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Masters Theses Student Theses and Dissertations

1967

The relation of heat transfer to mass transfer in vaporization The relation of heat transfer to mass transfer in vaporization

through porous membranes. through porous membranes.

Chung-Liang Yeh

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Recommended Citation Recommended Citation Yeh, Chung-Liang, "The relation of heat transfer to mass transfer in vaporization through porous membranes." (1967). Masters Theses. 5041. https://scholarsmine.mst.edu/masters_theses/5041

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'rHE REIJ1.TION OF HEAT ·rRAlJSFER

TO J.1ASS TRANSFER IN VAPOB.IZATICN

rrHROUGH POROUS IviEr'IBRll..NES

BY

CHUNG-LIAJ:.JG YEH - I 1 ,:os i-

A

THESIS

submitted to the faculty of

'rHE UNIVERSITY OF NISSOURI A'r ROLLA

in partial fulfillment of the requirements for the

Degree of

NASTER OF SCIENCE IN CHENICAL ENGINEERING

.)

.~ 3 .·· /' ... ;.· '"

. ) l l

~~. )) -.~

Approved by

ii

ABSTRACT

·rhe object of this investigation was to study the mass

and heat transport phenomena through porous, water-repellent

membranes. The investigation concerned the rate of vaporiza­

tion of salt water at a porous membrane surface, mass transfer

of vapor through the pores of the membrane, condensation of

vapor on the other surface of the membrane in contact with

a coolant (fresh water), and the undesired heat transfer by

conduction through the membrane.

The water-repellent membrane separated the two liquid

phases by surface tension forces and provided a vapor phase

in its pores. Membranes made of fiberglass and Teflon had

been found suitable for this study, and were used throughout

the investigation with several different thickness.

The temperature difference between the two liquid phases

maintained the driving force the corresponding vapor pres-

sure difference - for mass transfer. Also, it supplied the

driving force for the undesired heat transfer across the

membrane.

Theoretical and empirical correlations were proposed to

fit the experimental data. It was observed that diffusional

resistance is the major rate controlling factor for mass

transfer. The correlations developed predicted values of

mass transfer coefficient reasonably close to the experimental

values, but there were differences between the correlation

for heat transfer coefficient and the experimental values.

iii

It I·Jas observed that the mass transfer rate ranged from 0. 23 2 to 1.41 lb./ft. hr., vii th total heat transfer rates from

2 43.4 to 272 Btu./ft. hr •• The mass transfer coefficients

2 varied from 0.114 to 0.420 lb./ft. hr. in. Hg •• The heat

conducted through the membrane was used to calculate an over-

all heat transfer coefficients which varied from 5.6 to 21.9

I 2 0 Btu. ft. hr. F.

iv

ABSTR.l\c~r • • • • • • • • • • • • • • • • • • • • • • • LIST OF FIGURES. • • • • • • • • • • • • • • • • • • • LIST OF TABLES • • • • • • • • • • • • • • • • • • • • :tJ 0 IIEl.J C LA T URE • • • • • • • • • • • • • • • • • • • • •

PAGE ii vi vii viii

I. INTRODUCTION • • • • • • • • • • • • • • • • • 1

II. THEOREJIICAL ANALYSIS AND LITERATURE B.E.VIEt..r • • .3

A. r~Iembranes • • • • • • • • • • • • • • • • • .3 B. Theory of f•Iass Transfer • • • • • • . • • • 4

1. Equilibrium and 1'-1ass Transfer between Phases • • • . • • • • • • • • • • • 4

2. Nolecular l1ass Transport • • • • • • • 6 .3. Diffusion in Binary System • • • • • • 6 4. Separation Based on Mass Transfer • • • 8

c. Theory of Heat Transfer • • • • • • • • • • 8 D. Hechanism of Simultaneous Heat and Nass

Transfer through a Porous, Hater-repellent Hembrane. _ • • • • • • • • • • • 12

E. Jlheoretically Based Equations for Combined :Nass and Heat Transfer • • • • • • • • • 14

I I I • EXPERIIVIEN'l,AL • • • • • • • • • • • • • • • • • 25

25 28 28 28 .30 .32 .32 .34 .36

A. Apparatus • • • • • • • • • • • • • • • • • B. 11aterials • • • • • • • • • • • • • • • • • c. Procedures • • • • • • • • • • • • • • • •

1. :r-rembrane Preparation • • • • • • • • • 2. Experimental Procedure • • • • • • • •

D. Neasurements • • • • • • • • • • • • • • • E. Heat Loss Approximation • • • • • • • • • • F. Nethod of Calculations • • • • • • • • • • G. Data and Results • • • • • • • • • • • • •

IV. DISCUSSION • • • • • • • • • • • • • • • • • • .37

A. Introductory Remarks • • • • • • • • • • • .37 B. f·1embrane Characteristics • • • • • • • • • .38 c. Correlations Developed between the

Experimental Data and Theoretical Equations • • • • • • • • • • • • • • • • .38

1. I1ass Transfer by J.1olecular Diffusion. • .39 2. Heat Transfer by Conduction • • • • • • 46

D. Comparison of Results • • • • • • • • • • • 47 E. I1is cellaneous • • • • • • • • • • • • • • • 54

V. CONCLUSIONS • • • • • • • • • • • • • • • • • • 57

VI. RECOMJVlENDAT IONS • • • • • • • • • • • • • • • • 58

VII.

VIII.

APPEI·JDICES • • • • • • • • • • • • • • • • • • •

Appendix A - Naterials • • • • • • • • • . • • • Appendix B - Hembrane Characteristics and

Data for Heat Loss Approximation • • . • • • • Appendix C - Data and Results •••.••••• Appendix D - Computer Program • • . • • • . Appendix E - Least-squares Approximating

~echl'lique . . . . . . . . . . . . . . . . . . BIBLIOGB...4..PHY • • • • • • • • • • • • • • • • •

IX. ACKNOWLEDGEHENT • • • • • • • • • • • • • • • •

X. vrrA . . . . . . • • • • • • • • • • • • • • • •

v

PAGE

59

60

61 64 74

77

85

87

88

vi

LIST OF FIGURES

FIGURE Fil.GE

2.1 Rea t Conduction through a Wall, Placed betvJ"een Two Fluids of Temperature ts and tf •••••. 10

2.2 Simultaneous Nass and Heat Transfer through

.3.1

4.1

4.2

Porous, Water-repellent IIJ:embrane • • • • • • • . 15

Experimental Apparatus • • • • • • • . • . . • . 26

Reciprocal of Nass Transfer Coefficient versus Fl • • • • • • • • • • . • • • . • • . • 42

Reciprocal of r1ass 'l'ransfer Coefficient Versus F • • • • • • • • • • • • • • . • • • . 43 2

4 • .3 Vapor Pressure of \-later as a Function of

4.4

4.5

'rempera ture • • • • • • • • • • • • • • • • • . 41+

Heat Transfer Coefficient versus F.3

Heat jrransfer Coefficient versus F4

• • • • • . 48

• • • • • • 49

4.6 Experimental Heat Transfer Coefficient versus Heat Transfer Coefficient Calculated fron Equations 4.2 and 4.6 ••••••..•••.. 50

4.7 Experimental Heat Transfer Coefficient versus

4.8

4.9

heat Transfer Coefficient Calculated from Equations 4 • .3 and 4.6 •••••••...... 51

Reciprocal of Hass Transfer Coefficient versus F . . . • • • • • • • • • • • • • • • • . 53 5 Reciprocal of Eass I'ransfer Coefficient versus F6 • • • • • • • • • • • • • • . . . . • 55

vii

LIS'r OF 'l'ABLES

·i..1ABLE PAGE

B.1 r<!embrane Characteristics • • • • • • • • • • • • 62

3.2 Data for Heat Loss Approximation of Apparatus. • 6J

C.1 Data and Results of Run Number 1 b = 0.50 • • • • • • • • • 0 • • • 0 • 0 0 • • • 65

C.2 Data and Results of Run Number 2 b = 0.50 • • • • • • 0 • • • • • • • • • • • • 0 66

Co] Data and Results of Run Number J b = 1.0 • 0 • • • • • • • • • 0 • 0 • • 0 • 0 0 67

c.4 mta and Results of Run Number 4 b = 1.0 • 0 • • • 0 0 • • • • • • • 0 • • • • 0 68

Co5 Data and Results of Run Number 5 b = 2.0 • • • • 0 0 0 • 0 • 0 • 0 0 0 • 0 0 • • 69

c.6 Data and Results of Run Number 6 b = 2.0 • • • • • 0 • • • • • • • • • • • • • 0 70

C.? Data and Results of Run Number 7 b = 4.0 • • • • • • 0 • • • • • • • • 0 • • • • 71

c.s Data and Results of Run Number 8 b = 4.0 • • • • • • • • • • • • • • • • • • • • 72

C.9 Data Used for Least-squares Analysis • • • 0 • . 73

c

Viii

NOHEHCLATURE

A= area of membrane used for mass and heat transfer, ft. 2

b = a variable assumed to represent thickness of the mem­

brane, defined as gm. of glass fiber/0.115 ft. 2 standard

area of membrane prepared as described on page 62.

C = total molar concentration of the entire medi~~. lb. moles/ft.J

f = molar concentration of liquid I'Tater on fresh Hater side,

lb. moles/ft. 3

cs = molar concentration of liquid 't'later on salt water side,

lb. moles/ft.J

c1 = molar concentration of water vapor at the membrane surface

on salt water side, lb. moles/ft.J

c2 = molar concentration of water vapor at the membrane surface

on fresh w·ater side, lb. moles/ft. 3

2 DAB = binary gas diffusivity for system A - B, ft. /hr.

D =effective diffusivity, ft. 2/hr. e

E = boiling point elevation of salt solution, °F

HL = enthalpy of liquid 't\Ta ter at its cell inlet temperature,

:Stu./lb.

I~= enthalpy, of saturated water vapor at salt water bulk

temperature, Btu./lb. 2 hs = heat transfer coefficient on salt water side, Btu./ft.

0 hr. F. 2 hf = heat transfer coefficient on fresh water side, Btu./ft.

0 hr. F.

h = assumed heat transfer coefficient for either fresh or

salt water, Btu./ft. 2 hr. °F.

ix

Km = over-all mass transfer coefficient based on the driving

force of partial pressure differences, lb./ft. 2 hr. in. Hg.

k =thermal conductivity of solid, Btu./ft. 2 hr. °F/ft.

ke =effective thermal conductivity of membrane, Btu./ft. 2

hr. °F/ft.

I1A = molecular weight of component A, lb./mole

r,r "B = molecular weight of component B, lb./mole

NA molar flux of component A, lb. 2 2 = moles/ft. hr. or lb./ft. hr.

PT = power input to salt water chamber, watts

PL = heat losses from salt water chamber to surroundings, watts

Ps = equilibrium partial pressure of water vapor on the salt

water side, in. Hg.

pf = equilibrium partial pressure of water vapor on the fresh

water side, in. Hg.

p1 = partial pressure of water vapor on the membrane surface

on salt water side, in. Hg.

p2 = partial pressure of water vapor on the membrane surface

on fresh water side, in. Hg.

qc = flux of heat transfered by conduction through the mem-

2 brane, Btu./ft. hr.

q~ = flux of heat transfered through the liquid film,

2 Btu./ft. hr.

R = gas law constant

'r = absolute trmperature, 0 R. 0 T = average absolute temperature, R.

= bulk temperature of fresh water, °C.

0 room temperature, c. 0 = bulk temperature of salt water, c.

tf = bulle tel11perature of fresh 11ater, oF.

t.,. = bulk temperature 0

of salt v'later, Op

4- = temperature on the membrane surface on salt Hater side, "1

t2 = tenperature on the membrane surface on fresh uater side,

T' = over-all heat transfer coefficient based on only the .J c heat conducted through membrane, Btu./ft. 2 hr. 01:1

.!! •

VA = molecular volume of A, ft.3/mole

v molecular volume of B, 3 = ft. /mole B

\{ = volume of condensate collected, ml.

YA = mole fraction of Hater vapor in membrane pores

YA1 = mole fraction of water vapor on the. surface on salt

~rater side

yAZ = mole fraction of water vapor on the surface on fresh

i'later side

AHv = latent heat of vaporization, Btu./lb.

AP =driving force, (ps - pf), in. Eg.

~t =temperature drop across the membrane, (ts - tr),°F

g = time duration to collect \~ ml. of condensate, seconds

Tr = total pressure, in. Hg.

0.,., .!' •

01.;1 ... .

1

I. INfRCDUCriON

Research in membrane phenomena and theory has a long

history, especially for biological systems. Presently the

application of membranes in engineering is in a state of rapid

development. Processes of separation and purification based

on selective properties of membranes have been found to be of

great potential industrial importance.

Evaporation is the principal industrial method of separa­

ting a volatile solvent from a solution containing a non­

volatile solute. For example, mineral-bearing water is often

evaporated to give a solid-free product for boiler feed water,

for special process requirement, or for human consumption.

11ulti-effect evaporators are commonly used to increase the econ­

omy of evaporators over that of a single effect. Each effect

must normally be at a different pressure in order to obtain

a certain temperature drop across its heating.surface. I'he

Nhole system requires large spaces, and complex equipment.

A stage of flash evaporation requires only a liquid sec­

tion, a vapor space and a condensate section,but no heating

surface. With certain flow patterns, a porous l'Tater-repellent

membrane, with solution on one side and condensate on the

other side, can provide an infinitely large number of single

pore "stages". Hm'fever, there exist some disadvantages. I' he

membrane providing the required vapor space produces a resist­

ance to the mass transfer of vapor, and also the heat con­

ducted through the membrane causes extra heat consumption.

