Varying-volume Batch Reactor

These reactors are much more complex than the simple constant-volume batch reactor. Their main use would be in the microprocessing field where a capillary tube with a movable bead would represent the reactor (see Fig. 3.20). 

The progress of the reaction is followed by noting the movement of the bead with time, a much simpler procedure than trying to measure the composition of the mixture, especially for microreactors. Thus, 

This kind of reactor can be used for isothermal constant pressure operations, of reactions having a single stoichiometry. For such systems the volume is linearly related to the conversion, or 

We see, then, that accounts for both the reaction stoichiometry and the presence of inerts. Noting that 

Replacing V from Eq. 63a and Np from Eq. 65 we end up with the rate in terms of the conversion 

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The rate of decomposition of gaseous ethylene oxide (QFUO), to CH4 and CO, has been studied by Mueller and Walters (1951) by determination of the fraction (/A) of oxide (A) reacted after a definite time interval (f) in a constant-volume batch reactor. In a series of experiments, the initial pressure of the oxide (P 0) was varied. Some of the results are as follows ... 

For gas-phase variable-volume batch reactors, like the one shown schematically in Figure 6.2, F/f(T) varies during the operation. Assuming ideal gas behavior, the... 

First, consider constant-volume batch reactors (reactors whose volumes do not change during the operation), Vr(t) = V/ (0). In practice, this condition is satisfied either for gas-phase reactions when the walls of the reactor are stationary or when the reaction takes place in a liquid phase. In the latter case, the assumption is that the density of the liquid does not vary during the operation. For most liquid-phase reactions, the density variations are indeed quite small. 

Example 3-6, Why is the equilibrium conversion lower for the batch system than the flow sy.siem Will this always be the case for con.stant volume batch systems For the case in which the total concentration Cju is to remain constant as the inerts are varied, plot the equilibrium conversion as a function of mole fraction of inerts for both a PFR and a constant-volume batch reactor. The pressure and temperature are constant at 2 atm and 340 K. Only N-Oj and inen 1 are to be fed. 

The design of production plants for the manufacture of the three categories of product varies considerably. Fine chemicals are usually produced in batch reactors, which may also be used for the production of a variety of similar products. Fine chemicals usually have demanding product quality specifications and, consequently, a significant fraction of the production costs are involved in product purification and testing. Intermediate volume chemicals have less rigorous quality specifications than fine chemicals and are usually manufactured in product-specific-plants, either as batch or continuous flow processes. Bulk chemical production plants usually operate continuous flow processes... 

In a formal sense, Equation (2.38) applies to all batch reactor problems. So does Equation (2.42) combined with Equation (2.40). These equations are perfectly general when the reactor volume is well mixed and the various components are quickly charged. They do not require the assumption of constant reactor volume. If the volume does vary, ancillary, algebraic equations are needed as discussed in Section 2.6.1. The usual case is a thermodynamically imposed volume change. Then, an equation of state is needed to calculate the density. 

Then, the quantity of heat that could be removed in batch reactors whose volume varies from 11 to 1 m is calculated. In order to compare with experimental results, the temperature gradient is fixed at 45 °C (beyond which water in the utility stream would freeze and another cooling fluid should be used). The maximum global heat-transfer coefficient is estimated at an optimistic value of 500 W m K h The calculated value of the global heat transfer area of each batch reactor. A, is in the same range as the one given by the Schweich relation [35] ... 

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 ... 

When the density varies with conversion, the analogy between the batch reactor and the PFTR dt dx) is no longer appropriate. In the batch reactor with ideal gases, the density varies with conversion in a constant-pressure reactor but not in a constant-volume reactor. In a flow reactor, the reactor volume is fixed, no matter what the density. In a flow reactor the volumetric flow rate changes with conversion if there is a mole number change with ideal gases. 

