I n d . Eng. Chem. Res. 1990,29, 565-570
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PROCESS ENGINEERING AND DESIGN Continuous Flow System Demonstration and Evaluation of Thermal Efficiency for the Magnesium-Sulfur-Iodine Thermochemical Water-Splitting Cycle Susumu Mizuta" and Toshiya Kumagai Materials Research Division, National Chemical Laboratory f o r Industry, Tsukuba, Ibaraki 305, J a p a n
The Mg-S-I thermochemical water-splitting cycle, consisting of (1)redox reaction of sulfur dioxide and iodine with magnesium oxide in aqueous phase, (2) hydrolysis of magnesium iodide, (3) thermal decomposition of magnesium sulfate, and (4) thermal dissociation of hydrogen iodide, was studied. In reaction 1, magnesium sulfate is precipitated and separated from magnesium iodide solution by the common ion effect of magnesium ion under highly concentrated conditions. On the basis of the experimental results of the reaction conditions, yields of the constituent reactions, and the amount of water used in the cycle, thermal efficiency of the whole Mg-S-I cycle was evaluated to be 17-3970 as a function of the overall heat recovery (65-8576). A continuous flow system for the whole cycle including solid reactant transportation was developed and successfully demonstrated for 33 h with roughly constant production of 0.5 dm3 of hydrogen and 0.25 dm3 of oxygen per hour. Since the thermochemical water-splitting process was presented (Funk and Reinstrom, 1966) in 1966, a number of cycles have been proposed. Some of them were tried on a bench scale; however, no thermochemical cycle has ever been industrialized or commercialized. The present authors have studied the Mg-S-I cycle extensively since 1978 and at this time have succeeded in demonstrating the cycles with a continuous flow system including solid reactant transportation. Among the purely thermochemical cycle so far proposed, the Mg-S-I cycle system is considered to be the most feasible one for large-scale or industrial development. Because this is simple and all the operations and processes involved in the system are commonly used in chemical industries, the Mg-S-I watersplitting cycle is expressed as follows: 12(c)+ S02(g)+ 2H20(1)
343 K
H2S04(aq)+ 2HI(aq) (Rl-1)
343 K
2MgO(c) + H2S04(aq)+ 2HI(aq) MgS04(aq) + Mg12(aq) (R1-2) MgI2.6H20
673 K
MgO(c) + 2HI(g) + 5H,O(g)
MgSO,(c) SO&)
1268 K
MgO(c) + SO,(g)
1268 K
1268 K
S02(g) + '/202(g)
(R2) (R3-1) (R3-2)
(R4) 2HW HZk) + IZk) During the first part of the study (1978-1983), emphasis was placed on the process in which MgIz and MgSO, were not separated (Mizuta et al., 1978; Mizuta and Kumagai, 1979a, 1982a,b),where HI (H, evolving substance) and SO, (0,evolving one) were separated by the difference in decomposition temperatures of MgIz and MgS04. After fundamental studies of each cycle reaction (Kumagai et al., 1983, 1984a),batch system demonstration of the whole
cycle (Kumagai and Mizuta, 1983,1985; Mizuta and Kumagai, 1984,1985) was successfully performed by repeating the cycle operations 38 times, where solid reactants remained stationary and HI and SO3 gases were separately evolved at different stages by the temperature swing of reactants and apparatus. With this successful batch system demonstration, each of the constituent reactions was confirmed and the feasibility of the cycle was proved. Further studies were performed to evaluate thermal efficiency and to demonstrate a continuous flow system of the whole cycle including solid reactant transportation for the Mg12-MgS04 separating process. Although some of the results were published in part (Kumagai et al., 1984b; Kumagai and Mizuta, 1986; Mizuta and Kumagai, 1986), this publication gives a comprehensive and conclusive report of the final stage of the Mg-S-I cycle study.
