Continuous stirred tank reactor space time

Both reactions take place in liquid solution. If one desires to carry out these reactions in a continuous stirred tank reactor, determine the space time corresponding to a maximum yield of p-hydroxycumyl hydroperoxide. If the initial p-diisopropylbenzene dihydroperoxide concentration is 10 moles/m3, what are the concentrations of the various species in the effluent ... 

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... 

For a continuous stirred-tank reactor, the concentrations as a function of the reactor space time r are ... 

All steps from the second on amount to insertion of an ethoxy block between a previously inserted block and the —OH group, and so have very similar rate coefficients. Usually, the original alcohol reacts at a slighdy lower rate. If the reaction is carried out at constant partial pressure of ethene oxide, each insertion including the first is pseudo-first order in the alcohol or ethoxy alcohol reactant. With increasing reaction time in batch, successive adducts reach maximum concentrations and then decay to form higher adducts, as shown for a calculated case in Figure 5.11. The variation in yield structure with reactor space time in a continuous stirred-tank reactor is similar, but with less pronounced concentration maxima. 

Compared to batch processes, continuous processes often show a higher space-time yield. Reaction conditions may be kept within certain limits more easily. For easier scale-up of some enzyme-catalyzed reactions, the Enzyme Membrane Reactor (EMR) has been developed. The principle is shown in Fig. 7-26 A. The difference in size between a biocatalyst and the reactants enables continuous homogeneous catalysis to be achieved while retaining the catalyst in the vessel. For this purpose, commercially available ultrafiltration membranes are used. When continuously operated, the EMR behaves as a continuous stirred tank reactor (CSTR) with complete backmixing. For large-scale membrane reactors, hollow-fiber membranes or stacked flat membranes are used 129. To prevent concentration polarization on the membrane, the reaction mixture is circulated along the membrane surface by a low-shear recirculation pump (Fig. 7-26 B). 

These are systems where the state variables describing the system are lumped in space (invariant in all space dimensions). The simplest chemical reaction engineering example is thp perfectly mixed continuous stirred tank reactor. These systems are described at steady state by algebraic equations while in the unsteady state they are described by initial value ordinary differential equations where time is the independent variable. 

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). 

The conversion is a function of Dal and the axial dispersion characterized by Bo as shown in Figure 3.20. With decreasing Bo the conversion diminishes at constant Dal (constant space time). At Dal = 5 a conversion of A = 0.99 is attained in a plug flow reactor Bo = oo), whereas the conversion drops to X = 0.83 for Bo = 0 (continuous stirred tank reactor). 

A continuous stirred tank reactor (CSTR) with ideal mixing has a uniform concentration both in time and space. As an important consequence, the concentration at the output (c ) is the same as that prevailing in the 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) ... 

Thus, for Michaelis-Menten kinetics, a PFR type reactor, predominantly a packed-bed reactor (PBR, Figure 9.1b) is preferred to the continuous stirred-tank reactor (CSTR, Figure 9.1a), since it requires less biocatalyst to reach the same level of conversion. In this case, ideal reactors are those with high space time/yield to increase the efficiency of the transformation. PBRs with immobilized catalyst have a clear advantage in that voidage is low 34% compared to over 80-90% for CSTR [35]. However, if pH control is required, the use of a PFR is not advised. In case of substrate inhibition, a CSTR (Figure 9.1a) operated at high conversion is to be preferred. On the other hand, when product inhibition is pronounced, a... 

The construction of a laboratory-scale continuous stirred tank reactor (CSTR) resembles of that of a BR, but the reactor is equipped with an inlet and an outlet. Concentration and temperature gradients should be absent because of vigorous stirring. For a homogeneous CSTR, a constant volume and pressure are reasonable assumptions. The concentrations at the reactor outlet are measured as a function of the space time, that is, volumetric flow rate. The steady-state mass balance is written as (Chapter 3)... 

The method of lines (14) is used as the numerical technique In this method, by "finite differencing" the space variable (here axial length of reactor), the reactor is divided into a number of cells. Then the partial differential equations are converted into ordinary differential equations where time is the only independent variable. Each cell corresponds to a continuous stirred tank reactor. 

