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Designing Spiral-Plate Heat Exchangers Spiral-p,late ex~hangers offer compactness, a variety of f,low arrangements, efficient heat transfer, and low maintenance costs. lihese and other features are described, along with a shortcut design method.

P. E. MINTON, Union Carbide Corp.

Spirall heat exchangers have a number of advantages over conventional shell-and-tube exchangers: centrifugal forces increase heat transfer; the compact configuration results in a shorter undisturbed flow lengtH; relatively easy cleaning; and resistance to fouling: These curved-flow units (spiral plate and spiral tube") are particularly useful1 for handing viscous or .solids-containing fluids ..

water. Electrodes may also be wound into the assem. bly to ano.dlcally protect surfaces ag~inst: corrosion. Spiral-plate exchangers are normally designed' for, the full pressure of each passage. Because the turns of the spirall are of relatively large diameter, each turn must. contain its design pressure,, and plate thickness is somewhat restricted-for these three reasons, the maximum design pressure is 150 psi.,. although foX' smaller diameters the pressure. may sometimes be higher. J.:.imitations of materials of construction gov• ern design temperature.

Spiral-Plate-Exchanger Fabrication Flow Arrangements and Applications A spiral-plate excHanger is fabt'icated from two relatively long strips of plate, which, are spaced apart and wound around an open1 split center' to form a pair of concentric spiral 1passages. Spacing is maintained uniformly along the length of the spiral by spacer· studs welded to the. plates. For most services, both, fluid-flow channels are closed by alternate channels welded at both sides of the spiral plate (Fig. 1) .. In some applications, one of the channels is left completely open (Fig. 4) ,. the other closed at both sides of the plate.. These two types of construction' prevent the fluids from, mixing. Spiral-plate exchangers are fabricated from any material that can' be cold worked and welded, such' as: carbon steelj stainless steels, Hastelloy :m and: C, nickel and nickel alloys, aluminum alloys, titanium, and copper alloys.. Baked phenolic-resin coatings,, among others, protecti against corrosion from· cooling • Although the spiral-plate and spiral-tutJe exchangers or• aimHar, their applications. and methods of· fobricaticm ore. quit• different; Thi~ article i• devoted wholly. to the spital-plate exchanger; an article in tiM Ml:ly 18 i1we of Chemical fnginH,;ng wilt take up the 1-piral+tul:Je exchanger. · For infonnation on aheU-and-tvbe exchangen, se. Ref. 8, 9, The desion method presented is used: bf, Union Carbide Corp, for the thermal and hydraulic det,ign of· IP!irat-p ate exchangers, and, is lOme·

wllot,dilfe,...nt from that used by the fabricator. Reprinted from CHEMICAL ENGINEERING, May 4,. 1970• Copyright

The spiral assembly can' be fitted with covers to provide three flow patterns: (:1) both fluids in spiral flows; (2)' one fluid in spiral flow andi the other in · axial flow across the spiral; ( 3), one fluid: in spiral flow and the other' in a combination of axial and spiral i flow. For spiral flow in both channels,. the spiral assem. bly includes flat covers at both sides (Fig. 1). In this arrangement, the fluids usually flow· countercurrently., with the cold fluid entering at the periphery and Bowing toward' the core; and the hot fluid entering at the core andi flowing toward the periphery. 11his type of exchanger can be mounted with the axis either vertical or horizontal. It finds wide application' in liquid-to-liquid service,. and for gases or condensing vapors if the volumes are not too large for. the maximum flow area of 72 sq. in. For spiral flow in one channel, and axial flow in the other, the spiral assembly contains conical covers, diShed heads, or· extensions with, flat covers (Fig. 2). h1 this design, the passage for axial flow is open. on, both sides, and the spiral flow channel is welded on· both sides. This type of exchanger is suitable for' services in· ©• 1970' by McGtaw·Hill I no. 330· West 42nd St •• New York, N.Y·. 10036

2030368834

SPI,RAL·PLATE · EXCHANGERS

SPIRAL FLOW in both channels is widely

use~ig.

1

which there is a large difference in the volt.unes of the two liquids. This includes liquid-liquid service, heating or rooling gases, condensing vapors, or as reboilers. It may be fabricated with one or more passes on the axial-flow side. And it can be mounted with the axis of the spiral either vertical or horizontal (usually vertically' for condensing or boiling)'· For combiMtion flow, a conical cover dist:ibutes the fluid into its passage (Fig. 3). Part of the spiral is closed at• the top, and the entering fluid flows only through the center part of, the assembly; A flat• cover at the bottom• forces the fluid to Bow spirally before leaving the exchanger. This type is most· often used for condensing vapors (mounted vertically)'· Vapors &rst flow axially until I their volume is reduced sufficiently for finali condensing and subcooling in spiral flow. A modification of this type: the column-mounted condenser (Fig. 4). A bottom extension is flanged to· mate with the column. flange. Vapor flows upward through a large central tube and: then axially across the spiral, where it is condensed. Subcooling may be by falling~film. cooling or by controlling a level of condensate in the channel. In the latter case, the vent• stream leaves in spiraf flow. This type is also designed to allow condensate to dropointo an accumulator without appreciable subcooling.

FlOW is spiral in one channel, axial in other,.-Fig. 2

The spiral-plate exchanger offers many advantages over the shell-and-tube exchanger·: (1)' Single-flow passage makes it ideal for· cooling or heating sludges or slurries. Slurries can. be proc· essed in the spiral at velocities as low as 2 ft./sec. For some sizes and: design pressures, eliminating the spacer studs enables the exchanger to handle liquids having a high content. of fioers. (2) Distribution is good because of the single-Bow channel. {3) The spiraHplate exchanger. generally fouls at much lower rates tlian the shell-and-tube exchanger because of the single-How passage and curved-How. path. If it fouls, it can be effectively cleaned chemically because of the single-How path and reduced bypassing. Because the spiral can also be fabricated: with identical! passages, it is used for services in• which the switching of fluids allows one fluid to remove the scale deposited by the other.. Also, because the maximum' plate width is 6 ft.,. it is easily cleaned with. High-pressure water or steam. (4). This exchanger is well suited for heating or cooling viscous fluids because its LID' ratio is lower· than. that; of tubular exchangers. Consequently, lam• inar-flow heat .transfer is much higher for spiral plates. When' heating or cooling a viscous fluid, the spiral should be oriented with the axis horizontal. With

COMBINAnON FLOW is used to condense vapors-Fig. 3

the uis verticaL the viscous fluid stratifies and this reduces heat transfer as much as 50%. (5)' With both fluids fl.owing spirally, flow can be countercurrent (although not truly so, because, throughout the unit, each channel is adjoined by an ascending and a· descending turn of the other channel! and because heat-transfer areas are not equal for each side of the channel, the diameters. being different). A correction factor may be applied;l how~ ever, it is so small' it can generally be ignored. Countercurrent flow and' long passages make possible clbse temperature approaches and precise temperature control. {6) The spiral-plate exchanger avoids problems associated with differential thennal expansion in noncyclic service. (7) In axial flow, a large_flow area affords a low pressure. drop, which becomes especially important when condensing under vacuum. (8) This exchanger is compact: 2;000 sq. ft. of heat-transfer· surface in a 58-in.-dia. unit' with a 72in.-wide plate..

Umitations Besides Pressure In addition to the pressure limitation· noted earlier, the spiral-plate exchanger also has the followimg disadvantages: {1 Repairing it in the field is difficult. A leak cannot be plugged as in a shell~and-tube exchanger (however, the possibility of; leakage in a spiral is less because it is fabricated from' plate generally much thicker than tube walls). Should a spiral need I repairing, removing the covers exposes most of the welding 1

)

CHEMICAL ENGINEERING/MAY 4, 1970

MODifiiED combination flow serves on

colum~g. 4

of the spiral assembly. However, repairs on the inner parts of the plates are complicated. · (2) The spiral•plate exchanger is sometimes precluded from serviee in which thennal eyclmg is frequent. When used in cycling services, its mechani-. cal. design sometimes must• be altered to provide. for much higher stresses. Full-faced gaskets of compressed asl:lestos are not generally acceptable for cycling services because the growth' of the spiral! plates. cuts the gasket~ which results in' excessive bypassing and; in some cases,. erosion of the cover. Metal-to-metal seals are generally necessary. ( 3) This exchanger · usually should not be used when a hard deposit forms during operation, be- · cause the spacer studs prevent such' deposits hom being easily· removed by drilling. When1 as £or some pressures,. sucli studs can be omitted, this. !.imitatiOn is not present' ( 4) For spiral-axial' flow, the temperature difference must be corrected. The conventionali correction for cross flow applies. Fluids are not mixed\ flows are generally single pass. Axial B.ow may be multipass.

SHORT,tUT RATING METHOD The shortcut rating method for spiral-plate exchangers depends on the same technique as that

2030368836

SPIRAL-PLATE EXCHANGERS • • •

Empirical Heat-Transfer and Pressure-Drop Rel'ationshi'.p Eq. No. Mechanism or Restriction

EmpiricaliEquation-Heat Transfer

Spiral Flow (l) No phase change (liquid~'• N •• {2) No phase change (gas),N11.

h = (11 + 3:54.D,!Du)

> N 11u

> N 11...

