Desuhafion - Elscviet Publishing Company, Amsterdam - Printed in The Netherlands

A LOW TEMPERATURE MODEL FOR EQUILIBRATION RATES IN

FLASHING FLOW AND ITS DESIGN IMPLXATIONS

A. PORTEOUS

Departmenr of Mechanical Engineering, University of Giasgow (Scccrtand)

(Race&d April 14, 1969)

SUMhfARY

The rate at which flashing brine attains equilibrium is examined and a model developed from previoudy published data on brine flashing rates. The mode1 predicts that ffashing is an exponential decay process and correlates existing data for brine temperatures of 100 to 150°C.

Flash chamber design is examined on Ihe basis of the model and a novel concept in plant design obtained, based on the principle of unequilibrated brine flow; which leads to much shorter stage lengths for the same stage yield.

lNTRODUCi-ION

A major area of uncertainty in the design of multi-stage flash plants lies in the rate at which flashing brine attains equilibrium. Some studies have been done on modeis which postulate that bubble growth is the mechanism by which equili- bration takes place (Z-3). These models are probably quite v&id at the high temperature en? of the pIant at temperatures above roughly 150’F. However at the low temperature end, the hydrostatic head imposed by 18-24” of brine may we11 suppress nucleation and bubble growth in the bulk of the brine at the iow superheats of 3-5°F commonly in use.

Consider a stage temperature drop of 5°F and the equivaient pressure difference from this drop for the brine temperatures given in Table I.

TABLE I

Brine remperarure Pressure difference Head IQFl for AT = PF equivalent

(psi) (in. of brinej

I00 0.1524 4.25

:: 0.2496 0.3924 160 0.594

Desalination. 6 (1%9) 337-347

338 A. POR?EOUS

Thus for a brine depth of 24’ bubble growth in the bulk of the brine woutd not he anticipated at temperatures less than 140°F as the hydrostatic head would effectively inhibit the process- At even lower stage temperature drops, bubble growth woutd be effectively suppressed throughout the brine depth at the above temperatuntS,

The flashing mechanism must then be that of convective heat transfer. The 5y area where equifibration is mainly by convective {turbulent) heat transfer is the subject of this paper.

COXVEClWE WEAT TRANSFt-3 STAGE ANALYSlS

Consider a typical stage in a multi-stage Rash plant. Hashing takes place from the surfaces of a pool of brine, i.e. energy is removed from the brine to form

saturated vapaur at the stage pressure p,. Let

A, - brine surface area = L x B

AF - Bow area = B x D s - stage breadth

G - brine spesi&z heat D - depth of brine

% - hydraulic diameter h - heat transfer coefficient L - stage length f - residence time

tEE - brine Set temperature

fib - brine outlet temperature

G - boitif*g point elevation 2,’ - saturation temperature corresponding to the stage pressure ps.

6 - t,’ + f@ V - brine velocity

wz - brine flow rate entering the stage

WC2 - brine flow rate leaving the stage A???l - log mean temperature difference

The rate of energy transfer from the flashing brine is

Q= w;c, tBi - wZ cB b

if&N W,,then

k * = w, C,&I~ - b4J w

For convective: heat transfer, a rate equation can he used which makes use of a heat transfer coefficient h (yet to be determined) and a suitably defined log mean temperature difference ATm. Thus

lksai~nation. 6 (1969) 337-347

MODEL FOR 3RlNE FLASHING RAW 339

Q = h AaAT,

where (2)

AT, -_ ‘,i - ‘ff,F

ttri - 4 In -- ( )

(31

cilo- ts

Note that we are defining h in terms of the arbitrary area Aa = LB. Alter- native definitions would be to take all known interface areas i.e. LB + 2BD i- _

2f.D’ where D’ is the unmpp-essed depth, Such alternatives can be investigated .if desired. If proportions of chambers differ markedly this could be important. Meanwhile we give resuits in terms of this arbitrary choice.

