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Modelling and experimental investigation of a new type of thermochemical transformer based on the coupling of two solid-gas reactions
125
Chemical Engineering and Processing, 33 (1994) 125-134
Modelling and experimental investigation of a new type of thermochemical transformer based on the coupling of two solid-gas reactions E. Lepinasse, V. Goetz and G. Crozat CNRS, Institut de Science et Ginnie des Mat&au 66860 Perpignan-Ckdex (France)
et Prockdis, U.P. 8521 CNRS, UniversitC de Perpignan, 52 Avenue de Villeneuve.
(Received March 22, 1993; in final form December 1, 1993)
Abstract The feasibility of a thermochemical transformer based on the coupling of two solid-gas reactions has been demonstrated by a 1 kW experimental laboratory plant. A model has been built taking into account the dynamic coupling of the two reactors by the gaseous phase, and the consumption of the reactive medium in each reactor. The model has been validated by experimental results and is capable of simulating the running mode of the process for a series of working cycles.
Illtroduction Reversible solid-gas reactions are well suited to processes such as thermochemical transformers and storage systems. The large number of solid-gas couples that can be used makes it possible to produce energy over a wide range of temperatures (243-573 K) [ 11, thereby ensuring extensive use of such processes.
Monovariant reversible reactions occur in fixed bed reactors upon which non-equilibrium conditions are imposed by the double constraint of temperature and pressure. The basic process simply consists of a solidgas reactor coupled to an evaporator-condenser [Fig. l(a)]. The operating cycle of this trithermal process is illustrated in the Clapeyron diagram of Fig. l(b). This operates in two successive phases and is able to produce cold at a low temperature T, and heat at a medium temperature T,. The working modes of the evaporator and condenser are well known and detailed in the literature. Numerous studies regarding the running modes and the optimization of solid-gas reactors used for energy production are currently in progress [2-51. The solid reactant consumption model takes into account the coupling between the reaction dynamics on one hand and heat and mass transfer in the reactive medium on the other. The working modes of the basic process have been simulated [ 6,7], making it possible to size and design a 25 kW prototype for refrigeration [8]. Nevertheless, this kind of machine has a low coefficient of performance (COP) in refrigeration relative to compression systems. Indeed, taking into account only the
0255.2701/94/$7.00 SSDI 0255-2701(94)00512-G
(a)
Fixedbed solid/gas reactor
EV.XporatO~/CoIldUlS~
-l/r Fig. 1. (a) Basic scheme of a chemical heat pump. (b) The two successive
phases
of a chemical
heap pump cycle.
enthalpies of reaction and evaporation (and condensation), the ideal COP has an order of magnitude of 0.5. The large number of solid-gas couples that may be used (Fig. 2) make it possible to devise a new kind of machine working with two solid-gas reactions [9, lo]. This new process runs in the same way as the basic machine, but the liquid-gas equilibrium (Fig. 1) is replaced by a second solid-gas equilibrium. This modification suppresses the liquid phase and hence the process works independently of its position in space, which is very useful for a mobile piece of equipment. Furthermore, this modification improves the energy performance of the process. Taking into account the
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126 T(T) -38 Ln(P(bao)
-23
60
la7
?
3
.i
4 -WOO/T(K
Fig. 2. Equilibrium lines for the reactions of some chlorides 2. CaCl,(8/4); 3. SrCl,(S/l); 4. with ammonia. 1. BaCl,(S/O); 7. ZnCl,(4.2); 8. CaCl,(4/2); 5. ZnCl,(6/4); 6. MnCI,(6/2); 11. MnC1,(2/1). FeC1,(6/2); 9. MgC1,(6/2); 10. NiCl,(6/2);
thermal masses of the reactants [ 111, COPS which are related to the refrigeration temperature, power output and the salts used, have been estimated between 0.4 and 0.75. Nevertheless, designing and sizing these machines involve new problems. Indeed, for the basic system, it may be considered (as has verified experimentally) that the evaporator (or condenser) fixes the pressure level in the solid-gas reactor, with liquid-vapour equilibrium occurring instantaneously in comparison with the solid-gas reaction. The progress of the process is then directly linked to the rate of transformation of the solid reactant which is the limiting step. The positions of working points for the process in the Clapeyron diagram are well known [Fig. l(b)], i.e. pressure levels during successive phases, constraint temperatures imposed on the reactor. For the process involving two solid-gas equilibria, the working pressure is linked to the coupling of the two solid-gas reactors. For example, if the overall absorption rate of one salt is faster than the overall rate of desorption of the other, the working pressure of the process will decrease until the two rates are equal. The power produced depends directly on the coupling between the overall rates of the two reactive beds. The overall term includes the reaction dynamics of the salts and the heat and mass transfer in the reactive medium. Thus, it becomes apparent that an understanding, analysis and modelling of the coupling of two solid-gas reactors by the gaseous phase are fundamental to the management of these processes. In this article, the feasibility of a process involving two solid-gas reactors is demonstrated by means of a
l-2 kW experimental laboratory refrigeration plant. An adapted dynamic model of the process, which takes into account the dynamic coupling of the two reactors by the gaseous phase, has been built. An analysis of the real limitations imposed by heat and mass transfer occurring in the reactive medium (related to the reactor design) makes it possible to develop the best suited model. The model has been validated by comparison with experimental results and makes it possible to simulate the thermodynamic path [P(t), r(t)] of the working point of the process in the Clapeyron diagram. The aim of this study was to develop a model capable of dimensioning this new kind of thermochemical transformer, verifying its performance and controlling its operation.
Model@
the process
The solid -gas
reactors
The reactive medium used consisted of an inert graphite binder and a reactive salt [ 121. Analysis and modelling of the reaction rate of the medium require an adequate knowledge of the main phenomena that limit the reaction process. These may be of three types: (i) limitation by mass transfer; (ii) limitation by heat transfer; and (iii) limitation by chemical kinetics. Two characteristic dimensions may be defined in the medium: the grain level, i.e. the basic particle at which reaction occurs, and the porous solid matrix which is composed of a combination of the reactive particles and the inert graphite. In order to take the texture into account, the study and characterization of the reactive medium was carried out in two successive stages. Reaction
rate of the salt
Experimental measurements were made with a microcalorimeter (Setaram DSC 111). In the microcalorimetric method, the samples consisted of a few milligrams of the salts thus avoiding limitations arising from.mass or heat transfer in the macropores between the grains. In this way, all the grains of the reactive salts were subjected to the same pressure and temperature constraints. The transformation rate of the salt grains was determined as a function of the pressure and temperature conditions imposed [ 131. Experimental results obtained over a wide range of temperatures and pressures allowed the model of grain consumption of the sharp interface type [14] to be validated. The consumption of each grain takes place on a sharp interface separating the products and reactants; the reaction rate is the result of coupling between mass transfer (from the grain surface to the interface) and chemical reaction at the interface. Table 1 presents the main equations for the model which are detailed in ref. 14. The pressure Pi
127
TABLE
1. Equations
describing
the consumption
of a reactive
grain
Absorption
Desorption
A+nG-+B
B-+A+nG
Mass transfer Chemical kinetics Variation in grain size
Degree of transformation
