EXOTHERMIC BATCH PRODUCTIVITY OPTIMISATION VIA GENETIC AGLRITHM

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1 EXOTHERI TH PRODUTIVITY OPTIISTION VI GENETI GLRITH in Keng Tan, Heng Jin Tham and Kenneth Tze Kin Teo odelling, Simulation & omputing Laboratory, School of Engineering and Information Technology, Universiti alaysia Sabah, Jalan US, 884 Kota Kinabalu, Sabah, LYSI. Tel: +6883, Fax: hemical Engineering Programme, School of Engineering and Information Technology, Universiti alaysia Sabah, Jalan US, 884 Kota Kinabalu, Sabah, LYSI. Tel: +6883, Fax: STRT atch process is generally used to produce various high value-added products. lthough the batch productions are highly diverse, their common aim is to have an efficient control system to optimise the production of desired product while minimise the waste. In the traditional way, the goal is achieved by controlling the reactor temperature according to the predetermined optimal temperature profile. However, this optimal profile may not be able to limit the waste production. Hence, this work proposed genetic algorithm to perform optimisation of the batch productivity without referring to any reference values. ased on the simulation results, the genetic algorithm has better performance in raw materials utilisation than the predetermined optimal temperature profile. INTRODUTION atch process has attracted attentions due to its flexibility to handle various productions of high value-added product, such as specialty chemicals, agrochemicals, pharmaceuticals and etc. lthough batch process is able to adapt with different types of production, there is only one common aim which is to optimise the production of desired product while minimising the waste. Since there is no inflow and outflow during the process, the raw materials utility is fully relied on the reactor temperature especially for the exothermic reaction (Nisenfeld, 996). This is because the exothermic reactions will liberate heat during the process and consequently increases the reactor temperature. If the liberated heat is higher than the plant cooling capacity, the reaction will become unstable and hence, poses a safety issue to the plant personnel (Hazard Investigation, ). Previously, batch productivity optimisation is obtained by controlling the reactor temperature according to the predetermined optimal temperature profile (utaba et al., 6; Suatha and Pappa, ; Tan et al., ). lthough they can control the reactor temperature to follow the desired traectory effectively, the aim of minimising the waste may not be achieved. esides, the global price competition and escalating raw materials costs have also urged the batch industries to consider an effective way of utilising the raw materials (Fernandez et al., ). For these reasons, genetic algorithm is introduced to optimise the exothermic batch productivity. This work reports the performance of a G in exothermic batch process optimisation without referring to any reference values. The performance of the proposed G is then compared with the conventional dual mode controller (D) which uses the predetermined optimal temperature profile.

2 ETHODOLOGY atch Process odelling benchmark of batch process modelling, developed by ott and acchietto (989), is used in this study. It is assumed that a two-parallel, well-mixed, and irreversible liquid-phase exothermic reactions occur in the process, as shown in below. Reaction : + Reaction : + D where and are the raw materials, is the desired product, and D is the undesired by-product. Initially, all the raw materials are charged into the reactor and left to react for min. The acket surrounding the reactor is used to control the reactor temperature. Figure illustrates the schematic of the batch process system. ontroller T r gitator T Hot T c Valve Reactor Fluid flows out old Pump Flow meter Jacket Figure : Schematic of batch process system The dynamic modelling of batch process can be divided into two components: component balance and energy balance. The law of conservation of mass is applied to model the component balance of the reactor contents. The production/consumption rate of all substances and the each component balance are described in () and () respectively. R R k k () D R R ()

