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Optimization of the Temperature Profile of a Temperature Gradient Reactor for DME Synthesis Using a Simple Genetic Algorithm Assisted by a Neural Network Kohji Omata, Toshihiko Ozaki, Tetsuo Umegaki, Yuhsuke Watanabe, Noritoshi Nukui, and Muneyoshi Yamada* Tohoku University, Graduate School of Engineering, Department of Applied Chemistry, Aoba07, Aramaki, Aoba-ku, Sendai 980-8579, Japan Received October 15, 2002
Dimethyl ether (DME) from natural gas or coal via syngas (3CO + 3H2 f DME + CO2) attracts much attention as a high quality diesel fuel of the next generation. Considering the compact process based on the small-scale carbon resources, both low-pressure operation (at 1-3 MPa) and high one-pass conversion (90% CO conversion) are required to produce DME economically. A temperature gradient reactor (TGR) was effective for overcoming both the equilibrium limit of the reaction at high temperature and the low activity of the catalyst at low temperature. For example, 90% CO conversion and high STY (1.1 kg-MeOH eq./kg-cat./h) was attained at the same time in TGR at 280-240 °C, 3 MPa. For higher performance of the TGR, in the next step, optimization of the temperature gradient was required. A homemade program according to a genetic algorithm (GA) was used for the optimization. The catalyst bed was divided into 5 zones in series. The temperature of each zone was encoded to “gene” and the fitness of the “gene” was evaluated by CO conversion obtained in the reactor of which temperatures were set according to the gene. After a few generations of “evolution”, CO conversion (70%) higher than that in a conventional isothermal reactor (66%) was achieved at 1 MPa. For higher CO conversion, neural network, trained by the results in the preceding generations, was used to evaluate the “gene”. By this combination of GA and neural network, evolution of the temperature profile was accelerated and successfully optimized to give 71% CO conversion.
Introduction Dimethyl ether (DME), the target product of this study, has many advantages when it is used as a diesel fuel. So, it is one of the superior candidates for highquality diesel fuel in the next generation. From these points of view, DME production attracts much attention from companies such as NKK, Halder Topsoe A/S and Air Products & Chemicals for industrialization in a large-scale process. While it is synthesized in an industrial process by dehydration of methanol obtained from syngas, one-step DME process of 2500 t/d scale is required for economic production comparable with conventional LPG fuel according to the estimation by NKK.1 On the other hand, considering the compact process based on small-scale carbon resources, low pressure-operation and high one-pass conversion (90% CO conversion) are required to produce DME with high efficiency and good economics. More specifically, the process should be operated under the lower-limit of industrial process conditions, i.e., 5 MPa, or hopefully 1-3 MPa, comparable to the syngas pressure at the outlet of the reforming reactor. In such expected process, * Corresponding author. Tel: +81-22-217-7214. Fax: +81-22-2177293. E-mail:
[email protected]. (1) Adachi, Y.; Komoto, M.; Watanabe, I.; Ohno, Y.; Fujimoto, K. Fuel 2000, 79, 229-234.
both the recycling loop and pressure compression of syngas can be omitted, resulting in reduction of DME production cost. Since the direct synthesis of DME from syngas suffers from a severe equilibrium limit, catalysts to meet the above criteria are under development. The authors also prototyped a temperature gradient reactor (TGR).2 In a TGR, the temperature of catalyst bed at the inlet is high and the temperature of the catalyst bed decreases along with the down-flow of reaction gas as shown in Figure 1. While a high reaction rate is achieved to reach equilibrium conversion at the high temperature zone near the inlet, the conversion increases gradually along the temperature-equilibrium conversion curve toward the lower temperature zone. The possible conversion is determined by the equilibrium at reaction pressure and at the temperature at the outlet. High single-pass conversion of 90% and STY ) 1.1 kg-MeOH eq/kg-cat/h were achieved in TGR at the same time at 3 MPa.2 In the previous work, the temperature profile was fixed throughout the experiments. If the temperature profile is optimized, it is expected that the apparent activity is increased and operation at 1 MPa would be possible. In this study, the optimization was performed. (2) Omata, K.; Watanabe, Y.; Umegaki, T.; Ishiguro, G.; Yamada, M. Fuel 2002, 81, 1605-1609.
10.1021/ef0202438 CCC: $25.00 © 2003 American Chemical Society Published on Web 05/24/2003
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Figure 2. Multi-layered neural network. Figure 1. Configuration and temperature profile of TGR reactor; (9) setpoint, (b) reactor temperature.
