Material balance batch reactor

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. 

Other preparations and isolations. If damp methylenedi(nitroformamide) is allowed to stand for several days, the odor of formic acid is noticed, and MEDINA can be isolated from the residue (Ref 11, p 14). The details of scale-up to 150 lb batches, including exp details and flow sheets, and further scale-up with the aim of prodn of 1000 lbs are given. The report describes a fume-off and fire which occurred during the S3rd run. The cause was attributed to a stuck valve which allowed nitric acid to build up in the reactor (Ref 13, p 57). In Ref 16, p 73 there are cost analysis data for pilot plant and large scale prodn, flow sheet for a proposed coml plant, and material balances. The action of acet anhydr on N,Nf-bis(hydroxy-methyl)MEDlNA regenerates MEDINA (Ref 6) the diNa salt of N. N trinitrotrimethylene-diamine, on warming with me ale, ppts the Na salt of MEDINA... 

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 ... 

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 ... 

It becomes necessary to incorporate a total mass balance equation into the reactor model, whenever the total quantity of material in the reactor varies, as in the cases of semi-continuous or semi-batch operation or where volume changes occur, owing to density changes in flow systems. Otherwise the total mass balance equation can generally be neglected. 

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. 

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... 

If one considers a batch reactor in which the chemistry is characterized by a single extent of reaction, the material balance analysis presented in Section 8.1 indicates that the holding time necessary to change the fraction conversion from fA1 to fA2 is given by... 

In general, when designing a batch reactor, it will be necessary to solve simultaneously one form of the material balance equation and one form of the energy balance equation (equations 10.2.1 and 10.2.5 or equations derived therefrom). Since the reaction rate depends both on temperature and extent of reaction, closed form solutions can be obtained only when the system is isothermal. One must normally employ numerical methods of solution when dealing with nonisothermal systems. 

Consider a reaction represented by A +. . . - products taking place in a batch reactor, and focus on reactant A. The general balance equation, 1.51, may then be written as a material balance for A with reference to a specified control volume (in Figure 2.1, this is the volume of the liquid). 

In this chapter, we first consider uses of batch reactors, and their advantages and disadvantages compared with continuous-flow reactors. After considering what the essential features of process design are, we then develop design or performance equations for both isothermal and nonisothermal operation. The latter requires the energy balance, in addition to the material balance. We continue with an example of optimal performance of a batch reactor, and conclude with a discussion of semibatch and semi-continuous operation. We restrict attention to simple systems, deferring treatment of complex systems to Chapter 18. 

The interpretation of cA(t) comes from the realization that each cylindrical shell passes through the vessel as an independent batch. Thus, cA(/) is obtained by integration of the material balance for a batch reactor (BR). Accordingly, we may rewrite equation 16.2-11, in terms of either cA(x) or fA(x), as... 

The material balance for a batch reactor may be used to develop a differential equation which may be solved for the cA(t) profile (see equation 3.4-1) ... 

Heat and material balances of a batch reactor are derived in Section 2.6.2. In the present instance, the differential heat balance is Heat of reaction + Heat tranfer = Sensible heat gain or... 

By simplifying the general component balance of Section 1.2.4, the material balance for a batch reactor becomes... 

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. Figure 3.8 shows a batch reactor with a cooling jacket. Since there are no flows into the reactor or from the reactor, the total material balance tells us that the total mass, within the reactor, remains constant. 

The component material 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 material balance equation can be represented by... 

In the fed-batch (semicontinuous) operation mode, substrates are fed into the reactor but no material is removed from the reactor. Therefore, the total volume of the material within the reactor increases as a function of time. For this reactor type the mass balance for each component of the reaction mixture is given by... 

Ridelhoover and Seagrave [57] studied the behaviour of these same reactions in a semi-batch reactor. Here, feed is pumped into the reactor while chemical reaction is occurring. After the reactor is filled, the reaction mixture is assumed to remain at constant volume for a period of time the reactor is then emptied to a specified level and the cycle of operation is repeated. In some respects, this can be regarded as providing mixing effects similcir to those obtained with a recycle reactor. Circumstances could be chosen so that the operational procedure could be characterised by two independent parameters the rate coefficients were specified separately. It was found that, with certain combinations of operational variables, it was possible to obtain yields of B higher than those expected from the ideal reactor types. It was necessary to use numerical procedures to solve the equations derived from material balances. 

Make a material balance for any component A. For such an accounting we usually select the limiting component. In a batch reactor, since the composition is uniform throughout at any instant of time, we may make the accounting about the whole reactor. Noting that no fluid enters or leaves the reaction mixture during reaction, Eq. 4.1, which was written for component A, becomes... 

This gives the relationship between Cr and in a batch or in a plug flow reactor. To find the concentrations of the other components, simply make a material balance. An A balance gives... 

With throughflow of L its composition stays roughly constant when B is in excess. However, with a batch of L its composition slowly changes with time as B is being used up, but B is roughly constant in the reactor at any time, as shown in Fig. 22.5. Here the material balance at any time t becomes... 

If the above condition is not met, the calculations based solely on overall material balance do not take into account the dissolved unreacted A and B that remain in the liquid phase after the reaction in a batch reactor, or which may flow out of the reactor with the liquid in a continuous-flow system. This way, it is assumed that the removal of a reactant is purely a result of the reaction. 

Applying an overall material balance in the batch reactor and using eq. (4.120),... 

As there is no entering or leaving flow in the batch reactor, the material balance equation for a reactant A in a liquid of constant density is given as... 

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 ... 

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