Ind.
684
Eng. Chem. R e s . 1988, 27, 684-691
Nomenclature C, = specific heat capacity, kJ/(kgK) C,k, = specific heat capacity of component “k” inside the capsules in the liquid phase, kJ/(kgK) Cpk8= specific heat capacity of component “k” inside the capsules in the solid phase, kJ/(kgK) mGS= mass of Glauber’s salt undergoing phase change inside the capsules, kg mk = mass of component “k” inside the capsules, kg Qth = theoretical heat storage capacity of the contents of the capsules in the column, k J U = superficial velocity of water in the column U,, = minimum fluidization velocity Greek Symbol XGS = latent heat of phase change for Glauber’s salt, kJ/kg
Registry No. Glauber’s salt, 7727-73-3; borax, 1303-96-4; polypropylene, 9003-07-0.
Literature Cited Chadwick, D. G.; Sherwood, K. H. Report UWRL/P-81/05, 1981; NTIS, Washington, D.C. Chahroudi, D. In Proceedings Workshop on Solar Energy Storage Subsystems for Heating and Cooling of Buildings; Wiley: New York, 1975; p 56. Chen, J.; Nelson, R. Report ORNL/TM-8543, 1983; NTIS, Washington, D.C. Duffie. J. A.: Beckman. W. A. Solar Engineering - of , Thermal Processes; Wiley: New York, 1980. Fellchenfeld, H.; Swig, S. Znd. Eng. Chem. Prod. Res. Deu. 1985,24, 130. Fouda, A. E.; Despaul, J. G.; Taylor, J. B.; Capes, C. E. Sol. Energy 1984, 32, 57. Grace, J. R. In Handbook of Multiphase Systems; Hetsroni, G., Ed.; Hemisphere: Washington, D.C. 1982; Chapter 8.1.
Heine, D.; Abhat, A. In Proceedings of International Solar Energy Society Congress; New Delhi, India, 1978; Vol. I, p 500. Herrick, C. S.; Golibersuch, D. C. Information Series Report 77CRD006, 1977; General Electric Company, Schenectady, NY. Herrick, C. S.; Zarnoch, K. P. Technical Information Series, Report No. 79CRD249, 1979; General Electric Company, Schenectady, NY. Hodgins, J. W.; Hoffman, T. W. Can. J. Technol. 1955, 33, 293. Lane, G. A.; Best, J. S.; Clarke, E. C.; Glew, D. N. Report NSF/ RANN/RE/C-906/FR/76/1, 1976; NTIS, Washington, D.C. Lane, G. A,; Glew, D. N.; Clarke, E. C.; Rossow, H. E. In Proceedings of Workshop on Solar Energy Storage Subsystems for Heating and Cooling of Buildings; Wiley: New York, 1975; p 43. Marks, S. B. In Proceedings of 25th Intersociety Energy Conuersion Engineering Conference; Wiley: New York 1980; Vol. 1, p 259. Page, J. K. R.; Swayne, R. E. H. In Proceedings of International Conference on Energy Storage; Wiley: New York, 1981; Vol. 1, 165. Perry, R. H.; Chilton, C. H. Chemical Engineer’s Handbook, 5th ed.; McGraw-Hill: New York, 1973. Sozen, Z. Z. Ph.D. Dissertation, University of British Columbia, Vancouver, 1985. Telkes, M. Znd. Eng. Chem. 1952,44, 1308. Telkes, M. In Proceedings of Workshop on Solar Energy Storage Subsystems for Heating and Cooling of Buildings; Wiley: New York, 1975; p 17. Telkes, M. U S . Patent 3 986 969, 1976. Telkes, M. In Solar Materials Science; Murr, L. E., Ed.; Academic: New York, 1980; Chapters 11 and 12. Weast, R. C. CRC Handbook of Chemistry and Physics; CRC: Cleveland, 1976. Wood, R. J.; Gladwell, S. D.; O’Callaghan, P. W.; Probert, S. D. In Proceedings of International Conference on Energy Storage; Wiley: New York, 1981; Vol. I, pp. 145-158. Zahavi, E. I n t . J . Heat Mass Transfer 1971, 44, 835.
Received for review April 2, 1986 Revised manuscript received October 6 , 1987 Accepted October 21, 1987
Thermal Energy Storage by Agitated Capsules of Phase Change Material. 2. Causes of Efficiency Loss Zeki Z. Sozen,? John R. Grace,* and Kenneth L. Pinder D e p a r t m e n t of Chemical Engineering, University of British Columbia, Vancouver, B.C., Canada V 6 T 1 W 5
In an effort to further improve the heat storage efficiency and to determine which factors contribute most to losses in efficiency, capsules were tested in a rotating tube and in a rotating drum a t different speeds. Full capsule rotation around a horizontal axis improved the storage efficiency over the efficiencies achieved in part 1. Impacts resulting from motion in the drum gave small additional improvements in the efficiencies over those realized in the rotating tube, with a maximum storage efficiency of 83% for a stoichiometric Glauber’s salt mixture with 4% borax. At high rotation speeds, centrifugal forces had a negative effect. Heat storage efficiencies increased with addition of excess Na2S04and also with excess H 2 0 compared t o eutectic salt mixtures. On a storage per unit volume basis, 4 7 4 3 % by weight Na2S04was found t o be the optimum concentration, the corresponding optimum on a per unit mass basis being 44-47% by weight Na2S04. Segregation was found to account for less than half of the loss in heat storage capacity, the remainder being caused by subcooling and microencapsulation. Strong agitation and the presence of borax reduced the thermal efficiency loss due t o subcooling. Part 1 showed that Glauber’s salt, encapsulated in 25mm-diameter hollow spheres and agitated by water in a 0.34-m-diameter liquid fluidized bed, is a promising thermal energy storage system. The heat-transfer area, increased enormously by encapsulation, led to an average heat-transfer delivery or recovery rate of about 60 kW/m3 (based on the inside volume of the capsules) between 20 and 40 “C. Fluidization also provided uniform gentle Present address: Yasar Holding Company, Sehit Fethi Bey, Caddesi No. 120, Alsancak 35210, Izmir, Turkey.
