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Ind. Eng. Chem. Res. 1999, 38, 298-309
Experimental Tests and Predictive Model of an Adsorptive Air Conditioning Unit Florence Poyelle, Jean-Jacques Guilleminot,* and Francis Meunier LIMSI/CNRS, BP 133, F-91403, Orsay Cedex, France
An adsorption air conditioning unit has been built operating with a heat and mass recovery cycle and a zeolite-water pair. A new consolidated adsorbent composite with good heat transfer properties has been developed and implemented in the adsorber. At an evaporating temperature of 4 °C, the experimental specific cooling power (SCP) of 97 W‚kg-1 achieved represents a real improvement in comparison with those measured with a packed bed technology. At this evaporating pressure, the mass transfer resistance controls the process. Therefore, at higher evaporating temperature a COP of 0.68 and a SCP of 135 W‚kg-1 were experimentally achieved. A new model has been developed to take into account the mass transfer limitations. The model has been validated and can predict the average pressure inside the adsorber and the components temperature of the unit. A new high conductive material with enhanced mass transfer properties has been developed. The predictive model shows that a SCP of 600 W‚kg-1 and a COP of 0.74 could be achieved with this new material. Introduction After preliminary studies1 on adsorptive refrigeration in the 1920s, experimental feasibility studies of refrigeration systems were reinitiated for solar cooling applications2-5 in the late 1970s with the zeolite-water pair. Later on, experiments were dedicated to gas fired heat pumping or cooling.6-9 In those experiments, several pairs were used: NaX zeolite-water;10-12 active carbon-methanol;13 active carbon-ammonia;6,14 silica gel-water.15 Lots of efforts were devoted toward the performance improvements in terms of COP’s. Advanced cycles (uniform temperature adsorber cycles11 or thermal waves cycles6,16) were tested. An experimental COP of 0.65 was achieved with a two-adsorber uniform temperature cycle,10 and a COP of 1.19 was achieved with two-adsorber thermal wave cycle.17 In those two former studies, the pair is not the same. With the uniform temperature cycle, zeolite-water is used whereas active carbon-ammonia6,14 is used with the thermal wave cycle. An important drawback of the zeolite water pair is its low thermal conductivity of zeolite beds18,19 due in part to the low operating pressure which induces reduction of the heat transfer properties due to the Knudsen effect. The limitation does not exist for the active carbon-ammonia, which in that respect presents advantages. Several routes do exist to improve the thermal properties of zeolite water beds.20-22 In the experiment described in this paper, a consolidated material has been implemented in a pilot plant. This paper presents results obtained with this consolidated material. The analysis of experimental results shows that the behavior of the consolidated beds is very different of the behavior of unconsolidated beds. Therefore, it has been necessary to develop a new model taking into account the new characteristics of consolidated beds which are the mass transfer resistance. With that model, it is possible not only to describe our experimental results obtained on the pilot plant but also to predict performances of other plants. * Corresponding author.
Figure 1. A basic intermittent cycle.
Background Let us recall briefly the principle of an intermittent cycle (Figure 1) of an adsorptive refrigeration system. Basically, the closed machine consists of an adsorber filled with zeolite connected by pipes either with a condenser or an evaporator according to the cycle phase. Knowing the relation between water vapor pressure P and NaX zeolite temperature T in equilibrium at a given amount of water q adsorbed,23 adsorption isosters (dashed lines in Figure 1) and the solid adsorption cycle can be represented in a [ln(P), -1/T ] diagram. During the regeneration phase a-c (Figure 1) of the cycle, the adsorber is connected to the heater. Therefore, the zeolite temperature rises first along an adsorption isoster and then along an adsorption isobar. During this phase, the heater provides an amount of heat Qhr at Thr. Between the points b and c of this regeneration phase, an amount ∆q of water is desorbed from the adsorbent bed and condensed in the condenser at Pcd. The point a is determined by Pev, the evaporating pressure, and Tads, the minimum adsorber temperature, while the point c is determined by Pcd, the condensing pressure, and Treg, the temperature reached by the adsorbent at the end of the regeneration phase. During the second period of the cycle, the adsorption phase, the zeolite
10.1021/ie9802008 CCC: $18.00 © 1999 American Chemical Society Published on Web 12/08/1998
Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999 299
temperature decreases since the adsorber is connected to a cooler extracting it an amount of heat Qhs at Ths. Between the points d and a, the same amount ∆q is evaporated from the evaporator at Tev and then adsorbed. Among the four steps of the solid sorption refrigeration cycle a-d, this particular step da is the step of cooling production at the evaporator. The cooling production Qev is thus given by Qev ) Mz∆q [Lev(Tev) Cp(Tcd - Tev)], where Mz represents the total mass of zeolite in the system, Lev(Tev) the latent heat of vaporization of water, and Cp the liquid heat capacity. The performance of a refrigerating unit is characterized mainly with two parameters:
Qev Qhr
(1)
Qev Mzτc
(2)
COP ) SCP )
The cooling COP measures the ratio between the available energy at the evaporator Qev and the energy Qhr supplied to adsorbers by the high-temperature internal heat source. The specific cooling power, SCP (W‚kg-1), measures the cooling rate per unit mass of adsorbent which depends on the cycle time τc and on the total mass of zeolite Mz in adsorbers. SCP and COP are related as follows:
Qhr SCP ) COP Mzτc
(3)
dQhr )
Table 1. Characteristic Parameters of a Granular Bed Adsorber10,11 λ (W‚m-1‚ K-1) 0.1
The heat exchange analysis between the adsorber and the heat reservoir is developed by an effectiveness-NTU method; therefore, the differential energy balance is given by
m ˘ FCpFf(Thr
Figure 2. Adsorber technology: nonconsolidated adsorbent in grains embedded between fins; consolidated adsorbent composite; zeolite temperature profile, illustration of the heat conductance (hf, hw, λ/e) controlling the heat transfer in the adsorber.
