Stirred-tank reactors energy balance

The ideal continuous stirred tank reactor is the easiest type of continuous flow reactor to analyze in design calculations because the temperature and composition of the reactor contents are homogeneous throughout the reactor volume. Consequently, material and energy balances can be written over the entire reactor and the outlet composition and temperature can be taken as representative of the reactor contents. In general the temperatures of the feed and effluent streams will not be equal, and it will be necessary to use both material and energy balances and the temperature-dependent form of the reaction rate expression to determine the conditions at which the reactor operates. 

The steady-state form of the energy balance for a continuous stirred tank reactor is given by equation 10.1.4. 

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. 

The semibatch reactor is a cross between an ordinary batch reactor and a continuous-stirred tank reactor. The reactor has continuous input of reactant through the course of the batch run with no output stream. Another possibility for semibatch operation is continuous withdrawal of product with no addition of reactant. Due to the crossover between the other ideal reactor types, the semibatch uses all of the terms in the general energy and material balances. This results in more complex mathematical expressions. Since the single continuous stream may be either an input or an output, the form of the equations depends upon the particular mode of operation. 

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,... 

A first-law energy balance on the continuous-flow stirred-tank reactor gives the expression... 

In an ideal continuous stirred tank reactor, composition and temperature are uniform throughout just as in the ideal batch reactor. But this reactor also has a continuous feed of reactants and a continuous withdrawal of products and unconverted reactants, and the effluent composition and temperature are the same as those in the tank (Fig. 7-fb). A CSTR can be operated under transient conditions (due to variation in feed composition, temperature, cooling rate, etc., with time), or it can be operated under steady-state conditions. In this section we limit the discussion to isothermal conditions. This eliminates the need to consider energy balance equations, and due to the uniform composition the component material balances are simple ordinary differential equations with time as the independent variable ... 

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 ... 

The ideal stirred-tank reactor operates isothermally and hence at a constant rate. However, an energy balance is needed to predict the constant temperature when the heat of reaction is sufficient (or the heat exchange between the surroundings and reactor is insufficient) to cause a difference between... 

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. 

The most common problem in scaling up stirred tank reactors is the difficulty in maintaining the desired operating temperature. The current section assumes this is possible. Techniques for maintaining a desired energy balance are deferred to Chapter 5. 

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). 

Numerical simulations and analyses were performed for both the continuous stirred-tank reactor (CSTR) and the plug-flow reactor (PER). A comparison between the microkinetic model predictions for an isothermal PFR and the experimental results [13], is presented in Fig. 2 for the following conditions commercial low temperature shift Cu catalyst loading of 0.14 g/cm total feed flow rate of 236 cm (STP) min residence time r = 1.8 s feed composition of H20(10%), CO(10%), C02(0%), H2(0%) and N2(balance). As can be seen, the model can satisfactorily reproduce the main features of the WGSR on Cu LTS catalyst without any further fine-tuning, e.g., coverage dependence of the activation energy, etc, which is remarkable and provides proof of the adequacy of the... 

Two forms of simplified energy balance for stirred-tank reactor... 

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... 

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... 

As a consequence of the complete mixing, a continuous flow stirred tank reactor also operates isothermally. Therefore, in the steady state it is not necessary to consider the mass and energy balances simultaneously. Optimum conditions may be computed on the basis of the material balance alone, and then afterwards the energy balance is used, in principle (see Sec. 10.4), to determine the external conditions required to maintain the desired temperature. 

Multiple Steady States and Local Stability in CSTR.—In the two decades since the seminal work of van Heerden and Amimdson, there has been vast output of papers conoemed with the dynamic behaviour of stirred-tank reactors. Bilous and Amundson put the van He den analysis of local stability of the equilibrium state on a rigorous basis by use of linear stability theory. Their method is similar to the phase-plane treatments of thermokinetic ignitions and oscillations discussed here in Sections 4 and 3 (and preceded them dironologically). The mass and energy balance for the CSTR having a single reactant as feedstock may be expressed as ... 

It is desired to determine the steady-state temperature and concentration in a continuous stirred tank reactor in which an exothermic reaction is taking place. We want to determine conditions for both maximum and minimum cooling. The reactor is shown in Figme 2.22. The macroscopic material and energy balances are... 

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 the modeling of a reactor we need solutions of the equations of the balances of mass, energy, and impulse. For isothermal operation the energy balance is not needed. The impulse balance mostly only serves to calculate the pressure drop of a reactor. The definition of a suitable control space for balancing is important. In the simplest case, the variables - such as temperature and concentrations - are constant within the control space (stirred tank reactor). However, in many cases the system variables depend on the location, for example, in the axial direction in a tubular reactor. Then infinitesimal balances (differential equations) have to be solved to obtain integral data. 

The desired production capacity and the required reaction time (residence time) are two of the most important criteria when selecting a reactor suitable for a homogeneous process. Trambouze et al. [ 1 ] have proposed a chart that suggests the applicability limits of different kinds of reactors for various reactions (Figure 3.8). For slow reactions and low production capacities, a BR is typically chosen, whereas for larger production voliunes, a continuous reactor is preferred a cascade of stirred tank reactors or a tube reactor. In the next section, the mass and energy balances for homogeneous reactors will be considered in detail. 

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