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Ind. Eng. Chem. Res. 1996, 35, 2632-2639
Influence of Microporous Characteristics of Activated Carbons on the Performance of an Adsorption Cycle for Refrigeration Stephane Follin, Vincent Goetz,* and Andre´ Guillot CNRS-IMP, Institut de Science et Ge´ nie des Mate´ riaux et Proce´ de´ s Universite´ , Perpignan, Cedex, France
The performance of an adsorption refrigerating process, quantified by the coefficient of refrigerating performance (COP), depends on the adsorbent. From the Dubinin-Astakhov equation, it is possible to calculate the performance of a basic adsorption cycle, taking the characteristics of the adsorbate and the adsorbent into account. The influence of the physical characteristics of the adsorbent on performance is shown by way of the parameters of the Dubinin-Astakhov equation: total micropore volume, W0, characteristic energy, Eo; and exponent, n. The influence of the pore size dispersion is estimated thanks to the DubininStoeckli equation and by comparison of the performances simulated with measured characteristics of several activated carbons. This study shows that there exists, for given thermodynamic conditions, an activated carbon having optimal physical characteristics that allows us to obtain the best performance. 1. Introduction Numerous industrial applications such as air purification (Khale, 1953), drinking water treatment (Hyndshaw, 1965), and gas separation (Ruthven, 1984; Yang, 1987) use the adsorptive properties of activated carbons. Construction of adsorption refrigerating machines constitutes another application of these materials which is currently undergoing rapid development. Since both the working principle and the first commercial applications of the adsorption refrigerating cycle were 60 years old (Miller, 1929), this method of cold production, unexploited for some time, was abandoned for the advantage of the gas compression cycle, thus enabling greater efficiency. However, the study of adsorption refrigerating cycles has been kindled by new regulations on the use of CFC’s. These can be found in the Montreal Protocol edited in 1987 and in the new amendments made during the London Conference in 1990. Another important point is that, by using the natural stocking functions of these processes, this enables us to use delayed cold production in relation to using the phase of energy. All this has stimulated the study of adsorption refrigerating cycles. The Paris symposium took stock of the topicality of the research and the state of development of this kind of process (Meunier, 1992). There are numerous possibilities of exploitation of an adsorption cycle covering a large field of temperatures; for example, refrigeration and ice making from solar energy (Critoph, 1989), application of an adsorption cycle to automobile air conditioning (Suzuki, 1992), or cryogenics (Jones et al., 1990). From the basic discontinuous cycle (described in section 2), several processes were proposed to allow, on the one hand, for pseudocontinuous cold production and, on the other hand, improvement in the efficiency of the adsorption systems. Particular note should be taken here of the internal heat recovery system (Douss et al., 1988), cascading cycles (Douss and Meunier, 1989), and thermal wave system on the heating fluid (Shelton et al., 1988; Jones, 1992). Apart from the diversity of the processes, the working base of the cycle depends on the adsorbent-adsorbate pair. Thus, if the influence of the * To whom correspondence should be addressed.
Figure 1. Thermodynamic cycle of a basic refrigerating cycle.
adsorbate on energetic performance of the cycle was quantified in the case of the solar-powered refrigeration (Critoph, 1988), the role of the adsorbent has not been systematically characterized. Nevertheless, the experiments carried out by Passos et al. (1986) on a restricted number of activated carbons showed that the type of adsorbent used has an influence on the coefficient of performance (COP) of the basic cycle (the precise definition of COP will be explained in section 2). Several hundred activated carbons are either commercialized or studied in laboratories. As a result, it is possible to find a wide variety of results as to the performance obtained. The thermodynamic cycle of the adsorption refrigerating process depends on the physical characteristics of the adsorbents by way of the isosteres. The displacement of the isosteres will modify some data, in particular the quantity of adsorbate exchanged and the highest temperature of the cycle. In order to quantify the displacement of the isosteres, the Dubinin representation has been chosen. In spite of some limitations, which will be exposed in section 3, the variables of the Dubinin equations allow us to account for the evolution of some physical characteristics of the adsorbent. 2. Describing the Thermodynamic Cycle Figure 1 shows the thermodynamic cycle of a refrigerating adsorption machine, characterized by three temperature levels (Tevap, evaporating temperature; Tamb, condensing temperature and temperature at the
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Ind. Eng. Chem. Res., Vol. 35, No. 8, 1996 2633
