Batch reactors cycle times

Suppose reaction 12.3-1 is carried out in a batch reactor of volume V on a continual basis. To determine the rate of production, we must take into account the time of reaction (t in equation 12.3-2) and the down-time (td) between batches. The total time per batch, or cycle time, is... 

Reactor design what must be the volume of the CSTR in order to achieve the same performance as the 5 m3 semi-batch reactor with time-cycle of 2 hours and a conversion of 99% ... 

Alkanolamide from Coconut Oil. A 2 1 cocodiethanolamide (CDEA) can be produced using 6 moles of diethanolamine and 1 mole of rehned and bleached coconut oil. The materials are charged with the reactor and a small amount of catalyst (0.25-0.3% sodium methylate or sodium hydroxide) is added. The temperature of the batch is increased to 70-75°C at normal pressure. After 90 min, the reaction is completed. For a 10-t batch, total cycle time from charging the materials, heating them up, allowing the reaction to proceed to completion, and transferring the finished product takes at least 4 h. 

Another reason for using different reactor sizes along the CSTR train is the variation of polymerization rate with monomer conversion. This factor is not a major consideration if the final conversion is modest as in the case of styrene-butadiene rubber (SBR) processes. Normal exit conversions are 55 to 65% in such systems, and the residual monomer is recovered and recycled. If a very high conversion is desired one must deal with the problem that the polymerization rate is low at high conversions. The final reactor in the series needs to be very large if the desired conversion approaches 100%. Likewise, batch reaction cycle times become large if high conversions are desired. 

Type Reactor Cycle Time Throughput (g) Handling Batches Per Day Throughput (g) 5 ... 

Figure 22.13 Set points and flow sequences of a batch reactor cycle ( denotes externally set function of time).

For batch reactors, account has to be taken of the time required to achieve a given conversion. Batch cycle time is addressed later. 

Clearly, the time chart shown in Fig. 4.14 indicates that individual items of equipment have a poor utilization i.e., they are in use for only a small fraction of the batch cycle time. To improve the equipment utilization, overlap batches as shown in the time-event chart in Fig. 4.15. Here, more than one batch, at difierent processing stages, resides in the process at any given time. Clearly, it is not possible to recycle directly from the separators to the reactor, since the reactor is fed at a time different from that at which the separation is carried out. A storage tank is needed to hold the recycle material. This material is then used to provide part of the feed for the next batch. The final flowsheet for batch operation is shown in Fig. 4.16. Equipment utilization might be improved further by various methods which are considered in Chap. 8 when economic tradeoffs are discussed. 

The batch cycle time has been reduced from 2.6 to 1.3 hours. This means that a greater number of batches can be processed, and hence, if there are two reactors each with the original capacity, the process capacity has increased. However, the increase in capacity has been achieved at the expense of increased capital cost for the second reactor. An economic assessment is required before we can judge whether the tradeoff is justified. 

From diese various estimates, die total batch cycle time t(, is used in batch reactor design to determine die productivity of die reactor. Batch reactors are used in operations dial are small and when multiproducts are required. Pilot plant trials for sales samples in a new market development are carried out in batch reactors. Use of batch reactors can be seen in pharmaceutical, fine chemicals, biochemical, and dye industries. This is because multi-product, changeable demand often requues a single unit to be used in various production campaigns. However, batch reactors are seldom employed on an industrial scale for gas phase reactions. This is due to die limited quantity produced, aldiough batch reactors can be readily employed for kinetic studies of gas phase reactions. Figure 5-4 illustrates die performance equations for batch reactors. 

With semi-continuous (more properly, semi-batch) reactors only part of the charge is added at the beginning of the cycle. Usually some reaction time is allowed to pass before the remaining part of the charge is added in a controlled manner. Sometimes... 

If the enzyme charged to a batch reactor is pristine, some time will be required before equihbrium is reached. This time is usually short compared with the batch reaction time and can be ignored. Furthermore, 5o Eq is usually true so that the depletion of substrate to establish the equilibrium is negligible. This means that Michaelis-Menten kinetics can be applied throughout the reaction cycle, and that the kinetic behavior of a batch reactor will be similar to that of a packed-bed PFR, as illustrated in Example 12.4. Simply replace t with thatch to obtain the approximate result for a batch reactor. 