0888-5885/88/2627-0684$01.50/0
agitation of the capsules which led to much less loss in heat storage efficiency than under fixed bed conditions. On the other hand, the heat storage capacity of the phase change material (96 wt% Glauber’s salt and 4 wt % borax) in the fluidized bed system was about 60% of the theoretical value, leaving a considerable margin for further improvement. density gradients inside the capsules prevented full capsule rotation around horizontal axes through their centers, even at high superficial velocities. Therefore, complete suspension of the anhydrous sodium sulfate crystals was never obtained under fluidized bed conditions 0 1988 American Chemical Society
Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 685 Table I. Chemical Compositions (Percent by Weight) for Capsules of Different Compositions Used in the Experiments composisodium tion total phase-change material sulfate-water designation 9% Na9SOA 9% H 9 0 % borax % Na9SOA % HzO 4.0 58.7 41.3 A: 56.3 39.7 47.2 45.3 4.0 52.8 B: 50.7 C:
D: E:
Figure 1. Experimental equipment: (a, top) rotating drum; (b, bottom) rotating tube.
(see part l), providing one reason for losses in heat storage efficiencies. Herrick and Golibersuch (1977) and Herrick and Zarnoch (1970) attempted to prevent segregation of Glauber's salt by using a rotary system. Individual crystals of sodium sulfate decahydrateand anhydrous sodium sulfate adhered tenaciously to one another when they came into physical contact. As the freezing process continued, adhesion caused layers of the two salts to accumulateuntil all of the anhydrous sodium sulfate lay buried under decahydrate. This problem, which they call "microencapsulation", was overcome by adding 25% excess anhydrous sodium sulfate to replace the crystals coated by decahydrate. The further studies described in this paper were undertaken to determine the effect of different forms and intensities of mixing on the heat storage capacity of encapsulated Glauber's salt mixtures. Since only 83% energy storage and recovery could be achieved, segregation of the hydrated and unhydrated sodium sulfate crystals in the capsules was investigated, allowing the extent of microencapsulation to be inferred. A study of subcooling is used to choose the best combination of materials for encapsulation.
Experimental System and Procedure (a) Rotating Drum and Tube Experiments. The experimental setup used for the rotating drum experiments consists of a rotating drum, a variable-speed motor, a cold box, two constant-temperature water baths, a small calorimeter, and a chart recorder. As shown in Figure la, the rotating drum consists of eight compartments, each 146 mm inside diameter and 32 mm long. Each compartment has a fixed pin inside, located so that it will contact the capsule a t the bottom of the drum, bring it up to the top while the drum is rotating, and let it drop by gravity to the bottom again. While the pin is traveling from the top to the bottom, the capsule rotates at the speed of the drum.
45.1 42.3 37.9
50.9 53.7 58.1
4.0 4.0 4.0
47.0 44.1 39.5
53.0 55.9 60.5
The drum was placed in a 0.3 X 0.45 X 0.3 m rectangular box with ice at the bottom to keep the air temperature at around 10 "C and mounted on a 0.186-kW variable-speed motor by a shaft which passed through a hole in the box. It was possible to adjust the motor speed between 0.5 and 1750 rpm. Two constant-temperature water baths were used, one held at 20 "C and the other at 45 "C. Eight capsules, after resting a t least 5 h in the 45 "C water bath, were placed in the cool rotating drum for crystallization, one per compartment. They were removed after crystallization and placed in the 20 "C water bath overnight before the heat storage capacity was measured between 20 and 40 "C for comparison with the fluidized bed results (see part 1). The warm bath was kept a t 45 "C rather than 40 "C to allow a longer time for mixing the capsules in the drum while their contents were in a melted state. The calorimeter, a 0.5-L thermos bottle covered with 75-mm-thick Fiberglas insulation, was calibrated carefully to find the overall heat-transfer coefficient to or from the surroundings and the overall heat capacity. The temperature inside the calorimeter and that of the surrounding air were measured by using two calibrated copperconstantan thermocouples, connected through Omega-CJ electronic ice point compensators to a Servagor Model 220 two-pen recorder. The temperature curves were digitized and used for calculation of heat stored by the contents of the capsules, equal to the heat released during crystallization. Eight capsules were used for all calorimetric measurements. The rotating tube was a cylinder of inside diameter 25 mm and length 260 mm as shown in Figure lb. The inside diameter of the tube was large enough to allow filling of the tube but tight enough that the capsules would not rotate relative to the tube. The experimental procedure for the rotating tube was the same as for the rotating drum. The tube was placed in the same rectangular box and mounted on the same variable-speed motor. The tube was designed to give full rotation around a fixed horizontal axis passing through the center of the capsules, without subjecting the capsules to any other motion. In the case of the rotating drum, collision of the capsules with a fixed surface also occurred. Capsules of five different sodium sulfate compositions given in Table I were used to indicate whether excess anhydrous sodium sulfate or excess water is helpful in sustaining the energy storage efficiency and to provide information on the mechanisms for loss of storage capacity. Compositions were not studied outside the range covered in Table I because this would lead to low theoretical heat storage capacities. Experiments were performed at rotational speeds of 1, 3, 5, 10, and 25 rpm for the drum and 3.5, 10.5, and 17.5 rpm for the rotating tube. The rotational speed was not increased above 25 rpm for the drum and 17.5 rpm for the tube because there were no further gains in energy storage efficiencies above these values. The increased centrifugal