- Tz(t)) dt
(4)
hw (W‚m-2‚ K-1) 30-40
hf (W‚m-2‚ K-1)
K (m2)
100
10-9
COP
SCP (W‚kg-1)
cycle time (min)
0.67
20
360
difference between the heat reservoir and the adsorbent during a half-cycle, is defined as
∆T ˜ )
2 τc
∫0τ /2 (Thr - Tz(t)) dt c
where m ˘ F represents the mass-flow rate of the heat transfer fluid (HXF) and CpF represents its heat capacity. The effectiveness f of the heat exchanger defined as f ) (1 - exp(-NTU)) depends on the number of transfer units (NTU ) where NTU ) UA/m ˘ FCpF. A is the heat transfer surface area, and U is the overall heat transfer coefficient. As the process is of unsteady nature, U is determined by yielding the zero-order moment of the volumetrically averaged temperature.24 U is related to the three heat transfer parameters which control the heat transfer process (Figure 2). In the case of a cylindrical adsorber heated at the inner side, U is given by
Therefore, integrating (4) on the half-cycle of an intermittent cycle, the eq 3 may now be expressed as
1 1 1 ) + + UAo hfAi hwAo
A trivial way to increase SCP should be to increase ∆T ˜ using a higher heat source temperature. Other ways exists to increase SCP: Extended Surface Area. In a packed bed (Figure 2 and Table 1) a low wall heat transfer coefficient hw and a low effective thermal conductivity λ lead to a low overall heat exchange coefficient U. By extension of the surface area A0, using fins, the thermal resistance for convection 1/(hwA0) and conduction e/(λA0) were reduced. This technology was carried out by Douss10 and Zanife12 with a granular adsorbent embedded between fins. In spite of that, a low U explains the low SCP obtained and the magnitude of the cycle time used. But the advantage of operating long cycle times was that a good
[
(
)]
1 + a2 ln a a +1 4 1 - a2 1 - a2
r0 (5) λAo
with a ) r0/r1 and hf is the fluid heat transfer coefficient, hw, the wall heat transfer coefficient, and λ, the effective thermal conductivity. Ai and Ao refer to the inner and outer tube surface area. In this formula, the tube heat resistance is neglected. The adsorber temperature Tz(t) changes with time when the heat reservoir temperature Thr is constant. For a cylinder ∆T ˜ , the time average temperature
˘ FCpF(1 - exp(-NTU))(∆T ˜ /2)COP (6) Mz (SCP) ) m This last expression (6) shows clearly the different ways to increase the SCP at constant size or to reduce the adsorber size for a given SCP. Let us remark that the expression
˜ /2) as m ˘ FCpF f ∞ Mz (SCP) f UA(COP)(∆T
(7)
˘ FCpF(COP)(∆T ˜ /2) as UA f ∞ Mz (SCP) f m
(8)
300 Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999 Table 2. Experimental Heat and Mass Transfer Parameters of the New Consolidated Adsorbent
NEG composite with arteries
λ (W‚m-1‚ K-1)
hw (W‚m-2‚ K-1)
hf (W‚m-2‚ K-1)
K (m2)
5-10
500-1000
1000-3000
2 × 10-13
experimental COP (Table 1) was achieved, close to ideal COP calculated for such a double effect cycle. Heat Transfer Parameters Intensification. In order to increase the cooling power, lots of efforts have been devoted to enhance materials heat transfer properties.23,25-27 A new consolidated composite, mixture of a highly conductive matrix of natural expanded graphite (NEG provided by “Le Carbone Lorraine”) and zeolite grains adsorbent (provided by CECA), was developed.28 The heat and mass transfer characteristics have been determined and are presented in Table 2. In comparison with Table 1, a 50-fold improvement has been achieved in thermal conductivity while the wall heat transfer coefficient is increased 10-fold. But these improvements are at the expense of the mass transfer since the permeability decreases by 4 orders of magnitude. To overcome this problem of too low permeability, arteries are designed in the consolidated blocks axial direction to decrease the mass transfer resistance. Taking into account heat and mass transfer requirements, an adsorbent composite pellet was designed as sketched in Figure 2. The adsorbent blocks surround the tube inside which the liquid HXF flows. The reasonably high cinematic viscosity from 1.68 mm2‚s-1 at 20 °C to 0.26 mm2‚s-1 at 250 °C of the “Santotherm-D12” HXF used explains the value of the heat transfer coefficient hf. Description of a Two Adsorber Cycle with Heat and Mass Recovery (HMR Cycle). A one-adsorber process, as described in Figure 1, results in an intermittent cycle. Operating with a two-adsorber process, cooling production becomes quasi continuous (Figure 3). At the beginning of the cycle, the adsorber 1 is at the highest temperature of the cycle (point C) while adsorber 2 is at the lowest temperature of the cycle (point A). The cycle starts with a quasi-adiabatic mass recovery phase by connecting the two adsorbers via refrigerant fluid. A refrigerant fluid transfer takes place during the pressure equalization phase. This pressurization (depressurization) period occurs until the same pressure is obtained in both adsorbers; at this point (E and E′) the two adsorbers are disconnected. A slight mass dm was cycled during this phase as shown in Figure 3. Then, the heat recovery phase starts by exchanging heat Qr from adsorber 1 to adsorber 2 via the external HXF (Figure 3). During this phase, no heat is supplied by the external heat source; heat released by the hot adsorber is used to heat the cold adsorber. This heat recovery phase is stopped when adsorbers reach the same temperature (points F and F′). Then, the adsorber under heating is connected to the high-temperature heat source whereas the adsorber under cooling is connected to the heat sink. Adsorber 1 is cooled down to Tads by the cooler while adsorber 2 is heated up to Treg by the heater. So the half-cycle period ends and then a symmetric period can occur in which the heat recovery phase reduces the quantity of heat supplied by the heater to adsorber during the regeneration phase. Therefore, the COP increases. A 0.45 COP could be achieved with a purely intermittent
Figure 3. Advanced heat and mass recovery cycle (HMR cycle) consisting in two symmetrical periods, each being divided in three phases: (A) internal mass recovery phase; (B) internal heat recovery phase; (C) external adsorbent cooling or heating.
