Analysis of air dehumidification using liquid desiccant system

~ ) Pergamon 0960-1481 (94)E0010-3

Renewable Energy, Vol. 4, No. 5, pp. 519 528, 1994 Copyright © 1994 Elsevier Science Lid

Printed in Great Britain. All rights reserved 0960-1481/94 $7,00+0.00

ANALYSIS OF AIR DEHUMIDIFICATION USING LIQUID DESICCANT SYSTEM

MOUSTAFA M. ELSAYED Mechanical Engineering Department, King Abdulaziz University, P.O. Box 9027, Jeddah 21413,

Saudi Arabia

(Received 24 January 1994 ; accepted 21 February 1994)

Abstract --Analyses are presented for air dehumidification using a liquid desiccant system. The expression for the coefficient of performance of the system is derived in terms of the operating and design parameters where the effect of each parameter can be directly identified. Also, the expression for the maximum coefficient of performance expected from the system for a given operating condition is deduced. The operating ranges of flow rates of air and solution are examined. A methodology is presented to determine the optimum air temperature for the reconcentration of liquid desiccant, and the optimum flow rates of air and solution in the system. In addition, a parametric study is carried out to find out the factors that contribute to the improvements of the coefficient of performance.

1. INTRODUCTION

Liquid desiccant systems are proved to be very effec- tive in handling the latent load for an air conditioning system. One of their great advantages is that they use a low temperature heat source for the generation of the liquid system. At this low generation temperature, solar energy could be applied efficiently.

The performance of the liquid desiccant systems are mainly dependant on the processes of air dehumidification and the liquid desiccant regeneration. Packed beds are found to be very efficient for these two processes, and thus several research works have been directed to model the heat and mass transfer in these beds [1,2]. To predict the performance of packed beds for dehumidification, a one-dimensional model was developed by Factor and Grossman [3]. The model was slightly modified and used by other inves- tigators to predict the performance of the packed beds at various operating conditions [4-6].

The effectiveness model was introduced by some researchers to replace the one-dimensional finite difference model in order to save computation time. In this model, effectivenesses of heat transfer and/or mass transfer are used to predict the outlet air conditions, temperature and humidity ratio from the beds. Correlations have been developed for these effectivenesses [7,8]. Using the concept of number of transfer units NTU and the Merkel assumption usually associated with the modeling of cooling towers, Stevens et al. [9] derived analytical expressions for the effectiveness of heat transfer and mass transfer in

packed beds. With these results, predicting the performance of packed beds became a simple task.

The present work is dealing with the analysis of the liquid desiccant system shown in Fig. 1. The effectivenesses of heat and mass transfer in the packed beds are assumed to be known beforehand. The objective of the present work is to thermally analyze the system and to derive the conditions to design the system and evaluate its performance.

2. SYSTEM DESCRIPTION

Figure 1 shows a liquid desiccant system for air dehumidification. The system contains two loops : the air dehumidification loop; and the liquid desiccant solution regeneration (reconcentration) loop. In the air dehumidification loop air at a rate rha and state al enters the air dehumidification packed bed (ADPB), where it comes in direct contact with a counterflow of liquid desiccant solution at a rate of rh~. The dehu- midified air leaves the ADPB at state a2 and the weak solution leaves at state s2.

For continuous operation of the air dehumidification loop, the weak solution at state s2 must be regenerated (reconcentrated) and returned back to state sl. This is done by means of the liquid desiccant regeneration packed bed (LDRPB) and a series of heaters and heat exchangers, as depicted in Fig. 1. Ambient air (or any other source of air) is used for this purpose after being heated, along with the solution, to proper temperatures suitable for the regeneration

519

520

mo

@

M. M. ELSAYED

rha~

r~ s + rh w

H e a t e r

4

l,°-. l l*..'*°.l ,,

g I

~...j

, I e s I I

i S o l u t i o n ' ~ I I H . E . I

I I , I m

I

Fig. 1. Schematic drawing of a liquid desiccant system.

process. An air heat exchanger is used to recover heat from the humidified air leaving the bed at state a5 before it is exhausted to ambient. A solution heat exchanger is also used to preheat the weak solution going to LDRPB and to cool the strong solution returning to the ADPB. A water or air cooler is also used for further cooling of the strong solution before its entrance to ADPB.