686 Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 Table 11. Results of the Thermogravimetric Analysis of the Samples from the Capsules with Different Thermal Cycling Histories theoretically w t % NazSOl a t X J D , of expected % measd % capsule thermal cycling history of the capsule 0.05 0.35 0.65 0.95 efficiency efficiency 1 fresh 43.4 43.8 45.9 47.5 99 91 38.8 47.3 42.9 91 59 2 cycled in fluidized bed 38.6 38.8 52.0 42.6 88 59 3 cycled in fluidized bed 38.5 4 cycled in fixed bed 17.1 35.2 54.2 52.9 36.4 53.4 46.7 83 55 5 all cycles 34.7 6 all cycles 35.7 36.9 49.9 46.1 87 55 31.1 70.9 64.9 7 all cycles plus 12 fixed bed cycles 12.8
force probably countered the added mixing a t higher speeds. Theoretically a capsule underwent 3.5 rotations around its horizontal axis for each rotation in the drum. Hence, the rotational speed of the tube was adjusted to 3.5 times that of the drum to make the results comparable and to allow determination of the effect of collisions. Two thermal cycles were performed at each speed; only the second one was evaluated and reported in order to eliminate the influence of the previous conditions on the heat storage capacity of the capsules. Reproducibility in five repeated runs in both the rotating drum and rotating tube was found to be better than *O.6%. The results are reported on the basis of both weight and volume occupied by the phase change material because density changes with composition (Sozen, 1985). (b) Segregation. The concentration of Na2S04was determined for four vertical intervals by a differential gravimetric technique. The top and bottom positions, observable through the translucent plastic because of the air bubble and the white anhydride, were first marked with a crayon. The capsules were next immersed in liquid nitrogen to freeze their contents. Each frozen capsule (shell and contents) was then sliced vertically into two equal portions with a thin (0.3-mm-diameter) electrically heated wire. The layer of materials along the path of the wire was discarded, and a sharp knife was used to obtain samples at fractional distances of 0.05,0.35,0.65, and 0.95 from the top of the frozen mass of heat storage material. These samples were then analyzed by using a Perkin-Elmer Model TGS-2 thermogravimetric analyzer. Each sample, of size between 20 and 25 mg, was maintained a t liquid nitrogen temperature until analyzed. The analyses were made between 25 and 150 OC with a heating rate of 1 "C/min. Usually the sample had reached a constant weight by 90 OC. The water vapor was swept from the oven by a flow of nitrogen. Twenty-eight samples from seven capsules, representing five different histories of thermal cycling (see Table 11), were analyzed. For pure Glauber's salt, the concentrations were measured as 44.6 and 44.1 wt % sodium sulfate, which compare reasonably well with the theoretical value of 44.1 w t %. (c) Subcooling. To study the effect of borax as a nucleating agent, cooling tests were carried out using 0.2-kg samples of melted mixtures of different phase change materials. Glauber's salt mixtures containing 0 % , 3% , 4 % , and 5% by weight borax were used. Duplicate samples were placed in two Erlenmeyer flasks with copperconstantan thermocouples, melted, and then cooled in air at room temperature while the thermocouple outputs were recorded on a Servagor Model 220 chart recorder at 2-mV full-scale range. The averages of four tests on each mixture were recorded. In the case of the 4 wt % borax mixture, four additional tests were made in which the supernatant liquid was gently stirred without disturbing the crystals. To test for nucleating temperatures in the capsules, three capsules of each mixture shown in Table I, chosen
-
L44.1
r* v)
0
5
10 15 ROTATION SPEED ( r p m )
20
r
25
Figure 2. Heat gain efficiency for capsules of different compositions in the rotating drum as a function of rotational speed. Temperature range: 20-40 "C.
randomly from the capsules which had been cycled 84 times in the liquid fluidized bed, were heated to 40 "C to melt the phase change material. Then a copperconstantan thermocouple (Omega, 1.59-mm shield diameter) was inserted into each capsule through a drilled hole and sealed to prevent leakage. The thermocouple junction was located in the anhydrous sodium sulfate precipitate, approximately 1mm from the capsule's inner surface, the most likely region for nucleation to be initiated. Each capsule was immersed in 25 "C water in a constant-temperature bath and agitated with a smooth motion similar to that observed in the water fluidized bed. The thermocouple voltagetime curves were recorded and converted to temperature-time curves. To check the propagation of crystal growth, a small number of experiments were also conducted with a second thermocouple a t the center of the capsule. Temperature-time cooling curves were recorded for one capsule of composition D (Table I) without stirring and for one capsule each of compositions D and B subjected to gentle stirring similar to that observed in liquid fluidized beds. Experimental Results (a) Rotating Drum a n d T u b e Experiments. As shown in Figures 2 and 3, the heat storage efficiency of the capsules increased with rotational speed, both in the rotating drum and in the rotating tube, reaching a maximum at about 25 rpm in the drum and 15 rpm in the tube. The maximum efficiencies for stoichiometric Glauber's salt are 83% and 79% for the drum and tube, respectively. At high speeds, centrifugal forces begin to play a significant role, and, in addition, sliding of capsules was observed during the half turn in the rotating drum when capsules were not being lifted by the pins. The results in Figure 3 for a rotational speed of 0 correspond to the first fixed bed cycle following the rotating tube experiments. As shown in part 1, the efficiency would be lower still if subsequent cycles had been used. For non-zero rotational speeds, results were
Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 687
-
‘e
“1
THEORETICAL
EXPERIMENTAL
52.8
“
6
5
A
39.5
+
47.0 441
10
ROTATION SPEED (rpm)
In
20
15
35
Figure 3. Heat gain efficiency for capsules of different compositions in the rotating tube as a function of rotational speed. Temperature range: 20-40 O C .