2

For these reasons, a thorough study of mass and heat

transfer relations and their relative Inagnitudes is necessary

before commercializing this process.

The purpose of this investigation is to study the depend­

ence of mass and heat transfer properties on temperature dif­

ference and membrane thickness, and to study the relationships

between over-all heat transfer coefficients and over-all mass

transfer coefficients.

II. '.rHEORETICAL ANALYSIS

AND

LITERATURE REVIE\-1

J

In this section the relevent literature and theory are

reviewed with regard to membranes, diffusion, heat transfer,

and the mechanism of simultaneous mass and heat transfer

through a porous water-repellent membrane.

A. Hembrane:

A membrane is usually a form of gel with certain struc­

tural and permeability characteristics. Gels are colloidal

dispersions consisting of two phases: a solid dispersed phase

and a continuous liquid phase (28). Originally, most of the

membranes used in scientific investigations were natural mate­

rials such as animal sacs, fish bladders, and apple skin.

Presently, a variety of materials such as cellulose acetate,

synthetic resin, •reflon, and fiber glass are used in fabrica­

ting membranes.

filuch of the historical development of membrane theory

was stimulated by an attempt to explain transport phenomena of

biological systems. During this century, potential separation

processes based on membranes have become an attractive field of

study. Technical progress in dialysis, electrodialysis and

reverse osmosis is in such a state that they are widely applied

in engineering (18, 19), and show much promise for future applica­

tion. Recently, Rickles and Friedlander (21), and Findley (4)

have shown the highlights of new features of membrane application.

rhere are two types of membranes 't'rhich may be used in

separation processes. One type is homogeneous and consists

of only one apparent phase on a macroscopic scale. Another

4

type is heterogeneous and consists of more than one phase,

usually a solid phase and either a liquid or a gas phase. Ins ide

the homogeneous membrane, mass transfer by convection or hydrau­

lic flow is prevented by the membrane, whereas such mass

transfer may occur inside heterogeneous membranes. Heteroge­

neous membranes consisting of glass fiber, reflon, and air

were studied in this investigation.

A porous membrane separating two fluids may possess permi­

selectivity or transfer properties which are selective -- i.e.

permit transfer of some components but not of others. Hass

transfer through such membranes is normally by molecular diffu­

sion ( 29). 'rhe driving force for this movement is a concentra­

tion, thermal, or pressure gradient. Gas or vapor permeates

into the membrane and diffuses through the interstices of pores.

The rate of transfer by molecular diffusion is inversely

proportional to the square root of the molecular weight. rhe

water-repellent properties of the membranes studied served to

prevent liquids from penetrating the pores and thus maintained

the vapor space within the membrane.

B. 'rheory of Nass ·rransfer:

1. Equilibrium and Mass Transfer between Phases:

Equilibrium is the condition for all combinations of

phases such that net interchange of mass and energy is zero.

5

For all combinations not at equilibrium, the difference between

the existing condition and the equilibrium condition is a

driving force, or a potential difference, causing a change of

the system toward the equilibrium condition (5). \'ihen two sub­

stances or phases not at equilibrium are brought into contact,

there is a tendency for a change to take place and material

or energy will diffuse from a region of high concentration

(activity) to one of lm'l concentration (activity).

In all mass transfer operations, diffusion occurs in at

least one phase and often in both phases. The mechanism of

diffusion will be discussed later.

In evaporation of solutions, solvent diffuses through the

liquid phase to the interface between phases and then transfers

by diffusion, convection and, or, flow into the vapor phase

from the interface.

The action at the actual interface between the two phases

is important in the diffusion process. It is difficult to

obtain direct evidence of the action at the interface, but

it is commonly assumed that little or no resistance to mass

transfer exists at the interface itself. Goodgame and Sherwood

(7) have demonstrated equilibrium at the interface in one

experimental investigation. For the usual situation of low

and moderate diffusion rates in the individual phase, the

resistance to mass transfer at the interface is probably small.

'rhe relationship of mass transfer at a vapor-liquid interface

to vapor-pressure driving forces has been developed by Knudsen

( 12).

6

2. ~olecular hass Transport:

Molecular transport occurs as a movement of individual

molecules and results in the accompanying transport of mass,

heat and momentum. rhe transport of mass by individual molec-

ular motion is usually refered to as nr,1olecular diffusion".

Sherwood and Pigford (22) defined molecular diffusion as the

spontaneous intermingling of miscible fluids placed in mutual

contact, accomplished without the aid of mechanical mixing.

Diffusion may be induced by a concentration, thermal or pres-

sure gradient, or by other means. rhe most common cause of

diffusion is a concentration gradient of the diffusing campo-

nent. A concentration gradient tends to move the component

in such a direction as to equalize conentration and destroy

' the gradient ( 15). ·rransference of material due to convection

or turbulent mixing is refered to as "eddy diffusion". Eddy

duffusion is much more rapid than molecular diffusion cut

occurs only in spaces rather large compared to the pores of

a membrane.

Diffusion in liquids is fundamentallynot different fro~

diffusion in gases. In theory, the same laHS apply. I·lore

than one hundred years age (1855), Fick proposed a basic empir­

ical law of one-dimensional molecular diffusion ( 26), ~'lhich

is widely used in all diffusion problems.

3. Diffusion in Binary System:

Reasoning that diffusion along a concentration gradient

should be governed by a law analogous to Fourier's law of heat

7

conduction along a temperature gradient, Pick deduced that the

molar flux across a phase perpendicular to the direction of

the concentration gradient should be directly proportional to

the concentration gradient. A number of mathematical state­

ments of Fickts law have appeared in the literature.

For diffusion in a binary system, Fickts first law in

terms of NA, the molar flux, given by Bird, Stewart and

Lightfoot (1) is:

NA- yA(NA + NB) - CDABVYA (2.1)

\<lhere NA, NB - molar flux of A and B respectively

YA = mole fraction of A

c - total molar density of the entire medium at

some point along path

DAB = proportionality coefficient, or diffusivity

\1 = "gradient" or 11del 11 operator

This equation shows that the molar flux NA is the result of

two vector quantities: the molar flux which results from the

bulk flo.-r, yA (NA + NB), and the molar flux resulting from the

diffusion, CDAB VYA.

Equation 2.1 may be used directly if the system is one

of steady state. But, it is necessary to know the relation

between NA and NB, and to know the analytic expressions for C

and DAB as a function of position or yA in order to obtain a

solution. Since information is usually limited in diffusing

systems, and the resulting equations are not simple, various

averages and approximations are normally used.

4. Separation Based on I'1ass 'rransfer:

For mass transfer from one phase to another, usually

one component of the phase will transfer to a greater ex:tent

than another. 'rhis will cause a separation of the components

of the mixture. Hass transfer properties in separating a

mixture depend upon the phase characteristics, equilibrium

relations and ch.e.m.ical properties of the material to be pro­

cessed (6). In a gas-liquid system, if the liquid consists

of a nonvolatile solute and a volatile solvent, mass transfer

of the solvent to the gas phase will cause a complete separa­

tion of the solvent from solute. Evaporation is a typical

example of this kind of operation.

Hhen tlf;o liquid phases, one containing volatile compo­

nent A and nonvolatile component B and the other containing

pure A, are separated by a water-repellent membrane with gas­

filled pores, component A can be separated and transfered

from the solution to the pure A liquid by supplying any driv­

ing force which will produce a transfer of A in the vapor

phase.

c. Theory of Heat Transfer:

Local temperature difference causes, in all media, heat

flows such that thermal energy is transported from regions

of high temperature to regions of low temperature. Heat may

flow by one of three basic mechanisms: conduction, convection

and radiation.

In a solid body, the flow of heat is caused by the

transfering of molecular lcinetic energy from molecule to

molecule without appreciable net movement of molecules.

This is called conduction. In liquids, the molecules are

not confined to their locations, but move around and trans-

port kinetic energy in this way as by conduction. So long

as no macroscopic movement can be detected, this process is

still classified as conduction. In practice, heat flol'TS

through thin liquid films are considered as conduction.

Usually macroscopic movements are present in fluids and

9

transport heat by mixing or turbulence. rrhis mechanism is

known as convection. Radiation is a term given to the trans­

port of energy by means of electromagnetic waves. In these

experiments, conduction and convection are the important

types of heat transfer.

Consider a special case of heat transfer. In Fig. 2.1

is shown a solid wall separating two fluids. Suppose there

is a device for generating heat in Section I, and a mechan­

ical cooler in Section III. In Section I, the temperature of

the heated fluid adjacent to the heater is higher, so its

density is les.s than that of the unheated fluid at a distance

from the heater. The density difference causes some unbalance.

As a result of the unbalanced forces, a circulation is gen­

erated and it will bring the fluid to an approximately uniform

temperature, ts• This is the phenomena of natural convection.

In Section III, the same process requires that fluid adjacent

to the cooler has a lower temperature and higher density than

10

Heat Heat in out

qc

ts __,.

t 4-) tr .

G)

~ 4-)

~ CD I II III ~ (Hot fl.uid) (Solid (Cold fluid) CD wall) E-1

Distance, a. .....

Fig. 2.1 Heat Conduction throagh a Wall, Placed between Two Fluids ot Temperature t 8 and tr

11

the bulk o:f the fluid. ·rhe bullr temperature of fluid in

Section III is tf• Two thin stagnant films exist on each

side of the wall. .rhe interfacial temperatures between wall

and fluids are labelled t 1 and t 2 respectively.

Since there exists a temperature difference bet"t'leen the

two fluids, heat ltlill flow from the hot fluid through the

wall to the colder fluid. If the system is one of steady

state, there ~'lould be a constant heat flux, q • ·rhe heat c

transfer at the boundaries z = zl and z = z2 is given by

Net"lton• s "law of cooling" w1 th heat transfer coefficients he "" I

and hf respectively (2), i.e.:

. qc = hs(ts- tl) = hf(~t- tf) (2.2)

Then

t -t -q /h s 1 c s

(2.J)

and

( 2.4)

'rhe heat trans:fer in the solid wall is governed by a well­

knotm empirical lal'l deduce.d by Fourier ( J). The one-dimensional

:form of Fourier• s law of heat conduction is

Where qz

k

dt Tz

Then heat

and

---

q z -- k M

dz

heat flux in z direction

thermal conductivity

temperature gradient in z

conduction in a solid wall

q - -k

(2.5)

direction

can be expressed as:

(2.6)

12

(2.7)

Summing up equation 2.3, 2.4 and 2.7

q bqc q ts - tf = __.£ + -k + c

hs hf

= q <L + b + L) c hs k hf

(2.8)

For this type of heat transfer with constant heat flux, it

is customary to employ an over-all heat transfer coefficient

uc' as:

q = u ~t c c ( 2. 9)

L'Jhere q is heat flux and At is over-all temperaure dif­c

ference, ts - tf.

Comparing equation 2.8 with 2.9

The usual form of the rate equation is:

rate = driving force resistance

(2.10)

Then it can be seen that (ts - tf) is the over-all driving

force, and 1/Uc is the over-all resistance. Equation 2.10

expresses the fact that over-all resistance is the sum of

individual resistances.

D. .Iviechanism of Simultaneous Heat and Nass rransfer through

a Porous, Water-repellent Hembrane:

When a porous, water-repellent membrane, Section II in

Fig. 2.2, page 15, separates two fluids at appropriately dif-

,

13

ferent temperatures; one, fluid I, consisting of volatile

component A and nonvolatile solute, and the other, fluid III,

being condensate of A; the temperature gradient casues a

vapor pressure gradient of A. Under these gradients, mass

and heat will transfer from the high temperature region to

the low temperature region.

Hass is transfered from the hot fluid to the cold by the

following steady state processes:

(i) diffusion from the hot fluid to the membrane surface,

(ii) vaporization at the membrane surface,

(iii) flow or diffusion through pores of the membrane,

(iv) condensation at the membrane surface.

The mass transfered by pDocess (i) is by liquid phase diffu­

sion, as has been discussed previously (II. B. J). If non-

condensable gases are present in the pores of the membrane,

process (iii) is essentially gas phase diffusion in a multi­

component system. Consider the case in which there is only

one non-condensable gas, say component B, present in the mem-

brane. Then the analysis reduces to a problem of diffusion

in a binary system. For this type of problem, net mass trans­

fer is in the z direction only.

Equation 2.1 in one dimension is:

(2.11)

The non-condensable gas, B, stays stationary during pro­

cessing, so that NB = 0. Then equation 2.11 becomes

dyA

NA = YA NA - CDAB ~ (2.12)

14

It follows that the molar flux H1, can be exnressed as .. ...

CD dy NA = _ AB A

1-yA dz (2.13)

'rhe mechanism of heat transfer through the membrane is

quite similiar to t>Jhat has been discussed in II. c., except

some additional effects have to be considered. 'rhese are:

first, heat is conducted through not only solid membrane,

but also the pores in the membrane; second, the diffusing

vapors will be accompanied by their latent heat of vaporiza­

tion which will be transfered to the colder fluid upon

condensation. 'rhe conduction of heat in a gas, where there

is diffusion in the direction of heat flow, is greater than

if the gas were stagnant (23). In developing heat transfer

equations later, the concept of an effective thermal con­

ductivity, ke, which combines the complex conduction and

transport mechanism, will be introduced. The heat conduction

through the membrane may be written as:

(2.14)

Hhere q is heat flux through membrane by conduction and b c

is the thickness of the membrane.