(3) No phase change (!liquid), NR.,

h = (11

+ 3.54 D,/D 11 }

0~023cG (NM.)-• ·~Pr)-' 11

0.0144 cG• • (D,) -•.:

< N ~

No phase change (gas). N Re

k = 0.925 k [gcpL'IJ.P = 0·001

Jl [. 1.035 Z!'· (~)".·" (.#-)'" ,- , 16sL [-W d~H (d~ 0.125) z~ W + 1.;> L-

< 100

t>.P =

>N

(15~,

(Hi) No phase change, N11.

11..-

> 10,000

(19) Condensing

3,38~~~,): "(i;J" (~)

Notes: 1. NR..- = 20,000(D,/D/1) 0 " 2 .. G = W.pd(Ap,,) 3. Surface-condition factor

t>.P = 0;000 5 -;

d,H

t>.P = 4 x 10-' s d~'

(w)u L

t>.P =

(~')

-++

-t;

L [ W ]• [

(17) Condensing

AxiaJIFiow (18) No phase change, N 11 ,

Drop

aP = 0:0011

Spiral Flow (14) No phase change, N ~-~ressure

2

:

(d,

1.3

z•;•

/,H)\''

+ 0.125) \w ' + 1'.5 +

0.0115 z•'

1'L6]

!!.. + 1 + 0.03 H d,

d~?~-. (~)' • [ Oi0115,zo' ~ + 1 + 0.03 H J

for copper and steel= LO; for stainless steel= 1.7; for pol.ished surfaces= 2.5.

MA'20~EERING

for Rating Spiral-Plate Heat Exchangers-Table I Physical Property Factor

:o-:"umerical Factor

:..T, ~

= 20.6

X

,.....

z•·•"M•·•••

·'II

.

:,, ,.

W... (T;,-TL) flT 11 W ... (T"-T,,) flT11

X

= 19.6

X

-1 ..

.! 77,

=32.6

X

= 3.8

X

·II

~

1.18

= 167

X

X

M'''(z,)•·"

M''"Z'',

~

•• 11

M''"Zl'11

..,.'" -~

... r ..

.l.

z•·•4•M•·"'

X X

500

X

:.T,. = 278

W0·'(TH-TL)

X

8 .....

x·

z•l•M•ts -C8 2

ll.T. W•·•(TH-TL) ll.T11

Pt·o.r

P"···

c

k.. c

X

h.

~~: = 3,333

X

h

1

W'' A

X

cs•·•••

k, 1

X X X

d,

LH•·• d, LH•·• d, LH"i7•

£-I•H

X

H•t•L•t•

X X

ll.T.

w···A

X

ll.T11 W~TH-Td

X

ATM

WA

X

ll.T11 W(Tit-Td flT11

X

WA

X

ll.T11

(See Note 1) (See Note 1)

1

X

L•·•H•·•

X

1Ii

X

)

d, HL•·• d, H£0·" L•t3H•r•

X

1

1

X

X

(See Note 1

1

X

3

M•··•z•·•a•·'"

= 6,000

J.T, J.T,.

ll.T~r

X

= 0.619

J.T II

ll.T• W• 11 (T .. -Td

X

8 .,.

= 158

.·r

·;..!_ = 16.1

W'',A

X

cs•

J

W 2' 3 (T 11 -TL} flT 11

X

s"'' (,z.p.u

MecHanical Design Factor

Work Factor

d,"·'I'

(See Notes 2 and 3)

p _.1?._

LH 1

LH 1

LH

(See Note 1) (See

Note

1:)

CHEMICAL ENGINEERING/MAY 4,.1970

1

2030368838

SPIRAL·Pl.ATE.. EXCHANGERS •

for sheU.and~tube heat exchangers (which were discussed oy Lord, Minton and Slusser&). Primarily; the method combines into one relationship• the classical' empirical equations for fihn, heattransfer coefficients with• heat'-ballmce equations and with correlations tHat describe tHe geometry of the heat exc~ger. The resulting .overall; equation• is recast into three separate groups. that contain• factors relating to the physical properties of the fluid, the performance or duty of the exchanger, and the mechanical design or arrangement of the heat-transfer· surface. These groups are then multiplied tbgether' with• a numerical factor to obtain a product that is equal: to' the fraction of the total driving force-or log mean temperature difference (b.Tll or LMTD)that is dissipated across each element of resistance in the. heat-How path1 When the sum of the products for the individual resistance equa15 1, the trial design may be assumed to be satisfactory for heat: transfer. The physical significance is that the sum of the temperature drops. across each· resistance is equal to the total available t!.Tll· The pressure. drops for both' fluid~flow paths must be checked: to ensure that: both are within acceptable limits .. Usually, several trials are necessary to get a satisfactbry balance between heat transfer and pressure drop. Table I summarizes the equations used with the method for heat transfer and: pressure drop •. The columns on the left list the conditions to which each equation applies, and the second columns. gives the standard forms of the correlations for .6hn coefficients that are found in texts. The remaining columns in Table I: tabulate the numericaL physical property, work and mechanical design factors-all of which together. form tlie recast dimensional equation. 1'he product of these factors gives. the fraction of total temperature drop' or driving force ( tJ. T1/b.T11 ) across the. resistance. As stated, the sum of t!.Thl t!.T11 (the hot-fluid factor), tJ.T./tJ.TM (the cold-fluid factor)', b.T,/b.TJI. (the fouling factor), and AT..,/ti.T11 (the plate factor) determines the adequacy of: heat transfer. Any combinations of b.T1/ b.T11 may be used, as long as the orientation specified: by the equation matches that of the exchanger's flowpath .. The units in tHe pressure-drop eq1.1ations are consistent with those used for heat transfer. Pressure drop is calculated directly in psi.

Approximations and Assumptions For many organic liquids, thermal conductivity data are either· not available or difficult to obtain. JSecause molecular weights ('M) are known, the Weber equation, which, follows,. yields thermal conductivities. whose accuracies are quite satisfactory · for most design purposes: · k - 0.86 (q#'/M"')

u; on the other hand, the thermal conductivity

is lrnown, a pseudomolecular weight may be used: M -= 0.636 (c/k)l~ In what follows, each of tHe equations in Table I' i~ review~d, and the conditions in· which each equation apphes, as well as its limitations, are given 1 Jn, several' cases, numerical factors are inserted or appr?xim~tions made, so as to adapt the empirlcal relationshtps to the. design of spiral-plate exchangers. Such modifications have been• made to increase the accuracy, to simplify, or to Broaden the use of the ~ethod. Rather than by any simplifying approximations,. the accuracy of the method is limited by. that with which fouling factors, fluid properties and fabrication tolerances can be predicted.

Eq:uations tor: Heat; Transfer-Spiral Flow . Eq; (1):.-No Phase Change (Liquid), NR..

>

Na •.--

1~ for. liquids with Reynolds numbers greater than

the critical Reynolds number. Because the term (1 + 3.54 D,IDH) is not constant for any given heat, exchanger, a weighted average of 1.11 has oeen used for• this method. If a design is selected with a different value, the numerical factor can be. adjusted to reflect the new value. Eq. (2):..-No Phase Change ~Gas), N 11 , > NR.rc-is for gases with Reynolds numbers greater than the critical ReynoiCis number;. Because tlie Prandtl number of common• gases is appromately eq)Ja) to 0178: and the viscosity enters only as l-'o.2, the relationship of physical' properties for gases is essentially a constant. This constant, when combined with the numerical coefficient in Eq. (I) to eliminate the physical prop. erty factors for gases, results ih Eq. ( 2). As in Eq. (l )., the term (•1 + 3.54 D,/D'H) has been taken• ·as l.L Eq. (3)-No Phase Change (,Liquid), N 11 , < N 11 , . is for liquids in laminar Bow, at moderate ~T and with' large kinematic viscosity (p.Lfp). The accuracy of the correlation, decreases as the operating conditions or the geometry of, the heat-transfer surface are changed tQ increase the effect of natural convection. For a spiral plate:n (D/L)1 11 = [12 112 D,j(DHd,)"•J"' = 2"' (d,/dn)•"

The value of ( d,/d;, )1'6 varies from 0.4 to 0;6. A value of o,s for (d.ldH) 1' 8 has been used for this method.