Thus, from Eqs. (I), (2) and (3)

Now,

where /3 is the fraction Hence,

of equilibration achieved as defined by Silver (4).

h = - !I!!iZE In(a) AS

rearranging Eq. (4)

h’ hr(~) = - -

Wl

(‘4

(5)

where

now, W, = p AF Vand for a uniform velocity dist~but~o~ as wonId be expected in turbulent ffows in a uniform duct, a suitable residence time ? can be defined by t = (tjv) rearranging Eq. (5)

- h’r In(a) = --

P AF L (6)

or

In(a) = - h” t (71

~~u~i~i~~, 6 (1969) 337-347

340 A. PORTFiOUS

where, using chemical engineering terminology h” is a rate constant. Thus a plot

of In (CC) KS. I the residence time in the flash chamber should yield a line of slope -h”.

Using the data reported by Richardson-Westgarth (S), Figs. 1 and 2 were drawn. Fig.1 is a semi-log plot of ln c1 vs. t for brine temperatures of 100°F and 125°F respectively. Fig. 2 is also a semi-log plot of In a VS. t drawn to a larger scale for brine temperatures of 150°F and 200°F respectively.

The data can be fitted by a straight line in each case and this enables the

rate constants to be obtained. These are given in Table Il. The above constants are for brine depths of 1 Z-14’ depending on the experi-

mental data used. It is seen from Table II. and Figs. 1 and 2 that a distinct jump is observed

Fik 1. Unequilibrated fraction vs_ brine -ideuce time.

TABLE II

Brine temperature Rate cunstant I”F) {SCC-lj

100 1.1

125 1.83 150 2.3 200 9.3

Desalittation 6 (1%9) 337-347

MODEL FOR BRINE FLASHING RATES 341

Fig. 2. Uncquilibrated fraction S’S_ brine residenn? time.

in the rate constants above 150°F. This is probably due to a change in the flashing mechanism from convection to bubbie growth plus convection. The graphs of In cz vs. t for 100°F and 125°F both extend to the origin which would verify the exponential flashing mechanism arrived at for low temperatures. For 150°F and above, the graphs of In E vs. t do not slope back to the origin, but indicate a

“starting or initiating length” before equilibration commences. This may be due

to many factors.

(a) Perhaps the chamber construction caused flashing difficulties at the

higher temperatures.

(b) Some initial hydrostatic head effect may have been present thus inhibiting

flashing.

(c) The mechanism is almost wholly bubble growth and a finite time is

needed for the bubbles to grow and while growing they are swept along with the

brine, hence the initiation length concept.

However, what the pfots of In a vs. t do show is that a turbulent Bashing

mechanism can be postulated which satisfactorily fits the data from reference (5)

at temperatures below 150°F and brine depths of I2--14” with a At of 3°F. For the mechanism to be thoroughly verified or disproved more data will be required*.

l It is interesting lo note that more recent experimental (6) work on equilibration is said not to be in entire agreement with the results of reference (5).

Desalination, 6 (1969) 337-347

342 A. PORTEOUS

From the confirmation of the convective nature of the low temperature flashing m~hanism, a design correlation can now be obtained for stage length which embodies percentage equilibration and not the 99 % design point used in the Richardson-Westgarth correlation. This aspect is covered in the next section.

FLASH CHAMBfiR DFSIGN

This se&on is an attempt to evolve an expression which wilt satisfactorily yield the required chamber length for any desired percentage equilibration, briae depth and velocity based on the low temperature flashing mechanism.

From Eq. (4)

A3 =

where

and

A3 = BL

substituting Eqs. (9) and (IO) in (8) gives,

(10)

L (19

Now, the Reynolds number in the experiments reported in reference [5) was of order 2 x 105, i.e. high@ turbtdent. Hence it is reasonable to assume that the heat transfer coeficient h can he found from an expression of the form:

Nu = K, (Re)“(Pr)* (12)

where Q ‘u 0.8; b ‘u 0.4. ff the Prandtl number effkct is neglected for the moment, we have on

rearranging Eq. (12)

h (13)

where &, p_ p are constants at any one temperatlrre (as is the Prandtl number which can thus be incorporated in constant lu,). Le.

h = Kz m-t!’ J) t-a

m

04)

MODEL FOR BRINE FLA!SXfNG RATES 343

Substituting equation (14) in (11) we have

Now, D,,, for an open rectanguiar channel is given by

In the Richardson-~V~stgarth experiments, B hr 1.5D thus

0, = 1.70

substituting (17) into (I(i) we have

(17)

where K+ is an experimental constant found from a known data point at specit%zd L, 0, V and cc.

