Ind. Eng. Chem. Res. 1988,27, 310-316
310
study program with Arizona State University and International Business Machines Corp. The assistance of TaChing Wang, project associate in the Biomass Indirect Liquefaction Project, is gratefully acknowledged. Registry NO.Hz, 1333-74-0; CO, 630-08-0; COZ, 12438-9; CH4, 74-82-8; CzH4, 74-85-1; CzHs, 74-84-0; cellulose, 9004-34-6.
Literature Cited Antal, M. J.; Edwards, W. E.; Friedman, H. L.; Rogers, F. E. “A Study of the Steam Gasification of Organic Wastes”. Final Progress Report to US. Environmental Protection Agency, 1979; Princeton University, Princeton, NJ. Desrosiers, R. In -Biomass Gasification Principles and Technology”; Reed, T., Ed.; Noyes Data: Park Ridge, NJ, 1981. Graboski, M.; Bain, R. In “Biomass Gasification Principles and Technology”, Reed, T., Ed.; Noyes Data Park Ridge, NJ, 1981. Hillstrom, K. E. “Nonlinear Optimization Routines in AMDLIB”; Argonne National Laboratory: Chicago, 1976. Hunter, M. G. Masters Thesis, Arizona State University, Tempe, 1980. Kuester, J. L. “Conversion of Cellulosic Wastes to Liquid Fuels”. Interim Report to Waste Products Utilization Branch, Industrial Programs Division, DOE Contract DE-AC02-76CS40202, 1982; Arizona State University, Tempe. Kuester, J. L. “Thermal Systems for Conversion of Municipal Solid Waste, Volume 5, Pyrolytic Conversion: A Technology Status
Report”; Argonne National Laboratory: Chicago, IL, 1983. Kuester, J. L. “Conversion of Cellulosic Wastes to Liquid Hydrocarbon Fuels”. Interim Report to Waste Products Utilization Branch, Industrial Programs Division, DOE Contract DE-ACOZ76CS40202, 1984; Arizona State University, Tempe. Kuester, J. L.; Mize, J. H. “Optimization Techniques with FORTRAN”; McGraw-Hill: New York, 1973. Rensfelt, E.; Blomkvist, G.; Ekstrom, C.; Engstrom, S.; Espenas, B. G.; Liinanki, L. In “Energy from Biomass and Wastes”; White, J. W., Ed.; Institute of Gas Technology: Chicago, 1978. Sabin, E. W. Masters Thesis, Arizona State University, Tempe, 1979. Scott, L. C. Masters Thesis, Arizona State University, Tempe, 1982. Shariat, A. R. Masters Thesis, Arizona State University, Tempe, 1984. Smith, W. R.; Missen, R. W. “Chemical Reaction Equilibrium Analysis-Theory and Algorithms”; Wiley: New York, 1982. Walawender, W. P.; Raman, K. P.; Fan, L. T. Proceedings of BioEnergy 1980 World Congress and Exposition, Washington, DC, 1980. Walawender, W. P.; Eriksson, M. A.; Neogi, D.; Singh, S. K.; Fan, F. T. Paper presented at the AIChE annual meeting, Chicago, 1985a. Walawender, W. P.; Hoveland, D. A.; Fan, L. T. Ind. Eng. Chem. Process Des. Deu. 1985b,24, 813-817. Received for review June 4, 1986 Revised manuscript received June 12, 1987 Accepted September 22, 1987
Predictive Model and Experimental Results for a Two-Adsorber Solid Adsorption Heat Pump Nejib Douss, Francis
E. Meunier,* and Lian-Ming Sun
Laboratoire de Thermodynamique des Fluides B a t 5 0 2 ter (UA CNRS-Paris 91405 Orsay, Cedex, France
VI 874),Campus Uniuersitaire,
A predictive model for a two-adsorber adsorption cycle is presented. This simple lumped parameter model assumes that each component (adsorbers, evaporator, and condenser) is homogeneous. Experiments have been performed, with a zeolite NaX-water pair, to test t h a t model. An experimental heating coefficient of performance (COA) equal t o 1.56 is obtained for the two-adsorber cycle when the COA reaches only 1.38 for the intermittent cycle: these results are in close agreement with a model taking into account the thermal losses of the reactor. Moreover, a good qualitative agreement between the model and the experiment is observed for the dynamics of the cycle. A parametric study shows the importance of the design of the various components: for example, if the evaporator is undersized, the temperature of evaporation for the refrigerant fluid is much lower than the temperature of the evaporating load, which decreases the performance of the cycle. This model may be adapted t o other pairs than the zeolite-water pair studied here and will be extended t o the heat management with peaks in the demand.