3. ANALYSIS

Following the definitions of Refs [7-10], the effectivenesses of heat and mass transfer in packed beds are given as follows :

hai- hao (1) eh -- ha i - hsi

w~-Wo em Wi - W~i' (2)

where: hai and ha° are the enthalpy of air at inlet and outlet of bed, respectively; Wi and Wo are the humidity ratio of air at inlet and outlet of bed, respectively ; h~i is the enthalpy of air at the temperature of the solution entering the bed ; and ~ is the humidity

ratio of air in equilibrium with the solution entering the bed.

3.1. Air dehumidification process Ifehl and era1 are the effectivenesses of heat and mass

transfer, respectively, in the ADPB then eqs (1) and (2) reduce to the following

ha2 = hal--/~hl (ha l -hs l ) (3)

Wa2 = Wal--~ml ( W a l - ~sl) , (4)

where the state points of Fig. 1 are used. The rate of water removed from air then becomes

mw - - = Wal- Wa2 = eml (Wal- Ws~). (5) rh~

A salt balance for the ADPB then gives

rns/rha Z,2 = m,/ma + mw/ma Zs~' (6)

where Z is the salt concentration in the solution. A heat balance of the ADPB would give

(ms+rhw)CpsT~2--ms CpsTsl = maeh](ha,-hs0, (7)

where Cps is the average specific heat of solution over

Air dehumidification using liquid desiccant

the working range of temperature and concentration. The previous equation is reduced to the following :

-t- r e a l V ~s +~ps(hal -hs l ) l . (8) T~2 -- m~/ma_ rhw/ma[-Z- T~l Shl

521

~ ] + 2~/rh~ m e~h2(h~4-hs4 ) (18) /~'/s/ " a'~-/~w/ " a Cps

3.2. Solution regeneration process Similarly, if ~h2 and Sm2 are respectively the effec-

tivenesses of heat and mass transfer in the LDRPB, then eqs (1) and (2) give

has = hal -- ~h2 (ha4 -- hs4) (9)

Wa5 = Wa4--~rn2(W~- Ws~), (10)

where W~ is the humidity ratio of ambient air. Since water at a rate of rh~ must be removed from the solution, then a water balance for the air gives

- C, m2 (Ws~-- Wcc), (11) H;/a ~/a

i.e.

1 rnw/&a Ws4 = W~ q'-/]m2F~oo//~a. (12)

The equilibrium humidity ratio of air in contact with liquid desiccant solution is given as follows :

W'~= I4~ T~, Z), (13)

where T~ and Z are the solution temperature and concentration, respectively. Equations (12) and (13) are used together to determine the proper temperature T~4 to regenerate the solution of liquid desiccant.

A heat balance of LDRPB then gives

m~/m~+rh~/m~ rh~/rh a eh2 T~5- rs4+ .~-TZ--. ~-(ha4--hs4). (14)

rhJmw ms/ma tps

Similarly, the effectiveness of the air heat exchanger is defined as follows

Ta3 - T~ ~, - ( 1 9 )

Tas-- T~"

Therefore,

Ta3 = T~+e,a(Tas-T~). (20)

3.4. The COP of the system The enthalpy of moist air at temperature T and

humidity ratio W is given by

h = Cpa T-t- W(hfg,o~- CpvT), (21)

where Cpa and Cp~ are the specific heat of dry air and water vapour, respectively, and hfg.o is the latent heat of evaporation of water at 0°C. The thermal load removed in the air dehumidification process is then given as follows :

QL - - = ehl (ha~--hs~). (22) ~/a

The heat added to the air heater is given using eq. (22) as follows :

Fha ~ a (Cpa + W~ Cpv ) (Ta4 - Ta3), (23)

where Ta3 is given by eq. (20) and T~4 is a design parameter, its value set as follows :

3.3. Heat exchangers The effectiveness of heat transfer in the solution

heat exchanger is defined as follows :

T~4 >~ T~3. (24)

The heat added to the solution heater is also given as follows :

Ts5- Ts6 (15)

es - T s s - Ts2"

