Plug flow reactor mass balances

The solution strategy described above is based on writing a differential plug-flow reactor mass balance for each component in the mixture, and five coupled ODEs are solved directly for the five molar flow rates. The solution strategy described below is based on the extent of reaction for independent chemical reactions, and three coupled ODEs are solved for the three extents of reaction. Molar flow rates are calculated from the extents of reaction. The starting point is the same as before. The mass balance is written for component i based on molar flow rate and differential reactor volume in the presence of multiple chemical reactions ... 

Now, it is possible to integrate the plug-flow differential mass balance for conversion as a function of reactor volume ... 

Based on the kinetic mechanism and using the parameter values, one can analyze the continuous stirred tank reactor (CSTR) as well as the dispersed plug flow reactor (PFR) in which the reaction between ethylene and cyclopentadiene takes place. The steady state mass balance equations maybe expressed by using the usual notation as follows ... 

Plug flow reactor (PFR) with recycle. The recycle reactor is characterized by a non-zero value of R, that is the ratio between the mass flow rate of the recycled stream and the feeding rate Q. The material balance reads for this case as... 

Depending on tF/tc ratio, SBR operation can be compared with plug flow reactor (PFR) and completely mixed flow reactor (CMFR), (Weber DiGiano, 1995). In table 1 mass balance equations for SBR and continuous flow system are compared in which ... 

In the ideal plug-flow reactor (Figure 11.16) the continuous phase flows as a plug through the reactor i.e., there is no mixing or, in other words, no axial dispersion. Consequently, if a compound is consumed or produced, a concentration gradient will exist in the direction of flow. The mass balance is therefore first set up over an infinite small slice perpendicular to the direction of the flow with volume dV of the bioreactor. Assuming steady state and F =Fq=F, Equation (11.5) then is reduced to ... 

In a tubular reactor, the reactants are fed in at one end and the products withdrawn from the other. If we consider the reactor operated at steady state, the composition of the fluid varies inside the reactor volume along the flow path. Therefore, the mass balance must be established for a differential element of volume dV. We assume the flow as ideal plug flow, that is, that there is no back mixing along the reactor axis. Hence, this type of reactor is often referred to as Plug Flow Reactor (PFR). 

Figure 8.8 Mass balance in a plug flow reactor.

The mass balance for an isothermal transformation of a reactant A in a plug flow reactor operated at steady state can be established from Figure 2.2(a). This mass balance leads to the following relation between the contact time (r in h taken as the reverse of the weight hourly space velocity, for instance, in grams of reactant... 

To describe the reactor behavior, a simplified isothermal dispersed plug-flow reactor model was used. The well-known mass balance of this model for steady-state conditions can be formulated as [14, 15] ... 

In addition to these experiments, a simplified isothermal 1-D dispersed plug-flow reactor model of the membrane reactor was used to carry out theoretical studies [47]. The model used consisted of the following mass balance equations for the feed and sweep sides ... 

Again, the simple isothermal 1-D plug-flow reactor model provides a good basis for quantitative descriptions. This model allows to explore the potential of using series connections of several membrane reactor segments. The corresponding mass balance for a component i and a segment k can be formulated as follows ... 

Plug Flow Reactor A plug flow reactor (PFR) is an idealized tubular reactor in which each reactant molecule enters and travels through the reactor as a plug, i.e., each molecule enters the reactor at the same velocity and has exactly the same residence time. As a result, the concentration of every molecule at a given distance downstream of the inlet is the same. The mass and energy balance for a differential volume between position Vr and Vr + dVr from the inlet may be written as partial differential equations (PDEs) for a constant-density system ... 

Tubular Reactor with Dispersion An alternative approach to describe deviation from ideal plug flow due to backmixing is to include a term that allows for axial dispersion De in the plug flow reactor equations. The reactor mass balance equation now becomes... 

As has been seen in Sect. 3, the equations of mass, energy and momentum balances for batch and plug flow reactors generally constitute a system of ordinary differential equations, with initial values. It is convenient to write such a system in a compact vector form, viz. 

For an ideal plug flow reactor the mass balance in the steady state gives... 

These assumptions lead to the picture of the flow as that of a plug of fluidum with uniform properties being pushed through the tube. In a plug flow reactor the mass balance for a component A over an infinitesimal reactor element, as defined in Figure 7.1, gives ... 

Note that the uniform conditions in the reactor equal those at the reactor outlet, which implies that the production rate of A is also determined by the outlet conditions. The mass balance for a component in a CSTR is an algebraic equation, in contrast to the case of reactions in a batch or a plug flow reactor. For a single, irreversible first-order reaction and constant density, Eqn. 7.32 becomes ... 

Figure 7.3 also compares the evolution of the concentrations of the intermediate Q and the product in case of two first-order reactions in series in a CSTR with that in a batch or plug flow reactor. For constant density, the mass balance for the reaction components in a CSTR are ... 

Example 9.11 Modeling of a nonisothermal plug flow reactor Tubular reactors are not homogeneous, and may involve multiphase flows. These systems are called diffusion convection reaction systems. Consider the chemical reaction A -> bB described by a first-order kinetics with respect to the reactant A. For a nonisothermal plug flow reactor, modeling equations are derived from mass and energy balances... 

Figure 4.10 illustrates the results of typical calculations of the reaction mixture composition evolution in the plug flow reactor the calculations are made using the preceding relationships, the relevant mass balance equa tions, and literature data on Kpi at 210° C. The evolution in time of the ini tial product concentrations including DEB is seen to lead eventually to the situation when the inlet and outlet DEB concentrations become equal. This means that the proper choice of the composition of the initial reaction mix ture makes the process 100% selective in respect to the conversion of the initial reactants, benzene and ethylene, to EB (see Figure 4.10) even though no transalkylation reactor is used. 

The corresponding dimensionless mass balances for CO and H2 within interstitial voids in a plug-flow reactor are... 

For the isothermal tubular plug-flow reactor (PFR) discussed previously, the mass balance for the G gaseous components is... 

For each of the ideal reactor types, viz. ideal batch reactor, plug-flow reactor (PFR), and continuous-flow stirred-tank reactor (CSTR), continuity equations or design equations can be derived using mass (or rather molar) balance equations for each species involved. 

Different orders of deactivation will be used in the modeling. A simplification will be that the activity function for all components is the same. Using the reaction scheme given in figure 2 and the reaction rates as described by equation 1, in combination with a plug flow reactor model, mass balances can be derived for the different lumped groups, resulting in ... 

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