1965 Conference Paper

Thcoret ica l Calculat ions on the

Production of Water from the Atmosphere Absorption with Subsequent Recovery in a

by Solar Still

Raymond C. Hall Department of Chemical Engineering

KansasState University, Manhattan, Kansas

A p r o p o s e d cyc le for an a b s o r b e n t in t h e p r o d u c - t i o n o f p a l a t a b l e w a t e r f r o m t h e air is p r e s e n t e d . A C o m p o s i t i o n - P s y c h r o m e t r i e c h a r t is c o n - s t r u c t e d a n d is t h e n e m p l o y e d to c o m b i n e a t - m o s p h e r i c c o n d i t i o n s , c o n d i t i o n s in a so lar - s t i l l recovery u n i t , a n d e q u i l i b r i u m p r o p e r t i e s o f t h e a b s o r b e n t s u c h t h a t t h e o r e t i c a l l i m i t i n g o p e r a t - ing c o n d i t i o n s c a n be e s t a b l i s h e d . T h e u s e o f t h e c h a r t s is e x t e n d e d to s h o w h o w w a t e r recovered c a n be c h a n g e d w i t h c h a n g e in t e m p e r a t u r e - h u m i d i t y in var ious par t s o f t h e proces s . An e x a m p l e is g iven to i l l u s t r a t e h o w t h e C-P c h a r t s c a n be used to o b t a i n c o m p a r i s o n s b e t w e e n v a r i o u s p o t e n t i a l absorbers .

No a t t e m p t is m a d e t o s ize a n y e q u i p m e n t n o r is a t t e n t i o n g iven to e n e r g y r e q u i r e m e n t s .

A VAST quant i ty of water resides in the ambient atmosphere. I t is proposed that this water be re-

covered for general domestic use by absorption from the wet air into an appropriate absorbent with subse- quent separation of the water from the absorbent. A solar-type still is considered as a means for separating the product water from the absorbent. Tile separated water is taken as product and the water-lean absorbent,

( ® _----(

G/y o i b W a t e r le,~n ~ 0 @1 Glycol - 0 pump

FIG. 1--Schematic flow diagram.

glycol for example, is recycled to the absorption unit. A simplified schematic flow diagrmn incorporating the essential operational components of the proposed proc- ess is shown in Fig. 1.

P r o p o s e d E q u i p m e n t

The absorption tower can be a simple vertical plane, such as a sheet of plywood, over which the absorbent could be spread into a thin layer for contact with the air. The water-lean absorbent would be fed and dis- t r ibuted by appropriate means along the top of the tower and would flow downward by gravi ty as a thin liquid sheet, while making contact with and while absorbing water from the air. The water-rich absorbent would then be transferred by suitable tubing to the entrance of the solar still. The solar still would be of appropriate design; perhaps one of those now under- going general experimental s tudy and develop- n ! e l l t l ( p - 5a ) , 3 , 5 , 6

F a c t o r s R e l a t i n g to S e l e c t i o n o f Absorber

The theoretical limitations for "rod the effectiveness of production of water by this process depends on con- ditions in the atmosphere, on conditions inside the still, on the absorbent equilibrium proT)erties and on the inter-relationship between and among all of these factors. The purpose of this paper is to formulate method of calculation whereby all of these factors can be considered simultaneously. This is accomplished by

Cover transparent to Golar En~rqy

~ VVofer vaporizes from oolution and

Col~de175e5 ol7 cover

(~ Product Water

Presented at the Solar :Energy Conference, Phoenix, Ari- zona, March 15-17, 1965.

~" /001

T=20°F ---~ ) , \ \ \ \ <~-

T=~oon -- ~ \ ~ /zo°F----.----~ ~ Z:,°

N 20 aj

" 0 0.2 04~ O.G 0.8 LO ~ Ma~s°/o Glycol in ~olution

Fro. 2--Equilibrium relative humidity vs. com- position at T = 20°F and T = 120°F for several of the glycols.