at the interface was calculated by equating the molar fluxes of the transport term and the kinetic term. The model also takes into account the variations in grain size due to the large differences between the product and reactant volumes. Heat and mass transfer in the reactive medium The physical values relating to heat and mass transfer are the thermal conductivity of the bed, the heat exchange coefficient at the wall of the reactor and the permeability. The lamellar structure of graphite ensures good dispersion of the salt, thus avoiding the grain packing and giving a high permeability in the macropores of the mixture. Depending on the percentage of graphite and the density of the mixture, the permeability varies from a few Darcy to several tens of Darcy [ 151. Thus, it may be assumed that mass transfer in the macropores of the medium is not a limiting factor in the transformation of the reactive bed. The two solids which compose the reactive mixture are mixed together physically and then compressed inside the reactor. At high densities, an anisotropic mixture is obtained which is highly conductive perpendicular to the direction of compression, but less conductive parallel to the direction of compression [ 161. The high conductivity is primarily due to the graphite matrix and to the re-orientation of the graphite layer during compression. Depending on the percentage of graphite and the density of the mixture, the values obtained range between 2 and 15 W m-’ K-‘. In the highly conductive direction and for a bed a few centimetres in diameter, the latter may be assumed to be uniform in temperature. Simulated temperature profiles in a cylindrical reactor 2 cm in diameter, taking into account the coupling between grain consumption and conductive heat transfer in the bed, are presented in the Appendix. The results confirm the assumption of a uniform bed temperature for conductivity values up
to 5 W m-’ K-‘. Obviously, for very thick beds this assumption is no longer valid. If the heat-transfer fluid of the solid-gas reactor flows through the exchanger in a turbulent manner, the main limiting factor for heat transfer between the fluid and the reactive bed is the contact resistance between the reactor wall and the reactive medium. Indeed, the heat contact resistance between a porous solid and a reactor wall is generally high. A global heat exchange coefficient UP may be defined which includes the saltreactor contact resistance and the reactor-fluid heattransfer coefficient. It is considered that the temperature of the reactor wall is equal to the fluid temperature. The thermal heat capacity of the medium may be calculated by adding together the thermal heat capacities of the solid components, i.e. salt and graphite. Basic equations for the model of the reactors The system of equations is similar for the two type of reactors, with an opposite sign for the consumption or the production of heat (by the reaction) for a reactor in desorption or absorption. According to the physical properties of the medium, the development of the process may be described via the following thermal balances. For the thermal fluid: d T,,, MC Cpcdt = ~&xc~(Tsa,r - Tt,,t) + hambL,,
Varnb - Tfw)
+ 2h C,,,,
- Ttws)
(1)
where: MC CPC = ~4 C,,,, + M C,,,, For the salt:
(2)
128
TABLE 2. Characteristics of the reactors and the reactive mixtures Characteristics
BaCI,
Mn Cl2
Reactive Medium
volume of mixture density % graphite (by mass) mass of anhydrous salt mass of graphite mol of salt porosity of anhydrous mixture
6.45 x 10m3m3 507 kg mm3 35% 2.125 kg 1.145 kg 10.2 0.77
8 x 10-3m3 495 kg mm3 35% 2.570 kg 1.385 kg 20.4 0.75
Reactor
number of tubes diameter of tubes exchanger surface area diameter of casing number of baffles mass of heat exchanger total mass of reactor volume of thermal fluid
19 30.5-33.7 mm 0.95 m* 200-206 mm 4 12kg 20 kg 7.8 x 10m3m3
19 30.5-33.7 mm 1.20 m2 200-206 mm 5 15kg 23 kg 9 x 1O-3 m3
In these equations, the heat-transfer fluid which circulates in the exchangers is assumed to be at a uniform temperature which is equal to the mean outlet temperatures. Coupling
of the inlet and
the two reactors
dn, _ dndes habs _~_~ dt
Simultaneous solution of eqns. (1) -( 6) using expressions representative of the grain consumption (Table 1) may be carried out by an explicit method. This allows the process to be quickly simulated and enables the evolution of all of the characteristic variables of each reactor (Tthf, T,,,,, PB, X) to be followed as a function of time.
Reactive
laboratory
plant
mixtures
The salts selected for this demonstration were BaCI, (barium chloride) and MnCl, (manganese chloride),
may be expressed as:
Cl2 + 8AHB,,,2
+ 4NH, s Mn( NH&C&
+ 4AHMnc,*
The reactive mixtures, whose densities were 500 kg mm3 consisted of 35% graphite. The radial conductivity of such mixtures, which is independent of the salt employed, was 8 W m-’ K-’ [ 161. Reactors
The reactors were of the catalytic type (see Fig. 3). Each reactive mixture was enclosed in several stainless steel pipes of 3 cm in diameter, set in a casing with baffles through which the thermal fluid flows (in turbulent flow). The physical characteristics of each reactor are listed in Table 2. Measuring
dt
(6)
Experimental
BaCl, + 8NH, % Ba(NH,), Mn( NH,),Cl,
As the working mode of each reactor is known, modelling the whole process consists in coupling the two reactors via the gaseous phase. This is achieved by using heat and mass balances. Equations describing the coupling of the two reactors, one of which is in an absorption mode and the other in desorption, allow the number of moles of gas in the free volume of the system, and its temperature and pressure to be calculated. The assumptions made are: (i) ammonia is a perfect gas; and (ii) gas is desorbed at the temperature of the salt. On this basis the system of equations is: dt
whose reactions with ammonia
equipment
The two reactors (one containing BaCl,, and the other MnCI,) are connected by means of a tube fitted with a mass-flow meter, allowing the progress of the reactions to be measured. Each reactor is equipped for the measurement of the following working variables: (i) temperatures inside the reactive bed; (ii) pressure in the reactor; (iii) flow rate of the thermal fluid; and (iv) inlet and outlet temperatures of the thermal fluid. Global thermal &id-reactive coeficien t UP
bed heat exchange
From the experimental measurements, i.e. temperature of the fluid and of the reactive bed, instantaneous rates of reaction from the mass flow measurement of ammonia, the UP coefficients of each reactor may be directly calculated at each time step from the equation: nNH3 AH up = &xc,,(Tr,,f - T,,,)
(7)
129
two solid-gas reactors (one in absorption and the other in desorption) connected via a gaseous phase. The heat source and heat sink were not designed for automatic cycling operations. Each phase of the process was started manually, with a time lag between them. To obtain the required initial state in each solid-gas reactors, the two reactors were isolated from one another before starting each phase; the desired temperature constraints were then imposed and the experimental phase started when the salt equilibrium conditions had been reached in the two reactors.
Fig. 1. 2. 3. 4. 5. 6. I. 8. 9. 10. II. 12. 13. 14. 15. 16.
Qualitative description The two reactors were isolated. Constraint temperatures Tc(BaC~l)and TccMncr2)where imposed on the two reactors (Fig. 5). The salts were under equilibrium conditions at the points 1 for BaCl, and 1’ for MnCl, which are the initial states for this phase of the process. The initial conditions were:
3. Experimental laboratory plant. MnCl, reactor BaCI, reactor Gaseous circuit Thermal fluid circuit for MnCI, Thermal fluid circuit for BaCl, Mass flow of ammonia Pressure sensor Temperature sensor for the reactive medium Inlet temperature sensors for the thermal fluid Outlet temperature sensors for the thermal fluid Water/oil heat exchanger Volumetric flow sensor Electric heat resistance Pumps Expansion tank Water/ammonia heat exchanger
Tthr= r, T,,, = r, ZJ = P,pui(T,) x=0.1 I
at t=O
with: TcCBaClzj = 313 K for BaCl, TqMnC12)= 363 K for MnCl, The initial degrees of transformation employed for the reactions were 0.1, since the degrees of transformation for practical cycles lie between 0.1 and 0.9 (i.e. the end of the reaction is very time consuming). The preceding phase corresponds to an absorption for BaCl, and a desorption for MnCl,.
l:I 0.2
0.3
0.4
0.5
0.6
0.7 x
Fig. 4. Experimental values of U, in the two reactors tion of the degree of transformation.
as a func-
flow rate of ammonia where nNH3 is the instantaneous (In01 s-1). The values thus obtained were (Fig. 4) UtiBaCIZI= 160 W m-‘K-’ and UpcMnClt)= 220 W mP2 Km’. Model validation
The objectives of these experiments were: (a) to demonstrate the feasibility of a thermochemical transformer using two solid-gas reactors; and (b) to achieve a sound understanding of the dynamic behaviour of
-0.0034
-0.0032 T C(Bacl2)
-0.ca30
-0.0028
-0.0026 -1m
TC(Mrc12)
Fig. 5. Simulated operating points for one phase of the process in the Clapeyron diagram. Duration and evolution of the degree of transformation of each phase: 1 --t 2: Instantaneous. 2-3: t from 0 to 100s; Xfrom 0.1 to 0.17. 3-4: t from 100 to 1500 s; X from 0.17 to 0.75. 4-+5: from 1500 to 2500 s; X from 0.75 to 0.9. ( q pseudo-equilibrium area of BaCl, and H MnCl, [ 171)).