Therefore, the temperatures of the solutions leaving the heat exchanger become

Ts6 = Tss--es(Tss-- Ts2) (16)

T~3 = T~2+ mdma+mw/rhae~(Tss - Ts2). (17)

In terms of the inlet conditions to ADPB and LDRPB, eq. (17) could be expressed as follows :

Q.s (ms Ow) (25)

where T~4 is obtained from the solution of eqs (12) and (13) and Ts3 is given by eq. (18). The COP of the system is then defined as follows :

QL COP - - - (26) Qna + Qns

The rate of heat rejection to ambient in the solution cooler is given as follows :

522 M. M. ELSAYBD

O~ rJ'L = ~ Cp~ (T~6-- T~,). (27)

ma ma

/ 0 . 5 ~ ~2 0.1 Gs Pa t"ftraf/'is (29)

X¢ = ~\P~--Pa,/ Yf Pa(Ps--Pa)'

4. RANGES OF FLOW RATES

The performance and economy of the liquid desiccant system depends to a great extent on the flow rates of air and solution in both the ADPB and LDRPB. These flow rates are selected to provide the most economical operation of the system. However, there are several conditions that should be satisfied before carrying out any economical studies. These conditions are discussed below.

When air flows in a counter direction with a flow of liquid in a packed bed, the pressure drop in the air side is increased by the increase in the mass velocity of the air. There is a critical air mass velocity at which the pressure drop rises more rapidly and entrainment of liquid by the effluent air increases rapidly. This mass velocity of air is known as the flooding mass velocity, and it depends on the packing material, solution mass velocity, and the properties of both air and solution. Using the data given by Treybal [11], the flooding mass velocity of air is correlated to other operating parameters as follows :

logl0yf = -- 1.7676- 1.0715 log~0 xf

- 0.2934 (log~0xf) 2 , (28)

with

2.5 , i

where G~ and Gaf are the superficial mass velocity of solution and air at flooding conditions, respectively, and Cf is a constant that depends on the packing material [11]. Figure 2 presents the variation of the flooding air mass velocity for both the ADPB and LDRPB, with Gs/Gaf for some packing materials and using CaC12 solution. For design purposes it is usually recommended to use about 50-70% of the flooding air mass velocity [ 12] to avoid excessive pressure drop in the air side.

The minimum value of (rhs/r~a) for the system is determined from the performance of the dehumidification and the regeneration processes. Referring to Fig. 1, the dehumidification process is shown in Fig. 3. Since rhw << rha, eq. (8) is then reduced to the following :

~hl (hal - - hsl) Ts2 = Ts, + Cp, (rhJ&a) " (30)

So the temperature Ts2 of the solution leaving the bed is increased by the decrease in the ratio m,/rha. As T~2 increases, the humidity ratio ~ of air in equilibrium with the solution at T~2 is increased. From the humidity ratio distribution shown in Fig. 3 for the ADPB, it is clear that the maximum possible value of

is Wa~. If Wss2 exceeds this upper limit, the lower

I i I I

I / t

~E1.5

0.5

Raschin9 r ing (ce ramic ) Ber s a d d l e s (ceramic)

nominal s i z e

-- . _ . . __ 13 mm

0 I I I I I I , 0 1 2 3 4 5 6 7

G s l Gaf

Fig. 2. Flooding air mass velocity at various mass Velocity of CaCI2 solution (z = 0.4, 20 < T < 60°C) for beds using Rasching ring or Ber saddles packings. Based on data from Treybal [11].

%

W s :


// " ' 4 /I ,¢ j",'

~ ll:: Ill / i i i i

/" I.

....f f.("

.o_

"O

"1-

bed height (TSl) ( Ts2)mox Temperoture

( o ) (b) Fig. 3. The air dehumidification process: (a) distributions of humidity ratio along ADPB, and (b) plotting

of state points on the psychrometric chart.

