Continuous stirred tank reactors models

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

Example 5—Stability dependence on the set of inputs. Consider a continuous stirred-tank reactor modeled by the following equations, in continuous time ... 

CRE Chemical Reaction (or Reactor) Engineering CSF Continuous Surface Force CSS Continuous Surface Stress CSTR Continuous Stirred Tank Reactor model DCS Deferred Correction Source DM Dispersion Model... 

In the third case, the residence time distribution (RTD) of the solid becomes an important factor. Though the liquid RTD will again approximate closely to the perfectly mixed condition required for a continuous stirred tank reactor model except on a very large scale, generally the solid will not. Therefore the actual solid RTD must be determined as set out in Chapter 16 for a satisfactory reactor design to be made. 

Continuous stirred-tank reactor model (CSTR)... 

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). 

In the second model (Figure 5.1b), the mixed-flow or continuous well-mixed or continuous-stirred-tank (CSTR) model, feed and product takeoff are both continuous, and the reactor contents are assumed to be perfectly mixed. This leads to uniform composition and temperature throughout the reactor. Because of the perfect mixing, a fluid element can leave the instant it enters the reactor or stay for an extended period. The residence time of individual fluid elements in the reactor varies. 

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. 

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. 

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