THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING DESIGN OF FINNED-TUBE PARTIAL CONDENSERS Edwin H. Young Dennis J. Ward The research from which this paper resulted was carried out through Engineering Research Institute Project 1592, sponsored by the Wolverine Tube Division of Calumet and Hecla, Incorporated, Detroit, Michigan, June 1957 IP-219

DESIGN OF FINNED-TUBE PARTIAL CONDENSERS Finned tubes can be used to definite advantage in shell-andtube partial condenser applications. In vapor-gas cooler-condenser applications the gas film coefficient is usually of such a low magnitude that the added extended surface provided by finned tubes can be used to reduce the size of heat exchanger required. The economic savings are often quite considerable. The purpose of this article is to indicate how such units can be designed using existing finned-tube information which is available in the technical literature. The design of condensers for the condensation of vapors from noncondensing gases is complicated by unusual conditions of heat transfer not encountered in total condenser design. In condensing part of the vapors in a gas stream, all of the properties of the gas stream vary greatly as the condensable vapor is removed. The heat-transfer coefficient of the gas film, the mass rate of gas flow, and the physical properties of the gas stream can change considerably as condensation proceeds. The condensation depends upon the diffusion of the vapor molecules through the gas mixture to the condensing surface. This involves two types of diffusion: (1) molecular diffusion and (2) eddy diffusion. Molecular diffusion involves the movement of individual molecules of condensable vapor from the main bulk stream onto the condensate film under the influence of a concentration (partial pressure) gradient. Eddy diffusion is the movement of groups of molecules of the bulk stream by turbulent motion to the con -1

densate surface. The main resistance to condensation now occurs between the bulk stream of vapor and the surface of the condensate. Therefore, mass-transfer coefficients must be considered as well as heat-transfer coefficients in the mechanism of condensation rate. The usual overall heat transfer relationship Q = UoAATm (1) does not directly apply in this case since no method of calculating meantemperature differences based upon terminal conditions is applicable. An accurate method of determining such a ATm has long been sought. The usual logarithmic mean of the terminal temperature differences is inapplicable. The overall heat-transfer coefficient varies widely from point to point in a partial condenser, being high where the condensing vapors are relatively concentrated and low in zones where most of the condensable vapor has been removed. Thus no simple average heat-transfer coefficient is applicable. The overall heat-transfer relationship for the heat transfer occuring in partial condensers must be written as: dq dA = UAt where At = (t - tw) tc = condensate-gas interface temperature, ~F tw = tube wall temperature, ~F U = all resistances but the gas film (U comb. later on) or q dq A = | (2) UAt o -2

In general, it is not possible to integrate this relationship formally using analytical expressions for both U and At as functions of q. The method of Colburn and Hougen(l) is generally accepted as the basis for obtaining rigorous design of cooler-condensers. The method is tedious since it involves successive trial and error substitutions. A number of approximation methods have been published by Cairns(2), Bras ('4) Mickley(), and others. The rate of transfer of sensible heat from the gas stream on the shell side of the exchanger to the outside of the tubes is given by: dqs = ho (tg - to) (3) dA The rate of transfer of latent heat from the gas stream on the shell side of the exchanger to the fin side of the tubes due to mass transfer of condensible material to the tube surface is given by: dqL = K M(Pv - pc) (4) dA The total rate of heat transfer, given by the sum of (3) and (4) above, must be transferred through the tube and water film: q A htcM(tg - KM( Pc) (tc- tw) = Ut (5) Awer where: Btu h6 = heat-transfer coefficient in gas film, hr-ft2-~F tg = temperature of main bulk of the gas vapor mixture, ~F g tc = temperature of condensate at gas-condensate interface, ~F lb KM = mass-transfer coefficient, - (hr-ft2) per unit pressure -3