Vol. 10, No. 1, 1966 4l

NOMENCLATURE p~ = pressure of water at a given temperature and at

atmospheric pressure p~ = vapor pressure of water at. the same tempera-

ture R.H. = relative humidity

Sr = relative saturation, i.e. = R.H. = p~ (100) P,

S,~, = relative saturation in t h e ambient atmosphere Srs = relative saturation in the solar still 7'~ = temperature, ambient, dry bulh 7'~ = temperature of the surface on which condensa-

tion is taking place, dry bulb T~ = temperature of the liquid in the still 7'~ = temperature in the glycol recovery unit Tt = temperature of the glycol solution on the sur-

face of the absorption tower P = productivity = mass of water produced per

unit mass of liquid (water plus water-free ab- sorber) recycled per unit of humidity driving force

R = recovery = Y per total mass of fluid recycled l" = yield = mass of water recovered per unit mass

of water-free absorber per one cycle IV = mass of water per unit mass of dry absorber U = has units of A = finite change in

Numerical subscripts refer to locations in equipment for the cycle as shown in Figure 1, or, with reference to the composition-psychrometric chart, they refer to conditions of T, R.H., or composition at. the correspond- ing equipment location.

p lac ing p e r t i n e n t in fo rmat ion onto a single graph. Knowledge of these in te r re la t ionsh ips is necessary in o rder to de t e rmine whe the r or no t a g iven sy s t em will be theore t i ca l ly operab le and also to fo rmula te p rob- lems re la t ing to the process r equ i r emen t s of energy and mass t ransfer , to size var ious ope ra t iona l compo- nen ts of the sys tem, to eva lua t e the influence of changes

in solar ef fects , / rod to consider re la t ive mer i t s of var ious absorbents . Al l cons idera t ions are l imi t ed here to a t - mospher ic pressure . T e m p e r a t u r e s and humid i t i e s a t var ious po in ts t h r o u g h o u t the sys t em and the equi l ib- r ium proper t i e s of the abso rben t are considered.

N u m e r o u s subs tances , inc luding l iquids , exhib i t apprec iab le aff ini ty for water . The glycols are wide ly used in hygroscopica l funct ions and were a r b i t r a r i l y se lected for ini t ia l fo rmula t ion of p rob lems in th is s tudy . E q u i l i b r i m n d a t a on the glycols were t a k e n f rom an indus t r i a l source e.

D a t a on su lphur ic acid, ca lc ium chloride, sod ium hyd rox ide and l i t h ium chlor ide were also read i ly avai l - able; and these compounds are inc luded to d e m o n s t r a t e how compar i sons be tween var ious absorben t s can be made .

The re la t ionships be tween equ i l ib r ium re la t ive hu- m i d i t y and wate r -g lyco l composi t ions for several of the glycols at. t e m p e r a t u r e s of 20 and 120 deg F. are shown in Fig. 2. C o m p a r a b l e re la t ionsh ips exist for any o the r comi)ound t ha t might be considered as :m absorbent . More de ta i l ed plots of por t ions of Fig. 2, for e thy lene glycol, are shown in Fig. 3.

The Composition-Psychrometrie Chart

F o r a g iven compos i t ion of d ip ropy lene glycol i t was no ted , see Fig. 2, t h a t the equ i l ib r ium re la t ive h u m i d i t y is i n d e p e n d e n t of t empera tu re . Thus the equ i l ib r ium d a t a can be p lo t t ed on the usual t ype of p sych rome t r i e cha r t wi th lines of cons t an t re la t ive h u m i d i t y label led as the cor responding g lyco l -wate r composi t ion . This is shown in Fig. 4. I t is ev iden t t h a t equ i l ib r ium d a t a for the o the r glycols, inc luding those for which the equi- l i b r ium re la t ive hunf id i ty of a given compos i t ion changes wi th teml)era ture , can also be p lo t t ed on the p syc h rome t r i c cha r t where lines of cons t an t glycol- wa te r compos i t ion are not necessar i ly co-l inear wi th

15g

S.

.~_5C - -

~ 45

N

2 , 5 - -

2g

/o

I0 20 2,0

6 0 ~ - J ".,x~\ \

12 0 ~ - - \ " i 2 0 0 - - - J - J ~ ~

-Efhy/ene' G/ycol

~ m I - , i

w

9 0 /00

4 o - -

35

2 0

25

2 C - -

15

IG

8 2

[3+ 0

i

84

E t h y / e n e G l y c o /

X = 2 0 ° F 0 = 6 0 ° + = 100 ° [ ] = 1 2 0 °

92 94 96 98 40 5o 6o 7o so 8 6 8,3 90 /oo Mcrs~ % G l y c o l IV/o~3 % G l y c o l

FIG. 3--For ethylene glycol. A portion of Fig. 2 enlarged and for several temperatures.

