX : The wndewtiou

of vapour

from ga!i-vapour

nuxturw

In the same vay values of UAt, U and h,, have been calculated for the other points. These final values are hsted in Table 7 together with the values of Q and h,.

for chloform and air and 4 = 159 B.T.U./(hr) (sq ft) (“F) for the steam and air calculation, smce a constant value of h, = 1,860 was used for steam.

Evaluation of CT& The values of Uht at each point were calculated by substltuting in equation (1) the previously determined vanables, and solvmg for t, by trial and error. e.g. Point (2).

Chloroform aud dir

1

1

-=i-+iho a

c

1

=&+a& h, = 114 B.T.U./(iw) (sq ft) (“F) For fc = 87 3°F equation (1) becomes, 04s18

45(1156-878)+~

x 119 4 x 108 5 (9 600 -0 839)

= 114(8’7 8 - 59 7) = U(ll5 6 - 59 7) 8121 = 8146 = 55 3 u Average UAL = 8130 B.T.U /(hr) (sq ft) TJ = 56 6 B.T U /(hr) (sq ft) (“F) and the hypothetical coefficient IS 1st =

8180 (115 -

87.8)

= 118 B T.U./(hr)

(sq ft) (“P)

Fig. 2. Table 7

I

I

I

I

I

I

1

I

--

--

Chloroform and an

auld

3781

a 19

2569

848

4 17

1658

a9 8

647

5 46

1420

a44

52 2

704

1000

28 2

89 5

88 8

0483

1 15

179

5Om

840

(2)

87 a

0 528

0.86

114

8130

56 6

(8)

81 7

0 577

0.688

107

2409

47 8

(4)

707

0 621

0.565

103

1830

72 8

0 660

0482

101

68 7

0704 __-_____

0 393

98

(6)

Steam au

1 99

(1)

(5)

i

I

158 -_-113

996 499 0

10 0 __ _

--___

--

_-

(1)

121 4

0 737

1 59

159

8120

82 9

173

123

(2) I__

108.2

0 791

137

159

6260

68 7

121

1.58

(3)

97 0

0 842

1 20

159

4620

56 2

87 2

2 16

2831

(4)

87 8

0.877

107

159

as10

45 3

63 4

a 62

1205

84 0 0*891 --~--_ 816 0.906

102

159

2770

543

3 61

550

139

2340

46 i ~--------_ 869

47 9

427

0

(5) - ___(6)

0 98

-_--

185

--

7795 --

.5098

From a plot of l/Cti versus q, as m Fig. 2, equation (2) is graphically integrated to give the surface area required. The area obtained for the chloroform air system is 148 sq ft, which is equivalent to a condenser tube length of 5,911ft. For the steam and air system, the area is 1438sq. ft., or 5.76 ft tube length. The good agreement between the calculated areas and the expected area .of l-70 sq ft is apparent. It suggests that any further modification, such as that of SMITH is unnecessary, for the calculated area for the chloroform and au run agrees to within 2% of the expected and the calculated area for the steam and air run agrees to within 5%. Furthermore the modification of SMITH would lower the calculated area which would increase the deviation between calculated and expected areas. For these reasons the SMITH mod&zation was not applied, nor was any other allowance made in the calculations for the cooling of the condensate. The average condensate temperature, t,, at the bottom of the condenser, obtained by takmg the arithmetic mean of the wall temperature, t,,,, and the condensate surface temperature, t,, is calculate as 716’F for the chloroform and air system and 80+8“F for the steam and air system. These temperatures are lower than the expected average condensate temperatures of 80 0°F (80 O’C) and 84.l”F (84#‘C) for the respective chloroform and water condensate. This IS perhaps due to reheating of the condensate by the gas-vapour mixture before it can be separated from the nuxture in the expenmental apparatus. Colbarn Approximde

A plot of log p.

was made,

=

dP was found. The value of dH straight line 2 dt d% is also known from the humidity-vapour pressure equation and hence by application of the function of a function rule z results. dt

Since 112is evaluated

.

at ta, as suggested by COLBURN,m becomes *. dt Differentiation of equation (11) i = &

11 + c, (1 -

82)

(11)

-w

with rcspcct to t. remembenng

that

(12)

c, = C(&, + e(cupao) x Ii

and substitution of g gives an equation for the dt di between the temperature limits value of a chosen. This m&hod for evaluating the slope of the enthalpy line was found to be much simpler to Table 8

S&XUU

Chjorm and

and air

MT

--

Top

Vapourtemp., ir OF Watertemp.,fppOF Vapow pressure,p&m l

The approximate method of COLBURN [8] outhned previously was also applied to both systems. The results of the calculations for this method are given in Table 8. For the value of h, used here the effect of “/h, was quite considerable and m this case the accuracy of the method depends in part on the exact evaluation of the slope of the enthalpy versus temperature hne. Actually the most dlthcult part of this calculation is the determmatlon of m. The value of m in Table 8 was found as follows :

$

suggested by the Clausius-Clapeyron equatron, over the temperature range involved in each case, i.e. from mlet to outlet t#. From the resulting

Enthalpy, t, B.T.U./lb

i%thd

versus

%I Ai m at f8 4 % k

TotalB.T.U./lu ( G/C,) M&h. am (A% m Caleulatedareasqft Bq.uvalenttubela@hfi

186

Boilom

Top

I Bottom

94Q 166 8 &QBQ Q&4 608 58.5 170.3 0864 0*&Q: 0 391 O*lSl 485 147 ~~70 888 120%

105 101 06.5 282 ZQ.5 5.70 587 802 la8 0.60 179 98 a.87 a.89 -a781 3 la 515 2.85 83