X = latent heat of condensation, Btu/lb pv = partial pressure of vapor in main bulk of the gas vapor mixture, lb sq. in. PC = vapor pressure at tc, lb/sq. in. tw = water temperature, ~F Ucomb. = combined conductances other than the gas film _____1 (6) 1 + r + r rf + rm( +( ri +o hcond. Ai Aihi where: h = condensing film coefficient. cond. Other terms defined by Eq. (20) of Part I(9). The gas film heat transfer and mass transfer coefficients (h' 0 and K respectively) are obtained in the following manner. The fin side gas film heat transfer coefficient is obtained from Eq. (1) or Eq. (2) of (6) the third article of this series. The relationship for 19 fin-per-inch tubes in unbored shells is: (h De D.eG )0.6 1/5 ( )0.14 (7) k k CL C/ \ The fin side gas film mass transfer coefficient is obtained using the heat transfer coefficient obtained from Eq. (7) and the "j" factor relationships for heat and mass transfer. The heat transfer "j" factor is defined as: h ho Cp2/3 k/0.14 ( CpG \^ PI -4

The mass transfer "j" factor is defined as: 2/3 KMMM Pgf ( 4 () G Mv pDv Equating Eqs. (8) and (9) and simplifying, the mass transfer coefficient is obtained as: hoM ( CP Dv 2/3 o.14 MKM --- Cp MM Pgf k / (10) where: jh = heat-transfer "j" factor (dimensionless) h' = gas-film heat-transfer coefficient, Btu hr-ft2-OF Bru Cp = specific heat at constant pressure, lb - ~F lb G = mass velocity, -- of bulk stream hr - ft2 = viscosity, ft hr Btu k = thermal conductivity, hrft2-F/ft = masstranser factor (dimensionless) j-, = mass-transfer "j" factor (dimensionless) KM MM Mv Pgf Ib = mass-transfer coefficient, r-f p lb hr-ft2 per unit of pressure = molecular weight of gas-vapor mixture (average) = molecular weight of vapor = log mean partial pressure of noncondensable gas across film, lb/sq in. (Pg)at tg - (Pg) at tc T~ I 6 ~ the rgf (P ) at tg in (Pg) at tc noncondensable gas in the main Pg = partial pressure of body, lb/sq in. the -5

p = vapor density, lb/cu ft Dv = diffusion coefficient, sq ft/hr T3/2 D = 0.0166 [ 7/T2+ v [P(V 1/3 + V1/3) Li A + vB MA where: T = absolute temperature, ~Kelvin for T = ~Rankine, change constant to 0.0069 P = pressure, atmosphere VA,VB = molecular volumes(7) A' B MAiMB = molecular weights of gasses and condensing vapors The combined coefficient, Uomb, defined for finned tubes by Eq. 6 is dettermined in the following manner. The condensing coefficient, hcond., can be determined by the methods given in the second article of this series(8). The inside and outside fouling factors can be determined in the usual manner. The fin resistance of the tube can be obtained from Table 2 or Fig. 5 of the first article of this series(9). The inside coefficient and metal resistance are determined in the usual manner. The condensing and water film coefficients vary from the inlet end to discharge end of the exchanger. These resistances are usually small in comparison to the gas film resistance and the variation can ordinarily be neglected. To obtain an exact design exact design it is necesaary to graphically solve Eq. 2 for the heat transfer area. Partial condensers can have either a saturated vapor-gas feed or superheated vapor-gas feed. A different approach to the problem must be taken for the two cases. -6