For example, using the data of reference (5), for a value of 99 % equi~brat~u~ and brine temperature of 15O”F. (The value of the expouent 4 is taken as 0.8, it being reeognised that this value will require to be determined experimentally.) Eq. (18) then becomes

1;,,9,, = 2_@ D’.” yo.2

where L and D are in feet and V in f@ec_

(19)

Eq_ (l9) indicates that stage length is strongly dependent on the brine velocity. If the brine v&ocity were doubled and all other parameters held constant Eq. (19) predicts a 15% increase in chamber length, whereas the design correlatiuns developed in reference (2) wouId indicate an 85% increase in chamber length if the brine velocity were doubled. It should be emphasis~ that the design Eq. (i8) is for brine temperatures below SOoF whereas that of reference (5) makes use of data mainly taken at higher temperatures where bubble growth is the dominant factor. What is importzmt is that further work be dane in this area to delineate the boundaries between the two regimes and verify the predictions of Eq. (18). The shorter lengths predicted by Eq. (18) at the higher brine velocities could mean large savings in plant costs.

The recognition that gashing is a rate controlIed process prompts the

~e~tjffa~~on, 6 (1969) 337-347

344 A. PORTEOUS

question; why design a multi-stage flash plant for complete equilibration? As chamber length is a function of the fraction of equilibration, a multi-flash

plant can be designed on the basis of incomplete equilibration to give substantially

the same stage yield but with a much shorter stage length. This may readily be

illustrated by considering the first three stages of a conventional multi-stage flash

plant as shown in Fig.3. The stage vapour :iaturation temperatures are respectively

I 2 3

VAPOUR VAPOUR VWOUR TE.,‘XRATURE TEMPERATURE TEMPERATuaE

2OO.F 196. F wit= F

c -

I At-4-F At-d F At-4- F

Fig. 3. An example of a usual multi-flash system. Note: Purr water temperatures arc used on the flashing brine stream for illustration

purposes only.

2OO”F, 196OF and 192°F. the temperature drop per stage is 4’F with the gashing

brine stream entering thz first stage at 204°F and leaving it at 200°F havingattained

equilibrium with the vapour. (For illustration purposes pure water temperatures are used on the flashing brine stream, the boiling point elevation being neglected).

Fig.4 shows the corresponding first three stages transposed to a design which makes use of the incomplete equilibration principle. The flashing brine is made to

flow in a deliberately induced non-equilibrium condition by so constructing the

first stage that the brine does not equilibrate completely. In this case a 3°F stage temperature drop is allowed instead of the 4°F needed to attain equilibrium, Le.

the fraction of equilibration is 75%. In the second and subsequent stages the

normal 4°F temperature drop is allowed but the brine stream is always in an unequilibrated condition due to the extra 1 “F bulk superheat which is maintained

throughout its passage in the plant to the last stage where partial or complete equihbrarion may be allowed depending on the plant design. It is noted that in the plant of Fig. 4, the fraction of equilibration is 80% in thesecond and subsequent

stages. The 75% fraction of equilibration in the first stage is due to the fact that this is the stage used to initiate the unequilibration which is maintained throughout

Desalination. 6 (1969) 337-347

MODEL FOR BRINE FLASHING RATES 345

UEht INPUT SECTION

VAPOIJR TEMPERATURE

200-F TEMPERMURE

196 ‘3 TEMPERATURE

1829 F

At-S-F Lit-4” F At-4’ F

Fig. 4. An example of a parti-flash system. Note: Pure water temperatures are used on the flashing brine stream for ~liust~tion

purposes only.

the plant. Thus in all the stages except the first, the stage output is the same as that of Fig.3. The yield reduction in the first stage can be substantially recouped in the last stage (or an intermediate stage) if complete equilibration is ailowed.

Now, as has been shown the stage length L is a function of /I which if all other factors are held constant, is given by

L =Kln $--- ( ) -B

where K is a constant. Thus for the plant in Fig. 3 where j3 = 99 %.