523

par t of the bed would operate as an air humidifier. Thus the maximum possible value of T~2 would be that to make ~ = W,~ and this gives the minimum value of m~/rh, using eq. (30) as follows :

( m~ )min = gh~(ha, -- hs,) (31) Cp~ [(T~2)ma × - T~]"

Another minimum value of rhJma is also determined by studying the LDRPB. Using eq. (14), after neg- lecting mw compared to ms,

FF/ac/?~'/a ~h2 T~s = T~4 (h~4-h~4). (321 ,</m. Cp~

For a given ratio of r~o/rh~ and h~4 > ha4, the temperature T~5 decreases as (mjm~) is decreased. As T~5 is decreased, ~ is also decreased as shown in Fig. 4, The lowest possible value of ~ is 14<~4 as shown in the figure, to avoid possible air dehumidification in the bed. Thus the minimum possible value of 7~5 is the temperature at which ~ = ~a4" Equa- tion (32) then gives the minimum value of (mjrh~), as follows :

(/~/~ ( /~ ) /~h2(hs4- - ha4) (331 dT~jmi = ~ - Cps [ (T~4- - (T~5)m in ] "

Therefore the minimum value of m~/ma for the system would be

( ) m: ., m~ m a x ~ ( _ _ ~ , ( t / ~ ' / / (34) 7ma = ( \ m a J m i n \ m a / m i n )

5. OPTIMUM AIR TEMPERATURE LEAVING THE AIR HEATER

The opt imum value of T.4 is the temperature to make the minimum heat input to the system. Using the analysis in Section 3 and carrying out algebraic manipulat ion, the heat input to the system (QH = QHa-~- QHS) is expressed as follows :

- - = Cp~(1 /T/a ~a -~- --Es)

mo • ) rh~ + ~ - e,~ eh2Cpv (W~4 -- W~,)} Ts4 + - - Cp .... ma ) ma

x (1 -cO T~+ -7~-(W~ - W~)hfe,o C~Ch2 m a

e,a ) fm~ --Cpa.,~: ~('P'h2--gm2)I--{ ~Cp~T~] +ght(h~l--h~l) }

{ mjm., ) ,~,~ { x 1-- , " • . e~}+ - (e~:h2--1)

} q- fl Cpa ~(1 --~1,2) (Ts4-- T~41, (35)

where

524

w I j , ,

a 4 ~

bed height

M. M. ELSAYED

iI1~ I 11 ii 1 I

S P s , ~ / e s 5

I I I

(Tss)mi n Temperature

= Cpa,o~.-~-F, m2epv(Ws* 4 - W~)

Cpa,o o = Cpa-~CpvWeo , Cpa,s4 = Cpa-l-CpvW ~. (36)

In the above expression for Qn///'/a, the last term gives the contribution of the value of Ta4 to Qn/ri'la. Since Cpa,~/fl is ~ 1, then the last term in eq. (35) becomes

rh~ -7 - Cpa,o~[eh2(e~-- e~) + e,-- 1](T,4-- Ta4). (37) m a

The term between the square brackets is practically less than zero. Therefore (Ts4- T~4) should be as large as possible to keep QH/ffta at its minimum value. The optimum value of ~a4 then becomes

(Ta4)opt = Ta3 , ( 3 8 )

which suggests the elimination of the air heater, and this saves both the initial cost of the system and the energy cost to operate the system.

The above conclusion is based on the assumption that the effectivenesses eh2 and '~m2 are not affected by changing Tan, and also on the assumption of constant mass flow rates. When allowing to change rns/rh a, eq. (38) cannot be used and the optimum temperature Ta4 would be greater than Ts4 as discussed later in Section 7.4.

e

o i .

° -

-I-

ta) ( b ) Fig. 4. The solution regeneration process: (a) distribution of humidity ratio along LDRPB, and (b) plotting

of state points on the psychrometric chart.

obtained when all effectivenesses approach a value of unity. The expression for QH/rha then becomes

~--( W~-- W~) ( Cp,,Ts4 + hfg) ma ma min

/ ,~ / s /T~ /a (hal -hs l ) / fps -]ITI w - - T s l - 1- . , ~ ~ . [ - - ' C p s .