Heat Tramsfer Equations-Spirator Axial Flow Eq. (4}-Cond.ensing Vapor,. Vertical, NR.. < 2,100 -is for film condensation of vapors on a vertical plate with a terminal Reynolds number (41J'/~) of· less than' 2,l00. Condensate loading (or) for veftical plates is II' = W/2L. For Reynolds numbers above 2,100,. or fbr high Ptandtl numbers, the equation should be • adjusted by means of the Dukler plot, as discussed by Lord, Minton, andi Slusser.s To use Eq. ( 4)' most conveniently, the constant in it should be multiplied by the ratio of the value obtained by the Nusselt equation to the Dukler plot. 1'he preceding only applies to the condensation

of condensable vapors. Noncondensable gases in, the vapor decrease the &1m coefficient, the reduction depending on the relative sizes a£ the gas-cooling load and the total cooling and condensing duty. (A method for analyzing condensing in the presence of noncondensable g~~Ses is discussed by Lord, Minton and Slusser.~} Eq .. (5)-Condensate Subcooling, Vertical,. Na. < 2,100-is fbr laminar films flowing in layer form down vertical plates. ThiS equation is used when, the. condensate from' a vertical condenser is tb be cooled below the bubble point. In, such cases, it is convenient to treat the condenser-subcooler as two separate heat exchangers-the first operating only as a condenser, (no subcooling), and the second as a liquid cooler only. Fig. 5 shows the assumptions that must be made to determine the height of each section, so as to calculate intermediate temperatures that will · permit in, fum the calculation of the LMTID. Eq. ( 4) is used in combination with appropriate expressions for other resistances to heat transfer, tb calirulate the height of the subcooling section. In tlle case of the subcooling section only (See Fig. 5), the arithmetic mean temperature · difference,, [ ( T hm T..,.) + CThL - T.L)]/2, of the two fluids should be used instead of the log mean temperature difference ..

Equations for Heat Transfer-Axial Flow Eq. (6)-No Phase Change (Liquid)l NR.,

>

10;000

-is for liquids. with Reynoltls numbers greater than

Hl,OOO;. Eq. (7)-No Phase Change (Gas),. NR., > 10,000is for. gases with Reynolds numbero greater than 10,000 .. Again, because the physical property factor for common, gases is essentially a constant, thiS constant is combined with the numerical' factor in Eq. (:6) to get Eq, (7).

Eq. (8)-CondenMg Vapor,. HorU:ontal, Na. < 2,100-is for &1m condensation on spiral plates ar-

ranged for horizontal axial flow witli a terminal Reynolds number a£ less than 2,100. For a spiral plate, eondensate loading (r) depends on the length of the plate and spacing between adjacent plates. For any given' plate length and channel spacing, the heat-transfer area for each' 360-deg. winding of the spiral fucreases with the diameter of, the spiral. The number of revolutions affects the eondensate loading in two ways: ( 1) the heat-transfer area changes,. resulting in' more condensate being formed in the outer spirals; and (2) the effective length over which the condensate is formed is.determiiled by the number of revolutions and the plate width. 'Ilhe. equations presented depend: on a value for the effective number of spirals of: L/7. Therefore,. the eondensate loading is given by:.

r - W (1,000) 7 (12)/4HL- 21,000 W/HL This equation can be corrected if a design is. obtained with a significantly dilferent condensate loading. It does not include allowances for turbulence due to vapor-liquid sHearing or splashing of, the condensate. At high condensate loadings, the liquid condensate on the bottom of the spiral channels may blanket part of the exchanger,'s effective heat-transfer surface. Eq. (9)-Nucleate Boiling, Vertical-is for nucleate boiling on vertical plates. In a rigorous analysis of a thermosyphon reboiler, the calculation of heat transfer is combined with the hydrodynamics of the system to determine the circulating rate through the reboiler. How.ever, for most design purposes, tliis calculation is not necessary. For atmospheric pressure and higher, the assumption, of nucleate boiling over the full height of the plate gives. satisfactory results. The assumption of nucleate boiling over the entire height of the plate in. vacuum service produces overly optimistic results. (The mechanism of thermo-

Condensing zone

stiBCOOUNG·ZONE calculations depend on arittlmetic·mean tem· perature difference of, the tWo fluids instead of log·mean tem· perature differenoes-Fig. 5 CHEMICAL ENGINEERING/MAY 4, 1970

2030368840

SPIRAL·Pl.ATE EXCHANGERS • • •

syphon reboilers has been already discussed by Lord, Minton and Slt1sser.s. ') A surface condition factor, I, appears. in the empiri· cal correlations for boiling coefficients. This. is a measure of, the number of nucleation sites for, bubble formation on the heated surface. The equations for t!.Tt/tl.TII contaim,I' (the reciprocal of I), which Has values of 1.0 for copper and steel, 1.7 for stainless steel or chrome.nickel alloys, and 2.5 for polished surfaces.

Nomenclature A B

c c

D.

D. D. d,

I

G g.

Equations for Heat Transfer-Plate

H

Eq. ~10) and (llrHeat Transfer Through the Plate-are for calculating the plate factor. The integrated form of the Fourier equation is QlfJ (k..,A tl.'Pw)/X, with X the plate thickness. Expressed in the form of a heat-transfer coefficient; hw 12k..,/p. Eq. (10) is used whenever sensible heat transfer i.'i involved for either fluid. Eq. (H) is usedi when there is latent heat transfer for each fluidl

h

=

k

=

L

M

p p

t:J' Q s

Equations for Heat Transfer-Fouling Eq. (12) and (13)-Fouling-is for conduction of, heati through scale or solids deposits.. Fouling co• efficients are selected by the designer,. based upon his experience. Fouling coefficients of 1,000 to 500 (fouling factors ofi 0.001 to 0.002) normally require exchangers 10 to' 30% larger than for clean service; The selection of, a fouling factor is arbitrary because there is usually insufficient data for accurately assessing the degree of fouling that should be assumed for a (itiven design. Generally, fouling for a spiralplate exchanger' is considerably less than for shelland-tube exchangers. Because fouling varies with material. velocities and temperature, the extent to which this influences design depends on operating conditions and, to a great degree, the design· itself. Eq. (12) iS used for sensible heat transfer for either fluid, and Eq .. ( 13) when latent heat is transferred' on both sides ofi the. plate;

Equations for; Pressure

Dro~Spiral

Flow

Eq .. (U)-No PhDse Change Nth > N a ..-iS based on equations proposed by Sander.4 • 12 'Ilerm A in Sander's equation €an be closely approximated by. the value of 28/(d. + 0.125). Term B in Sander's equation accounts for the spacer studs. The factor 1.5 assumes 18 studs/sq. ft. and a stud dia. of 5/16 in. Eq. (15)-No Phase Change 100 < Na, < Na,.again is based upon the equation proposed by Sander. For, this flow regime, the. term A can be closely approximated' by the 'lalue of 103.5/(d, + 0.125). As in Eq .. (14h the factor of 1.5 accounts for the spacer studs. Eq. (16)-No Phase Ch4nge N 2 , < JOO:..aJso is based on the Sander eq1.1ations. For this flow regime,, term A can be closely approximated by the value of 2,170 d 1I.'f5. For this flow regime, the studs have

u w r

z

6

' I I

A

~£ P• I:, I:' IT

Heat-transfer area, sq. ft. Filln thickness (:0J00187, z r/ g, r) 111,.ft. Core dia., in. Specific liea.t, l3tu./ (lb.) ("F.) Equivalent dia., ft. Helix or spi.ral dia., R Exchanger outside dia.,in .. Channel spacing, in. Fanning friction factor, dimensionless Mass veloeity,lb./(hr.H!Iq. ft~) Gravitational I constant, ft,./. (hr.)• (4.18 x 1:0") Channel plate wi.dtli, in. Film coefficient of heat t:ransfer.,. Btu./ (hr.) (sq. ft.) (•F.) Thermal conductiVity, Btu./{hr.) (sq •. ft.) (•F;fft.) Plate length, ft. Molecular weight, dimensionless Pressure, psia. Plate thickness; in. Pressure drop,.psi. Heat transferred, Btu. Specific gravity (referred to water at 20 C.) Logarithmic mean temperature difference ·· (LM'IlD), •c. Overalll heat-transfer coefficient, Btu./. (hr.) (sq. ft.) eF.)· Flowrate, (lb./hr.) /1,000 Condensate loading, lb./. (hr.) (ft.) Viscosity, op. Time, hr. Heat of vaporization, Btu./lb. Viscosity, lb./.(hr.) (ft.) Liquidldensity, ll:L/cu1ft. Vapor density, lb.f.cu.ft. Surface condition factor, dimensionli!ss Surface tension, dynes/em.

Subscripts

11 c

I

. H

h L

m s w

Built fluid properties Cold stream Film fluid properties High temperature Hot stream .IJ.ow temperature Median temperature (1see Fig. 5) Scale or fouling material Wall, plate material

Dimensionless Groups

N...

N •• Nr.r

Reynolds number Critical Reynolds number Prandtl number

little effect· on the pressure drop,. and any such effect is included' in the Sander equation. Eq; (17rCondensing-is for calculating the pressure drop for· condensing vapors and is identical to that for no phase change, except for a facto11 of 0.5 used with the condensing equation. For total condensers, the weight rate of flow used in the calculation should be the inlet flowrate. Because the average Bow for partial condensers is greater than MAY 4,.1970/CHEMICAL ENGINEERING

2030368841

far total condensers,. the multip]ymg factor should be 0.7 instead of 0.5. Because the estimation of the pressure drop for condensing vapors is not clear-cut, the equation should be used only to approximate the. pressure drop, so as to prevent the design of exchangers with, excessive. pressure losses.

