Mass balance stirred-tank reactor

A mass balance for an arbitrary liquid-phase component in the stirred tank reactor is thus written as follows dci... 

Based on the kinetic mechanism and using the parameter values, one can analyze the continuous stirred tank reactor (CSTR) as well as the dispersed plug flow reactor (PFR) in which the reaction between ethylene and cyclopentadiene takes place. The steady state mass balance equations maybe expressed by using the usual notation as follows ... 

As will be shown later the equation above is identical to the mass balance equation for a continuous stirred-tank reactor. The recycle can be provided either by an external pump as shown in Fig. 5.4-18 or by an impeller installed within the reaction chamber. The latter design was proposed by Weychert and Trela (1968). A commercial and advantageously modified version of such a reactor has been developed by Berty (1974, 1979), see Fig. 5.4-19. In these reactors, the relative velocity between the catalyst particles and the fluid phases is incretised without increasing the overall feed and outlet flow rates. 

The mass balance for a continuous-flow, stirred-tank reactor with first-order reaction is... 

The mass balance of a continuous flow stirred-tank reactor (CSTR) with a first-order chemical reaction is very similar to the problem in Section 2.8.1 (p. 2-20). We just need to add the chemical reaction term. The balance written for the reactant A will appear as ... 

Stirred tank reactor (ST/ ). The differential mass balance referred to the azo-dye converted by bacteria (assuming unstructured model for the biophase, i.e., that it is characterized only by cell mass or concentration X) yields... 

Let us consider an ideal continuously stirred tank reactor with constant broth volume. The mass balance equation for substrate as a carbon source (Eq. 27), biomass (Eq. 28) and oxygen in the fermentation broth (Eq. 29) can be given for the liquid phase, as follows [65,66] ... 

The mass balance over a continuous stirred-tank reactor (CSTR) in the steady state yields for the average residence T... 

In the ideal batch stirred-tank reactor (BSTR), the fluid concentration is uniform and there are no feed or exit streams. Thus, only the last two terms in the previous equation exist. For a volume element of fluid (VL), the mass balance for the limiting reactant becomes (Smith, 1981 Levenspiel, 1972)... 

Figure 1-2 Operating parameters necessary for ozone mass balance(s) on a continuous-flow stirred tank reactor (for operation in semi-batch mode Ol - 0).

With these parameters we can set-up a mass balance on the system, which is the basis for evaluating the experimental results. The mass balance for the absorption (of any gas, e. g. ozone) in a continuous-flow stirred tank reactor (CFSTR) under the assumption that the gas and liquid phases are ideally mixed (cL = cLe, cG = cGe), are as follows ... 

A more comprehensive analysis of the influences on the ozone solubility was made by Sotelo et al., (1989). The Henry s Law constant H was measured in the presence of several salts, i. e. buffer solutions frequently used in ozonation experiments. Based on an ozone mass balance in a stirred tank reactor and employing the two film theory of gas absorption followed by an irreversible chemical reaction (Charpentier, 1981), equations for the Henry s Law constant as a function of temperature, pH and ionic strength, which agreed with the experimental values within 15 % were developed (Table 3-2). In this study, much care was taken to correctly analyse the ozone decomposition due to changes in the pH as well as to achieve the steady state experimental concentration at every temperature in the range considered (0°C [Pg.86]

Two dynamic alternatives to the static approach have been used in HO calibration and measurement. In the CSTR (continuously stirred tank reactor) approach, air containing the tracer or tracers flows into the reactor to balance the bulk flow out to the HO measuring devices, and the contents are stirred by a fan or other means. The HO chemical tracer is measured in the inlet flow to obtain [T]() and in the outlet flow to obtain [T], Mass balance requires... 

When the reactant ratio is unity (i.e., 0A= 1), the mass balance for component A in the continuous flow stirred tank reactor is... 

Consider an exothermic irreversible reaction with first order kinetics in an adiabatic continuous flow stirred tank reactor. It is possible to determine the stable operating temperatures and conversions by combining both the mass and energy balance equations. For the mass balance equation at constant density and steady state condition,... 

The equations that have been developed for design using these pseudo constants are based on steady-state mass balances of the biomass and the waste components around both the reactor of the system and the device used to separate and recycle microorganisms. Thus, the equations that can be derived will be dependent upon the characteristics of the reactor and the separator. It is impossible here to present equations for all the different types of systems. As an illustration, the equations for a common system (a complete mix - stirred tank reactor with recycle) are presented below. 