I. Background Several processes in heat management using discontinuous processes have been extensively studied during the last years, namely, heat storage (Bjurstrom and Carlsson, 1985) and sorption heat pumps [SAHP, solid adsorption (Alefeld et al., 1981; Ismail et al., 1984); MHHP, metal hydride (Bjurstrom et al., 1986; Dantzer and Orgaz, 1987; Supper et al., 1985); CHP, chemical (Bodiot and Spinner, 1985)l.
All these processes have the common property of being discontinuous in contrast with liquid absorption heat pumps. Very few studies exist of the heat integration in discontinuous processes (Vasenelak et al., 1986), especially *Present address: LIMSI-CNRS, BP 30,91406 Onay, Cedex, France.
when the process requires heating and cooling at the same time. In this paper we address that problem in the case of an adsorption heat pump: the heat integration is obtained through heat exchange between two adsorbers out of phase so as to minimize the heat needed from the external heat sources. The remainder of this paper is concerned with the presentation of a predictive model-and its matching to experiments-for a two-adsorber solid adsorption heat pump (SAHP).It represents the first step in a work whose final scope will be to build a numerical code in order (1) to design the various components of the heat pump and obtain the highest compatible performance with the constraints of the demand, (2) to assign the adsorbers for heat exchange to minimize the energy supply, and (3) to identify an eventual failing component in a working heat pump. As the operation of SAHP’s depends on a large number of parameters, several directions are possible in a model 0 1988 American Chemical Society
Ind. Eng. Chem. Res., Vol. 27, No. 2, 1988 311
4/
7
"I i Q
HEATING b
m
C
A'
/'
_I _
COOLING I
I
I
I
:I
I
r4stI Q con1,ng reserv0,r
-p-
CONDENSER
rl BOILER
ADSORBER
EVAPORATOR
HEAT TRANSFER FLUID LINES
VhTLR-OL HAT-EXCHUOER
PDSORSFW
____
Figure 2. Schematic of the two-adsorber unit.
sorption heat pump connected to outside heat sources of finite capacity. The pair used all along this paper will be zeolite-water (water being the refrigerant fluid); let us recall that an advantage of SAHP is that no moving parts exist in the refrigerating circuit.
- - - - REFRIGERANT LINE
-
EvQpDrQtOr
EVmAlm
REFRIGERANT LINE
- HEAT TRANSFER FLUID LINES Figure 1. Single adsorber cycle. (a, top) In a Clapeyron diagram. (b, middle) Schematic of the SAHP in sequence 1 (heating of the adsorber, condensation). Valve 1 closed, valve 2 open. (c, bottom) Schematic of the SAHP in sequence 2 (cooling of the adsorber, evaporation). Valve 1 open, valve 2 closed.
