Capacity with order batches

In a properly designed industrial scale reactor, feedstock conversion is achieved at a certain throughput capacity. In order to scale-up the reactor, heat and mass transport phenomena must be studied. This includes heat transfer phenomena, feedstock conversion kinetics and the movement of particles inside the reactor. In this work, both experimental and theoretical studies were carried out to investigate these phenomena. Two different configurations of moving and stirred bed reactors, the batch scale rotative and a continuous feed Process Development Unit (PDU), have been used to generate the data in accordance with the principle of similarity. A dynamic model to scale-up the reactor was then tested. 

A set of example problems were solved in order to test the proposed method. The one which will be presented here is the spesific problem tackled by Cerda et al. (1997), and later reconsidered and solved by Berber and Ozdemir (2003) with an objective of minimizing the total production time. This example is composed of 10 orders to be processed in 4 units, has 47 binary variables and 648 constraint equations All units are assumed to be available at the time of scheduling. Table 1 and 2 show the production and batch capacities of orders in every unit and set of predecessors, respectively. Production times of one batch of each product are given in Table 3, whereas the cleaning times are indicated in Table 4. 

On the other hand, if it is possible to use a temperature progression scheme and if one desires to obtain the maximum amount of the desired product per unit time per finit reactor volume, somewhat different considerations are applicable. If Ex > E2, one should use a high temperature throughout, but if E2 > Eu the temperature should increase with time in a batch reactor or with distance from the reactor inlet in a plug flow reactor. It is best to use a low temperature initially in order to favor conversion to the desired product. In the final stages of the reaction a higher temperature is more desirable in order to raise the reaction rate, which has fallen off because of depletion of reactants. Even though this temperature increases the production of the undesirable product, more of the desired product is formed than would otherwise be the case. Thus one obtains a maximum production capacity for the desired product. 

In order to validate the hypothesis mentioned above, the Ni retention capacity of the Lac Tio waste rock was estimated using a batch sorption test performed on a fresh (C1) and weathered (C4) sample, followed by a 3-step Sequential Extraction Procedure (or SEP). The batch sorption test was done using a 10 mg/L Ni solution with an initial pH of 6, an ionic force adjusted to 0.05 M with NaN03 and with a liquid/solid ratio of 25. Some of the batch sorption results are presented in Figure 3. 

A batch filling process involves a reaction, A + B = C. Initial charge of A is Vr0 liters at T0. B then is charged at the rate Vb liters/hr at Cb0 and T0. The enthalpy change of reaction, the density and the heat capacity are related by AHr/pCp = constant. The reaction is first order with respect to B. Obtain expressions for the behavior of T and nb with time. 

This is the most common mode of addition. For safety or selectivity critical reactions, it is important to guarantee the feed rate by a control system. Here instruments such as orifice, volumetric pumps, control valves, and more sophisticated systems based on weight (of the reactor and/or of the feed tank) are commonly used. The feed rate is an essential parameter in the design of a semi-batch reactor. It may affect the chemical selectivity, and certainly affects the temperature control, the safety, and of course the economy of the process. The effect of feed rate on heat release rate and accumulation is shown in the example of an irreversible second-order reaction in Figure 7.8. The measurements made in a reaction calorimeter show the effect of three different feed rates on the heat release rate and on the accumulation of non-converted reactant computed on the basis of the thermal conversion. For such a case, the feed rate may be adapted to both safety constraints the maximum heat release rate must be lower than the cooling capacity of the industrial reactor and the maximum accumulation should remain below the maximum allowed accumulation with respect to MTSR. Thus, reaction calorimetry is a powerful tool for optimizing the feed rate for scale-up purposes [3, 11]. 

