Batch reactors mean conversion

The process design of a batch reactor may involve determining the time (t) required to achieve a specified fractional conversion (/A, for limiting reactant A, say) in a single batch, or the volume (V) of reacting system required to achieve a specified rate of production on a continual basis. The phrase continual basis means an ongoing operation,... 

The participant A is identified by subscript a. Thus the concentration is Ca, the number of mols is na, the fractional conversion is xa, the partial pressure is pa, the rate of decomposition is ra. The capital letter A also is used on occasion instead of Ca. The flow rate in terms of mols is na but the prime ( ) is left off when the meaning is clear, The volumetric flow rate is V, reactor volume is Vr or simply V of batch reactors, the total pressure is... 

Kinetic data are frequently acquired in continuous reactors rather than batch reactors. These data permit one to determine whether a process has come to steady state and to examine activation and deactivation processes. These data are analyzed in a similar fashion to that discussed previously for the batch reactor, but now the process variables such as reactant flow rate (mean reactor residence time) are varied, and the composition will not be a function of time after the reactor has come to steady state. Steady-state reactors can be used to obtain rates in a differential mode by maintaining conversions small. In this configuration it is particularly straightforward to vary parameters individually to find rates. One must of course wait until the reactor has come to steady state after any changes in feed or process conditions. 

Batch Reactor. In a batch reactor there are no inlet or outlet streams In = Out = 0. The total feed is charged into the reactor at the beginning and no withdrawal is made until the desired conversion level has been reached. Hence a reaction process occurring in a batch reactor is an unsteady one. All variables change with time. In addition, we assume that it is a perfectly mixed batch reactor, so that the concentrations of the reaction components, reactants or products are the same over the whole reactor volume. This assumption allows us to consider applying the mole balance equation across the whole reactor. With the term reactor we mean the space where the reaction(s) take place. For liquid phase reactions the reactor volume is smaller than the size of the physical reactor. It is the volume of the liquid phase, where the reaction ) take(s) place. 

Nevertheless, the presence of a catalyst does not induce apparently a much lower selectivity to char in the conversion of methoxyphenol. In our batch reactor conditions, the default to the molar balance is around 20% meaning a selectivity in light products around 70%. These figures are close to those reported by Pttrocelli and Klein [12] in similar batch reactor conditions. The... 

The heterogeneously catalyzed alkoxylation of alpha-pinene and limonene over beta zeolite provides excellent results in both a discontinuous batch reactor and a continuous flow-type apparatus with a fixed bed reactor. In both reactors, the use of methanol as addition compound and limonene as feedstock gives l-methyl-4-[alpha-methoxy-isopropyl]-l-cyclohexene with the yield of 85% (conversion 93%, selectivity 92%). By means of variation of the reaction parameters, the limonene conversion can be adjusted within the range 40 - 90%. The selectivity to 1-methyl-4-[alpha-methoxy-isopropyl]-l-cyclohexene always remains at about 95%. 

The test requires the use of a standard batch of gas oil as a feedstock and a set of equilibrium fluid cracking catalysts with consensus mean conversion values assigned in a reactor of specified design. The gas oil and the set of equilibrium cracking catalysts are useful reference materials. Conversion for any equilibrium or laboratory-deactivated fluid cracking catalyst can be measured and compared to a conversion calibration curve. Conversion is measured by the difference between the amount of feed used and the amount of unconverted material. The unconverted material is defined as all liquid product with a boiling point above 216°C. 

Segregated Flow A real example is bead polymerization of styrene and some other materials. The reactant is in the form of individual small beads suspended in a fluid and retarded from agglomeration by colloids on their surfaces. Accordingly, they go through the reactor as independent bodies and attain conversions under batch conditions with their individual residence times. This is called segregated flow. With a particular RTD, conversion is a maximum with this flow pattern. The mean conversion of all the segregated elements then is given by... 

Consider two sets of measurements of a random variable. X—for example, the percentage conversion in the same batch reactor measured using two different experimental techniques. Scatter plots of X versus run number are shown in Figure 2.5-1. The sample mean of each set is 70%, but the measured values scatter over a much narrower range for the first set (from 68% to 73%) than for the second set (from 52% to 95%). In each case you would estimate the true value of X for the given experimental conditions as the sample mean. 70%. but you wouid clearly have more confidence in the estimate for Set (a) than in that for Set (bp... 

Con.sequemly. if we have the batch reactor equation for X(/) and measure the RTD experimentally, we can find the mean conversion in the exit stream. Thus, if we have the RTD, the reaction rate expression, then for a segregated flow sih nation (i.e model), we have sufficient information to calculate the conversion. An example that may help give additional physical insight to the segregation Summary Motes model is given in the Summary Notes on the CD-ROM. click the Back button just before section 4A.2. 

The integral in the last expression above is not a simple form and is best evaluated by numerical means. Use of the expansion factor is limited to reactions where there is a linear relationship between conversion and volume. For reactions that have complex sequences of steps, a linear relationship may not be true. Then we must rewrite the rate definition for a batch reactor ... 

To meet sensible design requirements, a number of reactors have to be connected in series. This means that conversion per reactor unit will be low and the simplifications made for the batch reactor (Section 4.2.3) will also apply to the continuous reactor. 

The physical meaning of this similarity between batch and plug flow reactors is the following When a mixture of reactants is subjected to reaction conditions for a certain period of time t in a batch reactor, or when the same mixture is passed through a plug flow reactor, where the same reaction conditions prevail, with a residence time x = f, the conversion in both cases must be the same. To put it... 

The main reaction leading to the desired product P is so rapid, that in the bulk of the reaction phase the conversion of B is complete. The reaction may be carried out in a semi-batch reactor or in a continuous stirred reactor. The feeing time in the semi-batch reactor and the mean residence time in the continuous reactor do not influence the conversion of 5, that is practically complete anyway. However, the feed rate of B and the meso-mixing rate will determine the formation of the undesired byproduct X. Esentially, the critical phenomena in a semi-batch reactor and in a CSTR are the same for this process. 

It is considered to carry out the same reaction in an upflow column, with a catalyst of the same material, but with a diameter of 4 mm. Estimate the required reaction volume, for a mean residence time of the liquid phase of 30 minutes (it is expected that the conversion will be the same as in the batch reactor). The Thiele modulus is proportional to the particle diameter, so for the larger catalyst particles is approximately 16, and the effectiveness factor is 1/16 (see eqs. (5.48) and (5.50)). This means that the required catalyst volume is 16 times larger, that is 16 x 0.1 x 10 = 16 m. When the bed has a void fraction of 0.5, die total effective reactor volume has to be 32 m. But this is only correct if the process rate is still determined by chemical kinetics. The gas/liquid mass transfer would be a possible limiting factor. One can make the following estimate The bubble hold-up in a stirred tmik and in an upflow column will both be on the order of 0.2. The bubble diameter will be on the order of 1 mm in the stirred tank, and 2 mm in the upflow column (with particles of 4 mm). 

Very high degrees of conversion (of end groups) are required, which means that either a batch reactor has to be used, or a continuous reactor with extremely low backmixing. 

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