Note that the rate of heat transfer through films does

not equal to q , but it includes in addition the latent heat c

associated with mass transfer.

E. Theoretically Based EqUation for Combined ~mss and Heat

Transfer:

Mass transfer between phases involves diffusional

I

I r (Hot Solutn)

'remp. t s

Equil. Ps

Liq. Cs

Equil. Vapor ·- - Cone-:- - - - r· -

I

I

II (Membrane)

b

r III I (Cold Condensate) I

tr

cr

Pr

I I

, __ 1 Equ11. Vapor ----·------1 Cone.

Fig. 2.2 S1multaaeo•• Mass aad Heat Transfer through Porous. Water-repellent Membrane

15

16

resistances in series. These diffusional resistances are

additive l·Ihen the mass transfer flux is constant along the

diffusion path at steady state. As shown in Fig. 2.2, the

diffusing component, A, has to face four resistances: a solu-

tion liquid film resistance on hot solution side, two inter-

facial resistances and a diffusion resistance in the membrane

pores. For low and moderate diffusion rates, the resistance

at the interface is. probably small and will be neglected in

most cases (16). Compared to resistance exerted by the men-

brane, liquid film resistance is assumed negligible.

In this particular investigation, the diffusing compo­

nent, A, and non-condensable gas, B, as discussed in II.D.

are water and air resp~ctively.

Equation 2.13 states that

CDAB dyA NA = - 1-YA dz

The system is at steady state and of constant crossectional

area along the transfer path, so

-dz = 0

Differentiating equation 2.13 with respect to Z

d CD dy - ( AB --l!) = 0 dz 1-YA dz

Since the diffusion path and area are not knoi'm, and since

adsorption and desorption might occur in the membrane pores,

it is necessary to define an effective diffusivity, De, to

replace the formallY defined diffusivity, DAB, for gas pairs.

17

Rewritten, the above equation is

d (CDe dyA) = O dz 1-y dz (2.15)

A

At moderate temperatures and pressures, the ideal gas law

holds for water vapor and air mixtures, so, the total con­

centration is:

c = rr Rr

Where rr = total pressure

R - gas constant

T - absolute temperature

The gas di~fusivity of a binary t i .L gas sys em g ven by Naxwell,

Jeans, and Champman is (24):

·r3/2 JFf D - d - k

AB - ff(V 1/3 + V 1/))2 . A B - 1 A B

Where d is numerical constant

VA, VB - molecular volume of A, and B (25)

MA, MB - molecular weight of A, and B.· Letting

d 1 k1 = ( 1/3 1/3)2

- , a constant for a JliB

VA + VB certain pair of gases.

product of C and De

.IT.. k rr3/2 = CDe - RT 1 1t

Where k 2 is a constant.

can be expressed as:

(2.16)

In these experiments on water vapor transfer through porous

membranes, the temperature difference between salt and fresh

water sides is less than 30°F., so it is reasonable to consider

CDe as a constant and having the value of ,_ CDe = k2 ~T

18

(2.17)

Where r is the arithmetic average absolute temperature in the

membrane. rrhen equation 2.13 and 2.-15 become:

k fF dy N = - 2 __J};.

A 1-yA dz (2.18)

k ~ _ddz ( 1 dyA) = o 2 ~ l. 1-yA dz

or

1 dy. £..... ( ~) = 0 dz 1-YA dz

(2.19)

The above differential equation is to be solved with the

following boundary conditions:

B. C. 1: at z

B. C. 2: at z = b, YA

Integrating equation 2.19 gives

- ln(1 - yA) = k 3z + k4

Applying the boundary conditions,

1 1 -YA1 k 3 = b ln

1-YA2

k 4 =-ln(1 - YA1 )

Substitute equations 2.21 and 2.22 into 2.20

z 1-YA - ln(1 - yA) = -b ln 1 - ln(1-YA1)

1-YA2

Rearranging the above equation gives

( 1 ) ( 1-YAz z/b 1 - YA = - YA1 )

1-YA1

On differentiating equation 2.23,

dy 1-~2 z /b ( 1-YA2) 1 - dzA = (1-YA1) (1-YA1) ln i-yA1 b

(2.20)

(2.21)

(2.22)

(2.23)

Combining with equation 2.23

dy A

- -= dz

Substituting equation 2.24 into equation 2.18, gives

IT 1-yA2 NA = 1c2 ln 1 b. -YAl

19

( 2. 24)

(2.2.5)

All these experiments were investigated under atmospheric

pressure, so the vapor-air mixture was inside the ideal-gas

region. 'rhen

:1. -lf and

Rewriting equation 2.25 in partial pressure form and taking

Naclaurin series expansion in order to obtain a form suitable

for linear least-squares analysis,

(2.26)

vlhere n = 1 , 2 , 3 , .• • • , GO

By neglecting terms of order higher than 2

(2.27)

20

Equation 2.27 sho~Ts mass transfer flux is a function of mem-

brane thickness, interfacial partial pressure of water vapor,

average temperature and operating pressure. Since interfacial

temperatures and their corresponding partial pressures are

not known, some modification has to be made to equation 2.27

in order to obtain an applicable equation.

'rotal heat transfered from hot fluid to cold is the sum

of heat transfered as vapor latent heat, qv, and heat con­

ducted through the membrane, qc. 'rhis heat will flow through

both films on each side of the membrane.

l'here:f'ore

(2.28)

(2.29)

Assuming equal film heat transfer coefficients on both sides

of the membrane. hs =. hf = h.

·rhen

If AI-lv

Equation

Hence

t -s

is the

q = v

2.14

tl = t2 - tf = latent

N A .t..H.v states

k e

heat of

=-b

qv + qc

h (2.30)

vaporization, then

(2.31)

(2.32)

rrh t difference between the two fluids e over-all tempera ure

21

is the sum of the individual temperature drops across the two

liquid films and the membrane, i.e.:

ts - tf = (ts - tl) + (tl - t2) + (t2 - tf)

Substituting equation 2.3~ into 2.)) gives

2 2ke ts - tf = h NA AHv +""bh(tl - t2) + (t1 - t2)

(2.33)

= ~ NAAliv + (~ + 1)(t1 ~ t 2 ) (2.34)

For moderate temperature differences, (ts - tf), it seems

reasonable to assume that

P1 + P2 ~ Ps + Pf

and (t1 - t 2 )/(ts - tf) ~ (p1 - P2)/(ps - Pf)

By these assumptions equations 2.34 and 2.27 can be expressed

as

or

(2.36)

And then from equation 2.)5, by substitution for (pl - P2 ),

2 2ke ts - tf) (.!L) ( J;) x ts - tf = h NA~Hv + (hb + 1)(Ps - Pf k2 .JT

NA (----)

Ps + Pf 1 +---211"'

t 8 - tf (2 Ps - Pf = NA ( P p ) h ( t - t ) ~Hv

s - f s f

2 2ke ...:E ,r J + i;(h'b"" + 1 ) If 21f+ P8 + Pr

(2.)7)

22

If w·e define an over-all mass transfer coefficient as follows:

NA = Km(Ps - Pf) = Km AP

Where /;lp = p - p s f

(2.J8)

Then, by combining equation 2.37 and 2.J8 and rearranging, the follov{ing equation t·rould be applicable:

1 2 (Ps - p 2 2ke lr2 = f)ARv b

h +- (- + 1)-ISn ts - tf kz hb JT2IT+ Ps + Pr

2 (Ps - Pf) till 4ke 1T'2 = Fi +-ts

v k2h (2Tf + Ps + Pr)/T - tf

2 1r2b + -k (2lt + 2 Ps + Pf)JT:

(2)~A 4ke 1T2 2 IT 2b = Fi ~t Hv + (k2h) ( 21f + Ps + Pf) .[T +( k2) ( 2Tr + Ps + pf) J¥

(2.J9) 1dhere AP = p s - p f , and ll t = t s - tf

The terms in parentheses are assumed approximately constant

in equation 2.39, and are in a form suitable for determination

as least squares coefficients of the parameters,

In this particular investigation, an important variable

is the membrane heat loss - heat transfered through the mem-

brane by conductfon, q • Since interfacial temperatures t 1 c and t 2 can not be directly measured, equation 2.14 is not prac-

tically applicable. For this reason, defining an over-all heat

transfer coefficient based on over-all temperature difference

is desirable.

23

Define over-all heat transfer coefficient, uc, according to

qc = Uc(ts - tf) = UcAt

Equation 2.14 states

1 b At -

(2.40)

u0 ke t 1 - t 2 (2.41)

From equation 2.34 and 2.38, we can get the following relation

2ke 2ke -+1 -+1

1 hb hb ------- - -------------- = ----------------t1 - t 2 2 2 A

At - h N A AH.v At - h Kin up Llliv

1 -At 1

2ke -+ 1 hb

- 2~~LU!v h At

By combining equation 2.41 and 2.42,

2k 2 b e + 1 h + ke L = ~ __ h_'E ____ - -------

uc Ke 2K A p 2 A P 1 T ~ t ~Hv 1 - h ~ A t A~

(2.42)

'rhe liquid film heat trans:fer coe:fficient is much larger than

the membrane effective conductivity-- b/ke>> 2/h, so we elim­

inate the term 2/h in the numerator of above equation without

introducing signi:ficant dif:ference. Then

b

1 Ka - --------~-----~ - 1- ~ K AE4Ey

h.in ~t

24

or

(2.43)

Here, also, the terms in parentheses are assumed approximately

constant and can be determined as least square coerficients

of the parameters:

1 b ,

In this investigation, the hot liquid used was 7% salt

solution. A 7% salt solution was calculated to have an ac­

tivity of water of o. 96. The cold liquid ~1as water condensate,

therefore:

Ps - 0.96 x (vapor pressure at ts)

Pr - vapor pressure at tf

This analysis suggests an experiment should measure water

mass transfer across membrane of various thickness as a func-

tion of bulk liquid temperature difference. These measurements

would provide values for the fundamental transport coefficients

for this process.

25

III. EXPERIHENTAL

A . Apparatus :

The apparatus used for this investigation consisted of

two chambers 2-1/8 inches in diameter formed by sections of

plastic pipe 1-1/2 inches thick with a membrane between them,

two electric heaters - one in the salt water section and the

other in the fresh water section, rubber gasketing, and the

necessary measuring devices. The plastic shells of the cham­

bers had holes for inserting heaters, filling tubes and vents.

Thermocouples were inserted through holes in two of the rubber

gaskets. The whole assembly was clamped together by two steel

flanges and four long bolts, and was covered with glass wool

for the purpose of insulation. The apparatus is illustrated

in Fig. 3.1, and its major components are described below:

'l'he I1embrane {Ivi): This is a porous, water-repellent membrane

made from fiber glass and Teflon. The Teflon imparts the

water-repellent character to the membrane. This property of

the membrane allows only water vapor to pass through the pores

and retains liquid at membrane surfaces. Membranes of four

different thickness were prepared for this investigation. The

detailed method of preparing the membranes will be discussed

later.

The Electric Heaters (H1 , H2 ): The electric heater in the salt

water section is the source of energy for evaporating the salt

water. 1'he other one, in the fresh water section, was used

to control the coolant temperature. Both heaters were made

26

Fig. ).1 Experimental Apparatus

A B1,B2 C1,C2 o,.,P2 E1,E2 F1,F2 G1,G2 GJ,G4 J M p R s1.s2 T1,T2 v1,v2 w z

Aa-bestos Vents Chambers for Salt and Fresh water Make up Line• Fresh Water outlet Steel F~es RUbber a.aket tor Inserting Thermocouples Rubber Gasket for Sealing Graduated cylinder ••bran• Pote~t1o:tneter :Reserto1r Plast1o Shells The:NDoouples variacs Wattmeter Plastic Plate

27

by inserting wound nichcrome wire into bent Pyrex glass tubes.

The Plastic Shells (s1 , s2 ): Two plastic shells with inside

diameter of 2-1/8 inches, separated by two rubber gaskets (G1

and G2 ) and membrane (M), created two chambers (c1 and c2 )

required for containing the salt water and fresh water respec­

tively. Holes were drilled to insert heaters (H1 and H2 ) and

tubings (B1 , B2 , n2 and E2 ). PVC plastic was used due to its

low heat conductivity, ease of fabrication, and availability.

I'he Plastic Plates and Asbestos (Z, A): The plate (Z) was

plastic 1/4 inch thick. It served to cover the salt water

chamber (c1 ), and also, having asbestos (A) between it and the

flange (F1 ), to reduce the heat loss.

'rhe 'rhermocouples (Tl, T2 ): rrwo Copper-Constantan ther­

mocouples were used,one on each side of the membrane. They

were placed right adjacent to the membrane surface, and the

measurements were considered to be bulk temperatures of salt

and fresh waters.

The ~va ter Reservoir ( R): 'rhe object of this reservoir was to

supply make up fresh water to the salt water chamber in order

to maintain the salt water concentration constant throughout

a run. It is a plastic container.

'rhe Variacs cv1 , v 2 ): Two "Adjust-a-Vel t" variacs were used

to adjust the power inputs to the electric heaters. Both were

made by Standard Electric Product Co., and had a range of 0-

140 volts.

28

'rhe Hattmeter (Vl): A wattmeter was used during this investiga­

tion to measure the power input to the electric heaters (H1 ).