cycle while 0.67 has been obtained experimentally with such a two-adsorber cycle.10 Experimental Setup (Figure 4). Adsorbers (Labeled 1). The experimental setup, sketched in Figure 4, consists of two adsorbers. Each adsorber is a tubular heat exchanger arranged in 4 rows of 4 tubes. The adsorbent composites are distributed in the form of rod around tubes as described in Figure 2. Each adsorber contains 5 kg of pure NaX zeolite, 1.3 kg of binder, and 1.8 kg of expanded natural graphite (ENG). The total heat exchange area is 0.51 m2 per adsorber. The net volume (adsorbent plus tubes) is 27 L/adsorber. Evaporator (2). A vertical falling film evaporator is used. Distributors with orifices may achieve a good distribution of liquid feed inside tubes whereas the liquid falls down and evaporates. The heating fluid (water) is supplied to the shell side. The evaporating surface is 0.94 m2. A magnetic pump is used for circulating the nonevaporated refrigerant liquid from the bottom to the top of the evaporator. Condenser (3). The condenser is a water-water shell-and-tube heat exchanger with 1.25 m2 tube side area where the heating fluid flows inside the tubes and the working fluid (water) condenses outside. At the condenser bottom, two receivers (4), one for each adsorber, collect and measure the condensing water which returns to the evaporator via a tube. Secondary HXF System. A single fluid processing is used for alternate heating and cooling of the adsorbers (batch processing). The HXF circuits are divided in a cooling and a heating loop. An inert gas blanket on the
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Figure 4. Experimental setup of an adsorptive air conditioning system: (s) primary heat transfer fluid; (‚‚‚) secondary heat transfer fluid; (s) refrigerant fluid.
expansion tank maintains a constant pressure (1 bar relative) above piping and permits full flow of fluid through the tank. A low viscosity fluid is required at low temperature (around to 40 °C) to achieve a high heat transfer coefficient up to 1000 W‚m-2‚K-1 while the pumping power remains quite small. According to these requirements, “Santotherm-D12” was selected to be the secondary heat transfer fluid. Primary Heating Source (5). For practical reason, in this setup, the heater is an electric heater (12 kW) which delivers heat to a mineral heating fluid (Seriola 1100). A heat exchanger links (8) this primary circuit to the secondary one during the heating phase of the cycle. For an actual air conditioning unit, this heat source could be replaced by a natural gas burner in the case of a gas-fired unit. Intermediate-Temperature Heat Sink. Cooling water, used as the heat sink (7) extracts heat from a water-oil shell and tube exchanger (9) to cool the secondary fluid during the cooling period of the adsorber and, in a parallel loop, extracts heat from the condenser. In each circuit there is a pump to flow the HXF. For an actual air conditioning unit, the cooler should be replaced by a fan for small applications or a cooling tower for larger applications. Low-Temperature Heat Source (6). An auxiliary heat source is used and provides heat to a water loop in order to balance the cooling load in the evaporator. Experimental Results The experiments were run on the adsorptive air conditioning prototype described above with a mass and heat recovery cycle. In order to calculate the experimental COP, a heat balance on the HXF is performed to determine the heat supplied to adsorbers and to the evaporator during a cycle. Then the experimental COP
is compared to the theoretical COP which is determined from the four internal operating temperatures (Treg, Tads, Tcd, Tev) achieved during the experimental cycle. Several runs have been carried out with several evaporating temperatures. Herein, results of two runs are presented. Experiments suitable for an air conditioning system have been carried out with the following operating parameters: heater adsorbent cooler condenser evaporator cycle time heat recovery time mass recovery time
230 °C 40 °C 40 °C 4 °C 60 min 7 min 3 min
Low Evaporating Temperature Tests. In Figure 5 are depicted the evolution of temperatures of both adsorbers of heat transfer fluid during a HMR cycle. The cycle phases are obviously outlined. During the mass recovery phase, the hot adsorber is depressurized and desorbs whereas the cold one is pressurized and adsorbs. As the process is adiabatic, the hot adsorber is cooled down whereas the cold adsorber is heated up. At the beginning of the heat recovery period, both adsorbers are connected via the HXF. The heat recovery rate is proportional to the temperature difference between the two adsorbers. At the beginning, the large temperature difference between both adsorbers, 160 °C, explains the fast variation of adsorber temperature. But at the end of this period, the temperature difference is reduced and the heat recovery time has to be long enough to allow the heat transfer between adsorbers. For real applications and to avoid a too large heat recovery time, the phase is stopped when the temperature difference reached 5 °C. Furthermore, an opti-
302 Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999
Figure 5. Temperature evolution of two adsorbers and the heating and cooling HXF during an experimental HMR cycle.
mum heat recovery time can be evaluated by the model described below and as indicated in Figure 12b. During the last phase, the adsorbers are connected to the external heat source or heat sink. At the beginning of this period, the large temperature difference between the heating or cooling fluid and the adsorbers explains the fast variation of adsorber temperature. The experimental mass cycled during a cycle is 0.68 ( 0.02 kg. The theoretical mass desorbed, according to the Dubinin equilibrium, determined from the measured pressure in the adsorber shell and the average temperature of the adsorbent, should be 0.75 kg. This difference can be explained by a pressure drop, at the end of the cycle, within the adsorbent between the boundary constraints and the pressure. So, a mass transfer resistance can be noted. An experimental COP of 0.41 is obtained instead of the 0.65 calculated. This low COP will be explained later in this paper by mass transfer resistance due to the low permeability (10-13 m2). The experimental SCP of 97 W‚kg-1 represents a real improvement in comparison with the granular bed adsorber technology13 (32 W‚kg-1). The predictive model developed for heat pump by Douss10 and taking into account only the heat transfer limitations is not adapted to this case where the mass transfer resistance is the major resistance and therefore controls the process. To underline the effect of mass transfer resistance, others experiments were carried out with the same operating temperature as the previous ones but with a shorter cycle time (20 min). A heat recovery cycle is used with a short heat recovery time of 1.5 min. The experimental COP is lower and reaches only 0.28, but the SCP remains fairly the same (95 W‚kg-1). According to eqs 1 and 2 the COP depends on the cycled mass since Qhr includes the sensible heat of the adsorber heat exchanger. On the contrary, SCP is not sensitive to the adsorber heat exchanger sensible heat. These last results strongly suggest that the mass transfer resistance is one of the major resistance for cycle operations. Experiments in which the mass transfer could not be the limiting parameter are necessary to confirm that point. High Evaporating Temperature Tests (Ter g 20 °C). A test was carried out at high evaporating temperature (Ter ) 29 °C) with a cycle time of 60 min and
Figure 6. Energy distribution in the adsorber during a HMR cycle.
