Analysis of air dehumidification using liquid desiccant system

RenewableEnergy, 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

Pergamon 0960-1481 (94)E0010-3

ANALYSIS OF AIR D E H U M I D I F I C A T I O N 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--Analysesarepresented for air dehumidification using a liquid desiccant system. The expression for the coefficientof 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 coefficientof performance.

1. INTRODUCTION Liquid desiccant systems are proved to be very effective 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 investigators 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 N T U 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 dehumidified 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

M. M. ELSAYED

520

rha~

mo

@

r~ s + rh w

,

Heater

I

es

I

I

4 i

I I I

Solution

'~

H.E.

I

I, Im

l,°-.l l*..'*°.l g

I

,,

I ~...j

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 eh -- hai - hsi

(1)

w~-Wo em

W i - 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 era1are the effectivenesses of heat and mass transfer, respectively, in the ADPB then eqs (1) and (2) reduce to the following ha2 = hal--/~hl (hal-hsl)

(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 - - = W a l - Wa2 = eml ( W a l - Ws~). rh~

(5)

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

521

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

T~2 -- m~/ma_ Shl -t-r rhw/ma[-Ze a l V~s T~l +~ps(hal-hsl)l.

(8)

3.2. Solution regeneration process Similarly, if ~h2 and Sm2 are respectively the effectivenesses 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 H;/a - ~/a C,m2(Ws~-- Wcc),

(11)

~]+

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

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

-

Ta3 - T~ Tas-- T~"

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),

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

T~5-

m~/m~+rh~/m~

rh~/rh a eh2 rs4+ .~-TZ--.~-(ha4--hs4).

ms/ma tps

rhJmw

(14)

3.3. Heat exchangers The effectiveness of heat transfer in the solution heat exchanger is defined as follows :

Ts5- Ts6 es -

Tss-

Ts2"

(15)

Therefore, the temperatures of the solutions leaving the heat exchanger become Ts6

=

Tss--es(Tss-- Ts2)

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

(16) (17)

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

(20)

3.4. The COP of the system The enthalpy of moist air at temperature T and humidity ratio W is given by

(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~).

(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 L D R P B then gives

(19)

Therefore,

h = Cpa T-t- W(hfg,o~- CpvT), i.e.

(18)

~/a

(22)

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 : T~4 >~ T~3.

(24)

The heat added to the solution heater is also given 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 :

COP - - -QL

Qna + Qns

(26)

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

M. M. ELSAYBD

522

O~ rJ'L

= ~ Cp~(T~6-- T~,). ma ma

Gs

(27) X¢ =

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 :

i

~E1.5

0

Yf

._..__

I 1

(28)

I

i

I

I

(ceramic) (ceramic)

13 mm

I 2

(29)

Pa(Ps--Pa)'

nominal s i z e

I/t

0

~\P~--Pa,/

(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 Wss2exceeds this upper limit, the lower

Raschin9 ring Ber s a d d l e s

0.5 --

0.1

~hl (hal -- hsl)

with ,

~ ~2

t"ftraf/'is

Ts2 = Ts, + Cp, (rhJ&a) "

logl0yf = -- 1.7676- 1.0715 log~0 xf

2.5

/0.5

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/Gaffor 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 :

4. RANGES OF FLOW RATES

- 0.2934 (log~0xf) 2 ,

Pa

I 3 Gsl

I 4

I 5

I, 6

7

Gaf

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

523

Air dehumidification using liquid desiccant

// ,¢" ' 4j",'/I

%

.o_

~ll:: Ill /

"O

ii ii /" I.

Ws:

....ff.(" bed height

"1-

(TSl) ( Ts2)mox Temperoture (b)

(o)

Fig. 3. The air dehumidification process: (a) distributions of humidity ratio along ADPB, and (b) plotting of state points on the psychrometric chart. part 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,) Cp~ [(T~2)ma× - T~]"

(31)

Another minimum value of rhJma is also determined by studying the LDRPB. Using eq. (14), after neglecting mw compared to ms, T~s = T~4

FF/ac/?~'/a~h2 (h~4-h~4). ,
(321

F o r 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<~4as 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 ~ = ~ a 4 " Equation (32) then gives the minimum value of (mjrh~), as follows :

(/~/~

(/~)/~h2(hs4-- ha4)

dT~jmi =

~-

(331

Cps[(T~4--(T~5)min

]"

7ma

m a x ~ ( _ _m: ~ =

, ( t / ~.,' /

(\maJmi n \ma/min)

/

The optimum 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 manipulation, the heat input to the system (QH = QHa-~-QHS) is expressed as follows :

/T/a =

Cp~(1 --Es)

~a -~-

--

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

ma

x (1 -cO

)

ma

T~+ -7~-(W~ - W~)hfe,o ma

C~Ch2

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

{

x 1--

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

( m~ )

5. OPTIMUM AIR TEMPERATURE LEAVING THE AIR HEATER

,

mjm., "

• .

