Well-stirred batch reactor

Peaking and Non-isothermal Polymerizations. Biesenberger a (3) have studied the theory of "thermal ignition" applied to chain addition polymerization and worked out computational and experimental cases for batch styrene polymerization with various catalysts. They define thermal ignition as the condition where the reaction temperature increases rapidly with time and the rate of increase in temperature also increases with time (concave upward curve). Their theory, computations, and experiments were for well stirred batch reactors with constant heat transfer coefficients. Their work is of interest for understanding the boundaries of stability for abnormal situations like catalyst mischarge or control malfunctions. In practice, however, the criterion for stability in low conversion... 

The reaction was carried out in a well-stirred batch reactor at 40 °C. Under these conditions,... 

The starting point for the development of the basic design equation for a well-stirred batch reactor is a material balance involving one of the species participating in the chemical reaction. For convenience we will denote this species as A and we will let (— rA) represent the rate of disappearance of this species by reaction. For a well-stirred reactor the reaction mixture will be uniform throughout the effective reactor volume, and the material balance may thus be written over the entire contents of the reactor. For a batch reactor equation 8.0.1 becomes... 

The data below are typical of those recorded in a well-stirred batch reactor. Initial concentrations were as follows. 

Applications of kinetic principles to industrial reactions are often useful. Initial kinetic studies of the esterification reaction are usually conducted on a small scale in a well stirred batch reactor. In many cases, results front batch studies can be used in the evaluation of the esterification reaction in a continuous operating configuration. 

Model. A difference equation for the material balance was obtained from a discrete reactor model which was devised by dividing the annulus into a two dimensional array of cells, each taken to be a well stirred batch reactor. The model supposes that axial motion of the mobile phase and bed rotation occur by instantaneous discontinuous jumps, between cells. Reaction occurs only on the solid surface, and for the reaction type A B + C used in this work, -dn /dt = K n - n n. Linear isotherms, n = BiC, were used, and while dispersion was not explicitly included, it could be simulated by adjusting the number of cells. The balance is given by Eq. 2, where subscript n is the cell index in the axial direction, and subscript m is the index in the circumferential direction. 

Three ideal reactor types are relevant from reactor theory [15], the two continuous flow types, the plug flow reactor (PFR) and continuous flow stirred tank reactor (CSTR), and the well-stirred batch reactor. The... 

Consider a well-stirred batch reactor of constant fluid volume V in which the reactions occurring are homogeneous. As the system for our macroscopic balances, we choose the fluid in the reactor volume V then the inflows Wn and outflows Wi2 vanish and no mass-transfer surface 0 is required. The species inventories are expressed in terms of fluid concentrations as... 

Its importance lies in the fact that the changes in composition in a reactor are not haphazard, but are of two distinct kinds. First, there are the advective changes due to material brought into the system or removed from it this may be by forced flow, convection, or diffusion. Second, there is the internal change of composition by reaction this change would be seen in a well-stirred batch reactor, for example, where advection has been deliberately eliminated. The advection will have to be expressed by certain terms in the material balance for a particular reactor, but the reactive changes are common to all types and deserve study first. 

The reaction is carried out in a well-stirred batch reactor at 40°C. Under these conditions, the esterification reaction can be considered as irreversible at conversions less than 70%. The following data were obtained using identical sulfuric acid concentrations in both runs. 

Membrane bioreactors have been modelled using approaches that have proven successful in the more conventional catalytic membrane reactor applications. The simplest membrane bioreactor system, as noted in Chapter 4, consists of two separate units, a bioreactor (typically a well-stirred batch reactor) coupled with an external hollow fiber or tubular or flat membrane module. These reactors have been modelled by coupling the classical equations of stirred tank reactors with the mathematical expressions describing membrane permeation. What makes this type of modelling unique is the complexity of the mecha-... 

The isothermal, constant volume, well-stirred batch reactor. Equation 6.1 can be simplified if, due to good mixing conditions, temperature and concentrations are uniform. According to Figure 6.2, integrating in the liquid volume we get... 

Figure 6.2 Schematic diagram of the isothermai, constant volume, well-stirred batch reactor...

When reaction is slow relative to mixing, A and B will become randomly distributed on the molecular scale before reaction occurs. Moreover, reaction will then be governed by classical kinetic laws. Supposing both reactions to have second order kinetics with k = 20 3 and mixing 1 moloffiwithl.l molofi4in a well-stirred batch reactor, the final product distribution is easy to calculate. The conversion of A and yield of R are 85.7% and 80.5% respectively and A, = 0.115. 

If one utilizes a slurry containing 1 kg/m of zeolite and 24 kg/m of amorphous substrate, determine the time necessary to achieve 98% conversion of the substrate to zeolite A in a well-stirred batch reactor. The conditions to be considered are isothermal operation at 100°C and a hydroxide concentration of 1.5 kmol/m. ... 

The above equations were already encountered in Section 1.1.2 of Chapter 1. The equations defining reaction rates were written there for a point , a volume in which the composition is uniform. This is also assumed here for the ideal, well stirred batch reactor, whatever its volume. 

The first criterion is simply the well-known analog between a plug flow continuous reactor and a well-stirred batch reactor mentioned above. The second criterion is the analogy between a continuous one-stage equilibrium flash and a batch equilibrium flash. Since some of the gas dissolves in the liquid and some of the liquid vaporizes, this criterion insures that the vaporization conditions are the same as well as Insuring that the concentration of any reaction Inhibiting reaction products, namely, H2S are the same. 

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