Mass balances for reactors

Input = output 4- disappearance -l- accumulation by reaction Mass balance for reactor 1. 

The dimensionless microscopic mass transfer equation presented at the beginning of this chapter has been simplified to obtain the one-dimensional mass balance for reactor design ... 

MASS BALANCES FOR REACTORS CONTAINING A SOLID REACTIVE PHASE... 

To illustrate the development of a physical model, a simplified treatment of the reactor, shown in Fig. 8-2 is used. It is assumed that the reac tor is operating isothermaUy and that the inlet and exit volumetric flows and densities are the same. There are two components, A and B, in the reactor, and a single first order reaction of A B takes place. The inlet concentration of A, which we shall call Cj, varies with time. A dynamic mass balance for the concentration of A (c ) can be written as follows ... 

Equations (1.1) to (1.3) are diflerent ways of expressing the overall mass balance for a flow system with variable inventory. In steady-state flow, the derivatives vanish, the total mass in the system is constant, and the overall mass balance simply states that input equals output. In batch systems, the flow terms are zero, the time derivative is zero, and the total mass in the system remains constant. We will return to the general form of Equation (1.3) when unsteady reactors are treated in Chapter 14. Until then, the overall mass balance merely serves as a consistency check on more detailed component balances that apply to individual substances. 

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. 

A mass balance for an arbitrary liquid-phase component in the stirred tank reactor is thus written as follows dci... 

Owing to the high computational load, it is tempting to assume rotational symmetry to reduce to 2D simulations. However, the symmetrical axis is a wall in the simulations that allows slip but no transport across it. The flow in bubble columns or bubbling fluidized beds is never steady, but instead oscillates everywhere, including across the center of the reactor. Consequently, a 2D rotational symmetry representation is never accurate for these reactors. A second problem with axis symmetry is that the bubbles formed in a bubbling fluidized bed are simulated as toroids and the mass balance for the bubble will be problematic when the bubble moves in a radial direction. It is also problematic to calculate the void fraction with these models. 

The catalyst prepared above was characterized by X-ray diffraction, X-ray photoelectron and Mdssbauer spectroscopic studies. The catalytic activities were evaluated under atmospheric pressure using a conventional gas-flow system with a fixed-bed quartz reactor. The details of the reaction procedure were described elsewhere [13]. The reaction products were analyzed by an on-line gas chromatography. The mass balances for oxygen and carbon beb een the reactants and the products were checked and both were better than 95%. 

The mass balance for a continuous-flow, stirred-tank reactor with first-order reaction is... 

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

Figure 4.9. Mass balancing for a gas-phase, tubular reactor.

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... 

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... 

For the reactor described in Figure 4.3, the general mass balance for component j at stage i is... 

In this chapter we consider the performance of isothermal batch and continuous reactors with multiple reactions. Recall that for a single reaction the single differential equation describing the mass balance for batch or PETR was always separable and the algebraic equation for the CSTR was a simple polynomial. In contrast to single-reaction systems, the mathematics of solving for performance rapidly becomes so complex that analytical solutions are not possible. We will first consider simple multiple-reaction systems where analytical solutions are possible. Then we will discuss more complex systems where we can only obtain numerical solutions. 

Again we have an infinite set of coupled equations. For the PFTR or batch reactor we can write these mass balances for condensation polymerizatioa The monomer A[ is lost by reacting with all the polymeis,... 

The catalytic reactor is an example where reaction occurs only at the boundary with a solid phase, but, as long as the solid remains in the reactor and does not change, we did not need to write separate mass balances for the soHd phase because its residence time Tj is infinite. In a moving bed catalytic reactor or in a slurry or fluidized bed catalytic reactor... 

The equations controlling the operation of ideal reactors are the energy balance and a mass balance for each reactant and product. 

However, for purposes of mass balance in reactors, the following rates have to be also considered the rate of reaction per unit volume of the fluid phase (ru) and per unit volume of reactor (R), defined as follows (Levenspiel, 1972) ... 

In the ideal batch stirred-tank reactor (BSTR), the fluid concentration is uniform and there are no feed or exit streams. Thus, only the last two terms in the previous equation exist. For a volume element of fluid (VL), the mass balance for the limiting reactant becomes (Smith, 1981 Levenspiel, 1972)... 

We can also consider the mass balance for a particular component in the total mass. Thus, for a component in a chemical reactor. 

The goal of CVD systems is to incorporate one or more materials into a bulk film at the deposition surface. Thus, comparing the atomic flux of reagents entering the reactor to the atomic flux incorporated into the bulk film is a measure of the system s effectiveness. The atomic mass balance for each element m is given by the following equation ... 

With these parameters we can set-up a mass balance on the system, which is the basis for evaluating the experimental results. The mass balance for the absorption (of any gas, e. g. ozone) in a continuous-flow stirred tank reactor (CFSTR) under the assumption that the gas and liquid phases are ideally mixed (cL = cLe, cG = cGe), are as follows ... 

If the liquid as well as the gas phases are ideally mixed (i. e. the reactor behaves like a completely mixed STR, often called CSTR) the degradation processes can easily be calculated from integral mass balances for ozone and the dissolved target substances,... 

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