Plug-flow reactors multiple reactions

Multiple reactions in parallel producing byproducts. Consider again the system of parallel reactions from Eqs. (2.16) and (2.17). A batch or plug-flow reactor maintains higher average concentrations of feed (Cfeed) than a continuous well-mixed reactor, in which the incoming feed is instantly diluted by the PRODUCT and... 

A batch or plug-flow reactor should be used for multiple reactions in series. 

In a recycle reactor, part of the exit stream is recycled back to the inlet of the reactor. For a stirred-tank reactor, recycle has no effect on conversion, since we are essentially just mixing a mixed reactor. For a plug flow reactor, the effect of recycle is to approach the performance of a CSTR. This is advantageous for certain applications such as autocatalytic reactions and multiple reaction situations where we have a PFR but really require a CSTR. 

It is worthwhile to compare the conversion obtained in an isothermal plug flow reactor with that obtained in a CSTR for given reaction kinetics. A fair comparison is given in Fig. 7.3 for irreversible first-order kinetics by showing the conversion obtained in both reactors as a function of To- The conversion of A obtained in a plug flow reactor is higher than that obtained in a CSTR. This holds for every positive partial reaction order with respect to A. For multiple reactions selectivities and yield enter into the picture. 

The mathematical model for the plug flow reactor with multiple reactions... 

The first step is to calculate limits for the reaction volume. One CSTR will give the maximum volume and a plug-flow reactor will give the minimum volume. The total reaction voliune for multiple CSTRs will lie somewhere between these two limits. After calculating the reaction volume, calculate the required heat transfer and the heat-transfer area. Then, either select a jacket, a coil, jacket plus a coil, or an external heat exchanger. 

A computational model for wastewater disinfection was developed by Emerick et al. (28). The user can define multiple equations for UV disinfection reactions. The reaction vessel is simulated as a plug flow reactor. A similar model called BioSys was developed by Zeidan (34). 

The design formulation of nonisothermal plug-flow reactors with multiple reactions follows the same procedure outlined in the previous section—we write design... 

Design and operation of gas-phase plug-flow reactors with multiple reactions where the pressure drop along the reactor is not negligible... 

A recycle reactor is a mathematical model describing a steady plug-flow reactor where a portion of the outlet is recycled to the Met, as shown schematically in Figure 9.5. Although this reactor configuration is rarely used in practice, the recycle reactor model enables us to examine the effect of mixing on the operations of continuous reactors. In some cases, the recycle reactor is one element of a complex reactor model. Below, we analyze the operation of a recycle reactor wifii multiple chemical reactions, derive its design equations, and discuss how to solve fiiem. 

Energy Balance for Multiple Reactions in Plug-Flow Reactors 544... 

Falling Off the Steady State 623 Nonisothermal Multiple Reactions 625 Unsteady Operation of Plug-Flow Reactors... 

In the previous examples, we have exploited the idea of an effectiveness factor to reduce fixed-bed reactor models to the same form as plug-flow reactor models. This approach is useful and solves several important cases, but this approach is also limited and can take us only So far. In the general case, we must contend with multiple reactions that are not first order, nonconstant thermochemical properties, and nonisothermal behavior in the pellet and the fluid. For these cases, we have no alternative but to solve numerically for the temperature and species concentrations profiles in both the pellet and the bed. As a final example, we compute the numerical solution to a problem of this type. 

At 325 K, the kinetic rate constant for the third reaction is 7 L/g mol min. Coupled mass and thermal energy transport with multiple reactions in a plug-flow reactor suggests that the temperature of the reactive mixture changes by about 4 °C from inlet (323 K) to outlet (327 K). 

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 ... 

The mass balance for a differential plug-flow reactor with multiple chemical reactions that operates at high-mass-transfer Peclet numbers allows one to replace... 

Aris et al. have primarily analyzed whether the steady-state multiplicity features in a CSTR arising from a cubic rate law also can arise for a series of successive bimolecular reactions [26]. Aris et al. have showed that the steady-state equations for a CSTR with bimolecular reactions scheme reduces to that with a cubic reaction scheme when two parameters e(=k,Cg/k j) and K(=kjC /k j) arising in system equations for the bimolecular reactions tend to zero. Aris et al. have shown that the general multiplicity feature of the CSTR for bimolecular reactions is similar to that of the molecular reactions only at smaller value of e and K. The behavior is considerably different at larger values of e and K. Chidambaram has evaluated the effect of these two parameters (e and K) on the periodic operation of an isothermal plug flow reactor [18]. 

Nevertheless, the inclusion of axial dispersion may be interesting from the point of view of the numerical methods used to solve the conservation equations or in studies regarding the appearance of multiple steady-state solutions [141, 142], Petersen [81] presented an analysis for a ID reactor in terms of the dispersion factor E, which is the ratio between the length of a plug-flow reactor (no dispersion) and the one for a reactor with dispersion yielding the same conversion (Lm). Due to the coordinate transformations employed, F is a function of oP = kDAefu (isothermal first-order reaction). Asymptotic solutions for the dispersion ratio were obtained and are given by... 

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