Review of the Constituent Reactions and Separation in HI Decomposition On the basis of experimental results in the equilibrium and kinetic studies, yields obtained for (Rl-l), (R1-2), (R2), (R3-11, (R3-2) and (R4) were 100, 95-10070, 95-loo%, 40%,99%, and 3170, respectively. Although temperatures as high as 1373 K are usually required for complete decomposition of MgSO, ((R3-1)), a 40% yield has been found to be achievable even at 1268 K when a carrier gas (air, for instance) is used (Kumagai et al., 1984a). Since the maximum yield of (R4) (equilibrium conversion) is 3170even a t 1268 K, several methods were studied for the separation of H2 from the mixed gas (H2, HI, 12, HzO) produced by (R4): (i) quenching from the reaction temperature to low temperature (1268 373 K), (ii) selective absorption of HI by MgO (MgO absorption method (Mizuta and Kumagai, 1979b)),and (iii) gas-phase electrolysis of HI (Kondo et al., 1983). The MgO absorption method is a gas separation process which the present authors have developed by taking advantage of the reversibility of (R2). Hydrolysis of MgI, hydrate ((R2))proceeds in the following
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o s a a - ~ a a ~ ~ ~ o ~ ~0 ~ 1990 ~ ~ American - o ~ ~ Chemical ~ ~ o ~ Society .~o~o
566
Ind. Eng. Chem. Res., Vol. 29, No. 4, 1990
Table I. Reaction Condition, Yield, and Enthalpy Change for Each of the Constituent Reactions of the Mg-S-I Cycle for the Calculation of Thermal Efficiency reaction or Drocess temD. K vield. % AH",kJ.mol-' 100 -153.2 (at 343 K) (Rl-1) 343 100 -299.8 (at 343 K) (Rl-2) 343 100 +350.4 (at 473 K) (R2-1) 473 +69.1 (at 523 K) 100 523 (R2-2) +86.8 (at 673 K) 100 673 (R2-3) +269.3 (at 1268 K) 31 1268 (R3-1)' +96.4 (at 1268 K) 100 (R3-2)" 1268 +13.5 (at 1268 K) 31 1268 (R4) -89.5 (at 523 K) 100 523 (R5)b 100 373 evaporation 100 condensation 373 l o 1 Quench method Icose A )
"Using carrier gas (air/S02 = 5 ) . bMgO absorption method.
three steps as previously reported (Mizuta and Kumagai, 1979~):
433-493 K
MgI,*GH,O(c) Mg(OH)I*H,O(c) + HI(g) + 4H,O(g) (R2-1)
I
322MqS0,
'
493-553 K
Mg (OH)I.H~O(C) '/,Mg,(OH)J(c) '/Mgz(OH)J(c)
+ '/zHI(g) + l/HzO(g) (R2-2)
553-673 K
MgO(c) + 1/2HI(g)+ 1/HzO(g) (R2-3)
Magnesium oxide selectively absorbes HI gas alone from the mixed gas (H,, HI, I,, H,O) at about 523 K, producing Mg2(OH),I by the following reaction (the reverse reaction of (R2-3)): MgO(c) + 1/HI(g) + '/H2O(g)
(-47591
i b l Ouench method Icose E l
-523 K
'/zMgz(OH)J(c) (R5) Yields of 80-95% have been experimentally obtained for this reaction. The residual gas (Iz, H,, and H20) is separable by cooling, while the absorbed HI gas is completely regenerated at 673 K by (R2-3). By use of this method, the excess amount of undecomposed HI (69% total HI) can be eliminated from H2 and recycled between 523 and 673 K without being cooled down to low temperature. Among these three separation processes, quenching is the most convenient to demonstrate the whole cycle because of its simplicity; however, it has not yet been determined which process is the most economical and feasible.