It is an A-C and D-C wattmeter made by the Weston Electric

Instrument Co ••

'rhe Potentiometer (P): A potentiometer was used to measure

the e.m.f. of the thermocouples (T1 and Tz) in millivolts.

After conversion to temperature units, it gives bulk tem­

peratures of salt and fresh waters.

'rhe Graduated Cylinders ( J) : The graduated cylinders were

used to collect and measure the amount of condensate which

was formed during the run. They were 10.0 ml. and 25.0 ml.

Pyrex glass cylinders.

Hiscellaneous: An electric stirrer, a hot plate and an oven

were used for preparing the membranes.

B. Materials:

The materials used in this investigation, their specifica­

tion, manufacturers or suppliers and uses are listed in

Appendix A, page 60.

C • Procedures :

1. Membrane Preparation: Membranes were prepared based on

a Standard "1 gram" membrane containing 1 gram of glass fiber

for a membrane 0.115 ft: in area. Such a membrane was prepared

in the following manners.

one gram of owens-Corning Fiberglas, type AA, 1 micron

29

in diameter, was weighed. About 1/2 of this glass fiber was

crushed with ordinary pliers to reduce the average fiber length.

The rest of the glass fiber was split into small pieces by

hand and placed in a plastic container which contained about

350 ml. of tap water. rhe purpose of crushing the glass fiber

is to improve the uniformity of the membrane. Five drops of

glacial acetic acid was added to acidify the mixture and to

make the glass fiber disperse easily. The contents were then

stirred 1qith an electric stirrer until a satisfactory disper­

sion occured. 'rhen 0.5 ml. of DuPont Teflon 30 B aqueous

dispersion was added to the above contents and mixed with the

stirrer for about ten minutes. The Teflon provides a water-

repellent property to the membrane. Then, about 5 ml. of

alumium sulfate (Alz(S04) 3J solution, 0.05 gram per ml. of

solution, were added, again stirring for about ten minutes.

The intended purpose of the alum is to cause coagulation of

'reflon. onto the glass fiber surface. Experiments have verified

its beneficial effects ( 9). ·rhe slurry thus formed \'las ready

for filtration.

·rhe slurry was then filtered by vacuum through a Buchner

funnel, 4.7 inches in diameter, and the filtrate was refiltered

through the glass fiber once again. ·The wet membrane formed

1-vas washed with distilled water before it was removed from

the funnel. Then it was placed in between sheets of paper

towels and rolled with a cylindrical steel pipe to remove most

of the water and to increase the density • The membrane t'fas

then allowed to air dry ~turallY at room temperature for

more than twelve hours. ·rhe · membrane was dried further by

heating between aluminum foil on a hot plate at low heat

setting and was pressed heavily with a wooden block.

)0

Finally, the membrane, which was dried as indicated above,

was heated on an oven at abo.ut 600°F. for 30 minutes approx­

imately. reflon is partially melted under this temperature,

so this baking served to combine the ·reflon particles and to

bond them to the glass fiber. It also provides membranes with

more strength. The membrane thus prepared was tested with

cold water as well as boiling water. If the membrane was

sufficiently water-repellent, then it was used in experiments.

During this investigation, membranes of four different

thickness were prepared by using all quantities in proportion

to the standard "1 gram" membrane. The same procedure was

followed in all cases. The materials used for making the

membrane are listed in Appendix A, page6o.

2. Experimental Procedure: The following is the procedure

used during making a run for one single membrane of any

thickness at a particular power input. The experimental

sketch is shown in Fig. ).1 and discussed under the section

of "Apparatus". To begin a run, 7% by weight sodium chloride

solution was filled through tubing n2 into salt water chamber

c1 • This replaced the air in the chamber. Then, the end of

tubing n2 was connected to the reservoir outlet tubing D1.

This permitted water transfer out of the salt water side to

be made up by fresh water, thus maintaining the concentration

31

constant. Salt water level was kept about 1/4 inch high in

vent B1 • Similarly, condensate (fresh water) chamber c2 was

filled with distilled water using tubing E2 until water was

visible in vent B2. This would remove air in the chamber c2 .

After connecting E2 to E1 , distilled water was again fed into

vent B2 until there was water coming out of the tip of tubing

E1. 'rhe tip of tubing E1 as well as fresh water level in vent

B2 were usually about 1/4 inch higher than the salt water

level. This ad·justment of levels was to make sure that the

flow of water out of tubing E1 was definitely due to evapora­

tion of hot salt water and not due to leakage of salt water

from chamber cl.

After the le~el adjustment, heating was started. The

electric heater H1 was used to heat up salt water, and the

desired power input was adjusted with the aid of a variac,

V1• The power input was indicated by the wattmeter W. Since

high temperature difference between salt and fresh waters

might cause internal condensation and spoil the membrane,

another electric heater H2 was used to control the desired

temperature of the fresh water side. The variac Vz was used

to adjust power input to the heater H2. Sufficient time

allowance was given to obtain a steady state, which was in­

dicated by constant values of temperatures. Heasurements

were then started on condensate outflow rate, temperatures of

salt and fresh waters, room temperature, power input to salt

water, and time. A measuring cylinder J was placed under the

tip of tubing El to collect and measure the condensate.

32

'rhe fresh water was checked i'tTith silver nitrate occa­

sionaly to determine whether or not appreciable chloride ions

were present, and if so, the run was discarded. The procedure

was to take 5 ml. of condensate collected and add J drops of

1 N silver nitrate solution, then it was compared to the

turbidity of' 5 ml. of 200 ppm salt solution with the same

amount of silver nitrate added.

Readings were taken for eight different membranes of four

different thickness at different power settings. A minimum

of four reproducible readings were taken at each power setting

during the runs. The membrane characteristics are listed in

Appendix B, rable B.1, page 62.

The power inputs were changed according to the require­

ments, by adjustment o~ the variacs v1 and v2 , and the proce­

dure o~ taking the readings was repeated after a new steady

state was achieved.

D. Neasurements:

Experimental measurements during each run were teo­

peratures on each side of the membrane, room temperature,

power input to the salt water chamber, volume of condensate

collected and time.

E. Heat Loss Approximation:

Although experimental apparatus was covered by glass wool

for t ~ the heat supplied to the salt water insulation, par o~

di i I n order to calculate chamber was lost to the surroun ng a r.

JJ

the amount of heat conducted through the membrane, an estimate

of the heat loss is required. One set of runs was made for

this purpose.

The apparatus 1-was assembled in the same way as shown in

Fig. 3.1 except that a piece of rubber gasket, 0.30 em. in

thickness, was used to replace the membrane, and an analogous

procedure ~;as followed as described in III. c. 2. I11easure-

ments were taken on power input to salt water chamber, tem-

pera tures of salt and fresh waters, and room temperature. I' he

dataare tabulated in Table B.2, Appendix B, page 63.

Since there was no mass transfer, all the pol'ler input to

the salt water chamber flowed out of the chamber - part of it

was lost to the surroundings and the rest of it was conducted

through the rubber gasket to the fresh water chamber. By

applying the least-squares approximating technique, the best

correlation obtained was

P = 0.0548(tcs - t 0 r) + 0.0950(t0 s - tcf)

Standard deviation of error = 0.1379

\vhere p _ power input to salt water chamber, watts 0

- temperature of salt water, C.

t oc. - temperature of fresh wa er, 0

- room temperature, C

(J.1)

I'he part of the heat that was conducted through the rubber

gasket to the fresh water side should be deducted from equation

3.1 to get the amount of heat lost to the surroundings. The

thermal conductivity of rubber was assumed to be 0.10 Btu./

hr. ft. 2 oF./ft. (14), which is equivalent to 0.00173 watt/em. 0 c.'

J4

The area of conduction was 0. 0246 ft. 2 or 22.9 em. 2. ·rhen the

rate of heat conduction through the rubber gasket to fresh

v-,ra ter chamber, Pc watts, is

p = 0.001~~ - 22.9(t - tcf) c O.J X cs

- 0.1.32(tcs - tcf) (.3.2)

Substracting equation .3.2 from equation .3.1, gives

PL = 0.0548(t - t ) - O.OJ70(t - t ) (J.J) cs cr cs cf

where PL - pow·er loss to the surroundings, 't'ia tts.

F. Hethod of Calculation:

The following steps explain how experimental data were

used to calculate over-all mass and heat transfer coeff1-

cients for any membrane thickness at a single power level to

the salt water side.

2 '}lhe total heat flux, <tr Btu./hr. ft. , 't<Tas calculated

from the follo't<Ting equation.

qT = (PT - PL) x J.41J/A

't'Ihere PT _ po't'ler· input to salt water chamber, watts

PL - po't'ler loss to the surrounQ.ings, from equation J.J,

l'J'atts 2

A - transfer area of the membrane = 0.0246 ft. 2

The flux of water, NA lb./hr. ft. is calculated from the

amount of condensate as follow:

NA = 3600 W/(454 SA)

Where w - volume of condensate collected, ml.

35

A- membrane area in ft. 2

e - time duration to collect W ml. of condensate in

seconds

The amount of heat i d f requ re or vaporization through the mem-

brane, qv Btu./hr. ft. 2 , was determined as follow

qv = NA (Hv - HL)

where I~ - enthalpy of saturated water vapor at the salt

water temperature, Btu./lb.

HL - enthalpy of liquid water at its inlet (room) tem­

perature, Btu./lb.

'rhe amount of heat conducted through the membrane, q Btu./ c

2 hr. ft. , was calculated as follows:

qc = qT - ~

The over-all heat transfer coefficient based on conduction, 2 0 Uc Btu./hr. ft. F., was evaluated from the equation

Uc = qc/(ts - tf)

l'lhere ts = temperature of salt water, 0 F.

:rhe mass transfer rates were related to vapor pressure dif­

ferences across the membrane. An over-all mass transfer coeffi-

cient, K , was used as a measure of mass transfer rates. The m

vapor pressures were calculated separately as follo~rs:

p = partial pressure of water vapor on the salt water s

side

_ vapor pressure in in. Hg. of pure water at ts x0.96,

't-lhere o. 96 was used as ac ti vi ty of water in the salt

solution.

pf _ partial pressure of water vapor on the fresh water

side

36

= vapor pressure of pure water at tf, in. Hg.

The over-all mass transfer coefficient, ISn. lb./hr. ft. 21n. Hg.,

is

G. Data and Results:

All the data taken during the investigation and the

results calculated from the data are tabulated in Table C.l

through C.8, Appendix C, page 65 through 72.

J7

IV. DISCUSSION

A. Introductory Remarks:

In this study of mass and heat transfer through porous,

water-repellent membranes, the object has been to investigate

mass and heat transfer coefficients, their dependence on mem­

brane thickness and temperatures, and the relationship between

the two types of transfer. As sho~m on page 22 and 2J, equa­

tion 2.38 and 2.40 state that

NA = JSn AP

and

qc = Uc At

Based on these relationships, correlations of the coefficients,

KJn and Uc, have been developed for expe.rimental data.

During this investigation, temperatures of salt and fresh

waters, membrane thickness and power supplied to salt water

chamber 1'lere considered as independent variables. 'l)he volume

of condensate collected per unit time and the amount of heat

conducted through the membrane were categorized as dependent

variables.

For run number 3, an additional rubber gasket was placed

between gasket G4 and flange Fz in Fig. ).1 to keep fresh

Water from contact with the flange. Also there was no power

input to the heater Hz, and the data were used in calculating

mass transfer coefficients only.

The data and correlation deve~oped by a previous author

(20) were used to check the consistency of the results.

38

B. J:Iembrane Characteristics:

The membranes used in this investigation were prepared

by using all quantities in proportion to the standard "1 gram"

membrane as described in III. C.1. The data tabulated in

Table, B.l, Appendix B, on thickness, density, and weight per

unit area o~ membrane were taken on the portion of the membrane

used ~or mass and heat trans~er experiments,, t-lh1ch were some­

't'J'hat thicker than the edges cut off. The membranes were not

completely uniform in thickness, and the thickness measurements

depend on the degree of compression during measuring. Thus,

the most reliable measured characteristics related to membrane

thickness were the quantities used in making up the membranes.

In this experiment, the make up weight of glass fiber

was used as a measure of thickness and was defined as the va-

riable b, where 2

b = weight of glass fiber in gra.ms per 0.115 ft.

of membrane.

J1embranes of b = 0.5, 1.0, 2.0 and 4.0 were used in this

investigation. This variable was used in all correlations as

the independent variable representing a measure of thickness,

or more accurately, a measure of thickness times density.

The experimental mass and heat transfer area was

2 0.0246 ft.

c. between the Experimental Data and Correlations Developed -

Theoretical Equations:

At each combination of membrane and power setting, at

39

least 4 replicate sets of data were talren. I d t .... n or er o s im-

plify the least-squares analysis one set of data (which was

already available on a data card) was used to represent each

combination of membrane and power setting. This set of data

i'ras the set having ISn_ and Uc values nearest to the average

for the particular conditions. This data is given in Table C.9,

Appendix c.

The experimental data and results were analyzed by using

the least-squares approximating technique. The aim of least-

squares approximation was to minimize the sum of the squares

of the differences between experimental dependent variable

values and the approximation equation values for the dependent

variable in terms of the desired independent variable parameter~.

Let 1,2, ••• , n be a sequence of parameters

defined for values of independent variables. ·rhe object is

to approximate dependent variable Y by a linear combination

of the \xj1

With the values of Bj, constants, to be determined. In order

to compare the variances of the errors, the form of the depend­

ent variable was maintained in most of the analyses attempted.