([13] and
130
At time t = 0, the two reactors were connected via the gaseous phase. The simulated thermodynamic paths of the working points of the two reactors are depicted in Fig. 5. Four different steps may be distinguished during the reactions: 1. Instantaneous equalization of the pressure in the two reactors: path from points 1 to 2 and 1’ to 2’ in the Clapeyron diagram (Fig. 5). 2. An almost adiabatic phase corresponding to the consumption of the avail&e heat in me reactive beds. This entails a decrease in temperature from TccBacln)to a temperature near the equilibrium temperature of the salt for the BaCl, reactor which is in desorption (endothermic reaction). At the same time, the temperature of the MnCl, reactor which is in absorption (exothermic reaction) increases from TccMnClz)to its equilibrium temperature. During this phase, which lasts approximately 2 min, the pressure changes as a function of the reaction rates in the two media. In the example shown in Fig. 5, absorption in the MnCl, reactor is faster than desorption in the BaCl, reactor, which leads to a decrease in the gas pressure. This phase corresponds to the path from 2 to 3 (2’ to 3’) in Fig. 5. 3. During the next phase corresponding to 60% of the overall reaction, the pressure is stabilized at a level which equalizes the rates of absorption and desorption. The working points on the Clapeyron diagram clearly show that the reactive-bed transformations take place at temperatures near the equilibrium values. This indicates significant thermal limiting by heat exchange between the thermal fluids and the reactive beds. This phase corresponds to the path from 3 to 4 (3’ to 4’) in Fig. 5. 4. When reactions are almost over, there is a decrease in the consumption (or production) of heat in the BaCl, (or MnCl,) reactors. The thermal fluxes exchanged with the thermal fluids entail: (a) the temperature in the BaCl, reactor increasing to Tc(BaC,2,;(b) the temperature in the MnCl, reactor decreasing to Tc(MnC,Z).This step of the reaction corresponds to the path from 4 to 5 (4’ to 5’) in Fig. 5. Model validation The simulation
accurately represents the progression of the process for characteristic variables such as the working pressure and the level of power consumed or produced by the reactor [Fig. 6(a,b)]. It also simulates the temperature variations in each reactor during the reaction fairly accurately [Fig. 6(c)]. When no parameters are adjusted for the simulation, the relatively good agreement between the experimental and the simulated values demonstrates the validity of the model used. Simulation
of practical working cycles
Throughout a practical working cycle the two reactors are continuously connected by the gaseous phase.
Power(w) 2500,
Time (s)
(4 Pressure (bar)
1.5 1.0 , . . 0
, , . . . . , . . , . , . . , . , . . . 500
loo0
1500
2occl
2500
Time (s)
(b) T fK)
313 309 305 301 291 500 Cc) O
loo0
1500
UMO Time
2500 (s)
Fig. 6. Simulated (----) and experimental (-) evolution of the principal variables during one phase of the process: (a) power, (b) pressure, and (c) temperature, as a function of time (the continuous dark line in Fig. 6(c) represents the evolution of the temperature inside the reactive bed for each reactor; grey lines represent the evolution of the experimental inlet temperatures of the thermal fluids).
Only by controlling the inlet temperatures of the thermal fluids is the sequence of the different phases obtained. A working cycle is simulated under thermodynamic constraints which allow discontinuous refrigeration at a temperature lower than 283 K. The heat sink used in this example is the ambient environment assumed to be
131
at 298 K. The constraint reactors are as follows: for BaCl,: for MnCl,:
in in in in
absorption, desorption, absorption, desorption,
temperatures
imposed
on the
Power (W) 2500 -
T,.abs(BaClzj= Tamb = 298 K T, des(BaC12j = 283 K T, abs(MnC,z)= Tam,, = 298 K T, deP(MnC,zj = 428 K
i Y
The cycle can be split into two successive phases for refrigeration. Refrigeration: low pressure phase The BaCl, reactor is in desorption. It consumes heat at a temperature below 283 K, the heat being supplied by the thermal Auid at 283 K which works as the refrigerant. At the same time, the MnCl, reactor is in absorption, and the heat produced is dissipated into the environment at 298 K.
i i
I
v 0
Regeneration phase First transition phase - path from 1 to 2 and 1’ to 2 in Fig. 7(a). The MnCl, reactor is now subjected to the the temperature T, des(MnC12). Under these conditions, temperature of the reactor increases and the reactive mixture goes from absorption conditions to desorption conditions. Desorption of MnCl, entails a pressure increase in the gaseous phase of the arrangement. At the same time the BaCI, reactor is subjected to its absorption temperature T, abs(BilC,zj.The pressure increase resulting from the desorption of the reactant MnCl, ensures that the BaCl, reactor goes from desorption conditions to absorption conditions. Chemical regeneration phase - path from 2 to 3 and 2’ to 3’ in Fig. 7(a). The working pressure of the process changes until the transformation rates of the salts in the two reactors become equal. Depending on the design of the two reactors, these transformation rates are determined by the coupling between the heat transfer from the thermal fluid to the reactive mixture at the wall and the consumption of salt grains. WP)
240
300
Time (mn)
(b)
T W 433-l
0
(4
60
120
180
240
3
0
Time (mn)
Fig. 7. (a) Example of discontinuous refrigeration at 283 K. Operating points of one cycle of the process in Clapeyron’s diagram: 1 + 2: first transition phase of regeneration. 2 -+ 3: chemical regeneration. 3 --t 4: second transition phase of regeneration. 4 + 1: refrigeration at 283 IL (b) Power levels (positive in absorption, negative in desorption) in the two reactors over several cycles: --, BaCl, reactor; ‘. ‘, MnCl, reactor. (c) Temperature levels in the two reactors over several cycles; temperature of the medium in the BaCI, reactor; - - - -, -, temperature of the thermal fluid of the BaCl, reactor; -, temperature of the medium in the MnCI, reactor; and ., temperature of the thermal fluid of the MnCl, reactor.
Second transition phase - path from 3 to 4 and 3’ to 4’ in Fig. 7(a). When the chemical regeneration phase is over, i.e. when a degree of transformation of 0.9 has been attained in the reactors, the MnCI, reactor is
132 TABLE 3. Simulation of the COP of the process COP
ideal
with thermal masses of reactants
with thermal masses of reactants + reactors
with thermal masses of reactants + reactors + thermal fluids
0.72
0.54
0.45
0.33
subjected to the temperature Tcabs~MnC,2~ = 298 K. As a result, it goes from desorption to absorption and this entails a decrease in the pressure of the gaseous phase of the arrangement. At the same time the BaCl, reactor is subjected to the temperature T, descRaC,2j. The decrease in pressure which arises as a consequence of the absorption of the MnCl, reactor ensures that the BaCl, reactor goes from absorption conditions to. desorption conditions. The working pressure drops until it reaches 0.26 bar, the point at which the transformation rates of the two salts become equal. The power levels and temperatures over several cycles are given in Figs. 7(b) and (c). It should be noted that for the constraint temperatures imposed upon the reactive mixtures the length of the refrigeration phase (of the order of 60 min) is greater than the length of the regeneration phase (of the order of 30 mm). The overall rate of transformation of the reactant varies with the imbalance imposed on the salt by the thermal fluid. This imbalance may be represented by a AT term where AT = T,,, - Tequi(P). In practice, the existence of this term enables the control of the length of each phase (refrigeration and regeneration) of the cycle. For example, the following lengths for the regeneration phase, as were obtained by simulation: a function of Tcdes~MnC,z~, for T, des(MnC12) = 428 K, length of regeneration phase = 30 min; for TcdescMnC12j = 438 K, length of regeneration phase = 23 min; and for Tcdes~MnC12~ = 448 K, length of regeneration phase = 19 min. The ideal COP of a process using the salts BaCl, and MnCl, may be obtained from the ratio of the reaction enthalpies of the two salts and is equal to 0.72. For a working cycle employing the following conditions: (i) the degree of transformation varies from 0.1 to 0.9 during each reaction (corresponding to a practical cycle); (ii) the same constraint temperatures employed as in the example shown in Fig. 7(a); and (iii) account taken of all the thermal masses, i.e. the thermal masses of reactants, reactors and thermal fluids, simulation gives a practical COP of 0.33. The reduction in comparison with the ideal COP can be shown to be a function of the different thermal masses. This makes it possible to rapidly identify potential improvements in a given machine in terms of its COP under real working conditions. The values obtained for the plant under test (Table 3) clearly show that for this kind of machine it
is also essential to optimize the exchangers or to develop
other kinds of exchanger such as heat pipes [ 181between the reactive mixture and the heat sources or heat sinks.