~/s//~/a "t-/~/w//~Ta /~/s/Fha -~-/'?/w//~a l #/a

(39)

The term between the square brackets is simply Ts2 as obtained by heat balance for the ADPB. Using eqs (5) and (11), the above equation reduces to the following:

Q~HaH min = ( W a l - l~sl)[fpvTs4t-hfg'°-fpsTs2]" (40)

The expression for (QH//~/a)rnin is simply the heat required to evaporate mw at Ts2 to vapour at Ts4. The maximum COP then becomes

C O P [max - - CPa(Tal - - Ts l ) -[- ( Wal - - ~ s l ) ( f p v T s l "q- hfg,o) ( ~/~al - - W~l)[fpvTs4 At- hfg,o - Cps T~:]

(41)

and, since (Cpv Ts4- Cps Ts2) << hfg,o and Cpv Tsl '(<~ hfg,o, then

6. MAXIMUM THEORETICAL COP OF THE SYSTEM

To get the maximum theoretical COP of the system, the minimum value of QH should be used. This is

Cpa(Zal - Tsl ) COP [max = 1 + hfg,o(Wal- I4~) " (42)

This suggests that COPlm,x depends only on the inlet condition of air and desiccant solution to the ADPB


Table 1. Parametric data and results of various computer runs

Run Value of the changed Parameters in run 1 number parameter*

m~ = (rh~)mi,, m~ = rh~ and Ta4 = Ts4 1 Z,~ = 20°C 2 T~ = 30°C, W~ = 0.0216 W~ = 0.0117 3 W~ = 0.015 Zi = 0.4 4 Z1 = 0.35 T~I = 20°C 5 T~I = 25°C 8ml : ~hl = l 6 ~ml = ~hl = 0 . 8

em2 = ~h2 = 1 7 /]m2 = ~h2 = 0 , 8

e~ = 1 8 e, = 0.8 e~ = 1 9 ~ = 0.8 T~ = 40°C 10 T~ = 30°C W~ = 0.0284 11 W~ = 0.019

*Other parameters are the same as run 1.

525

and not on the flow rates or the input condi t ions to the L D R P B .

7. RESULTS

The previous analysis is used to predict the performance of the liquid desiccant system at var ious opera t ing condit ions. Calc ium chloride solut ion is used as the liquid desiccant. To demons t ra te the use of the previous analysis, 11 compute r runs are carried out at the opera t ing condi t ions shown in Table 1. R un I is used as a basic r un and in each o ther run only one pa ramete r is changed f rom its value in r un 1. In the following, the results of these 11 runs are discussed.

7.1. Effect of various parameters The results of the 11 computer runs are summarized

in Table 2. F r o m the results in the table one could conclude tha t the COP of the system is improved by increasing ea, e~ and /o r increasing the difference ( T , t - T~) as indicated by eq. (42). The COP is also

improved by the decrease in (Wa~-Ws3 . The gen- era t ion tempera ture Ts4 is increased by the increase in ~ ( W ~ t - W ~ ) due to the increase in the a m o u n t of mois ture removal f rom the air dur ing the air dehu- midif icat ion process. The COP decreases drastically as T,~ gets higher than T,~.

The dependence of the m i n i m u m allowable flow rate of solut ion per kg of air flowing to the A D P B is also shown in Table 2. The results in the table are those due to eq. (34), wi thou t account ing for eqs (28) and (29) which depend on the type of packing material . The rate of heat rejection f rom the system QL/th~ is also shown in Table 2. Its value is t remen- dously increased by increasing (T~-T~) and /o r decreasing e~. The table also gives the values of QL/m,, Qn/ra., Ts4 and cOelmax for runs 1 to 11.

7.2 Effect of changing (riadm,) Chang ing ms/ma, with (rhJrha) >>- (mdrha)m~n, is found

not to affect the COP, (Qc/tha) or Ts4 at as = 1. As ~s decreases, changing (ms/rna) starts to affect bo th the

Table 2. Results of computer runs I-11

Run {rh~'~ QL/rha Qn/rh, Qc/rh, T,4 number ~ ) m ~ m (kJkg- ' ) (kJkg -1) (kJkg ~) (°C) COP COPLm,x