Theoretically, the volume of a batch reactor is equal to that of a plug flow reactor however, batch reactors are never operated at 100% capacity and cycle times are always greater than reaction times. The combination of these leads to the conclusion that switching from B2C gives an inherent reduction in the reactor volume. 

A major problem to be solved for multiproduct plants is the occurrence of disparities in the cycle times and size requirements for the different stages. In the following it will be assumed that the size factors as well as the cycle times of all units are independent on equipment size. This assumption is usually relaxed in further stages of the design. In case of batch heating and cooling, or reactors operated in semi-continuous mode, this is necessary in order to adopt the cycle times to the capacity of equipment, which is related to batch size. 

With many batch processes, the production rate will decrease during the production period for example, batch reactors and plate and frame filter presses, and there will be an optimum batch size, or optimum cycle time, that will give the minimum cost per unit of production. 

Operating conditions. Optimization variables such as batch cycle time and total amount of reactants have fixed values for a given batch reactor system. However, variables such as temperature, pressure, feed addition rates and product takeoff rates are dynamic variables that change through the batch cycle time. The values of these variables form a profile for each variable across the batch cycle time. 

In Figure 14.24, the reactor limits the batch cycle time, that is, it has no dead time. On the other hand, the evaporator and stripper both have significant dead time. Figure 14.26 shows the schedule for an arrangement with two reactors operating in parallel. With parallel operation, the reaction operations can... 

Suppose Table 1-1 represents the yield obtained vs. time for each reactor cycle. If the reactor cycle is 8 hours and produces 15,000 lb of product per batch, then if the cycle time were cut to 5 hours the yield would be 13,250 lb per batch. The rates of production would be 1,875 lb / hr for the former and 2,650 lb / hr for the latter. For a plant operated 8,000 hours per year this would give a production rate of 15,000,000 lb / yr for the former and 21,206,000 lb / yr for the latter. A change of this sort would necessitate no increase in reactor capacity, but it would require changes in the recovery and recycle systems other than those solely due to the increase in capacity. 

The performance of a batch reactor may be optimized in various ways. Here, we consider the case of choosing the cycle time, tc, equation 12.3-5, to maximize the rate of production of a product. For simplicity, we assume constant density and temperature. 

The Diels-Alder liquid-phase reaction between 1,4-benzoquinone (A, C6H4O2) and cy-clopentadiene (B, C5H6) to form the adduct CnHm02 is second-order with a rate constant kx = 9.92 X 10 6 m3 mol 1 s 1 at 25°C (Wassermann, 1936). Calculate the size (m3) of a batch reactor required to produce adduct at the rate of 125 mol h 1, if cAo = cBo = 100 mol m 3, the reactants are 90% converted at the end of each batch (cycle), the reactor operates isothermally at 25°C, and the reactor down-time (for discharging, cleaning, charging)... 

A liquid-phase reaction, A products, was studied in a constant-volume isothermal batch reactor. The reaction rate expression is (-rA) = kAcA, and k = 0.030 min 1. The reaction time, t, may be varied, but the down-time, td, is fixed at 30 min for each cycle. If the reactor operates 24 hours per day, what is the ratio of reaction time to down-time that maximizes production for a given reactor volume and initial concentration of A What is the fractional conversion of A at the optimum ... 

The hydrolysis of methyl acetate (A) in dilute aqueous solution to form methanol (B) and acetic acid (C) is to take place in a batch reactor operating isothermally. The reaction is reversible, pseudo-first-order with respect to acetate in the forward direction (kf = 1.82 X 10-4 s-1), and first-order with respect to each product species in the reverse direction (kr = 4.49 X10-4 L mol-1 S l). The feed contains only A in water, at a concentration of 0.050 mol L-1. Determine the size of the reactor required, if the rate of product formation is to be 100 mol h-1 on a continuing basis, the down-time per batch is 30 min, and the optimal fractional conversion (i.e., that which maximizes production) is obtained in each cycle. 

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