Experimental Section Reaction. In-situ DME synthesis was performed in a tubular reactor made of stainless steel (SUS 316, 9.53 mm o.d., 7.53 mm i.d.). The reactor was heated by five outer ring heaters controlled by individual thermocouples and temperature controllers. When the temperature setpoint of each heater was the same, the reactor works as the conventional isothermal fixed-bed reactor. On the other hand, a temperature gradient was produced in the TGR by using a different temperature setpoint of each heater. A typical temperature setpoint and reactor temperature are shown in Figure 1. T1 is the temperature setpoint of the inlet zone, and T5 is that of the outlet zone. Because the catalyst beds are not isolated in the tubular reactor and insulation is not used between the heating ring, the temperature of the catalyst bed is influenced by the adjoining heater. Especially when the temperature setting is low and that of the above zone is very high, the temperature of catalyst bed can be higher than the setpoint. Copper catalyst (Su¨d-Chemie Catalysts Japan Inc., MDC-3), crushed and sieved to 20/30 mesh granules, was used for methanol synthesis, and γ-alumina (330 m2/g, 0.76 mL/g, 20/30 mesh) was used as a methanol dehydration catalyst. Both granules were mixed (1:1 by weight) in a transparent vial and charged in the reactor. The height of the catalyst bed was 12.5 cm. Syngas (H2/CO/CO2/Ar ) 60/30/5/5) was used for both activation and reaction. Activity of the mixed catalyst was measured at 1 MPa. The flow rate was 44 mmol/h and catalyst weight was 2.2 g (W/F ) 50 g h mol-1). Products and reaction gas were analyzed with micro-GC equipped with TCD (Agilent technologies, Model M-200, with molecular sieve 13X and PPU column). Main products were DME and CO2. Small amounts of methane and methanol were formed. It takes about 1 h to measure CO conversion at steady state after changing temperature settings. So about 10 to 15 kinds of temperature profile were tested daily. If a temperature profile is the same as that in the former generation in the optimization step, the CO conversion measured at the former generation was again used for evaluation. Since the same catalyst was used, at the first and the last runs of the day, CO conversion under standard conditions was
checked to confirm the reproducibility of catalytic activity. CO conversion was used as fitness of every gene. Theory. Among the many optimization methods, the genetic algorithm (GA) attracted much attention because of its features. It has analogies to natural evolution processes. At first, the real world is coded as a gene, usually in binary code. Then the gene evolves by natural selection. GA performs a multi-directed search by maintaining a population of potential solution and encourages information generation. The authors successfully applied GA using binary code as gene for catalyst optimization for methanol synthesis.3 Using the program and HTS (High Throughput Screening) reactor,4 we found a new optimum catalyst composition for the low-pressure reaction.5,6 In the optimization of the methanol synthesis catalyst, steps of determination of catalyst composition by GA program, catalyst preparation, activity test, and feedback to GA program, were repeated before satisfactory optimization. While in that case catalyst preparation is automated and activity test is parallelized i n that case, the activity test is not parallelized in optimization of TGR. The activity test is, therefore, ratedetermining in the optimization loop. So, a neural network was also used for mapping of the catalytic activity to replace the laborious experimental activity test. The network consists of an input layer, association layers, and an output layer (Figure 2). The neurons in these layers are connected to all neurons in the adjacent layers but not to those in the same layer. The trained neural network was used instead of experimental steps to evaluate the temperature profile. Among many type of a neural network, a back-propagation network (BPN) has been successfully applied to catalyst design by estimating the relationship between material properties and its catalysis. In their pioneering work, Hattroi and Kito applied BPN to investigate the basicity of mixed oxide, activity for butane oxidation, selectivity for oxidative dehydrogenation of ethyl benzene, and so on.7 BPN is also a promising tool to (3) Omata, K.; Umegaki, T.; Ishiguro, G.; Yamada, M. Sekiyu Gakkaishi (J. Jpn. Pet. Inst.) 2001, 44 (5), 327-331. (4) Omata, K.; Ishiguro, G.; Yamada, M. Sekiyu Gakkaishi (J. Jpn. Pet. Inst.) 2000, 43 (4), 317-319. (5) Omata, K.; Umegaki, T.; Watanabe, Y.; Ishiguro, G.; Yamada, M. Shokubai (Catalysts & Catalysis) 2001, 43 (6), 379-381. (6) Omata, K.; Umegaki, T.; Watanabe, Y.; Yamada, M. Prepr. Pap.s Am. Chem. Soc., Div. Fuel Chem. 2001, 46 (2), 408-409. (7) Hattori, T; Kito, S. Catal. Today 1995, 23, 347-355.
