Plug mass balance

In the present study, the UASB reactor was modeled in terms of the dispersed plug flow and the Monod type of rate equations to constmct the differential mass balance equations fcs- the anaerobic biodegradation of single and multiple substrates components of the volatile fetty acids. 

The UASB tractor was modeled by the dispensed plug flow model, considering decomposition reactions for VFA componaits, axial dispersion of liquid and hydrodynamics. The difierential mass balance equations based on the dispersed plug flow model are described for multiple VFA substrate components considaed... 

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 ... 

The component mass balance equation, combined with the reactor energy balance equation and the kinetic rate equation, provide the basic model for the ideal plug-flow tubular reactor. 

As with the stirred tank model, mass balance equations can be developed to describe mass transfer in plug flow. In this case, it is convenient to define the system as a differential cylindrical section of the tube, with length Az and volume nD2 Az/4, where D is the tube diameter. This system is fixed in space and may... 

When fluid velocity is constant, a component mass balance for a chemical species A in plug flow can be written 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 ... 

Here the pseudo-homogeneous rate r is related to the surface reaction rate r" through the area of active catalyst per unit volume of reactor. Assuming further a plug-flow regime, the integration of the mass balance equation for this simple rate expression gives an expression for CO conversion ... 

For movement of the gases, various treatments can be used. The simplest is to use mass balances down the flow channel. This is the same as saying that there is plug flow and the pressure remains uniform. 

The complete unsteady-state model for adsorption-desorption and surface reactions of the plug flow laboratory reactor was based on the following equations NH3 mass balance on the catalyst suiface ... 

Figure 2-9 Sketch showing correspondence between time in a batch reactor and position a in a plug-flow tubular reactor. The mass-balance equations describe both reactors for the constant-density situations.

We can therefore replace dt by dz/u in all of the preceding differential equations for the mass balance in the batch reactor and use these equations to describe reactions during flow through a pipe. This reactor is called the plug-flow tubular reactor, which is the most important continuous reactor encountered in the chemical industry. 

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 ... 

Note that the gas-phase concentration CGz varies with the distance from the entrance z due to the plug-flow condition. If the gas phase is in complete mixed flow, then CG z - CG>0. Finally, the component mass balance around the catalyst is... 

The experiment in Fig. 36 has been analyzed according to the usual plug-flow model of the test microreactor. In this case, the ammonia mass balance equations were modified in order to include the oxidation reaction R5 in Table V, which was considered to proceed via adsorbed ammonia NH3. Moreover, the mass balance for gaseous nitrogen was introduced... 

Rearranging the mass balance gives [A ] = F — [HA], which can be plugged into the Ka expression to give... 

In most adsorption processes the adsorbent is contacted with fluid in a packed bed. An understanding of the dynamic behavior of such systems is therefore needed for rational process design and optimization. What is required is a mathematical model which allows the effluent concentration to be predicted for any defined change in the feed concentration or flow rate to the bed. The flow pattern can generally be represented adequately by the axial dispersed plug-flow model, according to which a mass balance for an element of the column yields, for the basic differential equation governing llie dynamic behavior,... 

From the mass balance equation for an assumed plug flow we have... 

To illustrate we consider a homogeneous tubular reactor. The simplest model is given by plug flow and the design equations are obtained from the mass-balance equations by taking the mass balance over an element of length Al. This is expressed in the formula... 

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 balances [Eqs. (Al) and (A2)] assume plug-flow behavior for both the gas/vapor and liquid phases. However, real flow behavior is much more complex and constitutes a fundamental issue in multiphase reactor design. It has a strong influence on the reactor performance, for example, due to back-mixing of both phases, which is responsible for significant effects on the reaction rates and product selectivity. Possible development of stagnant zones results in secondary undesired reactions. To ensure an optimum model development for CD processes, experimental studies on the nonideal flow behavior in the catalytic packing MULTIPAK are performed (168). 

Under fairly low gas velocity conditions where U is close to t/mf or the bed is in particulate fluidization, the plug flow assumption for the gas phase can be reasonably made [Wen and Fane, 1982]. Considering the sublimation of species A from the solid phase to the gas phase, the mass balance on the concentration for species A in the gas phase, Ca, over the incremental height AH can be expressed as... 

The pattern of flow through a packed adsorbent bed can generally be described by the axial dispersed plug flow model. To predict the dynamic response of the column therefore requires the simultaneous solution, subject to the appropriate initial and boundary conditions, of the differential mass balance equations for an element of the column,... 

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... 

Additional information on the plug flow fixed bed reactors and on the heat and mass balance equations can be found in the Handbook of Heterogeneous Catalysis[15] and in the classical books devoted to chemical engineering kinetics.113,141... 

This value can now be plugged back into the first mass balance equation, which we previously rearranged with d on the left hand side, Equation (12) ... 

One of the simplest models used to describe the performance of tubular reactors is the well-known isothermal one-dimensional plug flow tubular reactor (PFTR) model. The mass balance of this model for steady-state conditions, the simultaneous occurrence of M reactions and a constant volumetric flow rate V is ... 

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 ... 

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... 

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

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