Space time plug flow reactor

In the absence of plug flow, the space time is equal to the mean residence time in the reactor, (see Chapter 13 from the fourth edition of Elements of Chemical Reaction Engineering now on the DVD-ROM). TTiis time is the average time the molecules spend in the reactor. A range of typical processing times in terms of the space time (residence time) for industrial reactors is shown in Table 2-4. 

Space time ST is equal to the residence time in a plug flow reactor only if the volumetric flowrate remains constant throughout the reactor. The residence time depends on the change in the flowrate through the reactor, as well as V/u. The change in u depends on the variation in temperature, pressure, and the number of moles. The concept of SV with conversions in the design of a plug flow reactor is discussed later in this chapter. 

The space time and reactor volume required to accomplish the specified conversion in a plug flow reactor are sufficiently high that they make... 

This equation is the basic relation for the mean residence time in a plug flow reactor with arbitrary reaction kinetics. Note that this expression differs from that for the space time (equation 8.2.9) by the inclusion of the term (1 + SAfA) and that this term appears inside the integral sign. The two quantities become identical only when 5a is zero (i.e., the fluid density is constant). The differences between the two characteristic times may be quite substantial, as we will see in Illustration 8.5. Of the two quantities, the reactor... 

For isothermal operation at 500 °C and 5 atrp, it was shown that the space time required to achieve 90% conversion was 29.9 sec. Compare this value with the mean residence time of the material in the plug flow reactor. 

In order to reduce the disparities in volume or space time requirements between an individual CSTR and a plug flow reactor, batteries or cascades of stirred tank reactors ard employed. These reactor networks consist of a number of stirred tank reactors confiected in series with the effluent from one reactor serving as the input to the next. Although the concentration is uniform within any one reactor, there is a progressive decrease in reactant concentration as ohe moves from the initial tank to the final tank in the cascade. In effect one has stepwise variations in composition as he moves from onfe CSTR to another. Figure 8.9 illustrates the stepwise variations typical of reactor cascades for different numbers of CSTR s in series. In the general nonisothermal case one will also en-... 

The ratio of equations 8.3.58 and 8.3.57 gives the relative total space time requirement for a cascade of stirred tank reactors vis a vis a plug flow reactor. 

Equations B, D, and F may now be solved simultaneously to determine the required space time in the plug flow reactor. 

Let xp and xc represent the space times of the plug flow reactor and the continuous stirred tank reactor respectively. Consider the following reactor combination... 

TP space time for a plug flow reactor PE pseudo equilibrium... 

Tan et al. [29] demonstrated the use of a plug flow reactor of immobilized Lactobacillus kefiri cells for the synthesis of the intermediate (5I )-hydroxyhexane-2-one. This immobilized-cell reactor operated at a maximum conversion yield of 100% and a selectivity of 95%. The production of (5/ )-hydroxyhexane-2-one was extended to an operation time of 6 days. During this time (91 residence times), a space-time yield of 87gL xday 1 and a productivity of 07 8 gwet cell weight 1 were obtained. 

Find the space-time needed for 80% conversion of a 50% A-50% inert feed to a plug flow reactor operating at 215°C and 5 atm (C o = 0.0625 mol/liter). 

Consider a gas-phase reaction 2A R + 2S with unknown kinetics. If a space velocity of 1/min is needed for 90% conversion of A in a plug flow reactor, find the corresponding space-time and mean residence time or holding time of fluid in the plug flow reactor. 

In an isothermal batch reactor 70% of a liquid reactant is converted in 13 min. What space-time and space-velocity are needed to effect this conversion in a plug flow reactor and in a mixed flow reactor ... 

For reactions with arbitrary but known rate the performance capabilities of mixed and plug flow reactors are best illustrated in Fig. 6.2. The ratio of shaded and of hatched areas gives the ratio of space-times needed in these two reactors. 

The parameters for PFRs include space time, concentration, volumetric flow rate, and volume. This reactor follows an integral reaction expression identical to the batch reactor except that space time has been substituted for reaction time. In the plug flow reactor, concentration can be envisioned as having a profile down the reactor. Conversion and concentration can be directly related to the reactor length, which in turn corresponds to reactor volume. 

The mass balance for an isothermal transformation of a reactant A in a plug flow reactor operated at steady state can be established from Figure 2.2(a). This mass balance leads to the following relation between the contact time (r in h taken as the reverse of the weight hourly space velocity, for instance, in grams of reactant... 

In eq 4 the rate is the time derivative of the conversion curve, which can be constructed from the observed conversion-time behavior by mathematical treatment, such as differentiation formulae or polynomial or spline interpolation, provided the product analysis is fast enough to follow the reaction. The same approach can be followed in principle for the plug flow reactor if data is collected at various space-time values. 

Based on the above relation, for most practical operations, this reactor behaves much hke the plug-flow reactor, where ReF = pdtL/pOT, ReM = pdiNjp. Here, 0T is the average residence time. The relationship between power consumption and mixing time reveals the similarity of this vessel to the double helical-ribbon mixer. The fraction of dead space in this apparatus appears to be small. The relationships described above are valid for the fluids in the viscosity range of 50-5000 poises. 

At constant pressure and granted ideal plug flow, the behavior of a tubular reactor at steady state is mathematically analogous to that of a batch reactor A volume element of the reaction mixture has no means of knowing whether it is suspended tea bag-style in a batch reactor or rides elevator-style through a tubular reactor being exposed to the same conditions it behaves in the same way in both cases. As in a batch reactor, what is measured directly are concentrations—here in the effluent—and a finite-difference approximation is needed to obtain the rate from experiments with different reactor space times and otherwise identical conditions. For a reaction without fluid-density variation ... 

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... 

Comparison with Eqn. (8.8) for a batch reactor shows the mathematical analogy between plug-flow and batch reactors. The batch reactor results obtained in the preceding paragraph can be transposed to the plug-flow reactor, provided that a space time tq is defined for the plug-flow reactor as ... 

It is worthwhile to compare the conversion obtained in an isothermal plug-flow reactor (PFR) with that obtained in a CSTR for given reaction kinetics. Figure 8.12 shows a fair comparison for irreversible first-order kinetics by plotting the conversion in both reactors as a function of space-time Xq-... 

Deflnitions. The basic elements of Markov chains associated with Eq.(2-24) are the system, the state space, the initial state vector and the one-step transition probability matrix. Considering refs.[26-30], each of the elements will be defined in the following with special emphasize to chemical reactions occurring in a batch perfectly-mixed reactor or in a single continuous plug-flow reactor. In the latter case, which may simulated by perfectly-mixed reactors in series, all species reside in the reactor the same time. 

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. 

Ordinary differential equations govern systems that vary either with time or space, but not both. Examples are equations that govern the dynamics of a CSTR or the steady state of mbular reactors. Both the dynamics of a CSTR and the steady state of a plug-flow reactor are governed by first-order ordinary differential equations with prescribed initial conditions. The steady-state tubular reactors with axial dispersion are governed by a second-order differential equation with the boundary conditions spec-... 

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