A. DESIGN OF PARTIAL CONDENSERS WITH SATURATED FEED For the design of partial condensers in which the saturated vapor-gas mixture enters and condensation proceeds along the saturation line without superheating or supercooling, the method of Colburn and Hougen(l) is applicable. Figure 1 shows the cooling-condensing path followed by a saturated feed stream through the heat exchanger. The heat exchanger is broken up into a series of temperature drop zones as indicated in Fig. 1. The total heat transferred in each zone is computed, sensible plus condensing load. The corresponding water temperatures at these zones are obtained from a heat balance. Equation 7 is solved for each zone by a trial and error procedure on tc. A plot is then made of 1 versus q and the area under the curve is obUcomb.At tained to give the required heat transfer area. B. DESIGN OF PARTIAL CONDENSERS WITH SUPERHEATED FEED Figure 2 shows the cooling-condensing path followed by a superheated feed stream through the heat exchanger. The problem now consists of determining this path. The most convenient method to use is that of Bras(3) which involves the use of the following relationship. 2/3 dt Pgf k t in which Ap = Pv - Pc, see Fig. 3. and At = tg - t, see Fig. 3. -7

Procedure for the design of partial condenser with superheated vapors in an unsaturated condition: (1) Composition of vapor-gas mixture entering the unit must be known. (2) Entering temperature and pressure entering the unit must be known. (3) The partial pressure of the condensible vapor is determined from the composition. (4) Heat-transfer and mass-transfer coefficients can be calculated by use of Eqs. 7 and 10 (except that Pgf, the log mean partial pressure of the noncondensable gas across the film lb/in2 is unknown). Trial-anderror solution of Eq. 5 is required giving the temperature and vapor pressure at the condensate layer. (5):.At/Ap can be evaluated and dp/dt calculated from Eq. 11. (6) Straight lines are drawn with slope of dp/dt and followed for short distances and the process repeated until the outlet gas temperature is reached as indicated in Fig. 3. (7) About 5 to 10 points are usually sufficient. (8) The solving of Eq. 5 from point to point gives UAt values for a graphical solution of Eq. 2 as indicated in Fig. 5. -8

C. APPROXIMATION METHODS The simplest approximation method is to evaluate the terminal overall coefficients and use an average overall coefficient in conjunction with the logarithmic mean temperature difference. The accuracy of the method rapidly decreases as the difference between the inlet and outlet overall coefficients increases. Also the use of the logarithmic mean temperature difference implies assumptions which are usually not valid for partial condensers. A more reliable method consists of multiplying a mean gas film heat transfer coefficient by the ratio of the total to sensible heat transfer for the unit as indicated by Carrier and Anderson(10) qS + q\ h = hK-t - ) (12) qs The outside weighted coefficient, h, is then used in Eq. 20 of the first article(9) in place of h'. This overall coefficient can be used with an integrated temperature difference as indicated by Gilmour(1) to obtain the required area. Cairns has presented a method of formally integrating Eq. 2 if the UAt versus q curve is of parabolic shape(2). The required heat transfer area is given by: +T^/2 dq A = / ------ (13) (aq2 + bq + c) -qT/2 -9

2 [(UAt)2 + (UAt) - 2UAt)mid a - 2 (UAt), = heat flux at the gas-vapor outlet (UAt)mid = heat flux at a point in the cooler-condenser where half the total heat has been transferred. (UAt)2 = heat flux at the gas-vapor inlet Equation 13 has three solutions; when b2 = 4ac -2' + A = (14) aq + b] _q( when b2 > 4ac [ a1 (aq + b - Vb2 - 4ac A = - ln - - - (15) aq + b + b- 4acJ ( for b2 < 4ac A = tan-1 a t a (16) A 4ac b2 V4ac - b2 As indicated above, this method requires knowing the values of (UAt) at each end of the cooler-condenser and at a point in the cooler-condenser where half the total heat removed has been transferred. It is then possible to calculate the values of the constants a, b, and c in Eq. 13. The appropriate integrated equation (14, 15, or 16) is then solved depending on whether b2 > 4ac. The required area for the conditions specified is thus obtained. The only limitation on this method is that (UAt) when plotted against q must approach a part of a parabola.

