Nonideal reactors tubular

The reactors treated in the book thus far—the perfectly mixed batch, the plug-flow tubular, and the perfectly mixed continuous tank reactors—have been modeled as ideal reactors. Unfortunately, in the real world we often observe behavior very different from that expected from the exemplar this behavior is tme of students, engineers, college professors, and chemical reactors. Just as we must learn to work with people who are not perfect, so the reactor analyst must learn to diagnose and handle chemical reactors whose performance deviates from the ideal. Nonideal reactors and the principles behind their analysis form the subject of this chapter and the next. 

We first consider nonideal tubular reactors. Tubular reactors may be empty, or they may be packed with some material that acts as a catalyst, heat-transfer medium, or means of promoting interphase contact. Until now when analyzing ideal tubular reactors, it usually has been assumed that the fluid moved through the reactor in piston-like flow (PFR), and every atom spends an identical length of time in the reaction environment. Here, the velocity profile... 

Residence time the residence time t takes into account the time in which each fluid element or molecule passes through the reactor and it depends on the molecules velocity inside the reactor therefore, it depends on the flow in the reactor. Residence time is equal to space time if the velocity is uniform in a cross section of the reactor, as in ideal tubular reactors. This situation is not valid to tank reactors, since the velocity distribution is not uniform. In most nonideal reactors, the residence time is not the same for all molecules, leading to variations in radial concentrations along the reactor and therefore, the concentration in the tank and at the reactor outlet is not uniform. That means we need to define initially the residence time and calculate the residence time distribution for each system. 

The reactors with recycle are continuous and may be tanks or tubes. Their main feature is increasing productivity by returning part of unconverted reactants to the entrance of the reactor. For this reason, the reactant conversion increases successively and also the productivity with respect to the desired products. The recycle may also be applied in reactors in series or representing models of nonideal reactors, in which the recycle parameter indicates the deviation from ideal behavior. As limiting cases, we have ideal tank and tubular reactors representing perfect mixture when the recycle is too large, or plug flow reactor(PFR) when there is no recycle. 

Nonideal batch reactors may have Nonideal tubular reactors may have... 

Nonideal tubular reactor models, inclusion of interpellet axial dispersion in,... 

Packed-bed reactors, 21 333, 352, 354 Packed beds, 25 718 Packed catalytic tubular reactor design with external mass transfer resistance, 25 293-298 nonideal, 25 295... 

Transpired wall reactors Nonideal tubular reactors may have concentrations that vary in the r and 0 directions... 

In earlier chapters, tubular reactors of several forms have been described (e.g., laminar flow, plug flow, nonideal flow). One of the most widely used industrial reactors is a tubular reactor that is packed with a solid catalyst. This type of reactor is called fixed-bed reactor since the solid catalyst comprises a bed that is in a fixed position. Later in this chapter, reactors that have moving, solid catalysts will be discussed. 

Here we use a single parameter to account for the nonideality of our reactor. This parameter is most always evaluated by analyzing the RTD determined from a tracer test. Examples of one-parameter models for a nonideal CSTR include the reactor dead volume V, where no reaction takes place, or the fraction / of fluid bypassing the reactor, thereby exiting unreacted. Examples of one-parameter models for tubular reactors include the tanks-in-series model and the dispersion model. For the tanks-in-series model, the parameter is the number of tanks, n, and for the dispersion model, it is the dispersion coefficient D,. Knowing the parameter values, we then proceed to determine the conversion and/or effluent concentrations for the reactor. 

The dispersion model is also used to describe nonideal tubular reactors. In this model, there is an axial dispersion of the material, which is governed by an analogy to Pick s law of diffusion, superimposed on the flow. So in addition to transport by bulk flow, UAqC, every component in the mixture is transported through any cross section of the reactor at a rate equal to [—DaAddCldz)] resulting from molecular and convective diffusion. By convective diffusion we mean either Aris-Taylor dispersion in laminar flow reactors or turbulent diffusion resulting from turbulent eddies. 

Aside from these large-scale, macroscopic deviations from ideal flow patterns, nonideal F t) responses can arise from diffusion within the reactor, from velocity profiles in tubular reactors that deviate from the plug-flow pattern, or from combinations of the two effects. It is the sum combination of all such processes that constitute what we have called mixing effects on chemical reactor performance In what follows, we will first attempt to develop a model adequate for the types of F t) and C t) behavior illustrated in Figures 4.3(b) and 4.4(b), then attempt to extend these ideas to modeling some of the more pathological behavior illustrated in Figure 5.1. 

Figure 5.14 (b) Effect of nonideal exit-age distribution on Type III selectivity in a tubular flow reactor (mixing-cell model). 

In Figure 5.14a the effect of nonideal flow on conversion in a tubular flow reactor was presented in terms of the CSTR model for a first-order reaction. Repeat this calculation for a second-order reaction and... 

In practice, pure-component molar enthalpies are employed to approximate A/7rx. This approximation is exact for ideal solutions only, when partial molar properties reduce to pure-component molar properties. In general, one accounts for more than the making and breaking of chemical bonds in (3-35). Nonidealities such as heats of solution and ionic interactions are also accounted for when partial molar enthalpies are employed. Now, the first law of thermodynamics for open systems, which contains the total differential of specific enthalpy, is written in a form that allows one to calculate temperature profiles in a tubular reactor ... 

Results from the previous section in this chapter illustrate how and when interpellet axial dispersion plays an important role in the design of packed catalytic tubular reactors. When diffusion is important, more sophisticated numerical techniques are required to solve second-order ODEs with split boundary conditions to predict non-ideal reactor performance. Tubular reactor performance is nonideal when the mass transfer Peclet number is small enough such that interpellet axial dispersion cannot be neglected. The objectives of this section are to understand the correlations for effective axial dispersion coefficients in packed beds and porous media and calculate the mass transfer Peclet number based on axial dispersion. Before one can make predictions about the ideal vs. non-ideal performance of tubular reactors, steady-state mass balances with and without axial dispersion must be solved and the reactant concentration profiles from both solutions must be compared. If the difference between these profiles with and without interpellet axial dispersion is indistinguishable, then the reactor operates ideally. 

Calculate the effect of recycle on the conversion in tubular reactors with plug flow. NONIDEAL FLOW PATTERNS AND POPULATION BALANCE MODELS 655... 

Estimate the conversion for the first order reaction in a nonideal tubular flow reactor. The residence time distribution is characterized by measured E function. The mean residence time can be calculated with Equation 3.14 applying the trapezoidal method. Compare the result with the conversion that could be obtained in ideal PER and CSTR for the same mean residence of 10 min. -El = k cf, k = O.lSmin" ... 

Eor a tubular reactor, the ideal behavior limit is the PER, that is, the velocity profile is flat, and in the radial direction, we have perfect mixing. In this scheme, the nonideality would be the absence of plug-flow behavior. Plug-flow behavior in a tubular reactor starts after the boundary layer formation is completed. Therefore, if the reactor is not long... 

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