1 2.39 13.5 13.5 13.2 49 1.0 1.0 2 2.64 48.9 38.3 48.2 53.8 1.26 1.26 3 2.48 21.8 21.9 21.4 50.7 1.0 1.0 4 2.06 10.2 10.1 10.0 44.8 1.0 1.0 5 2.58 2.51 7.60 2.36 47.4 0.33 0.33 6 2.39 10.8 10.8 10.6 48.4 1.0 1.0 7 3.00 13.5 13.5 13.2 49.8 1.0 1.0 8 2.39 13.5 15.4 13.2 49.0 0.87 1.0 9 2.39 13.5 34.8 34.5 49.0 0.39 1.0

10 2.39 13.5 13.5 13.2 49.0 1.0 1.0 11 1.67 13.5 13.5 13.2 42.9 1.0 1.0

526 M. M,

COP and (QUraa), but not T,4. Figure 5 depicts the variation of the COP and (QUrh~) with ( r V / s / / ~ / a ) m i n for runs 1-11 in Table 1, but with e, = 0.8. The value of (rh~)~, for each run is found to be the same as depicted in Table 2. F rom the figure, one finds that increasing rh~ causes the COP to drop and (Q~/m~) to increase. The variation of (QUrh~) with m, is linear as shown in the figure. F rom the figure, it is concluded that the system should be operated with rh, as close as possible to (rh,)~, to improve the COP, reduce QUvh~ and reduce the pumping power to circulate the.

7.3. Effect of changin# (ria~lm,) Changing (moo/ma) for runs 1-11 has no effect on

all performance parameters of the system, except (m,/m~)~i, and T~4 where the variations are given in Table 3. As shown in the table, (rhUm,)~ ~ of the system increases linearly with the increase in (rhoo/m~), while

,:o.,. / / 4

?. 4 o 1

.E

0

0.8

0.6

0 u 0.4

0 .2

0.0 1 2 3 4 5 6 7

Fig. 5. Variation of COP and Q~lm~ with (niiUt%)~. for computer runs 1 to 11 using data in Table 1 but with e~ = 1.

ELSAYED

T~4 decreases in a non linear way with the increase in rh~/ma. The results shown in the table are, however, for ea = I.

When 8a becomes less than 1, as is practically the case, the COP is also found to depend on m~/rh,. Results of the variation of COP with (rh~/ma), cal- culated for runs 1-11 but with 8a = 0.8, are shown in Fig. 6. As shown in the figure, the COP decreases as (rhoo/rn,) is increased, except for run 11 where the trend is reversed. The increase in COP in run 11 is, however, negligible. The variation of T~4 with (m~/rha) at ~a = 0.8 is the same as that at ~a = 1.0, which is tabu- lated in Table 3. A designer should then compromise between improving the COP with low fan cost for rh~o/rha, and high Ts4 and thus more energy cost.

7.4. Optimum flow rates and optimum Ta4 It was shown that to improve the COP of the system

one should have T,4 = Ta3, i.e. no need to use an air heater. This conclusion is true only when fixing the value of (mUrha) in the system, in addition to fixing other design and operating parameters. Figure 7 shows the slight decrease in the COP if an air heater is used to heat the air to a temperature Ta4 above/ ' ,4.

As it was also shown before, the COP is improved by reducing (~hUrha), with the largest value of the COP to be obtained when (mUma) = (rh,/rh,)mi~. The value of (mUvh~)~ is practically the same as (m"Urh,)m~n when eq. (34) is used. In this case, (mUma)~, is decreased as

I I I 1.2 "" ' -2 - , . - - . E a = 0 . 8 ,[

1 .0

0 .8

u 0.6

0.4

0 .2

- 11--:

- - 3 , 4 . . £

\ g

0 I I I 0 0.5 1 1.5 2

~oo/rha Fig. 6. Variation of COP with (~o~/m,) for computer runs 1

to 11 using data in Table 1 but with ea = 0.8.


