Space time, CSTR 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-... 

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-... 

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-... 

In this section the size requirements for CSTR cascades containing different numbers of identical reactors are compared with that for a plug flow reactor used to effect the same change in composition. One may define a space time for an entire cascade (x, ) in terms of the ratio of the sum of the component reactor volumes to the inlet volumetric flow rate. Hence,... 

For the first criterion, one compares the reactor volumes based on the average residence time for a given extent of reaction or final conversion. The average residence time depends on the reaction kinetics and therefore the reaction rate, which in turn depends on whether the reaction takes place at constant volume or variable volume. In a system at constant volume, one obtains directly a ratio between the volumes, because the average residence time is equal to space time which is defined as the ratio between reactor volume and inlet volumetric flow in the reactor. For the same conversion, the ratio between volumes is proportional. Since the average residence time in a PFR reactor is similar to the reaction time in a batch reactor, we may assume that they have similar behaviors and then we compare only the ideal tubular reactors (PFR — plug flow reactor) to the ideal tank reactors (CSTR—continuous stirred-tank reactor). 

Figure 3.30. Basic reactor concept and concentration-versus>time and concentration-versus-space profiles. DCSTR, discontinuous stirred tank reactor SCSTR, semicon-tinuous stirred tank reactor CSTR, continuous stirred tank reactor CPFR, continuous plug flow reactor NCSTR, a cascade of N stirred vessels.

What is the difference between the clock time of a batch reactor (BR) and the space time of the plug-flow reactor (PFR) and continuously stirred tank reactor (CSTR) ... 

Eqs. 1 to 3 relate the rate of production Rj of the balanced reaction component y to the molar amounts or their derivatives with respect to the time variable (reaction time or space time, see above). From the algebraic eq. 2 for the CSTR reactor the rate of production, Rj, may be calculated very simply by introducing the molar flow rates at the inlet and outlet of the reactor these quantities are easily derived from the known flow rate and the analytically determined composition of the reaction mixture. With a plug-flow or with a batch reactor we either have to limit the changes of conversion X or mole amount n7 to very low values so that the derivatives or dAy/d( //y,0) or dn7/d/ could be approximated by differences AXj/ (Q/Fj,0) or An7/A, (differential mode of operation), or to measure experimentally the dependence of Xj or nj on the space or reaction time in a broader region this dependence is then differentiated graphically or numerically. 

There are a few other points worthy of note that become evident on closer inspection of the equations developed in Illustrations 9.2 and 9.3. First, except for the case where 2/ 1 = 1 Plug flow or batch reactor requires a lower space or holding time than a CSTR to achieve the maximum concentration of intermediate. The more this ratio departs from unity, the greater the difference in space times. This fact becomes evident on substitution of numerical values into equations (C) and (G) of Illustrations 9.2 and 9.3, respectively, or when plots of Cv/Cao versus kiT are prepared for various ratios of 2/ 1 [see, e.g., Lev-enspiel (5)]. In general, for series reactions, the maximum possible yields of intermediates are obtained when fluids of different compositions (different stages of conversion) are not allowed to mix. 

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