end of the adsorption; Ted, temperature at the end of the desorption) and two associated pressure levels (Pevap, corresponding to the saturating vapor pressure at Tevap; Pcond, corresponding to the saturating vapor pressure at Tamb). An adsorption refrigerating machine works on a four-phase cycle: isosteric heating, desorption/ condensation, isosteric cooling, and adsorption/evaporation. During the first stage (A, B), the adsorber is isolated from the evaporator and the condenser. The adsorber is heated, which increases the pressure from Pevap to Pcond. During this stage, the quantity of heat Q(AfB) is supplied to the machine. When the saturating vapor pressure is reached at Tamb, the adsorber is connected to the condenser and continues to be heated until the temperature reaches Ted (B, C). During this isobar stage, the quantity of heat Q(BfC) is supplied to the machine. So during this stage, the quantity of heat Qcond is rejected at Tamb. The third stage (C, D) is the isosteric cooling one. The adsorber is once again isolated, and then it cools down until the pressure reaches Pevap. During this stage, the quantity of heat Q(CfD) is rejected. The last stage (D, A) starts as soon as the saturating vapor pressure in the adsorber is reached at Tevap. The adsorber is connected to the evaporator. It adsorbs the adsorbate vapor and continues to cool down until the temperature reaches Tamb. It is this last stage of the cycle which is the productive one. The quantity of heat Qevap is extracted from the environment to cool. Also during this stage, the quantity of heat Q(DfA) is rejected to infinite sink at Tamb. The performance of such a cycle can be evaluated by the coefficient of the refrigerating performance (COP). The COP of a basic cycle is defined as the ratio between the quantity of heat Qevap drawn from the environment and the quantity of heat that must be supplied to the system.
COP )
Qevap Q(AfB) + Q(BfC)
(1)
The COP calculated in this study is the thermodynamic one which takes into account the heat balance on the refrigerant and the adsorbent. The real COP of such a cycle takes into account the heat balance on the adsorber and on the different heating fluids and all other components which also make up the process. 3. Theory of the Volume Filling of the Micropores In order to study the influence of the adsorbent, it is necessary to know the quantity of gas adsorbed at each point of the cycle. Thus, the use of a general approach allows a perception of adsorption isotherms in a large field of pressures and temperatures. It also gives us the opportunity to extrapolate some isotherms apart from those in the experimental field. This study is based on the activated carbons which are of interest due to their adsorptive properties. These materials usually have a pore width below 2 nm (also called micropores) (IUPAC, 1985). The approach of Dubinin makes it possible to connect the adsorption isotherms, which characterizes the activated carbon adsorbate pairs, and to predict the values accurately. It also makes it easier to connect the adsorption isotherms with a pore size distribution (PSD).
Figure 2. Comparison between the correlations of Dubinin (a) and McEnaney (b) for Eo ) f(xt).
The Dubinin theory is based on the work of Polanyi (1928). The adaptation of the Polanyi potential theories leads to the Dubinin-Astakhov (D-A) equation (Dubinin, 1960):
[ ( )]
W ) W0 exp -
A βEo
n
(2)
where A, the adsorption potential is
()
A ) RT ln
Po P
(3)
W is the volume of gas (adsorbate) adsorbed at the relative pressure (P/Po), and W0 is the total micropore volume. The exponent n lies in the range 1-3; its value depends on the type of adsorbent. The value n ) 2 leads to the Dubinin-Radushkevich (D-R) equation for a relatively homogeneous adsorbent. Of course, this classification depends on the size of the adsorbed molecule (Suzuki, 1989). The affinity coefficient β is an adjustment parameter concerning the adsorbate from which we can obtain just one characteristic curve, W ) f(A) for one adsorbent and several adsorbates. It is generally agreed that benzene is the reference vapor and β(C6H6) is equal to 1. Eo is the characteristic energy representative of the microporous structure. The simulation of the adsorption potential in the micropores (Everett and Powl, 1976) showed that the minimum potential energy in the micropores increases when the pore width decreases. Taking that the characteristic energy Eo is a function of the PSD within the absorbent, Dubinin (Dubinin and Plavnik, 1968; Dubinin and Stoeckli, 1980) and McEnaney (1987) have shown an inverse correlation between Eo and the pore size (Figure 2). These correlations are obtained from data resulting from experiences of small-angle X-ray scattering (SAXS). The Dubinin-Stoeckli relation is
x)
k 10 Eo
(4)
-3
with
k ) 13.028 - 1.53 × 10-5(10-3Eo)3.5
(5)
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2634 Ind. Eng. Chem. Res., Vol. 35, No. 8, 1996
and x, the half-width for a slit-shaped pore, being
xt ) 2x
(6)
when the McEnaney relation is
Eo ) 41.26 exp(-0.56xt)103
(7)
These two relations give an average value of the pore size according to Eo. Pons and Grenier (1986) have shown that the D-A equation is no longer valid for small adsorbed quantities or, on the contrary, for large adsorbed quantities close to saturation level due to the differences observed between predicted values (adsorbed quantity and isosteric heat of adsorption) and experimental values. The working conditions of the modeled cycles described in this study respect the validity range of the D-A equation, as indicated in section 4. In order to explain the heterogeneity of the PSD of some adsorbents, Dubinin and Stoeckli (1980) put forward a solution to describe the adsorption isotherms of these materials, by taking into consideration the D-R equation (n ) 2). This relation is based on the hypothesis that there is a random formation of micropores according to a normal law:
[
]
W0 (xo - x)2 dW ) exp dx 2σ2 σx2π
Figure 3. Comparison of D-R plots for experimental data: KF1500/CO2 and KF1500/NH3 (W0 ) 0.65 cm3‚g-1).