that aims to optimization and control such processes. (1) The first direction is the use of "black box" techniques in which the details of heat and mass transfer inside the system are ignored. In that case, adaptive control strategies (Seborg et al., 1986) provide a promising approach for poorly understood processes. (2) The second direction is the use of "white box" techniques based on a detailed and predictive model of the process. Such techniques can be used only if the process is completely understood (kinetics as well as heat and mass transfer). (3) The third direction is the use of "gray box" techniques based on a simplified model for the process and using usual identification methods for the parts of the process which are not described by a detailed model. Such an approach has been proposed by Filippi et al. (1986) for optimization and control of semibatch adsorbers when the detailed understanding of the chemical kinetics is not a t hand. This paper is concerned with a white box approach, and we propose a numerical code to describe as precisely as possible the operation of a two-adsorber adsorption heat pump connected to outside heat sources of finite capacity. Karagiorgas and Meunier (1987) have used that approach to describe the operation of a single adsorber ad-
11. Description of a Two-Adsorber Zeolite-Water Adsorption Cycle
Single Adsorber Cycle (Figure 1). To simplify our presentation, let us consider first the case of a single adsorber (or intermittent) cycle. The SAHP consists of an adsorber filled with zeolite connected to an evaporator and a condenser (the working fluid is water). Two valves can open or close the connections between the adsorber and the condenser or evaporator. A glass receiver is used to measure the amount of condensed water. The three components are connected (via heat transfer fluids: oil or water) to the four external heat sources as follows: heating phase (Figure lb), adsorber to boiler and condenser to intermediate temperature heat sink; cooling phase (Figure IC),adsorber to water-oil heat exchanger (WOHE)and evaporator to low-temperature heat source. In a Clapeyron diagram (log P, - l / T ) , the single adsorber cycle is represented as follows (Figure la): Heating Phase (abc). The adsorber is heated from Ta* to Tma.When the pressure in the adsorber reaches the condensing pressure, condensation starts. The heat input during this step is Qah (Figure l a ) while the heat output a t the condenser is Q,. Cooling Phase (cda). The adsorber is cooled from Tto Tad. When the pressure in the evaporator reaches the evaporating pressure, evaporation starts. The heat input during this phase a t the evaporator is Q,,, while the heat output at the intermediate heat exchanger is Qcda. The coefficients of performance of this single adsorber cycle are defined as follows: COP = Qev/Qabcis the efficiency of the cooling effect; COA = (Q, + Qcda)/Qah is the efficiency of the heating effect. Two-Adsorber Cycle (Figure 2). To operate a twoadsorber cycle, two adsorbers are needed; one adsorber is connected to the condenser, while the other is connected to the evaporator (Figure 2). A two-adsorber cycle is not simply the sum of two single adsorber cycles out of phase (Figure 4a) since two heat recovery phases (corresponding to the first and third sequences; Figure 4b) are introduced in the cycle. The four components of the SAHP (adsorber, desorber, evaporator, and condenser) are interconnected (for mass transfer) via the working fluid (water) and are coupled to the four external heat sources via the heat-transfer fluids (oil or water); during the four sequences of the cycle, the evaporator and the condenser are always connected to the
312 Ind. Eng. Chem. Res., Vol. 27, No. 2, 1988 Table I. Connections of the Adsorbers during the Four Seauences of a Cvcle' working fluid thermal connections connections sequence phase adsb 1-adsb 2 adsb 1-condenser 1 heat recov. adsb 2-evaporator adsb 1-condenser 2 heating/cooling adsb 1-boiler adsb 2-WOHE adsb 2-evaporator adsb 1-adsb 2 adsb 1-evaporator 3 heat recov. adsb 2-condenser 4 heating/cooling adsb 1-WOHE adsb 1-evaporator adsb 2-condenser adsb 2-boiler
0 Path i n the diagram
Of f i g
3
c
a
e:
d
b
el
0
"Adsb = adsorber.
Figure 4. Cycle sequence chart for two-adsorber heat pump systems. (a) Two-adsorber cycle without internal heat recovery. (b) Two-adsorber cycle with internal heat recovery. AOSORBER i
AOSORBER 1 AOSORBER 2
K02 2937
ADSORBER 2
Tad5
c
Adsorber2
Y"
" ' 3
Ts
Figure 3. Two-adsorber cycle in a Clapeyron diagram: (-) ber 1, (-) adsorber 2.