3 where R i is the reaction rate of Reaction i, k i is the reaction rate constant of Reaction i, is the molar concentration of substance n, and n is the changing rate of substance n. Since both of the reactions are temperature dependence, the reaction rate constant for both reactions can be modelled using rrhenius equation, as shown in (3). E k T ai k k exp i oi, where i =, (3) r where k i is the frequency factor of Reaction i, E ai is the activation energy of Reaction i, k is the oltzmann constant, T r is the reactor temperature in unit Kelvin. On the other hand, first law of thermodynamics is used to model the energy balance of reactor and acket. Equation (4) and (5) model the energy inside the reactor and acket respectively. dt ( Q r exo Q ) dt r dt F ( T T ) dt r V c Q (4) (5) where Q exo and Q are the exothermic heat released and heat transferred from acket to reactor respectively, r is total molar concentration of reactor contents, is the heat capacity of reactor contents, T and T c are the acket and fluid temperature respectively, F is the fluid flow rate, is the fluid density, is the heat capacity of the fluid, and V is the volume of the acket. The Q exo and Q can be defined as shown in (6) and (7) respectively. Here, the initial temperature for T r and T are assumed to be 5. exo i i, where i =, (6) (7) r r where H i is the enthalpy change of Reaction s, U is the heat transfer coefficient between the acket and reactor, r is the surface area of reactor conducts with the acket. Other important physical variables of the process are described in (8) and (9) respectively, where n =,,, D. The plant parameters are shown in Table I. (8) r n where is the heat capacity of substance n. n r n pr (9) 3

4 Table I Plant parameters Parameter Value Parameter Value Parameter Value W 3 kg kmol kj kmol - - E a /k 7 K W kg kj kmol - kmol - - E a /k K W 3 kg 7.57 kj kmol - kmol - - kg m -3 W D 6 kg kj kmol - kmol - - kg m -3. Gkmol kj kmol - - V.69 m 3 k o k o F s - 79 Pkmol - s -.58 m 3 s - Genetic lgorithm odelling U.687 kw m - - r 6.4 m G is proposed to optimise the exothermic batch productivity based on the biological to manipulate the acket inlet fluid temperature, T c with a sampling time of 6 sec. The framework of G is shown in Figure. First, the real-number chromosome representation technique is applied to represent the potential solutions (fluid temperature). fter a few trials, results showed that 5 population size is enough for this work. The manipulated variables are bounded in the range of to. Initialise Population Fitness Evaluation New Offspring Stopping riterion Reached? No Selection Yes Optimum Solution rossover utation Figure : Framework of genetic algorithm Reproduction Each chromosome is then evaluated by a fitness function in order to distinguish their suitability to the process optimisation. In this work, the fitter chromosome is able to maximise the production of the desired product while minimise the undesired product. The optimisation function, J as defined in () is applied to evaluate the fitness of each 4

5 chromosome. The chromosome with high fitness value will receive preferential treatment in procreation process later. Ranking selection technique is implemented to select the chromosomes into a mating pool so that the mating pool will not dominated by those high fitness value chromosomes. max J dt dt T c 6. 5 c D () During the crossover operation, two chromosomes (parents) are randomly selected from the mating pool. Then, with a probability of 9 %, both selected parents will exchange some of their information with each other and create two new chromosomes (offspring), whereas they have % of chances to duplicate themselves into the new generation. The blending (arithmetic) technique is employed in this crossover operation, as expressed in () and (). The first offspring generated using this technique is merely the compliment of the second offspring. () () where x i is the offspring i, P i is the parent i, and is the random number in [, ]. The newly created offspring will have a % chances to be mutated in order to avoid the potential solutions trap into the local maxima. During the mutation, a new chromosome is randomly selected from the entire solution space. The evolutionary process is stopped when th generation is reached, and it will return the optimal fluid temperature to the plant. Figure 3 illustrates the optimisation strategy using the G. G T c Plant Figure 3: lock diagram of batch optimisation via genetic algorithm RESULTS ND DISUSSIONS T r, T,,,, D In this study, the consumption rate of the limiting reactant (substance ) is limited to be kmol so that the optimisation performance of the proposed G and the D can be compared equitably. The configuration of the D is taken from ott and achietto (989), which is well tuned for this case. The optimisation performance of G and D are shown in Figure 4 and Figure 5 respectively. In general, in one cycle of batch process can be divided into three stages. t the beginning of the process (first stage), the reactor contents should be heated up to a certain temperature to enable the chemical reactions to take place. From the results, this circumstance happens during min to min when full heating is given to the reactor, and before the production starts. It can be observed from the Figure 4(b) that the fluid temperature determined by the G is not a smooth straight line during this period compared to the performance of D, as shown in Figure 5(b). This is because G is a stochastic search method that searches the optimal solution through the entire solution space. In some cases, such as a batch process, there is not only one optimal solution in the solution space, and hence it affects the G output response to have a small fluctuation. 5

