Reactor plug-flow homogeneous

Let Lp be the length of the simple ideal plug-flow homogeneous reactor with no dispersion for the same value of CA/CAm, and tp be the required residence time in the plug-flow reactor i.e. in equation A Dl = 0,... 

Example 3.3. Balances for Plug-Flow Homogeneous Reactors (PFR)... 

Polymers and Plastics Reactant/catalyst blending Thermal homogenization Plug-flow finishing reactors... 

Runaway criteria developed for plug-flow tubular reactors, which are mathematically isomorphic with batch reactors with a constant coolant temperature, are also included in the tables. They can be considered conservative criteria for batch reactors, which can be operated safer due to manipulation of the coolant temperature. Balakotaiah et al. (1995) showed that in practice safe and runaway regions overlap for the three types of reactors for homogeneous reactions (1) batch reactor (BR), and, equivalently, plug-flow reactor (PFR), (2) CSTR, and (3) continuously operated bubble column reactor (BCR). 

The above equations are the same as those of the plug-flow tubular reactor for homogeneous reactions (Smith, 1981 Levenspiel, 1972). The differential form of equation (3.122) can be written in several equivalent forms (Levenspiel, 1972) ... 

Analogous expressions can be written for a plug flow tubular reactor that ideally has zero mixing in the axial direction and is completely homogeneous radially. A step change imposed on Ci in such a system produces an identical step change in Coui after a lag of 0 sec. Thus, for / > 0 for such a reactor,... 

Under steady-state conditions in a plug-flow tubular reactor, the onedimensional mass transfer equation for reactant A can be integrated rather easily to predict reactor performance. Equation (22-1) was derived for a control volume that is differentially thick in all coordinate directions. Consequently, mass transfer rate processes due to convection and diffusion occur, at most, in three coordinate directions and the mass balance is described by a partial differential equation. Current research in computational fluid dynamics applied to fixed-bed reactors seeks a better understanding of the flow phenomena by modeling the catalytic pellets where they are, instead of averaging or homogenizing... 

We now consider a homogeneous first-order reaction conduced in a plug-flow, tubular reactor. The process is adiabatic. We will now be concerned with the fluid velocity through the reactor instead of the agitation of the fluid. We will also be concerned with the reactor s diameter D and its length L as well, but not its volume per se. The reaction remains the same the effective reaction rate constant is defined as... 

Another classification refers to the shape of the vessel. In the case of the laboratory vessel installed with a stirrer, the composition and temperature of die reaction is homogeneous in all parts of die vessel. This type of vessel is classified as a stiiTcd tank or well mixed reactor. Where there is no mixing in the direction of flow as in the cylindrical vessel, it is classified as a plug flow or tubular flow reactor. 

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. 

The alternative to batch mode operation is continuous operation. In the continuous mode there is a continuous flow of medium into the fermentor and of product stream out of the fermentor. Continuous bioprocesses often use homogenously mixed whole cell suspensions. However, immobilised cell or enzyme processes generally operate in continuous plug flow reactors, without mixing (see Figure 2.1, packed-bed reactors). 

Equations 12.7.48 and 12.7.39 provide the simplest one-dimensional mathematical model of tubular fixed bed reactor behavior. They neglect longitudinal dispersion of both matter and energy and, in essence, are completely equivalent to the plug flow model for homogeneous reactors that was examined in some detail in Chapters 8 to 10. Various simplifications in these equations will occur for different constraints on the energy transfer to or from the reactor. Normally, equations 12.7.48 and 12.7.39... 

The physical situation in a fluidized bed reactor is obviously too complicated to be modeled by an ideal plug flow reactor or an ideal stirred tank reactor although, under certain conditions, either of these ideal models may provide a fair representation of the behavior of a fluidized bed reactor. In other cases, the behavior of the system can be characterized as plug flow modified by longitudinal dispersion, and the unidimensional pseudo homogeneous model (Section 12.7.2.1) can be employed to describe the fluidized bed reactor. As an alternative, a cascade of CSTR s (Section 11.1.3.2) may be used to model the fluidized bed reactor. Unfortunately, none of these models provides an adequate representation of reaction behavior in fluidized beds, particularly when there is appreciable bubble formation within the bed. This situation arises mainly because a knowledge of the residence time distribution of the gas in the bed is insuf-... 

The reactor model adopted for describing the lab-scale experimental setup is an isothermal homogeneous plug-flow model. It is composed of 2NP + 2 ordinary differential equations of the type of Equation 16.11 with the initial condition of Equation 16.12, NP + 3 algebraic equations of the type of Equation 16.13, and the catalytic sites balance (Equation 16.14) ... 

For a homogeneous gas-phase reaction occurring in a plug-flow reactor, explain briefly under what circumstances tlr < 1. Consider each factor affecting this ratio separately. Give an example (chemical reaction + circumstance(s)) for illustration. Assume steady-state operation and... 

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 ... 

Stoichacmetry and reaction equilibria. Homogeneous reactions kinetics. Mole balances batch, continuous-shn-ed tank and plug flow reactors. Collection and analysis of rate data. Catalytic reaction kinetics and isothermal catalytic radar desttpi. Diffusion effects. 

The solution procedure to this equation is the same as described for the temporal isothermal species equations described above. In addition, the associated temperature sensitivity equation can be simply obtained by taking the derivative of Eq. (2.87) with respect to each of the input parameters to the model. The governing equations for similar types of homogeneous reaction systems can be developed for constant volume systems, and stirred and plug flow reactors as described in Chapters 3 and 4 and elsewhere [31-37], The solution to homogeneous systems described by Eq. (2.81) and Eq. (2.87) are often used to study reaction mechanisms in the absence of mass diffusion. These equations (or very similar ones) can approximate the chemical kinetics in flow reactor and shock tube experiments, which are frequently used for developing hydrocarbon combustion reaction mechanisms. 

FlameMaster v3.3 A C+ + Computer Program for OD Combustion and ID Laminar Flame Calculations. FlameMaster was developed by H. Pitsch. The code includes homogeneous reactor or plug flow reactors, steady counter-flow diffusion flames with potential flow or plug flow boundary conditions, freely propagating premixed flames, and the steady and unsteady flamelet equations. More information can be obtained from http //www.stanford.edu/group/pitsch/Downloads.htm. 

The kinetics of a homogeneous liquid reaction are studied in a flow reactor, and to approximate plug flow the 48-cm long reactor is packed with 5-mm nonporous pellets. If the conversion is 99% for a mean residence time of 1 sec, calculate the rate constant for the first-order reaction... 

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