(8)
Finally, the D-S equation becomes
W)
W0 2x1 + 2mσ2A2
[
exp -
mxo2A2
][
1+ 1 + 2mσ2A2 xo erf σx2x1 + 2mσ2A2
(
)]
(9)
xo is the half-width of micropores for the maximum of the distribution function. σ is the standard deviation of the distribution.
m)
1 β2k2
(10)
In this study, the D-S equation will enable us to introduce an additional parameter, σ, which will show the influence of pore size dispersion. The aim of this paper is to define the influence of the microporous characteristics on the performance of a basic adsorption refrigerating cycle. Ammonia was chosen as the adsorbate, due to its excellent energetic characteristics. Nevertheless, the adsorption isotherm of a polar fluid, such as ammonia, on activated carbons is often different from that of a nonpolar fluid, such as carbon dioxide. This is preeminently found in the case of very low adsorbed quantities. There are several possible explanations: the reactivity of surface groups of activated carbons or else the presence of very small pores (σlj for ammonia is equal to 0.29 nm, while σlj for carbon dioxide is equal to 0.4 nm) (Reid et al., 1987). In order to visualize these differences, experimental adsorption isotherm measurements of ammonia and carbon dioxide on cellulose-based ACF (Toyobo KF1500) were taken. Adsorption equilibria were measured volumetrically at 253, 263, 273, 298, 323, and 353 K, at pressures up to 20 bar. This ACF has been chosen following numerous studies and experimental work
Figure 4. Comparison of D-A plots for experimental data: KF1500/CO2 and KF1500/NH3. Parameters of the D-A equation are W0 ) 0.65 cm3‚g-1, Eo ) 17 000 J‚mol-1, and n ) 1.58.
carried out by Kaneko et al. (1987). Figures 3 and 4 show the D-R and the D-A curves by using the affinity coefficient β. The accordance between the two curves is excellent except for the highest potentials (A), which correspond to low adsorbed quantities. The working boundaries of the refrigerating cycle (described in section 2) are drawn in Figures 3 and 4. These boundaries are defined by points A and C of the cycle (Figure 1), and they show that the thermodynamic conditions are compatible with the D-R equation. Some variations concerning the temperature independence of the Polanyi theory should be noted with ammonia, particularly between the isotherm at 253 K and the isotherm at 353 K. In spite of these limitations, the D-A equation is sufficiently accurate to calculate the adsorbed quantities. The conclusions given in this article are not directly linked to the hypotheses and relations of Dubinin. The variation of the COP as a function of the isosteres and the evaporating temperature is independent of the relation used. On the other hand, numerical values, for example, optimal pore size for a given temperature, are directly linked to the relations of Dubinin. Some limitations exist which have been presented previously. The most difficult to deal with is certainly the empirical character of these relations. Surely a more general thermodynamic approach, that presented by Balbuena and Gubbins (1993), is intellectually more satisfactory, although for the determination of a PSD, it is necessary
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Ind. Eng. Chem. Res., Vol. 35, No. 8, 1996 2635 Table 1. Definition of Each Working Point of a Basic Refrigerating Cycle parameters working pt
known
unknown
A(W0,Eo) B(W0,Eo) C(W0,Eo,Ted) D(W0,Eo,Ted)
Tamb, Pevap qr, Pcond Ted, Pcond qw, Pevap
qr (richest isostere) Tsd qw (weakest isostere) Tsa
Fo )
Figure 5. Pore size distribution for AX21. (s) PSD determined by using the relation of Dubinin with bimodal Gaussian distribution. The CO2 isotherms were measured volumetrically at 253 K at pressures up to 20 bar. (- - -) PSD determined by using LennardJones simulation and a nonlocal functionnal density theory (Lastoskie et al., 1993).