Another approximation method also based upon the assumption of a parabolic curve of (UAt) versus q is that involving the use of the graph by Carey and Williamson(12). The graph gives a factor f which is used to multiply the mid-point heat flux (UAt)mid to obtain the mean heat flux. An alternate graphical procedure involving polar diagrams has been presented by Bras(4). The method is limited to the Colburn and Hougen (saturated gas-vapor mixture feed) method(). The method gives the exact solution and does not require a parabolic q versus (UAt) curve. The tedious successive approximation computations of the Colburn-Hougen method are greatly reduced by the graphical procedure using the polar diagram. D. GAS PHASE CONDENSATION The previous discussions are based on the assumption of surface condensation, i.e., the condensation of the condensable vapor occurs on the surface of the bare or finned tube. The graphical integration method of Colburn and Hougen assumes that the heat transfer and mass transfer mechanisms operate without interaction. As the gas-vapor mixture flows past the cooling surface, mass and sensible heat are transferred at rates proportional to their respective driving forces. In some systems, particularly those involving high molecular weight vapors and low diffusivity,mass transfer is slower than heat transfer. In such a case either supersaturation or condensation in the gas phase then follows. -11

(15) Schuler and Abell have presented an interesting and useful design method involving a vapor phase condensation correction factor to allow for gas phase condensation or "fog formation". No attempt will be made to review the method here. The reference should be consulted by those encountering the problem in the design of cooler-condensers in which fog formation is expected to occur. -12

EXAMPLE OF PARTIAL CONDENSER DESIGN INVOLVING SUPERHEATED FEED A. STATEMENT OF DESIGN PROBLEM A 50-50 weight percent mixture of ethane and pressure of 160 psia and 225~F is to be cooled at tube heat exchanger at the rate of 150,000 lb per ing tower water is available at 90~F and is to be ature not to exceed 110~F. Comparable designs of and plain tube units will be provided. The tubes Admiralty tubes, 14 BWG at the ends. B. TUBE SPECIFICATIONS 1. Finned-Tube Characteristics 14 BWG Plain End Tube Trufin 195065-26 Admiralty tube N = 19 fins/in. do = 0.737 in. dr = 0.640 in. wall thickness = 0.065 in. mean fin thickness = 0.016 in. di = 0.510 in. AO = 0.438 ft2/ft Ai = 0.1336 ft2/ft Ao/Ai = 3.28 (Xt)(0.510)2 A = 0.001418 ft2/tube (576) De = 0.0559 ft (for fluid flow) 2. Plain Tube Characteristics 14 BWG Tube OD = 0.750 in. ID = 0.584 in. wall thickness = 0.083 in. pentane at a total 1000F in shell-andhour. Treated coolheated to a temperfinned-tube units are to be 3/4-inch-OD -13

Ao = 0.1965 sq. ft/ft Ai = 0.153 sq. ft/ft Ao - - 1.285 Ai t(o.584)2 Acs = 0.00186 ft2/tube 576 FINNED TUBE UNIT C. PRELIMINARY HEAT-EXCHANGER ARRANGEMENT Assume a 43-inch-ID shell containing 1300 tubes on a 1 in.-45~ square pitch with a single pass counter-current flow on shell-andtube sides. The shell side has baffles with 25 per cent window cut on the diameter and spaced at 2.5 ft intervals. The required length of the tubes is to be determined. D. SAMPLE CALCULATIONS FOR FINNED-TUBE UNIT 1. Flow Areas Cross-flow areas / shell diameter Number of tubes on centerline = ( pitch1 \ pitch \/ 7 43 5 =K41 - 1) = 29 1.414 / Number of tubes in flow path = 2(29) + 1 = 59 (on zig-zag path) Number of spaces for flow = 58 plus the ends (due to floating head backing plates) Cross-flow face area = (- (2.5) [58 + 2 = 12.5 ft2 12 -14