Table 3. Dependence of (rh~/m~)~, and T~4 on (rh~/m~) for runs 1-11 (using input data of Table 1)

527

(mst~/a)min Ts4 ( ° C )

Run (rh~/ma) = (m~/ma) = number 0.5 1 1.5 2 0.5 1 1.5 2

1 1.24 2.4 3.61 4.93 51.7 49.0 48.0 47.5 2 1.52 2.64 3.80 5.0 59.5 53.8 51.5 50.2 3 1.34 2.48 3.69 5.0 54.7 50.7 49.2 48.4 4 1.06 2.06 3.12 4.22 46.8 44.7 44 43.6 5 1.23 2.59 4.25 6.3 49.4 47.7 47.1 46.8 6 1.21 2.39 3.67 50.7 50.7 48.4 47.6 47.2 7 1.59 3.0 4.47 6.05 53.0 49.8 48.5 47.9 8 1.24 2.39 3.6 4.93 51.7 49.0 48.6 47.5 9 1.24 2.39 3.61 4.93 51.7 49.0 48.0 47.5

10 1.24 2.39 3.61 4.93 51.7 49.0 48.0 47.5 11 0.90 1.67 2.47 3.32 46.4 42.9 41.5 40.8

Ta4 is increased, as suggested by eq. (33). The cal- culat ion showed that , if the system is to be opera ted a t (?~/s/B~/a)min, then as Ta4 is increased the increase or decrease in the C O P would be due to the effects of b o t h decreasing (rhdrh~)m~ and increasing T~. Figure 8 depicts the var ia t ion of the C O P with (Ta4- T~4). In this case, it is shown tha t as Ta4 is increased the C O P

is improved to a po in t where it s tarts to decrease again. The tempera ture Ta4 at the largest C O P would be the o p t i m u m heat ing tempera ture of the air heater. No te tha t for each value of (rh~/rh~) there is an op t i m um value of T~4 and a cor responding op t i m um value of (rndrha), and these o p t i m u m values depend on the design and opera t ing condi t ions of the system.

Figure 8 also depicts the var ia t ion of (T~4 - T~3) with (Ta4- T~,). As (T~4- Ts3) approaches zero, there would be no need for solut ion heaters and only air heaters are used.

1.0 t ' , , I ' I 10 moo ms 2.0 ~1

= o 5 =

0.8

0.6 ( "l'z4 = ~ IO.

0 v 0.4

0.2

0.0 0

C O P

Opt imiza t ion of the flow rates and Ta4 is usually done based on economy. In this case the above pro- cedure provides the basis for such opt imizat ion.

1 0

- 6 ,....q.

i,.? I -, 4

0

1 . 0

8 0 . 8

0 . 6

"" 0 4 ~ 0 0"4 I,--

I

" 0 .2

, I ~ I , I , I , 0

4 8 12 16 2 0

( Ta4 - T s 4 ) , °C

Fig. 7. Variation of COP and (Ts4-- T,3) with (Ta4-- T,) for system with eh] = ~ml = eh2 = era2 = ea = es = 0.8, m~/rha = 0.5 and rhs/rh~ = 2.0. Other design and operating param-

eters are the same as in run 1.

' '

0.5 ~ -'~ ~ a ~

1 0 (Ts4 =51.7 ~: ) 2102--'. \ ( T s 4 = 4 9 °C)

_ \ '~ \ \ - \

(~s4 = 47 5~:)",, \

\ , I , I , I , I ,"',

I ' I ' I ' . I ' I

- ~ a = Wha in

..f__..]

.0.5 . . . .

?" I 1 .0 .

16 20 0 . 0 , I , I

0 4 8 12

( To4- Ts4 ) Fig. 8. Variation of COP and (T~4-T~3) with (Ta,-T~4) for systems with eh, = ~ml = /~h2 = era2 = ~a = es = 0 .8 a n d ms/rha = (rn,/rha)mm at various values ofth~/t~t a. Other design

and operating parameters are the same as in run 1.

528 M.M. ELSAYED

8. CONCLUSION

Analysis of a liquid desiccant system is presented. The analysis is used to derive the following :

(a) expression of the C O P of the system in terms of the operating conditions ;

(b) expression for the maximum possible COP for the system at a given operating condition.

