Perfect Mixing Reactors

According to the construction of perfect mixing reactors, or cascade of flow mixing reactors, they can be classified as vertical and horizontal tanks equipped with different 

The fluid in the mixing reactor is perfectly mixed which distinguishes it from the plug flow reactor. It allows maximal use of the reaction volume without the formation of dead fluid zones. A wide residence time distribution of reactants is observed in this type of reactor. 

Typically, the steady state mode of a mixing reactor is characterised by isothermal conditions. Therefore, the temperature field in the reaction zone can be changed during the process (generally for the cascade mixing reactors). 

In mixing reactors, the heat balance is characterised by a temperature increase, due to the adiabatic heating of the reaction mixture, and the heat removal rate (without taking into account the boiling process) [4]  

The ideal models presented here allow us to study the processes at constant values of temperature and concentration in a reactor, i.e., under steady state conditions. Under the real conditions of chemical production, the physical processes of heat and mass transfer (heat conduction, diffusion, convection, turbulence, and so on) play an essential role. 

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The material balance for steady-state operation of a perfectly mixed reactor is ... 

Equation 9-15 gives the conversion expression for the second order reaction of a macrofluid in a mixed flow. An exponential integral, ei(a), which is a function of a, and its value can be found from tables of integrals. However, the conversion from Equation 9-15 is different from that of a perfectly mixed reactor without reference to RTD. An earlier analysis in Chapter 5 gives... 

The name continuous flow-stirred tank reactor is nicely descriptive of a type of reactor that frequently for both production and fundamental kinetic studies. Unfortunately, this name, abbreviated as CSTR, misses the essence of the idealization completely. The ideality arises from the assumption in the analysis that the reactor is perfectly mixed, and that it is homogeneous. A better name for this model might be continuous perfectly mixed reactor (CPMR). 

Fig. 1. Examples of the kinetic curves during ethylene polymerization by chromium oxide catalysts. Support—SiOs temperature—80°C polymerization at constant ethylene pressure in perfect mixing reactor. Curve 1—catalyst reduced by CO at 300°C. Curve 2— catalyst activated in vacuum (400°C) polymerization in the case of (1) and (2) in solvent (heptane) ethylene pressure 10 kg/cm2 02 content in ethylene 1 ppm, HsO 3 ppm. Curves 3, 4, 5, 6—catalyst activated in vacuum (400°C) polymerization without solvent ethylene pressure 19 (curve 3), 13 (curve 4), 4 (curve 5), and 2 (curve 6) kg/cm2 02 content in ethylene 1 ppm, HsO = 12 ppm.

For a perfectly mixed reactor, all fluid elements have an equal chance of leaving the reactor, so that for a small time increment At, the probability that a given fluid element will leave is just the ratio of the mass of fluid leaving to the total mass contained within the reactor. 

The system is sketched in Fig. 3.1 and is a simple extension of the CSTR considered in Example 2.3. Product B is produced and reactant A is consumed in each of the three perfectly mixed reactors by a first-order reaction occurring in the liquid. For the moment let us assume that the temperatures and holdups (volumes) of the three tanks can be different, but both temperatures and the liquid volumes are assumed to be constant (isothermal and constant holdup). Density is assumed constant throughout the system, which is a binary mixture of A and B. 

Example 15.13. The irreversible chemical reaction A B takes place in two perfectly mixed reactors connected in series as shown in Fig. 15.3. The reaction rate is proportional to the concentration of reactant. Let Xj be the concentration of reactant A in the first tank and X2 the concentration in the second tank. The concentration of reactant in the feed is Xg. The feed flow rate is F. Both Xo and F can be manipulated. Assume the specific reaction rates ki and >n Mch tank are constant (isothermal operation). Assume constant volumes Vi and 1. ... 

Bubble columns (BCs) and stirred tank reactors (STRs) are the most frequently used types of reactors in laboratory ozonation experiments. Bubble columns can be roughly assumed to behave like perfectly mixed reactors with respect to the liquid phase, provided the ratio of height (h) to diameter (d) is small hid < 10). 

Identifying the Parameters of an Unsteady State Perfectly Mixed Reactor... 

The process is described by the mathematical model of a nonisothermal, unsteady state, continuous and perfectly mixed reactor. It is defined by the beloiv differential equations ... 

This research method can be better illustrated by a concrete example. The investigated process example described in the next section is an organic synthesis, which takes place in a perfectly mixed reactor. 

Calculate the RTD of a perfectly mixed reactor using an impulse of n moles of a tracer. 

Thus, for a perfectly mixed reactor (or often called completely backmixed), the RTD is an exponential curve. 

Sun and Khang [1990] extended their theoretical analysis to compare a CMTR with a PBIMTR, a conventional plug-flow reactor (PFR) and a conventional continuous stirred tank (perfect mixing) reactor (CSTR) under the same condition of a fixed amount of catalyst. Three types of general reactions were considered to account for the variation in the overall change in the number of moles due to reaction. 

Membrane reactor stability. Multiple steady states have been found in continuous stirred tank reactors (perfect-mixing reactors) or other reactors where mixing of process streams take place. This phenomenon is also evident in membrane reactors. The thermal management of a membrane reactor should be such that the reactor temperatures provide a stable range of operation. 

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. 

The differential Eqs.(3.13-2) were solved numerically [59] for the case of a continuous perfectly mixed reactor. 

In [57] the equations were integrated numerically for the case where the reactions take place in a continuous perfectly mixed reactor. 

Several models have been suggested to simulate the behavior inside a reactor [53, 71, 72]. Accordingly, homogeneous flow models, which are the subject of this chapter, may be classified into (1) velocity profile model, for a reactor whose velocity profile is rather simple and describable by some mathematical expression, (2) dispersion model, which draws analogy between mixing and diffusion processes, and (3) compartmental model, which consists of a series of perfectly-mixed reactors, plug-flow reactors, dead water elements as well as recycle streams, by pass and cross flow etc., in order to describe a non-ideal flow reactor. 

Z+1 designates the number of states, i.e. Z perfectly mixed reactors in the flow system as well as the tracer collector designated by As shown later, the probabilities Si(0) may be replaced by the initial concentration of the fluid elements in each state, i.e. Cj(0) and S(0) will contain all initial concentrations of the fluid elements. The one-step transition probability matrix is given by Eqs.(2-16) and (2-20) whereas pjk represent the probability that a fluid element at Cj will change into Ck in one step, pjj represent the probability that a fluid element will remain unchanged in concentration within one step. 

In treating a certain configuration, the first step is to define the states that the system can occupy. By a state is meant, the concentration Ci in a perfectly mixed reactor i or at the inlet or the exit of a plug-flow reactor, that the system (fluid element) can occupy. The states will be designated by Ci, C2,... whereas the state space SS, will read ... 

Plug flow-perfectly mixed reactor systems (chapter 4.4). 

Perfectly mixed reactors are the key element for conducting chemical processes and in simulation of complex flow systems. Other synonyms are mixed reactor, back mix reactor, an ideal stirred reactor and the CFSTR (constant flow stirred tank reactor). As the name implies, it is a reactor in which the contents are well stirred and uniform throughout. Thus, the exit stream from this reactor has the same composition as the fluid within the reactor. 

The flow configuration comprising of two perfectly-mixed reactors of volumes Vi and V2 is demonstrated in Fig.4.3-1. A tracer in a form of a pulse input is introduced into reactor 1 and is transferred by the flow Qi into reactor 2 where it is assumed to accumulate. Thus, this reactor is a "dead" or "absorbing" state for the tracer, i.e. C = 0 in Fig.4-1. 

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