Conclusion and outlook Operating an experimental plant and thereby acquiring data at a significant power level (of the order of l-2 kW) has proved valuable, making it possible to demonstrate the feasibility of employing a thermochemical transformer based on the coupling of two solidgas reactions. It has also allowed an analysis and a sound understanding of the numerous phenomena which interact when two such reactors are coupled via the gaseous phase, with one reactor being in absorption and the other in desorption. Constant interaction between two reactive mixtures means that the working pressure of the process responds to the constraint temperatures imposed on each reactor. The evolution of pressure in the process provides continuous autoregulation, and stabilization of the pressure corresponds to equality of the transformation rates of the two reactive mixtures. The development of a model for the principal transfers which occur at the level of the reactive grains, the reactors and their coupling enable operations in the process to be simulated in terms of the power levels, pressures and temperatures in the system as verified by the experimental results. The simple model employed, which reflects the reactor design and the characteristics of the reactive bed, quickly simulates the sequence of the different phases occurring during a working cycle. It is well-suited to the simulation of more complex processes such as these using internal heat recovery [IX]. This kind of model could be developed as an investigation tool in several different ways. Thus, the analysis of the thermal behaviour of each reactor during its reactions clearly indicates the importance of thermal transfer between the thermal fluid and the reactive medium. Optimization of the exchanger makes it possible to have turbulent flow in the thermal fluid (and therefore a high heat exchange coefficient between the fluid and the reactor wall). Consequently, an improvement in the heat transfer between the reactive medium and the reactor wall now seems necessary.
133
Another consequence of this type of simulation model would be to allow the feasibility of a given application to be quickly estimated. It could also be used to optimize the sequencing of the energy-production and transition phases by testing various possible values for the different criteria involved: cycle duration, mass of ammonia cycled, power output and temperature output of the thermal fluids. Subsequent development of such a model could lead to an integrated regulation system which could, for example, provide refrigeration at a constant temperature.
Nomenclature
COP c pthf
S react T amb TC T cabs?
Tcdes
Tequi
T salt T rhf T thfe 3 Tthfs
UP
Vol.
coefficient of performance specific heat of the thermal fluid, J kg-’ K-’ reactor-ambient environment heat-exchange coefficient, W me2 K-’ diffusivity, m2 s-’ kinetic coefficients for absorption and desorption, (mol of gas) me2 s-’ mass flow of thermal fluid, kg SC’ heat capacity of reactor, J K-’ heat capacity of reacting mixture, J K-’ heat capacity of thermal fluid, J K-’ mol of gas absorbed or desorbed number of mol of gas number of grains of salt per unit volume number of reacting mol of gas per grain pseudo-equilibrium pressure in absorption or desorption, Pa constraint pressure, Pa equilibrium pressure, Pa gas pressure, Pa pressure at the reacting interface, Pa radius of the interface radius of a grain perfect gas constant surface area of thermal fluid-reacting medium exchanger, m2 surface area reactor-ambient air exchanger, m2 ambient temperature, K constraint temperature, K constraint temperature in absorption or desorption, K equilibrium temperature, K reacting mixture temperature, K thermal fluid temperature, K thermal fluid input, output temperature, K thermal fluid-reactive mixture heat exchange coefficient, W m-’ K-’ volume of gas in the process, m3
X
degree of transformation
A.
equivalent thermal conductivity, W m-’ K-’ equilibrium temperature drop, K enthalpy of reaction, J (mol of gas) -’
AT
AH
of reactant
References 1 B. Spinner, Les transformateurs thermochimiques $ ammoniac, Proc. Symp. Solid Sorption Refrig., Paris, 1992, pp. 145-152. 2 K. Speidel and M. Kleinemayer, Solar cooling process using chemical reactions, Proc. Symp. Solid Sorption Refrig., Paris, 1992, pp. 288-293. 3 S. V. Shelton, Solid adsorbent heat pump system, US Put. 4 610 148 (Sept. 9, 1986); Dual bed heat pump, US Pat. 4 694 659 (Sept. 22, 1987). 4 P. Neveu and J. Castaing, Solid-gas chemical heat pump: fields of application and performance of the internal heat of reaction recoveryprocess,J.Heat.RecoverySyst.CHP, 23( 1993)233-251. 5 E. Lepinasse, Transformateur thermochimique: Nouveau concept bast sur le couplage de deux r&actions solide-gaz, Doctorate Thesis, Univ. Perpignan, 1992. 6 M. Lebrun and B. Spinner, Simulation for the development of solid-gas chemical heat pump pilot plants. Part 1. Simulation and dimensioning, Chem. Eng. Process., 28 (1990) 55-66. 7 M. Lebrun, Simulation for the development of solid-gas chemical heat pump pilot plants. Part 2. Simulation and optimizationofdiscontinuousandpseudo-continuousoperating cycles, Chem. Eng. Process., 28 (1990) 67-77. 8 M. Lebrun and P. Neveu, Conception, simulation dimensioning and testing of an experimental chemical heat pump, ASHRAE Trans., 98 (1992) 420-429. 9 S. Mauran, B. Spinner, G. Crozat and P. Neveu, Caloduc chimique, pro&d& de rCgtn&ration d’un tel caloduc et utilisation de ce caloduc, Fr. Pat. 88 04 165 (30 Mars, 1988). 10 U. Rockenfeller and L. Kirol, Solid vapor compound chemical heat pumps for industrial application, Rep. DE-AC07-76 ID0 1570 (1988). 11 V. Goetz, F. Elie and B. Spinner, The structure and performance of single effect solid-gas chemical heat pump, J. Hent Recouery Syst. CHP, 13 (1993) 79-94. 12 C. Coste, G. Crozat and S. Mauran, Pro&d& de mise en Deuvre de r&actions gaz-solide, Fr. Pat. 83 09 885 (June 15, 1983); Extension US Pat. 4 595 774 (June 17, 1986). 13 A. Marty, Etude par microcalorimCtrie de la rtactivith de deux ammniacates de chlorure de manganbse, J. Thermal. Anal., 37 (1991) 479-498. 14 V. Goetz and A. Marty, A model for reversible solid-gas reactions submitted to temperature and pressure constraints: simulation of the rate of reaction in solid-gas reactor used as chemical heat pump, Chem. Eng. Sci., 47 (1992) 4445-4454. 15 S. Mauran, Flux de gaz en milieu poreux rkactif d&formable. Relation entre texture, prop%& mbcaniques et transfert, incidence sur la mise en ceuvre des rkactifs et les performances de pompes $ chaleur chimiques solide-gaz, Doctorate Thesis, Univ. Perpignan, 1990. 16 D. Heinry, Pompe Bchaleur chimiquesolide-gaz: comportement d’un reacteur r&g&n& par des chauds, Doctorate Thesis, Univ. Perpignan, 1992. 17 M. Furrer, E.I.R. Ber. No. 392, Wiirlingen (Suisse), 1980. 18 M. Lebrun, S. Mauran and B. Spinner, Dispositifpour produire du froid et/au de la chaleur par rkaction solide/gaz g&s par caloducs gravitationnels, Fr. Pat. 89 13 913(Cktober 13, 1989).
134
Appendix
Reactorcsntrs
Temperature profiles in a cylindrical reactor of 1 cm radius (R,), taking into account the coupling between grain consumption and conductive heat transfer in the bed, may be obtained as follows. The thermal balance in absorption can be calculated by assuming that heat transfer takes place only in the radial direction and that convective transfer between the reactive gas and the solid medium is ignored. On this bases we have:
Wsll
361
Gmsmint
temperature
Tc
3s3 0
i
4
6 8 10 radius(mm)
0
2
0
14
4
6
8
10
6
8
10
W - hial grad(T))+ nsalt is the equivalent thermal conductivity (Wm-’ K-l) and C, is the specific heat capacity of the reactive bed (J mP3 K’). The boundary and initial conditions are:
where &dial
Atr=&;
- &dial F
= UPD”, - T(r)1
s=O
At t = 0;
T(r) = T, and X(r) = 0
+ 4NH, % Mn(NH,),Cl,
353 0
In the example given (see Fig. Al), the reaction is: Mn(NH,),Cl,
361
353
aT
Atr=O;
361
2
4
6
8
10
Fig. Al. Temperature profiles inside a cylindrical reactor of 1 cm radius during an absorption reaction: T,= 353 K; P,= 2 bar. Evolution of the profiles as a function of the equivalent heat conductivity (U,, = 180 W m-2 K-‘). Curve 1, profile at t = 1 min; curve 2, profile at t = 5 min; and curve 3, profile at t = 20min.
+ 4AH,,,,,
It is also considered that the constraint temperature T, at the wall and the constraint pressure P, are constant throughout all the reaction with P, = 2 bar and T, = 353 K.
As indicated by the simulated profiles, it may be assumed that for conductivities of the order of 8 W m-’ K-’ there is no significant temperature gradient in the bed.
