Material balance tubular reactor

Tubular flow reaclors operate at nearly constant pressure. How the differential material balance is integrated for a number of second-order reactions will be explained. When n is the molal flow rate of reactant A the flow reactor equation is... 

Tubular flow reactors usually operate at nearly constant pressure. For a reactant A, the differential material balance is ... 

As can be seen for infinite recycle ratio where C = Cl, all reactions will occur at a constant C. The resulting expression is simply the basic material balance statement for a CSTR, divided here by the catalyst quantity of W. On the other side, for no recycle at all, the integrated expression reverts to the usual and well known expression of tubular reactors. The two small graphs at the bottom show that the results should be illustrated for the CSTR case differently than for tubular reactor results. In CSTRs, rates are measured directly and this must be plotted against the driving force of... 

There are a variety of limiting forms of equation 8.0.3 that are appropriate for use with different types of reactors and different modes of operation. For stirred tanks the reactor contents are uniform in temperature and composition throughout, and it is possible to write the energy balance over the entire reactor. In the case of a batch reactor, only the first two terms need be retained. For continuous flow systems operating at steady state, the accumulation term disappears. For adiabatic operation in the absence of shaft work effects the energy transfer term is omitted. For the case of semibatch operation it may be necessary to retain all four terms. For tubular flow reactors neither the composition nor the temperature need be independent of position, and the energy balance must be written on a differential element of reactor volume. The resultant differential equation must then be solved in conjunction with the differential equation describing the material balance on the differential element. 

Consider the segment of tubular reactor shown in Figure 8.3. Since the fluid composition varies with longitudinal position, we must write our material balance for a reactant species over a different element of reactor (dVR). Moreover, since plug flow reactors are operated at steady state except during start-up and shut-down procedures, the relations of major interest are those in which the accumulation term is missing from equation 8.0.1. Thus... 

In Section 11.1.3.1 we considered the longitudinal dispersion model for flow in tubular reactors and indicated how one may employ tracer measurements to determine the magnitude of the dispersion parameter used in the model. In this section we will consider the problem of determining the conversion that will be attained when the model reactor operates at steady state. We will proceed by writing a material balance on a reactant species A using a tubular reactor. The mass balance over a reactor element of length AZ becomes ... 

The equation describing the steady-state material balance for tubular packed bed reactors can be obtained from the more general relation (12.7.28) by omitting the terms corresponding toTadial transport of matter. Hence the material balance relation becomes... 

A laminar-flow reactor (LFR) is rarely used for kinetic studies, since it involves a flow pattern that is relatively difficult to attain experimentally. However, the model based on laminar flow, a type of tubular flow, may be useful in certain situations, both in the laboratory and on a large scale, in which flow approaches this extreme (at low Re). Such a situation would involve low fluid flow rate, small tube size, and high fluid viscosity, either separately or in combination, as, for example, in the extrusion of high-molecular-weight polymers. Nevertheless, we consider the general features of an LFR at this stage for comparison with features of the other models introduced above. We defer more detailed discussion, including applications of the material balance, to Chapter 16. 

In this liquid phase reaction, it may be assumed that the mass density of the liquid is unaffected by the reaction, allowing the material balance for the tubular reactor to be applied on a volume basis (Section 1.7.1, Volume 3) with plug flow. 

P8.01.04. PACKED TUBULAR REACTOR HEAT AND MATERIAL BALANCES... 

For a process in a packed tubular reactor like that of P8.01.02, the steady material balance is derived there as... 

Data for the process of dehydrogenation of ethylbenzene to styrene in a tubular packed reactor are given by Jenson Jeffreys (Mathematical Methods in Chemical Rngineering, 424, 1977). The energy and material balances are like... 

The component material 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. 

Petersen [12] points out that this criterion is invalid for more complex chemical reactions whose rate is retarded by products. In such cases, the observed kinetic rate expression should be substituted into the material balance equation for the particular geometry of particle concerned. An asymptotic solution to the material balance equation then gives the correct form of the effectiveness factor. The results indicate that the inequality (23) is applicable only at high partial pressures of product. For low partial pressures of product (often the condition in an experimental differential tubular reactor), the criterion will depend on the magnitude of the constants in the kinetic rate equation. 

In a tubular reactor the concentration varies from point to point along a flow-path, as shown by the solid curve in Fig. 3.3-2, right. The material balance... 