42 Solar Energy

C. ~ Char t for

D I P R O P Y L E N E ~o . . . . . . . . . . . . . S' 7 O p e r a t i o n W t h o,e ISI~ LINEAR ,

6, T~ = 8 0 ° F , ~,~L~ o~ I c - / L # ' ~ F 5\ % ~. ~ /

_ O 0 f i rs -- 190 F o ~ -_L: / #< 4 i Sr~ = 60% o,,/ /

5o~03 at

1- /@

0 ~0 160 T e m p e r a t u r e , °F 190

FIG. 4 - -For dipropylene glycol. Lines of cons tan t l iquid phase composi t ion lie on lines of cons tan t re la t ive humidi ty . Num- bers in circles refer to location on equipment shown in Fig. 2.

O.7- C.P Chart for CaCI 2 / ,.., , OPERATIONS ,~r / ~, o . 6 s _ _ - Ta= Tc= 60°F Aot~;ot~d /

.e °'6 Ti=110 & 220 °F / / S =40 Io &:o5~ ~-RH=

0.4.

5 N Q 3 . Brock

~ I D COMPLE~S~ ~ " ~ " ~

60 DRY BULB °F. 110 120

]PIG. 6 - -For calcium chloride. Influence of format ion of solids (,n l imi t ing operat ional ranges.

those of constant relative humidity. This is shown in Fig. 5. I t is thus apparent that equilibrium data for any coinpom~d can be plotted as lines of constant composi- tion on the psychrometric chart. These plots are termed composition-psychrometric charts, or simply C-P charts.

The potential utility of this type of plot lies in the fact that all information pertinent to the operation of a unit, such as the one diagrammed in Fig. 1, is con- tained on a single plot.

Use o f C - P C h a r t s

As an example of a use of this type of plol, consider a situation in which the operating conditions are:

S,~ = 6 0 % ; T t = T, = 80°F.

T~ = 100°F. (A temperature drop of 20 ° for heat transfer driving force.)

T, = 190°F. (Farber (4,,r) indicates that this tem- perature is attainable.)

Absorbent is dipropylene glycol. Assume that equilibrium is attained between vapor

C.P. C h a r t f o r

E T H Y L E N E G L Y C O L / / I / O p e r a t i o n s h o w n f o r / / I / ( : } , ~ /

6O'F I c = l a = u U e " ~ i ~ " ' / A ,

, / : / + , j

] ] T

60 DRY BULB,°F 120

FI(~. 5 For ethylene glycol. Lines of constant l iqu id composi- t ion do not necessarily lie co-linear with lines (if cons tan t rela- t ive humidi ty .

and liquid phases throughout all portions of the equipment.

Water-lean glycol enters the tower, Fig. 1, at the top, picks up water as it moves down the tower and the water-rich glycol then leaves at the bottom. The temperature, humidity, and composition conditions of the water-glycol system at points 1 and 2 of Fig. 1 are correspondingly marked on Fig. 4. In the solar still the liquid layer is heated to Tz ; this point is shown as number 3 on both Figs. 1 and 4. In the still the water is separated from the glycol until the liquid phase reaches an equilibrium corresponding to a saturated humidity S,~, i.e. to a condensation temperature of T~, point 5: thus the conditions of the liquid stream as it leaves the still are shown at point 4. For simplicity plug flow of the liquid phase through the still is assumed. As the water-lean glycol is lmmped back to point 1 its teml)erature is reduced from T~ to Tt = 7"0, while its composition remains constant. Thus the cycle repeats itself, on Fig. 1 the glycol is circulated from the absorption tower to the still and then back to the tower, etc. The corresponding cyclic path of conditions of temperature, of equilibrium relative humidity, and of composition of the liquid phase water-glycol system is shown on Fig. 4. The quanti ty of product water leaving at point 6 is, by direct material balance, found by taking the difference in glycol compositions between either points 3 and 4 or points 1 and 2. If compositions are labelled, on the graphs, as W pounds of water per pound of glycol, the yield, Y, is found by direct sub- traction, e.g., on Fig. 4, W2 -- IV4 =- 0.1762 -- 0.0204 = 0.1558 pounds of water produced for each pound of dry glycol cycled.

