Modeling Continuous stirred tank reactor

Kinetic models can be used to link the reactor design with its performance. The reaction rate may be expressed by power law functions, by more complex expressions, as Langmuit-Hinselwood-Hougen-Watson (LHHW) correlations for catalytic processes, or by considering user kinetics. There are two ideal models, continuous stirred tank reactor (CSTR) or plug flow (PFR), available in rating mode (reaction volume fixed) or design mode (conversion specified). 

Over 25 years ago the coking factor of the radiant coil was empirically correlated to operating conditions (48). It has been assumed that the mass transfer of coke precursors from the bulk of the gas to the walls was controlling the rate of deposition (39). Kinetic models (24,49,50) were developed based on the chemical reaction at the wall as a controlling step. Bench-scale data (51—53) appear to indicate that a chemical reaction controls. However, flow regimes of bench-scale reactors are so different from the commercial furnaces that scale-up of bench-scale results caimot be confidently appHed to commercial furnaces. For example. Figure 3 shows the coke deposited on a controlled cylindrical specimen in a continuous stirred tank reactor (CSTR) and the rate of coke deposition. The deposition rate decreases with time and attains a pseudo steady value. Though this is achieved in a matter of rninutes in bench-scale reactors, it takes a few days in a commercial furnace. 

Mixing Models. The assumption of perfect or micro-mixing is frequently made for continuous stirred tank reactors and the ensuing reactor model used for design and optimization studies. For well-agitated reactors with moderate reaction rates and for reaction media which are not too viscous, this model is often justified. Micro-mixed reactors are characterized by uniform concentrations throughout the reactor and an exponential residence time distribution function. 

Nomura and Fujita (12), Dougherty (13-14), and Storti et al. (12). Space does not permit a review of each of these papers. This paper presents the development of a more extensive model in terms of particle formation mechanism, copolymer kinetic mechanism, applicability to intervals I, II and III, and the capability to simulate batch, semibatch, or continuous stirred tank reactors (CSTR). Our aim has been to combine into a single coherent model the best aspects of previous models together with the coagulative nucleation theory of Feeney et al. (8-9) in order to enhance our understanding of... 

Consider a continuous-stirred-tank reactor (CSTR) with cooling jacket where a first order exothermic reaction takes place. It is required to derive a model relating the extent of the reaction with the flowrate of the heat... 

GP 9] [R 16] By finite-element reactor modeling, it was shown that for conversions as large as 34%, concentration differences within the mini wide fixed-bed reactor of only less than 10% are found [78], Thus, the reactor approximates a continuous-stirred tank reactor (CSTR). This means that the mini wide fixed-bed reactor yields differential kinetics even at large conversions, larger than for reactors used so far (< 10% conversion). 

An nth-order reaction is run in a continuous stirred-tank reactor. The model and program are written in both dimensional and dimensionless forms. This example provides experience in the use of dimensionless equations. 

The reaction is carried out in a non-cooled, continuous stirred-tank reactor (Fig. 5.58), and it is required to find the effect of changes in the reactor inlet conditions on the degree of polymerisation obtained. The model is that of Kenat, Kermode and Rosen (1967). 

One of the simplest models for convective mass transfer is the stirred tank model, also called the continuously stirred tank reactor (CSTR) or the mixing tank. The model is shown schematically in Figure 2. As shown in the figure, a fluid stream enters a filled vessel that is stirred with an impeller, then exits the vessel through an outlet port. The stirred tank represents an idealization of mixing behavior in convective systems, in which incoming fluid streams are instantly and completely mixed with the system contents. To illustrate this, consider the case in which the inlet stream contains a water-miscible blue dye and the tank is initially filled with pure water. At time zero, the inlet valve is opened, allowing the dye to enter the... 

In Section 11.1.3.2 we considered a model of reactor performance in which the actual reactor is simulated by a cascade of equal-sized continuous stirred tank reactors operating in series. We indicated how the residence time distribution function can be used to determine the number of tanks that best model the tracer measurement data. Once this parameter has been determined, the techniques discussed in Section 8.3.2 can be used to determine the effluent conversion level. 

Continuous Stirred Tank Reactor (CSTR). The conversion degree of the azo-dye, the reaction volume (V) and the volumetric flow rate (Q) of the dye-bearing stream are related to each other through the material balance referred to the dye and extended to the reactor volume. Assuming an unstructured model for the biophase, the material balance yields... 