adsorQev2
same heat source (low-temperature heat source and intermediate-temperature heat sink), while the adsorbers may be connected either to the boiler or to the water-oil heat exchanger (WOHE) or between each other. The connections of the adsorbers, during the four sequences of a cycle (Figure 4) are summarized in Table I. A two-adsorber cycle may be represented in a Clapeyron diagram (Figure 3). The thermodynamic path of the sequences is represented as (abel, cdeJ heat recovery, (elc) external heating, and (e2a)external cooling. The heat recovery steps are very important since they are responsible for the enhancement of the efficiencies. Meunier (1985) has shown that using an infinite number of adsorbers with ideal heat recovery between adsorbers, it was possible-with the given conditions of operating temperatures-to get a cooling COP much higher than 1 (1.85) equal to 68% of the ideal Carnot COP corresponding to the operating temperatures. In contrast with that proposed heat management, a two-adsorber cycle without heat recovery (Figure 4a) has the same efficiency as an intermittent cycle. Heat Balances. First Sequence (Internal Heat Recovery). Adsorber 1 is heated from Tadsto Tel,while adsorber 2 is cooled from T,, to Te2(Figures 3 and 4). The temperature difference AT = Te2- Tel is the temperature drop necessary for the heat transfer to take place. The heat input Q1 to adsorber 1 is the sum of two terms: KO,(coming from the boiler) and K2 provided by adsorber 2. We have Q1 = KO,+ K2 (Figure 5 ) . Second Sequence (External Heating and Cooling). Adsorber 1is heated by the external heat source until T,, (Figure 3) is reached, while a t the same time adsorber 2 is cooled to Tadsby the external intermediate heat exchanger. The heat input to adsorber 1is Q'l, while the heat output of adsorber 2 is Kr2. The third and fourth sequences are respectively similar to the first and second ones. But this time adsorber 2 requires heating, while adsorber 1 needs cooling. The heat exchanged is as follows: In the third sequence, the heat input to adsorber 2 (Q2) is divided into two parts: the contribution of the boiler (Kol)and of adsorber 1 ( K J .
!hPJi
EVAPORATOR
CONDENSER
GJ'PUT
HEAT
rwo
HEAT
ADSORBER C Y C L E
Figure 5. Heat flowing out of and into the two-adsorber SAHP during a cycle.
In the fourth step, the heat input to adsorber 2 is Q2, while the heat output of adsorber 1 is K;. The heat of evaporation is Qevl for adsorber 1 and Qev2 for adsorber 2, while the heat of condensation is Qcl for adsorber 1 and Qcz for adsorber 2. The efficiencies of the two-adsorber cycle are (Figure 5 ) Qevi + Qev2 COP = Q'i + Q'z + Koi + Koz as the cooling efficiency and Qci + Qc2 + K'I + K'2 COA = Q'i + Q'2 + Koi + KO, as the heating efficiency. Kol and KO,appear in the denominator since they are supplied by the boiler. This point is an artifact of the experimental setup; it could be easily avoided by using another experimental configuration.
111. The Model 111.1. Assumptions. To get a simplified numerical simulation, the following realistic assumptions are made: (1)Each component (adsorbers, evaporator, and condenser) is homogeneous. This assumption leads to a set of ordinary differential equations. (2) Thermodynamical equilibrium exists in each component. Assumption 2 has been checked experimentally for the adsorbers since Karagiorgas and Meunier (1986) have shown that for heat rates less than 750 W/kg of zeolitewhich is the case in our experiment except a t the very beginning of the recovery phase-equilibrium is attained. 111.2. Interaction between the Heat Pump and the Four Outside Heat Sources. Three kinds of heat exchange between the unit and the heat sources are used; they lead to three distinct ODE'S.
Ind. Eng. Chem. Res., Vol. 27, No. 2, 1988 313 I
where
Ah 'Ttl A 1
I
Bi = cp,+ 2, + e,Cpe
condenser: [Mz, d ~ / d t ] L ( T c )= zc dTc/dt
(i = 1,2)
+ EcmecCpe(Tc - Tee) (3)
u
r r H Boiler
Adsorber
4,
'Tb
Reservoir b ' ' b'
Adsorber I
cooler of the condenser: EcmecCpe(Tc - Tee) = McCpe dTec/dt
hh , T h
U,A,(Th - Toj) + Mrcph dTh/dt = E1mhrcph(Tz1 -
+ AH de,/dt) (6)
evaporator: (Mz1 dt,/dt)[L(Tev) - Cpe(Tc - Tev)l + z e v dTev/dt = EevmevCpe(Toi - Tev) (7) The state equation for the adsorbent-adsorbate equilibrium during condensation is (Rios, 1985) (8) log (Pc(Tc))= ak2) + b ( e 2 ) / T z 2
Adsurber
,-Evaporator
I
Figure 7. Couplings with temperature constraints. (a, top) Indirect coupling. (b, bottom) Direct coupling.