2 ZZMqSO,,ZMgO
(-375 5 )
I C )MgO absorption nethod I case
Evaluation of Thermal Efficiency For an evaluation of thermal efficiency, the reaction conditions and yield in the Mg-S-I cycle were chosen as shown in Table I based on the experimental results. The enthalpy change for each of the constituent reactions was also listed. Yields for (Rl-l), (Rl-2), (R2-1), (R2-2), (R2-3), (R3-2), (R5), evaporation, and condensation were reasonably set at 100%. The ratio of the amount of carrier gas to that of SOz (air/S02 in moles) in (R3-1) and (R3-2) was set at 5.0. Since the yield of (R4) (equilibrium conversion) is 31% even at 1268 K, that of (R3-1) was therefore set at 31 % in order to balance the O2 and H2 production. By use of the values shown in Table I, the thermal efficiency of the whole cycle was evaluated for the following three typical cases (Kumagai et al., 1984b). Case A. (i) The ratio of the amount of H 2 0 to that of Mg12produced by (Rl-1) and (Rl-2) (Hz0/Mg12in moles) is set a t 50; (ii) the quenching process from the reaction temperature to low temperature (1268 373 K) is adopted for the separation of H2 from the mixed gas (H,, HI, 12,
-
,
C1
Figure 1. Material and heat flow sheets of the Mg-S-Icycle. Heat inputs (+) and outputs (-) are indicated in brackets in kilojoules. Heat input for (R2) includes enthalpies of reaction and of heating the materials from 473 to 673 K.
H,O) produced by (R4). This case nearly corresponds to the operating conditions of the batch system demonstration previously reported (Kumagai and Mizuta, 1983,1985; Mizuta and Kumagai, 1984, 1985). Case B. (i) H20/Mg12 is set at 10; (ii) quenching is adopted for the separation of H2 (similar to case A). This case roughly corresponds to the operating conditions of the continuous flow system demonstration to be described later. Case C. (i) H20/Mg12is set at 10 (similar to case B); (ii) the MgO absorption method is adopted for the separation of H2. Material and heat flow sheets for cases A, B, and C are shown in Figure la, b, and c, respectively, for the production of 1 mol of HP. Since the yields of (R3-1) and (R4)
Ind. Eng. Chem. Res., Vol. 29, No. 4, 1990 567 Remaining in solution
O
l
285 8kJ
5 08 M 200
400
600
800
IO00
1200
200
400
600
BOO
1000
'
O
1200
10 i a 1 Quench method i cose B 1
0 Reaction enthalpy
m
15
20
25
30
i b l MqO ObSOrpllQn method (caseCi Evaporation or condensation
Haotinp or cooling materials
Figure 2. Heat input and output versus temperature for the production of 1 mol of Hz.
Figure 4. Separability of MgSO, from MgIz(aq) after SOz absorption with MgO and HI-Iz-HzO slurry a t 303 K.
N1 2 - M N r
mixed lokllm l H l , H 2 , l ~ , ~ O lmixed pas
WgSO,!!K
YpO t SO,
503-s02t302
'I'
MpO p a M r r
Figure 3. Concept for isolation of the HI evolving zone and SO, evolving zone by powder sealing. Table 11. Total Heat Input (ZQ'), Output (EQ-), and Thermal Efficiency (7) as a Function of the Overall Heat Recovery ( r n )for the Production of 1 mol of H,
case A case B case C
9955.7 4397.5 3320.3
9669.9 4111.6 3034.4
8 17 21
16 32 39
were 31%, almost 3 times the theoretical amount of sulfate and iodide is recirculated. Each of the heat inputs and outputs, shown in Figure l b and c, was classified into (i) the reaction enthalpy, (ii) the heat of evaporation or condensation, and (iii) the enthalpy of heating or cooling materials and plotted for a variety of temperature regions (343-1268 K) as shown in Figure 2. It is found that the heat requirements in the lower temperature region (300-700 K) are much larger than those in the higher one ( 1200 K). The thermal efficiency (77) is defined by the following equation N
where AHof(H20(l)),Q+i, 85, and rj are the enthalpy of formation of water (liquid state) at 298 K (-285.83 kJ. mol-'), heat input, heat output, and rate of heat recovery, respectively. Neither experimental nor reasonable data for heat recovery for each of the steps is available; thus, the overall (average) heat recovery (ri = constant = ro for all j ' s ) was assumed and set a t 65% or 85%. Calculated values of CQ+,CQ-,and 17 are shown in Table 11. It is found that the thermal efficiency of the cycle for case A (8-16%) is very low, while those for cases B (32%) and C (39%) are considered competitive enough with water electrolysis (-30%) when the overall heat recovery is set
Figure 5. Schematic diagram for continuous flow system demonstration of the Mg-S-I cycle (hydrogen-producing unit (top left), oxygen-producing unit (top right), Mg1,-MgSO, separating unit (bottom)).