to make some hypotheses that by nature are more or less empirical or qualitative. Thus, following the employed method and especially following our own limitations to each of them, PSDs can be different (Russell and LeVan, 1994). Determining a PSD with the help of the relations of Dubinin requires us to respect these limitations. To illustrate the weak difference obtained between various methods of PSDs determination, the PSD for the activated carbon AX21, determined by the relations of Dubinin (eq 9) and by the density functional approach of Lastoskie et al. (1993), is shown in Figure 5. It is necessary to notice the good agreement obtained for the micropore distribution (between 10 and 15 Å) by these two very different methods. 4. Influence of the Adsorbent on the COP of a Basic Cycle From the D-A equation, we can determine the isosteres for an adsorbent/adsorbate couple with respect to the physical characteristics of the adsorbent (W0, xt). Each point of the cycle is known from the basic refrigerating cycle. First of all, activated carbons are considered to be homogeneous in order to determine the influence of parameters, total micropore volume, W0, and pore size, xt, on the performance of the cycle. Later in this study, the adsorbent is considered to be heterogeneous to show the influence of pore size dispersion on performance. 4.1. Thermodynamic and Working Data of a Basic Cycle. The affinity coefficient β of ammonia is equal to 0.28 (Critoph, 1988). At the beginning of this study, the adsorbent, whatever its pore size, is considered to be homogeneous and leads to n ) 2. This will determine the influence of Eosthat is to say, the average pore width xtsand W0 on the COP of a basic cycle. The influence of the parameter n and then of pore size dispersion will be studied later. The density of the adsorbed vapor is supplied by the Dubinin relation (1960):
T - Tb F(T) ) Fb - (Fb - Fo) Tc - Tb with
(11)
8MPc RTc
(12)
Pc and Tc are the pressure and the temperature at the critical point. M is the molecular weight, and Fb is the density at the boiling state Tb. The saturating vapor pressure is obtained from the Clapeyron equation:
ln(Po) ) -
∆H ∆S + RT R
for T < Tc
(13)
with ∆H ) 23 361.2 J/mol and ∆S ) 193.168 J/(mol‚K) (reference Po ) 1 Pa) and by extrapolation of this equation for T > Tc. The temperature of the infinite sink (Tamb) is fixed at 303 K. Three evaporating temperatures, 273, 258, and 248 K, are taken into consideration. 4.2. Method of Calculation of the COP. Each point of the cycle is characterized by q ) f(T,P). The D-A equation gives us all the variables and, thus, each point of the cycle (see Table 1). For each value of W0 (W0 varies between 0.2 and 1.2 cm3/g), the COP is calculated as a function of Eo and Ted. To determine the maximal COP for each Eo, the temperature at the end of the desorption, Ted, varies between 323 K (the lowest temperature for a cycle to be achieved) and the highest limit. This highest limit is determined for qads being equal to 1 mol with respect to the validity of the D-A equation. The richest isoster (noted qr) is determined by
[(
qr(W0,Eo) ) W0F(Tamb) exp -
( )) ]
RTamb Pcond ln βEo Pevap
n
(14)
In order to determine Tsd, it is necessary to solve the following equality which depends on Eo and W0:
[(
(
)) ]
RTsd Po(Tsd) n ln ) βEo Pcond RTamb Pcond ln W0F(Tamb) exp βEo Pevap
W0F(Tsd) exp -
[(
( )) ] n
(15)
The weakest isoster (noted qw) is determined by
[(
qw(W0,Eo,Ted) ) WoF(Ted) exp -
(
)) ]
RTed Po(Ted) ln βEo Pcond
n
(16)
Tsa is obtained by solving the following equality which is a function of W0, Eo, and Ted:
[(
(
)) ]
RTsa Po(Tsa) n ln ) βEo Pevap RTed Po(Ted) ln W0F(Ted) exp βEo Pcond
W0F(Tsa) exp -
[(
(
)) ] n
(17)
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2636 Ind. Eng. Chem. Res., Vol. 35, No. 8, 1996
Figure 6. COP as a function of Eo (∆Eo ) 2000 J mol-1) and Ted with W0 ) 0.8 cm3‚g-1, n ) 2, and Tevap ) 273 K.