If the compositions vary with position in the reactor, which is the case with a tubular reactor, a differential element of volume SV, must be used, and the equation integrated at a later stage. Otherwise, if the compositions are uniform, e.g. a well-mixed batch reactor or a continuous stirred-tank reactor, then the size of the volume element is immaterial it may conveniently be unit volume (1 m3) or it may be the whole reactor. Similarly, if the compositions are changing with time as in a batch reactor, the material balance must be made over a differential element of time. Otherwise for a tubular or a continuous stirred-tank reactor operating in a steady state, where compositions do not vary with time, the time interval used is immaterial and may conveniently be unit time (1 s). Bearing in mind these considerations the general material balance may be written ... 

The equations used for these simulations of fed-batch reactors are similar to Eqs. (4.3)-(4.6), but the reactor volume is time-varying and a feed term is present ... 

If fluid density does not vary with conversion, use same plots as for constant-volume batch, with reactor space time t substituted for time t. 

For batch-reactor systems in which the volume varies while the reaction is proceeding, the volume may usually be expressed either as a function of time alone or of conversion alone, for either adiabatic or isothermal reactors. Consequently, the variables of the differential equation (2-6) can be separated in one of the following ways ... 

However this "definition" is wrong It is simply a mole balance that is only valid for a constant volume batch system. Equation (1-1) will not apply to any continuous-flow reactor operated at steady state, such as the tank tCSTR) reactor where the concentration does not vary from day to day (i.c.. the concentration is not a function of time). For amplification on this point, see the section "Is Sodium Hydroxide Reacting " in the Summary Notes for Chapter 1 on the CD-ROM or on the web. 

Vary the parameters and plot A as a function of r. [2nd Ed. P4-31] Designed to reinforce the basic CRE principles through very straightforward calculations of CSTR and PER volume.s and batch reactor lime. This problem was one of the most frequently assigned problems from the 2nd Edition. [2nd Ed. P4-4]... 

Now we can really see why the CSTR operated at steady state is so different from the transient batch reactor. If the inlet feed flow rates and concentrations are fixed and set to be equal in sum to the outlet flow rate, then, because the volume of the reactor is constant, the concentrations at the exit are completely defined for fixed kinetic parameters. Or, in other words, if we need to evaluate kab and kd, we simply need to vary the flow rates and to collect the corresponding concentrations in order to fit the data to these equations to obtain their magnitudes. We do not need to do any integration in order to obtain the result. Significantly, we do not need to have fast analysis of the exit concentrations, even if the kinetics are very fast. We set up the reactor flows, let the system come to steady state, and then take as many measurements as we need of the steady-state concentration. Then we set up a new set of flows and repeat the process. We do this for as many points as necessary in order to obtain a statistically valid set of rate parameters. This is why the steady-state flow reactor is considered to be the best experimental reactor type to be used for gathering chemical kinetics. 

Steady state. We would, however, like to demonstrate that it is still possible to achieve the specific concentration associated with that steady state. Certainly, this will require a special operating regime to achieve (which shall be detailed in the following sections), but this will always be with the intention that the reactor is operated under bateh conditions—that is, with a distinct cycle time where the state variables of the batch reactor (volume, concentration, etc.) do, in fact, vary for the duration of this period. 

In a closed system, such as a batch reactor, the characteristic property varies with the reaction time. In an open system (such as continuous reactor), it varies with position or space time. In this case, the space time is defined as the ratio between the volume or mass of the reactor system and the inlet mixture flow. The schematic representation of the two systems is displayed in Figure 1.1. 

For gas-phase reactions, such as in a plug-flow batch reactor at constant pressure, the volume varies according ... 

The fundamental equations above describing the operation of stirred-flow reactors are valid whether the reaction takes place at constant volume or not. It is important to distinguish here carefully between the volume of the physical enclosure in which the system reacts and the volume V occupied by a given mass of the reacting system. Both are not necessarily equal. Furthermore, while it is clear that F, is practically invariant, F almost always varies with extent of reaction in an isothermal system, except if the reaction mixture is an ideal gas contained in a batch reactor or passed through a flow reactor (provided that in the latter case the reaction is not accompanied by a change in number of moles). 

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