Batch reactor, balance

The batch reactor balance for a simple A + B C reaction becomes... 

For a simple A + B — C reaction the semi-batch reactor balance is... 

Unsteady material and energy balances are formulated with the conservation law, Eq. (7-68). The sink term of a material balance is and the accumulation term is the time derivative of the content of reactant in the vessel, or 3(V C )/3t, where both and depend on the time. An unsteady condition in the sense used in this section always has an accumulation term. This sense of unsteadiness excludes the batch reactor where conditions do change with time but are taken account of in the sink term. Startup and shutdown periods of batch reactors, however, are classified as unsteady their equations are developed in the Batch Reactors subsection. For a semibatch operation in which some of the reactants are preloaded and the others are fed in gradually, equations are developed in Example 11, following. 

Since the volume depends on conversion or time in a constant pressure batch reactor, consider the mole balance in relation to the fractional conversion X. From the stoichiometry. 

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

Balance equations for batch reactors may all be viewed as special cases of the following general equation... 

A batch reactor has no input or output of mass after the initial charging. The amounts of individual components may change due to reaction but not due to flow into or out of the system. The component balance for component A, Equation (1.6), reduces to... 

The ideal, constant-volume batch reactor satisfies the following component balance ... 

The most important characteristic of an ideal batch reactor is that the contents are perfectly mixed. Corresponding to this assumption, the component balances are ordinary differential equations. The reactor operates at constant mass between filling and discharge steps that are assumed to be fast compared with reaction half-lives and the batch reaction times. Chapter 1 made the further assumption of constant mass density, so that the working volume of the reactor was constant, but Chapter 2 relaxes this assumption. 

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 component balance for a variable-volume but otherwise ideal batch reactor can be written using moles rather than concentrations ... 

For a perfectly mixed batch reactor, the energy balance is... 

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. 

The following data were collected in an isothermal, constant-volume batch reactor. The stoichiometry is known and the material balance has been closed. The reactions are A B and A C. Assume they are elementary. Determine the rate constants kj and kn-... 

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 ... 

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. 

This paper presents the physical mechanism and the structure of a comprehensive dynamic Emulsion Polymerization Model (EPM). EPM combines the theory of coagulative nucleation of homogeneously nucleated precursors with detailed species material and energy balances to calculate the time evolution of the concentration, size, and colloidal characteristics of latex particles, the monomer conversions, the copolymer composition, and molecular weight in an emulsion system. The capabilities of EPM are demonstrated by comparisons of its predictions with experimental data from the literature covering styrene and styrene/methyl methacrylate polymerizations. EPM can successfully simulate continuous and batch reactors over a wide range of initiator and added surfactant concentrations. 

Aqueous Phase Hass Balances. The usual material balances for the active species in the aqueous solution are considered. With respect to the case of homopolymerization (4) the conplexity of the resulting equations is increased because of the cross propagation and termination terms. For the batch reactor considered in this wortt, the following equations arise ... 

Generally, the temperature changes with time or, equivalently, with distance from the reactor inlet (for flow reactors). This change is usually controlled well in reaction calorimeters but can become uncontrolled in other conventional laboratory flow or (semi)batch reactors. The balance equations of a batch reactor for a single reaction of a-th order kinetics are given by ... 

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

For batch reactors, there is no flow into or out of the system, and those terms in the component balance equation are therefore zero. 

For semi-batch reactors, there is inflow but no outflow from the reactor and the outflow term in the above balance equation is therefore zero. 

It is assumed that all the tank-type reactors, covered in this and the immediately following sections, are at all times perfectly mixed, such that concentration and temperature conditions are uniform throughout the tanks contents. Fig. 3.10 shows a batch reactor with a cooling jacket. Since there are no flows into the reactor or from the reactor, the total mass balance tells us that the total mass remains constant. 

The component mass balance, when coupled with the heat balance equation and temperature dependence of the kinetic rate coefficient, via the Arrhenius relation, provide the dynamic model for the system. Batch reactor simulation examples are provided by BATCHD, COMPREAC, BATCOM, CASTOR, HYDROL and RELUY. 

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

The influence of gassing rate and stirrer speed on an oxidation reaction, in an aerated batch reactor, are to be investigated. The outlet gas is assumed to be essentially air, which eliminates the need for a gas balance for the well-mixed gas phase. 

The experimental method used for this kinetie study is reaetion ealorimetry. In the ealorimeter, the energy enthalpy balance is continuously monitored the heat signal can then be easily converted in the reaction rate (in the case of an isothermal batch reactor, the rate is proportional to the heat generated or consnmed by the reaction). The reaction orders and catalyst stabihty were determined with the methodology of reaction progress kinetic analysis (see refs. (8,9) for reviews). 

The reactor system, where the kinetic experiments were carried out can be described as a semi-batch reactor. Only the synthesis gas (H2 and CO) was fed into the reactor continuously during the experiments, while 1-butene and the solvent were in the batch mode. All reactions took place in the liquid phase. The mass balance for an arbitrary component in the gas is given by... 

There are a variety of limiting forms of equation 8.0.3 that are appropriate for use with different types of reactors and different modes of operation. For stirred tanks the reactor contents are uniform in temperature and composition throughout, and it is possible to write the energy balance over the entire reactor. In the case of a batch reactor, only the first two terms need be retained. For continuous flow systems operating at steady state, the accumulation term disappears. For adiabatic operation in the absence of shaft work effects the energy transfer term is omitted. For the case of semibatch operation it may be necessary to retain all four terms. For tubular flow reactors neither the composition nor the temperature need be independent of position, and the energy balance must be written on a differential element of reactor volume. The resultant differential equation must then be solved in conjunction with the differential equation describing the material balance on the differential element. 

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