Indirect Coupling with Power Constraint (Figure 6a): Ci(T,, - Tiu) = Q i r - MiCpi dT,,/dt The heat conductance Ci between the ith heat source (ir) and the ith component of the heat pump (iu) depends on the mass flow rate mi of the heating fluid and on the effectiveness of the heat exchanger Ei: Ei = 1 - exp(-UiAi/miCpi) = exp(-N,,) Ci= m.C .E. I pl 1
Indirect Coupling with Temperature Constraint (Figure 7a): Qi = UiAi(TiU- Toi) where Toi = constant inlet temperature of water and T,, = temperature of adsorber i. Direct Coupling with Temperature Constraint (Figure 7b): Q i = C;(Toi - Tiu) 111.3. Governing Equations. The equations will be distinct depending on the sequences. During the Nonrecovery Sequences. The heat balances on the various components are as follows: boiler (Figure 6a): Qb dt = hfbCph dTh + ?hhbCph&(Th - Tz2) dt (1) adsorber 2: E&hbCph(Th - Tz2) = Mz2(B2 dTz2/dt + A H dtz/dt) (2)
+ b(el)/Tzl
(9)
~(€1)
where a(€,)and b(t,) are polynomials of third degree a(€,)= a. + ale, + a2e; + a3t3
b(e,) = bo l
Th)
(5) adsorber 1: ElmhrCph(Tz1 - T h ) = Mzl(B1 dTz,/dt
and during evaporation is log ( P e v ( T e v ) ) =
e
(4)
cooling exchanger (WOHE) (Figure 7a):
E?b Adsorberl
Figure 6. Coupling of the reservoir with the adsorbers. (a, top) Indirect coupling with power constraint. (b, bottom) Heat recovery step.
+ Qc
+ bit, + b2tZ2+ b3t3
During the Heat Recovery Step. The global heat balance (Figure 6b) is MbCph dTb + M,i(Bi dT,i + AH del) + Mz2(B2dT,2 + AH dt2) = 0 (10) The heat balance for adsorber 2 is M ~ 2 @ 2dTz2 + AH de2) = E2bmhbCph(Tb- T22) dt
(11)
The heat balance for adsorber 1 is Mb/mhb dTb/dt = &bTzi
E2b(l
- E1b)Tz2-
+ E2b(l
- E l b ) ) T b (12)
with E,b
= 1- exp(-U,A,/ri2.hbCph)
(i = 192)
Numerical Simulation. The above 1 2 equations (eq 1-12) can't be solved analytically, and a numerical solution technique should be used. This system may be arranged to the form r', = f(t,r,) i = 1,2,...,12 Implicit differencing gives r , n + l = rp + Atf(tn+W,r,n+1/2) where At is the time step, n is the time discrete index, tn+1/2 = l / 2 ( t n tn+l),and I'zn+1/2 = 1/2(rLn + r;+l). This is a set of nonlinear equations that has to be solved iteratively at each step. Herein, we make use of the Newton-Raphson method to find roots of nonlinear equations (r;+l). Owing to stiffness of the above-obtained set of ODE'S, stability of the numerical solution is difficult to be guaranteed even if one takes a relatively small time step, At. Consequently, numerical results are qualitative, but not strictly quantitative, and discrepancies between experiments and model may be due to that point.