a heat recovery time of 15 min. The reason why this test was carried out was to see if a better COP could be achieved when the evaporating pressure is higher resulting in better mass transfer in the adsorbers. The quantity of mass desorbed (1.0 ( 0.02 kg) is now in agreement with the prediction given by the equilibrium adsorption Dubinin correlation. That means that the measured pressure is the same as the pressure within the adsorbent, at least at the beginning and at the end of the cycle. Therefore, at this evaporating pressure level, the mass transfer does not control the process anymore. The COP achieved is 0.68. This COP is comparable to the value 0.67 obtained by Douss10 under almost the same temperature conditions. The average SCP provided by the evaporator during a cycle is 135 W‚kg-1 and represents a 5-fold increase in comparison with the SCP achieved with the zeolite pellet bed heat exchanger technology.10 The energy provided to an adsorber during a heating half cycle is distributed as shown in Figure 6 desorbed mass
COP
SCP
1.0 ( 0.02 kg
0.68
135 W‚kg-1
The Model Assumptions. Douss10 developed a simple lumped parameter model with the assumption that the thermodynamic equilibrium exists in each component. In particular in the adsorbent, the mass transfer resistance is assumed to be negligible. This model is well adapted
Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999 303
to experiments when the permeability is high, which is the case for nonconsolidated beds. New consolidated materials exhibit very good thermal properties but lead to a high mass transfer resistance. The low experimental performances observed in the previous experiment at low evaporating pressure and short cycle time are due to a pressure drop within the adsorbent. Therefore, a new model which takes into account the mass diffusion through the adsorbent has been developed to describe our experiments. This new model is similar to the previous version dealt with by Douss,10 except for the adsorber where a mass transfer resistance exists. Each component (adsorbers, condenser, evaporator) is homogeneous, which means that each adsorber could be represented by one temperature and one pressure. The global heat exchange coefficient U between the HXF and adsorbers is linked to physical parameters hf, hw, λ/e (eq 5). This method offers the advantage of keeping a simple lumped parameter U while introducing the physical and geometrical parameters. The model used is presented in details in the Appendix. The mass transfer in the adsorber is treated as follows: The partial differential equation describing the mass balance (eq A.1) is integrated over the adsorbent volume. A parabolic pressure profile through the bed (eq A.5) is taken, and an average volumetric pressure is obtained (eq A.8) whereas the bed temperature is assumed to be uniform. These assumptions lead to a set of nonlinear ordinary equations which is solved by the Gear-Nordsiek method. Determination of Unknown Parameters. Most of physical parameters of these ODE’s are known (geometric parameters, physical constants) or determined experimentally elsewhere (Dubinin parameters as W0, D, and n or the effective thermal conductivity λ of the consolidated adsorbent bed). Others are calculated via a well-known correlation proposed in the literature: the fluid heat transfer coefficient, hf. The correlation used is of the form29
Nu )
(f/8)RePr 1.07 + 12.7(f/8)1/2(Pr2/3 - 1)
where the friction factor f is obtained from the expression f ) (1.82 log10 Re - 1.64)-2. Re is obtained by recording the fluid mass flow during test. The heat exchange between the HXF and the adsorber is determined by an effectiveness-NTU method as explained in paragraph 2. The overall heat transfer coefficient based on the outer side surface area is given by 1/(UAo) ) 1/(hfAi) + 1/(heAo), where he is the internal heat transfer coefficient between the solid adsorbent and heat exchanger. The thermal exchange in the adsorbent is controlled by two parameters (hw, λ, Figure 2). The heat loss convection coefficients of each component are determined experimentally by some specific tests (Table 3). Only two unknown extra parameters are needed to fit the model and to account for the process with a satisfactory accuracy. The parameters have been identified by comparing experimental data and model. These extrinsic parameters are the wall heat transfer coefficient hw, used in the U expression (eq 5) and the permeability K, derived from the Darcy law, used in the expression of the effective permeability (eq A.10). One
Table 3. Heat Loss Convection Coefficients Experimentally Determineda Hoh, Hoc (W‚K-1)
Hb, Hc (W‚K-1)
H1 (W‚K-1)
Hcal (W‚K-1)
2
10
1.6
1.8
a
Hoh and Hoc represent the heat losses of the heating and cooling secondary heat transfer fluid to the ambient. Hb and Hc represent respectively the heat losses of the heater and the heat losses of the cooler to the ambient. H1 represents the heat losses from the adsorbent to the adsorbent shell. Hcal represents the heat losses from adsorber shell to the ambient.
Figure 7. Evolution of one adsorber temperature and pressure during a HR cycle at evaporating temperature of 4 °C.
of them, hw controls the heat transfer; the other one K is relative to the mass transfer. The diffusion coefficient D (D ) 3.0 × 10-4 m2‚s-1) of water in the NGE composite has been determined independently from the diffusion coefficient of argon in the same composite which has been measured elsewhere by means of a stationary method.30 The two diffusion coefficients are in the same ratio as the square roots of their molecular mass.31 This D value may be compared with the microporous diffusivity (Dp ) 9 × 10-5 m2‚s-1) of water in NaX pellet measured by means of a frequency thermal response method using IR detector.32 The D value may be also compared with the microporous diffusivity32 of water in NaX crystal, between 10-9 m2‚s-1 and 5 × 10-10 m2‚s-1, which is close to the value (D ) 9 × 10-11 m2‚s-1) obtained by means of a NMR technique.33 Two independent experiments are used to identify K and hw: For the first (Figure 7, Table 4, test I) at low evaporating pressure and short cycle time, the mass transfer is the main resistance and so controls the process; therefore, K could be identified with a good precision. During this experiment, the adsorber temperature and the pressure are recorded; however the pressure inside the adsorbent is not measured. The
304 Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999 Table 4. Comparison of the Desorbed Mass during a Cycle: Experiment and Modela evaporating temp (°C) cycle time (min) cycled mass (kg) (expt) cycled mass (kg) (model)
test I
test II
4 20 (Figure 7) 0.29 0.30
29 60 (Figure 8) 1.0 1.07
test III 25 20 0.63 0.64
test IV 4 60 (Figure 5) 0.67 0.69
a Tests I and II: experimental tests used to identify the heat and mass transfer parameters. Tests III and IV: comparison between experiment and model using values identified with the two previous tests.