The continuous production of aliphatic chiral alcohols was demonstrated by Leuchs et al. as shown in Scheme 6.20 by using continuous stirred tank reactor (CSTR). The CRED from Lactobacillus brevis was used in a biphasic system with MTBE as cosolvent to reduce aliphatic ketones with the general structure 53. It was shown that inaeasing the chain length resulted in a decreased yield due to less available substrate in the aqueous phase. The continuous process was run with a ketone concentration of 100 mmol/L and IPA was used as the reductant (1 mol/L). It was also demonstrated that 200 rpm was ideal for longevity of the enzyme. Doubling the residence time did not lead to a sigttificant increase in the space-time yield [30]. 

Schroer et al. developed a continuous process for the asymmetric reduction of methyl acetoacetate using iso-propanol as a cosubstrate in a continuously stirred tank reactor using an ultrafiltration membrane for retention of cells [52]. The bioreduction was run continuously for 7 weeks with exceedingly high substrate and cosubstrate concentration of up to 2.5 and 2.8 mol/L. Maximal space-time yield of about 700 g/L/day was achieved. 

Biocatalysts in nature tend to be optimized to perform best in aqueous environments, at neutral pH, temperatures below 40 °C, and at low osmotic pressure. These conditions are sometimes in conflict with the need of the chemist or process engineer to optimize a reaction with respect to space-time yield or high product concentration in order to facilitate downstream processing. Furthermore, enzymes and whole cells are often inhibited by products or substrates. This might be overcome by the use of continuously operated stirred tank reactors, fed-batch reactors, or reactors with in situ product removal [14, 15]. The addition of organic solvents to increase the solubility of substrates and/or products is a common practice [16]. 

It is important to understand that the time constant xp of a process, say, a stirred tank is not the same as the space time x. Review this point with the stirred-tank heater example in Chapter 2. Further, derive the time constant of a continuous flow stirred-tank reactor (CSTR) with a first-order chemical reaction... 

Example 4.5 Derive the state space representation of two continuous flow stirred-tank reactors in series (CSTR-in-series). Chemical reaction is first order in both reactors. The reactor volumes are fixed, but the volumetric flow rate and inlet concentration are functions of time. 

The continuously operated stirred tank reactor is fed with reactants at the same time as the products are removed by an overflow or a level control system (Figure 8.1). This ensures a constant volume and, consequently with a constant volume flow rate of the feed, a constant space hme. We further assume the reactor contents... 

The condition expressed by the Bodenstein approximation rx = 0 is often misleadingly called a steady state. It is not. It is not a time-independent state, only a state in which a specific variation with time (or reactor space time) is small compared with the others. In fact, some older textbooks applied what they called the steady-state approximation to batch reactions in order to derive the time dependence of the concentrations, unwittingly leading the incorrect presumption of a steady state ad absurdum. And a continuous stirred-tank or tubular reactor may, and usually does, come to a true steady state, even if the Bodenstein approximation is and remains inapplicable. [The approximation compares process rates r, it is irrelevant for its validity whether or not the reactor comes to a steady state, that is, whether the rates of change, dC /dr, become zero.]... 

FIGURE 1.2 A comparison of the space-time yields, or saving in reactor volume achieved by carrying out a continuous process to the same degree of conversion in a single stirred tank reactor, versus two CSTRs operating in series. (Adapted from Wynne [19], with permission.)... 

Neither V nor any of the undesirable product species are present in the feed stream. For both a plug flow reactor and a single continuous flow stirred-tank reactor determine the maximum yields of V that can be obtained in the limit at which the conversion of A approaches 100%. Prepare plots of the effluent concentrations of all species versus reactor space time for each type of reactor. To quantify the concentration of the undesired products in the effluent, consider the dimerization reaction (2A D) as the only significant reaction. 

Figure 9.5 Dependence of effluent species concentrations on reactor space time for both a plug flow reactor and an individual continuous flow stirred-tank reactor.

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