at 85%. Generally speaking, the heat recovery (rj) is greatly dependent on the temperature difference between the heat input and output. Therefore, when the temperature dependence of heat recovery is taken into account, for example, ri is set at 100% for Ti C T j and 0% for Ti > Tj(the temperature level of heat input and output is denoted as Ti and Ti, respectively), the thermal efficiency decreases to 14% for case B and 22% for case C, respectively. On the other hand, if waste heat a t 300-700 K is cheaply available from some other heat sources such as chemical plants, steel making plants, or cement kilns, that is, if heat requirements lower than 700 K can be neglected, the thermal efficiency would be raised to more than 50%. At any rate, at this fundamental stage of research and development, it seems difficult to determine precisely the thermal efficiency value. The present authors consider that the value would exist between 15% and 50%.
Efforts To Improve the Thermal Efficiency As a result of the eyaluation of thermal efficiency as described above, it has become clear that the amount of H 2 0used in (Rl-1) and (Rl-2) should be reduced to about 10 mol per 1 mol of MgIz production. However, as previously reported (Kumagai et al., 1984a; Mizuta and Ku-
568 Ind. Eng. Chem. Res., Vol. 29, No. 4, 1990
A
Figure 6. Cycle apparatus. (a) Hydrogen-producing unit (reactor 2, reactor 4, and condenser). (b) Oxygen-producing unit (reactor 3 and reactor 1). (c) Mg12-MgS04 separating unit (filter (right) and evaporator (left)).
magai, 1984,1985), when the concentration of the mixed acid (H+)is higher than 4 mol/kg of H20 (i.e., the amount of H20 used in (Rl-1) is less than 55 mol), an unfavorable side reaction takes place as follows: H,SO,(aq) + 6HI(aq) S(c) + 312(c) + 4H20(1) (R6) Thus, a simple reduction of the amount of H 2 0 is impossible. On the other hand, MgO has been found to completely prevent this sulfur-formingreaction by quick production of MgI, and MgSO, through (Rl-2) even under highly concentrated conditions. Since the presence of MgO seemed essentially necessary to reduce the amount of H20, the present authors considered that MgO powder should be transported from the high-temperature area ((R2) or (R3)) to the low-temperature area ((Rl-1) and (Rl-2)) and that the mixed aqueous solution of MgSO, and MgI, produced in the low-temperature area should be transported back to the high-temperature area again. In addition, with respect to continuous transport of the Mg12-MgS04mixture from the low-temperature area to the high-temperature area, care should be taken to isolate the HI evolving zone from the SO3 evolving zone because mixing of these gases is dangerous as well as inefficient. For this purpose, an experiment on powder sealing was tried as shown in Figure 3. This attempt was unsuccessful since the complete sealing of the gases was incompatible with smooth powder flow. During this experiment, however, precipitation of MgSO, from the MgI, solution was found to occur under highly concentrated conditions. If MgI, and MgSO, are essentially separable, such an isolation process as powder sealing becomes unnecessary. Thus, an Mg1,-MgSO, separating process was chosen (Kumagai and Miguta, 1986, Mizuta and Kumagai,1986). In the next section, detailed experiments and results are described for the separation of MgI, and MgS0,.