Figure 8. HR cycle at high evaporating pressure in a (ln P, -1/ T) diagram: (O) experiment, pressure in the adsorber shell; (s) model, pressure in the adsorber shell; (‚‚‚) model, average pressure in the adsorbent.
experiment tells us that the adsorbate mass cycled is much less than expected from equilibrium. Therefore, varying the permeability, it is possible to find the permeability which fit between the experiment and simulated curves for the variation of the adsorbent temperature versus time. With that permeability, it is possible to evaluate the pressure from the model inside the adsorbent and to get the adsorbate cycled mass. As a good agreement with experiment is obtained, the permeability is assumed to have this value during all the process. During the evaporation process and until the end of the cycle, due to a low permeability, the pressure inside the adsorbent remains inferior to 5 Pa. The cycle time (20 min) does not make it possible for the pressure to increase and to achieve the saturating pressure (750 Pa) corresponding to the evaporator HXF temperature. A second experiment is performed with a long cycle time and at relatively high evaporating pressure (Table 4, test II, Figure 8). A pressure drop is noted during the evaporation process but not at the end of the cycle where the pressure inside the adsorbent achieves the constraint pressure given by the evaporator HXF: the mass transfer is no more a limiting effect. The heat transfer in the adsorber becomes a major limitation.34 So, hw over such an experiment has been determined. To obtain a good fit between experiment and model, two hw values are determined, one for the adsorbent heating phase (hw ) 1000 W‚m-2‚k-1) and an other one for the adsorbent cooling phase (hw ) 500 W‚m-2‚k-1). These two values underline the pressure effect on the wall heat transfer coefficient at low pressure. The wall heat transfer coefficient depends strongly on the vapor thermal conductivity. During the adsorbent cooling phase, the pressure inside the adsorbent can be very low (Figure 7), and at the wall vicinity, the vapor thermal conductivity decreases according to the Knudsen effect. Therefore its contribution to the wall heat transfer coefficient is reduced and can explain the lower value during the adsorbent cooling phase. This pressure effect on the wall heat transfer coefficient is negligible
Figure 9. Comparison between the effective permeability identified by the model and the experimental measurement. Table 5. Values of Identified Parameters heat transfer params
mass transfer param
hw ) 500 W‚m-2‚K-1 during the adsorber cooling phase hw ) 1000 W‚m-2‚K-1 during the adsorber heating phase
K ) 1.3 × 10-12 m2
during the condensation process because of the higher pressure inside the adsorbent and can explain the higher hw value determined. The heat and mass transfer parameters identified are listed in Table 5. The identified values are consistent with the experimental values measured elsewhere by a stationary procedure. hw values ranging between 500 and 1000 W‚m-2‚K-1 are similar to experimental measurements23 where the wall heat transfer coefficient of consolidated composite, depending on the pressure, ranges from 400 to 3000 W‚m-2‚K-1. Similarly, the effective permeability Keff is also in good agreement with permeability measurements28 (Figure 9) of adsorbent composite with and without spacer (Figure 2) in the range 0-10 000 Pa. A good qualitative and quantitative agreement between model and experiment is observed. So the assumptions made to develop the model and especially the mass transfer in the adsorbent are reasonable approximations. The model explains the low desorbed mass (test I) and underlines the pressure drop between the vapor pressure in the adsorber shell and the actual pressure in the adsorbent during the evaporationadsorption phase. Parametric Study. Influence of the Permeability on Performance. The pressure inside the adsorbent is very sensitive to the adsorbent permeability (Figure 10 and Table 6). During the evaporating-adsorption process the pressure drop between the vapor in the shell of the adsorber and the adsorbent itself can be important. At the end of evaporating phase, the pressure in the adsorbent remains lower than the imposed evaporating pressure, and therefore, the cycled mass is lower than expected. But a 10-fold improvement in permeability could be sufficient (K ) 1.3 × 10-11 m2) for a better operation, and therefore, a SCP of 220 W‚kg-1 can be achieved.
Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999 305
Figure 10. Influence of the effective permeability K on the cycled mass during a cycle with the same sources operating temperatures. Table 6. Influence of the Permeability on SCP of the Intermittent Cycle intermittent cycle 10-12
K ) 1.3 × K ) 6.3 × 10-12 m2 K ) 1.3 × 10-11 m2 m2
SCP (W‚kg-1) 129 197 220
Predictive Performance of a High Conductive Adsorbent with Good Mass Transfer Properties. A very new high conductive composite (λ ) 25 W‚ m-1‚K-1, hw ) 2500-3000 W‚m-2‚K-1) with good mass transfer properties (Keff ) 10-9 m2) is currently being under test.35 The model using these constraints shows the temperature evolution achieved with an HMR cycle under the conditions listed (Figure 11) as follows:
Figure 11. Temperature evolution of the two adsorbers with the new adsorbent (Patent, 1996).
