Perfectly-mixed stirred tank

Perfectly mixed stirred tank reactors have no spatial variations in composition or physical properties within the reactor or in the exit from it. Everything inside the system is uniform except at the very entrance. Molecules experience a step change in environment immediately upon entering. A perfectly mixed CSTR has only two environments one at the inlet and one inside the reactor and at the outlet. These environments are specifled by a set of compositions and operating conditions that have only two values either bi ,..., Ti or Uout, bout, , Pout, Tout- When the reactor is at a steady state, the inlet and outlet properties are related by algebraic equations. The piston flow reactors and real flow reactors show a more gradual change from inlet to outlet, and the inlet and outlet properties are related by differential equations. 

Reactor design usually begins in the laboratory with a kinetic study. Data are taken in small-scale, specially designed equipment that hopefully (but not inevitably) approximates an ideal, isothermal reactor batch, perfectly mixed stirred tank, or piston flow. The laboratory data are fit to a kinetic model using the methods of Chapter 7. The kinetic model is then combined with a transport model to give the overall design. 

We have just described a completely segregated stirred tank reactor. It is one of the ideal flow reactors discussed in Section 1.4. It has an exponential distribution of residence times but a reaction environment that is very different from that within a perfectly mixed stirred tank. 

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. 

Hereafter we will treat only perfectly mixed stirred-tank reactors, which are considered, and rightly so, as the reference reactors. We consider a rather general case of biotransformation processes involving aerated systems comprising both water and hydrophobic compounds. These last components are often volatile, as in the case of aroma. As a result, losses by gas stripping can be important. 

The limiting cases of continuous reactors considered in most reactor design textbooks are the perfectly mixed stirred tank and the plug-flow tube. These reactors can differ significantly in the amount of mixing and, therefore, the residence time distribution. The plug-flow tube (PFT) is assumed to be without any axial mixing. Hence, at steady state, the residence time distribution of the material in the effluent stream is represented by the Dirac function as shown by Equation (8.1) ... 

The residence time distribution function E i) of the growing latex particles in a perfectly mixed stirred tank reactor is defined as follows ... 

Show then that a packed bed is equivalent to Z/dp perfectly mixed, stirred tanks in series. Use the typical Pma value of 2. By extending this analogy to radial dispersion, show that the number of perfectly mixed cells in the radial direction is 5(R/dp) when Pmr = 10. 

In order to calculate the rate of polymerisation, the monomer concentration in the particles, [M,]p, the average number of radicals per particle, n, the number of particles, Np, as well as the reactivity ratios should be available. The calculation of [M,]p has been described in Section 4.2. The calculation of n and Np can be found in Chapters 2 and 3 of this book. Note that to calculate the time evolution of the instantaneous copolymer composition, the time history of the variables [M,]p, n and Np must also be known. The unreacted or free monomer present in the reactor can be computed from the general macroscopic material balance for a perfectly mixed stirred tank reactor by omitting inlet and outlet streams ... 

The macroscopic material and energy balances for semi-batchwise operated perfectly mixed stirred tank reactors are given by Equations 4.24 and 4.25, respectively ... 

We demonstrate the use of arclength.continuation.m for the study ofmultiple steady states in a nonisothermal CSTR. Consider a perfectly-mixed stirred-tank reactor with A reacting to form B... 

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