Chemical Engineering and Processing, 33 (1994) 125-134
Modelling and experimental investigation of a new type of thermochemical transformer based on the coupling of two solid-gas reactions E. Lepinasse, V. Goetz and G. Crozat CNRS, Institut de Science et Ginnie des Mat&au 66860 Perpignan-Ckdex (France)
et Prockdis, U.P. 8521 CNRS, UniversitC de Perpignan, 52 Avenue de Villeneuve.
(Received March 22, 1993; in final form December 1, 1993)
Abstract The feasibility of a thermochemical transformer based on the coupling of two solid-gas reactions has been demonstrated by a 1 kW experimental laboratory plant. A model has been built taking into account the dynamic coupling of the two reactors by the gaseous phase, and the consumption of the reactive medium in each reactor. The model has been validated by experimental results and is capable of simulating the running mode of the process for a series of working cycles.
Illtroduction Reversible solid-gas reactions are well suited to processes such as thermochemical transformers and storage systems. The large number of solid-gas couples that can be used makes it possible to produce energy over a wide range of temperatures (243-573 K) [ 11, thereby ensuring extensive use of such processes.
Monovariant reversible reactions occur in fixed bed reactors upon which non-equilibrium conditions are imposed by the double constraint of temperature and pressure. The basic process simply consists of a solidgas reactor coupled to an evaporator-condenser [Fig. l(a)]. The operating cycle of this trithermal process is illustrated in the Clapeyron diagram of Fig. l(b). This operates in two successive phases and is able to produce cold at a low temperature T, and heat at a medium temperature T,. The working modes of the evaporator and condenser are well known and detailed in the literature. Numerous studies regarding the running modes and the optimization of solid-gas reactors used for energy production are currently in progress [2-51. The solid reactant consumption model takes into account the coupling between the reaction dynamics on one hand and heat and mass transfer in the reactive medium on the other. The working modes of the basic process have been simulated [ 6,7], making it possible to size and design a 25 kW prototype for refrigeration [8]. Nevertheless, this kind of machine has a low coefficient of performance (COP) in refrigeration relative to compression systems. Indeed, taking into account only the
0255.2701/94/$7.00 SSDI 0255-2701(94)00512-G
(a)
Fixedbed solid/gas reactor
EV.XporatO~/CoIldUlS~
-l/r Fig. 1. (a) Basic scheme of a chemical heat pump. (b) The two successive
phases
of a chemical
heap pump cycle.
enthalpies of reaction and evaporation (and condensation), the ideal COP has an order of magnitude of 0.5. The large number of solid-gas couples that may be used (Fig. 2) make it possible to devise a new kind of machine working with two solid-gas reactions [9, lo]. This new process runs in the same way as the basic machine, but the liquid-gas equilibrium (Fig. 1) is replaced by a second solid-gas equilibrium. This modification suppresses the liquid phase and hence the process works independently of its position in space, which is very useful for a mobile piece of equipment. Furthermore, this modification improves the energy performance of the process. Taking into account the
0 1994-
Elsevier Science S.A. All rights reserved
126 T(T) -38 Ln(P(bao)
-23
60
la7
?
3
.i
4 -WOO/T(K
Fig. 2. Equilibrium lines for the reactions of some chlorides 2. CaCl,(8/4); 3. SrCl,(S/l); 4. with ammonia. 1. BaCl,(S/O); 7. ZnCl,(4.2); 8. CaCl,(4/2); 5. ZnCl,(6/4); 6. MnCI,(6/2); 11. MnC1,(2/1). FeC1,(6/2); 9. MgC1,(6/2); 10. NiCl,(6/2);
thermal masses of the reactants [ 111, COPS which are related to the refrigeration temperature, power output and the salts used, have been estimated between 0.4 and 0.75. Nevertheless, designing and sizing these machines involve new problems. Indeed, for the basic system, it may be considered (as has verified experimentally) that the evaporator (or condenser) fixes the pressure level in the solid-gas reactor, with liquid-vapour equilibrium occurring instantaneously in comparison with the solid-gas reaction. The progress of the process is then directly linked to the rate of transformation of the solid reactant which is the limiting step. The positions of working points for the process in the Clapeyron diagram are well known [Fig. l(b)], i.e. pressure levels during successive phases, constraint temperatures imposed on the reactor. For the process involving two solid-gas equilibria, the working pressure is linked to the coupling of the two solid-gas reactors. For example, if the overall absorption rate of one salt is faster than the overall rate of desorption of the other, the working pressure of the process will decrease until the two rates are equal. The power produced depends directly on the coupling between the overall rates of the two reactive beds. The overall term includes the reaction dynamics of the salts and the heat and mass transfer in the reactive medium. Thus, it becomes apparent that an understanding, analysis and modelling of the coupling of two solid-gas reactors by the gaseous phase are fundamental to the management of these processes. In this article, the feasibility of a process involving two solid-gas reactors is demonstrated by means of a
l-2 kW experimental laboratory refrigeration plant. An adapted dynamic model of the process, which takes into account the dynamic coupling of the two reactors by the gaseous phase, has been built. An analysis of the real limitations imposed by heat and mass transfer occurring in the reactive medium (related to the reactor design) makes it possible to develop the best suited model. The model has been validated by comparison with experimental results and makes it possible to simulate the thermodynamic path [P(t), r(t)] of the working point of the process in the Clapeyron diagram. The aim of this study was to develop a model capable of dimensioning this new kind of thermochemical transformer, verifying its performance and controlling its operation.
Model@
the process
The solid -gas
reactors
The reactive medium used consisted of an inert graphite binder and a reactive salt [ 121. Analysis and modelling of the reaction rate of the medium require an adequate knowledge of the main phenomena that limit the reaction process. These may be of three types: (i) limitation by mass transfer; (ii) limitation by heat transfer; and (iii) limitation by chemical kinetics. Two characteristic dimensions may be defined in the medium: the grain level, i.e. the basic particle at which reaction occurs, and the porous solid matrix which is composed of a combination of the reactive particles and the inert graphite. In order to take the texture into account, the study and characterization of the reactive medium was carried out in two successive stages. Reaction
rate of the salt
Experimental measurements were made with a microcalorimeter (Setaram DSC 111). In the microcalorimetric method, the samples consisted of a few milligrams of the salts thus avoiding limitations arising from.mass or heat transfer in the macropores between the grains. In this way, all the grains of the reactive salts were subjected to the same pressure and temperature constraints. The transformation rate of the salt grains was determined as a function of the pressure and temperature conditions imposed [ 131. Experimental results obtained over a wide range of temperatures and pressures allowed the model of grain consumption of the sharp interface type [14] to be validated. The consumption of each grain takes place on a sharp interface separating the products and reactants; the reaction rate is the result of coupling between mass transfer (from the grain surface to the interface) and chemical reaction at the interface. Table 1 presents the main equations for the model which are detailed in ref. 14. The pressure Pi
127
TABLE
1. Equations
describing
the consumption
of a reactive
grain
Absorption
Desorption
A+nG-+B
B-+A+nG
Mass transfer Chemical kinetics Variation in grain size
Degree of transformation