Root metal projected area = (Dr)(L)(No. of tubes) = (o.64) (2.5)(59) = 7.86 ft2 Fin metal projected area = (Fin thickness)(Do-Dr)(fins/ft)(No. of tubes)(L) 0.016 0.737 - 0.64\.=.. —- o6 —-- (19)(12)(59)(2.5) = 0.362 ft2 \ 12 / \ 12 / Free cross-flow area = 12.5 - 7.86 - 0.36 = 4.28 ft2 Total cross-sectional area of shell t(43)2 = ____= 10.05 ft2 576 (43)2 Window area(13) = (0.15355) = 1.97 ft2 144 1.97 Number of tubes in window area = (1300) = 255 tubes 10.05 Free flow area in baffle window = (0.737 )2 1.97 - 255 E7 = 1.97 - 0.75 = 1.22 ft2 576 Geometric mean area = (1.22)(.28) = 2.30 ft2 2. Calculation of Heat Load Assume that the partial pressure of pentane leaving the exchanger will equal the vapor pressure. Then the partial pressure of pentane in the exit gas stream is 15.0 psi (from vapor pressure curve, see Fig. 4). Therefore, the mole fraction of pentane in the exit stream is ( ) = 0.0938. Assuming that no ethane condenses, moles per hour of ethane in exit stream = (75)000) 30 2,500. Therefore, moles per hour of pentane vapor in exit gas stream = 2 500(00938) = 258. (1.ooo - 0.0938) -15

Lb/hr of pentane vapor leaving = (258)(72) = 18,600 lb/hr. Lb/hr of pentane liquid leaving = (75,000 - 18,600) = 56,400 lb/hr. Lb/hr of ethane gas leaving = 75,000 lb/hr. The path selected for computing the heat removed was to condense the pentane at 225~F, cool the condensate to 100~F, and cool the gases from 225~F to 100~F. Heat Removed: Condensing = (56,400)(113) = 6,370,000 Btu/hr Condensate cooling = (56,400)(0.60)(225-100) = 4,220,000 Btu/hr Cooling pentane vapor = (18,600)(0.425)(225-100) = 990,000 Btu/hr Cooling ethane vapor = (75,000)(0.46)(225-100) = 4,310,000 Btu/hr Total Q = 15,890,000 Btu/hr 3. Determination of Water Requirements Temp rise of water = (110-90) = 20~F Lb water/hr = 15,890000 = 794,500 lb/hr 20 Ft3/hr of water = 794,500 12800 ft/hr 62 4. Water Velocity in Tubes Acs = 0.001418 ft2/tube Tube side-flow area = (1300)(0.001418) = 1.84 ft2 Velocity inside tubes at avg water conditions = 12.800 (3600)(1.84) = 193 ft/sec 5. Determination of Resistances to Heat Transfer (a) Fouling, inside = 0.001 (from TEMA) (17) (b) Fouling, outside = 0.0005 (from TEMA)(17) -16

X Ao (c) Metal Resistance - K Am = Dr - Di.4 (0.0534 - 0.0425) Am = -T ---- = 3.14 in Dr 0.0534 i In 042in Di 0.0425 = 0.1535 ft2/ft length. hr-~F-ft2(outside) Btu (0.065)(0.0438) rm (12) (64) (0.1535) = 0.00024 (d) Water side coefficient(14): 0.8 Vt hi = 150 (1 + 0.011 tw) 0.2 di where: Vt di tw =velocity, ft/sec = inside diameter of tubes, in. =average water temperature, ~F.'. h 1 150(2.10)(1.69) 0.874 hr-oF-ft2(inside) = 610 ____ Btu (e) Condensing Coefficient The condensing coefficient will vary throughout the exchanger, being lowest at the inlet, where there is a large temperature difference driving force for heat transfer, and highest at the outlet. Often the coefficient may be assumed constant, due to the controlling nature of the gasfilm resistances. A calculation is included here to illustrate the procedure. -17

