Continuous stirred tank reactor mass balance

Coupled mass and thermal energy balances are required to analyze the nonisother-mal response of a well-mixed continuous-stirred tank reactor. These balances can be obtained by employing a macroscopic control volume that includes the entire contents of the CSTR, or by integrating plug-flow balances for a differential reactor under the assumption that temperature and concentrations are not a function of spatial coordinates in the macroscopic CSTR. The macroscopic approach is used for the mass balance, and the differential approach is employed for the thermal energy balance. At high-mass-transfer Peclet numbers, the steady-state macroscopic mass balance on reactant A with axial convection and one chemical reaction, and units of moles per time, is... 

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. 

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... 

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... 

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. 

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 ... 

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). 

For a closed chemical system with a mass action rate law satisfying detailed balance these kinetic equations have a unique stable (thermodynamic) equilibrium, lim c( )=Cgq. In general, however, we shall be concerned with chemical reactions that are maintained far from chemical equilibrium by flows of reagents intoand out of a continuously stirred tank reactor (CSTR). In this case the chemical kinetic equation (C3.6.1) must be supplemented with flow terms... 

X H kJ/mol. Since the sticking coefficient of H2 on Cu( 111) is not known, the prefactor for the sticking and the activation energy of the Cu(l 10) surface was used as areliable approximation. From the kinetic gas theory, a preexponential factor Aads = 9.2 x 10 (torr-s) was derived for our model. In our calculation we assumed 132 /xmol/gr active sites based on theexperimental results of Muhler et al. [6] for the Cu/Zn0/Al203 based on a H/ = H (2 Cu) = 1 1 stoichiometry. Under the conditons of perfect mixing gas phase condition is uniform throughout the bed. The reactor mass balance for a transient continuous stirred tank reactor was used in the form... 

If component i participates in several chemical reactions in a well-mixed continuous-stirred tank reactor (CSTR) with volume Vcstr, then the macroscopic mass balance at large mass transfer Peclet numbers is... 

For each of the chemical species participating in the mechanism, a mass balance equation must be written. The appropriate form of the mass balance for the specific type of reactor at hand must be used. Two of the most common types of reactors used in industry are the CSTR (continuous stirred tank reactor) and the tubular reactor. The corresponding mathematical models for their idealized forms, based on transport phenomena equations and available in any standard chemical reactor text [17, 18], are the ideal CSTR and the ideal model for the plug flow tubular reactor (PFR). The ideal CSTR model is given by Equation 12.1 ... 

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) ... 

Because component concentrations are uniform throughout a continuous stirred tank reactor, a mass balance can immediately be constructed over the entire reactor. At steady-state conditions, the following algebraic equation is obtained describing the mass balance equation for a component A over the entire continuous stirred tank reactor ... 

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). 

We can use such an empirical relation in combination with the mass balances such as eqs. (3.12) and (3.21) for designing other batch reactors. We can also use these empirical relations in designing continuous stirred tank reactors, as will be seen in section 3.3.2. 

The construction of a laboratory-scale continuous stirred tank reactor (CSTR) resembles of that of a BR, but the reactor is equipped with an inlet and an outlet. Concentration and temperature gradients should be absent because of vigorous stirring. For a homogeneous CSTR, a constant volume and pressure are reasonable assumptions. The concentrations at the reactor outlet are measured as a function of the space time, that is, volumetric flow rate. The steady-state mass balance is written as (Chapter 3)... 

In the absence of any appreciable diffusional effects, the mass balance for the shallow bed (differential bed) is that for a continuously-stirred tank reactor ... 

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 ... 

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 ... 

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