at the interface was calculated by equating the molar fluxes of the transport term and the kinetic term. The model also takes into account the variations in grain size due to the large differences between the product and reactant volumes. Heat and mass transfer in the reactive medium The physical values relating to heat and mass transfer are the thermal conductivity of the bed, the heat exchange coefficient at the wall of the reactor and the permeability. The lamellar structure of graphite ensures good dispersion of the salt, thus avoiding the grain packing and giving a high permeability in the macropores of the mixture. Depending on the percentage of graphite and the density of the mixture, the permeability varies from a few Darcy to several tens of Darcy [ 151. Thus, it may be assumed that mass transfer in the macropores of the medium is not a limiting factor in the transformation of the reactive bed. The two solids which compose the reactive mixture are mixed together physically and then compressed inside the reactor. At high densities, an anisotropic mixture is obtained which is highly conductive perpendicular to the direction of compression, but less conductive parallel to the direction of compression [ 161. The high conductivity is primarily due to the graphite matrix and to the re-orientation of the graphite layer during compression. Depending on the percentage of graphite and the density of the mixture, the values obtained range between 2 and 15 W m-’ K-‘. In the highly conductive direction and for a bed a few centimetres in diameter, the latter may be assumed to be uniform in temperature. Simulated temperature profiles in a cylindrical reactor 2 cm in diameter, taking into account the coupling between grain consumption and conductive heat transfer in the bed, are presented in the Appendix. The results confirm the assumption of a uniform bed temperature for conductivity values up
to 5 W m-’ K-‘. Obviously, for very thick beds this assumption is no longer valid. If the heat-transfer fluid of the solid-gas reactor flows through the exchanger in a turbulent manner, the main limiting factor for heat transfer between the fluid and the reactive bed is the contact resistance between the reactor wall and the reactive medium. Indeed, the heat contact resistance between a porous solid and a reactor wall is generally high. A global heat exchange coefficient UP may be defined which includes the saltreactor contact resistance and the reactor-fluid heattransfer coefficient. It is considered that the temperature of the reactor wall is equal to the fluid temperature. The thermal heat capacity of the medium may be calculated by adding together the thermal heat capacities of the solid components, i.e. salt and graphite. Basic equations for the model of the reactors The system of equations is similar for the two type of reactors, with an opposite sign for the consumption or the production of heat (by the reaction) for a reactor in desorption or absorption. According to the physical properties of the medium, the development of the process may be described via the following thermal balances. For the thermal fluid: d T,,, MC Cpcdt = ~&xc~(Tsa,r - Tt,,t) + hambL,,
Varnb - Tfw)
+ 2h C,,,,
- Ttws)
(1)
where: MC CPC = ~4 C,,,, + M C,,,, For the salt:
(2)
128
TABLE 2. Characteristics of the reactors and the reactive mixtures Characteristics
BaCI,
Mn Cl2
Reactive Medium
volume of mixture density % graphite (by mass) mass of anhydrous salt mass of graphite mol of salt porosity of anhydrous mixture
6.45 x 10m3m3 507 kg mm3 35% 2.125 kg 1.145 kg 10.2 0.77
8 x 10-3m3 495 kg mm3 35% 2.570 kg 1.385 kg 20.4 0.75
Reactor
number of tubes diameter of tubes exchanger surface area diameter of casing number of baffles mass of heat exchanger total mass of reactor volume of thermal fluid
19 30.5-33.7 mm 0.95 m* 200-206 mm 4 12kg 20 kg 7.8 x 10m3m3
19 30.5-33.7 mm 1.20 m2 200-206 mm 5 15kg 23 kg 9 x 1O-3 m3
In these equations, the heat-transfer fluid which circulates in the exchangers is assumed to be at a uniform temperature which is equal to the mean outlet temperatures. Coupling
of the inlet and
the two reactors
dn, _ dndes habs _~_~ dt
Simultaneous solution of eqns. (1) -( 6) using expressions representative of the grain consumption (Table 1) may be carried out by an explicit method. This allows the process to be quickly simulated and enables the evolution of all of the characteristic variables of each reactor (Tthf, T,,,,, PB, X) to be followed as a function of time.
Reactive
laboratory
plant
mixtures
The salts selected for this demonstration were BaCI, (barium chloride) and MnCl, (manganese chloride),
may be expressed as:
Cl2 + 8AHB,,,2
+ 4NH, s Mn( NH&C&
+ 4AHMnc,*
The reactive mixtures, whose densities were 500 kg mm3 consisted of 35% graphite. The radial conductivity of such mixtures, which is independent of the salt employed, was 8 W m-’ K-’ [ 161. Reactors
The reactors were of the catalytic type (see Fig. 3). Each reactive mixture was enclosed in several stainless steel pipes of 3 cm in diameter, set in a casing with baffles through which the thermal fluid flows (in turbulent flow). The physical characteristics of each reactor are listed in Table 2. Measuring
dt
(6)
Experimental
BaCl, + 8NH, % Ba(NH,), Mn( NH,),Cl,
As the working mode of each reactor is known, modelling the whole process consists in coupling the two reactors via the gaseous phase. This is achieved by using heat and mass balances. Equations describing the coupling of the two reactors, one of which is in an absorption mode and the other in desorption, allow the number of moles of gas in the free volume of the system, and its temperature and pressure to be calculated. The assumptions made are: (i) ammonia is a perfect gas; and (ii) gas is desorbed at the temperature of the salt. On this basis the system of equations is: dt
whose reactions with ammonia
equipment
The two reactors (one containing BaCl,, and the other MnCI,) are connected by means of a tube fitted with a mass-flow meter, allowing the progress of the reactions to be measured. Each reactor is equipped for the measurement of the following working variables: (i) temperatures inside the reactive bed; (ii) pressure in the reactor; (iii) flow rate of the thermal fluid; and (iv) inlet and outlet temperatures of the thermal fluid. Global thermal &id-reactive coeficien t UP
bed heat exchange
From the experimental measurements, i.e. temperature of the fluid and of the reactive bed, instantaneous rates of reaction from the mass flow measurement of ammonia, the UP coefficients of each reactor may be directly calculated at each time step from the equation: nNH3 AH up = &xc,,(Tr,,f - T,,,)
(7)
129
two solid-gas reactors (one in absorption and the other in desorption) connected via a gaseous phase. The heat source and heat sink were not designed for automatic cycling operations. Each phase of the process was started manually, with a time lag between them. To obtain the required initial state in each solid-gas reactors, the two reactors were isolated from one another before starting each phase; the desired temperature constraints were then imposed and the experimental phase started when the salt equilibrium conditions had been reached in the two reactors.
Fig. 1. 2. 3. 4. 5. 6. I. 8. 9. 10. II. 12. 13. 14. 15. 16.
Qualitative description The two reactors were isolated. Constraint temperatures Tc(BaC~l)and TccMncr2)where imposed on the two reactors (Fig. 5). The salts were under equilibrium conditions at the points 1 for BaCl, and 1’ for MnCl, which are the initial states for this phase of the process. The initial conditions were:
3. Experimental laboratory plant. MnCl, reactor BaCI, reactor Gaseous circuit Thermal fluid circuit for MnCI, Thermal fluid circuit for BaCl, Mass flow of ammonia Pressure sensor Temperature sensor for the reactive medium Inlet temperature sensors for the thermal fluid Outlet temperature sensors for the thermal fluid Water/oil heat exchanger Volumetric flow sensor Electric heat resistance Pumps Expansion tank Water/ammonia heat exchanger
Tthr= r, T,,, = r, ZJ = P,pui(T,) x=0.1 I
at t=O
with: TcCBaClzj = 313 K for BaCl, TqMnC12)= 363 K for MnCl, The initial degrees of transformation employed for the reactions were 0.1, since the degrees of transformation for practical cycles lie between 0.1 and 0.9 (i.e. the end of the reaction is very time consuming). The preceding phase corresponds to an absorption for BaCl, and a desorption for MnCl,.
l:I 0.2
0.3
0.4
0.5
0.6
0.7 x
Fig. 4. Experimental values of U, in the two reactors tion of the degree of transformation.
as a func-
flow rate of ammonia where nNH3 is the instantaneous (In01 s-1). The values thus obtained were (Fig. 4) UtiBaCIZI= 160 W m-‘K-’ and UpcMnClt)= 220 W mP2 Km’. Model validation
The objectives of these experiments were: (a) to demonstrate the feasibility of a thermochemical transformer using two solid-gas reactors; and (b) to achieve a sound understanding of the dynamic behaviour of
-0.0034
-0.0032 T C(Bacl2)
-0.ca30
-0.0028
-0.0026 -1m
TC(Mrc12)
Fig. 5. Simulated operating points for one phase of the process in the Clapeyron diagram. Duration and evolution of the degree of transformation of each phase: 1 --t 2: Instantaneous. 2-3: t from 0 to 100s; Xfrom 0.1 to 0.17. 3-4: t from 100 to 1500 s; X from 0.17 to 0.75. 4-+5: from 1500 to 2500 s; X from 0.75 to 0.9. ( q pseudo-equilibrium area of BaCl, and H MnCl, [ 171)).