-
Separation of MgIz and MgS04 in (Rl-1) and (Rl-2) Since the solubility of MgS0, in H 2 0 at 20 "C is 2.96 mol/kg of H20, while that of MgI, is 5.03 mol/kg of H20, the solubility difference between these two salts is not so
great. However, preferential precipitation of the hydrate of MgS04 was observed as the concentration of the mixed solution increased. To quantitatively clarify this phenomenon, the following experiment was performed. A mixed gas of SO2and 02,evolved by (R3-1) and (R3-2) (thermal decomposition of MgS0, and SO3), was introduced into a mixture of MgO powder and 12-HI-H20 solution, which corresponds to the products of (R2) and (M), containing excess MgO and HI (3.22 equiv) since the yield of (R4) is 31%. Whereupon the SO2alone was absorbed in the powder-solution mixture, 0,was separated, and a slurry of the hydrate of MgS0, with MgI, solution was obtained. After the filtration of the slurry, the precipitate and solution were analyzed. By X-ray powder diffraction analysis, MgSO4.7H20 or MgSO,=H,O was found in the precipitate, while the composition of the solution was determined by iodometry and chelatometry. Subtracting the excess amount of initially contained MgO and HI (finally converted to MgI,) from the total material balances, the net reaction is expressed as follows:
303 K
2MgO(c) + 12(c)+ mH20(l) + SO,(g) Mg12-(m-7)H,0(aq) + MgS04-7H20(c) (Rl)
+
373K
2MgO(c) + 12(c) mH20(1) + S02(g) MgI,.(m-l)H,O(aq) + MgSO,*H,O(c) (Rl') The fractions of MgSO, precipitated or remaining in solution at 303 K are shown in Figure 4 as a function of the amount of H 2 0 used (m = H20/12in moles). It is readily apparent that the fraction of MgSO, separated is higher as less H20 is used. When the precipitate is MgS04-7H20 at 303 K, satisfactorily high separability (>95%) appears for m < 20, and for an m value of 15, a yield of 98% is achieved. If the temperature of (Rl) is set at 373 K, the precipitate is MgSO4.H20,and the m value is expected to decrease to 10, which is close to the conditions for case B or C in the evaluation of thermal efficiency. This separability is much higher than the values expected by the difference in solubilities, so the result is considered to be attributable to the common ion effect of Mg2+. The filtration process was
Ind. Eng. Chem. Res., Vol. 29, No. 4, 1990 569 very fast and easy because the crystals of the hydrate of MgS0, were grown up to a size of 100 pm during the gradual bubbling of SO, gas in (Rl). Separation of MgSO, was found to be not only chemically but also physically smooth and successful. It should be emphasized that MgS0, can be separated only by the bubbling of SO, gas into the mixture of MgO, I,, and MgI, solution, while a simple evaporation of the mixed solution of MgI, and MgSO, would cause a formation of unfilterably small particles of hydrates of MgS0, or coprecipitation of both salts. The reason why the present authors failed to notice such a direct separation of MgSO, and MgI, during the early part of this study (Mizuta et al., 1978) is not only because the common ion effect of Mg2+was overlooked but also because the mode in order of mixing of the reactants was not varied. At any rate, it was confirmed that MgSO, and MgI, can be smoothly separated at satisfactorily high efficiency (>95%) with the m values of 10-15. The MgI,-MgSO, separating system has many advantages as follows: (1)The amount of H 2 0 used in (Rl) is small (10-15 mol of H20/MgI,, so that a thermal efficiency higher than 30% to case B or C ) is achievable. (2) The whole cycle system is flexibly divided into three subunits, namely, (i) Hz producing unit, (ii) O2producing unit, and (iii) MgI,-MgSO, separating unit. (3) Process design for a continuous flow system including solid reactant transportation is possible since special care for isolation of the HI evolving zone from the SO, evolving zone is unnecessary. From the viewpoint of scaling up the cycle apparatus, continuous solid reactant transportation is considered to be very important and necessary, not only to avoid the repetitious heating and cooling of the reactors but also to solve the problems concerning heat exchange between solid reactants and heating fluids.
