Reactions nth-order

Equation 5-247 is a polynomial, and the roots (C ) are determined using a numerical method such as the Newton-Raphson as illustrated in Appendix D. For second order kinetics, the positive sign (-r) of the quadratic Equation 5-245 is chosen. Otherwise, the other root would give a negative concentration, which is physically impossible. This would also be the case for the nth order kinetics in an isothermal reactor. Therefore, for the nth order reaction in an isothermal CFSTR, there is only one physically significant root (0 < C < C g) for a given residence time f. 

For an nth order reaction of a macro fluid. Equation 9-16 is substituted into Equation 9-6 to give... 

The reaction rate per unit volume of particle 5H, for an nth-order reaction is then given by ... 

Relatively few kinetic schemes admit analytical solutions. This section is concerned with those special cases that do, and also with some cases where preliminary analytical work will ease the subsequent numerical studies. We begin with the nth-order reaction. 

Example 15.16 Apply the bounding theory to an nth-order reaction, = —kd. ... 

Given that the decomposition of SrC03 is a simple nth order reaction and that the rate consteUit is 4 x lO" mol/sec. at 865 °C, calculate the amount of SrO formed in 10.0 minutes from the original 1.0 mol of powder, if the reaction is a first-order reaction. 

Consider an nth-order reaction the equivalent dimensionless model for the stirred-tank reactor becomes... 

Figure 5.4. Batch reactor with simple nth-order reaction.

TANK and TANKD - Single Tank with Nth-Order Reaction... 

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. 

Figure 5.30. A continuous-tank reactor with nth-order reaction.

The tubular reactor, steady-state design equation is of interest here. The dimensional and dimensionless forms are compared for an nth-order reaction. 

Steady-state conversions for both continuous tank and tubular reactors are compared for nth-order reaction kinetics. 

For a plug-flow tubular reactor with nth-order reaction at steady state,... 

For nth-order reaction in terms of fraction conversion, Xa for a tank... 

This program is designed to simulate tracer experiments for residence time distributions based on a cascade of 1 to 8 tanks-in-series. An nth-order reaction can be run, and the steady-state conversion can be obtained. The important parameters to change are as follows for the tracer experiments k, CAINIT, and CAO ( = 0 for E curve, = 1 for F curve). For reaction studies, the parameters to change are n, k, CAO, and CAINIT. 

Eight tanks In series with nth-order reactions. 

Revise the program to include nth-order reaction. Evaluate the conversion for first-order reaction from the dynamic model. Compare this with the conversion calculated from the E curve. Show by simulation that the two are equal only if the reaction is first order. 

Comparison of performance of single CSTR and plug flow reactor for the nth-order reactions... 

For a reaction whose rate-concentration curve rises monotonically (any nth-order reaction, n > 0) the reactors should be connected in series. They should be ordered so as to keep the concentration of reactant as high as possible if the rate-concentration curve is concave (n > 1), and as low as possible if the curve is convex n < 1). 

More generally, for an nth-order reaction, the half-life is given (from equation 3.4-9) by... 

The development of an analytical expression for tj in Example 8-4 is for a first-order reaction and a particular particle shape (flat plate). Other orders of reaction can be postulated and investigated. For a zero-order reaction, analytical results can be obtained in a relatively straightforward way for both tj and flat plate and 8-15 for a sphere). Corresponding results can be obtained, although not so easily, for an nth-order reaction in general an exact result can be obtained for and an approximate one for tj. Here, we summarize the results without detailed justification. 

For an nth-order reaction, the diffusion equation corresponding to equation 8.5-12 is... 

Note that the dimensionless parameter PAR is the ratio of the residence time, L/v, and the reaction time for an nth-order reaction, 1 /kCA0. ... 

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