([13] and
130
At time t = 0, the two reactors were connected via the gaseous phase. The simulated thermodynamic paths of the working points of the two reactors are depicted in Fig. 5. Four different steps may be distinguished during the reactions: 1. Instantaneous equalization of the pressure in the two reactors: path from points 1 to 2 and 1’ to 2’ in the Clapeyron diagram (Fig. 5). 2. An almost adiabatic phase corresponding to the consumption of the avail&e heat in me reactive beds. This entails a decrease in temperature from TccBacln)to a temperature near the equilibrium temperature of the salt for the BaCl, reactor which is in desorption (endothermic reaction). At the same time, the temperature of the MnCl, reactor which is in absorption (exothermic reaction) increases from TccMnClz)to its equilibrium temperature. During this phase, which lasts approximately 2 min, the pressure changes as a function of the reaction rates in the two media. In the example shown in Fig. 5, absorption in the MnCl, reactor is faster than desorption in the BaCl, reactor, which leads to a decrease in the gas pressure. This phase corresponds to the path from 2 to 3 (2’ to 3’) in Fig. 5. 3. During the next phase corresponding to 60% of the overall reaction, the pressure is stabilized at a level which equalizes the rates of absorption and desorption. The working points on the Clapeyron diagram clearly show that the reactive-bed transformations take place at temperatures near the equilibrium values. This indicates significant thermal limiting by heat exchange between the thermal fluids and the reactive beds. This phase corresponds to the path from 3 to 4 (3’ to 4’) in Fig. 5. 4. When reactions are almost over, there is a decrease in the consumption (or production) of heat in the BaCl, (or MnCl,) reactors. The thermal fluxes exchanged with the thermal fluids entail: (a) the temperature in the BaCl, reactor increasing to Tc(BaC,2,;(b) the temperature in the MnCl, reactor decreasing to Tc(MnC,Z).This step of the reaction corresponds to the path from 4 to 5 (4’ to 5’) in Fig. 5. Model validation The simulation
accurately represents the progression of the process for characteristic variables such as the working pressure and the level of power consumed or produced by the reactor [Fig. 6(a,b)]. It also simulates the temperature variations in each reactor during the reaction fairly accurately [Fig. 6(c)]. When no parameters are adjusted for the simulation, the relatively good agreement between the experimental and the simulated values demonstrates the validity of the model used. Simulation
of practical working cycles
Throughout a practical working cycle the two reactors are continuously connected by the gaseous phase.
Power(w) 2500,
Time (s)
(4 Pressure (bar)
1.5 1.0 , . . 0
, , . . . . , . . , . , . . , . , . . . 500
loo0
1500
2occl
2500
Time (s)
(b) T fK)
313 309 305 301 291 500 Cc) O
loo0
1500
UMO Time
2500 (s)
Fig. 6. Simulated (----) and experimental (-) evolution of the principal variables during one phase of the process: (a) power, (b) pressure, and (c) temperature, as a function of time (the continuous dark line in Fig. 6(c) represents the evolution of the temperature inside the reactive bed for each reactor; grey lines represent the evolution of the experimental inlet temperatures of the thermal fluids).
Only by controlling the inlet temperatures of the thermal fluids is the sequence of the different phases obtained. A working cycle is simulated under thermodynamic constraints which allow discontinuous refrigeration at a temperature lower than 283 K. The heat sink used in this example is the ambient environment assumed to be
131
at 298 K. The constraint reactors are as follows: for BaCl,: for MnCl,:
in in in in
absorption, desorption, absorption, desorption,
temperatures
imposed
on the
Power (W) 2500 -
T,.abs(BaClzj= Tamb = 298 K T, des(BaC12j = 283 K T, abs(MnC,z)= Tam,, = 298 K T, deP(MnC,zj = 428 K
i Y
The cycle can be split into two successive phases for refrigeration. Refrigeration: low pressure phase The BaCl, reactor is in desorption. It consumes heat at a temperature below 283 K, the heat being supplied by the thermal Auid at 283 K which works as the refrigerant. At the same time, the MnCl, reactor is in absorption, and the heat produced is dissipated into the environment at 298 K.
i i
I
v 0
Regeneration phase First transition phase - path from 1 to 2 and 1’ to 2 in Fig. 7(a). The MnCl, reactor is now subjected to the the temperature T, des(MnC12). Under these conditions, temperature of the reactor increases and the reactive mixture goes from absorption conditions to desorption conditions. Desorption of MnCl, entails a pressure increase in the gaseous phase of the arrangement. At the same time the BaCI, reactor is subjected to its absorption temperature T, abs(BilC,zj.The pressure increase resulting from the desorption of the reactant MnCl, ensures that the BaCl, reactor goes from desorption conditions to absorption conditions. Chemical regeneration phase - path from 2 to 3 and 2’ to 3’ in Fig. 7(a). The working pressure of the process changes until the transformation rates of the salts in the two reactors become equal. Depending on the design of the two reactors, these transformation rates are determined by the coupling between the heat transfer from the thermal fluid to the reactive mixture at the wall and the consumption of salt grains. WP)
240
300
Time (mn)
(b)
T W 433-l
0
(4
60
120
180
240
3
0
Time (mn)
Fig. 7. (a) Example of discontinuous refrigeration at 283 K. Operating points of one cycle of the process in Clapeyron’s diagram: 1 + 2: first transition phase of regeneration. 2 -+ 3: chemical regeneration. 3 --t 4: second transition phase of regeneration. 4 + 1: refrigeration at 283 IL (b) Power levels (positive in absorption, negative in desorption) in the two reactors over several cycles: --, BaCl, reactor; ‘. ‘, MnCl, reactor. (c) Temperature levels in the two reactors over several cycles; temperature of the medium in the BaCI, reactor; - - - -, -, temperature of the thermal fluid of the BaCl, reactor; -, temperature of the medium in the MnCI, reactor; and ., temperature of the thermal fluid of the MnCl, reactor.
Second transition phase - path from 3 to 4 and 3’ to 4’ in Fig. 7(a). When the chemical regeneration phase is over, i.e. when a degree of transformation of 0.9 has been attained in the reactors, the MnCI, reactor is
132 TABLE 3. Simulation of the COP of the process COP
ideal
with thermal masses of reactants
with thermal masses of reactants + reactors
with thermal masses of reactants + reactors + thermal fluids
0.72
0.54
0.45
0.33
subjected to the temperature Tcabs~MnC,2~ = 298 K. As a result, it goes from desorption to absorption and this entails a decrease in the pressure of the gaseous phase of the arrangement. At the same time the BaCl, reactor is subjected to the temperature T, descRaC,2j. The decrease in pressure which arises as a consequence of the absorption of the MnCl, reactor ensures that the BaCl, reactor goes from absorption conditions to. desorption conditions. The working pressure drops until it reaches 0.26 bar, the point at which the transformation rates of the two salts become equal. The power levels and temperatures over several cycles are given in Figs. 7(b) and (c). It should be noted that for the constraint temperatures imposed upon the reactive mixtures the length of the refrigeration phase (of the order of 60 min) is greater than the length of the regeneration phase (of the order of 30 mm). The overall rate of transformation of the reactant varies with the imbalance imposed on the salt by the thermal fluid. This imbalance may be represented by a AT term where AT = T,,, - Tequi(P). In practice, the existence of this term enables the control of the length of each phase (refrigeration and regeneration) of the cycle. For example, the following lengths for the regeneration phase, as were obtained by simulation: a function of Tcdes~MnC,z~, for T, des(MnC12) = 428 K, length of regeneration phase = 30 min; for TcdescMnC12j = 438 K, length of regeneration phase = 23 min; and for Tcdes~MnC12~ = 448 K, length of regeneration phase = 19 min. The ideal COP of a process using the salts BaCl, and MnCl, may be obtained from the ratio of the reaction enthalpies of the two salts and is equal to 0.72. For a working cycle employing the following conditions: (i) the degree of transformation varies from 0.1 to 0.9 during each reaction (corresponding to a practical cycle); (ii) the same constraint temperatures employed as in the example shown in Fig. 7(a); and (iii) account taken of all the thermal masses, i.e. the thermal masses of reactants, reactors and thermal fluids, simulation gives a practical COP of 0.33. The reduction in comparison with the ideal COP can be shown to be a function of the different thermal masses. This makes it possible to rapidly identify potential improvements in a given machine in terms of its COP under real working conditions. The values obtained for the plant under test (Table 3) clearly show that for this kind of machine it
is also essential to optimize the exchangers or to develop
other kinds of exchanger such as heat pipes [ 181between the reactive mixture and the heat sources or heat sinks.