These dependent variable forms were 1/Km and Uc in this investiga-

tion.

1. Hass Transfer by I'Iolecular Diffusion:

Equation 2 • .39 derived previoUSlY for 1/~ is

40

( 4.1)

Hhere terms in parentheses are assumed approximately constants

and are in forms suitable for determination 1 as east-squares

coefficients of the following parameters:

AP AH rr 2 rr 2b .6 t ~..;). v '

(2IT+ Ps + pf)./T, (2fT+ Ps + Pr)/¥.

I1he equation obtained by least-squares analysis "based on the

above parameters was as follows

1 AP 2 -- o.oo4J5- a~+ z.sz --~n __ _ Km At (2 fr+ Ps + Pr){F

Standard deviation of error = SE = 0.5406

This equation is shown in Fig. 4.1.

( 4. 2)

Comparing the first term of equation 4.2 to that of equa­

tion 4.1, the liquid film heat transfer coefficient, h, should

be about 460 Btu./ft. 2 hr. °F. Findley, in previous experi­

ments, glued a thermocouple on the membrane surface to measure

the interfacial temperature and obtained data indicating a value

of h of approximately 500 Btu./ft. 2 hr. °F. Further, comparing

the second and the third terms of equation 4.2 to those of eq~a­

tion 4.1, it shows that kz and ke have the values of 0.74J and

215. The average density and thickness of membranes are 0.226 gm./

cm.J and 0.00188 ft. per gram of make up glass fiber, respectively.

41

Then the value of' effective thermal conductivity is 215 x

0.00188 = 0.404 Btu./ft. 2 hr. °F/ft •• The composition of the

membrane and vapor space was used to estimate an average ther­

mal conductivity of 0.0575, using values of thermal conductiv­

ity l'reighted according to the volume fractions (see Appendix B).

The value of lr2 obtained 'tl;as used with equation 2.17 to deter-.... 0

mine De l'Ti th T = 492 R. This value of De after converting

units of thickness to feet proved to be 0.62 ft. 2/hr.. ·rhis

compares well 'N'ith.a value of 0.78 ft. 2/hr. at 492°R estimated

from the value in the literature (17) times the void fraction

of 0.91. This deviation of 20% is believed to be quite rea­

sonable in view· of the torturous path through which diffusion

occurs.

1rhe agreement between values of De and h obtained from

the least-squares equation, and those estimated from the com­

position and previous experiments appears to be sufficient

to confirm the mechanism of diffusion as the rate controlling

factor. It is possible that the deviation of the ke value

could be attributed to small errors in the rate of conde1wate

accumulation, or to other experimental errors.

Rao {20) in his thesis pointed out that b( Cl..t - E)' l'There

E is the boiling point elevation, has a strong effect on over­

all mass transfer resistance. 1/~· Modifying equation 4.1

by adding a parameter, b( ~ t _ E)/ T, where T is average

absolute temperature and E is 1.4, the following equation was

obtained

. ,.0 r-1

' . {:{) f-ri ........ . s.:: ..;

N . .J.) CH

• H ~

~I~

42

10

LEGEND

0: 0 • 5 f'Iembrane ...

.&.= 1.0 Membrane

s: 2.0 Membrane

Y: 4.0 Membrane • .....

.3

2

1

0 2 5 7 9 10

Fig. 4.1 Bectprooal of MaSs TrN&t~1"er Coefficient vs . F 1

AP . 1r 2 F1 • O. G-J.S "n Afl.y + 2.52 (Z·lr+ p + P ) l"f

• r

·Tr2s + 2.69 , see equation 4.2 {21f+ P• + •r>l'f

43

10

LEGEND

0: 0.5 l~embrane 8 8: 1 • 0 lllembrane .

..c El: 2.0 Nembrane r-1 7 ' • tC Y: 4. o r~rembrane ~

• 6 ~ .,...

C\l 5 • .J.) ft.t

• 4 E ..

"I~ J

2

1

0

Fig. 4.2 Reciprocal of Mass Transfer Coefficient vs. F2

P2 • o. Oo42S '}~AlLy + ·3. !6 Tt' 2 .u (2TI+ p8 + Pr)JT

b( 4 t - 1.4) 2 + 0.939. . . Jf b + 24-.3

(2TT+ P~ + Pr)ff

see equation 4.3

44

1 -= y~

o. 00425 ~~ Aliv + 3.16 TT 2 (21{+ p + p )JT s f ".l..

SE = 0.3970

'I' his equation is shown in Fig. 4. 2. The reduction in SE in

equation 4.3 compared to equation 4.2 is barely significant

(4.J

to the 5% probability level, but comparing Fig. 4.1 to Fig. 4.2,

the improvement does not appear to justify the extra term.

Perhaps the improvement is due to a systematic experimental

error or to some modifying factor of minor importance.

A number of other parameters were tried by such techniques,

but they did not tend to reduce the residual variance.

Findley (4), 'ranna (27), and Rao (20) have shown that

there might be a tendency to produce internal condensation

at high values of At. Fig. 4. 3 shows that conditions l'Ti th

a large ~t would more probably involve saturated vapor condi­

tions inside the membrane. In Fig. 4.3, ts and tf are salt

and fresh water temperatures. If partial pressure and tem­

perature vary linearly with thickness through the membrane,

the condition within the membrane, represented by the line

from t to t ~would come much closer or cross saturation s f>'

conditions in the case of larger At values than in a run

With small~t values. It is also shown in Fig. 4.J that,

at higher operating temperature, a higherAt is endurable

Without causing internal condensation. Internal condensation

might cause a continuous liquid channel through the membrane,

. til ~

. ~ ...... ..

A .. ,...

Q)

+> C\1

:::=:::

G-1 0

Q)

t-1 ;:s I'll I'll Q)

f-1 P-t

f.; 0 A

~ 6

5

I I

... ~t=1o ~ I k bt•15 ~ I

4 130 160 170 140 150

Temperature, t, op

Fig. 4.) Vapor Pressure of water as a Function of

Temperature ( 1 0)

180

46

and it would probably increase membrane heat conductivity,

ke• Also an additional mass transfer resistance would arise

as a result of the occurence of condensation and re-evaporation

from droplets blocking membrane pores. Fig. 4.1 and 4.2 sho\-1

that the experimental results agree fairly "t'lell l'li th the assump­

tion that mass transfer through the membrane is by molecular

diffusion.

2. Heat Trans fer by Conduction:

Equation 2.43 derived previously for Uc is

(4.4)

'rhe equation obtained by least-squares approximation based on

the parameters 1/b and Km ll P ~H was b :a:c v

1 Km /).P (4 5) U0 = 15.6 b - 0. 0912 b "1\taHV •

SE - 4.878

and it is shown in Fig. 4.4.

According to equation 4.5, the value of ke should be 15.6

Which is considerably different from the ke of 215 obtained

from equation 4,2. In addition, it is obVious from Fig. 4.4

that the fit of the data would be much better if an empirical

constant or another parameter were included in the results.

Even with another constant the data do not indicate the agree-

4 For this reason, and the presence ment obtained in Fig. .1. f elt that the above of more possibilities for error, it iS

equation does not adequately represent the heat transfer by

h is necessary for conduction, and that an empirical approac

best fit. Investigation l'ias made of several semi-empirical

parameters, and the best approximating equation obtained 't';as

Uc - 9.20 t - 0.0627 5!! AP Aflv + 6.58 b At

S-r.- - 2. 822 l!,

( 4. 6)

and it is shown in Fig. 4.5. Probably the following five

reasons can explain the errors in the correlation for Uc:

(i) internal condensation affects the value of ke,

(ii) ke might be a variable instead of a constant,

depending upon temperature and vapor phase composi-

tion,

(iii) the heat losses approximation given by equation

J.J might not be accurate, or the heat loss relation-

ship may have varied, possibly with air circulation

conditions,

(iv) errors in experimental Km values used in the correla-

tions would cause errors in Uc values,

(v) latent heat of vaporization is very high, a small

error introduced in measurement of condensate

would cause large effect on the value of De·

Comparisons are made for the values of experimental Uc to

those calculated entirely from experimental conditions - i.e.

calculating KID from equation 4.2 and 4.J, then calculati:r..g De

from equation 4.6 using calculated values of Km• They are

Shown in Fig. 4.6 and 4.7. Figures 4.5, 4.6, and 4.7 all

seem to be quite similar.

D. Comparison of Results:

Two groups of experiments have been performed before, on

48

LEGElJD

0: 0.5 Hembrane

A: 1.0 f·1embrane

G.: 2.0 Hembrane

Y: 4.0 r·1embrane

~ 20

0 . ,_, ~

(\1 0 0 .

.p ~

' • ::s .p ~

.. 0

::>

0 10 20 )0

F1g. 4.4 Heat ·rranster coettioient vs. FJ

1 Klr,.AP F; .. 15.6 b - 0,0912-b' ~Ally , see equation 4.5

JO LEGEND

0 . 0.5 l'Iembra.ne . A . 1.0 Nembrane . [!] . 2.0 l·Iembrane .

r:y •= 4.0 Nembrane 0 0

. H ..c G

(\j . .p 0 ft.!

' . ::3 .p r:q

. 0

p A 10 0

r::J

l!l A .[!l

e:l

10

Fig. 4.5 Heat Transfer Coeft1c1ent vs. F4

1 Km ,6P F4 • 9.20 b- 0.0627 b AtAHv + 6.58,

see equation 4.6

..-1 ~ .p ~ Q)

a ori F-t Q)

P4

~ ..

';:)0

26

10

0

LEGEND

0: 0.5 f•1embrane

.&..: 1.0 I:Lembrane G

El: 2.0 Hembrane 0 Y: 4.0 Hembrane

0

'Y A y

0 [!I

m .-mA

I!J

10 20

u , Calottlated 'from F4:uati'OnB 4.2 and 4.6 c

Fig. 4. 6 EXperimental Heat Tr&YSS:f'er Coefficient vs.

Heat Transfer Coefficient Calculated from

Equationa 4.2 and 4.6

50

.. C)

::>

51

26 LEGEND

0: 0.5 llfembrane

A: 1.0 f'Iembrane 0 A

2.0 Membrane 0 ~: 4.0 Membrane

0

0 t!J .. ..

0 1!1

0

U0 , Calculated from Equations 4.) and 4.6

Fig. 4.7 Experimental Heat Transfer Coefficient vs.

Heat Transfer Coefficient Calculated from

Equations 4.J and 4.6

5? ·-

the same type of apparatus, by previous authors (20, 27).

T'anna ( 27) concluded that diffusional resistance is not

the rate controlling factor for nass transfer. But the data

and results obtained during this investigation appear to

confirm the fact that mass transfer through water-repellent

membranes is by diffusion. rhe temperature differences of

these experiments were considerably less than those of I'anna•s

experiments. As has been discussed before, high f::l. t night

cause internal condensation and decrease mass transfer rates.

Thus his results should not be expected to produce the sace

conclusions as this investigation.

Rao ( 20) has developed a correlation for 1/!Sn, that

provided the best fit for his data, as follol'lS:

1 K

m

AP _ 0 • 0126 ( At - 1 . 4) b + 0. 00134 ~ t 6 liv

+ o • 3 54 ( A t - 1 .L~ )

SH' = 0.2688 J..J

(4.7)

using the same parameters as given by the above equation,

the following equation was obtained by fitting the data of

this investigation, i.e.

1 - = o. 049 3 ( At - 1 • 4) b + o. oo 303 ~ ~ A liv

+ 0.136 ( ~ t - 1.4)

SE = 0.7477

( 4. 8)

a d 4 8 By comparing coefficients in n 1 t 1s sho1-rn in Fig. • •

equation 4. 7 and 4. 8, it shows that they l·rere significantly

diff'erent.

53

10

LEGEND

0 . 0.5 J.Tembrane . £ : 1.0 I1e:m.brane .

.0 G): r-l 2.0 Hembrane

' . ._f9 •= 4.0 I•Iembrane r'-l y • ~

..-1

C\1 . 8 .p G-t

• J..l 4 ..t:: .&\. ..

'""'IJ=l 3

2

0 1 2 3 4 5 6 8 7 9 10

F5

Fig. 4.8 Reciprocal of r~SS Transfer Coefficient vs. F ..

5

AP F5 = O. o49J{A t - 1.4 )b + 0. OOJOJ At Aily

+ 0.1J6(At -1.4), see equation 4.8

I

I

On the other hand, by using the same parameters as in

equation L~.2 to fit }1aors data, the folloHing equation is

obtained

l -

54

{ 4. 9)

S,.., == 0. 647 5 .J:!,

and 1 t is Shot<In in Fig. 4. 9. In his results, the values of

1/JSn were generally v;ri thin 20.% of the values predicted by

equation 4.9. Comparing equation 4.2 to equation 4.9, it shovTS

that the coefficients of all three terms are reasonably close

to each other in the tHo equations. 'rhis fact emphasizes

that diffusional resistance might be the rate controlling

factor for mass transfer. The differences between the equa­

tions are Probably due to differences in membrane preparation.

E. r·Iiscellaneous:

Findley (4) predicted that, t'lith the elimination of non­

condensable gases from the pores, it should be possible to

obtain mass transfer by flow and rates should be considerably

higher. Six runs have been made to eliminate air by steaming

or boiling the membrane in the apparatus prior to testing.