If the compositions vary with position in the reactor, which is the case with a tubular reactor, a differential element of volume SV, must be used, and the equation integrated at a later stage. Otherwise, if the compositions are uniform, e.g. a well-mixed batch reactor or a continuous stirred-tank reactor, then the size of the volume element is immaterial it may conveniently be unit volume (1 m3) or it may be the whole reactor. Similarly, if the compositions are changing with time as in a batch reactor, the material balance must be made over a differential element of time. Otherwise for a tubular or a continuous stirred-tank reactor operating in a steady state, where compositions do not vary with time, the time interval used is immaterial and may conveniently be unit time (1 s). Bearing in mind these considerations the general material balance may be written ... 

The basic equation for a tubular reactor is obtained by applying the general material balance, equation 1.12, with the plug flow assumptions. In steady state operation, which is usually the aim, the Rate of accumulation term (4) is zero. The material balance is taken with respect to a reactant A over a differential element of volume 8V, (Fig. 1.14). The fractional conversion of A in the mixture entering the element is aA and leaving it is (aA + SaA). If FA is the feed rate of A into the reactor (moles per unit time) the material balance over 8V, gives ... 

In these equations Vcr/v- rr, the residence time in tank r. Equation 1.46 may be compared with equation 1.37 for a tubular reactor. The difference between them is that, whereas 1.37 is an integral equation, 1.46 is a simple algebraic equation. If the reactor system consists of only one or two tanks the equations are fairly simple to solve. If a large number of tanks is employed, the equations whose general form is given by 1.46 constitute a set of finite-difference equations and must be solved accordingly. If there is more than one reactant involved, in general a set of material balance equations must be written for each reactant. 

Let us consider unit volume of the reaction mixture in which concentrations are changing with time this unit volume may be situated in a batch reactor or moving in plug flow in a tubular reactor. Material balances on this volume give the following equations ... 

Consider a steady flow of reactant A to products at constant density through an element of radius r, width 8r, and height 81 in a tubular reactor at isothermal condition. Suppose that radial and axial mass transfer is expressed by Fick s law, with (D and (De)r as effective diffusivities. The rate at which A reacts is (-rA), mol/m3 sec. A material balance on a tubular element of radii r and r + 8r and height 81 is carried out from... 

Related Calculations. (1) Integral analysis may be used on data from any reactor from which integral reaction rate data have been obtained. The preceding procedure applies equally well to data from an integral tubular-flow reactor, if the tube-flow material balance... 

These basic rate models were Incorporated Into a differential mass balance In a tubular, plug-flow reaction. This gives a set of coupled, non-llnear differential equations which, when Integrated, will provide a simulation model. This model corresponds to the Integral reactor data provided by experimentation. A material balance Is written for each of the four components In our system ... 

Consider first the tubular reactor. From the material balance (Table 3.5.1), it is clear that in order to solve the mass balance the functional form of the rate expression must be provided because the reactor outlet is the integral result of reaction over the volume of the reactor. However, if only initial reaction rate data were required, then a tubular reactor could be used by noticing that if the differentials are replaced by deltas, then ... 

Like axial dispersion, radial dispersion can also occur. Radial-dispersion effects normally arise from radial thermal gradients that can dramatically alter the reaction rate across the diameter of the reactor. Radial dispersion can be described in an analogous manner to axial dispersion. That is, there is a radial dispersion coefficient. A complete material balance for a transient tubular reactor could look like ... 

The analysis presented in this chapter can be used to describe reaction containers of any type—they need not be tubular reactors. For example, consider the situation where blood is flowing in a vessel and antibodies are binding to cells on the vessel wall. The situation can be described by the following material balance ... 

Write down in dimensionless form the material balance equation for a laminar flow tubular reactor accomplishing a first-order reaction and having both axial and radial diffusion. State the necessary conditions for solution. 

Consider a PFR operating at nonisothermal conditions (refer to Figure 9.4.1). To describe the reactor performance, the material balance. Equation (9.1.1), must be solved simultaneously with the energy balance. Equation (9.2.7). Assuming that the PFR is a tubular reactor of constant cross-sectional area and that T and C, do not vary over the radial direction of the tube, the heat transfer rate Q can be written for a differential section of reactor volume as (see Figure 9.4.1) ... 

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