}

)

e~}+

,~,~

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

(34) where

-

{

(e~:h2--1)

(35)

524

M. M. ELSAYED

wI

iI1~I

j,,

11ii 1I S

e o i.

°-

P

s, ~ /es5 -I-

a

4

I I

~

I

(Tss)min Temperature

bed height 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

= 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). ma

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

/,~/s/T~/a (hal-hsl)/fps -]ITIw - T s l - 1- , . ~ ~ . [--'Cps ~/s//~/a "t-/~/w//~Ta /~/s/Fha -~-/'?/w//~a l #/a

(37)

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 ,

ma min

(38)

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 '~m2are not affected by changing Tan, and also on the assumption of constant mass flow rates. When allowing to change rns/rha, eq. (38) cannot be used and the optimum temperature Ta4 would be greater than Ts4 as discussed later in Section 7.4. 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

.

(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~HaHmin = ( 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 -- Tsl) -[- ( Wal -- ~ s l ) ( f p v T s l "q- hfg,o) ( ~/~al -- W~l)[fpvTs4 At-hfg,o- CpsT~:]

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

COP [max

=

Cpa(Zal - Tsl )

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

525

Air dehumidification using liquid desiccant Table 1. Parametric data and results of various computer runs Run number

Parameters in run 1 m~ = (rh~)mi,,m~ = rh~ and Ta4 = Z,~ = 20°C W~ = 0.0117 Zi = 0.4 T~I = 20°C 8ml :

1 2 3 4 5

Ts4

Value of the changed parameter* T~ = 30°C, W~ = 0.0216 W~ = 0.015 Z1 = 0.35 T~I = 25°C

~hl =

l

6

~ml = ~hl = 0 . 8

em2 = ~h2 =

1

7

/]m2 = ~h2 = 0 , 8

e~ = 1 e~ = 1 T~ = 40°C W~ = 0.0284

8 9 10 11

e, = 0.8 ~ = 0.8 T~ = 30°C W~ = 0.019

*Other parameters are the same as run 1.

a n d n o t o n the flow rates or the i n p u t conditions to the L D R P B .

7. R E S U L T S

The previous analysis is used to predict the perf o r m a n c e of the liquid desiccant system at various operating conditions. Calcium chloride solution is used as the liquid desiccant. To d e m o n s t r a t e the use o f the previous analysis, 11 c o m p u t e r runs are carried o u t at the operating conditions s h o w n in Table 1. R u n I is used as a basic r u n a n d in each o t h e r r u n only one p a r a m e t e r is changed from its value in r u n 1. In the following, the results o f these 11 runs are discussed.

i m p r o v e d by the decrease in ( W a ~ - W s 3 . The generation t e m p e r a t u r e Ts4 is increased by the increase in ~(W~t-W~) due to the increase in the a m o u n t of moisture removal from the air d u r i n g the air dehumidification process. The COP decreases drastically as T,~ gets higher t h a n T,~. The dependence of the m i n i m u m allowable flow rate o f solution per kg o f air flowing to the A D P B is also s h o w n in Table 2. The results in the table are those due to eq. (34), w i t h o u t a c c o u n t i n g for eqs (28) a n d (29) which d e p e n d o n the type of packing material. The rate of heat rejection from the system QL/th~ is also s h o w n in Table 2. Its value is tremendously increased by increasing (T~-T~) a n d / o r decreasing e~. The table also gives the values o f QL/m,, Qn/ra., T s 4 a n d cOelmax for runs 1 to 11.

7.1. Effect of various parameters T h e results o f the 11 c o m p u t e r runs are s u m m a r i z e d in T a b l e 2. F r o m the results in the table one could conclude t h a t the COP of the system is improved by increasing ea, e~ a n d / o r increasing the difference ( T , t - T~) as indicated by eq. (42). T h e COP is also

7.2 Effect of changing (riadm,) C h a n g i n g ms/ma, with (rhJrha) >>-(mdrha)m~n,is f o u n d n o t to affect the COP, (Qc/tha) or Ts4 at as = 1. As ~s decreases, c h a n g i n g (ms/rna) starts to affect b o t h the

Table 2. Results of computer runs I-11 Run number

{rh~'~

QL/rha

Qn/rh,

Qc/rh,

T,4

~) m ~ m

(kJkg-')

(kJkg -1)

(kJkg ~)

(°C)

COP COPLm,x

1 2 3 4 5 6 7 8 9 10 11

2.39 2.64 2.48 2.06 2.58 2.39 3.00 2.39 2.39 2.39 1.67

13.5 48.9 21.8 10.2 2.51 10.8 13.5 13.5 13.5 13.5 13.5

13.5 38.3 21.9 10.1 7.60 10.8 13.5 15.4 34.8 13.5 13.5

13.2 48.2 21.4 10.0 2.36 10.6 13.2 13.2 34.5 13.2 13.2

49 53.8 50.7 44.8 47.4 48.4 49.8 49.0 49.0 49.0 42.9

1.0 1.26 1.0 1.0 0.33 1.0 1.0 0.87 0.39 1.0 1.0

1.0 1.26 1.0 1.0 0.33 1.0 1.0 1.0 1.0 1.0 1.0

526

M. M, ELSAYED

COP and (QUraa), but not T,4. Figure 5 depicts the variation of the COP and (QUrh~) with (rV/s//~/a)mi 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 r o m 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 r o m 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

T~4 decreases in a n o n 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), calculated 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 tabulated 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~nwhen eq. (34) is used. In this case, (mUma)~, is decreased as I

o .E

1

1.2

I

""'-2-,.--.