Continuous Flow Demonstration On the basis of the fundamental and engineering studies described above, a continuous flow system (Kumagai and Mizuta, 1986; Mizuta and Kumagai, 1986) with solid reactant transportation was constructed to demonstrate the whole Mg-S-I cycle as illustrated in Figure 5. This demonstration roughly corresponds to case B. In this demonstration, quenching was adopted because of its simplicity. The MgO absorption method (case C) was avoided because of its associated engineering problems of the packed bed in the solid reactant continuous flow. Gas-phase electrolysis of HI was also avoided from a purely thermochemical standpoint. The cycle apparatus constructed is shown in Figure 6. The reactors were made of quartz and Pyrex glass, and electric furnaces were used as heat sources. The system consisted of three main parts: (i) H2 producing unit, (ii) 0, producing unit, and (iii) Mg1,-MgSO, separating unit. On this small laboratory scale, raking out or lifting up a small amount of hydrate of MgSO, to transport it from the filter to reactor 3 was considered inefficient and difficult (in the case of a large-scale plant, handling of a solid is far easier). Thus, we dissolved the hydrate of MgS0, again into H,O obtained by the partial evaporation of the MgI, solution. T o produce the MgSO, solution, excess water was used, and the total amount of water ( m value) was set at 30. Thus, the initial amount of the reactants was set at 1.5 mol of MgSO,, 1.5 mol of MgI,, and 45.0 mol of HzO. The detailed cycle operations concerned with Figure 5 are as follows. The MgI, solution, pumped up from the reservoir, is dripped into reactor 2. It is immediately dried and hydrolyzed by (R2) at 673 K. The HI evolved is allowed to thermally dissociate by (R4) at 1268 K in reactor 4, and the resultant gas mixture (H2-HI-12-H20) is con-
densed to separate H, from the HI-I,-H20 mixed solution. Similarly, the MgSO, solution, pumped up and dripped into reactor 3, is allowed to dehydrate and decompose by (R3) at 1268 K. The resultant SO2-0, mixed gas is bubbled in reactor 1 where (Rl) takes place to separate O2 and to regenerate MgI, and MgSO,. Since the solid product of (R2) and (R3), i.e., MgO powder, is not sticky, the quartz screw conveyers are easily rotated by small magnetic motors unless the dripping rates of the solutions are excessively higher than their evaporation rates (rate of heat supply from the electric furnaces). Thus, MgO powder is smoothly transported to the end of the reaction tubes and falls down into the condenser or reactor 1. The precipitated MgS04.7H,0 powder is separated by filtration. The powder is dissolved again into H,O obtained by the partial evaporation of the MgI, solution in order to recover the MgSO, solution. The whole system was successfully operated for 33 h, where all the chemical reactions proceeded smoothly and all the reactants including solids were circulated. Roughly constant production of 0.5 dm3 of H2and 0.25 dm3 of 0, per hour was achieved. No troubles such as side reactions or an accumulation of undecomposed reactants were found during the operation. If an automatic control system for the cycle apparatus is completely established, more than several hundreds or thousands of hours of operation would be possible. As described before, thermal efficiency of the cycle is greatly dependent on heat recovery and not necessarily higher than that of water electrolysis. However, facility investment for the cycle plant equipment is assumed to be far lower than that for the electric power generation plus electrolyzer system. Thus, if the total cost of hydrogen production from water and heat source is taken into account, the Mg-S-I cycle is considered still competitive with water electrolysis. Conclusion (i) Feasibility of the Mg-S-I cycle was completely confirmed by the continuous flow system demonstration including solid reactant transportation. The cycle can be operated below 1268 K when carrier gas is used for decomposition of MgSO,. (ii) On the basis of the experimental results of the reaction conditions, yields of the constituent reactions, and the amount of the water used in the cycle, the thermal efficiency of the whole Mg-S-I cycle was evaluated to be 17-39% as a function of the overall heat recovery (65-8570). Registry No. H,, 1333-74-0; O,, 7782-44-7; I,, 7553-56-2; SO,, 7446-09-5; MgO, 1309-48-4; MgI,, 10377-58-9; H,SO,.Mg, 748788-9; HI. 10034-85-2; water, 7732-18-5.
