The perfectly mixed continuous reactor

Continuous stirred tank reactors (CSTR s) are used extensively in industry, and also in pilot installations. They are mostly applied for liquid phase processes. 

In section 1.2 the concept of the CSTR was introduced, and its merits briefly described. When the mixing is strong and the reactions that take place in the reactor are not too rapid, the reactor may be considered as perfectly mixed. Because these assumptions are in some cases quite realistic, the concept of the perfectly mixed continuous reactor is useful. 

It may be added here that a CSTR can be a practical tool for determining reaction kinetics, because perfect mixing can often be approached on a small scale. The interpretation of the results is then much simpler than for batch and semi-batch reactors. 

The calculation of the conversion in perfectly mixed reactors is relatively simple, because all of the reaction takes place at constant concentrations. Also, the mass balance is very simple, because the exit concentrations are the same as the concentrations in the reactor. For constant density we find 

F is the volume flow passing through the reactor, and V the volume of the reaction mixture in the reactor. The concentration of A in the feed stream and in the reactor are, respectively,. and c.  

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For the perfectly mixed continuous reactor, the CSTR, the ratio VT/ Fy only represents the mean residence time, /p,av however, it is still possible to compare the performance of the CSTR with the performance of the BR by letting the mean residence time fp av = t. Interestingly, when the reaction rate shows a positive dependence on reactants concentration, the BR is more effective than the CSTR. This is because the batch reactor experiences all the system compositions between initial and final values, whereas the CSTR operates at the final composition, where the reaction rate is smaller (under the above hypotheses). Finally, one can compare the two continuous reactors under steady-state conditions. The CSTR allows a more stable operation because of back-mixing, which however reduces the chemical performance, whereas the PFR is suitable for large heat transfer but suffers from larger friction losses. 

In this chapter the most important operation modes of reactors are considered. Models are developed by combining simple reaction kinetics for single-phase reactions with mass balances for five ideal model reactors the ideal batch reactor the semi-batch reactor the plug flow reactor the perfectly mixed continuous reactor and the cascade of perfectly mixed reactors. For isothermal conditions, conversions can be calculated on the basis of chemical kinetics only. 

For the perfectly mixed continuous reactor we use the following mass balances ... 

In Oiapter 3 the importance of mixing in chemical reactors was indicated with the defmition of two ideal reactor types the plug flow reactor, in which no mixing takes place at all, and the perfectly mixed continuous reactor, with infinite mixing rates. The concept of mixing itself, however, was not analysed. 

In section 3.4 the selectivities of competitive and consecutive reactions were calculated for two reactor types the batch or plug flow reactor (no backmixing), and the perfectly mixed continuous reactor. The following general conclusions can be formulated in terms of backmixing ... 

The perfectly mixed, continuous-how stirred tank reactor (CSTR)... 

The same consecutive reactions considered in Prob. 6.18 are now carried out in two perfectly mixed continuous reactors. Flow rates and densities are constant. The volumes of the two tanks (P) are the same and constant. The reactors operate at the same constant temperature. 

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. 

Flush The flush reaction path model is analogous to the perfectly mixed-flow reactor or the continuously stirred tank reactor in chemical engineering (Figure 2.5). Conceptually, the model tracks the chemical evolution of a solid mass through which fresh, unreacted fluid passes through incrementally. In a flush model, the initial conditions include a set of minerals and a fluid that is at equilibrium with the minerals. At each step of reaction progress, an increment of unreacted fluid is added into the system. An equal amount of water mass and the solutes it contains is displaced out of the system. Environmental applications of the flush model can be found in simulations of sequential batch tests. In the experiments, a volume of rock reacts each time with a packet of fresh, unreacted fluids. Additionally, this type of model can also be used to simulate mineral carbonation experiments. 

Finally, several alternate names have been used for what here is called the perfectly mixed flow reactor. One of the earliest was continuous stirred tank-reactor, or CSTR, which some have modified to continuous flow stirred tank reactor, or CFSTR. Other names are backmix reactor, mixed flow reactor, and ideal stirred tank reactor. All of these terms appear in the literature, and must be recognized. 

Lumped systems are systems in which the state variables describing the system are lumped in space (invariant in all space dimensions). The simplest example is the perfectly mixed continuous-stirred tank reactor. These systems are described at steady state by algebraic equations, whereas the unsteady state is described by initial-value ordinary differential equations for which time is the independent variable. 

The calculation of the conversion of chemical reactions in perfectly mixed continuous reactors is simpler than for the cases of batch- and plug flow reactors. On the basis of data obtained for a given chemical reaction in a batch-reactor, the conversion in perfectly mixed continuous reactors can be calculated easily. 

In considering the chemical kinetics of complex reaction systems the differential selectivities are directly relevant, but for reactor design the use of integral selectivities is often more practical. Note that for perfectly mixed continuous reactors differential and integral selectivities are the same. 

In the second model (Fig. 2.16) the continuous well-stirred model, feed and product takeoff are continuous, and the reactor contents are assumed to he perfectly mixed. This leads to uniform composition and temperature throughout. Because of the perfect mixing, a fluid element can leave at the instant it enters the reactor or stay for an extended period. The residence time of individual fluid elements in the reactor varies. 

The principle of the perfectly-mixed stirred tank has been discussed previously in Sec. 1.2.2, and this provides essential building block for modelling applications. In this section, the concept is applied to tank type reactor systems and stagewise mass transfer applications, such that the resulting model equations often appear in the form of linked sets of first-order difference differential equations. Solution by digital simulation works well for small problems, in which the number of equations are relatively small and where the problem is not compounded by stiffness or by the need for iterative procedures. For these reasons, the dynamic modelling of the continuous distillation columns in this section is intended only as a demonstration of method, rather than as a realistic attempt at solution. For the solution of complex distillation problems, the reader is referred to commercial dynamic simulation packages. 

If three perfectly mixed continuous stirred tank reactors of equal volume were used in series flow instead, what would the required volume be ... 

Write the component continuity equations for a perfectly mixed batch reactor (no inflow or outflow) with first-order isothermal reactions ... 

Sometimes useful information and insight can be obtained about the dynamics of a system from just the steadystate equations of the system. Van Heerden Ind. Eng. Chem. Vol. 45, 1953, p. 1242) proposed the application of the following steadystate analysis to a continuous perfectly mixed chemical reactor. Consider a nonisothermal CSTR described by the two nonlinear ODEs... 

In this chapter we study the steady-state design of perfectly mixed, continuously operating, liquid-phase reactors. The effects of a wide variety of reaction types, kinetics, design parameters, and heat removal schemes are explored. The important elfects of design conversion and design temperature on heat transfer area and other process parameters are quantitatively studied. 

Kinetics can also be studied at surface science conditions. Feed can be leaked at a constant rate into the chamber containing the crystal face, and the gas is removed at a constant rate by the pumps. The composition of the chamber gas can be continuously monitored by mass spectrometry. The pressure in the reaction chamber is low enough to ensure Knudsen flow The gaseous molecules collide almost exclusively with the exposed solid surfaces, and the system behaves as a perfectly mixed flow reactor (CSTR). Experiments in the transient regime with various forcing functions can be performed, and response times can be orders of magnitude smaller than those at atmospheric pressure. The catalytic oxidation of CO on Pt(llO) was one of the first studies of this type (33). 

Typical extraction curves obtained in our laboratory scale apparatus show that Murphree s efficiency ( E ) varies with the nature of the solvent and with mixing time figure 7 . From the linear dependence of E/l-E on mixing time, it may be concluded that our centrifugal contactor can be assimilated to a perfectly stirred continuous reactor of which the characteristic equation is (19)... 

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