Equations for Pressure Drop--Axiali Flow Eq .. (:18}-No Phase Change N.,

>

10,000-is an

expression• of the Fanning equation for noncompressi~ ble fluids,.in which the friction factOr f. in, the Fanning equation = 0.046/N.,u. The equation has been revised to• account for pressure lbsses in the inlet and outlet nozzles, and the irnlet and outlet heads. The equation also, includes the correction for the spacer studs in the flow. eliannels. Eq. (19}-Conden.ring-again is identical to, that for no phase change, except for a factor of 0.5. Again. for partial condensers,. a value of 0.7 should be used instead of 0.5. For condensing pressure drop, only approximate results. should: be expected, which themselves should be used only to prevent designs that would result in excessive pressure losses. For overhead condensers, the pressure drop in the center tube must be added to the pressure drop calculated from Eq. (19).

Hot side Na. • (10,(!)()() X 6.225/(24 X 3.35) • 714 CoiC:I aide Na, • (lOiOOO X 5.925)/(24 X 8) • 309

Because the ftuids willi be in· lamimar flow, spiral flow is selected for the heat exchanger design. From Table I, the appropriate expressions for rating are: Eq. (3)' for both fluids, Eq. (10). for the plate, Eq, (12) for fouling and Eq. (15) far pressure drop.

Heat-Transfer Calculations Now; substitute values: Hot side, Eq. (3):

~T.!.. aTJI -

This example applies the rating method to the design of a liquid~Jiquid spiral-plate heat exchanger under the following conditions:

6 [

Coldi Side

Flowrate, lb./hr................. 6,225 5,,925 200 60 Inlet temperature, •c.. . . . . . . . . . . Outlet temperature, •c.. . . . . . . . ... I20 I 50.4 V:iscoeity, cp. . . . . . . . . . . . . . . . . . .. .. 3. 35' . 8 Specific heat, Btu./lb.;oF.... ... . ... 0.71 0.66 Molecular, weight................. 200.4 200.4 Specific ~Vfovity............... ... 0 . 843 liL843 Allowable yressure drop, psi.. . . . . . I I' Material o construction ........... stainless steel (k - Ul) (Z,/z.)u•: . . . . . . .. . . . . . . . . . . . . . . I I

Preliminary Calculations

=

Heat transferred 61225 X (200-120) X 1.8 X 0,11: 636,400 Btu./hr.

=

t.T11 (or LMTD) • (~ - 49.4)/ln(60/4U) • 54.5 C. For a flrst trial, the approximate surface can be calculated' using an assumed overall heat-transfer coefficient, U, of 50 :Btu./(hr.) (sq.. ft.) (°F.): A - 636,400/(50 X I.8 X 54.5) = I30 sq. ft.

Because this is a small exchanger, a plate width of 24 in. is assumed. Therefore, L i30/ (2 X 2). 32~5 ft. A channel spacing of % in. for both. fluids is also assumed. The Reynolds number for spiral flow can be calculated from the expressiont

=

N •• "' IO,OOO (JV/HZ)

Therefore: CHEMICAL ENGINEERING/MAY 4, 1970

·~5~ 80 J[ 241~·~~2.5]

• 32.6 X3.775 X 4.967 X 0.001387, • 0.848

Colli side, Eq. (3): 1 111

aT. _ ·[ 200.4 .• t:.TM 32.6 0.843'... 0.375 [ 24111 X 32.5,

111

][

5.925 X9C:U ]'X . 54.5

J

= 32.6 X 3.775 X 5.431 X 0.001387 • 0.927 Foulin.g, Eq. ( 12):

t:.T, _ 6 OOO f. 0J66 J [ 5.925 X 90.4 J [ . I J t.TJI - , 1,000 54.5 32.5 X 24 • 6,000 X 0;00066 X 9.828 X 0.001282 • 0.050 Flate,. Eq. (10):

E'· .., 500 [~'66-J f 5.925 X 9CMJ [ t:.'/111

Hot Side

· '~].

L

SAMPLE CALCUlATIONS

ConditiODs

200 4

32.6[ 0:843'.. , X

=

O.I25 ] 54.5 32.5 X 24 = 500 X 01066 X 9.828 X 0.0001603 • 0.052 10

L

•

Some Spi,r,ai-Piate Exchanger; Standar;ds-Table Ill Plate

Widths,, lin. 4 6 12 12 18 18 24 24 30 36 48

Outside 018., Maximum, .lin.

32 32 32 58 32

Core

Dia.,ln•. 8 8 8 l2 8

12 58 32 8 58 12 12 58 58 12 12 58 6C' 58 12 12 72 58 ahannel spacings, in.: 3/16 (12 in. maximum width.), 114 (48 ;n. maximum width), 5/16, %. %. %. 3f4 and: l. Plate thiCknesses: stainless steel) 14-3 U.S. gage; car· bon steel, ~. 3/16, 114 and 5/16 in.

2o3oasss42

SPIRAL·PLATE EXCHANGERS

Sum of Products (SOP):

+ 0.927 + 0.050 + 0.052

SOP = 0.848

= 1.877

Because S0P is greater than 1, the assumed: heat _xchanger is inadequate. The smface • area must be enlarged by increasing the plate width or the plate .length. Because, in all the equations 1 L applles directly, the follbwing new length is adopted: 1.877 X 32.5 - 61i ft.

Hot side, Eq. (15): 0;843

[

[-6·~]

X

0.375 X 24

1.035 X 3.35112 X 1 X 24112 (0.375+ 0.125) 6.2251 12

t:.P ·- 0.07236 X 0.6917 X 9.202 =- 0J461i psi.

X

f 1.035 X8 X 1 X 24 16] ti (0.375 + €1.125) 5.925112 + LS+ 61 11 :

112

,

Because the pressure drop is less than the allowal:lle; the spacing can• be decreased. For the second trial, ¥4 in. spacing for botH channels is adoptedl Because the Heat-transfer· equation for every factor except the plate varies directly witH d,, a new SOP· can be calculated~ t:.Tl/llTM "" 0.848 (0.25/0.375) tJ.T;/tJ.7'M = 0.927 (0;25/0.375) t:.T,/ATII = 0.052 (0;25/0.375) tJ.T,./tJ.TM = 0.050 SOP - 0;565 + 0.618 + 0.050 + 0.052 L = 1.285 X 32.5 = 41.8 ft. A = 41.8 X 2 X 2 = 167 sq. ft.

The author thanks American Heat Reclaiming Corp. for. providing figures and for permission to use certain design.standards. He is also grateful to the Union Carbide Corp .. for permission to publish this article.

H

2.

3. 4:

= 0.565 = 0.618 = 0.035

5.

== 1.285

8;

6. 7.

9 ..

10.

The new pressure drop becomes: Hot side:

J[-·6·~~~-] 0.25 X 24

Acknowledgements

References

t:.P = 0.07236 X 0.6583 X 13.55 = 0.645 psi.

llP- [' 0.001 X41.8 0.843

•

16 J

J[--5.9~] 0.375 X 24

11. 12.

X

13. 14.

1.035 X 3.35112 X 1 X 24 112 [ --M75 X 6.225112 ·--

+ 81f112

For a spiral-plate exchanger, the best design• is often• that• in. which• the outside diameter approximately equals the plate width.

+ 1.5 + 6f

Cold side, Eq .. (,15): t:.P .. [1).(101 X 61 0.843

Ds = [15.36 X L (d,. -t+ d;, + 2p) + Q2jtl• Ds = 115,36 (4L8) [0,25 + 0:25 + 2 (0.125)) Ds-= 23.4 in.

Design summary: Plate width.. . . . . .. . .. .. .. . 24 in. Plate length.............. . . . 41.8 ft Channel spacing............ 1/4 in .. (both sides) Spiral diameter.. .. . . . .. . . . . 23.4 in .. Heat-transfer area... . . . . . . 167 sq. ft. Hot-side pressure drop ..... 0.607 psi. Cold~side pressure drop ..... 0. 861 psi. U... ... . . . . . . ... . . . . . . ... . . . 38.8 Btu./(hr.)(sq.ft.)("F.)•

Pr,essur;e-Drop Cal.culations

4 p .. [ 0.001 X.61 ]

The diameter of the outside spiral can now be calculated with Table II and the following equation:

+ ·1.5 +

16 ] 411:8-

15. 16.

tJ.P - 0;04958 X 1.037 X 11.80 = 0.607 psi.

Baird, M. H. I.. MoCrae, W .. Rumford. F .. and Sle--. C. G. M.. Some Consldera.tlon" on Heat Tm.naofer In SpLI"al Plate Heat Exchangers, Chem. Eng. Science., 7, 1 and 2, 1957, p. 112. BLasius, H.. Dae .\hnlichkeit.sgesets bel Rlebunpvorgangzen in Flussigkeiten, Fonol&uug81&e/t. Ul, 1913. Colbu~n,.A. P .. A Method of CoJ:TelaUng Forced•ConW~e tlon Heat TTansfer Da.ta and e. Comparison With Fluid F'rlot.lon, A.ICI&F: TMM., !9, 1'933, p. 1174. HargiS, A. M ... Beok.mann, A. T. and Lola.oonoa., JL J.,. Applica.tion6 of Spiral' Plate Heat: Ex

View more...
P. E. MINTON, Union Carbide Corp.