Four tests have resulted in membrane failure or leakage due

to Pressure sur.ges or internal condensation. 'fhe other tl'To

runs have indicated no appreciable change in evaporation

rates attained.

55

7 ·-. ,0 r-t

6 .......... . bO ~ . 5 ~ s:: ..-t

N 0® . 4 +> \-4 ({;) G .

f.-! 3 ~

"IJ 2

1

0 8

Fig. 4.9i~ Reciprocal of Mass Transfer Coefficient vs. F6

~f.

. Data of Ro ..... o (20)

56

Thus far lt has been indicated in this investigation

that the rate controlling factor for mass transfer throuc;h met'l-

brane is the diffusional resistance, Considering that the

lo1v-er the molecular "t-reight of non-condensable gas the higher

the diffusivity, serveral attempts (5 runs) have been made to

replace air by helium. The results of tests 'tV"ith heliurr: and

air ·v1ere inconclusive, probably because of membrane variation,

but indications were that the use of helium increased K values ill

obtained.

.,

57

V. CONCLUSIONS

'rhe follo~'J'ing conclusions have been drawn from the data

and results obtained during this work:

(1) Diffusion through a trapped stagnant gas appears to be

the rate controlling mechanism for mass transfer through the

membrane.

(2) Over-all heat transfer resistance based on heat con-

ducted through the membrane is a linear function of membrane

thickness, but follows a theoretical equation (equation 4.4)

only after addition of an empirical constant (equation 4.6).

(3} Experimental values for De, ke, and h calculated under 2 2

the conditions used were 0.62 ft. /hr., o.4o4 Btu./ft. hr.

°F/ft., and 460 Btu./ft. 2 hr. °F respectively.

5t

VI. HECCHI'·IEEDATIOlJS

·The follolling reconnendations are suggested for further

study in this field:

(1) Effects of membrane characteristics of particle size,

composition, and particularly density, on the coefficients,

JSn and U c should be evaluated.

(2) High values of temperature differences are a possible

source of trouble in future experiments because of the possbil­

ity of internal condensation. Additional study of the effect

of high temperature difference is recommended, particularl~r

if in an apparently economical range.

(3) The effect of elimination of non-condensable gases from

the pores and replacement of non-condensable gases by low

molecular 1'feight gases should be further studied.

(4) The next step in the evaluation of this process should

be Pilot plant type experiments, 1-11 th the design of such a

Pilot plant based on the results of this investigation. Such

experiments should provide information on performance at high

temperatures and pressures and continuous flot'l conditions·

59

VII. APPENDICES

60

APPENDIX A

MATERIALS

Salt (Sodium Chloride): Reagent grade NaCl was used for

preparing 7.0% by weight salt solution for evaporation.

Distilled Water: Steam condensate from the condensate line

was used.

Silver Nitrate: Reagent grade silver nitrate solution was

used to test the condensate for the presence of Cl- ions.

Teflon Dispersion: E. I. Dupont•s Teflon JO-B dispersion

was used for making the membranes. It is an aqueous disper­

Sion containing 59.0 to 61.0% solids. It has a density of

1.5 gm./cm.J, a PH of 10.0 and a viscosity of 15.0 centipoise

at room temperature.

Q.lass Fiber: owens-Corning "Fiberglas", Type AA, of size

1 micron in diameter was used for making the membranes.

~uminum Sulfate: Reagent grade aluminum sulfate crystals

were used for preparing 0.05 gm./ml. solution.

~etic Acid: Glacial acetic acid of reagent grade was used.

APPENDIX B

I1EMBB.AJ.'JE CHARACTERISTICS

AND

DATA FOR HEAT LOSS APPROXIMATION

61

This appendix includes the characteristics of the mem­

branes used during the investigation, and the experimental

data used for heat loss approximation of the apparatus.

Run No.

1

2

3

4

5 6

7

8

Note:

1.

2.

3.

4.

5.

6.

7.

8.

9.

62

'rABLE 13.1

Nembrane Characteristics

b Heasured gm. glass ~vt. per 'rhick- Wt. per fiber per unit area ness Density 0.115 ft.2 gm./cm.2

unit ar~a in. gm./cm.J lb./ft.

0.50 .0076 .020 .150 .0277

0.50 • 0105 .026 .159 .OJ84

1.0 .0139 .033 .166 . 0508

1.0 .01.36 .038 .124 .0497

2.0 .0280 .062 .178 .102

2.0 .0286 .069 .163 .104

4.0 .0511 .082 .246 .187

4.0 .0457 .101 .156 .167

Data on these membranes were measured after the transfer experiments.

Transfer area in experiments was 0.0246 ft. 2

~a4ao of Teflon to glass fiber in the membranes 1s • gm./gm.

~.

Density and thermal conductivity of Teflon are 2.20 gm./c~.J and 0.11 Btu./ft.2 hr. oF/ft. (8), respectively.

Volume fraction of glass fiber and Teflon are 0.0603 and 0.0.314, respectively. 3 Average density of all the membranes compressed = 0.226 gm./cm.

Average thickness of all the membranes compressed=0.00188b ft.

Average void fraction of all the membranes compressed= 0.91

Average uncompressed membrane densitY= 0.168 gm./cm. 3

(not used in calculations)

63

TABLE B.2

Data f'or Heat Loss Approximation of Apparatus

'Temp. of Temp. of

Power Salt Fresh Room

Input tvater Water Temp.

P, watts tcs• oc 0 tcf• C tor' oc

2.00 37.2 26.9 21.0

4.00 60.6 38.9 22.0

4.00 61.6 41.7 22.2

4.00 62.7 43.9 22.5

4.00 65.2 47.1 20.5

4.00 67.4 50.5 22.0

4.00 69.2 54.6 22.0

5.90 77.0 46.8 21.5

6.00 81.6 55.1 23.0

6.00 91.2 67.8 23.5

6.00 95.2 73.8 22.0

64

APPENDIX C

DATA AND RESULTS

The experimental data taken during the investigation and

the results obtained are included in this appendix. The vapor

pressure of 1·1ater at the salt and fresh water temperatures

are obtained from the equation {11)

log10 Pc _ x (a' + btx + ctx3) P - T' 1 + dtx

where p _ vapor pressure in atm.

Pc - 218.167 atm.

T - t°C + 273.16

X - Tc - T

Tc - 647.27

a• = 3.2437814

bt - 5.86826 x 1o-3

ct - 1.1702379 X 10-8

Cl - 2.1878462 X 1o-J

TABLE C .1

Run Number 1 (b = 0.50)

Temp. of Temp. of V.P. of V.P. of Amt. of Power Salt Fresh Salt Fresh Conden-Input Water water Water Water sate PT,watts ts, oF tr, oF Ps,in.Hg. Pr,1n.Hg. w, ml.

Mass Trans. Coeff .

Time Km , Dura- lb./hr. tion sq.ft. 9, sec. in. Hg .

Heat Trans . Coeff. Uc, Btu./hr. sq.ft. OF

0'\ \.1\

TABLE C.2

Run Number 2 (b = 0.50)

Temp. of Temp. of V.P. of V.P. of Amt. of Time Salt Fresh Conden- Dura-

Heat Trans. Coeff. Uc, Btuy'hr.

~ ~

TABLE C.]

Run Number J (b = 1.0)

Hass Heat Trans. Trans. Coeff. Coeff.

Temp. of Temp. of V.P. of V.P.of Amt. of 'l'ime ~:/hr. u%, Power Salt Fresh Salt Fresh Conden- Dura- B u./hr. Input Water Water WAter Water sate tion sq.ft. sq. ft. PT,watts ts, oF tr, oF p8 ,in.Hg. Pr,1n.Hg. W,ml. <9, sec. in.Hg. Op

•. ,,.J •~7\.lfe \_}._:;,:~

4.40 5602. 0.31 7.95 5363. 0.3Q

I i . ..., 'J ~ ~ ....... ' • • •• - • L '.- • - •• ~- 4. 15 3 1 71. 0. 29 oo tse; 7".\ 146.10 B. ~o 1. 31 1. rr---·117o. o. 3?.

tn:~o 14.\0

.. l4t.?Q • .,Q.~<1

146.51 ~.75 1.?1 2.50 1685. 0.32 1~0.~2 1?.30 10.27 2.40 1181. 0.32 161.1~ 1?.54 lQ_~48 2.45 1198. 0.32 161.18 Il.'>~ lO.zt~ .?.30 ll7R. 0.31 l5Q.~7 12.0Q 10.08 7.15 3556. 0.32 --177.~1 17.70 15.30 h.QO 2813. 0.33 17~.64 17.A~ 15.77 3.?0 1324. ~or.~3~Rr----------

-r7A.64 17.~0 1~.77 1.10 121A. 0.40 17~.64 17.AO 15.77 13.?0 5355. 0.3q

Q4.93 ?.5~ l.6R 1.?0 1~46. 0.?4 ~~-~? ?.5R 1.70 1.20 170?. 0.26

.~-~ ···~"' lefl t.uu tlbO. u. __ . Q~.40 ?.5R 1.70 3.4~ 470R. O.?h 1~1.1n ~.69 2.17 5.00 3000. 0.35 1~4.~? ~.Rl ?.26 ?.30 1340. 0.36

--T'1 c; • 'c; ---- ". ~ c; '. lt T."7'f---nrmr. o. ~7 lO~.oA ~.70 7.72 10.~0 614R. 0.1~ 110.01 ~.17 1.S~ 1.05 Q}O. 0.7A llO.~? ~.n~ ~.,7 6.7, 3lAO. 0.26 , '11 • 4 1 A. l '7 1 • 6 0 ___,-~- V) 4 () lt'l).. n ~------t?o.o~ ~.to ~.57 13.,0 q71,. O.?O 1~~.~0 ~.6? ~.7~ 7.~5 4q43. 0.13

0\ --.,J

Power Input T,watts

. ·-.oo .oo .0()

Temp. of Salt Water

0 t 8 , F

Temp. of Fresh \'later

0 tr, F

TABLE C.4

Run Number 4 (b = 1.0)

V.P. of Salt Water p8 ,1n.Hg.

V.P.of Fresh Water pr,1n.Hg.

Amt. of Conden­sate W,ml.

Time Dura­tion e,sec.

Nass Trans. Coeff. k'm, lb./hr. sq.ft. in.Hg.