+
314
Ind. Eng. Chem. Res., Vol. 27, No. 2, 1988
Table 11. Physical Parameters Used for t h e Computations zeolite NaX-H20 boiler adsorber 1 adsorber 2
= 0.41 kg/s UIA, = 360 UzAz = 360 a. = 8.9 /"C w /"C Mb = 40 kg M,, = 27.5 M,, = 23.5 -ai = 9.54 kg kg x 10-4 21 = 54380 Zz = 50000 = 4.52 X J/"C 10-7 J/"C a, = -4.48 x 10-11 khb
w
b, = 3400 bl = 0.55344
b2 = -1.69
lo4
condenser evaporator reservoir UkA, = 1300 U&, = 200 m h r = 0.28 kg/s W/"C W/OC niw= 0.47 niev= 0.43 M,= 20 kg kg/s kg/s 2, = 2500 Z, = 9352 J/"C J/"C
b, = 1.66 X
Table 111. Heat a n d Mass Balance for Single-Adsorber and Two-Adsorber Cycles single adsorber two adsorbers exut theorv exDt theorv 21 160 f 1050 23200 32496 i 1650 31060 adsorber input, kJ adsorber 18592 f 950 20 900 29 220 i 1450 26 000 output, kJ 21870 f 800 22720 evaporation, 11099 f 400 11360 kJ 21 558 f 800 22380 10730 f 400 11190 condensation, kJ 0.524 0.49 0.673 0.73 COP 1.386 1.38 1.56 1.56 COA 2.88 2.88 COPC 3.88 3.88 COAc
IV. Experimental Results: Comparison with the Model IV.l. Heat and Mass Balances. In order to make full use of the model, we have determined the values of physical parameters appearing in the equations (Table 11). Experiments of two-adsorber and single-adsorber cycles have been performed with the following initial conditions: for adsorber 1, Tz,,o= Tads= 60 OC, = 26 mbar; for adsorber 2, T,,, = T,, = 200 "C, P2,0= 80 mbar. Typical experimental and theoretical results of heat and mass balances are presented in Table I11 and Figure 5. In Table I11 the adsorber input heat, for the two-adsorber cycle, is the sum of the heat coming directly and indirectly from the boiler. These experimental results show that a two-adsorber cycle gives a 12% increase of the COP and a 28% increase of the COA. This improvement proves to be the great advantage of the heat recovery stage. The performances of the two cycles studied in this paper may be compared to the ideal Carnot efficiencies (COPc and COAc in Table 111) and to other pairs: the cooling efficiencies of the single-adsorber and two-adsorber cycles represent respectively 18% and 23% of the ideal Carnot efficiency; the heating efficiencies represent respectively 35% and 40% of the Carnot efficiency; these performances are good when compared to other pairs; the cooling efficiency of the LiBr-water pair ranges from 0.6 to 0.7, while for the water-ammonia pair it ranges from 0.4 to 0.5. From Table 111, it can be noted that the experimental COA is less than 1 + COP, which can be easily explained by the losses on the adsorbers: as the heating phase of the adsorber is shorter than the cooling phase, the COA is affected much more by the losses than is the COP. Influence of the Heat Losses of the Adsorbers on the Efficiencies. Taking into account that the cooling phase is twice as long as the heating phase, we assume that the heat losses on the adsorbers during the cooling phase are 2 times the heat losses during the heat phase, we then have Cophi = Q d Q 2 + 1/3Qh1)-~ COAhi = (Q, + K1 - 2/3QhJ(Q2
X
constants C,, = 836 J/(kg "C) C,, = 4180 J/k"C) C, = 2000 J/(kg "C)
+ 1/3Qhi)-'
Table IV. Influence of t h e Heat Losses on t h e Thermodynamic Performances of Cycles intermittent two-adsorber cycle cycle losses COP1 COAl COP2 COA2 model no 0.49 1.49 0.73 1.83 0.48 1.38 0.71 1.55 model Qhl = 2120 kJ expt 0.52 1.38 0.67 1.57 Log P mbar
I b ' C
t
/
4
A,
i 'UA Figure 8. Two-adsorber cycle in a (log P, 2') diagram: iment, (-) modelization. ? 2 1;
(-e)
exper-
TzoC
3
Figure 9. Histories of the zeolite temperature in the ith adsorber: experiment, (-) modelization. (-a)
where Qhl represents the global (heating and cooling phases) heat losses on the adsorber. As presented in Table IV, the heat losses have much more influence on the two-adsorber cycle than on the intermittent cycle. IV.2. The Dynamics of a Cycle. The experimental results are compared to calculations in Figures 8-11. A very good qualitative agreement between the model and the experience is observed; nevertheless, differences have to be noted. The qualitative agreement is excellent for the history of the temperature of zeolite except around the recovery step: thermal shock does exist that the model does not
Ind. Eng. Chem. Res., Vol. 27, No. 2, 1988 315 Q
5 o1
L o g P mbar
kW
I
.
ADSORBER 1 :HEATING EVAPORATOR
3 0-
0
VADSORBER 1
COOLING
mADSORBER 2
HEATING
CONDENSER
C '
U 5 A 5 = 4000 W
T, 1
,
I
,
I
I
,
I
I
I
I
,
l
,
l
I
=
400
I
i
OC
I
I
.
the various components. Q
(