The determination of the condensing coefficient involves a trial-and-error computation which can be solved only when the gas-condensate interface temperature is known. Since the AT is large in this inlet section, assume hc = 600 Btu/hr-~F-ft2. This is checked after establishing tc. (f) Fin Resistance For this tube, rf = 0.00011 (see Table 2 or Fig. 5 of Ref. 9). (g) Determination of (U m) in Eq. 5. comb 1 comb. Ac A 1 0 o + ri - + rm + rf + rt + hi A hcond. 1 Ucomb = comb. 3.28 1 - + 0.00328 + 0.00024 + 0.00011 + 0.0005 + 610 600 1 Btu = 89.5 0.01118 hr-~F-ft2(outside area) (h) Determination of Gas-Film Coefficient Reference is made to Eq. 7. = 0.155 -- k'\k) k V The physical properties of the gas-vapor mixture are: The physical properties of the gas-vapor mixture are:

Cp = 0.478 ik = 0.0245 k = 0.01445 Substituting: 0.0559 x010155. = 0.155.055.4 x 50.00245 "1/3 E 0.14 2.30 x 0.0245 \ 0.01445 a.14 assuming ( - \^w = 1; 0.01445 ho = ---- * (183.5) 0.0559 = 47.6 Transfer Coefficient (i) Determination of Mass From Eq. 10: h M, Cp p Dv2/3.14 KM CP M Pgf k ( It is assumed that ( ) = 1 Substituting in the equation for Dv: (o.oo69)(18,ooo) 1 1 D = - + =0.0332 ft2/hr (lo.9)(8.64)2 30 72 The density is computed to be: p = 0.961 lb/ft-3 MM = 30(0.706) + 72(0.294) = 42.4 lb/lb-mole Mv = 72 lb/lb-mole Substituting (47.6)(30) (o.478)(42.4)Pgf 70.3 = - (1.04) = Pgf /0.478 x 0.961 x 2.003322/3 \ 0.01445 0 73.2 Pgf -19

(j) Evaluatic Reference )n of UAt Product i is made to Eq. 5. KM(PV - Pc) ho (tg - tc) + = — Ucomb. (tc - tw) Pgf (70.5)(132) (7-Pc).6 (225-tc) = 89.5 (tc - 110 Pgf 47. Assume tk ) iat tc pc Pg Pgf = 160~F = vapor pressure = 44 psia (from Fig. 4) = 114 psia. Trial, does (70.5)(132)(47-44) 47.6 (225-160) + = 89.5 (50)? 5095 + 244 = 3559 # 4475 4475 no Assume that tc Pc Pgf gf = 153~F = 41 psia = 116 Trial, does (70.5)(132)(6) 47.6 (72) +- (89.5)(43)? 116 5430 + 480 = 3850 no 3910 f 3850 Apparently, tc = 154~F approx. Therefore, use a value of UAT = 3880 (k) Determination of Point "c" (see Fig. 4) Eq. 11 is used to determine the slope, dPv of the line A-C on dt Fig. 4. -20

cdp (P-PV) / r2/ Ap v r dt Pgf \Sc At Locating the temperature of 154~F on Fig. 4 the condensate surface temperature, tc, on the vapor pressure curve, the value of P is determined as 7 Then, dp dt dt /160-41\ 0.88 \ f6 \ 116 o0.8155 \72/ (1) Check c UAT AT Uo )f Assumed Condensing Coefficient = 3880 = 225-110 = 115~F = 33.8 Btu/hr-~F-ft2 (outside area) AT hc t c Uo 33.8 At = 600 From Reference (115) = 6.47~F hcond = 0.725 ( / f g1/4 Uf 1/4 1 1/4 4 SDeq \At c For this bundle, N = 0.40 (X)0'5 = 19 CN = 0.76 (using Freon 12 line of Fig. 1 N14 of the 2nd article8) x1/4 l/ 0.627 = 3.35 -21