Figure 6 for calcium chloride, comparable to Fig. 5 for ethylene glycol, is shown here to demonstrate how the problem of formulation of solid complexes can be stated mid how such complexes can place severe limits on the range of operation of many potential absorbents.

Vol. 10, No. 1, 1966 43

0.7: - C.P. CHART FOR , ETHYLENE GLYCOL ~=o.64o / o6! -- ~Ta_ ~ ~ / ~

To: Tt= ° "~ F o.5-- ~:o.4eo- z_

t

60 DRY BULB °F 8 9 3 96 110 120

FIG. 7--For ethylene glycol. Influence of change in T1 on opera- li(m characteristics of the system.

h h h T~ Tj night day

DRY BULB °F

Fro. 8--The influence of day-night conditions on the produc- tion cycle for a constant absolute humidity of the atmosphere.

For another exmnple of utility of this type of plot consider the following:

Sr~ = 40~7~;Tt = T~ = 60°F.

Tc = T, = 60°F. (A theoretical but unobtainable ul t imate limit.)

Absorbent is ethylene glycol (Fig. 5 is applicable.) Assume tha t equilibrium is attained throughout all

of the system.

Question: How do changes in T~ influence the opera- tion of the plant under this set of conditions?

A study of Fig. 7 rapidly shows that the unit will be inoperable for Tz below 89.4°F. and that the recovery (pounds of product water per pound of dry glycol cycled) rises rapidly as T1 increases. Specific calcula- tions on recovery as a function of T~ can be made directly and quickly. The influence of T~. on recovery can be handled in a comparable fashion.

Day a n d N i g h t Operat ions

A comparison between day and night operation is of great value. Although there may be considerable variation between day and night relative humidity, the absolute humidity will tend to remain almost constant. For example consider an absorbent which, for a given composition, shows a constant equilibrium relative hunfidity over a wide range of temperatures and consider a situation in which the absolute humidi ty remains constant at 15 ram. Hg for both day and night. Take T~ = T~ + 5, take T~, day = 90°F and take T~, night = 70°F. with Tt for both day and night = 130°F. From Fig. S it is apparent tha t the unit is inoperable during the day but is readily operable at. night. Studies of this type will be needed in order to evaluate the potential of energy reservoirs such tha t recovery can be made during the non-solar hours. 7

Use of C-P Charts for O p t i m i z a t i o n

Selection of the "bes t " or, more properly, of an

optinmln absorbent for the process outlined in Fig. 1 requires consideration of nmnerous factors. Included in such factors are: a) Initial investment; purchase costs of absorber, b) Magnitude of absorbent to air contact area; size, i.e. costs of equipment, c) Anticipated life of the absorber. Stabili ty of the molecule against breakdown under the influence of solar radiation and when exposed to temperatures necessary in the re- covery refit, d) Thermodynamic properties including heats of wetting and of solution as well as heat losses during cyclic changes in sensible heat. e) Heat- t ransfer characteristics, especially thermal diffusivity, f) Liquid characteristics associated with energies of pumping; i.e. viscosity and density, g) Losses of absorber througt~ vaporization etc. h) Potential health hazards, i) Corro- sive actions on encasing and supporting materials.

Several of these factors are associated with the quant i ty of product water obtained per cycle of absorb- ing liquids. The C-P charts are useful in studying these factors. Production of water can be considered on at least three different bases. If Y is yield, R is recover- ability, and P is productivity, then:

A Ill water (I) ~I~ -- IF4 = AW = YU (Ill '~bs<~rber)(cyele-)

5W Y RU

(II) W, + 1 lb water Ib ,d)sorller + it) -dlsorber lb -d)sorber

& lb water (lb water) (cycle)

U

R PU

(III) &. - - R . H . 4 appropriate unit of humidity driving force

Selection of the Y, R, or P tha t would be used, the manimr in which it would be employed and the weight which would be given to those to incorporate into an optimizing process are beyond the scope of this paper.

44 Solar Energg

TABLE 1--RELATIVE PRODUCTIVITY FOR VARIOUS ABSORBENTS

(Ignoring formation of solids, etc.)