Literature Cited Funk, J. E.; Reinstrom, R. M. Energy Requirements in the Production of Hydrogen from Water. Ind. Eng. Chem. Process Des. Deu. 1966, 5 , 336. Kondo, W.; Mizuta, S.; Oosawa, Y.; Kumagai, T.; Fujii, K. Decomposition of Hydrogen Bromide or Iodide by Gas Phase Electrolysis. Bull. Chem. Soc. J p n . 1983, 56, 2504. Kumagai, T.; Mizuta, S. Laboratory Scale Demonstration of the Mg-S-I Cycle for Thermochemical Hydrogen Production. Chem. Lett. 1983, 679. Kumagai, T.; Mizuta, S. Laboratory Scale Demonstration of the Mg-S-I Cycle for Thermochemical Hydrogen Production. Ind. Eng. Chem. Process Des. Deu. 1985, 24, 795. Kumagai, T.; Mizuta, S. Continuous-Flow Demonstration of the Mg-S-I Cycle for Thermochemical Hydrogen Production. Chem. Lett. 1986, 1986, 125. Kumagai, T.; Okamoto, C.; Mizuta, S. Dissolution of MgO into the H,SO,-HI Acid Mixture. Nihon Kagaku Kaishi 1983, 1583. Kumagai, T.; Okamoto, C.; Mizuta, S. Thermal Decomposition of Magnesium Sulfate and Separation of the Product Gas Mixture. Denki Kagaku 1984a, 52, 812.
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Kumagai, T.; Shindo, Y.;Mizuta, S. Thermal Efficiency of the MgS-I Cycle for Thermochemical Hydrogen Production. Denki Kagahu 1984b, 52, 839. Mizuta, S.; Kumagai, T. Effect of Addition of Metal Ions on Separation of (H,SO,-HI) Acid Mixture. Proceedings of the 46th Annual Meeting of the Electrochemical Society of Japan, Osaka, May 1979a, A-104. Mizuta, S.; Kumagai, T. Selective Absorption of Hydrogen Iodide Gas by Magnesium Oxide. Denki Kagaku 1979b, 47, 105. Mizuta, S.; Kumagai, T. Hydrolysis of Magnesium Iodide Hexahydrate. Denki Kagaku 1979c, 47, 100. Mizuta, S.; Kumagai, T. Thermochemical Hydrogen Production by the Magnesium-Sulfur-Iodine Cycle. Chem. Lett. 1982a, 81. Mizuta, S.; Kumagai, T. Thermochemical Hydrogen Poduction by the Magnesium-Sulfur-Iodine Cycle. Bull. Chem. So?. J p n . 1982b, 55, 1939. Mizuta, S.; Kumagai, T. Progress Report on the Thermochemical Hydrogen Production by the Mg-S-I Cycle-Laboratory Scale Demonstration. In Hydrogen Energy Peogress V , Froceedings of the 5th World Hydrogen Energy Conference, Toronto, Canada.