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process and generalize experimental data. It can facilitate approximation of catalytic activity under untested reaction conditions.8-11 The tool is also useful for optimization of catalyst composition.12 Hou et al. reported the active catalyst for ammoxidation of propane optimized using BPN trained by 23 experimental data. After training, BPN can show the relation between catalyst component (P, K, Cr, Mo, V, Al2O3/ SiO2 ratio) and the activity. Cundari et al. combined BPN with GA as an optimization tool to find a better catalyst on the basis of Hou’s data.13 In this study, GA alone was first applied for optimization of the temperature profile of TGR. The temperature profile was optimized with the homemade GA program used for catalyst composition optimization.3 The temperature profile was expressed as 30-bit binary code. Every 6 bits expresses the setpoint of the temperature controller according to the following equation:
setpoint ) 100 + 3 × n
(1)
where n is a decimal of the 6 bits binary code. For example, the temperature setpoint in Figure 1 is coded to “111000011101011001101100101100”. The first 6 bits “111000” is 56 () 32 + 16 + 8) and the setpoint ) T1 ) 100 + 56 × 3 ) 168. In the same manner, T2 ) 187, T3 ) 175, T4 ) 232, and T5 ) 232 °C. Thus, 100-289 °C is assigned to each temperature controller; however, as shown in Figure 1, attention should be paid to the fact that the temperature profile of the catalyst bed is the result of the temperature setting and the temperature profile itself is not the controllable variable. Selection by roulette rule, one-point crossover, and mutation were included in the program. From the parent generation, genes with high fitness (in this case, high CO conversion) are selected stochastically. Then, some pairs exchange their code as crossover. For example, if (1110000111101011001101100101100) and (1010010101110110101010101001001) exchange the code at 1, then the resulting codes are (111000011110110101010101001001) and (101001010101011001101100101100) with higher or lower fitness. After that, some codes get mutation, by which the bit code is altered. For example, a mutation at 1 1 1 of (11100001111011011101010101001001) results in (111000011110110001010101001001). Thus genes of the next generation are decided. Only the fitness evaluation routine was modified to convert the binary code into a temperature setting. Population size was 20, probability of crossover was 10%, and probability of mutation was 1.5% in the program. Neural Connection (SPSS Inc.) was used to build a neural network. The number of nodes of the input layer is 5, as shown in Figure 2, which accept T1, T2, T3, T4, and T5, while the output layer of one node gives CO conversion. The numbers of nodes of the two hidden layers were 18 and 4. This architecture was determined by trial and error to achieve rapid training without overtraining.
Results and Discussion Catalytic activity was measured in a conventional isothermal fixed-bed reactor. Maximum CO conversion (8) Kikukawa, N.; Makino, M. Shigen-to-Sozai 1994, 110, 479-486. (9) Sasaki, M.; Hamada, H.; Kintaichi, Y.; Ito, T. Appl. Catal. A: General 1995, 132, 261-270. (10) Berger, D.; Landau, M. V.; Herskowitz, M.; Boger, Z. Fuel 1996, 75 (7), 907-911. (11) Sharma, B. K.; Sharma, M. P.; Roy, S. K.; Kumar, S., Tendulkar, S. B.; Tambe, S. S.; Kulkarni, B. D. Fuel 1998, 77 (15), 17631768. (12) Hou, Z.-Y.; Dai, Q.; Wu, X.-Q.; Chen, G.-T. Appl. Catal., A: General 1997, 161, 183-190. (b) Huang, K.; Chen, F.-Q.; Lu¨, D.-W. Appl. Catal., A: General 2001, 219, 61-68. (13) Cundari, T. R.; Deng, J.; Zhao, Y. Ind. Eng. Chem. Res. 2001, 40, 5475-5480.
Figure 3. Effect of temperature on CO conversion in an isothermal reactor at 1 MPa, H2/CO/CO2/N2 ) 60/30/5/5, W/F ) 10, 50 g h mol-1.
was 66% at 250 °C, 1 MPa, W/F ) 50 g-h/mol (Figure 3). At higher temperature CO conversion decreases by an equilibrium limit, while at lower temperature CO conversion is low because of a low reaction rate. The advantage of a TGR will be clarified if CO conversion in a TGR is higher than the 66% CO conversion of the isothermal reactor. Temperatures at the reactor inlet (top layer, T1) and outlet (bottom layer, T5) during optimization are shown in Figure 4. Because the squares are plotted according to only T1 and T5, it is possible that T2, T3, and T4 are different from each other even if two squares are overlapped. Likewise, the activity of adjoining squares may be different. While T1 converges on 268 °C, T5 convergence is not clear especially after the fifth generation. These phenomena would suggest that better genes appear in the descending generation. In Figure 5, CO conversion at first-eighth generations are illustrated. The CO conversions of every generation are sorted and only those higher than 66% are shown in the figure; thus, if the resulting CO conversion by some temperature profile ()gene) is below 66%, the bar is not drawn in Figure 5. As shown clearly, the maximum CO conversion increases and the population of high CO conversion also increases as generation alternation proceeds. Temperature profiles for the maximum CO conversions (a) in an isothermal reactor, (b) at first generation, (c) at third generation, and (d) at fifth generation are shown in Figure 6. The maximum CO conversion was, 66.4%, 67.6%, 68.1%, and 70.1%, respectively. In the TGR used in this study, thermal insulation between the temperature zones is not enough. So, five layers influence one other. A desirable temperature profile for high CO conversion is that shaped like an S-curve. It should be difficult to calculate and find the setpoint, especially at the third reactor layer shown in Figure 6d because the influences from second and fourth layer are so complicated. This result suggests an excellent advantage of optimization using GA. As shown in Figure 5, the maximum conversion record at the fifth generation is not broken until the eighth generation, where the average CO conversion
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Figure 4. Convergence of temperature profile of the TGR.