The COP is determined by
(
)
∫TT
Q(AfB) )
∫TT
sd
amb
ed
sd
)
Cpadn +
qr C dT M pliq
qr - qw qr - qw - Cpliq (Tamb - Tevap) M M (18)
Qevap ) ∆H
Q(BfC) )
(
Figure 7. COP as a function of total micropore volume W0 and pore size xt with Tevap ) 273 K and n ) 2.
Cpadn +
(
)
q(T,P)P Cpliq + M
(
Qst(T)
(19)
)
∂q(T,P) ∂T
P
dT (20)
Using eq 2, the second part of eq 20 may be written as
∫TT
q(T,P)P Cpliq dT ) M Po(T) Treg W0F(T) RT exp ln Tdc M βEo Pcond
ed
[(
sd
∫
( )] ] ]
) [[
n
Cpliq dT (21)
Figure 8. COP as a function of total micropore volume W0 and pore size xt with Tevap ) 258 K and n ) 2.
The isosteric heat of adsorption is written as
(
Qst ) RT2
)
∂ ln(P) ∂T
(22)
q
P ) f(T,q) is expressed by combining eqs 2 and 11. The third term of eq 20 becomes
∫TT
ed
sd
( ) [( (
Qst(T)
∫TT
ed
∂q(T,P) ∂T ∆H +
dT )
P
Fb - Fo
)
TβnEon
A1-n + n
(Tc - Tb)F(T) A n Fo - Fb A nn 1+ A W0F(T) exp βEo Tc - Tb βEo T
)[
sd
[ ( ) ][
( ) (
∆H A
)]]] dT (23)
5. Results and Discussion
Figure 9. COP as a function of total micropore volume W0 and pore size xt with Tevap ) 248 K and n ) 2.
Figure 6 shows, for a fixed value of the total micropore volume, W0, the coefficient of performance, COP, as a function of Eo and Ted. Figures 7, 8, and 9 show, for three evaporating temperatures, the variation of the COP as a function of pore width with the help of eq 4 linking Eo and xt.
According to these three figures, whatever the cold production temperatures are and for a given pore width, an increase of the total micropore volume, W0, leads to an improvement of the COP. This improvement is due to an increase of the mass of refrigerant exchanged during the cycle.
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Ind. Eng. Chem. Res., Vol. 35, No. 8, 1996 2637
Figure 10. Isosteres with W0 ) 0.8 cm3‚g-1, Eo ) 12 000 J‚mol-1, and n ) 2.
Figure 11. Isosteres with W0 ) 0.8 cm3‚g-1, Eo ) 35 000 J‚mol-1, and n ) 2.
On the other hand, the influence of the pore width over the COP values differs according to the evaporating temperature. When Tevap is equal to 273 K, there is no maximum of the COP as a function of the pore size, whatever the total pore volume is (for W0 ) 0.2 cm3/g, the maximum of the COP can be considered to be xt ) 1.9 nm). For Tevap ) 248 or 258 K, a maximum of the COP which depends on W0 and pore size exists. These variations are due to the isosteres moving as a function of Eo. Figure 10 shows the isosteres obtained for W0 ) 0.8 cm3/g, Eo ) 12 000 J/mol, and n ) 2. This represents an average pore width of 2.2 nm. The isosteres are very close together and are located near the saturating vapor pressure curve (only the isosteres lying in the validity range of the D-A equation are represented). The different starting points for the three cycles (point A in Figure 1) are obtained by the intersection of the evaporating pressure at Tevap with the ambient temperature Tamb. With the type of adsorbent represented by the isosteres of Figure 10, the optimum COP is obtained at Tevap ) 273 K, which is no longer the case at Tevap ) 248 or 258 K. The richest isostere represented by point A varies quickly according to the pressure level Pevap. When the evaporating pressure is fixed by Tevap ) 273 K, the quantity of adsorbate that can be exchanged is still sufficient. Also, the fact that the isosteres are contracted allows a lower temperature at the end of desorption, Ted, which minimizes the quantity of heat to be supplied. When Tevap is equal to 248 or 258 K, the quantity of adsorbate that is able to exchange is too low, and the value of the COP decreases. Figure 11 shows the displacement of the isosteres when Eo increases. The increasing of Eo will involve shifting the isosteres to the highest temperatures. It will also increase the slopes of the isosteres (Qst), as well as increase the space between them for an equal quantity