Spirall heat exchangers have a number of advantages over conventional shell-and-tube exchangers: centrifugal forces increase heat transfer; the compact configuration results in a shorter undisturbed flow lengtH; relatively easy cleaning; and resistance to fouling: These curved-flow units (spiral plate and spiral tube") are particularly useful1 for handing viscous or .solids-containing fluids ..

water. Electrodes may also be wound into the assem. bly to ano.dlcally protect surfaces ag~inst: corrosion. Spiral-plate exchangers are normally designed' for, the full pressure of each passage. Because the turns of the spirall are of relatively large diameter, each turn must. contain its design pressure,, and plate thickness is somewhat restricted-for these three reasons, the maximum design pressure is 150 psi.,. although foX' smaller diameters the pressure. may sometimes be higher. J.:.imitations of materials of construction gov• ern design temperature.

Spiral-Plate-Exchanger Fabrication Flow Arrangements and Applications A spiral-plate excHanger is fabt'icated from two relatively long strips of plate, which, are spaced apart and wound around an open1 split center' to form a pair of concentric spiral 1passages. Spacing is maintained uniformly along the length of the spiral by spacer· studs welded to the. plates. For most services, both, fluid-flow channels are closed by alternate channels welded at both sides of the spiral plate (Fig. 1) .. In some applications, one of the channels is left completely open (Fig. 4) ,. the other closed at both sides of the plate.. These two types of construction' prevent the fluids from, mixing. Spiral-plate exchangers are fabricated from any material that can' be cold worked and welded, such' as: carbon steelj stainless steels, Hastelloy :m and: C, nickel and nickel alloys, aluminum alloys, titanium, and copper alloys.. Baked phenolic-resin coatings,, among others, protecti against corrosion from· cooling • Although the spiral-plate and spiral-tutJe exchangers or• aimHar, their applications. and methods of· fobricaticm ore. quit• different; Thi~ article i• devoted wholly. to the spital-plate exchanger; an article in tiM Ml:ly 18 i1we of Chemical fnginH,;ng wilt take up the 1-piral+tul:Je exchanger. · For infonnation on aheU-and-tvbe exchangen, se. Ref. 8, 9, The desion method presented is used: bf, Union Carbide Corp, for the thermal and hydraulic det,ign of· IP!irat-p ate exchangers, and, is lOme·

wllot,dilfe,...nt from that used by the fabricator. Reprinted from CHEMICAL ENGINEERING, May 4,. 1970• Copyright

The spiral assembly can' be fitted with covers to provide three flow patterns: (:1) both fluids in spiral flows; (2)' one fluid in spiral flow andi the other in · axial flow across the spiral; ( 3), one fluid: in spiral flow and the other' in a combination of axial and spiral i flow. For spiral flow in both channels,. the spiral assem. bly includes flat covers at both sides (Fig. 1). In this arrangement, the fluids usually flow· countercurrently., with the cold fluid entering at the periphery and Bowing toward' the core; and the hot fluid entering at the core andi flowing toward the periphery. 11his type of exchanger can be mounted with the axis either vertical or horizontal. It finds wide application' in liquid-to-liquid service,. and for gases or condensing vapors if the volumes are not too large for. the maximum flow area of 72 sq. in. For spiral flow in one channel, and axial flow in the other, the spiral assembly contains conical covers, diShed heads, or· extensions with, flat covers (Fig. 2). h1 this design, the passage for axial flow is open. on, both sides, and the spiral flow channel is welded on· both sides. This type of exchanger is suitable for' services in· ©• 1970' by McGtaw·Hill I no. 330· West 42nd St •• New York, N.Y·. 10036

2030368834

SPI,RAL·PLATE · EXCHANGERS

SPIRAL FLOW in both channels is widely

use~ig.

1

which there is a large difference in the volt.unes of the two liquids. This includes liquid-liquid service, heating or rooling gases, condensing vapors, or as reboilers. It may be fabricated with one or more passes on the axial-flow side. And it can be mounted with the axis of the spiral either vertical or horizontal (usually vertically' for condensing or boiling)'· For combiMtion flow, a conical cover dist:ibutes the fluid into its passage (Fig. 3). Part of the spiral is closed at• the top, and the entering fluid flows only through the center part of, the assembly; A flat• cover at the bottom• forces the fluid to Bow spirally before leaving the exchanger. This type is most· often used for condensing vapors (mounted vertically)'· Vapors &rst flow axially until I their volume is reduced sufficiently for finali condensing and subcooling in spiral flow. A modification of this type: the column-mounted condenser (Fig. 4). A bottom extension is flanged to· mate with the column. flange. Vapor flows upward through a large central tube and: then axially across the spiral, where it is condensed. Subcooling may be by falling~film. cooling or by controlling a level of condensate in the channel. In the latter case, the vent• stream leaves in spiraf flow. This type is also designed to allow condensate to dropointo an accumulator without appreciable subcooling.

FlOW is spiral in one channel, axial in other,.-Fig. 2

The spiral-plate exchanger offers many advantages over the shell-and-tube exchanger·: (1)' Single-flow passage makes it ideal for· cooling or heating sludges or slurries. Slurries can. be proc· essed in the spiral at velocities as low as 2 ft./sec. For some sizes and: design pressures, eliminating the spacer studs enables the exchanger to handle liquids having a high content. of fioers. (2) Distribution is good because of the single-Bow channel. {3) The spiraHplate exchanger. generally fouls at much lower rates tlian the shell-and-tube exchanger because of the single-How passage and curved-How. path. If it fouls, it can be effectively cleaned chemically because of the single-How path and reduced bypassing. Because the spiral can also be fabricated: with identical! passages, it is used for services in• which the switching of fluids allows one fluid to remove the scale deposited by the other.. Also, because the maximum' plate width is 6 ft.,. it is easily cleaned with. High-pressure water or steam. (4). This exchanger is well suited for heating or cooling viscous fluids because its LID' ratio is lower· than. that; of tubular exchangers. Consequently, lam• inar-flow heat .transfer is much higher for spiral plates. When' heating or cooling a viscous fluid, the spiral should be oriented with the axis horizontal. With

COMBINAnON FLOW is used to condense vapors-Fig. 3

the uis verticaL the viscous fluid stratifies and this reduces heat transfer as much as 50%. (5)' With both fluids fl.owing spirally, flow can be countercurrent (although not truly so, because, throughout the unit, each channel is adjoined by an ascending and a· descending turn of the other channel! and because heat-transfer areas are not equal for each side of the channel, the diameters. being different). A correction factor may be applied;l how~ ever, it is so small' it can generally be ignored. Countercurrent flow and' long passages make possible clbse temperature approaches and precise temperature control. {6) The spiral-plate exchanger avoids problems associated with differential thennal expansion in noncyclic service. (7) In axial flow, a large_flow area affords a low pressure. drop, which becomes especially important when condensing under vacuum. (8) This exchanger is compact: 2;000 sq. ft. of heat-transfer· surface in a 58-in.-dia. unit' with a 72in.-wide plate..

Umitations Besides Pressure In addition to the pressure limitation· noted earlier, the spiral-plate exchanger also has the followimg disadvantages: {1 Repairing it in the field is difficult. A leak cannot be plugged as in a shell~and-tube exchanger (however, the possibility of; leakage in a spiral is less because it is fabricated from' plate generally much thicker than tube walls). Should a spiral need I repairing, removing the covers exposes most of the welding 1

)

CHEMICAL ENGINEERING/MAY 4, 1970

MODifiiED combination flow serves on

colum~g. 4

of the spiral assembly. However, repairs on the inner parts of the plates are complicated. · (2) The spiral•plate exchanger is sometimes precluded from serviee in which thennal eyclmg is frequent. When used in cycling services, its mechani-. cal. design sometimes must• be altered to provide. for much higher stresses. Full-faced gaskets of compressed asl:lestos are not generally acceptable for cycling services because the growth' of the spiral! plates. cuts the gasket~ which results in' excessive bypassing and; in some cases,. erosion of the cover. Metal-to-metal seals are generally necessary. ( 3) This exchanger · usually should not be used when a hard deposit forms during operation, be- · cause the spacer studs prevent such' deposits hom being easily· removed by drilling. When1 as £or some pressures,. sucli studs can be omitted, this. !.imitatiOn is not present' ( 4) For spiral-axial' flow, the temperature difference must be corrected. The conventionali correction for cross flow applies. Fluids are not mixed\ flows are generally single pass. Axial B.ow may be multipass.

SHORT,tUT RATING METHOD The shortcut rating method for spiral-plate exchangers depends on the same technique as that

2030368836

SPIRAL-PLATE EXCHANGERS • • •

Empirical Heat-Transfer and Pressure-Drop Rel'ationshi'.p Eq. No. Mechanism or Restriction

EmpiricaliEquation-Heat Transfer

Spiral Flow (l) No phase change (liquid~'• N •• {2) No phase change (gas),N11.

h = (11 + 3:54.D,!Du)

> N 11u

> N 11...

