Calculation of reactor volume

With cold shot cooling the calculation of reactor volumes by the versus curve becomes more complicated because different amounts of feed are involved in each stage. We can also cold shot cool with inert fluid. This will affect both the versus Xp and T versus Xp curves. 

Calculation of reactor volume and space time yields... 

The design of a continuous-flow reactor involves the calculation of reactor volume (V) required to achieve a specified conversion (x f) of the reactant given the amount of fluid (flow rate q) processed in the reactor and the concentrations of reactants (C,io) ir> the feed. The design equations are derived (Section 2.2.1) by writing the steady-state molal balance equation for the limiting reactant. The design equations for an ideal CSTR and an ideal PFR (represented in Figures 3.1 and 3.2) are as follows ... 

Assuming ideal gas behaviour, calculate the reactor volume needed for a 90% conversion of A if the process is conducted (i) isothermally at 1000 K and (ii) adiabatically with an inlet temperature of HOOK. 

The simultaneous solution of eqns. (72) and (79) when h is not zero is generally achieved by a numerical method which considers small increments in reactor volume and then iterates the calculation of the resulting temperature and fractional conversion in a manner similar to that described for Sect. 2.5.3 for a batch reactor. Cooper and Jeffreys [3] give an illustrative example, together with a computer flow diagram, for calculating the reactor volume. 

Retention factors were calculated using the equation retention factor = 1 + ln[a/(n -P i)]/x), where a is the amount of dendrimer inside the reactor after the experiment b the amount of dendrimer that went through the membrane x the number of reactor volumes flushed with substrate solution. 

RTD studies were carried out by Jagadeesh and Satyanarayana (lEC/PDD 11 520, 1972) in a tubular reactor (L = 1.21 m, 35 mm ID). A squirt of NaCl solution (5 N) was rapidly injected at the reactor entrance, and mixing cup measurements were taken at the exit. From the following results calculate the vessel dispersion number also the fraction of reactor volume taken up by the baffles. 

Calculate the reactor volumes required to process 100 liter/min of 3 molar A in the aqueous reaction A -4 2B for PFTR and CSTR reactors. 

Calculate the reactor volume to process 10 moles/h of to this conversion in... 

The Matlab program given in Figure 2.61 performs these calculations for a given value of reactor volume VR. 

Pick a value of reactor volume VR (to be varied over a range of values) and calculate the capital cost using the economic data given in Table 2.6. 

Sizing the reactor implies calculating, besides reactor volume, the heat-transfer area of the cooling coils and of the FEHE. We assume constant volumetric flows and coolant temperature, and neglect the temperature dependence of the reaction heat and physical properties. With these assumptions, the mathematical model of the reactor which includes the energy balance is given by ... 

STRs are usually never completely filled unless top withdrawal of the liquid is required. At the top of the reactor, we will allow some empty volume, called head space. Blaasel [15] recommends allowing 15% head space for reactors less than 1.9 m (500 gal) and 10% head space for reactors greater than 1.9 m (500 gal). After calculating the reaction volume, then add the headspace according to these rules to obtain the reactor volume. After calculating the reactor volume, select a standard reactor from a manufacturer. A standard reactor is less expensive than a reactor made-to-order. Table 7.3 lists standard-size reactors, which will vary somewhat from manufacturer to manufacturer. In Table 7.3, the rated capacity is the reaction volume, and the actual volume includes the head-space. Because the manufacturer has allowed for headspace in this case, we need not allow headspace according to the above rules. 

After calculating the reactor volume, the next step is to calculate the heat-transfer area. The reactant concentration, and therefore the heat-transfer rate decreases as the reaction proceeds. We have to calculate the heat-transfer area when the heat-transfer rate is a maximum, which is at initial conditions. First, calculate the initial rate of reaction, rAo, from Equation 7.8.4, and then calculate the heat transferred using Equations 7.8.1, 7.8.2 and 7.8.18 to 7.8.21. Next, determine the heat-exchanger type using Equations 7.8.11 and 7.8.15. 