Conclusion and outlook Operating an experimental plant and thereby acquiring data at a significant power level (of the order of l-2 kW) has proved valuable, making it possible to demonstrate the feasibility of employing a thermochemical transformer based on the coupling of two solidgas reactions. It has also allowed an analysis and a sound understanding of the numerous phenomena which interact when two such reactors are coupled via the gaseous phase, with one reactor being in absorption and the other in desorption. Constant interaction between two reactive mixtures means that the working pressure of the process responds to the constraint temperatures imposed on each reactor. The evolution of pressure in the process provides continuous autoregulation, and stabilization of the pressure corresponds to equality of the transformation rates of the two reactive mixtures. The development of a model for the principal transfers which occur at the level of the reactive grains, the reactors and their coupling enable operations in the process to be simulated in terms of the power levels, pressures and temperatures in the system as verified by the experimental results. The simple model employed, which reflects the reactor design and the characteristics of the reactive bed, quickly simulates the sequence of the different phases occurring during a working cycle. It is well-suited to the simulation of more complex processes such as these using internal heat recovery [IX]. This kind of model could be developed as an investigation tool in several different ways. Thus, the analysis of the thermal behaviour of each reactor during its reactions clearly indicates the importance of thermal transfer between the thermal fluid and the reactive medium. Optimization of the exchanger makes it possible to have turbulent flow in the thermal fluid (and therefore a high heat exchange coefficient between the fluid and the reactor wall). Consequently, an improvement in the heat transfer between the reactive medium and the reactor wall now seems necessary.
133
Another consequence of this type of simulation model would be to allow the feasibility of a given application to be quickly estimated. It could also be used to optimize the sequencing of the energy-production and transition phases by testing various possible values for the different criteria involved: cycle duration, mass of ammonia cycled, power output and temperature output of the thermal fluids. Subsequent development of such a model could lead to an integrated regulation system which could, for example, provide refrigeration at a constant temperature.
Nomenclature
COP c pthf
S react T amb TC T cabs?
Tcdes
Tequi
T salt T rhf T thfe 3 Tthfs
UP
Vol.
coefficient of performance specific heat of the thermal fluid, J kg-’ K-’ reactor-ambient environment heat-exchange coefficient, W me2 K-’ diffusivity, m2 s-’ kinetic coefficients for absorption and desorption, (mol of gas) me2 s-’ mass flow of thermal fluid, kg SC’ heat capacity of reactor, J K-’ heat capacity of reacting mixture, J K-’ heat capacity of thermal fluid, J K-’ mol of gas absorbed or desorbed number of mol of gas number of grains of salt per unit volume number of reacting mol of gas per grain pseudo-equilibrium pressure in absorption or desorption, Pa constraint pressure, Pa equilibrium pressure, Pa gas pressure, Pa pressure at the reacting interface, Pa radius of the interface radius of a grain perfect gas constant surface area of thermal fluid-reacting medium exchanger, m2 surface area reactor-ambient air exchanger, m2 ambient temperature, K constraint temperature, K constraint temperature in absorption or desorption, K equilibrium temperature, K reacting mixture temperature, K thermal fluid temperature, K thermal fluid input, output temperature, K thermal fluid-reactive mixture heat exchange coefficient, W m-’ K-’ volume of gas in the process, m3
X
degree of transformation
A.
equivalent thermal conductivity, W m-’ K-’ equilibrium temperature drop, K enthalpy of reaction, J (mol of gas) -’
AT
AH
of reactant
References 1 B. Spinner, Les transformateurs thermochimiques $ ammoniac, Proc. Symp. Solid Sorption Refrig., Paris, 1992, pp. 145-152. 2 K. Speidel and M. Kleinemayer, Solar cooling process using chemical reactions, Proc. Symp. Solid Sorption Refrig., Paris, 1992, pp. 288-293. 3 S. V. Shelton, Solid adsorbent heat pump system, US Put. 4 610 148 (Sept. 9, 1986); Dual bed heat pump, US Pat. 4 694 659 (Sept. 22, 1987). 4 P. Neveu and J. Castaing, Solid-gas chemical heat pump: fields of application and performance of the internal heat of reaction recoveryprocess,J.Heat.RecoverySyst.CHP, 23( 1993)233-251. 5 E. Lepinasse, Transformateur thermochimique: Nouveau concept bast sur le couplage de deux r&actions solide-gaz, Doctorate Thesis, Univ. Perpignan, 1992. 6 M. Lebrun and B. Spinner, Simulation for the development of solid-gas chemical heat pump pilot plants. Part 1. Simulation and dimensioning, Chem. Eng. Process., 28 (1990) 55-66. 7 M. Lebrun, Simulation for the development of solid-gas chemical heat pump pilot plants. Part 2. Simulation and optimizationofdiscontinuousandpseudo-continuousoperating cycles, Chem. Eng. Process., 28 (1990) 67-77. 8 M. Lebrun and P. Neveu, Conception, simulation dimensioning and testing of an experimental chemical heat pump, ASHRAE Trans., 98 (1992) 420-429. 9 S. Mauran, B. Spinner, G. Crozat and P. Neveu, Caloduc chimique, pro&d& de rCgtn&ration d’un tel caloduc et utilisation de ce caloduc, Fr. Pat. 88 04 165 (30 Mars, 1988). 10 U. Rockenfeller and L. Kirol, Solid vapor compound chemical heat pumps for industrial application, Rep. DE-AC07-76 ID0 1570 (1988). 11 V. Goetz, F. Elie and B. Spinner, The structure and performance of single effect solid-gas chemical heat pump, J. Hent Recouery Syst. CHP, 13 (1993) 79-94. 12 C. Coste, G. Crozat and S. Mauran, Pro&d& de mise en Deuvre de r&actions gaz-solide, Fr. Pat. 83 09 885 (June 15, 1983); Extension US Pat. 4 595 774 (June 17, 1986). 13 A. Marty, Etude par microcalorimCtrie de la rtactivith de deux ammniacates de chlorure de manganbse, J. Thermal. Anal., 37 (1991) 479-498. 14 V. Goetz and A. Marty, A model for reversible solid-gas reactions submitted to temperature and pressure constraints: simulation of the rate of reaction in solid-gas reactor used as chemical heat pump, Chem. Eng. Sci., 47 (1992) 4445-4454. 15 S. Mauran, Flux de gaz en milieu poreux rkactif d&formable. Relation entre texture, prop%& mbcaniques et transfert, incidence sur la mise en ceuvre des rkactifs et les performances de pompes $ chaleur chimiques solide-gaz, Doctorate Thesis, Univ. Perpignan, 1990. 16 D. Heinry, Pompe Bchaleur chimiquesolide-gaz: comportement d’un reacteur r&g&n& par des chauds, Doctorate Thesis, Univ. Perpignan, 1992. 17 M. Furrer, E.I.R. Ber. No. 392, Wiirlingen (Suisse), 1980. 18 M. Lebrun, S. Mauran and B. Spinner, Dispositifpour produire du froid et/au de la chaleur par rkaction solide/gaz g&s par caloducs gravitationnels, Fr. Pat. 89 13 913(Cktober 13, 1989).
134
Appendix
Reactorcsntrs
Temperature profiles in a cylindrical reactor of 1 cm radius (R,), taking into account the coupling between grain consumption and conductive heat transfer in the bed, may be obtained as follows. The thermal balance in absorption can be calculated by assuming that heat transfer takes place only in the radial direction and that convective transfer between the reactive gas and the solid medium is ignored. On this bases we have:
Wsll
361
Gmsmint
temperature
Tc
3s3 0
i
4
6 8 10 radius(mm)
0
2
0
14
4
6
8
10
6
8
10
W - hial grad(T))+ nsalt is the equivalent thermal conductivity (Wm-’ K-l) and C, is the specific heat capacity of the reactive bed (J mP3 K’). The boundary and initial conditions are:
where &dial
Atr=&;
- &dial F
= UPD”, - T(r)1
s=O
At t = 0;
T(r) = T, and X(r) = 0
+ 4NH, % Mn(NH,),Cl,
353 0
In the example given (see Fig. Al), the reaction is: Mn(NH,),Cl,
361
353
aT
Atr=O;
361
2
4
6
8
10
Fig. Al. Temperature profiles inside a cylindrical reactor of 1 cm radius during an absorption reaction: T,= 353 K; P,= 2 bar. Evolution of the profiles as a function of the equivalent heat conductivity (U,, = 180 W m-2 K-‘). Curve 1, profile at t = 1 min; curve 2, profile at t = 5 min; and curve 3, profile at t = 20min.
+ 4AH,,,,,
It is also considered that the constraint temperature T, at the wall and the constraint pressure P, are constant throughout all the reaction with P, = 2 bar and T, = 353 K.
As indicated by the simulated profiles, it may be assumed that for conductivities of the order of 8 W m-’ K-’ there is no significant temperature gradient in the bed.