fll
35
1 40 45 50 55 WEIGHT PERCENT SODIUM SULFATE
I
I
PI1
60
Figure 4. Theoretical and experimental heat storage capacity of the capsules per unit volume for the rotating drum.
reproducible over many cycles. Figures 2 and 3 indicate that the percentage heat storage efficiency is less for a Na2S04concentration of 44.1 wt % , corresponding to the stoichiometric Glauber’s salt composition, than for higher or lower concentrations. Higher efficiencies were recorded in all cases for an excess of water (39.5 wt 70 Na2S04)and for excesses of sodium sulfate (47.070, 52.870, and 58.7% by weight Na2S04). While the reported efficiencies, based on the theoretically possible heat storage capacity at given compositions, provide valuable information, they cannot be used to compare heat storage capacities a t different compositions. This is because the theoretical heat storage capacity varies strongly with composition, making it difficult to compare published results (e.g., Biswas (1977),Herrick and Zarnoch (1979),and Fouda et al. (1984)). Comparison is even more difficult where additives were present (Marks, 1982; Chen and Nelson, 1983). The applicability and accuracy of the standard methods, ASHRAE 94-77 Methods of Testing Thermal Storage Devices Based on Thermal Performance, (1977) and NBSlR 74-634 (Kelly and Hill, 1974),for testing heat storage devices have given rise to serious questions (Marshall, 1981). Although studies have been conducted to develop standard methods for comparing latent heat systems (Cole et al., 19831, the resulting methods are long and complex. A simple and effective method for comparing heat storage capacities is presented in Figures 4 and 5. The maximum theoretical storage capacity on a per unit encapsulated volume basis is plotted with and without allowance for the 4% borax present. Similar theoretical curves for other temperature intervals have been provided
40 45 50 55 WEIGHT PERCENT SODIUM SULFATE
60
Figure 5. Theoretical and experimental heat storage capacity of the capsules per unit volume for the rotating tube.
by Sozen (1985). The maximum theoretical heat storage capacity corresponds to stoichiometric Glauber’s salt, i.e., 44.1 wt % Na2S04,the theoretical capacity decreasing sharply when the sodium sulfate concentration is either increased above or decreased below this value. Hence, higher heat storage efficiencies, expressed as percentages of the theoretical capacity a t the given composition, may correspond to lower absolute heat storage capacities. While storage efficiencies are a minimum a t 44.1% Na2S04 (Figures 2 and 3), the absolute storage capacity is near its maximum value at that composition, the maximum being achieved a t about 47-53% by weight Na2S04(Figures 4 and 5). As shown by Sozen (19851, very similar results are obtained if heat storage capacities are plotted on a per unit mass basis rather than a per unit volume basis, the optimum Na2S04concentration shifting downward slightly to 44-47 % by weight. It should be noted that Figures 4 and 5 compare systems only from a heat storage point of view. In detailed comparisons, other factors such as the heat-transfer rate, cost, and temperature interval must also be considered. (b) Crystal Segregation and Microencapsulation. The results of the thermal gravimetric analyses of the seven capsules of known previous history are shown in Table 11. Fresh designates capsules which were not thermally cycled after they were filled. These capsules were filled a t temperatures above 32.4 “C, and their contents were crystallized while the capsules were being vigorously agitated before they were stored. Hence, the contents of the capsules went through one thermal cycle during the encapsulation (filling) process. Cycled in fluidized bed represents capsules which had been subjected to 84 thermal cycles in the fluidized bed system (see part 1). Cycled in fixed bed refers to capsules which had undergone 12 cycles under fixed bed conditions. All cycles designates capsules which experienced 96 cycles in the fluidized bed, 1 2 cycles in the fixed bed, and then 5 recovery cycles again in the pilot-scale fluidized bed (see part 1). All cycles plus 12 fixed bed cycles is the same as the previous case but with 12 additional thermal cycles under fixed bed conditions. From Table I1 it can be seen that, even for a fresh capsule, after a single cycle there is a slight difference in concentration from top ( X J D , = 0.05) to bottom, indicating some separation of anhydrous sodium sulfate. Capsules 4 and 7, which were heated and cooled 12 times in a fixed bed, showed the largest concentration variation. Since there is no agitation in a fixed bed to disperse the anhydrate during the part of the thermal cycle when liquid is present, the anhydrate remained at the bottom and became more and more covered by Glauber’s salt during
688 Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 Table 111. Results of the Subcooling Experiments Performed in Erlenmever Flasks nucleacrystallition zation composition and mixing pattern temp, “C temp, “C Glauber’s salt, no borax, vigorously mixed 16.6 32.4 3 wt % borax, 97 wt % Glauber’s salt, 29.0 31.8 vigorously mixed 4 wt % borax, 96 wt % Glauber’s salt, 30.4 31.8 vigorously mixed 4 wt % borax, 96 wt % Glauber’s salt, 28.3 30.4 gently mixed 5 wt % borax, 95 wt % Glauber’s salt, 30.3 31.7 vigorously mixed ~