When heating castor oil, drying oil and acetic acid forms. During the reaction the acid evaporates from the solution. Calculate the reactor volume, the type and area of the heat exchanger, and the mixer power. 

After selecting a reactor type and catalyst configuration, the next step is to calculate the reactor volume. Before undertaking a detailed calculation, we need to estimate the reactor volume. A quick estimate is sometimes needed to check an exact calculation or to prepare a budget for a proposal. For packed bed or homogenous reactors, the space velocity is a way of rapidly sizing reactors. Space velocity is defined as the ratio of the volumetric feed flow rate to the reaction volume or the ratio of mass feed flow rate to the catalyst mass. The volu-... 

First, select a reactor arrangement and catalyst configuration. The next step is to select a reactor model for calculating the reaction volume. An exact model of reactor performance must include mass transfer of reactants from the fluid to the catalyst sites within the pellet, chemical reaction, and then mass transfer of products back into the fluid. Table 7.13 lists the steps, and Figure 7.5 illustrates the processes involved. Here, only simple models are of interest to estimate the reaction volvune for a preliminary design. The reaction volume is that volume occupied by the catalyst pellets and the space between them. We must provide additional volume for internals to promote uniform flow and for entrance and exit sections. The total volume is called the reactor volume. After calculating the reactor volume, the next step is to determine the reactor length and diameter. 

The third way to check a numerical result—and perhaps the first thing you should do when you get one—is to see if the answer is reasonable. If, for example, you calculate that a cylinder contains 4.23 X 10 2 gf hydrogen when the mass of the sun is only 2 X 10 kg, it should motivate you to redo the calculation. Vou should similarly be concerned if you calculate a reactor volume larger than the earth (10 m ) or a room temperature hot enough to melt iron (1535°C). If you get in the habit of asking yourself, "Does this make sense every time you come up with a solution to a problem—in engineering and in the rest of your life—you will spare yourself considerable grief and embarrassment. 

The reaction described by the data i Tables 2-1 and 2-2 is to be carried out in a PFR. The entering molar flow rate is 5 mol/s. Calculate the reactor volume necessary to achieve 80% conversiou in a PFR. (a) First, use one of the integration formulas given in Appendix A.4 to determine the PFR reactor volume, (b) Next, shade the area in Figtae 2-1 which when multiplied by would give the PFR volume, (c) Make a qualitative sketch of the conversion, X, and the rate of reaction, down the length (volume) of the reactor. 

The previous examples show that if we know the molar flow rate to the reactor and the reaction rate as a function of conversion, then we can calculate the reactor volume necessary to achieve a specified conversion. The reaction rate does not depend on conversion alone, however. It is also affected by the initial concentrations of the reactants, the temperature, and the pressure. Consequently, the experimental data obtained in the laboratory and presented in Table 2-1 as -ta for given values of X are useful only in the design of full-scale reactors that are to be operated at the same conditions as the laboratory experiments (temperature, pressure, initial reactant concentrations). This conditional relationship is generally true i.e., to use laboratory data directly for sizing reactors, the laboratory and full-scale operating conditions must be identical, Usually, such circumstances are seldom encountered and we must revert to the methods described in Chapter 3 to olrtain — ta as a function of X. 

We have shown that in order to calculate the time necessary to achieve a given conversion X in a batch system, or to calculate the reactor volume needed to achieve a conversion X in a flow system, we need to know the reaction rate as a function of conversion. In tins chapter we show how this functional dependence is obtained. First there is a brief discussion of chemical kinetics, emphasizing definitions, which illustrates how the reaction rate depends on the concentrations of the reacting species. This discussion is followed by instructions on how to convert the reaction rate law from the concentration dependence to a dependence on conversion. Once this dependence is achieved, we can design a number of isothermal reaction systems. 

Calculate the reactor volume necessary to achieve 98% of the equilibrium conversion of benzene in a... 

---