6 The second stage can be categorised as the stage when the reaction rate increases rapidly. This stage is the critical stage due to the huge amount of exothermic heat being released and causes the reactor temperature to increase rapidly. Hence, the cooling system plays an important role in order to avoid the thermal runaway. The results show that the reaction starts when the reactor temperature is around 6, as shown in Figure 4(b) and Figure 5(b) at min. During the first part in this stage, both controllers continue to give full heating to the reactor whereas the cooling is given during the second part of this stage. For G, the full heating is given during min to min in order to speed up the production rate using high temperature, as shown in Figure 4(a), whereas the D only gives full heating during min to 8 min with the purpose of increasing the reactor temperature up to the reference point in the shortest time, as shown in Figure 5(b). It can be observed from the results that the waste production started at min due to the high temperature. In order to limit the waste production, the G gives full cooling during min to 3 min. onversely, the D tried to maintain the reactor temperature to the desired traectory than limit the waste production. Therefore the waste is produced linearly since min until the batch ends, as shown in Figure 5(a). 4 D 8 D 8 6 X: Y: X: Y: Time (min) (a) Production Profile X: Y:.7986 X: Y: Time (min) (a) Production Profile Reactor Jacket Fluid 4 Reactor Jacket Fluid Reference Time (min) (b) Temperature Profile Figure 4: Performance of genetic algorithm Time (min) (b) Temperature Profile Figure 5: Performance of dual mode controller 6

7 In the last stage, the G seems to slowly reducing the reactor temperature in order to limit the waste production, and at the same time ensuring the production of desired product is increased, as shown in Figure 4. The Figure 4(a) shows that the G is able to harvest 6.58 kmol of desired product and.796 kmol of undesired by-product D, whereas the D, as shown in Figure 5(a), only harvests 5.47 kmol of desired product and.4 kmol of undesired by-product D. The results show that the desired product harvested by the G is 5.3 % more than the D, whereas the waste produced by the G is 34.4 % less than the D. Hence, it can be concluded that the performance of G which does not referring to the reference temperature is able to optimise the raw materials utilisation more efficiently than the conventional method that follows the predetermined optimal temperature profile. Table II summaries the performance of the proposed G and the conventional D controller in optimise the batch productivity. Table II Performance of the proposed genetic algorithm and the conventional dualmode controller in optimising the batch productivity Optimisation Performance Genetic lgorithm Dual-ode ontroller Product (kmol) Undesired Product D (kmol) ONLUSIONS In this paper, G is proposed to optimise the raw materials utility for an exothermic batch process without referring to any optimal temperature profile. The performance of the developed G is examined using a benchmark exothermic batch process model. The results show that the proposed method can perform better than the conventional D which follows an optimal temperature profile. In future, the work will be focusing on optimising the G development in handling with various uncertainties and to improve the robustness of G. KNOWLEDGEENTS The authors would like acknowledge the financial support of Universiti alaysia Sabah (US) under Postgraduate Scholarship Scheme. REFERENES OTT,. J. & HIETTO, S Temperature control of exothermic batch reactors using generic model control. Industrial and Engineering hemistry Research, 8 (8), FERNNDEZ, I., RENEDO,. J., PEREZ, S. F., ORTIZ,. & NN,.. review: energy recovery in batch processes. Renewable and Sustainable Energy Reviews, 6(4): HZRD INVESTIGTION.. Hazard Investigation: Improving Reactive Hazard anagement. U.S. hemical Safety and Hazard Investigation oard. Washington, U.S. Dec. 7

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