Plug flow reactor design equation

To achieve desired conversions predicted by ideal design equations, plug flow is required. This implies turbulent flow and higher energy costs if packing is used. Mass transfer can also be a problem. Axial diffusion or dispersion tends to decrease residence time in the reactor. High values of the length-to-diameter ratios (L/D > 100) tend to minimize this problem and also help heat transfer. 

For convenience, Tables A.3a and A.3b in Appendix A provide the design equations and auxiliary relations used in the design of plug-flow reactors. Table A.4 provides the energy balance equation. 

Hence, when designing a plug-flow reactor with a heating/cooling fluid whose temperature varies, we have to solve either Eq. 7.4.3 or 7.4.5 simultaneously with the design equations and the energy balance equation of the reactor. 

Equation 7.5.16 is the dimensionless, differential energy balance equation for cyhndrical tubular flow reactors, relating the temperature, 0, to the extents of the independent reactions, Z s, and P/Pq as functions of space time t. To design a plug-flow reactor, we have to solve design equations (Eq. 7.1.1), the energy balance equation (Eq. 7.5.16), and the momentum balance (Eq. 7.5.12), simultaneously subject to specified initial conditions. 

This example summarizes all the tools (i.e., ODEs and supporting algebraic equations) that are required to design a plug-flow reactor at high mass and heat... 

After the rates have been determined at a series of reactant concentrations, the differential method of testing rate equations is applied. Smith [3] and Carberry [4] have adequately reviewed the designs of heterogeneous catalytic reactors. The following examples review design problems in a plug flow reactor with a homogeneous phase. 

By comparing the design equations of batch, CFSTR, and plug flow reactors, it is possible to establish their performances. Consider a single stage CFSTR. 

The Plug Flow Reactor (PFR)—Basic Assumptions and Design Equations... 

Consider j plug flow reactors connected in series and let/i,/2,/3, -fh >/ represent the fraction conversion of the limiting reagent, leaving reactors 1, 2, 3,. J. For each of the reactors considered above, the appropriate design equation is 8.2.7. For reactor z,... 

For these conditions the general design equation for a plug flow reactor (8.2.7) becomes... 

For a plug flow reactor the appropriate design equation for the reaction at hand is ... 

These properties are those of the stream entering the plug flow reactor. The design equation for this reactor is... 

For steady-state operation of a plug flow reactor the basic design equation (equation 8.2.9) can be written as... 

In eqn. (62), which is the basic form of the design equation for a plug-flow reactor, V is the reactor volume, G is the total mass flow through the reactor, Cao is the concentration of A at inlet in moles per unit mass of feed, Xa is the fractional conversion of A and r is the reaction rate. 

In contrast to the design equations for batch and plug-flow reactors, eqns. (5) and (62), the design equation for the continuous stirred tank reactor does not contain an integral sign. Figure 14 shows [ A]o/r plotted... 

The viability of one particular use of a membrane reactor for partial oxidation reactions has been studied through mathematical modeling. The partial oxidation of methane has been used as a model selective oxidation reaction, where the intermediate product is much more reactive than the reactant. Kinetic data for V205/Si02 catalysts for methane partial oxidation are available in the literature and have been used in the modeling. Values have been selected for the other key parameters which appear in the dimensionless form of the reactor design equations based upon the physical properties of commercially available membrane materials. This parametric study has identified which parameters are most important, and what the values of these parameters must be to realize a performance enhancement over a plug-flow reactor. 

In Chapter 3, the analytical method of solving kinetic schemes in a batch system was considered. Generally, industrial realistic schemes are complex and obtaining analytical solutions can be very difficult. Because this is often the case for such systems as isothermal, constant volume batch reactors and semibatch systems, the designer must review an alternative to the analytical technique, namely a numerical method, to obtain a solution. For systems such as the batch, semibatch, and plug flow reactors, sets of simultaneous, first order ordinary differential equations are often necessary to obtain the required solutions. Transient situations often arise in the case of continuous flow stirred tank reactors, and the use of numerical techniques is the most convenient and appropriate method. 

Equation 5-307 is the design performance equation for a plug flow reactor at constant density. Figure 5-30 shows the profiles of these equations. 

The area of l/(—rA) versus CA or XA plots is determined for all design equations for batch, CFSTR, and plug flow reactors by employing the Simpson s rule. 

Assuming that the reaction is second order, the design Equation 5-307 for a plug flow reactor is... 

For the plug flow reactor, the design equation at 10% conversion XA = 0.1 is... 

As an alternate expression for plug-flow reactors, the more general case can be considered in which the reactant i enters the reactor already partly converted with this initial conversion, designated as Xio, taking the place of the zero conversion assumed initially in Eq. (59). The resulting design equation equivalent to Eq. (59) is... 

Equations (59) and (60) are in a form often used for tubular, idealized, plug-flow reactors when the reaction rate is based on the volume of the reactor. When the reaction is heterogeneous, such as one occurring on the surface of a catalyst, it is common practice to base the reaction rate on the mass of the catalyst rather than on the volume of the reactor and substitute ric for r,. The resulting design equation equivalent to Eq. (60) is... 

Develop a plug-flow-reactor design equation from the material balance. To properly size a reactor for this reaction and feedstock, a relationship between reactor volume, conversion rate of feed,... 

These were calculated by numerical integration of Equation (8). SD must be less than SD if an ideal plug-flow reactor is to be designed and operated. 

To carry out the integrations in the batch and plug-flow reactor design equations (2-9) and (2-16), as well as to evaluate the CSTR design equation (2-13), we need to know how the reaction rate —r varies with the concentration (hence conversion) of thereacting species. This relationship between reaction rate and concentration is developed in Chapter 3,... 

If both sides of the plug-flow reactor design equation (2-16) are divided by the entering volumetric flow rate and then the left-hand side is put in terms of space time, the equation takes the form... 

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