In addition, it is shown that the system has a minimum value of (rhs/rna) which depends on the operating conditions of the system. I f the system is operated at (rhs/rha)< (rhs/rha)min, air humidification may partly take place in the A D P B or air dehumidification may partly take place in the LDRPB. The analysis also showed that for opt imum operation, i.e. high COP :

(a) there is no need for an air heater if the system is operated at a prespecified (rhs/rha)min ;

(b) there is an opt imum temperature Ta4 > T~4 if the system is operated at rh~ = (rh~)mi n ;

(C) the value of (rhJrha)mm depends on the design and operating parameters of the system ; and

(d) the value of (rhJma) for the system should be as close as possible to (rhJrna)mi,.

The selection of (rhoo/rh~) of a system is mainly a matter of economical compromise between high C O P and low T~4 and T~4.

NOMENCLATURE

Cp specific heat (J kg -1 °C) COP coefficient of performance

G superficial mass velocity in packed bed, i.e. mass flow rate per unit cross sectional area of bed (kg s- 1 m 2)

h enthalpy of moist air (J kg-~ dry air) hrg,o latentheatofevaporationofwaterat0°C(Jkg -j)

th mass flow rate (kg s -~) Qc heat rejection load from solution (W) QH heating load (W) QL dehumidification thermal load (W)

T temperature (°C) W humidity ratio of air (kg water/kg dry air) Z concentration of salt in the solution of liquid

desiccant (kg of salt/kg solution) e effectiveness of a heat exchanger

em effectiveness of mass transfer in a packed bed eh effectiveness of heat transfer in a packed bed # viscosity (Pa s) p density (kg m 3).

Subscripts a air

al, a2 . . . . state point of air (see Fig. 1) af air at flooding condition

i input to packed bed o output of packed bed s solution of liquid desiccant

sl, s2 . . . . state point of solution (see Fig. 1) v water vapour w water

l, 2 ADPB and LDRPB, respectively oo ambient.

Superscript * equilibrium condition of air in contact with liquid

desiccant solution.

REFERENCES

1. G. O. G. L~f, T. G. Lenz and S. Rao, Coefficients of heat and mass transfer in a packed bed suitable for solar regeneration of aqueous lithium chloride solution. Trans. ASME, JSEE 106, 387-392 (1984).

2. P. Gandhidasan, C. F. Kettleborough and M. R. Ullah, Calculation of heat and mass transfer coefficients in a packed tower operating with a desiccant-air contact system. Trans. ASME, JSEE 108, 123-128 (1986).

3. H. M. Factor and G. S. Grossman, A packed bed dehumidifier/regenerator for solar air conditioning with liquid desiccant. Solar Energy 24, 541-550 (1980).

4. P. Gandhidasan, M. R. Ullah and C. F. Kettleborough, Analysis of heat and mass transfer between a desiccant- air system in a packed tower. Trans. ASME, JSEE 109, 89-94 (1987).

5. H. N. Gari, M. M. Elsayed and A. M. Radwan, Solar cooling by liquid desiccant, final report of project No. 057/408. Scientific Research Administration, King Abdulaziz University, Saudi Arabia (1988).

6. A. M. Radwan, H. N. Gari and M. M. Elsayed, Para- metric study of a packed bed dehumidifier/regenerator using CaCI2 liquid desiccant. Renewable Eneryy 3, 49-60 (1993).

7. M. R. Ullah, C. F. Kettleborough and P. Gandhihasan, Effectiveness of moisture removal for an adiabatic coun- terfiow packed tower absorber operating with CaCl2-air contact system. Trans. ASME, JSEE 110, 98-101 (1988).

8. P. Gandhihasan, Reconcentration of aqueous solutions in a packed bed: a simple approach. Trans. ASME, JSEE 112, 268-272 (1990).

9. D. I. Stevens, J. E. Braun and S. A. Klein, An effectiveness model of liquid-desiccant system heat/mass exchangers. Solar Energy 42, 449-456 (1989).

10. M. M. Elsayed, H. N. Gari and A. M. Radwan, Effec- tivenesses of heat and mass transfer in packed beds of liquid desiccant system. Renewable Energy 3, 661-668 (1993).

11. R. E. Treybal, Mass Transfer Operations. McGraw-Hill, New York (1980).

12. R. H. Perry, Chemical Engineers Handbook, 6th edn. McGraw-Hill, New York (1984).

Documents

Analysis of air dehumidification using liquid desiccant system