each cycle. At the same time, the former water of hydration remained a t the top of the capsule. In each of the tests on precycled capsules (2-7), the maximum concentration occurred at X,/D, = 0.65. It is possible that a block of anhydrate which is not attached to the lower surface forms in the lower half of the capsule. The next-blast column in Table I1 lists the theoretically expected efficiency of heat storage for each capsule, based on the measured profiles of the amounts of hydrated and unhydrated salt for each thermal history. While the values are not expected to be accurate since the concentration profile given by four points cannot exactly predict the profile throughout the capsule, they should be sufficiently accurate to indicate whether segregation alone can explain the measured losses in efficiency. The heat storage efficiencies of capsules 1, 2, 3, 5, and 6 which had been measured during the fluidized bed experiments (part 1) are given in the last column in Table 11. For the “fresh” capsule, only 91% heat storage efficiency was measured, while segregation calculations indicate that a 99% efficiency would be expected. This suggests that about 8% of the decrease in efficiency is due to factors other than bulk segregation for fresh capsules. On the average, 89-90% heat storage efficiency was expected from segregation tests from capsules 3 and 4, but only 59% was realized in practice. The sum of the contributions of factors other than bulk segregation to the loss of efficiency is therefore approximately 30% of the theoretical heat storage capacity for this case. For capsules 5 and 6, the discrepancy is again about 30%. Herrick and Zarnoch (1979) introduced the term “microencapsulation” to refer to the burying of sodium sulfate crystals, rendering them inaccessible to water. Microencapsulation may be responsible for the substantial loss in storage efficiency not accounted for by the macroscopic gradients in concentration, i.e., by bulk segregation. Microencapsulation may be augmented by an increase in the size of the crystals after the first few cycles and/or the formation of “chunks” of encapsulated precipitate. From the magnitude of the unaccounted losses of efficiency, it is clear that bulk segregation may well be less important than microencapsulation, depending on such factors as crystal size, degree of subcooling, cooling rate, etc. (c) Subcooling. Table III contains the results of cooling tests carried out in Erlenmeyer flasks with different borax concentrations. Under vigorous mixing conditions, Glauber’s salt without borax as the nucleating agent was found to subcool to 16.6 “C, compared to its crystallization temperature of 32.4 “C (Hodgins and Hoffman, 1955). The nucleation temperature is seen to increase with addition of borax but levels out a t about 4 wt % borax. The crystallization temperature decreases with borax concentration but remains almost constant above 3% borax. Under vigorous stirring, 4 wt % borax is probably optimal for achieving a low degree of subcooling without sacrificing
-*----0
Nucleation temp.
4 Crvstalization
d0
43
i0
temo
5’5
WEIGHT PERCENT SODIUM SULFATE
Figure 6. Average nucleation and crystallization temperatures for capsules of different compositions.
the crystallization temperature. The effect of agitation can be seen by comparing the results in Table I11 for 4% by weight borax. For the test in which only the supernatant liquid was gently stirred without disturbing the bottom precipitate, the nucleation and crystallization temperatures fell to 28.3 and 30.4 “C, respectively, compared with 30.4 and 31.8 “C for vigorous mixing. Telkes (1975) reported that 3-5 w t % borax initiates Glauber’s salt crystallization at 27.2 O C . The degree of mixing was not reported, but these tests were likely carried out under fixed bed conditions. I t would appear that part of the improvement in heat storage capacity under mixing conditions is due to a reduced degree of subcooling. The nucleation and crystallization temperatures measured by a thermocouple 1.0 mm from the bottom inside surface of the capsule subjected to gentle agitation are plotted against sodium sulfate concentration in Figure 6. The sodium sulfate concentration is seen to have little or no influence on the crystallization temperature in the concentration range studied. The nucleation temperature rises to a weak maximum of 27.4 “C a t 44.1% by weight sodium sulfate and levels out a t higher concentrations a t about 26.7 “C.The lower nucleation temperature at 39.5 wt % sodium sulfate is likely due to a decrease in the amount of borax in crystal form because of its dissolution in the extra water. The results of the tests with two thermocouples in the capsules are shown in Figure 7. For fixed bed conditions (Figure 7a), nucleation starts near the wall. Temperature gradients in the gently agitated capsules (parts b and c of Figure 7) are significantly less than in the fixed capsules (part a). In addition, the cooling period to reach the nucleation temperature is longer in the fixed capsule. The higher crystallization temperature was transported almost immediately to the center from the bottom in the agitated capsules, whereas there was a considerable time delay in the fixed capsule. Almost equal crystallization temperatures a t the bottom and center of the gently agitated capsules (parts b and c ) indicate that the sodium sulfate concentration at the center is a t or above 33.4 wt % (the solubility of sodium sulfate in water a t 32.4 “C).As soon as Glauber’s salt is formed, however, the concentration at the center decreases and the crystallization temperature decreases. At a higher overall sodium sulfate concentration (Figure 7c), the decline begins a t a later time because of the higher concentration of sodium sulfate a t the center. For the fixed capsule (Figure 7a), the crystallization temperature is low, and it is difficult to estimate the time at which crystallization begins because of the temperature difference between the bottom and center. Subcooling and
Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 689
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Figure 7. Temperature vs time for two positions inside capsules cooled in a water bath at 25 O C : (a, top) fixed capsule, composition D (see Table I); (b, middle) gentle agitation, composition D; (c, bottom) gentle agitation, composition B.
low rates of heat transfer can reduce the heat storage efficiency. While the present results do not indicate the magnitude of the reduction, they do indicate that the reduction will be minimized by vigorous stirring, by higher sodium sulfate concentrations, and by improved heat transfer within the capsules.