(3) No phase change (!liquid), NR.,

h = (11

+ 3.54 D,/D 11 }

0~023cG (NM.)-• ·~Pr)-' 11

0.0144 cG• • (D,) -•.:

< N ~

No phase change (gas). N Re

k = 0.925 k [gcpL'IJ.P = 0·001

Jl [. 1.035 Z!'· (~)".·" (.#-)'" ,- , 16sL [-W d~H (d~ 0.125) z~ W + 1.;> L-

< 100

t>.P =

>N

(15~,

(Hi) No phase change, N11.

11..-

> 10,000

(19) Condensing

3,38~~~,): "(i;J" (~)

Notes: 1. NR..- = 20,000(D,/D/1) 0 " 2 .. G = W.pd(Ap,,) 3. Surface-condition factor

t>.P = 0;000 5 -;

d,H

t>.P = 4 x 10-' s d~'

(w)u L

t>.P =

(~')

-++

-t;

L [ W ]• [

(17) Condensing

AxiaJIFiow (18) No phase change, N 11 ,

Drop

aP = 0:0011

Spiral Flow (14) No phase change, N ~-~ressure

2

:

(d,

1.3

z•;•

/,H)\''

+ 0.125) \w ' + 1'.5 +

0.0115 z•'

1'L6]

!!.. + 1 + 0.03 H d,

d~?~-. (~)' • [ Oi0115,zo' ~ + 1 + 0.03 H J

for copper and steel= LO; for stainless steel= 1.7; for pol.ished surfaces= 2.5.

MA'20~EERING

for Rating Spiral-Plate Heat Exchangers-Table I Physical Property Factor

:o-:"umerical Factor

:..T, ~

= 20.6

X

,.....

z•·•"M•·•••

·'II

.

:,, ,.

W... (T;,-TL) flT 11 W ... (T"-T,,) flT11

X

= 19.6

X

-1 ..

.! 77,

=32.6

X

= 3.8

X

·II

~

1.18

= 167

X

X

M'''(z,)•·"

M''"Z'',

~

•• 11

M''"Zl'11

..,.'" -~

... r ..

.l.

z•·•4•M•·"'

X X

500

X

:.T,. = 278

W0·'(TH-TL)

X

8 .....

x·

z•l•M•ts -C8 2

ll.T. W•·•(TH-TL) ll.T11

Pt·o.r

P"···

c

k.. c

X

h.

~~: = 3,333

X

h

1

W'' A

X

cs•·•••

k, 1

X X X

d,

LH•·• d, LH•·• d, LH"i7•

£-I•H

X

H•t•L•t•

X X

ll.T.

w···A

X

ll.T11 W~TH-Td

X

ATM

WA

X

ll.T11 W(Tit-Td flT11

X

WA

X

ll.T11

(See Note 1) (See Note 1)

1

X

L•·•H•·•

X

1Ii

X

)

d, HL•·• d, H£0·" L•t3H•r•

X

1

1

X

X

(See Note 1

1

X

3

M•··•z•·•a•·'"

= 6,000

J.T, J.T,.

ll.T~r

X

= 0.619

J.T II

ll.T• W• 11 (T .. -Td

X

8 .,.

= 158

.·r

·;..!_ = 16.1

W'',A

X

cs•

J

W 2' 3 (T 11 -TL} flT 11

X

s"'' (,z.p.u

MecHanical Design Factor

Work Factor

d,"·'I'

(See Notes 2 and 3)

p _.1?._

LH 1

LH 1

LH

(See Note 1) (See

Note

1:)

CHEMICAL ENGINEERING/MAY 4,.1970

1

2030368838

SPIRAL·Pl.ATE.. EXCHANGERS •

for sheU.and~tube heat exchangers (which were discussed oy Lord, Minton and Slusser&). Primarily; the method combines into one relationship• the classical' empirical equations for fihn, heattransfer coefficients with• heat'-ballmce equations and with correlations tHat describe tHe geometry of the heat exc~ger. The resulting .overall; equation• is recast into three separate groups. that contain• factors relating to the physical properties of the fluid, the performance or duty of the exchanger, and the mechanical design or arrangement of the heat-transfer· surface. These groups are then multiplied tbgether' with• a numerical factor to obtain a product that is equal: to' the fraction of the total driving force-or log mean temperature difference (b.Tll or LMTD)that is dissipated across each element of resistance in the. heat-How path1 When the sum of the products for the individual resistance equa15 1, the trial design may be assumed to be satisfactory for heat: transfer. The physical significance is that the sum of the temperature drops. across each· resistance is equal to the total available t!.Tll· The pressure. drops for both' fluid~flow paths must be checked: to ensure that: both are within acceptable limits .. Usually, several trials are necessary to get a satisfactbry balance between heat transfer and pressure drop. Table I summarizes the equations used with the method for heat transfer and: pressure drop •. The columns on the left list the conditions to which each equation applies, and the second columns. gives the standard forms of the correlations for .6hn coefficients that are found in texts. The remaining columns in Table I: tabulate the numericaL physical property, work and mechanical design factors-all of which together. form tlie recast dimensional equation. 1'he product of these factors gives. the fraction of total temperature drop' or driving force ( tJ. T1/b.T11 ) across the. resistance. As stated, the sum of t!.Thl t!.T11 (the hot-fluid factor), tJ.T./tJ.TM (the cold-fluid factor)', b.T,/b.TJI. (the fouling factor), and AT..,/ti.T11 (the plate factor) determines the adequacy of: heat transfer. Any combinations of b.T1/ b.T11 may be used, as long as the orientation specified: by the equation matches that of the exchanger's flowpath .. The units in tHe pressure-drop eq1.1ations are consistent with those used for heat transfer. Pressure drop is calculated directly in psi.

Approximations and Assumptions For many organic liquids, thermal conductivity data are either· not available or difficult to obtain. JSecause molecular weights ('M) are known, the Weber equation, which, follows,. yields thermal conductivities. whose accuracies are quite satisfactory · for most design purposes: · k - 0.86 (q#'/M"')

u; on the other hand, the thermal conductivity

is lrnown, a pseudomolecular weight may be used: M -= 0.636 (c/k)l~ In what follows, each of tHe equations in Table I' i~ review~d, and the conditions in· which each equation apphes, as well as its limitations, are given 1 Jn, several' cases, numerical factors are inserted or appr?xim~tions made, so as to adapt the empirlcal relationshtps to the. design of spiral-plate exchangers. Such modifications have been• made to increase the accuracy, to simplify, or to Broaden the use of the ~ethod. Rather than by any simplifying approximations,. the accuracy of the method is limited by. that with which fouling factors, fluid properties and fabrication tolerances can be predicted.

Eq:uations tor: Heat; Transfer-Spiral Flow . Eq; (1):.-No Phase Change (Liquid), NR..

>

Na •.--

1~ for. liquids with Reynolds numbers greater than

the critical Reynolds number. Because the term (1 + 3.54 D,IDH) is not constant for any given heat, exchanger, a weighted average of 1.11 has oeen used for• this method. If a design is selected with a different value, the numerical factor can be. adjusted to reflect the new value. Eq. (2):..-No Phase Change ~Gas), N 11 , > NR.rc-is for gases with Reynolds numbers greater than the critical ReynoiCis number;. Because tlie Prandtl number of common• gases is appromately eq)Ja) to 0178: and the viscosity enters only as l-'o.2, the relationship of physical' properties for gases is essentially a constant. This constant, when combined with the numerical coefficient in Eq. (I) to eliminate the physical prop. erty factors for gases, results ih Eq. ( 2). As in Eq. (l )., the term (•1 + 3.54 D,/D'H) has been taken• ·as l.L Eq. (3)-No Phase Change (,Liquid), N 11 , < N 11 , . is for liquids in laminar Bow, at moderate ~T and with' large kinematic viscosity (p.Lfp). The accuracy of the correlation, decreases as the operating conditions or the geometry of, the heat-transfer surface are changed tQ increase the effect of natural convection. For a spiral plate:n (D/L)1 11 = [12 112 D,j(DHd,)"•J"' = 2"' (d,/dn)•"

The value of ( d,/d;, )1'6 varies from 0.4 to 0;6. A value of o,s for (d.ldH) 1' 8 has been used for this method.