Figure 5. CO conversion over 66% at every generation in the TGR at 1 MPa.
decreases reversely. As described in the “Theory” section, genes of the next generation are selected stochastically. So it is even possible that the best gene of the generation does not survive to the next generation. In this case, gene #11 or #12 in the seventh generation could not survive to the eighth generation. Furthermore, a new convergence point of T5, as shown in Figure 4, appears at 100 °C after the sixth generation, while almost all of the genes aggregate at the fifth generation. These phenomena suggest the maximum at the fifth generation is not the global maximum but rather the local one. To find the global maximum, more generation alternation will be required. It demands, however, much
experimental effort and time because the TGR reactor is not parallelized. The neural network of the back-propagation type (BPN) was applied to learn the relation between temperature setting and the resulting CO conversions. Seventy-five individual settings in the first to seventh generations were used for training, and 5 settings of the eighth generation were used for validation to avoid overtraining of back-propagation. The numbers of nodes of the hidden two layers were 18 and 4 with which backpropagation proceeded smoothly without over-training. The trained BPN was used as a fitness evaluation subroutine in the GA program. Figure 7 shows the
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Figure 6. Temperature profile for maximum CO conversion (a) in the isothermal reactor and at (b) first, (c) third, (d) fifth generation; (9) setpoint, (b) reactor temperature.
Figure 7. network.
“Evolution” of CO conversion on the neural
maximum CO conversion of each generation after the experimental eighth generation. It increases rapidly after the 25th generation to reach 98% at the 39th generation.
Figure 8. Operations for a new generation.
Similar phenomena are often observed in natural evolution. If a new combination of gene with high fitness to environment appears by mutation or crossover, the evolution will be accelerated. The change of the best gene before and after the CO conversion jump at the 31st and 32nd generations was investigated as shown in Figure 8. The best gene in the 31st generation can be generated from the best in the 30th generation by mutation. If the 22nd bit is converted from 1 to 0, CO conversion increases from 78.1% to 82.4%. On the other hand, three mutations are necessary for evolution from the best in the 31st generation to the best in the 32nd generation. It never happens in our program. Only crossover between the good genes can explain the appearance of the best gene. Between the sixth and seventh bits, they exchange their code as shown in Case 2 in Figure 8. The important point is that such useful evolution does not occur easily. Before that, the population of excellent genes should be increased because all operations are based on a stochastic process. So, a
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Since the training data is derived from the “evolution process” during the first to seventh generations, it should contain bias and should not distribute uniformly. The BPN was then retrained using the experimental result of the above maximum setting and isothermal (250 °C) data. The optimum temperature profile predicted from the retrained BPN is illustrated in Figure 9. The CO conversion was experimentally measured again, and 71.1% CO conversion was achieved this time. Conclusion
Figure 9. Temperature profile for maximum CO conversion by retrained neural network; (9) setpoint, (b) reactor temperature.
plateau is often observed before rapid evolutionary improvement. CO conversion should be lower than the equilibrium conversion of 1 MPa and of the temperature of the reactor bottom. Since the bottom temperature is 196 °C at the 39th maximum setting and so the equilibrium conversion is over 95% (Figure 3), the predicted value is not an impossible value. The temperature setting of the maximum at the 39th generation (289, 226, 145, 238, 196 °C), however, resulted in 69.7% CO conversion in an experimental activity test.
A temperature-gradient reactor (TGR) was effective to overcome both the equilibrium limit of the DME synthesis from syngas at high temperature and the low activity of catalyst at low temperature. The optimization of the temperature gradient was attempted by genetic algorithm (GA). After a few generations, CO conversion (70%) higher than that in a conventional isothermal reactor (66%) was achieved. For further evolution, a neural network was introduced to evaluate the fitness of the gene instead of an experimental activity test. By this combination, evolution was accelerated and the temperature profile was successfully optimized to give the highest CO conversion (71%). Acknowledgment. We acknowledge financial support from Research for the Future Program of JSPS under the Project “Synthesis of Ecological High Quality Transportation Fuels” (JSPS-RFTF98P01001). EF0202438