SCP or COP: Which Cycle Time? For a given cycle time, the COP and the SCP depend mainly on the heat recovery time. With this particular material,32 the mass transfer resistance is no longer a limiting effect. With the same operating temperature of the sources, each curve of Figure 12a shows the variation of COP versus SCP, for one given cycle time when the heat recovery time varies from 5 to 1 min. Several curves are depicted for various cycle times from 15 to 4 min. A maximum in the COP is reached for each cycle time and the envelope of their curves yields an operational optimum for COP versus SCP. Figure 12b shows the same results in terms of COP versus heat recovery time. The
projection of the previous envelope on the plan (COP versus HR time) gives the optimum heat recovery time for the maximum COP determined in Figure 12a. It is not possible to achieve at the same time a good COP and a high SCP; the optimum point for operation (optimum cycle time and heat recovery time) can be different and may be opposite. In this operating configuration, the best COP of 0.74 is achieved with a rather long time cycle (15 min) and a heat recovery time of 4 min, but the corresponding SCP is low, 420 W‚kg-1. A higher SCP can be attained (790 W‚kg-1) with a shorter time cycle (5 min) with an intermittent cycle (without heat recovery), but the corresponding COP ) 0.38 is rather low. More generally, in Figure 12a, the envelope (dash gray lines) of all the curves is the characteristic curve describing the optimum operating conditions for a given machine and enables us to answer to the following question: which are the optimum operating conditions for a cooling production of 1 kW‚kg-1? The envelope shows that a cycle time of 8 min, obtained by linear interpolation, is suitable and will give the best COP (0.66). Moreover, Figure 12b makes it possible to know which heat recovery time to use (80 s). These two curves obtained by the model are the operating curves of the machine. Conclusion An adsorptive air conditioning unit operating with a heat and mass recovery cycle and a zeolite-water pair has been built and tested. A high conductive adsorbent composite developed by LCL and LIMSI was used. A 50-fold improvement has been achieved on the effective thermal conductivity of the adsorbent (from 0.1 W‚ m-1‚K-1 in the case of a granular bed to 5 W‚m-1‚K-1 for the adsorbent composite). In the same time, the wall transfer coefficient enhancement represents a 20-fold increase (from 30 W‚m-2‚K-1 to 500-1000 W‚m-2‚K-1). But the mass transfer characterized by an effective permeability falls down due to material consolidation (from 10-9 m2 to 10-12 m2). Experimental tests carried out with an evaporating temperature of 4 °C with a heat and mass recovery cycle and a cycle time of 60 min leads to low performances due to a mass transfer resistance (COP ) 0.41), but the SCP achieved (97 W‚kg-1) represents a real improvement when compared with a previous technology using granular bed as adsorbent. At this evaporating temperature, the mass transfer resistance controls the process. At higher evaporating temperature (T ) 25-30 °C), the mass transfer resistance effect decreases due to higher pressure. Therefore the COP reaches 0.68 whereas the SCP is 135 W‚kg-1. At this evaporating pressure level, the heat resistance in the adsorber controls the process. A new model has been developed describing the evolution of the components of the unit during a heat and mass transfer cycle and taking into account mass transfer limitations. The major contribution of the model is to predict the evolution of an average pressure inside the adsorbent. The model has been validated by several experiments. Two parameters are required to run the model. These two parameters are the wall heat transfer coefficient, hw, and the effective permeability, Keff. All the other parameters are measured directly by
306 Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999
Figure 12. (a) Parametric study of the COP-SCP function for different cycle times (15-10-7-5-4 min) when the heat recovery time varies (5-4-3-2-1 min). (b) Parametric study of the COP-heat recovery time at different cycle times (15-10-7-5-4 min).
appropriate experiments. A good agreement is achieved between the model and the experimental measurements. A new high conductive adsorbent with enhanced mass transfer properties has been developed recently. The predictive model shows that, for example, a SCP of 600 W‚kg-1 and a COP of 0.74 could be achieved. SCP and COP are dependent. Clear-cut objectives have to be defined by industrials: which is the most important target (small size or energetic efficiency)? The unit design will clearly depend on the objective. To extract a given cooling load, the operating curves (Figure 12a,b) give the optimum operating conditions (cycle time and heat recovery time) to achieve the best COP. Acknowledgment The authors acknowledge the financial support from the “Gaz de France” and the CNRS. The authors thank also Mr. J. B. Chalfen for his technical assistance and for carrying out some experimental runs and Mrs. A. Choisier for her technical support. Nomenclature Ai ) internal heat transfer area of the tube of the heat exchanger (m2) A0 ) external heat transfer area of the tube of the heat exchanger (m2) c ) concentration of water vapor (m3/m3 of adsorbent) λ/e ) bed heat transfer conductance (W‚m-2‚K-1) ∆T ˜ ) average temperature between the heat source/sink and the zeolite adsorber (°C) ∆m ) mass of water desorbed/adsorbed during a cycle (kg) Cip ) heat capacity of the oil of the component i (J‚kg-1‚ °C-1) COP ) cooling coefficient of performance D ) diffusivity of water in NGE composite (m2‚s) E ) heat exchanger efficiency f ) friction factor hf ) fluid heat transfer coefficient (W‚m-2‚K-1) hw ) wall heat transfer coefficient (W‚m-2‚K-1) Hoh ) heat losses of the heating loop of the secondary HXF (W‚K-1) Hoc ) heat losses of the cooling loop of the secondary HXF (W‚K-1) H1 ) heat losses from the adsorbent to adsorber shell (W‚K-1)
Hoc ) heat losses from the adsorber shell to the ambient (W‚K-1) Hb ) heat losses of the boiler (W‚K-1) Hc ) heat losses of the cooler (W‚K-1) Hcal ) heat losses between the adsorbent and the shell (W‚K-1) Keff ) effective permeability of the adsorbent (m2) K ) permeability of the adsorbent (m2) Lev ) latent heat of evaporation (kJ‚kg-1) Mi ) mass of the component i Mz ) mass of pure activated zeolite in each adsorber (kg) m ˘ i ) mass flow in heat exchanger (kg‚s-1) Pcd ) condensing pressure (Pa) Pe ) vapor pressure in the dead volume of the adsorber (Pa) Pev ) evaporating pressure (Pa) Psat ) saturating pressure (Pa) p˜ ) average pressure in the adsorber (Pa) Pr ) Prandl number q ) local mass of water adsorbed in adsorbent (kg‚kg-1 of pure adsorbent) q˜ ) average mass of water adsorbed in adsorbent (kg‚kg-1 of pure adsorbent) Qhr ) total heat provided to the adsorber during the a-c period by the heater (J) Qhs ) total heat extracted from the adsorber during the cda period by the cooler (J) Re ) Reynolds number R ) gas constant r0 ) interior radius of adsorbent (m) r1 ) external radius of adsorbent (m) S ) total heat exchanger surface (m2) SCP ) cooling rate (W‚kg-1 of pure adsorbent) t ) time (s or min) T ) temperature (°C) Ta ) ambient temperature (°C) Tev ) evaporating temperature (°C) Tcd ) condensing temperature (°C) Tads ) minimum adsorbent temperature (°C) Treg ) maximum adsorbent temperature (°C) Thr ) heat reservoir or boiler temperature (°C) Ths ) heat sink or cooler temperature (°C) U ) global heat exchange coefficient (W‚m-2‚K-1) Vd ) dead volume of the shell (m3) v ) vapor velocity (m‚s-1) Greek Letters λ ) effective thermal conductivity of the adsorbent (W‚m-1‚K-1) ) porosity of adsorbent bed Fs ) density of adsorbent (kg‚m-3)
Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999 307
The pressure follows a parabolic profile:
p ) ar2 + br + c
(A.5)
The parameters a-c are calculated with the boundary conditions (Figure 2)
|
∂p )0 ∂r r)r0
(A.6)
P|r)r1 ) pe
(A.7)
and with the adsorbent average volumetric pressure p˜ :
p˜ )
r12
2 - r02
∫rr pr dr 1
(A.8)
0
By integrating eq A.1 and taking into account (A.6A.8), we obtain
Figure 13. Heating and cooling adsorber phases.