Heat Tramsfer Equations-Spirator Axial Flow Eq. (4}-Cond.ensing Vapor,. Vertical, NR.. < 2,100 -is for film condensation of vapors on a vertical plate with a terminal Reynolds number (41J'/~) of· less than' 2,l00. Condensate loading (or) for veftical plates is II' = W/2L. For Reynolds numbers above 2,100,. or fbr high Ptandtl numbers, the equation should be • adjusted by means of the Dukler plot, as discussed by Lord, Minton, andi Slusser.s To use Eq. ( 4)' most conveniently, the constant in it should be multiplied by the ratio of the value obtained by the Nusselt equation to the Dukler plot. 1'he preceding only applies to the condensation

of condensable vapors. Noncondensable gases in, the vapor decrease the &1m coefficient, the reduction depending on the relative sizes a£ the gas-cooling load and the total cooling and condensing duty. (A method for analyzing condensing in the presence of noncondensable g~~Ses is discussed by Lord, Minton and Slusser.~} Eq .. (5)-Condensate Subcooling, Vertical,. Na. < 2,100-is fbr laminar films flowing in layer form down vertical plates. ThiS equation is used when, the. condensate from' a vertical condenser is tb be cooled below the bubble point. In, such cases, it is convenient to treat the condenser-subcooler as two separate heat exchangers-the first operating only as a condenser, (no subcooling), and the second as a liquid cooler only. Fig. 5 shows the assumptions that must be made to determine the height of each section, so as to calculate intermediate temperatures that will · permit in, fum the calculation of the LMTID. Eq. ( 4) is used in combination with appropriate expressions for other resistances to heat transfer, tb calirulate the height of the subcooling section. In tlle case of the subcooling section only (See Fig. 5), the arithmetic mean temperature · difference,, [ ( T hm T..,.) + CThL - T.L)]/2, of the two fluids should be used instead of the log mean temperature difference ..

Equations for Heat Transfer-Axial Flow Eq. (6)-No Phase Change (Liquid)l NR.,

>

10;000

-is for liquids. with Reynoltls numbers greater than

Hl,OOO;. Eq. (7)-No Phase Change (Gas),. NR., > 10,000is for. gases with Reynolds numbero greater than 10,000 .. Again, because the physical property factor for common, gases is essentially a constant, thiS constant is combined with the numerical' factor in Eq. (:6) to get Eq, (7).

Eq. (8)-CondenMg Vapor,. HorU:ontal, Na. < 2,100-is for &1m condensation on spiral plates ar-

ranged for horizontal axial flow witli a terminal Reynolds number a£ less than 2,100. For a spiral plate, eondensate loading (r) depends on the length of the plate and spacing between adjacent plates. For any given' plate length and channel spacing, the heat-transfer area for each' 360-deg. winding of the spiral fucreases with the diameter of, the spiral. The number of revolutions affects the eondensate loading in two ways: ( 1) the heat-transfer area changes,. resulting in' more condensate being formed in the outer spirals; and (2) the effective length over which the condensate is formed is.determiiled by the number of revolutions and the plate width. 'Ilhe. equations presented depend: on a value for the effective number of spirals of: L/7. Therefore,. the eondensate loading is given by:.

r - W (1,000) 7 (12)/4HL- 21,000 W/HL This equation can be corrected if a design is. obtained with a significantly dilferent condensate loading. It does not include allowances for turbulence due to vapor-liquid sHearing or splashing of, the condensate. At high condensate loadings, the liquid condensate on the bottom of the spiral channels may blanket part of the exchanger,'s effective heat-transfer surface. Eq. (9)-Nucleate Boiling, Vertical-is for nucleate boiling on vertical plates. In a rigorous analysis of a thermosyphon reboiler, the calculation of heat transfer is combined with the hydrodynamics of the system to determine the circulating rate through the reboiler. How.ever, for most design purposes, tliis calculation is not necessary. For atmospheric pressure and higher, the assumption, of nucleate boiling over the full height of the plate gives. satisfactory results. The assumption of nucleate boiling over the entire height of the plate in. vacuum service produces overly optimistic results. (The mechanism of thermo-

Condensing zone

stiBCOOUNG·ZONE calculations depend on arittlmetic·mean tem· perature difference of, the tWo fluids instead of log·mean tem· perature differenoes-Fig. 5 CHEMICAL ENGINEERING/MAY 4, 1970

2030368840

SPIRAL·Pl.ATE EXCHANGERS • • •

syphon reboilers has been already discussed by Lord, Minton and Slt1sser.s. ') A surface condition factor, I, appears. in the empiri· cal correlations for boiling coefficients. This. is a measure of, the number of nucleation sites for, bubble formation on the heated surface. The equations for t!.Tt/tl.TII contaim,I' (the reciprocal of I), which Has values of 1.0 for copper and steel, 1.7 for stainless steel or chrome.nickel alloys, and 2.5 for polished surfaces.

Nomenclature A B

c c

D.

D. D. d,

I

G g.

Equations for Heat Transfer-Plate

H

Eq. ~10) and (llrHeat Transfer Through the Plate-are for calculating the plate factor. The integrated form of the Fourier equation is QlfJ (k..,A tl.'Pw)/X, with X the plate thickness. Expressed in the form of a heat-transfer coefficient; hw 12k..,/p. Eq. (10) is used whenever sensible heat transfer i.'i involved for either fluid. Eq. (H) is usedi when there is latent heat transfer for each fluidl

h

=

k

=

L

M

p p

t:J' Q s

Equations for Heat Transfer-Fouling Eq. (12) and (13)-Fouling-is for conduction of, heati through scale or solids deposits.. Fouling co• efficients are selected by the designer,. based upon his experience. Fouling coefficients of 1,000 to 500 (fouling factors ofi 0.001 to 0.002) normally require exchangers 10 to' 30% larger than for clean service; The selection of, a fouling factor is arbitrary because there is usually insufficient data for accurately assessing the degree of fouling that should be assumed for a (itiven design. Generally, fouling for a spiralplate exchanger' is considerably less than for shelland-tube exchangers. Because fouling varies with material. velocities and temperature, the extent to which this influences design depends on operating conditions and, to a great degree, the design· itself. Eq. (12) iS used for sensible heat transfer for either fluid, and Eq .. ( 13) when latent heat is transferred' on both sides ofi the. plate;

Equations for; Pressure

Dro~Spiral

Flow

Eq .. (U)-No PhDse Change Nth > N a ..-iS based on equations proposed by Sander.4 • 12 'Ilerm A in Sander's equation €an be closely approximated by. the value of 28/(d. + 0.125). Term B in Sander's equation accounts for the spacer studs. The factor 1.5 assumes 18 studs/sq. ft. and a stud dia. of 5/16 in. Eq. (15)-No Phase Change 100 < Na, < Na,.again is based upon the equation proposed by Sander. For, this flow regime, the. term A can be closely approximated' by the 'lalue of 103.5/(d, + 0.125). As in Eq .. (14h the factor of 1.5 accounts for the spacer studs. Eq. (16)-No Phase Ch4nge N 2 , < JOO:..aJso is based on the Sander eq1.1ations. For this flow regime,, term A can be closely approximated by the value of 2,170 d 1I.'f5. For this flow regime, the studs have

u w r

z

6

' I I

A

~£ P• I:, I:' IT

Heat-transfer area, sq. ft. Filln thickness (:0J00187, z r/ g, r) 111,.ft. Core dia., in. Specific liea.t, l3tu./ (lb.) ("F.) Equivalent dia., ft. Helix or spi.ral dia., R Exchanger outside dia.,in .. Channel spacing, in. Fanning friction factor, dimensionless Mass veloeity,lb./(hr.H!Iq. ft~) Gravitational I constant, ft,./. (hr.)• (4.18 x 1:0") Channel plate wi.dtli, in. Film coefficient of heat t:ransfer.,. Btu./ (hr.) (sq. ft.) (•F.) Thermal conductiVity, Btu./{hr.) (sq •. ft.) (•F;fft.) Plate length, ft. Molecular weight, dimensionless Pressure, psia. Plate thickness; in. Pressure drop,.psi. Heat transferred, Btu. Specific gravity (referred to water at 20 C.) Logarithmic mean temperature difference ·· (LM'IlD), •c. Overalll heat-transfer coefficient, Btu./. (hr.) (sq. ft.) eF.)· Flowrate, (lb./hr.) /1,000 Condensate loading, lb./. (hr.) (ft.) Viscosity, op. Time, hr. Heat of vaporization, Btu./lb. Viscosity, lb./.(hr.) (ft.) Liquidldensity, ll:L/cu1ft. Vapor density, lb.f.cu.ft. Surface condition factor, dimensionli!ss Surface tension, dynes/em.

Subscripts

11 c

I

. H

h L

m s w

Built fluid properties Cold stream Film fluid properties High temperature Hot stream .IJ.ow temperature Median temperature (1see Fig. 5) Scale or fouling material Wall, plate material

Dimensionless Groups

N...

N •• Nr.r

Reynolds number Critical Reynolds number Prandtl number

little effect· on the pressure drop,. and any such effect is included' in the Sander equation. Eq; (17rCondensing-is for calculating the pressure drop for· condensing vapors and is identical to that for no phase change, except for a facto11 of 0.5 used with the condensing equation. For total condensers, the weight rate of flow used in the calculation should be the inlet flowrate. Because the average Bow for partial condensers is greater than MAY 4,.1970/CHEMICAL ENGINEERING

2030368841

far total condensers,. the multip]ymg factor should be 0.7 instead of 0.5. Because the estimation of the pressure drop for condensing vapors is not clear-cut, the equation should be used only to approximate the. pressure drop, so as to prevent the design of exchangers with, excessive. pressure losses.