Deq) = 3.5 (from 2nd article8) *hcond= 4.14 Kf3 Pf2 ) g 1/4.1/. 4 K Pf / fif tf F 90 156 110 159 130 160 150 161 170 161.5 = 154-3.2 = 150.8~F = 161 (* Kf f \) lb a'cond = 4.14'(161) = 665 Btu/hr-~F-ft2 (outside area) (This assumed value was 600.) F. DETERMINATION OF REQUIRED HEAT TRANSFER AREA 1. Finned-Tube Unit Calculations were made for other points by the above procedure and are listed in Table I. A plot of 104/UAt vs q/104 is given in Fig. 5. The shaded area of the curve represents the solution of Eq. (2). -22

TABLE I COMPUTED VALUES FOR FINNED-TUBE UNIT Gas Condensate Water Pentane Temp Film Temp Temp Vapor Q/10 UAt U0 10o/ ~OF F ~F lb/hr Btu/hr Btu/hr-ft2 Btu/hr-ft2oF hr-ft2/Btu 225 154 110 75,000 3880 33.8 2.58 200 145 106.6 67,350 266.85 5600 38.6 2.78 175 134 103 58,150 550.4 2930 40.7 3.41 150 121 98.5 45,100 893.0 2150 41.7 4.65 125 104 93.8 29,700 1265 1190 38.4 8.40 110 99 91.1 22,900 1472 690 36.5 14.5 100 94 90 18,500 1590 368 36.8 27.4 TABLE II COMPUTED VALUES FOR PLAIN TUBE UNITS Gas Condensate Water Pentane Temp Film Temp Temp Vapor Q/104 UAt UO 10/At ~F ~F ~F lb/hr Btu/hr Btu/hr-ft2 Btu/hr-ft2 hr-ft 2/Btu 225 157 100 75,000 6060 52.7 1.65 200 148 107.1 70,900 224.6 5290 57.0 1.89 175 136 103.1 59,200 539.5 4240 59.0 2.36 150 122 98.5 46,000 889.0 3000 58.4 3.33 125 107 93.8 29,700 1265 1750 56.2 5.70 110 100 91.1 22,900 1472 1070 55.4 9.35 100 94 go90 18,500 1590 524 52.4 19.10 -23 -

A = 0 dq = 9840 ft2 ULt The area per foot of length = 0.438 ft2/ft Length of tubing required = 2240 ft Using 1300 tubes, the required length is 17.25 ft. Using an 18-ft exchanger provides 4.3% excess area. 2. Plain Tube Unit The required area was found to be 6550 ft for the same shell-and-tube arrangement. This requires 25.7 ft of exchanger; the use of two 14-ft units provides an excess area of 8.95%. 3. Checks of Finned Tube Area by Carey and Williamson Method (see Reference 12) Y1 = (UAt)inlet = 3880 Ym Y-2 Ym;Ym Yl (t)mid = = (t)outlet = = 2370 = 6.45 368 2370 368 = 2370 = 0.61 3B50" Using these values, f from chart is = 0.685...Mean driving force = fym = (0.685)(2370).'.(ULt)mean = 1625.:A = 15,900,000 = 9780 sq ft as compared with 1625 9840 sq oft -24

G. COMPARISON OF INITIAL COSTS 1. Finned Tube Unit The cost of the finned tube exchanger is obtained from a recent article by Kern and Associates(16) as: Finned tube unit cost = $26,000 2. Plain Tube Unit The cost of the bare tube exchangers is obtained from the same article (6) as: Bare tube costs (per shell) = $16,200 or Total cost = 2 x 16,200 = $32,400 3. Comparison of Costs Use of the finned tube exchanger yields a saving of: $32,400 - $26,000 = $6,400 -25 -

P g (inlet) 0 P g(outlt) tg(outlet) ~~tI g'(inlet) T,~F FIGURE 1. VAPOR PRESSURE CURVE SHOWING COOLING-CONDENSING PATH OF SATURATED VAPOR I -26