Classical chemical reaction engineering provides mathematical concepts to describe the ideal (and real) mass balances and reaction kinetics of commonly used reactor types that include discontinuous batch, mixed flow, plug flow, batch recirculation systems and staged or cascade reactor configurations (Levenspiel, 1996). Mixed flow reactors are sometimes referred to as continuously stirred tank reactors (CSTRs). The different reactor types are shown schematically in Fig. 8-1. All these reactor types and configurations are amenable to photochemical reaction engineering. 

Yeast cells (Candida lipolytica) can convert n-paraffins to SCR The process developed by BP uses a continuous stirred tank reactor under sterile conditions. The SCP is harvested by centrifugation and then spray-dried. The mass balance equation (Eq. 9.4) shows that less heat is generated and that a little less oxygen is needed than for the methane process. 

To derive the overall kinetics of a gas/liquid-phase reaction it is required to consider a volume element at the gas/liquid interface and to set up mass balances including the mass transport processes and the catalytic reaction. These balances are either differential in time (batch reactor) or in location (continuous operation). By making suitable assumptions on the hydrodynamics and, hence, the interfacial mass transfer rates, in both phases the concentration of the reactants and products can be calculated by integration of the respective differential equations either as a function of reaction time (batch reactor) or of location (continuously operated reactor). In continuous operation, certain simplifications in setting up the balances are possible if one or all of the phases are well mixed, as in continuously stirred tank reactor, hereby the mathematical treatment is significantly simplified. 

For each of the ideal reactor types, viz. ideal batch reactor, plug-flow reactor (PFR), and continuous-flow stirred-tank reactor (CSTR), continuity equations or design equations can be derived using mass (or rather molar) balance equations for each species involved. 

Stratco unit with the single mixer on one end is approximated by a single mixed tank, as shown in the upper part of the figure. However, the Kellogg cascade unit has a series of compartments with mixers and olefin is sparged into each compartment to keep the concentration low so that it reacts with the isobutane rather than polymerizing. The tank-in-series model may be used to model this type of unit and this is shown in the lower part of the figure. A mass balance can be made for a stirred tank reactor readily because the composition is the same everywhere in the vessel. 

The reactor models considering complete mixing may be subdivided into batch and continuous types. In the continuous stirred tank reactor (CSTR) models, an entering fluid is assumed to be instantaneously mixed with the existing contents of the reactor so that it loses its identity. This type of reactor operates at uniform concentration and temperature levels. For this reason the species mass balances and the temperature equation may be written for the entire reactor volume, not only over a differential volume element. Under steady-state conditions, the species mass and heat balances reduce to algebraic equations. 

Generalized function mostly unit operations like continuous stirred tank reactor or plug flow reactor for react and distillation column or evaporator for separate" and also new combined operations assumptions are necessary due to lack of some data in advance calculations with linear mass- and energy balances short-cut methods ... 

In Example 5-3 the temperature and conversion leaving the reactor were obtained by simultaneous solution of the mass and energy balances. The results for each temperature in Table 5-7 represented such a solution and corresponded to a diiferent reactor, i.e., a different reactor volume. However, the numerical trial-and-error solution required for this multiple-reaction system hid important features of reactor behavior. Let us therefore reconsider the performance of a stirred-tank reactor for a simple single-reaction system. 

Solution Figure 6-1 Oo describes a step-function input of tracer of concentration Cq for a series of ideal stirred-tank reactors. A mass balance on the j reactor in a series of n is, according to Eq. (3-1),... 

The mass balance of reacting component for the first of a series of ideal stirred-tank reactors (see Secs. 4-6 and 4-7) is... 

Stirred tank reactor as no fluid enters or leaves the reactor the mass balance of every compound is defined by the reaction rate only. To determine the time t necessary to reach the desired conversion x the reciprocal rate equation has to be integrated from zero to the desired conversion x ... 

This chapter will explain the principles underlying chemical reactions, and it will go on to generalize these principles to the case of several concurrent reactions with large numbers of reagents and products. Then we shall extend to the case of chemical reaction the principles of mass balance and energy balance presented in Chapter 3. Finally we shall explain in detail how to simulate a gas reactor and a continuous stirred tank reactor (CSTR). 

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