For a batch reactor

From the mass balance equation for a batch reactor... 

The component balance for a batch reactor. Equation (1.21), still holds when there are multiple reactions. However, the net rate of formation of the component may be due to several different reactions. Thus,... 

Suppose there are N components involved in a set of M reactions. Then Equation (1.21) can be written for each component using the rate expressions of Equations (2.7) or (2.8). The component balances for a batch reactor are... 

The general conclusion is that density changes are of minor importance in liquid systems and of only moderate importance in gaseous systems at constant pressure. When they are important, the necessary calculations for a batch reactor are easier if compositions are expressed in terms of total moles rather... 

Using V, we can write the design equations for a batch reactor in very compact form ... 

Example 4.2 used the method of false transients to solve a steady-state reactor design problem. The method can also be used to find the equilibrium concentrations resulting from a set of batch chemical reactions. To do this, formulate the ODEs for a batch reactor and integrate until the concentrations stop changing. This is illustrated in Problem 4.6(b). Section 11.1.1 shows how the method of false transients can be used to determine physical or chemical equilibria in multiphase systems. 

A relatively simple example of a confounded reactor is a nonisothermal batch reactor where the assumption of perfect mixing is reasonable but the temperature varies with time or axial position. The experimental data are fit to a model using Equation (7.8), but the model now requires a heat balance to be solved simultaneously with the component balances. For a batch reactor. 

Note that ai will gradually increase during the course of the reaction and will reach its saturation value, agjKu, when B is depleted. Dropping the accumulation term for ai i) represents a form of the pseudo-steady hypothesis. Since component B is not transferred between phases, its material balance has the usual form for a batch reactor ... 

If the enzyme charged to a batch reactor is pristine, some time will be required before equihbrium is reached. This time is usually short compared with the batch reaction time and can be ignored. Furthermore, 5o Eq is usually true so that the depletion of substrate to establish the equilibrium is negligible. This means that Michaelis-Menten kinetics can be applied throughout the reaction cycle, and that the kinetic behavior of a batch reactor will be similar to that of a packed-bed PFR, as illustrated in Example 12.4. Simply replace t with thatch to obtain the approximate result for a batch reactor. 

Solution The initial conditions for a batch reactor are S=So and X=Xq at 1 = 0. Equation (12.13) gives the cell growth when there is inhibition by the product ... 

Equation (12.15) governs substrate consumption. For a batch reactor with all the substrate charged initially,... 

In the above reactions, I signifies an initiator molecule, Rq the chain-initiating species, M a monomer molecule, R, a radical of chain length n, Pn a polymer molecule of chain length n, and f the initiator efficiency. The usual approximations for long chains and radical quasi-steady state (rate of initiation equals rate of termination) (2-6) are applied. Also applied is the assumption that the initiation step is much faster than initiator decomposition. ,1) With these assumptions, the monomer mass balance for a batch reactor is given by the following differential equation. 

In this paper we formulated and solved the time optimal problem for a batch reactor in its final stage for isothermal and nonisothermal policies. The effect of initiator concentration, initiator half-life and activation energy on optimum temperature and optimum time was studied. It was shown that the optimum isothermal policy was influenced by two factors the equilibrium monomer concentration, and the dead end polymerization caused by the depletion of the initiator. When values determine optimum temperature, a faster initiator or higher initiator concentration should be used to reduce reaction time. 

By considering the small region in the emulsion phase where the distribution of the gas concentration can be regarded as flat, the equation for a batch reactor can be adapted and the following relationship is finally obtained. 

GL 19] [R 9] [P 20] Both the kinetic constant and the activation energy were lower for a micro-reactor test unit than for a batch reactor (micro/batch 15323 =... 

Based on the above scheme and data concerning rates of individual reactions, fictitious experimental results for a batch reactor were generated in the form of initial and final concentrations for all components of the reaction mixture (see Table A-1). Identify the stoichiometry based on these data. The desired precision for 3 is 10 ... 

By simplifying the general component balance of Sec. 1.2.4, the mass balance for a batch reactor becomes... 

For heterogeneous catalytic reactions, the rate of reaction is often expressed as the number of moles of component reacting per unit time, per unit mass of catalyst. For a batch reactor... 

For a batch reactor, under constant volume conditions, the component mass balance equation can be represented by... 

For a batch reactor system only the accumulation and dissipation terms are important. Thus... 

A simulation model needs to be developed for each reactor compartment within each time interval. An ideal-batch reactor has neither inflow nor outflow of reactants or products while the reaction is carried out. Assuming the reaction mixture is perfectly mixed within each reactor compartment, there is no variation in the rate of reaction throughout the reactor volume. The design equation for a batch reactor in differential form is from Chapter 5 ... 

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... 

For a batch reactor, the only possible input and output terms are by reaction, since there is no flow in or out. For the reactant A in this case, there is output but not input. Equation 1.5-1 then reduces to... 

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