Variable volume reactor operation

Variable Volume CSTR Operation (Fed-Batch and Transient Reactor Operation)... 

Solution. Note that this is a variable volume reactor since it operates at a constant temperature and pressure. The rate expression for the reaction, r, is... 

Flow reactors usually operate more nearly at constant pressure, thus at variable volume with gases. An apparent residence time is defined as the ratio of the reactor volume to the inlet volumetric rate,... 

It is obvious that if the gas-phase constitutes only one pure compound A, the use of eq. (3.365) is not sound, because it leads to zero values of the derivative and it seems that the equation is not needed. The latter is true only when the conversion of A is too low and so Qg can be considered practically constant. For systems of variable volume, eq. (3.360) or the equation derived in the previous example can be applied instead. The equation derived in the previous example specifically shows that it is the change of volume (flow rate) of the gas phase that affects the reactor operation and not the concentration change, since the concentration of A is constant throughout the reactor. Of course, the change of flow rate is due to the change in moles (xA is variable). 

So far in dealing with tubular reactors we have considered a spatial coordinate as the variable, i.e. an element of volume SV, situated at a distance z from the reactor inlet (Fig. 1.14), although z has not appeared explicitly in the equations. For a continuous flow reactor operating in a steady state, the spatial coordinate is indeed the most satisfactory variable to describe the situation, because the compositions do not vary with time, but only with position in the reactor. 

One important issue of the fed-batch operation is the variable volume of material in the reactor and its effect on heat transfer area. If jacket cooling is used, the heat transfer area covered by the liquid in the reactor will be proportional to the volume of the liquid at any point in time. However, if the reaction liquid is circulated through an external heat exchanger, the full heat transfer area is available throughout the batch cycle. 

Time is still an important variable for continuous systems, but it is modified to relate to the steady-state conditions that exist in the reactor. This time variable is referred to as space time. Space time is the reactor volume divided by the inlet volumetric flow rate. In other words, it is the time required to process one reactor volume of feed material. Since concentration versus real time remains constant during the course of a CSTR reaction, rate-data acquisition requires dividing the difference in concentration from the inlet to the outlet by the space time for the particular reactor operating conditions. 

Three forms of the reactor operator, R(Y), are shown in Figure 3. These are generally differential operators which operate on each monomer and polymer species to describe the effects of accumulation and the physical processes which move material in and out of the reactor or reactor element. The concentration of a specific species is given by the variable Y. In a simple batch reactor, the reactor operator, RB, is merely defined as the rate of accumulation of a certain species with time per unit volume of reactor—i.e., the rate of change of concentration of the species. 

The CSTR operator, Rc, has an identical term to describe accumulation under transient operation. The algebraic sum of the two other terms indicates the difference of in-flow and out-flow of that species. This operator also describes semibatch or semicontinuous operation in cases where the volume can be assumed to be essentially constant. In the more general case of variable volume, V must be included within the differential accumulation term. At steady state, it is a difference equation of the same form as the differential equation for a batch reactor. 

Polymerization reactions require stringent operating conditions for continuous production of quality resins. In this paper the chain-growth polymerization of styrene initiated with n-butyllithium in the presence of a solvent is described. A perfectly mixed isothermal, constant volume reactor is employed. Coupled kinetic relationships descriptive of the initiator, monomer, polystyryl anion and polymer mass concentration are simulated. Trommsdorff effects (1) are incorporated. Controlled variables include number average molecular weight and production rate of total polymer. Manipulated variables are flow rate, input monomer concentration, and input initiator concentration. The... 

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... 

Below, we analyze the operation of variable-volume, gaseous batch reactors and describe how to apply the design equation for different cases. 

The design equation for gaseous variable-volume batch reactors was derived under two assumptions (i) AU the species are gaseous, and (ii) the mixture behaves as an ideal gas. In some operations, one or more of the species (especially heavier products generated by the reaction) may be saturated vapor. In this case, any additional amount generated will be in a condensed phase (liquid). While the ideal gas relation provides a reasonable approximation for the volume of species in the vapor phase, it cannot be applied for dieir volume in the liquid phase. Below, we modify the design equations for a variable-volume batch reactor with saturated vapors. 

Discussed the operation of gaseous, variable-volume batch reactors. 

This problem requires an analysis of coupled thermal energy and mass transport in a differential tubular reactor. In other words, the mass and energy balances should be expressed as coupled ordinary differential equations (ODEs). Since 3 mol of reactants produces 1 mol of product, the total number of moles is not conserved. Hence, this problem corresponds to a variable-volume gas-phase flow reactor and it is important to use reactor volume as the independent variable. Don t introduce average residence time because the gas-phase volumetric flow rate is not constant. If heat transfer across the wall of the reactor is neglected in the thermal energy balance for adiabatic operation, it... 

In developing the solution to Illustration 13.1, we utilized a variation of the traditional material balance on a batch reactor that is often useful in the analysis of biochemical transformations carried out in batch and semibatch modes of operation. In particular, we took into account variations in the volume of the broth in the bioreactor by first converting concentrations of biomass and substrate into the total quantities of these materials present in the bioreactor. In so doing we were implicitly recognizing that the proper form of a material balance on species i for variable-volume situations is... 

From the discussion in Example 5.2, semibatch operation with continuous addition of DAA to hypochlorite appears to be the preferred mode of reactor operation. Using the same nomenclature as in that example, and employing the equations summarized in Table 10.2 for different variable volume semibatch reactions, the following equation can be written for component i in reaction j ... 

In a variable-volume batch reactor operated at constant temperature and pressure. 

Flow reactors usually operate at nearly constant pressure, and thus at variable density when there is a change of moles of gas or of temperature. An appai ent l e.sidence time is the ratio of reactor volume and the inlet volumetric flow rate. 

A parallel reactor system has an extra degree of freedom compared with a series system. The total volume and flow rate can be arbitrarily divided between the parallel elements. For reactors in series, only the volume can be divided since the two reactors must operate at the same flow rate. Despite this extra variable, there are no performance advantages compared with a single reactor that has the same total V and Q, provided the parallel reactors are at the same temperature. When significant amounts of heat must be transferred to or from the reactants, identical small reactors in parallel may be preferred because the desired operating temperature is easier to achieve. 

ILLUSTRATION 8.4 DETERMINATION OF REQUIRED PLUG FLOW REACTOR VOLUME UNDER ISOTHERMAL OPERATING CONDITIONS—VARIABLE DENSITY CASE... 

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