Equations for Pressure Drop--Axiali Flow Eq .. (:18}-No Phase Change N.,

>

10,000-is an

expression• of the Fanning equation for noncompressi~ ble fluids,.in which the friction factOr f. in, the Fanning equation = 0.046/N.,u. The equation has been revised to• account for pressure lbsses in the inlet and outlet nozzles, and the irnlet and outlet heads. The equation also, includes the correction for the spacer studs in the flow. eliannels. Eq. (19}-Conden.ring-again is identical to, that for no phase change, except for a factor of 0.5. Again. for partial condensers,. a value of 0.7 should be used instead of 0.5. For condensing pressure drop, only approximate results. should: be expected, which themselves should be used only to prevent designs that would result in excessive pressure losses. For overhead condensers, the pressure drop in the center tube must be added to the pressure drop calculated from Eq. (19).

Hot side Na. • (10,(!)()() X 6.225/(24 X 3.35) • 714 CoiC:I aide Na, • (lOiOOO X 5.925)/(24 X 8) • 309

Because the ftuids willi be in· lamimar flow, spiral flow is selected for the heat exchanger design. From Table I, the appropriate expressions for rating are: Eq. (3)' for both fluids, Eq. (10). for the plate, Eq, (12) for fouling and Eq. (15) far pressure drop.

Heat-Transfer Calculations Now; substitute values: Hot side, Eq. (3):

~T.!.. aTJI -

This example applies the rating method to the design of a liquid~Jiquid spiral-plate heat exchanger under the following conditions:

6 [

Coldi Side

Flowrate, lb./hr................. 6,225 5,,925 200 60 Inlet temperature, •c.. . . . . . . . . . . Outlet temperature, •c.. . . . . . . . ... I20 I 50.4 V:iscoeity, cp. . . . . . . . . . . . . . . . . . .. .. 3. 35' . 8 Specific heat, Btu./lb.;oF.... ... . ... 0.71 0.66 Molecular, weight................. 200.4 200.4 Specific ~Vfovity............... ... 0 . 843 liL843 Allowable yressure drop, psi.. . . . . . I I' Material o construction ........... stainless steel (k - Ul) (Z,/z.)u•: . . . . . . .. . . . . . . . . . . . . . . I I

Preliminary Calculations

=

Heat transferred 61225 X (200-120) X 1.8 X 0,11: 636,400 Btu./hr.

=

t.T11 (or LMTD) • (~ - 49.4)/ln(60/4U) • 54.5 C. For a flrst trial, the approximate surface can be calculated' using an assumed overall heat-transfer coefficient, U, of 50 :Btu./(hr.) (sq.. ft.) (°F.): A - 636,400/(50 X I.8 X 54.5) = I30 sq. ft.

Because this is a small exchanger, a plate width of 24 in. is assumed. Therefore, L i30/ (2 X 2). 32~5 ft. A channel spacing of % in. for both. fluids is also assumed. The Reynolds number for spiral flow can be calculated from the expressiont

=

N •• "' IO,OOO (JV/HZ)

Therefore: CHEMICAL ENGINEERING/MAY 4, 1970

·~5~ 80 J[ 241~·~~2.5]

• 32.6 X3.775 X 4.967 X 0.001387, • 0.848

Colli side, Eq. (3): 1 111

aT. _ ·[ 200.4 .• t:.TM 32.6 0.843'... 0.375 [ 24111 X 32.5,

111

][

5.925 X9C:U ]'X . 54.5

J

= 32.6 X 3.775 X 5.431 X 0.001387 • 0.927 Foulin.g, Eq. ( 12):

t:.T, _ 6 OOO f. 0J66 J [ 5.925 X 90.4 J [ . I J t.TJI - , 1,000 54.5 32.5 X 24 • 6,000 X 0;00066 X 9.828 X 0.001282 • 0.050 Flate,. Eq. (10):

E'· .., 500 [~'66-J f 5.925 X 9CMJ [ t:.'/111

Hot Side

· '~].

L

SAMPLE CALCUlATIONS

ConditiODs

200 4

32.6[ 0:843'.. , X

=

O.I25 ] 54.5 32.5 X 24 = 500 X 01066 X 9.828 X 0.0001603 • 0.052 10

L

•

Some Spi,r,ai-Piate Exchanger; Standar;ds-Table Ill Plate

Widths,, lin. 4 6 12 12 18 18 24 24 30 36 48

Outside 018., Maximum, .lin.

32 32 32 58 32

Core

Dia.,ln•. 8 8 8 l2 8

12 58 32 8 58 12 12 58 58 12 12 58 6C' 58 12 12 72 58 ahannel spacings, in.: 3/16 (12 in. maximum width.), 114 (48 ;n. maximum width), 5/16, %. %. %. 3f4 and: l. Plate thiCknesses: stainless steel) 14-3 U.S. gage; car· bon steel, ~. 3/16, 114 and 5/16 in.

2o3oasss42

SPIRAL·PLATE EXCHANGERS

Sum of Products (SOP):

+ 0.927 + 0.050 + 0.052

SOP = 0.848

= 1.877

Because S0P is greater than 1, the assumed: heat _xchanger is inadequate. The smface • area must be enlarged by increasing the plate width or the plate .length. Because, in all the equations 1 L applles directly, the follbwing new length is adopted: 1.877 X 32.5 - 61i ft.

Hot side, Eq. (15): 0;843

[

[-6·~]

X

0.375 X 24

1.035 X 3.35112 X 1 X 24112 (0.375+ 0.125) 6.2251 12

t:.P ·- 0.07236 X 0.6917 X 9.202 =- 0J461i psi.

X

f 1.035 X8 X 1 X 24 16] ti (0.375 + €1.125) 5.925112 + LS+ 61 11 :

112

,

Because the pressure drop is less than the allowal:lle; the spacing can• be decreased. For the second trial, ¥4 in. spacing for botH channels is adoptedl Because the Heat-transfer· equation for every factor except the plate varies directly witH d,, a new SOP· can be calculated~ t:.Tl/llTM "" 0.848 (0.25/0.375) tJ.T;/tJ.7'M = 0.927 (0;25/0.375) t:.T,/ATII = 0.052 (0;25/0.375) tJ.T,./tJ.TM = 0.050 SOP - 0;565 + 0.618 + 0.050 + 0.052 L = 1.285 X 32.5 = 41.8 ft. A = 41.8 X 2 X 2 = 167 sq. ft.

The author thanks American Heat Reclaiming Corp. for. providing figures and for permission to use certain design.standards. He is also grateful to the Union Carbide Corp .. for permission to publish this article.

H

2.

3. 4:

= 0.565 = 0.618 = 0.035

5.

== 1.285

8;

6. 7.

9 ..

10.

The new pressure drop becomes: Hot side:

J[-·6·~~~-] 0.25 X 24

Acknowledgements

References

t:.P = 0.07236 X 0.6583 X 13.55 = 0.645 psi.

llP- [' 0.001 X41.8 0.843

•

16 J

J[--5.9~] 0.375 X 24

11. 12.

X

13. 14.

1.035 X 3.35112 X 1 X 24 112 [ --M75 X 6.225112 ·--

+ 81f112

For a spiral-plate exchanger, the best design• is often• that• in. which• the outside diameter approximately equals the plate width.

+ 1.5 + 6f

Cold side, Eq .. (,15): t:.P .. [1).(101 X 61 0.843

Ds = [15.36 X L (d,. -t+ d;, + 2p) + Q2jtl• Ds = 115,36 (4L8) [0,25 + 0:25 + 2 (0.125)) Ds-= 23.4 in.

Design summary: Plate width.. . . . . .. . .. .. .. . 24 in. Plate length.............. . . . 41.8 ft Channel spacing............ 1/4 in .. (both sides) Spiral diameter.. .. . . . .. . . . . 23.4 in .. Heat-transfer area... . . . . . . 167 sq. ft. Hot-side pressure drop ..... 0.607 psi. Cold~side pressure drop ..... 0. 861 psi. U... ... . . . . . . ... . . . . . . ... . . . 38.8 Btu./(hr.)(sq.ft.)("F.)•

Pr,essur;e-Drop Cal.culations

4 p .. [ 0.001 X.61 ]

The diameter of the outside spiral can now be calculated with Table II and the following equation:

+ ·1.5 +

16 ] 411:8-

15. 16.

tJ.P - 0;04958 X 1.037 X 11.80 = 0.607 psi.

Baird, M. H. I.. MoCrae, W .. Rumford. F .. and Sle--. C. G. M.. Some Consldera.tlon" on Heat Tm.naofer In SpLI"al Plate Heat Exchangers, Chem. Eng. Science., 7, 1 and 2, 1957, p. 112. BLasius, H.. Dae .\hnlichkeit.sgesets bel Rlebunpvorgangzen in Flussigkeiten, Fonol&uug81&e/t. Ul, 1913. Colbu~n,.A. P .. A Method of CoJ:TelaUng Forced•ConW~e tlon Heat TTansfer Da.ta and e. Comparison With Fluid F'rlot.lon, A.ICI&F: TMM., !9, 1'933, p. 1174. HargiS, A. M ... Beok.mann, A. T. and Lola.oonoa., JL J.,. Applica.tion6 of Spiral' Plate Heat: Ex

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