Tank Reactor with Complete Backmixing

In the modeling of a tank reactor, it is assumed that the gas, liquid, and solid phases exist at the same temperature. The energy balance can then be set up for the entire reactor volume, because the temperature and concentration gradients are absent. For a system with one reaction, the balance becomes 

The physical interpretation of Equation 6.57 is the same as for the energy balance of a PER (Equation 6.48). 

Equation 6.7 gives an expression for the catalyst mass, and the heat transfer to/ffom the surroundings is expressed by 

Inserting Equations 6.7 and 6.58 into the energy balance. Equation 6.57, yields 

If the heat capacities, CpL and Cpc, are approximated as temperature-independent. Equation 6.59 can be simplified to 

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The coimterpart of the ideal plug flow reactor is the ideal continuous stirred-tank reactor with complete backmixing of the rection mass. Because of the ideal mixing, the reaction rate is constant, and a simple design equation is obtained for the catalysis reactor (Eq. 14-3). 

Let us consider the mass balance of two kinds of three-phase reactors bubble columns and tube reactors with a plug flow for the gas and the liquid phases, and stirred tank reactors with complete backmixing. Modeling concepts can be implemented in most existing reactors backmixing is typical for slurry reactors, bubble columns, and stirred tank reactors, whereas plug flow models describe the conditions in a trickle bed reactor. The interface between the gas and the liquid is supposed to be surroimded by gas and liquid films. Around the catalyst particles, there also exists a liquid film. In gas and liquid films, physical diffusion, but no chemical reactions, is assumed to take place. A volume element is illustrated in Figure 6.15. 

Below we will look at three ideal gas-liquid reactor types a column reactor with a plug flow in the gas and liquid phases, a tank reactor with complete backmixing, and a BR. The main volume elements in gas-liquid reactors are displayed in Figure 7.16. The bulk gas and liquid phases are delimited by thin films where chemical reactions and molecular diffusion occur. However, the reactions do take place in the bulk phase of the liquid as well. 

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). 

It is useful to examine the consequences of a closed ion source on kinetics measurements. We approach this with a simple mathematical model from which it is possible to make quantitative estimates of the distortion of concentration-time curves due to the ion source residence time. The ion source pressure is normally low enough that flow through it is in the Knudsen regime where all collisions are with the walls, backmixing is complete, and the source can be treated as a continuous stirred tank reactor (CSTR). The isothermal mole balance with a first-order reaction occurring in the source can be written as... 

Another alternative for three-phase catalytic reactors with suspended catalyst particles is to use mechanically agitated tank reactors (Figure 6.7). In a tank reactor, the flow profile can approach complete backmixing. 

For a completely backmixed tank reactor, an energy balance can be written in a manner similar to Equation 7.198. The energy balance now describes the whole reactor volume. For systems with only one equation, the energy balance obtains the form... 

The residence time distribution of a reactor is a function of the axial mixing within the reactor. The extreme cases are I) the ideal continuous stirred tank reactor (CSTR) with complete mixing and, 2) the ideal plug flow reactor (PFR) without any backmixing of the liquid during its flow through the reactor. The behavior of real reactors lies between these extremes. 

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