The classical CRE model for a perfectly macromixed reactor is the continuous stirred tank reactor (CSTR). Thus, to fix our ideas, let us consider a stirred tank with two inlet streams and one outlet stream. The CFD model for this system would compute the flow field inside of the stirred tank given the inlet flow velocities and concentrations, the geometry of the reactor (including baffles and impellers), and the angular velocity of the stirrer. For liquid-phase flow with uniform density, the CFD model for the flow field can be developed independently from the mixing model. For simplicity, we will consider this case. Nevertheless, the SGS models are easily extendable to flows with variable density. 

ASCSTR - Continuous Stirred Tank Reactor Model of Activated Sludge System... 

In this model the aeration tank is modelled as a continuous stirred tank reactor. 

The CRE approach for modeling chemical reactors is based on mole and energy balances, chemical rate laws, and idealized flow models.2 The latter are usually constructed (Wen and Fan 1975) using some combination of plug-flow reactors (PFRs) and continuous-stirred-tank reactors (CSTRs). (We review both types of reactors below.) The CRE approach thus avoids solving a detailed flow model based on the momentum balance equation. However, this simplification comes at the cost of introducing unknown model parameters to describe the flow rates between various sub-regions inside the reactor. The choice of a particular model is far from unique,3 but can result in very different predictions for product yields with complex chemistry. 

Both the mass-transfer approach as well as the diffusion approach are required to describe the influence of mass transport on the overall polycondensation rate in industrial reactors. For the modelling of continuous stirred tank reactors, the mass-transfer concept can be applied successfully. For the modelling of finishers used for polycondensation at medium to high melt viscosities, the diffusion approach is necessary to describe the mass transport of EG and water in the polymer film on the surface area of the stirrer. Those tube-type reactors, which operate close to plug-flow conditions, allow the mass-transfer model to be applied successfully to describe the mass transport of volatile compounds from the polymer bulk at the bottom of the reactor to the high-vacuum gas phase. 

There are several control problems in chemical reactors. One of the most commonly studied is the temperature stabilization in exothermic monomolec-ular irreversible reaction A B in a cooled continuous-stirred tank reactor, CSTR. Main theoretical questions in control of chemical reactors address the design of control functions such that, for instance (i) feedback compensates the nonlinear nature of the chemical process to induce linear stable behavior (ii) stabilization is attained in spite of constrains in input control (e.g., bounded control or anti-reset windup) (iii) temperature is regulated in spite of uncertain kinetic model (parametric or kinetics type) or (iv) stabilization is achieved in presence of recycle streams. In addition, reactor stabilization should be achieved for set of physically realizable initial conditions, (i.e., global... 

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. 

Many reviews and several books [61,62] have appeared on the theoretical and experimental aspects of the continuous, stirred tank reactor - the so-called chemostat. Properties of the chemostat are not discussed here. The concentrations of the reagents and products can not be calculated by the algebraic equations obtained for steady-state conditions, when ji = D (the left-hand sides of Eqs. 27-29 are equal to zero), because of the double-substrate-limitation model (Eq. 26) used. These values were obtained from the time course of the concentrations obtained by simulation of the fermentation. It was assumed that the dispersed organic phase remains in the reactor and the dispersed phase holdup does not change during the process. The inlet liquid phase does not contain either organic phase or biomass. 

The perfectly stirred reactor (PSR) or continuously stirred tank reactor (CSTR) is an idealization that proves useful in describing laboratory experiments and can often be used in the modeling of practical situations. As illustrated in Fig. 16.4, gases enter the reactor with a mass-flow rate of m, a temperature of T, and a mass-fraction composition of Y . Once inside the reactor, the gases are presumed to mix instantaneously and perfectly with the gases already resident in the reactor. Thus the temperature and composition within the reactor are perfectly uniform. 

R. L. Curl was the first to work out this model for the case of a chemical process with zero-order drop conversion which is carried out in a continuous stirred tank reactor (C8). His theory, somewhat modified, is given at the end of this section. 

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... 

As a model of a certain poorly agitated continuous stirred-tank reactor of total volume V, it is supposed that only a fraction w is well mixed, the remainder being a dead-water zone. Furthermore, a fraction / of the total volume flowrate v fed to the tank by-passes the well-mixed zone completely (Fig. 2.24a). 

Fig. 2.24. Model of a poorly agitated continuous stirred-tank reactor (a) Flow model fraction / of flow v by-passes only a fraction w of tank volume V is well-stirred (b) Equivalent C, curves for pulse input...

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