pe Keff 24r1(pe - p˜ ) dq˜ dp˜ (A.9) + Fs ) RT dt dt RT µ (r - r )2(5r + 3r ) 1 0 0 1
µ ) dynamic viscosity of the vapor phase τc ) cycle time (s or min) τhr ) heat recovery time (s or min) τhm ) mass recovery time (s or min)
with
Subscripts
Keff ) K + D
0 ) initial 1 ) adsorber 1 2 ) adsorber 2 b ) boiler c ) cooler cd ) condenser ev ) evaporator i ) inner o ) outside oc ) secondary cooling fluid oh ) secondary heating fluid sh ) adsorber shell z ) adsorbent
µ pe
(A.10)
Heat Balance. Except for the adsorber for which a mass transfer resistance occurs, the temperature evolution of the source and the intermediate heating fluid are calculated by solving heat balance on the various components.
boiler: ˘ bEb(Toh - Tb) + Hb(Ta - Tb) ) MbCbp Wb + m
dTb dt (A.11)
cooler: m ˘ cEc(Tce - Tc) + Hc(Ta - Tc) ) McCcp
Appendix Except for the adsorbers, where the heat and mass transfer equations are dealt with, the predictive model solves a set of ODE which yields the temperature evolution of 12 nodes of the system (Figure 13). Mass Balance. Adsorbent. Inside the adsorbent, the mass balance can be written as
dTc (A.12) dt
secondary heating fluid: ˘ bEb(Tb - Toh) + m ˘ ohEi(Tzi - Toh) + m Hoh(Ta - Toh) ) MohCoh p
dToh (A.13) dt
secondary cooling fluid: oq oc ) -div(Jm) + Fs ot ot
(A.1)
˘ cEc(Tc - Toc) + m ˘ ocEi(Tzi - Toc) + m Hoc(Ta - Toc) ) MocCoc p
with
Jm ) vc - D∇c
(A.2)
Jm is the mass flux density taking into account the convective and diffusive terms. The vapor velocity v follows the Darcy law:
v)-
K dp µ dr
p ) cRT
(A.3) (A.4)
dToc (A.14) dt
adsorber 1 during the adsorber heating phase: ˜ z1 - Toh) + Hcal(Tcal1 - T ˜ z1) ) m ˘ ohE1(T dq˜ 1 dT ˜ z1 (A.15) ˜ z1,P ˜ z1) + Qst Mz1 C1p + Clq˜ 1(T dt dt
(
)
adsorber 2 during the adsorber cooling phase ˜ z2 - Toc) + Hcal(Tcal2 - T ˜ z2) ) m ˘ ocE2(T dq˜ 2 dT ˜ z2 ˜ z2,P ˜ z2) + Qst Mz2 C1p + Clq˜ 2(T (A.16) dt dt
(
)
308 Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999
shell of the adsorber 1 H1(Ta - Tcal1) + Hcal(Tz1 - Tcal1) ) M1calCcal p
dTcal dt (A.17)
shell of the adsorber 2: H2(Ta - Tcal2) + Hcal(Tz2 - Tcal2) ) M2calCcal p
dTcal2 dt (A.18)
condenser: ˜ c0 - Tcd) + Mz2 m ˘ cdEcd(T
dq˜ 2 (Lcd - Ccd(Tev - Tcd) ) dt dTcd McdCcd (A.19) p dt
evaporator: ˜ r0 - Tev) + Mz1 m ˘ evEev(T
dq˜ 1 (Lev - Cev(Tcd - Tev) ) dt dTev MevCev (A.20) p dt
Constitutive Equations. The state equation for the adsorbate-adsorbent equilibrium is given according to Dubinin et al.36 The parameters are determined elsewhere.22
( ( (
˜ ) ) W0F(T ˜ z) exp -D T ˜ z ln q˜ ) φ(T ˜ z,P
)) )
Psat(T ˜ z) P ˜z
n
(A.21) If one knows two of three variables T ˜ z and q˜ , the Dubinin equation makes possible the calculation of the adsorbent pressure P ˜ z. The vapor pressure pe inside the adsorber but outside the adsorbent is determined as follows:
pe ) Psat(Tev) during the evaporation phase (A.22) pe ) Psat(Tcd) during the condensation phase (A.23) There is no pressure drop between the evaporator or condenser and the adsorbers. During the isosteric phase, the shell dead volume Vd of the adsorber and the mass balance between the mass of gas in the dead volume and the mass adsorbed are considered.
dpe dq˜ ) -RMzT/Vd dt dt
(A.24)
Mass Recovery Phase. During this phase, the two adsorbers are connected via the refrigerant fluid. The pressure pe of the two adsorbers is determined by the same way as during the isosteric phase but with a dead volume equal to Vd1 + Vd2.
(
)
dpe dq˜ 1 dq˜ 2 ) -RT Mz1 + Mz2 /(Vd1 + Vd2) (A.25) dt dt dt The same yielded pressure Pe(t) is the boundary condition of the two adsorbers and makes it possible to yield the mass q1 and q2 in the adsorbents and therefore the pressure P1 and P2.