An exothermal reaction is to be performed in the semi-batch mode at 80 °C in a 16 m3 water cooled stainless steel reactor with heat transfer coefficient U = 300 Wm"2 K . The reaction is known to be a bimolecular reaction of second order and follows the scheme A + B —> P. The industrial process intends to initially charge 15 000 kg of A into the reactor, which is heated to 80 °C. Then 3000 kg of B are fed at constant rate during 2 hours. This represents a stoichiometric excess of 10%.The reaction was performed under these conditions in a reaction calorimeter. The maximum heat release rate of 30Wkg 1 was reached after 45 minutes, then the measured power depleted to reach asymptotically zero after 8 hours. The reaction is exothermal with an energy of 250 kj kg-1 of final reaction mass. The specific heat capacity is 1.7kJ kg 1 K 1. After 1.8 hours the conversion is 62% and 65% at end of the feed time. The thermal stability of the final reaction mass imposes a maximum allowed temperature of 125 °C The boiling point of the reaction mass (MTT) is 180 °C, its freezing point is 50 °C. 

In order to increase the efficiency of such a batch process and to reduce the inconvenience of discontinuous operation when the extractor is decompressed and opened for replacing the spent material against fresh one the extraction volume is spread over three or four vessels. These are switched into the gas circulation in a battery-type sequence utilizing the countercurrent principle. This means the extractor containing already depleted material is first contacted with the fresh gas and the extractor with the fresh material containing the full extract concentration is contacted in the second or last position in order to benefit as much as possible from the dissolving capacity of the gas. 

Since this initial work, analysis of these batch systems has been further expanded to include reactant consumption, beginning with the work of Rice, Allen, and Campbell. Furthermore, an excellent study of stability with a generalized nth order reaction rate and the effect of the heat capacity of the reactor walls (when Le 1) was presented by Balakotaiah, Kodra, and Nguyen. They verified previous work which showed the boundary to runaway behavior occurs when two inflection points appear in the reaction trajectory between the initial and final states. In the limit of 7 oo and 6c = 0, the safe criteria under adiabatic conditions (a = 0) is given as B < Le + /n) and for highly exothermic reactions (B 1) with large cooling (a > 1) the safe criteria approaches Semenov s classical result x/B > e. 

The reactor stability decreases with increasing values of a, since the fraction converted at the peak temperature is lower when ATa j is higher. One study showed that the allowable value of 9 for a first-order reaction ranged from 2.4 to 1.1 as a increased from about 7 to 70 [11,12]. There have been many other studies of the stability of tubular reactors and batch reactors, and some complex correlations for the stability limit allowing for changes in coolant temperature with length and the thermal capacity of the reactor wall [13]. However, it is generally not necessary to get the exact stability limit. The conservative criterion that 6> < 1 is often used unless calculations for different conditions show that even with 9 > the reactor is definitely stable to all likely disturbances. 

To be applied industrially, performance must be superior to that of the existing catalytic systems (activity, regioselectivity and recyclability). The use ofionic liquid biphasic technology for nickel-catalyzed olefin dimerization proved to be successful and this system has been developed and is now proposed for commercialization. However, much effort remains if the concept is to be extended to non-chloroaluminate ionic liquids. In particular, the true potential ofionic liquids (and mixtures containing ionic liquids) could be achievable if an even more substantial body of thermophysical and thermodynamic properties were amassed in order that the best medium for a given reaction could be chosen. As far as industrial applications are concerned, the easy scale-up of two-phase catalysis can be illustrated by the first 0X0 commercial unit with an initial capacity of 100 000 tons extrapolated by a factor of 1 24 000 (batch-wise laboratory development to production reactor) after a development period of 2 years [4]. 

The excellent sorption capacity of the hypercrosslinked mesoporous poly-DVB with respect to selective removal of P2M from its mixtures with albumin and other semm proteins, combined with superior hemocompat-ibility of the beads surface modified with poly(N-vinyl)pyrrolidone, justified the manufacturing of an experimental batch of the material for initial clinical studies. The polymer was named BetaSorb (RenalTech International, USA) and was used in 300 mL cylindrical polysrdfone devices that were steam-sterilized and filled with normal saline containing 1000 lU heparin. The device was placed in line with the dialysis circuit, upstream of the dialyzer, in order to not affect the pressure drop across the dialyzer membrane. The blood flow was maintained at the customary value of 400 mL/ min, again the optimal flow rate for the dialyzer. The complete setup of the combined hemoperfusion-hemodialysis treatment [361] is displayed in Fig. 15.2. 

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