adsorbed. In both cases, Tevap ) 248 or 258 K, during the displacement of the isosteres (and increasing Eo), an optimum exists between the exchanged quantity of adsorbate and the heat to be supplied in order to achieve a cycle. This optimum represents the best compromise between increasing the exchanged quantity of adsorbate and, on the one hand, the value of ∆T to achieve a cycle or, on the other hand, the isosteric heat of adsorption. The maximal COPs obtained for a basic adsorption refrigerating cycle working with ammonia as the refrigerant are (W0 ) 0.8 cm3/g) as follows: for a cold
Table 2. Values of xt (nm) for the Maximum of COP as Function of W0 and Tevap for n ) 2 W0, cm3‚g-1 Tevap, K
0.2
0.4
0.6
0.8
1.0
1.2
273 258 248
1.25 0.9
1.4 1.0
1.4 1.1
1.6 1.1
1.6 1.2
1.6 1.25
production at 273 K, the COP is equal to 0.5; for a cold production at 258 K, the COP is equal to 0.38; and for a cold production at 248 K, the COP is equal to 0.32. Table 2 recapitulates the optimal pore size as a function of Tevap and W0. These results show that structural characteristics of activated carbon affect the performance of an adsorption refrigerating cycle. The results shown in this first part concern the activated carbons considered as homogeneous (n ) 2). Unfortunately, activated carbons do not offer these ideal characteristics: high total pore volume and a narrow PSD. Most of the activated carbons studied offer large differences compared with the D-R representation (n ) 2) (Rand, 1976; Marsh, 1987). Indeed, the activated carbon preparation, while increasing the total pore volume, leads to an increase of the pore size as well as of the dispersion (RodriguezReinoso, 1991). These same activated carbons studied with the help of the D-A equation lead to exponents n mainly lie in the range 1.2-1.6. The influence of the D-A equation parameters on performance, for some activated carbons, is given in Table 3. Moreover, Jagiello and Schwarz (1992) have shown that the exponent value can be connected to the pore size dispersion. Figure 12 shows the evolution of the maximum of the COP as a function of the pore size when n varies. Decreasing n indicates an increase of the pore size dispersion and, therefore, a more widened PSD. Therefore, there is no longer influence of a particular pore size and the isosteres are less sensitive to the variation of xt. The COP calculated in a such case is inferior to that calculate with n ) 2, but it is less sensitive to the value of xt. 6. Conclusion For a homogeneous activated carbon, the influence of the optimal pore size parameter depends on the evaporating temperature. It is necessary to notice that
+
+
2638 Ind. Eng. Chem. Res., Vol. 35, No. 8, 1996 Table 3. Values of COP Determined by Simulation for Two Evaporating Temperatures, Tevap, and for Some Activated Carbonsa Tevap ) 273 K
Tevap ) 248 K
C-A
W0, cm3/g
n
Eo, J/mol
COP1
COP2
COP3
COP1
COP2
COP3
AC35 DEG LH NORIT RB PKST KF1500 KL93 TA60 TA90 BPL
0.42 0.53 0.86 0.41 0.26 0.65 0.81 0.47 0.6 0.42
2.15 1.31 1.32 2 2 1.5 1.6 1.7 1.5 1.5
17 700 14 000 10 900 19 500 21 100 17 000 19 200 21 300 19 000 20 000
0.42 0.41 0.46 0.4 0.34 0.42 0.44 0.39 0.41 0.37
0.41 0.46 0.53 0.4 0.34 0.44 0.46 0.4 0.44 0.4
0.44 0.46 0.53 0.43 0.38 0.47 0.5 0.45 0.47 0.44
0.26 0.22 0.23 0.26 0.22 0.28 0.31 0.26 0.27 0.24
0.25 0.23 0.17 0.26 0.22 0.3 0.33 0.28 0.3 0.26
0.27 0.29 0.33 0.27 0.22 0.31 0.33 0.28 0.3 0.27
a COP1: COP calculated with experimental characteristics; W , E , and n determined from the D-A equation. COP2: COP calculated 0 o with the same W0 and Eo as COP1 but with n ) 2. COP3: COP calculated with the same W0 as COP1 but with n ) 2 and optimal pore size. AC35, DEG, LH, NORIT RB, and PKST from Critoph (1988). KF1500, KL93, TA60, TA90, and BPL from this work; adsorption data obtained gravimetrically (TG DSC 111 SETARAM).