Heat Trans. Coeff. Uc, Btu./hr. sq.ft. OF

~~~- 0.4~ 26.26 1130. o. 37 ?q~--··---·---

l2qo. o.42 ?1.37 ?340. 0.32 13.40 1829. 0.34 11.04 ,.,, 0~ Il.OA

0.33 11.50 0.32 15.92 0.32 12.57

eJU J."TJ.eC-. c>e7P Ue.JU :Je ... U t:..l:;)l.e o.-31---~~~--rr

15~.71 t4o.6n s.qo 6.26 12.17 48?8. 0.32 12.92 17?.66 1~4.97 13.~0 9.00 6.17 149?. 0.32 13.P? 174.94 1~7.7? 1~.~? 0 .~2 4.~0 1078. 0.31 12.40

-------rrfl.~6 I'iR.4I 14.~7 q.9o -r.n·---- 899. o.3o -rr~-- .. 177.\? 1~Q.54 14.~~ 10.07 3.70 898. 0.29 12.07 11e.11 160.6~ 14.96 10.~~ 3.6o A65. o.?9 11.91 tR0.12 160.61 19.1? l?.Rl ~.tn ~96. 0.?7 10.65

---~- 3. l 0 I) 7 4. 0. 27 6. 74 1.10 ~98. 0.?6 10.46 ?.61 492. 0.26 6.55

187.04 167.17 lR.6~ 1?.09 5.60 10?0. 0.27 5.54 ~--TW"r."" t "1.11 '"· &4 tz. ne 11.11 -~----~~o7.- -rr.--zr ~. ?6

()'\

co

TABLE C.5

Run Number 5 (b = 2.0)

Nass Heat ;rrans. .rrans. Coeff. Coeff.

Temp. of Temp. of V.P. of V.P. of Amt. of ·rime I<m, Uc, Po'tier Salt Fresh Salt Fresh Conden- Dura- lb./hr. Btu./hr. Input \•Tater \'later Water Water sate tion sq.ft. sq.ft. PT,watts 0 tr,oF p8 ,in.Hg. pf,in.Hg. W,ml. e,sec. in.Hg. oF t 8 , F

~-~1ft ttf>.~~ ~.~.. ~-''- '·" ,_,., ''~· ~-~' 12.44 ~.oo tth.A1 q;.1o 3.12 r.12 t.eo rs21. o.z3 to.r9 --~.oo 117.0~ a~.52 3.14 1.72 2.20 2227. 0.2? 10.32 5.00 117.07 95.64 1.14 1.72 6.10 6378. 0.22 11.05 ~.on l2R.5t ltt.an 4.33 2.Rl 2.47 ?421. 0.22 10.15 r;. no 129.42 1 1?. 5" 4. 44 z. 87 2. 6rr-------- -z4o7. -- -----u-; zz ---~-;n-~.oo t3o.~q 11~A11 4.56 2.03 2.so 22eo. 0.22 7.5' 5.00 1?9.07 112.25 4.40 2.84 7.57 7103. 0.22 8.6R o.oo 16?.40 14~.06 10.36 7.19 3.57 1466. 0.?5 12.11 [U.OO 161.611 ___ 147.03 lO.nP 7.37 5.t:;o 71R4. 0.25 <?.R6 0.00 165.17 147.60 11.07 7.48 4.50 lPOl. 0.?2 9.50 o.oo 163.69 146.73 10.~9 7.32 13.57 5451. 0.24 10.19 0.00 165.62 14R.0'1 11.19 7.57 1.47 ______ 1297. 0.24 5.74

, ......... ,..,.0-=. -mJ-------Tbl)~ ''+R .1 q 11. 2' 1 .l)q .,-~1n ·· · · m-s~--- o. ?4 ~~-o?l_ .. c.on 165.~~ 14A.~l ll.'A 7.6? 9.57 ~57Q. o.24 5.65 ~.00 1PS.15 167.~6 17.60 1?.?4 3.Q7 945. 0.25 q.02 ~.06 1P7.40 1AQ. 0 5 lq.41 l?.Ql 10.60 753?. 0.?5 R.7~ 5.no tot.ot 17":\.?o 10.(}7 11.96 PJ.<:J4 46oo. o.?? a.cm -'s.06 lR5.~? lA7.7~ 17.A6 lO.R~ 5.67 l~ll. O.?l 5.9? s.oa l?~.3q l~l.P? ln.~4 tO.A4 ?.no 6oo. o.?3 6.4~

... _~1l.~.!L_ _______ 1~4.-11_ _!_~ _ _!_,_~ _____ _!_!_.!_11__ _____ to. 8~ _____ ~_f!_?J 1911· 9!22__ __ _ __ 6. 3(, ______ _

0'\ \.()

Pol'ler Input PT,watts

TABLE c.6

Run Number 6 {b = 2.0)

Nass Heat 'l'rans. rrans. Coeff. Coeff.

Temp. of Temp. of V.P. of V.P. of Amt. of 'rime Km, Uc, Salt Fresh Salt Fresh Conden- Dura- lb./hr. Btu./hr. Water \-later water water sate tion sq.ft. sq.ft. ts,oF tr,oF p8 ,in.Hg. Pr,in.Hg. W,ml. e,sec. in.Hg. Op

•·" '·• '·"' t.M ~.... o.~~ 12. ?1. A7.94 2.63 1.35 5.3o 625o. o.~ t:>."TT qp.R~ ?.70 1.39 1.00 1165. 0.21 11.97 ~7.00 7.60 1.31 9.60 112RO. 0.21 12.13

1~2.37 1~4.46 3.66 2.26 1.45 . 1703. 0.?0 13.49 1 2l. A1 1 !l5. 79 3. 70 2. 35 1.1)1) -d-- {()57. ~20 -rzt0T ___ _ 124.47 107.0R 3.~7 2.44 3.10 3442. 0.?0 1?.57 175.31 107.0~ 3.97 7.44 1.40 1562. 0.19 11.84 1?4.2R 106.?1 3.~6 2.3R 7.60 _R664. 0.10 12.61 156.14 136.9A A.99 5.67 1.40 61A. 0.?3 15.74 __ _ 1~9.~q 140.10 Q.63 ~.16 6.RO ?737. 0.23 10.Q5 16?.?5 141.16 10.37 6.~7 5.00 7009. 0.72 10.35 163.65 143.04 10.67 6.65 3.RO . 1570. 0.19 10.56

-- - r6-r. 31 ~-1 q 1 o. 33 6. 6 A 7T~1J?:r -- ----sTTu-.- -------o-~n- " - ... 1Rq.53 170.PQ 1R.A7 13.19 5.70 1466. 0.22 lAA.?l l70.A7 }R.73 13.19 5.00 1795. 0.2?

1') .. 'lO ~~

-...)

0

TABLE C.?

Run Number 7 (b = 4.0)

Nass Heat Trans. .rrans. Coeff. Coeff.

Temp. of Temp. of V.P. of V.P. of Amt. of rime y u Power Salt Fresh Salt Fresh Conden- Dura- l"¥5ihr. B%~./hr. Input Water Watgr Water vlater sate tion sq.ft. sq.ft. PT,watts ts,oF tf, F p8 ,1n.Hg, pf,1n.Hg. W,ml, e,sec. in.Hg. op

--!Ia lM!J~ "!~3 ~!~ '~~ t:ro t~n~ 8: ~~ l~6-- --~.00 123.0Q Q4.63 3.7? 1.66 ~.30 4322. 0.12 11.80 ~.00 125.37 Q7.50 3,Q6 1.81 2.10 ?760. 0.11 11.66 ~.oo 121.21 99.3~ 4.17 l.Q? t.Ro 2167. 0.12 10.56 -rs--;rrn--- I ?9. 4 5 103. q Q 4. 4c; 7. 2 3 -r.-gu-- ---·- .. "TJ1JT. ______ \J. 17 ·---~uu-··

5.00 131.2q 105.23 4.67 2.31 2.10 ?302. 0.12 8.01 ~.00 13?.82 106.47 4.R7 2.40 1.90 2064. 0.12 7.74

.00 131.16 105.?3 4.66 '· 31 5.QO _ ___!!758. 0.12 8.58 • J .L J " , • -:--; 7 ~ • ~- -· __ 1 .-~ • _ J .L - J • l.J '· 1 c_ !"~l .....,. t" • \1 • _,_ .J 1 t_J • ,J

161.32 139.30 Jn.on 6.03 5.60 3?00. 0.14 R.Ql 162.~6 l3Q.88 10.47 6.12 2.90 1647. 0.13 8.00 164.76 l3Q.73 10.Q6 6.10 1.50 811. 0.12 5.99 1AT.A4 1'39.BO 10.77 6.11 7~-l)·ry--·~ 1360. 0.1'3 ~u-· 16?.36 }3Q.31 10.35 6.03 17.50 7018. 0.13 7.77 lRt.qn l61.?A 16,?9 t0.4Q s.no 3660. o.l? 10.54

'. . . ., l p 1 • 7 6 l ~ 1 • p '+ 1 6. 2 4 1 0. 64 l • ~ () . ') q 2. 0. 1 3 1 0. 8 () ••.A ... >< ·lfP.nq 11)?.4~ 1A.v; 1o.An 2:-n11 qoq. 11.13 to.53 --·-181.~~ 160.10 16.16 10.10 11.10 484A. 0.13 7.82

~---------------------------------------------------------------------------------------~

-..,J ~

TABLE c.B

Run Number 8 (b = 4.0)

I·Iass Heat rrans. rrans. Coeff. Coeff.

'J~emp. of remp. of V.P. of V.P. of Amt. of ·rime Km. De, Power Salt Fresh Salt Fresh Conden- Dura- lb./hr. Btu./hr. Input Water Water Hater Water sate tion sq.ft. sq.ft. PT,watts ts,oF tr,oF p8 ,1n.Hg. Pr,in.Hg. W,ml. e,sec. in.Hg. OF

__ • \J, ., • L .L l. ov Jm! ~---- K! ~~ ----{!.;: A.?.8 6.21 1.40 1442. O.lS 5.11 A.43 6.30 2.0S 1983. 0.1~ 3.34

I __ ... J -~ ., _ • •• _ • _ _ _ _ 8 • o 1 6 • 16 6 • c; 2 . . . " q o 8 • _ o • t 6 _ . 6 • 2 n tn on pq q4 Jht l? 16 31 12 o7 z;f;rr---------r--o-c;-o·;--------u;-rr-------n;-crrt 4.~7 ?012. 0.19 B.O~ 5.60 2306. O.lq 7.49

I I"' • " .. ~ " ~ ... ., . - -· . ~ . ~ - . -- - ·- - --- 1 3 • o 1 c; 314 • o • 1 Q 1. ,;; 1 ___ _ 2.9o 198.13 1A3.R5 73.1° 17.72 4.31 1301. 0.20 A.oA ,.qn 199.73 lA4.76 ?3.9Q 18.09 10.10 3213. 0.18 7.65

i·~ ~g~:~' l":ti i~:~ li:41 1::'~ i~ii: &:l~ Z:6~ .I • ------- ... -·-· -------------- .. ·------------ -----------

-..,) l\)

l.

Power Input IP ...

5.~~

't=gg -.oo l .oo .()')

-·t!~ci l.oo ' .l') .80

.O'l t.lf)

't:~~ ,-.on ,,.0()

; • 00 18.00

'J.O'l 'J.()f) ,,.nn l . ()()

• 1)0 1 .no

'S.OI1 ').l')f)

10.0') tit. f)() "·nn -;.f)n A.O'l

10.11() ~.()()

1 n. oo t1.f!:tf'l

Temp. of Salt Water

0 -

·tt~.~~ lCJl.l1 1~?.45 ll'5.5R l4Q. l 1 179.?6 ]OS.4S 130.5? ]')').73 lA8.99 l8').Qf) 110.4? l ?3.P.3 140.34 11~-"A l?l.1A 1'5C5.71 1 74.04 }Qf).}Q 1 1 7. 07 17().()7 lf-1.1-.Q }f.,').AA }P7.4() 1P4.11 11'1. 0 1 l-:>?.~7 1f..?.7c:; loq·c;" 1~'1.~7

l ~ l • 1'' 1 ""'·Q" 1"'1.7f, ,,,.,_,7 \A"l.l-.7 ,..,..,_?"'

TABLE C.9

Data Used for Least-squares Analysis

·remp. of Fresh Water

0 -. ~~-"· 1 ~6.(}6

}F-,7.0t; 104."3'~ lV-t.Rl l'1~.9R 1 7 6.'51 l??.O? l4n.7" l'59.S7 1 7 P.. 64

Q'5.lt0 1 114.c:;? llg.')? l0R.77 lf'l7. 0 ? 1 4(). A 0 1"7.?? 17().')F,

QC:::. ,..,,.

ll?.?c:; l'tA. 71 }4A.1} l f")r).Q')

lA-:>.c:;t+ Q 7. Q '•

1 ")1, • '• /-., 1 '• ~ • l ,, 1 70.01"1

n7. r;'")

1 0 r • ., .\

1 -:\'"' • on l!,l.r>l, 1 '• n • 1 ,, 1 A~"' • 1 1 1 ... , •• ...,,,

V.P. of Salt Water

'· fW) 7.97 16.'11

3.01 7.49

l5.1Q ?l.QS

4.SR 8.9?

1?.11 17.~7

?.')Q

3. 'H r::;. Q7 1.?() 1.r::;r, q.q;:>

11.04 l<"~.A()

1.1c::: 4. '• l

1 0. 71 l 1 • ., q 1A.4S 17.1'1

? • ,._ ~ ~.~A

1".~'· 1 0 ')" . .

~ '17 . .

'•. ,, 7 1f".'•r:l 1 ".

.,., 0 ,..., .

lf-."" .,,_,,

V.P. of Fresh Water

-

'·" 5.68 17..09

?.;:>5 ').17

11.23 15.0'> 1.77 7. :p

10.10 1'>.80

1.71 ?.?6 3.'5? ?.')7 ?.'51 A.?1 c.c;4

13. l., l. 71 ?.AS 7.33 7.A3

l?.C4 l o. qc:;

1 • 1 c; ?.?f.. f...,, q

11. ?? 1 • q., ., • :q A.l 1t

lf).".t.. , • 1 q ,.,_"..,

t·~. 1?

Amt. of Conden­sate W.ml

4.6tt 3.40 q.oo 1.70 6.40 ?.?7 7.00 4.4'1 l. 75 7.1'5 3.20 3.40 2.30 6.?'5 1.?0 R.77

1 2. 17 4."() 1.10 ,.,.tn 7.~7

11."7 q.c;7

Jr'l. f. I) q. :::'7 c;.-:\f) 1.4'5 c:;.n, r::;.7"1 .,.11') c:;.of) 7.Q1 l.:l'1 ~."'.,

1 ~.rn ''l.7fl

·rime Dura­tion e

4~1 • 1183. 2123. 1895. ?B47.

') 8 2. 1???. 5602. 1170. 1'556. 13?4. 470~. 1340. 3160. 1200. ~HQO. 4~2R. 107R.

J:;74. 617A. 7101. 5451. )r::;79. ?53? • 1911. ~::>c:;n.

1 7n~. -:>()nQ.

14t..~. ?71-.,0. A 7c:; q • l'A7.

t;;<1?. r, '1 n n • ~ ~ 71 •• ~,,,_

Nass ·:rrans. Coeff. Km, lb./hr. sq.ft. in.H

O.ltl 0.36 0.31 0.18 0.34 0.30 0.?7 0.31 0.3? 0.32 0.38 0.?6 0.1() 0.?6 0.42 0.11 0.~? 0.31 0.?7 0.22 0.22 0.24 o. ?4 0.?4 0.22 o. ?l 0.?0 0.?? O.?? (). t 1 n.12 0.13 0.13 f). 1 ~ f).lQ O.l•

Heat ·rrans. Coeff. Uc, Btu./hr. sq.ft. Op

lf..A.3 16.94

Q.Qt) ? 1. <ll ?1.77. P).06 13.tJR --------------

?1.37 11.'50 12;.Q2 12.40

f-..74 ll.O«:; 8.6~

10.39 5.61:; A.76 6.36

1?. 31 13.40 tn.3c; 7.4?

1 1 • ,.,_,., P.s:;q A.OO

1 0. PO A.?f.,

7. "l 7.6"

b