I

Ea = 0 . 8

1.0

,[

- 11--: --3,4..£

0

0.8

0.8

u 0.6

\g

0.6

0 u

0.4

0.4 0.2

0.2

0

0.0 1

2

3

4

5

6

7

0

I 0.5

I 1

I 1.5

2

~oo/rha 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.

Fig. 6. Variation of COP with (~o~/m,) for computer runs 1 to 11 using data in Table 1 but with ea = 0.8.

527

Air dehumidification using liquid desiccant Table 3. Dependence of (rh~/m~)~, and T~4on (rh~/m~) for runs 1-11 (using input data of Table 1) (mst~/a)min

Run number

Ts4 ( ° C )

(rh~/ma) =

0.5

1 2 3 4 5 6 7 8 9 10 11

1.24 1.52 1.34 1.06 1.23 1.21 1.59 1.24 1.24 1.24 0.90

(m~/ma) =

1

1.5

2

0.5

1

1.5

2

2.4 2.64 2.48 2.06 2.59 2.39 3.0 2.39 2.39 2.39 1.67

3.61 3.80 3.69 3.12 4.25 3.67 4.47 3.6 3.61 3.61 2.47

4.93 5.0 5.0 4.22 6.3 50.7 6.05 4.93 4.93 4.93 3.32

51.7 59.5 54.7 46.8 49.4 50.7 53.0 51.7 51.7 51.7 46.4

49.0 53.8 50.7 44.7 47.7 48.4 49.8 49.0 49.0 49.0 42.9

48.0 51.5 49.2 44 47.1 47.6 48.5 48.6 48.0 48.0 41.5

47.5 50.2 48.4 43.6 46.8 47.2 47.9 47.5 47.5 47.5 40.8

Ta4 is increased, as suggested by eq. (33). T h e calculation showed that, if the system is to be o p e r a t e d a t (?~/s/B~/a)min, t h e n as Ta4 is increased the increase or decrease in the C O P would be due to the effects o f b o t h decreasing (rhdrh~)m~ a n d increasing T~. Figure 8 depicts the v a r i a t i o n of the C O P with ( T a 4 - T~4). In this case, it is s h o w n t h a t as Ta4 is increased the C O P is i m p r o v e d to a p o i n t where it starts to decrease again. The t e m p e r a t u r e Ta4 at the largest C O P would be the o p t i m u m heating t e m p e r a t u r e of the air heater. N o t e t h a t for each value of (rh~/rh~) there is a n o p t i m u m value o f T~4 a n d a c o r r e s p o n d i n g o p t i m u m value o f (rndrha), a n d these o p t i m u m values depend o n the design a n d o p e r a t i n g conditions o f the system. Figure 8 also depicts the v a r i a t i o n of (T~4 - T~3)with ( T a 4 - T~,). As (T~4- Ts3) a p p r o a c h e s zero, there would be n o need for solution heaters a n d only air heaters are used. 1.0

t

moo

'

,

=o5

,

I

ms

2.0

=

'

( "l'z4 =

0

0.4

COP

'

-

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6

0

4

~

I 8

12

'~

\

"" ~ I,--

,

I 16

,

0 20

( 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 parameters are the same as in run 1.

= 4 9 °C)

\ \

,

0

I

,

I

I

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I

\

,

I

,

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I

'.I

0 0

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-~a=

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0.6

4

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\(Ts4

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

~

,

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-

0.8

0.2 I

(Ts4 =51.7 ~:)

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4

8

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,

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1 0

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0"4

....

1.0.

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v

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0.6

O p t i m i z a t i o n of the flow rates a n d Ta4 is usually d o n e based o n economy. In this case the a b o v e procedure provides the basis for such optimization.

0.2 0.0

?" ,

0

4

I 8

,

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16

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20

( 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)mmat 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 C O P for the system at a given operating condition. In addition, it is shown that the system has a minim u m value of (rhs/rna) which depends on the operating conditions of the system. If 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 L D R P B . The analysis also showed that for optimum operation, i.e. high C O P : (a) there is no need for an air heater if the system is operated at a prespecified (rhs/rha)min ; (b) there is an optimum temperature Ta4 > T~4 if the system is operated at rh~ = (rh~)min ; (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 .... af i o s sl, s2 .... v w l, 2 oo

state point of air (see Fig. 1) air at flooding condition input to packed bed output of packed bed solution of liquid desiccant state point of solution (see Fig. 1) water vapour water ADPB and LDRPB, respectively 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 desiccantair 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, Parametric 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 counterfiow 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, Effectivenesses 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).