Heat Recovery Period. During the heat recovery phase, the two adsorbers are connected via the secondary heating fluid.
m ˘ ohE1(Tz1 - Toh) + m ˘ ohE2(Tz2 - Toh) + oh Hoh(Ta - Toh) ) Mrec oh Cp
dToh (A.26) dt
In the heat recovery phase, Mrec oh , the mass of the secondary heating fluid is quite different and lower than in the case of heating phase Moh, where the heating fluid flows through the heat exchanger. Literature Cited (1) Miller, E. B. The development of silica gel refrigeration. Refrig. Eng. 1929, 17-4, 103-108. (2) Tchernev, D. I. Solar Energy Cooling with Zeolites. Proc. NSF/RANN Solar Collector Workshop, New York, 1974, 122. (3) Meunier, F. Utilisation des cycles a` sorption pour la re´frige´ration solaire. J. AFEDES 1977, Feb 16; Cahier AFEDES 1978, 5-57. (4) Guilleminot, J. J.; Meunier, F. Etude expe´rimentale d’une glacie`re solaire utilisant le cycle ze´olithe NaX-Eau. Rev. Gen. Therm., Fr. 1981, 23. (5) Sakoda, A.; Suzuki, M. J. Solar Energy Eng. 1986, 108, 239. (6) Miles, D. J.; Sandborn, D. M.; Nowakowski, G. A.; Shelton S. V. Gas-fired sorption heat pump development. Heat Recovery System CHP 1993, 13 (4), 347-351. (7) Alefeld, A.; Maier-Laxhuber, P.; Rothmeyer, M. Int. Conf. Energy Storage (Brighton, U.K.) 1981. (8) Ismaı¨l, I.; Meunier, B.; Brandon, M.; Merigoux, J. Proc. XVI Int. Congr. Refrig. 1983, 2, 363. (9) Delgado, R.; Choisier, A.; Grenier, P.; Ismail, I.; Meunier, F.; Pons, M. Proceedings IIR Jerusalem; IIR, Ed.; 1987; pp 181187. (10) Douss, N.; Meunier, F.; Sun, L. M. Predictive model and experimental results for two adsorber solid adsorption heat pump. Ind. Eng. Chem. Res. 1988, 27 (2), 310-316. (11) Douss, N. The`se Paris VII, 1988. (12) Zanife´, T.; Meunier, F. J. Heat Recovery Syst. CHP 1992, 12-2, 131-142. (13) Zanife´, T.; Meunier, F.; Chalfen, J. B. Proceedings of the XVIII International Congress of Refrigeration, Montreal; Aug 1017, 1991. (14) Critoph, R. E., Turner, H. L., Activated Carbon-Ammonia Adsorption Cycle Heat Pumps; Proceedings of CEC-British Gas International Workshop on Absorption Heat Pumps, April 1988, London, U.K. (15) Sakoda, A.; Suzuki, M. J. Chem. Eng. Jpn. 1984, 17, 52. (16) Pons, M.; Laurent, D.; Meunier, F. Appl. Thermal Energy 1996, 16 (5), 395-404. (17) Miles, D. J.; Shelton, S. V. Design and Testing of a Solid Adsorption Heat Pump System. Appl. Thermal Eng. 1996, 16 (5), 389-394. (18) Sahnoune, H. Mesure de la conductivite´ d’un ze´olithe supporte´e. Thesis, 1988; p 88. (19) Guilleminot, J. J.; Gurgel, G. Heat Transfer Intensification in adsorbents beds of adsorption thermal devices. Presented at the 12th Annual ASME International Solar Energy Conference, Miami, FL, April 1990. (20) Sahnoune, H.; Grenier, Ph. Chem. Eng. J. 1989, 40, 4554. (21) Spinner, B.; Touzain, P. Workshop Carbon, Paris, July 1990. (22) Mauran, S.; Lebrun, M.; Prades, P.; Moreau, M.; Spinner, B.; Drapier, C. FR Patent 91-0303, April 11, 1991. (23) Guilleminot. Thesis, University of Dijon, 1978. (24) Sun, L. M.; Feng, L. M.; Pons, M. Numerical investigation of adsorptive heat pump systems with thermal regeneration under uniform pressure conditions. Int. J. Heat Mass Transfer 1997, 40 (2), 281-293. (25) Guilleminot, J. J.; Choisier, A.; Chalfen. Proceedings of the International Absorption Heat Pump Conference; ASME: Fairfield, NJ, 1993; EAS Vol. 31, pp 401-406.
Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999 309 (26) Guilleminot, J. J.; Choisier, A.; Chalfen, J. B.; Nicolas, S.; Reymonet, J. L. Heat Recovery Systems CHP 1993, 13-4, 215220. (27) Guilleminot, J. J.; Chalfen, J. B.; Poyelle P. XIXth Congress IIR/IIF, Aug 20-25, 1995, The Hague, The Netherlands, Vol. IVa, pp 261-268. (28) Patent SNEA-LCL, WO 91/15292, 1991. (29) Petukhov, B. S. In Advances in Heat Transfer; Irvine, T. F., Hartmelt, J. P., Eds.; Academic Press: New York, 1970; Vol. 6. (30) Chalfen, J. B. LIMSI document no. 93-26. Personal communication, 1993. (31) Dullien, F. A. V. Porus Media. Fluid Transport and Pore structure, 2nd ed.; Academic Press, Inc.: New York, 1992. (32) Bourdin, V.; Grenier, Ph.; Meunier, F.; Sun, L. M. Thermal Frequency Response Method for the Study of Mass Transfer Kinetics in Adsorbents. AIChE J. 1996, 42(3).
(33) Pfeifer, H., Surface Phenomena Investigated By Nuclear Magnetic Resonance. Phys. Rep. (Phys. Lett. Sect. C) 1976, 26 (7), 293. (34) Poyelle, F.; Guilleminot, J.-J.; Meunier, F. Analytical Study of a Gas Fired Adsorptive Air Conditioning System. ASHRAE Trans. 1996, 102, Pt 1. (35) Patent SNEA-LCL, WO 96/12762, 1996. (36) Dubinin, M. M.; Bering, B. P.; Serpinskii, V. V. J. Colloid Interface Sci. 1966, 21, 378.
Received for review March 31, 1998 Revised manuscript received September 2, 1998 Accepted September 3, 1998 IE9802008
