Basic Stirred Tank Modeling

Accumulation = Mass Into - Mass Out of of Mass System System 

Assuming that the density p and cross-sectional area A are constant gives 

The describing relation is a first-order differential equation of the initial-value class of differential equations. That is, the initial condition Z(t = 0) is known and the height of the tank as a function of time Z(t) is the desired result. 

The file fun32.m defines the right hand side of the differential equation 3.2.2 which we are solving. This file is shown below. 

Computational Methods for Process Simulation Tank Height 

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Specific reactor characteristics depend on the particular use of the reactor as a laboratory, pilot plant, or industrial unit. AH reactors have in common selected characteristics of four basic reactor types the weH-stirred batch reactor, the semibatch reactor, the continuous-flow stirred-tank reactor, and the tubular reactor (Fig. 1). A reactor may be represented by or modeled after one or a combination of these. SuitabHity of a model depends on the extent to which the impacts of the reactions, and thermal and transport processes, are predicted for conditions outside of the database used in developing the model (1-4). 

Temperature control in a stirred-tank heater is a common example (Fig. 2.9). We will come across it many times in later chapters. For now, we present the basic model equation, and use it as a review of transfer functions. 

When the basic system was operated as a continuous packed bed reactor, the analytical model developed here allows us to describe the performance of all types of reactors, from a continuous stirred tank reactor (CSTR) to a plug flow reactor (PFR). It was shown that the information-processing function depends on the reactor type, the flow rate through the reactor, the concentration of the cofactor in the feed stream, the values of Vm,i, the presence of internal inhibitors, and the cycle time of the input signal. 

The simplest model of a bubbling fluidized bed, with uniform bubbles exchanging matter with a dense phase of catalytic particles which promote a continuum of parallel first order reactions is considered. It is shown that the system behaves like a stirred tank with two feeds the one, direct at the inlet the other, distributed from the bubble train. The basic results can be extended to cases of catalyst replacement for a single reactant and to Astarita s uniform kinetics for the continuous mixture. 

The modelling of real food webs can be an exceedingly complicated task but, to illustrate the basic technique, a situation may be defined where a continuous stirred-tank biological reactor contains two species, one the predator, the other the prey. The food for the prey is assumed to enter as the sterile feed stream to the reactor, so that the predator may only consume the prey which grows in the reactor. Material balances can be drawn up for the process in much the same way as has... 

The cell model is a generalization of a class of models such as the completely mixed tanks-in-series model and the back-flow mixed tanks-in-series model. The common characteristic of this model is that the basic mixing unit is a completely mixed or stirred tank. This model has been employed extensively from the early days of chemical engineering to the present (1. ... 

Based on these observations [93] proposed a modified model containing two time constants, one for the liquid shear induced turbulence and a second one for the bubble induced turbulence. The basic assumption made in this model development is that the shear-induced turbulent kinetic energy and the bubble-induced turbulent kinetic energy may be linearly superposed in accordance with the hypothesis of [128, 129]. Note, however, that [82] observed experimentally that this assumption is only valid for void fractions less than 1 %, whereas for higher values there is an amplification in the turbulence attributed to the interactions between the bubbles. The application of this model to the high void fraction flows occurring in operating multiphase chemical reactors like stirred tanks and bubble columns is thus questionable. 

As the main responsible for the changes in the material balance, the chemical reactor must be modelled accurately from this point of view. Basic flowsheeting reactors are the plug flow reactor (PFR) and continuous stirred tank reactor (CSTR), as shown in Fig. 3.17. The ideal models are not sufficient to describe the complexity of industrial reactors. A practical alternative is the combination of ideal flow models with stoichiometric reactors, or with some user programming. In this way the flow reactors can take into account the influence of recycles on conversion, while the stoichiometric types can serve to describe realistically selectivity effects, namely the formation of impurities, important for separations. Some standard models are described below. 

There are three basic homogeneous reactor models (DCSTR, CSTR, and CPFR, Fig. 3.30) that can be considered ideal cases for calculating conversion. The equations for balancing all reactor models derive from the conservation of mass equation, Equ. 2.3. The equation for a balancing all types of ideal continuous stirred tank reactors (idCSTR) (c = Cr) can uniformly be based on a consideration of the following (see Fig. 3.36) ... 

We consider the TAP reactor as a basic kinetic device for systematic studies of reaction-diffusion systems. In this chapter, we are going to (i) present and analyze models of different TAP configurations with a focus on their possibilities with respect to characterizing active materials and unraveling complex mechanisms, and (ii) demonstrate relationships between TAP models and other basic reactor models, that is, models for the ideal continuous stirred-tank reactor (CSTR), batch reactor (BR) and plug-flow reactor (PER). In some situations, the TZTR can be considered a simple building block for constracting the various models. 

This chapter deals with basic fundamentals of novel reactor technology and some of green reactor design softwares and their applications. Basic understanding of flow pattern in stirred-tank reactor by computational fluid dynamics and simulation of CSTR model by using ASPEN Plus were mainly presented in this chapter. 

Basically, the simple batch equation predicts the behavior when recirculation occurs because of low conversion per pass through the reactor. If we use the data in Example 4.2, the conversion per pass will be 1 — exp[—less than 0.3%. Working below the limiting current density it will be even smaller. It is immaterial in practice whether in a batch recirculation system the reactor is operating in a plug-flow or stirred-tank mode. Therefore, we can use the model equations derived for the batch reactor unless there are special circumstances such as, for example, the use of a three-dimensional electrode cell with a high active specific electrode area. 

Two basic approaches are often used for fluidized bed reactor modeling. One approach is based on computational fluid dynamics developed on the basis of the mass, momentum, and energy balance or the first principle coupled with reaction kinetics (see Chapter 9). Another approach is based on phenomenological models that capture the main features of the flow with simplifications by assumption. The flow patterns of plug flow, CSTR (continuous-stirred tank reactor). 

For continuous flow reactors, the two ideal models are the plug flow reactor and the continuous stirred tank reactor. In the plug flow reactor (PFR), which is basically a pipe within which the reaction occurs, the concentration, pressure, and tenperature change from point to point. The performance equation is... 

Figure 3.2 Aggregation of two-phase basic elements to multicompartment models for a stirred tank with single and double impeller [6].

Two basic physical models (a) the stirred tank or compartment (b) the 1-D pipe. 

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