P n finla t 0.^111 %! I I l ~, _?tg, P (inlet) CO~ p g (outlet) I t 1 (outlet) I tg (inlet) T,OF FIGURE 2. VAPOR PRESSURE CURVE SHCWING COOLING-CONDENSING PATH OF SUPERHEATED FEED

LI' heated teed c \ lr B -g v LU D dPv u~%~~ / ^ E Sloped~LU~~ p /^^<f ~~~~~~~dt Saturation H Operating line line tc TEMPERATURE FIGURE 3. ILLUSTRATION OF PROCEDURE FOLLOWED TO OBTAIN CONDENSING PATH FOR SUPERHEATED FEED

- 6zSH1~ocIEOo3 riVIAHV Ha arILI aGTI MI HiLVci OISNZI3OD do l't 5moI1I o00 O0g 001 10 9 auD4uad jo ajnssaid JodDA 01 gl CZ 0 _o n 5'!9

28 26 24 22 20 CQ 18 I-D 1 14?, -,12 I 10 8 6 4 2< 43 inch ID finned tube unit area required = 9840 sq ft Q BTU 106 HR FIGURE 5. GRAPHICAL SOLUTION OF EQ. 2 FOR 7XAMPLE DESIGN

REFERENCES 1. Colburn, A. P. and Hougen, 0. A., "Design of Cooler Condensers for Mixtures of Vapors with Noncondensing Gases," Ind. and Eng. Chem., Vol. 26, No. 11, 1934, pp. 1178-1182. 2. Cairns, B. C., "Approximation Methods for Designing Cooler-Condensers," Chemical Engineering Science, Vol. 3, 1954, pp. 215-227. 3. Bras, G. H. P., "Shortcut to Cooler Condenser Design," Chem. En., Vol. 60, 1953, pp. 190-192. 4. Bras, G. H. P., "Polar Diagrams Speed Cooler-Condenser Design," Pet. Refiner, Vol. 36, 1957, pp. 149-154. 5. Mickley, H. S., "Design of Forced Draft Air Conditioning Equipment," Chem. Eng. Prog., Vol. 45, 1949, p. 739. 6. Young, E. H. and Ward, D. J., Design of Finned Tube Heaters and Coolers, IP-218, University of Michigan, May 1957. 7. Brown, G. G. and Assoc., Unit Operaticns, J. Wiley and Sons, Table 54, p. 515. 8. Young, E. H. and Ward, D. J., Design of Finned Tube Condensers, IP-184, University of Michigan, October 1956. 9. Young, E. H. and Ward, D. J., Fundamentals of Finned Tube Heat Transfer, IP-172, University of Michigan, August 1956. 10. Carrier, W. H..and Anderson, S. W., "The Resistance to Heat Flow Through Finned Tubing,' Heating, Piping, and Air Conditioning, May 1944, ASHVE Journal Section, pp. 304-318. 11. Gilmour, C. H., "Shortcut to Heat Exchanger Design - VI," Chem. Eng., 61, p. 212. 12. Carey, W. F. and Williamson, G. J., Inst. Mech. Engrs. Steam Group Proc., 1950, 163, pp. 41-53. 13. Perry, J. H., Chemical Engineers' Handbook, 3rd Edition, McGrawHill, 1954, p. 52. 14. McAdams, W. H., Heat Transmission, 3rd Edition, McGraw-Hill, 1954, p. 228. 15. Schuler, R. W. and Abell, V. B., "Heat Transfer and Mass Transfer in Cooler Condensers: Titanium Tetrachloride-Nitrogen System," Preprint 12, Heat Transfer Symposium, AIChE National Meeting, Louisville, Ky., March 1955. -51

16. Kern, D. Q. and Associates, "Compare Exchanger Costs Quickly," Pet. Refiner, Vol. 35, Aug. 1956. 17. "Standards of Tubular Exchanger Manufacturers Association," 3rd Edition, TEMA, New York, 1953. -32

UNIVERSITY OF MICHIGAN 3 I#1IIILO3035 I9