Absorbent I W~ I |V4

LiC1 ' 4.6 [ 2.4 NaOH , .4 I 1.5 Cu Cle 2.8 1.5

H~ SO4 Eth. G. Dip. G.

2.2 1.1 0.7 0.2 0.2 0.1

AW ~ 11"4 q- 1

2.2 3.4 1.9 2.5 1.3 2.5

2.1 1 1.1 c.5 1 . 2 0.1 1.1

i

AW*

IV4 + 1

O. 65 O. 76 O. 52

0.52 0.41 0.09

* In each case A(R.H.) is the same, hence this column gives relative values of P.

The following is given as an example of how the C-P charts can be employed in comparing several com- pounds on the basis of P, all other factors being equal, when a given set of circumstances exists.

Given C-P charts for sodium hydroxide, lithium chloride, sulfuric acid, calcium chloride, ethylene glycol and dipropylene glycol are available. These C-P charts were prepared, each on a separate sheet of transparent paper and all to the same scale. Conditions of operation are S~a = 70%, T~ = 95°F, T~ = 130°F. From Fig. 8, R.H.4 = 38%.

Wanted: How does P change with the absorbent? To solve this problem the series of C-P Charts, with

the proposed cycle traced onto them, were stacked, one on top of the other, all with axes co-linear, and the stack was then placed on a glass-top table with trans- mitted light passing through the stack. Data on W2 and W4 for the various compounds were read directly.

Results are given in Table 1. Sodium hydroxide gave the highest P.

Extension of the use of C-P Charts for coral)arable considerations of Y and of R is immediate.

Other Uses o f C-P Charts

Further study of the plots, such as Fig. 4, 5, 6, 7, etc. will point to other calculations that can be nmde. These include statements on heat-transfer requirements through the surface of the condenser surface in con- junction with temperature drops obtainable and per- missible.

L i m i t a t i o n s o f Th i s Paper

All of the treatments presented here have ignored the vapor pressure of the absorber. If this value is

above a very small figure (.'ontamination of the product

water will result and losses to the atmosphere wouhl

be appreciable, replacement costs would have to be

considered. I t should be emphasized that this paper does not

treat the kinetics of the nmss and energy transfer, does not consider magnitudes of energy requirements in phase changes, nor does it deal with fluid-flow require- ments, i.e. Reynolds numbers and energies of pumping. No consideration is given to relative costs, chemical stability to corrosion properties or to health aspects

of any of the potential absorbents.

S u m m a r y

In summary, the graph obtained by plotting equilib- rium data for a given absorbent over the standard psychrometric data forms a set of information from which, when combined with information obtained from the equilibrium plot of mass of water per unit mass of absorbent against relative humidity, conclu- sions regarding theoretical feasibility and operational

limitations can be read directly and from which prob- lems relative to practical design can be easily and

realistically formulated.

REFERENCES

1--U. S. Dept. of Interior. Saline Water Conversion Report for 1959.

2--Dow Chemical Company, Midland, Michigan. Glycols, Properties and Uses (1956, 1961).

3--Howe, Everett D. Descriptive Pamphlet Circular, Solar Still and Inclined-Tray Solar Still with Copper-Foil Water Basin. U. of Calif. College of Engineering, Sea Water Con- servation Laboratory, 1301 South 46th Street, Richmond Calif. (12 Sept. 1963).

4--Farber, Erich A. Solar Water Heating Technical Progress Report No. 9, XIV, No. 2. U. of Florida (Feb., 1960) (p. 7).

5--Grume, W. N., et. al. Natural and Forced Convection Solar Stills. J. Sanitary Engineering Div., Proc. Am. Soc. Civil Engineers. SA 1 (Jan., 1962).

6~Zarem, A. M., D. 1). Erway (Editors). Introduction To The Utilization of Solar Energy. (U. of Calif. Eng. & Sciences Extension Series). McGraw-Hill (1963). Library of Con- gress Cat. card no. 62-13209, Chapter 12.

7--Hall, R. C. Possibilities and Limitations on the Use of Latent Energy of Vaporization in Energy Reservoirs. Solar Energy, 8, No. 3 (July, 1964), p. 99.

Vol. 10, No. t, 1966 45