15-20. J u l y 1984; Veziroglu, T. N., Taylor, J. B., Eds.; International Association for Hydrogen Energy, Pergamon Press: New York. 1984; Vol. 2, Chapter 9, pp 421. Mizuta, S.; Kumagai, T. Progress Report on the Thermochemical Hydrogen Production by the Mg-S-I Cycle-Laboratory Scale Demonstration. Int. J . hydrogen Energy 1985, 10, 651. Mizuta, S.; Kumagai, T. Progress Report on the Mg-S-I Thermochemical Water-Splitting Cycle-Continuous Flow Demonstration. In Hydrogen Energy Progress V I , Proceedings of the 6th World Hydrogen Energy Conference, Vienna, Austria, July 1986; Veziroglu, T. N., Getoff, N., Weinzierl, P., Eds.; International Association for Hydrogen Energy, Pergamon Press: New York, 1986; Vol. 2, Chapter 6, p 696. Mizuta, S.; Kumagai, T.; Hakuta, T. Hydrogen Production by the Thermochemical Decomposition of Water. Jpn. Patent 1067586, .Jpn. Tokugan Sho 53-163372, 1978.
Received f o r review March 13, 1989 Accepted October 23, 1989
Simultaneous Production Planning and Scheduling in Multiproduct Batch Plants Deepak B. Birewar and Ignacio E. Grossmann* Department of Chemical Engineering, Carnegie Mellon C'nicersitj, Pittsburgh, Pennsylvania 15213
Production planning and scheduling are intimately linked activities. T h e production goals set a t the planning level depend on marketing considerations but must account for the ability to implement them a t the scheduling level. Hence, ideally, planning and scheduling should be analyzed simultaneously. However, this is in general a very difficult task given the large combinatorial nature of just the scheduling problem in itself. In this work, based on a previously developed LP flowshop scheduling model by Birewar and Grossmann that can effectively aggregate the number of batches belonging to each product, a multiperiod LP model is proposed for the simultaneous production planning and scheduling of multiproduct batch plants that may consist of one or several nonidentical parallel lines. Inventory costs, sequence-dependent clean-up times and costs, and penalties for production shortfalls are readily accounted for in this model. The actual schedule to achieve the production goals predicted by the planning problem is derived by applying a graph enumeration method to the results from the simultaneous planning and scheduling model or by any other scheduling method. Several examples are presented to illustrate the proposed method.
Introduction Production planning and scheduling in multiproduct batch plants are closely related activities. The major objective in production planning is to determine production goals over a specified time horizon given marketing forecasts for prices and product demands and considerations of equipment availability and inventories. Thus, planning is basically a macrolevel problem that is concerned with the allocation of production capacity and time and product inventories, as well as labor and energy resources, so as to determine the production goals that maximize the total profit over an extended period of time into the future (e.g., a few months to a few years). Scheduling, on the other hand. is the microlevel problem that is embedded in the production planning problem and that is commonly considered only for a short-term horizon (e.g., order of a few weeks). Scheduling involves deciding upon the sequence in which various products should be processed in each equipment so as to meet the production goals that are set by the planning problem. A major objective here is to efficiently utilize the available equipment among the multiple products to be manufactured to an extent necessary to satisfy the production goals. * Author to whom correspondence should be addressed.
Thus, its clear that decisions made at the production planning level have a great impact at the scheduling level, while the scheduling in itself determines the feasibility of carrying out the production plans. Thus, ideally both activities should be analyzed and optimized simultaneously. However, this is in general a very difficult task given that even optimizing the scheduling problem in isolation for fixed production demands is a nontrivial problem. Most optimization problems for scheduling have been shown to be NP-complete (Garey et al., 1976). This is, for instance, the case in the flowshop scheduling problem where each product follows the same sequence through a set of processing stages. Despite the apparent simplicity of flowshop scheduling, this problem can become computationally expensive to optimize for various scheduling policies like UIS (unlimited intermediate storage), FIS (fixed intermediate storage), NIS (no intermediate storage), and ZW (zero wait). UIS flowshop scheduling has been shown to be NP-complete for three or more stages (Garey et al., 1976). The ZW policy is NP-complete for makespan minimization if the number of stages is more than two (Graham et al., 1979). Suhami (1980) has shown that the NIS problem is NP-complete if the number of stages is greater than two. This implies that the computational effort required to solve these problems to optimality can be quite high given the potential exponential increase in
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