which is the core of the process, affects the global performance of these processes. With a study such as this, it is possible to estimate the performance of an adsorption refrigerating cycle which can be easily transposed to any type of refrigerant. This method can also be applied to all the different cycles without difficulties (internal heat recovery system, cascading cycle, etc.). It can find out which activated carbon is the most adapted to a process working within the given thermodynamic conditions. Acknowledgment This work was part of a CNRS-ECOTECH contract (1993-1997) with the support of the ADEME. Nomenclature Figure 12. COP as a function of pore size for three values of exponent n with W0 ) 0.6 cm3‚g-1 and Tevap ) 248 K.
an activated carbon optimized for a given evaporating temperature can entail an increase of the COP of the order 15-30%, what is not negligible. On the other hand, if Tevap varies and especially when it decreases, there is a decreasing tendency for COP. A less homogeneous activated carbon presents a worse performance then a homogeneous activated carbon, but it is less sensitive to variations of the evaporating temperature. An other conclusion of this study is that an increase of W0 does not entail systematically an improvement of performance; for example, for a evaporating temperature equal to 248 K (Figure 9), an activated carbon having a W0 equal to 0.8 cm3/g and a pore size close to 2 nm gives the same COP as an activated carbon having a W0 equal to 0.4 cm3/g and a optimal pore size of 1 nm. The COP is therefore even, but the thermodynamic cycle is different. Thus, according to the imposed constraints, the temperature of the heat source, the possibility of heat recovery, etc., it is possible to find the activated carbon most adapted for an application. Obtaining the best performance results from a compromise between the greatest W0, the optimal pore size, and the dispersion. The single observation of the parameter W0 cannot lead to the estimate of the level of performance of a basic adsorption refrigerating cycle. Of course, increasing the performance of an adsorption refrigerating process, so as to reach a good performance level (COP ) 1), hinges on the study of a more advanced cycle. Nevertheless, it is certain that even for more advanced cycles, the activated carbon or, more generally, the adsorbent,
A: COP: C p: Cpads: Eo: k: n: M: P: P o: q: Q: R: T: W: W0: x: xo:
xt: ∆H: ∆S: ∆T:
adsorption potential (J‚mol-1) coefficient of performance (cooling effect) specific heat (J‚mol-1‚K-1) specific heat of the adsorbent (J‚g-1‚K-1) characteristic energy of adsorption (J‚mol-1) structural parameter (kJ‚nm‚mol-1) exponent of the Dubinin-Astakhov equation molecular weight pressure (bar) saturating vapor pressure (bar) adsorbed quantity (g of adsorbate‚g-1 of adsorbent) quantity of heat exchanged (J‚g-1 of adsorbent) perfect gaz constant (J‚mol-1‚K-1) temperature (K) adsorbed volume (cm3 of adsorbate‚g-1 of adsorbent) total pore volume (cm3 of adsorbate‚g-1 of adsorbent) half-width for a slit pore (nm) half-width for a slit pore for the maximum of the distribution function (Dubinin-Stoeckli equation) (nm) slit pore width (nm) enthalpy of transformation (J‚mol-1) entropy of transformation (J‚mol-1‚K-1) maximal temperature difference during a cycle running (Ted - Tamb)
+
+
Ind. Eng. Chem. Res., Vol. 35, No. 8, 1996 2639
Subscripts adn: ads: amb: b: c: cond: des: ed: evap: liq: r: sa: sc: st: w:
adsorbent adsorption ambient boiling critical condensing desorption end of desorption evaporating adsorbed vapor rich isostere start of adsorption start of condensing isosteric weakest isostere
Greek Symbols β: F: σ: σlj:
affinity coefficient density (g‚cm-3) standard deviation for the pore size distribution (Dubinin-Stoeckli equation) (nm) Lennard-Jones diameter (nm)
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Received for review October 29, 1995 Accepted May 3, 1996X IE950638X X Abstract published in Advance ACS Abstracts, June 15, 1996.