Discussion In general, efficiencies were somewhat higher in the drum than in the rotating tube a t corresponding speeds, presumably because collisions of the capsules with the inner surface of the drum helped redisperse crystals which settled while capsules were lifted from the bottom of the drum. However, the difference in efficiencies was only 1-10%, indicating that collisions do not play an overriding role for the conditions studied. At low speeds, some stratification was observed in the capsules. An increase in rotational speed is more effective a t higher Na2S04
concentrations (see Figure 2), probably because of a larger air space (leading to more vigorous mixing) for capsules with higher Na2S04concentrations. The maximum heat storage efficiency for capsules containing stoichiometric Glauber’s salt with 4 % borax was about 83%, achieved at a rotational speed of about 25 rpm in the rotating drum. Hence, even with vigorous mixing it was not possible to recover 100% of the theoretically expected heat storage capacity from a eutectic (44.1 w t %) Glauber’s salt mixture. Since a uniform suspension of the anhydrous salt crystals appeared to be maintained in the drum tests, it would appear that prevention of segregation by macroscopic mixing is not sufficient to assure complete recovery of the theoretical heat storage capacity. Even if all crystals remain in suspension, some anhydrous sodium sulfate can apparently still be enveloped by a layer of Glauber’s salt. The thermogravimetric analyses of samples from the capsules and the results of Herrick and Zarnock (1979) support this view. Microencapsulation of anhydrous sodium sulfate crystals also helps to explain the observed influence of mixture composition. Concentrations higher than 44.1% by weight result in a larger volume of anhydrous sodium sulfate precipitate upon incongruent melting of the mixture. Although part of the excess anhydrous Na2S04from the noneutectic portion is also enclosed by Glauber’s salt during crystallization, the remainder is hydrated to Glauber’s salt, replacing sodium sulfate present in the initial Glauber’s salt portion of the mixture, now microencapsulated as anhydrous salt. If all available water forms Glauber’s salt, there should be 100% recovery of the theoretically possible heat storage capacity. Mixtures containing less than 44.1% by weight Na2S04form less anhydrous precipitate upon heating, leaving fewer anhydrous sodium sulfate crystals in the medium and hence less NazSO4to be enveloped by Glauber’s salt. Biswas (1977) suggested using a congruent melting mixture of sodium sulfate and water to avoid sodium sulfate segregation. A mixture of 33.4% by weight sodium sulfate and 66.6% by weight water melts congruently a t 32.4 OC. However, this composition does not prevent formation of anhydrous sodium sulfate crystals because the mixture undergoes some subcooling, even in the presence of borax. With 4% by weight borax present, nucleation usually starts a t about 27 “C. The solubility of sodium sulfate in water a t this temperature is about 24.5% by weight (Sozen, 1985). Although congruent melting compositions at first appear to prevent reduced efficiencies, the considerable decrease in the theoretical heat storage capacity at reduced sodium sulfate concentrations results in a smaller absolute heat storage capacity (Figures 4 and 5). In addition, congruently melting mixtures do not eliminate the need for mixing during thermal cycling since Glauber’s salt crystals settle under gravity. When the mixture is warmed, about 15% by weight Glauber’s salt crystals settle as anhydrous sodium sulfate crystals due to incongruent melting. Diffusion of sodium sulfate is too slow to dissolve the precipitate in the short cycle times encountered in most daily storage applications. Unless mixed, the upper layers remain unsaturated and the precipitate causes reduced heat storage efficiencies as for incongruent melting mixtures.
Schematic Model for Crystallization Steps The evolution of the contents of the capsules can now be described during a typical cycle to explain the fluidized bed results. Figure 8a shows schematically the conditions after first heating the Glauber’s salt to 32.4 O C . While borax is present both in solution (soluble part) and in the
690 Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988
Q-
b)
/
I \
At -27
/'-
\
C
-
C)
\
At
20 C
/
\-/' /
I I
Figure 8. Schematic showing changes in a capsule containing 96 wt % Glauber's salt and 4 w t % borax during a thermal cycle.