L 99% = 4.6 K

and for the plant in Fig. 4 where B = 80% for the second and subsequent stages

L 80% = 1.61 K

h is seen therefore that a substantial reduction of stage length is possible

by using the unequilibrated arrangement. (The name “parti-flash” has been suggested as descriptive of this type of design (7) and a UK Provisional Patent specification (8) has Seen obtained for it_)

It is, of course, realised that stage length is not governed by equilibration considerations only but by geometric and other factors such as condenser tube bundle insertion, access ports, demister plan area, etc. However, in the larger capacity MSF plants now envisaged or under construction with capacities of 5 mgd or greater, stage leogth will not be so intimately bound up with room for

Desaiination, 6 (1%9) 337-347

346 A. PORTEIOUS

tube bundles, access ports, etc. and equilibration considerations to obtain design

stage yield may well be the dominant factor.

The penalty or economic trade-off in going to pat&flash plant construction is a reduction in performance ratio due to the restriction on stage yield and hence

heat recovery placed on the first or unequilibration initiation stage of the parti-

f&h plant. As an example a conventional MSF plant with a performance ratio of 8 at the operating conditions of Fig. 3 would, if transposed to the operating

conditions of Fig 4 have a performance ratio of 7.4. There is thus a trade-off

between steelwork ar.d foundation cost reduction and extra brine heating costs.

If the whole of the predicted plant length reduction were in fact obtained, it would certainty be advantageous to use parti-flash.

The major problem in the above design is to control the flow of the un-

equilibrated brine from stage to stage. An experimental three stage flashing rig is being constructed at Glasgow University to study the associated brine transfer problems.

CONCLUSION

1. A method has been presented for displaying equilibration rate data with time as a variable thus underlining its importance.

2. A model has been developed (and verified as well as existing data permit) for low temperature equilibration rates.

3. The model predicts that flashing is an exponential decay process and from the data available characteristic time constants have been found for the experimental data in reference (5).

4. A design equation for chamber length has been developed which is more comprehensive than the only published correlation and which takes account of the following variables, percentage equilibration, brine depth and brine velocity. Tbe only variable not accounted for is temperature.

5. The normal design procedure of designing for complete equilibration has been questioned in the light of the foregoing work. A novel plant design based on unequilibratcd brine flow has been proposed which it is hoped will lead to substantial economies in steelwork costs for large capacity multi-stage flash plants.

FUTURE WORK

The implications of this paper shoutd be pursued, namely an investigation of low temperature flashing rates over a wide range of brine velocities in order to check the validity of the model and a study of interstage transfer of the flashing brine stream at various fractions of equilibration.

Desalination, 6 (I%91 337-347

MODEL FOR BRINE FLASHING RATES 347

ACKNOWLEDGEMENT

The assistance and constructive criticism provided by Professor R. S. Silver has greatly aided the development of this work.

REFERENCES

1. A. N. Dnxso~ AND R. S. SILVER, Desalinatkm, 2 (1967) 175-195. 2. R. I. H~v.rs A!JD D. C. LFSLIE. Desdinarion, 2 (1967) 329-336. 3. A. N. DICKSON AND J. K. R~A~IE, Scme basicaspects of the Bash distillation process, Nwleur

Desahkzrion. (Proc. IAEA Symp., Madrid. Nov. 1958), Elxvier. Amsterdam, 1969. pp. 859- 877.

4. R. S. SILVER, Some problems in research in the multi-stage flash distillation process. Proc. First Intern. Sympsium on Wurer Desalination. Washington. D.C. October 3-9. 1965, 2( 1967) I-12

5. Chamber geometry in multi-stage flash evaporators. Opirp of Saline Warm Report. November 1963 by Richardson-Westgarth.

6. H. C. SIMPSOX Visit to OfFice of Saline Water, Washington. D.C. and to Wtightsvilfe Heath Test Facility, North Carolina. Ukrersi~~ of Srra&&ie Report, At;gust 1968.

7. R. S. SILVER. Private Communiution, September JQ68. 8. A. PORTEOUS. Brit&h Parent Application No_ 54831. November 1968.

Desalination, 6 (1%9) 337-347