Calculation of batch time

The procedure for the calculation of space time for a PFR is similar to the procedure for the calculation of batch time for a batch reactor as the design equations are similar. 

Graphical integration for calculation of batch time for Example 4.3... 

Calculation of the time required to reach a particular conversion is the main objective in the design of batch reactors. Knowing the amount of reactant converted, i.e. the amount of the desired product formed per unit volume in this reaction time, the volume of reactor required for a given production rate can be found by simple scale-up as shown in the example on ethyl acetate below. 

From Equation 7.8.5, calculate the batch time, ts. Because we do not have values for tp, tn, tc> and tsc for this reaction, we will have to make use of the times given in Table 7.10 for polymerization reactions. Except for the charging time and cooling times, select the worst case from Table 7.10. We will assume that it takes the same time to cool the reactor as it does to heat the reactor. We have some control over the time it takes to charge the reactor. By adjusting a control valve, assume that we can charge the reactor in 1.5 hours. Thus, the batch time, from Equation 7.8.5,... 

If the first reaction is slow and the second reaction is fast, it will be extremely difficult to produce species B. If the first reaction (formation of B) is fast and the reaction to form C is slow, a large yield of B can be achieved. However, if the reaction is allowed to proceed for a long time in a batch reactor, or if the tubular flow reactor is too long, the desired product B will be converted to C. In no other type of reaction is exactness in the calculation of the time needed to carry out the reaction more important than in consecutive reactions. 

We now have all the material available for the graphical calculation of distillation conditions by the McCabe-Thiele method. This is one of the most used and simplest methods for the calculation of batch and continuous distillations of binary mixtures. It involves the simplifying assumptions that the molar heats of evaporation of the components and their mixtures are identical, and there are no heat losses from the column the consequence ist that the vapour and liquid flow rates, in moles per unit time, are constant throughout any section of the column, provided there is no addition or withdrawal of material. 

This equation can be used for calculation of drying time in batch drying. Substituting this equation into Equation 3.112 and integration from the initial Xq to final moisture content Xf, the drying time is obtained... 

The punq) characteristic is again required to evaluate variable rate and pressure filtration. The result normally required is a calculation of the time taken to filter a knorvn volume or mass of slurry. The cake depth is also inportant as most filters are of the batch type and this d th must be less than the clearance within the filter. 

Fig. 10. Model calculations of the time development of transient T iring patterns in a batch reactor using the six-variable model of reactions (l)-(3) and (10). [MA]o = 3 x 10 M, [Llo = 8.2 X 10 M, [ClO lo = 1 X 10 M, [S]o = 0.1 M. Length is 5 mm shown horizontally. Total time is 30 minutes shown vertically. Number of gridpoints is 400. Rate constants and diffusion coefficients are in the fourth column of Table II.

The interactive studies were followed by a series of batch calculations in which the xenon atom was dragged at a constant rate from the cavity to a location well into the solvent (total distance of approximately 1.8 nm, depending on the starting location of the xenon atom) in fixed time intervals Ixitween 1... 

Equivalent-Area Concept The preceding equations for batch operations, particularly Eq. 11-35 can be appliedforthe calculation of heat loss from tanks which are allowed to cool over an extended period of time. However, different surfaces of a tank, snch as the top (which would not be in contact with the tank contents) and the bottom, may have coefficients of heat transfer which are different from those of the vertical tank walls. The simplest way to resolve this difficulty is to nse an equivalent area A in the appropriate equations where... 

The concept of a well-stirred segregated reactor which also has an exponential residence time distribution function was introduced by Dankwerts (16, 17) and was elaborated upon by Zweitering (18). In a totally segregated, stirred tank reactor, the feed stream is envisioned to enter the reactor in the form of macro-molecular capsules which do not exchange their contents with other capsules in the feed stream or in the reactor volume. The capsules act as batch reactors with reaction times equal to their residence time in the reactor. The reactor product is thus found by calculating the weighted sum of a series of batch reactor products with reaction times from zero to infinity. The weighting factor is determined by the residence time distribution function of the constant flow stirred tank reactor. 

The glycolysis of PETP was studied in a batch reactor at 265C. The reaction extent in the initial period was determined as a function of reaction time using a thermogravimetric technique. The rate data were shown to fit a second order kinetic model at small reaction times. An initial glycolysis rate was calculated from the model and was found to be over four times greater than the initial rate of hydrolysis under the same reaction conditions. 4 refs. 

In the flowshop example, when we branch, we have to calculate the start-times of the new batch to be scheduled. Here are the rules that can accomplish this ... 

For a single-product plant the calculation of equipment sizes is straightforward. First the limiting cycle time ti is determined using Eqn. (7.4-14) or Gantt charts. The batch size is then evaluated for an assumed production capacity Q and available production time H ... 

For the ZW (zero wait) policy idle times (slacks) between consecutively produced batches may appear in all stages including the one that defines the bottleneck. It should be noted that the slacks are only a function of consecutive pairs of batches. Therefore, the slacks for each pair of batches can easily be calculated a priori with the binary variable for any two consecutive batches ... 

If a batch process is being considered, or if the rate of energy generation or removal varies with time, it will be necessary to set up a differential energy balance, similar to the differential material balance considered in Chapter 2. For batch processes the total energy requirements can usually be estimated by taking as the time basis for the calculation 1 batch but the maximum rate of heat generation will also have to be estimated to size any heat-transfer equipment needed. 

Example 14.1 Consider again the chlorination reaction in Example 7.3. This was examined as a continuous process. Now assume it is carried out in batch or semibatch mode. The same reactor model will be used as in Example 7.3. The liquid feed of butanoic acid is 13.3 kmol. The butanoic acid and chlorine addition rates and the temperature profile need to be optimized simultaneously through the batch, and the batch time optimized. The reaction takes place isobarically at 10 bar. The upper and lower temperature bounds are 50°C and 150°C respectively. Assume the reactor vessel to be perfectly mixed and assume that the batch operation can be modeled as a series of mixed-flow reactors. The objective is to maximize the fractional yield of a-monochlorobutanoic acid with respect to butanoic acid. Specialized software is required to perform the calculations, in this case using simulated annealing3. 

A batch process consists of the four steps given in Table 14.7. For repeated batch cycles of the same process, calculate the cycle time for ... 

A batch process manufactures Product 1 and Product 2 in the same process. The manufacture of both products involves three steps with durations given in Table 14.9. Calculate the cycle time and makespan for one batch each of Product 1 and Product 2 with no delay between the two batches for ... 

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