crystals, for simplicity it is excluded in the schematic presentation. Lidenotes the saturated sodium sulfate solution, Sithe anhydrous sodium sulfate crystals, and Li, the saturated solution in the interstices between the crystals. The solubility of sodium sulfate in water a t 32.4 "C is 33.4 wt %. Therefore, 16 wt % Glauber's salt in the capsule is expected to be in the form of anhydrous sodium sulfate crystals at 32.4 "C. When the capsule is cooled below 32.4 "C, we have shown that nucleation does not start until about 27 "C due to subcooling. In Figure 8b, L, is the saturated (24.3 wt % sodium sulfate) solution, S , represents the crystal which were present a t 32.4 "C (Figure 8a),Ssbdenotes additional crystals formed due to the decrease in solubility with decreasing temperature, and L,,is the saturated solution in voids between the crystals, assumed to be in the particulate form. During the transition from b to c, crystallization of Glauber's salt takes place. The form of the anhydrous sodium sulfate crystals before the crystallization of Glauber's salt is critical to the heat storage (or release) efficiency. Two extreme possibilities are a uniform suspension of crystals in the capsule and a single crystalline block at the bottom. It seems probable that a uniform suspension of crystals was obtained in the tests at a rotational speed of 25 rpm in the rotating drum where the heat storage efficiency was 83%. This indicates that causes other than bulk segregation account for a loss of about 17% of the theoretical heat storage capacity. Incongruent melting must be indirectly involved in this loss, but complete recovery solely by keeping the anhydrous sodium sulfate in suspension seems impossible. The first fixed bed cycle after the rotating drum and rotating tube experiments lies between the two extremes, with all crystals precipitated a t the bottom, but in particulate form rather than as a single crystalline block. A t 20 "C (Figure 8c), there would have to be a uniform solid containing only Glauber's salt if complete crystallization (100% heat storage efficiency) had been achieved. Since this is not the case, even when the crystals are uniformly suspended, there must be portions of the heat storage medium with different compositions. Sfrepresents anhydrous sodium sulfate present in b which has been hydrated to form Glauber's salt, S,, designates solid Glauber's salt precipitated from the saturated liquid (L, in stage 2), Lf denotes saturated sodium sulfate solution (15.2 wt % sodium sulfate a t 20 "C), and Lf,is also saturated sodium sulfate solution, the part of L,,in stage 2 which was unable to hydrate the precipitate. Under vigorous mixing, the contents would form an almost uniform mixture. For fixed capsules, there will be segregation similar to that indicated schematically in Figure 8c.
Figure 8d represents the first stage of the second cycle after the melting process. If the crystallization was performed under fixed bed conditions with no external agitation during melting, the sodium sulfate concentration in the liquid at the top of the capsule will remain a t about 15.2 wt % (saturation composition at 20 "C) because diffusion of sodium sulfate is too slow to saturate the solution, Lf, in the time needed for melting. The upper liquid, Li in Figure 8d, therefore remains unsaturated. The amount of sodium sulfate needed to saturate the liquid (Li) forms anhydrous sodium sulfate crystals and adds to the precipitate (Si).If no agitation is supplied before the second stage of each cycle, the sodium sulfate concentration in Lidecreases with each cycle, meaning that more anhydrous sodium sulfate precipitates, causing an additional loss in the heat storage efficiency. Upon repeated cycling, if sufficient agitation is not supplied, the anhydrous Na2S04precipitate has a tendency to form large lumps, decreasing the surface area available for hydration. This results in a loss in the heat storage efficiency. If the amount of mixing is sufficient to keep the anhydrous sodium sulfate crystals in a dispersed particulate form, the capsule will repeat stages a-c in each thermal cycle. In the fluidized bed in part 1,the agitation was sufficient to keep the liquid saturated in stage a of each cycle and to keep some anhydrous sodium sulfate in suspension. Therefore, the heat storage efficiency was reproduced in each cycle. On the other hand, some lumps of precipitate were observed in the fluidized capsules. As a result, the heat storage efficiency was only about 60%. During the first fixed bed cycle after the fluidized bed cycles, the heat storage efficiency of the capsules fell to 53.2%. The importance of having the precipitate in particulate form becomes evident when these values are compared with the 61.9% efficiency found during the first fixed bed cycle after the rotating drum and rotating tube experiments. The difference is clearly due to the presence of lumps in the precipitate. The agitation which accompanies fluidization improves the efficiency, but it is still below the first fixed bed cycle efficiency with a particulate precipitate.
Conclusions Jn the rotating tube experiments, full rotation of the capsules around a horizontal axis passing through their centers resulted in a heat storage efficiency of up t o 75-83% of the theoretical capacity for eutectic Glauber's salt mixtures with 4 wt % borax. Addition of collisions in the rotating drum led to a small increase in storage efficiency at the equivalent speed. The results demonstrate that it is not possible to recover the entire theoretical heat storage capacity of stoichiometric Glauber's salt mixtures, even under vigorous mixing conditions. Addition of excess sodium sulfate or excess water increased the heat storage efficiencies based on the theoretical heat storage capacities at those compositions. On the other hand, the heat storage capacity per unit volume or per unit weight of phase change material, the most important parameter from a system economics point of view, was found to be maximum between 44.1 wt % Na2S04 (eutectic Glauber's salt mixture) and 53 w t % Na2S04. Thermogravimetric analyses of samples from the capsules with different thermal cycling histories show that bulk segregation of anhydrous sodium sulfate is not the only reason for the loss of heat storage capacity. Microencapsulation of anhydrous sodium sulfate beneath a layer of Glauber's salt is a t least as important. Increased subcooling, larger crystal sizes, and shorter cooling periods
I n d . E n g . Chem. Res. 1988,27, 691-697
enhance microencapsulation. Four weight percent borax in Glauber's salt is effective in achieving a low degree of subcooling without unduly reducing the crystallization temperature. Both nucleation and crystallization temperatures increase with stronger agitation.
Acknowledgment
69 1
Chen, J.; Nelson, R. Report ORNL/TM-8543, 1983; NTIS, Washington, D.C. Cole, R. L.; Hull, J. R.; Lwin, Y.; Cha, Y . S. Report ANL-82-89,1983;
NTIS. Washindon. D.C.
