CSTR material balance

Example (d) The rate equation and the CSTR material balance of this process are ... 

If changes in the volume due to reaction can be neglected, then the CSTR material balance can be written in terms of concentrations to give (v = volumetric flow rate that is, volume per unit time) ... 

Al-Saleh et al. [Chem. Eng. J., 37 (1988) 35] performed a kinetic study of ethylene oxidation over a silver supported on alumina catalyst in a Betty reactor. At temperatures between 513-553 K and a pressure of 21.5 atm, the observed reaction rates (calculated using the CSTR material balance) were independent of the impeller rotation speed in the range 350-1000 rpm (revolutions per minute). A summary of the data is ... 

In Section 3.5 recycle reactors and particularly a Berty reactor were described. At high impeller rotation speed, a Berty reactor should behave as a CSTR. Below are plotted the dimensionless exit concentrations, that is, C(t)/C°, of cis-2-butene from a Berty reactor containing alumina catalyst pellets that is operated at 4 atm pressure and 2000 rpm impeller rotation speed at temperatures of 298 K and 427 K. At these temperatures, the cis-2-butene is not isomerized over the catalyst pellets. At t = 0, the feed stream containing 2 vol % cis-2-butene in helium is switched to a stream of pure helium at the same total flow rate. Reaction rates for the isomerization of cis-2-butene into 1-butene and trans-2-butene are to be measured at higher temperatures in this reactor configuration. Can the CSTR material balance be used to ascertain the rate data ... 

A continuous stirred tank reactor battery CSTR) Material balances ... 

Mathematically, multiplicities become evident when heat and material balances are combined. Both are functions of temperature, the latter through the rate equation which depends on temperature by way of the Arrhenius law. The curves representing these b ances may intersect in several points. For first order in a CSTR, the material balance in terms of the fraction converted can be written... 

Simple combinations of reactor elements can be solved direc tly. Figure 23-8, for instance, shows two CSTRs in series and with recycle through a PFR. The material balances with an /i-order reaction / = /cC are... 

Material and energy balances of common types of reactors are summarized in several tables of Sec. 7. For review purposes some material balances are restated here. For the /ith stage of a CSTR batteiy,... 

Continuous. stirred tank reactor (CSTR), with the effluent concentration the same as the uniform vessel concentration. With a mean residence time t = V /V, the material balance is... 

Ideal CSTR Witt a step input of magnitude Cy the unsteady material balance is... 

Conditions at steady state are determined by heat and material balances. Such balances for a CSTR can be put in the form. 

Such a differential equation together with a rate equation for the main reactant constitutes a pair that must be solved simultaneously. Take the example of a CSTR for which the unsteady material balance is... 

As another example of the first interac tion, a potential parameter in the analysis of the CSTR is estimating the actual reactor volume. CSTR shown in Fig. 30-7. The steady-state material balance for this CSTR having a sin e reaction can be represented as ... 

As can be seen for infinite recycle ratio where C = Cl, all reactions will occur at a constant C. The resulting expression is simply the basic material balance statement for a CSTR, divided here by the catalyst quantity of W. On the other side, for no recycle at all, the integrated expression reverts to the usual and well known expression of tubular reactors. The two small graphs at the bottom show that the results should be illustrated for the CSTR case differently than for tubular reactor results. In CSTRs, rates are measured directly and this must be plotted against the driving force of... 

Evaluations of the measurements are based on the transient material balance equation for CSTR ... 

The material balance function for a CSTR, m(C,T) is the transient material balance equation ... 

This program helps calculate the rate of methanol formation in mol/m s at any specified temperature, and at different hydrogen, carbon monoxide and methanol concentrations. This simulates the working of a perfectly mixed CSTR specified at discharge condition, which is the same as these conditions are inside the reactor at steady-state operation. Corresponding feed compositions and volumetric rates can be calculated from simple material balances. 

The component material balances for an ideal CSTR are the following set of algebraic equations ... 

The design equations for a CSTR do not require that the reacting mixture has constant physical properties or that operating conditions such as temperature and pressure be the same for the inlet and outlet environments. It is required, however, that these variables be known. Pressure in a CSTR is usually determined or controlled independently of the extent of reaction. Temperatures can also be set arbitrarily in small, laboratory equipment because of excellent heat transfer at the small scale. It is sometimes possible to predetermine the temperature in industrial-scale reactors for example, if the heat of reaction is small or if the contents are boiling. This chapter considers the case where both Pout and Tout are known. Density and Q ut wiU not be known if they depend on composition. A steady-state material balance gives... 

The material balance on a single CSTR operating at steady state may be represented by ... 

If the case of an irreversible first-order reaction is considered, a material balance on the nth CSTR gives... 

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... 

Consider a constant-density reaction with one reactant, A - products, as illustrated for a liquid-phase reaction in a CSTR in Figure 3.6. One experiment at steady-state generates one point value of (—rA) for the conditions (cA, q, T) chosen. This value is given by the material balance obtained in Section 2.3.2 ... 

These rate laws are coupled through the concentrations. When combined with the material-balance equations in the context of a particular reactor, they lead to uncoupled equations for calculating the product distribution. For a constant-density system in a CSTR operated at steady-state, they lead to algebraic equations, and in a BR or a PFR at steady-state, to simultaneous nonlinear ordinary differential equations. We demonstrate here the results for the CSTR case. 

For the CSTR case, illustrated in Figure 7.2, suppose the feed concentration of monomer is cUo, the feed rate is q, and the reactor volume is V. Using the material-balance equation 2.3-4, we have, for the monomer ... 

For continuous operation of a CSTR as a closed vessel, the general material balance equation for reactant A (in the reaction A vr C +. .. ), with a control volume... 

Third, for a CSTR, the accumulation term in the material-balance equation 14.3-2 or -3 becomes... 

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