,., • '50' o.so 0.'50 o.c;o 0.50 0.50 0.50 I.on I.oo 1.00 1.00 1.00 1.00 l.OD 1.00 1.00 1.00 1.0(} 1.on ?.00 2.00 2.00 ?.00 2.00 ?.00 ?.00 ?.00 ?.on 7.00 1t .oo 4.00 4.on 4.()0 4.00 4.'ll') 4.no

""" \....)

74

APPENDIX D

COI.fPUTER PROGRAM

The program used for the computations described in this

thesis is given in this appendix. The program was written in

Fortran IV language and was run in IBI1 360 system.

/JGB /FTC

GO LIST

Cl YEH

C C***l7748L~X041 Y~H, C. L. S.0001 ~~1Tt(3,100)

S.0002 ~~l1t(3 1 20C) S.0003 A=3.2438 S.0004 B=~.B683E-3

S.COC5 C=l.l702E-S S.OOC6 0=2.1878t-3

·-- •. ---··•- - ' • •• T --- ·--- -- ----·-- --•-••• o •••--••-•••- ·--···•·-•- -~· •''

S.GGG7 AR=0.0246

ll/l~/66 RACS

S.G008 lC RtADtl,300)E~S,EMF,TCR,Xl,R,TlME,PGW S.OCC9 EMS=E~S+TCR/24.49

S.COlO E~f=EMf~TCR/24.49

S.OOll l~ttMS-2.45C)2G,20,30

S.0012 20 TCS=EMS*24.49 "'"··-~--·--·"-. - ~ ··- -~·------ -·-------------------~---- - .. ·----~-~-----------

S.C013 GC 10 40 S.0014 3G TCS=60.0+tE~S-2.450)*21.74 S.0015 40 lf(EMf-2.4~0)50,5~,60 S.0016 ~G TCF=EMF*24.49 S.0017 GG TC 70 S.OOl8 oC TCF=60.0+(E~F-2.450)*2l.74 '5~.0019 70 TFS='( r'cs~·i~*«Tcs=·ffRTltloo.-::rcR-) )*1.8+32.0 S.OOLU lff=(TCF-2.*<TCF-TCR)/(100.-TCR))*l•8+32.0 S.0021 OT=TFS-Tff S.0022 Hl=ll2c.l+C.396*(TFS-150.) S.0023 h2=1.8*TCR ~. oo24 .,.~=J~~.Li1-.!,~~-~--·· S.OC25 wH=w*3600./(454.*TIME*AR) S.0026 Ql=PG~*3.4128/AR s.oc~7 QV=~r*<Hl-H2> S.OOlB OQ=~T-QV S.0029 HTC=LQ/DT

OO'J2

oo3o ·-·----·- ,~~31~ .11- res -------------------=====-=-============== ..... ==~·-=,~·=·---··---

I oo 1 o 1

-..:> '-"

S.0031 AS=2.303*X/CTCS+273.16J*CA+B*X+C*X**3J/Cl.+O*X) 5.0032 Y=374.ll-TCF 5.0033 AF=2.103*Y/CTCf+273.16)*(A+d*Y+C*Y**J)/(l.+O*Y) S.0034 P~=b~2B.?*tXP(-AS) S.003? PF=t;28.5*~XP(-A~)

~.0036 Pt=PS*O.Y6 S.0037 CP=~f-PF S.00~8 ~TC=~H/DP S.003~ ~RITE(3,400)TFS,TFF,OT,OP,WH,HTC,~TC S.C040 IF(Xl-l.)lC,80,80 S.004l 80 STuP S.0042 luO FORMAT(lbl) s. 0043 200 fOt:tMA t ( 5-i;3-t:iTFS-,-:rx-;3-HT-FF ;ax-, 2H0i ~-ax, 2HOP, 9X, l HW, 8X, 3HHTC, 7 X, 3HWTC)

S.0044 300 FORMAT(7fl0.4) S.0045 400 fORMAT(4fl0.2,fl0.4,fl0.2,fl0.5) S.0046 END

~NO LF.COMPlLATION MAIN /DATA

SIZE OF COMMON 00000 PROGRAM 01480 >

--J 0'-

APPENDIX E

LEA.ST-SQUARES APPROXIIvlATING TECHNIQUE

The type of equation used :for analyzing the data and

result is

n y - 5: BjXj

j=l

77

where {xj}, j = 1, 2, .3' ••••• , n are a sequence of parameters

computed from independent variables, Bj 's are least-squares

constants, and Y is the dependent variable.

The program used for the computation of least-squares

constants is given in thiS appendix. It was prepared in

Fortr.an IV language, and was run on IBiv1 .360 system.

0014 0011) 0016 0017

• 0018

0=2.1878462E-3 AR=0.024

DO 13 1=1,7 GO TO t1,1,2,3,3,4,4l,l

GO TO S 2 T(J)=1.0

GO TO 5 3 T(J1=2 •

GO TO 5

GO TO 5 14 T ( J ) = T ( J- 1 )

)

--

5 READt1,300lEMS,EMF,TCR,Xl,W,TIME,POW -----------EMS=EMS+TCR/24.49 EMF=E~F +TCR/24.4

-..;] co

·~

' .

. ) S-TCF)

(l.+O*R

( 1. +0* s)

? • ' I I

I

"""' \0

.0070

.0071

.0072

.0073

.0074

.0075

.0076

.0017

X(l,ll=AAAA Xft,Zl=BBBB X(l,3)=1. MJ=3

5'>5 CONTlNUE

I :aeV,I..,

s ..... S.Ol02

S.OlO S.Ol04 s.o1os S.Ol06 '5.0107

.0108 s.o1oq S.0110 s.o111 S.Oll2

.0113 S.Oll4

• 0115 • 0116 .0117 ---.Otl 8

'!I 21

c c

25

2

29 '30

XTFCIJ=SUM FINO INVERSEOF XTX : XI BY GAUSSIAN ELIMI NATION WlTH PIVOTING SET UP AUGMENTED MATRIX OF XTX. AND CHANGE THE NAME AS A

Jl=MJ+l MJ2=2*MJ DO 30 I=I.MJ DO 25 J=l.MJ A( I ,J}=XTXf {yJ)

DO 30 K=MJl,MJ2 I l=K-MJ lFtll-1129,28,29 ACI,Kl=l. GO TO 30 Atl,KI=O. CONTINUE SSSS=l • MARK=O • NMI=MJ-1 NN=2*MJ

__ 31

5,40,

CX> .....

Afl,l)=AfMAX,l) AfMAX,l )=TEMP IF ( NPLS V-l) 51

60 SSSS=-SSS 61 J= 62 J=J+l

' 51

lf(AtJ,I)l63,65,63 3 CON ST=-A ( J, I} I A (I ,.I)

l=I-1 64 L=l+l

A(J,Ll=A(J,Ll+A(I,Ll*CONS IF(l-NPLSYl64,65.64

65 IF(J-MJ)62.66.62 66 If(l-NMll32,67,32

II -:::: c COMPUTE DETERMlNANTtA) -67 TEMP= l.

1=0. 68 l=I+l

IF( AC I, t) )69,71,69 69 TEMP=TFMP*A(l,I) _-.:l:...:.F C l- MJ l 6 8 17 0, 6 8 70 DET=S<\SS*TEMP

GO TO 7 71 MARK= 1 1? IF(MARK-ll7~,9QQ,73 ~ I=MJ

81 l=l+l --- BACK SUt\STITUTJON

co 1\)

.0179

.0180

.0181

.018

.0183

.0184

.0185

.0186 .0187 .018 .0189 .0190 .0191 .0192 .0193 .0194 .0195

S.Ol96 s.o1Q7

5.019

c

86 87

88

89

F ( J)

+1

~0 ROR

r

co \..0

I • ... ·a aa rere·••L•..w•t~ ... ,..~.-• .:.-.n - ·- - ==-

C}l

92

qqq qq

100 101

''v

P(J)

co -{:::"

VIII. BIB-<=LIOGR.APHY

1. Bird, B. B. , Stewart, w. E-11Trans:port Phenoraena, n Jo~ • and Lightfoot, 1960, 'P• 520. \~iley and Sons,

. ' ~~. l .• ,

Inc., ;;c;; c ,. ,• '~ . . .

2. Ibid., p. 284.

3. Ibid., p. 245.

4. Findley, 11 • E. , uva.poriza t-;. :1 thr I & EC Pro c. Des and Dev ovn 1 o6ugh Foro6u.s Ecmbra.ncs ', _.-_.,;;;..;._..;:;...;;._.;;...:-..=...;;;..=::...::•~=-=:.::.....::::.;:.:...:.. • , o • , p • 2 2 · , 1 .. pr 11 , 1 ~: u 7 .

5. Foust_, A. S •, et a]..' "Pr::i_nciples of Unit cperation::; " John Wiley and Sons, Inc.. New Yorl{, 1959. p. 2. '

6. Ibid., p. 20.

Goodgame, '.I'. H. , Sherwood. 3: 37 ( 19 54- ) •

T. K., Cheo. Enc-:-;;. Sc.,

8. Hood, R. H .• , "Designing H~at Exchanger in l'cflo~1," Chem. b"'ne;r., Vol. 74, No. j_1, p. 101, !•:ay 22, 1~!~7.

9. Jhawar, H. N. , nSpecial Pr-oject on Nembranc::;," tnptfbl ~; :·.r :• Report tot'J'a.rds Bachelor's J)egree in Chen. Engr., t'n1v· :--sity of Nissouri at Rol~a • Rolla, Hissouri, 1967.

10. Keenan, J. H., Keyes, F. Giir • , "Thermodynanic Fropert!r:!": of Steam, n 1st ed. , John 1f..Jir :1ley and Sons, !Jew York, 191t7,

11.

12.

13.

14.

15.

16.

17.

18.

p. 28-33.

Ibid., p. 14. ti ~ ,.e .f' ro.,..e-- " 1~ .. ("lrl '";-··~~'>''

Kennard, E. H., nKine c ..L- .u ory o ... ~~ ·..:., ~ '-" ......... :, , ... -

Hill Book co. , NeW York, 1- 938, P. 65-69 ·

Lews \•I T(' ·wh1 trr»an, W • ' • .L-. ' d "r'\ ("*fl ...... c~ ......... •/ .. ~?~t , ...... ~ .. c:;- • ' In • ~:r..g • ...,. • ...... • ... · . .; .... '· ... ./ I .. •.. . .•

Lll sport J:= :roperties," Chc::o. Er'e::. :;ar.dbc c ..

4they,. P • E • • "T3ra.nH Eci:i- tor I·icGral.;-'H1ll ?:,cor: ,:;c ·' ed. ,. PerrY, • • ' '

New York, 1963, P• J-211 • J C::: nuni t cpero.t1ons c'!' C}:c::i r. ... al McCabe, W. L., Smi. th, •., ~;.,ol{ c ·· · ···o_,..·- "r·,'l ~ ,.. .. " Englneeri ng' " J.!cGra>~-EiJ.-'- .uv o • ' . • c" " •. ·. • • ~ ' • ,. . . : .

Ib·d ~ •• p. 611.

Ibid. • p. 928. 9-:l- ys l.s n Chem. Mr. !~and boo~:. Monet, G. p,, "EJ.ectrod~L tor,'J-:cGraw-01- ::;ook Co ..

4th ed., perrY• J • 11 • ~~ New York,. 196.3, P• 17 ~·

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

Office of Saline Water, Dept. of Interior, nSaline w t Conversion Report for 1965," Supt. of Documents u '; er Govt. Printing Office, \iashington, D. c. • ' · ·

Rao, y. B. I 11 Study of Nass Trans:fer through Porous viater repellent Nembrane as a Function of Ivlembrane Thickness -and Rates of Heating," Unpublished Master's Thesis Libra University of tvlissouri at Rolla, Rolla, Hissouri, 196?. ry'

Rickles, R.N., and Friedlander, H. Z., "The Basics of Nembrane Permeation," Chern. Engr., Vol. 73, No. 9, p. 163 April, 1966. '

Sherwood, T. Extraction," 1952, p. 1 •

Ibid., p. 91.

Ibid. I p. 10.

Ibid., p. 10.

K., 2nd

and Pigford, R. L. 1 "AbSorption and ed., McGraw-Hill Book Co. , New York,

Tanford, c., nphysical Chemistry of Macromolecules," John Wiley and Sons, Inc., New York, 1961, p. 346.

Tanna, V. V. , nStudy of !>lass Transfer through Porous Water-repellent Jl1embrane," Unpublished 1•1aster' s 'rhesis, Library, T1957, University of Missouri at Rolla, Rolla, I-11ssouri, 1966.

Tuwiner, s. B., "Diffusion and Membrane Technology," Reinhold Publication Corp., New York, 1963, p. J.

Ibid. , p. 1.

IX. ACKNOvlLEDGEr·:ENT

The author wis.hes to express his sincere app :recia tion to

his research advisor, Dl::'. H. E. Findley, Associat € Professoi ..

in Chemical Engineering. for his guidance and sug ~est ions dur­

ing this investigation. He also would like to ex:)Jress his

thanks to the Office of Saline Water, U. S. Dept. of Interior,

for the research assistanship.

·rhe author is also deeply indebted to his fa:t::nny for

their encouragement and continuous moral support.

X. VITA

r.rhe author HaS born 011 September 2.3' 19.39' in Tokyo'

Japan. He attended high school in I-lan, Taiwan, Rep. of

China, and graduated in June 1958. After high school, the

author entered Tunghai University, Taichung, Taiwan, Rep. of

China, in September 1958, and graduated in June 1962 with the

degree of B. s. in Chemical Engineering. He served in the

Rep. of China Army one year and was employed by Mobil-China­

Allied Chemicals Corp. from September 196.3 to August 1965.

The author enrolled in the Graduate School of University

of Hissour1 at Rolla in January 1966.