2tbtl 28.5 458 la8 7.98 1.96 a ia 5.74 0.42 0.29 159 159 9.65 151) -7.795 12.B B55 2.40 8.6

lLc.cAmk:The

umduuation

use than standard mathematical methods, such as the Differentiated Gregory-Newton method and the Legmnge Interpolation Method. As long as the temperature range involved is relatively small, so that the variation in latent heat of vapourisation is small, then the method is quite applicable. Using this method the following equation was obtained :

of vapow fromgawwapow

mixture3

dA = element of sur&ce area

increment of total heat transferred per unit time aoceleration due to gravity 4-M x l@ ft/(hr)* msllll velocity (lb/(hr) (sq ft) film cwrnc~ent of heat transfer, B.T.U./(hr) (sq ft) (“W 4, = combmed water, met.4 wall and scale conductances h, = condcnlcate hd = dirt or scale h,,, = metal wall di K’ PO h, = combmed conductaneea other than the gas 43 + c(nopour) (t - 32) + 6 at=(l-popTw8 film lb, = gas film where for chloroform and air K’ = 8080 4 = 4/M - W dA tr, = water film and for steam and air 1y’=s999 H = humidity of mixture, lb/lb dry gas The final value of the area required as shown s = enthalpy of saturated gas-vapour mixture, B.T.U./lb of dry gas in Table 8 gives areas for both calculations sI = enthalpy of enturated gas-vapour mixture at & approximately 40% greater than ls needed, which B.T.U./lb of dry gas is reasonable considering firstly the assumptions &,* = enthalpy of saturated gas-vapour mixture at the on which the method is based and secondly the temperature of the wohng water B.T.U./lb dry fact that an oversize area 1s obtained. For the P (Ai)ln= logarithmic mean of a, and im* cases studied the method IScertainly conservative 3 = heat transfer or ma% transfer factor from the point of view of capacity. k = thermal conductavlty, B.T.U./(hr) (sq ft) (‘F/ft) X = molar mass transfer coefflclent, lb molea/ @q ft) (at@ CONCLUSION L =length,ft The design procedure put forward by COLBURN m = slope of curve of aW* verdus I M = molecular weqht and HOWEN applied to known conditions has M,=air been found to give an area which IS in good MM = average gas-vapour agreement with the expected area for the systems MI, = condensable vapour chloroform and aw, and steam and air. The MS = Inert gas modification of this method proposed by SMITH p = part& pressure, atm pc = vapour pressure at h has been found unnecessary. ps = non-condensable gas partml pressure III the The approximate method of COLBUEN applied -WY to the same conditions has been shown to give an pa’ = that *acent to condensate surface area which is conservative from the point of view pp/ = logarithmic mean of p, and pa’ of capacity. PO= vapour pressure q = heat transferred, B.T.U./hr ACKNOWLEKWAENT T = absolute temperature, OR t = temperature, OF It is with pleasure that acknowledgment is made = average condensatetemperature to Professor J. P. BAXTEB for his assistance in 2 = condeusates&ace temperature this work. ‘r = gafwapour mixturetemperature b = wall temperature t, = water tempexature NOTATION A# = overalltemperaturedrop R=W!a,fIqft U = over-all coeilicrent of heat transfer, B.T.U./(hr) e = speed heatat con&antpreaaure B.T.U./(B) (“F) c, = humrd heat B.T.U./(lb) (“F) (sq ft) (“F) u,/r,total gas-film heat transfer coemcient per unit d --OftUbe.,ft de = equivalent diameter, ft enthalpy difference, B.T.U./(hr) (sq ft) (B.T.U./ D = diffusion c&Went, ft=/hr lb)

nr,

x

I

& = gc, = G = h =

R.

c. CAxluve :

The condensatkm

of vapour fromgas-vapour

r = mass rate of flow, lb/(hr) (it of wetted perimeter)

c = mscoruty, lb,‘(hr) (ft) p = den&y, lb/cu. ft.

Sc = -$, DQ NR~ = 7,

REFlZltENCES

[l] BBOULEY,L. A. and Wm, C. R.; Ind. Eng. Chem. lB51 43 1841-8. [B] CHIL~N, T. I-I.and Comuaxu, A. P.; Ind. Eing. Chem. 1B84 26 1188-7. [8] COLBUBN,A. P. and Inst. Mech. Engrs. (London) Proc. 1SSl 164 448-58. [4] COLBUIIN, A. P. and HOUOEN, 0. A.; Ind. Eing. Chem. 1084 26 1178-82. [8] PE~UY, J. H.; Chemical Engineers’ Handbook, 8rd Ed., p. 888, New York, Mffiraw-Hill Book Co. 1050. [6] PEB~Y, J. H.; Ibid. p. 478. [7] PEBRY, J. T. K.; Absorption and H.; Ibid. p. 470. [8] SHERWOOD, Extra&on, 1st Ed., p. 21, New York, McGraw Hdl Book Co. 1887. [0] L. Snvxu; Inst. Chem. Engrs. (London) Trans. 1047 25 80-42. [lo] SMITH,J. C. ; Ind. Eng. Chem. 34 1248-S% (1842).

h = latent heat of vapourisatlon, B.T.U./lb

Pr = y,

mlxtm

Prandtl number Schmidt number Reynolds number

188