Fouda, A. E.; Desiault,J. G.; Taylor, J. B.; Capes, C. E. Sol. Energy
1984, 32, 57. Herrick, C. S.; Golibersuch, D. C. Technical Information Series Report 77CRD006, 1977; General Electric Company, Schenectady,
NY.
Financial assistance from the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged.
Nomenclature
D, = inside diameter of capsule X,= distance coordinate measured downward from top inside surface of capsule Greek Symbol
= fraction of theoretical latent heat and sensible heat gained by contents of the capsules during heating cycle Registry No. Glauber's salt, 7727-73-3; borax, 1303-96-4; sodium sulfate, 7757-82-6.
Literature Cited Biswas, D. R. Sol. Energy
1977, 19, 99. Chahroudi, D. In Proc. Workshop on Solar Energy Storage Subsystems for Heating and Cooling of Buildings; NTS: Charlottesville, VA, 1975; p 56.
Herrick, C. S.; Zarnoch, K. P. Technical Information Series Report 79CRD249, 1979; General Electric Company, Schenectady, NY. Hodgins, J. W.; Hoffman, T. W. Can. J. Technol. 1955, 33, 293. Kelly, G. E.; Hill, I. E. N B S I R 74-634,Method of Testing for Rating Thermal Storage Devices Based on Thermal Performance; National Bureau of Standards: Washington, D.C., 1974. Marks, S. B. CHEMTECH 1982, March, 182. Marshall, R. In Proceedings of International Conference on Energy Storage; NTS: Brighton, UK, 1981; Vol. I, p 129. Methods of Testing Thermal Storage Devices Based on Thermal Performance; The American Society of Heating, Refrigeration and Air Conditioning Engineers: New York, 1977, Method ASHRAE 94-77. Sozen, Z. Z. Ph.D. Dissertation, University of British Columbia, Vancouver, 1985. Telkes, M. Ind. Eng. Chem. 1952, 44, 1308. Telkes, M. Proc. Workshop on Solar Energy Storage Subsystems for Heating and Cooling Buildings; NTS: Charlottesville, VA, 1975; p 17. Telkes, M. U.S.Patent 3 986 969, 1976.
Received for review April 2, 1986 Revised manuscript received October 6, 1987 Accepted December 4, 1987
A Critical Evaluation of the Plug-Flow Idealization of Tubular-Flow Reactor Data Andrew Hall Cutler,tt Michael Jerry Antal, Jr.,*tand Maitland Jones, Jr,e D e p a r t m e n t of Mechanical Engineering, University of Hawaii a t Manoa, Honolulu, Hawaii 96822, and D e p a r t m e n t of Chemistry, Princeton University, Princeton, N e w Jersey 08544
Numerous limitations accompany the use of the plug-flow treatment of tubular-flow reactor data. In this paper we present design criteria, summarizing the findings of earlier workers, which overcome these limitations and assure the legitimacy of the plug-flow idealization. By use of a laminar-flow reactor designed t o satisfy these criteria, studies were made of the vapor-phase thermolysis of tert-butyl alcohol, whose rate law is well established. A state-of-the-art nonlinear leasbsquares kinetics algorithm was used t o analyze the tubular-flow reactor data. When the plug-flow idealization was employed, calculated values of E and In A were found to enjoy good agreement with literature values obtained by using other techniques. These results lead us to conclude t h a t a well designed tubular-flow reactor can be a source of high-quality rate data when idealized as a plug-flow reactor. Because the magnitude of the renewable biomass resource within the U.S.A. is comparable to the national demand far gasoline (OTA, 1980), there is increasing interest in the thermochemical conversion of biopolymers to high-value chemicals and fluid fuels. High yields of vapor-phase monomers and related species are obtained when biopolymers are rapidly heated in an oxygen-free environment (Diebold and Scahill, 1985; Hopkins et al., 1984). Secondary reactions of these vapor-phase materials form more stable alkanes and alkenes as well as carbon oxides and water (Milne and Soltys, 1983; Antal, 1981, 1983a,b, 1985a,b). Because the hydrocarbon-forming reactions occur primarily in the vapor phase, fundamental studies of the thermolysis of vapor-phase species derived 'University of Hawaii at Manoa.
* Current address:
Energy Science Laboratories, P.O.Box
85608, San Diego, CA 92138-5608. f Princeton University.
0888-5885/88/2627-0691$01.50/0
from the pyrolysis of biopolymer materials, and related model compounds, are the key to the development of new technologies for utilizing the biopolymer resource. Unfortunately, both the pyrolytic vapors of biopolymer materials and the simpler model compounds which mimic their chemistry are condensable at room temperature and are often difficult to synthesize. Moreover, the hydrocarbon-forming thermolysis reactions typically begin above 600 "C, and some of their products are also condensable at temperatures below 300 "C. Becausde of these ccnstraints, conventional methods (including batch reactors, shock tubes, and turbulent-flow reactors) are not well suited for high-temperature, vapor-phase thermolysis studies of biopolymer-related materials. On the other hand, bench-scale tubular-flow reactors possess various design features which enable them to cope with the constraints imposed by biopolymer materials. For this reason, increasing attention (Antal, 1981, 1983a,b, 1985a,b; Stein et al., 1983; Cutler et al., 1987) is being given to the use 1988 American Chemical Society
