Constant density isothermal reaction

Most kinetic experiments are run in batch reactors for the simple reason that they are the easiest reactor to operate on a small, laboratory scale. Piston flow reactors are essentially equivalent and are implicitly included in the present treatment. This treatment is confined to constant-density, isothermal reactions, with nonisothermal and other more complicated cases being treated in Section 7.1.4. The batch equation for component A is... 

For reaction A -> products constant-density, isothermal, steady-state operation. Second term is related to exponential integral see Table 14.1. 

The feed is charged all at once to a batch reactor, and the products are removed together, with the mass in the system being held constant during the reaction step. Such reactors usually operate at nearly constant volume. The reason for this is that most batch reactors are liquid-phase reactors, and liquid densities tend to be insensitive to composition. The ideal batch reactor considered so far is perfectly mixed, isothermal, and operates at constant density. We now relax the assumption of constant density but retain the other simplifying assumptions of perfect mixing and isothermal operation. 

All the results obtained for isothermal, constant-density batch reactors apply to isothermal, constant-density (and constant cross-section) piston flow reactors. Just replace t with z/u, and evaluate the outlet concentration at z = L. Equivalently, leave the result in the time domain and evaluate the outlet composition t = L/u. For example, the solution for component B in the competitive reaction sequence of... 

Example 4.13 Determine the outlet concentration from a loop reactor as a function of Qi and q for the case where the reactor element is a PFR and the reaction is first order. Assume constant density and isothermal operation. 

Example 14.1 Consider a first-order reaction occurring in a CSTR where the inlet concentration of reactant has been held constant at uq for f < 0. At time f = 0, the inlet concentration is changed to Up Find the outlet response for t > 0 assuming isothermal, constant-volume, constant-density operation. 

Example 14.5 A CSTR is operating at steady state with a first-order reaction. It is desired to shut it down. Suppose this is done by setting = 0 while maintaining Qout = Q until the reactor is empty. Assume isothermal, constant-density operation with first-order reaction. 

Determine the fractional Ailing rate QflulQ that will All an isothermal, constant-density, stirred tank reactor while simultaneously achieving the steady-state conversion corresponding to flow rate Q. Assume a second-order reaction with aj kt = 1 and t = 5 h at the intended steady state. 

In this section we discuss the mathematical forms of the integrated rate expression for a few simple combinations of the component rate expressions. The discussion is limited to reactions that occur isothermally in constant density systems, because this simplifies the mathematics and permits one to focus on the basic principles involved. We will again place a V to the right of certain equation numbers to emphasize that such equations are not general but are restricted to constant volume batch reactors. The use of the extent per unit volume in a constant volume system ( ) will also serve to emphasize this restriction. For constant volume systems,... 

We do this for isothermal constant-density conditions first in a BR or PFR, and then in a CSTR. The reaction conditions are normalized by means of a dimensionless reaction number MAn defined by... 

For an nth-order isothermal, constant-density reaction in a BR or PFR (n 1), equa-... 

A performance comparison between a BR and a CSTR may be made in terms of the size of vessel required in each case to achieve the same rate of production for the same fractional conversion, with the BR operating isothermally at the same temperature as that in the CSTR. Since both batch reactors and CSTRs are most commonly used for constant-density systems, we restrict attention to this case, and to a reaction represented by... 

Table 18.1 Comparison of PFR and CSTR for series-reaction network A -4 B -+ C (isothermal, constant-density system K = kz/ki)...

For a relatively small amount of dispersion, what value of Pei would result in a 10% increase in volume (V) relative to that of a PFR (Vpf) for the same conversion (/a) and throughput (q) Assume the reaction, A - products, is first-order, and isothermal, steady-state, constant-density operation and the reaction number, Mai = at, is 2.5. For this purpose, first show, using equation 20.2-10, for the axial-dispersion model with relatively large Per, that the % increase s 100(V - V pfWpf = 100MAi/Pei. 

It has been suggested that the experimental isothermal kinetic rate constants of some reactions at near and supercritical conditions could not be explained solely by the thermodynamic pressure effect, but from the combination of local composition enhancement and density augmentation around reactants. 

Consider a tubular reactor where a chemical reaction changes the concentration of the fluid as it moves down the tube. Assuming first-order chemical reaction, isothermal reactor, and constant density, the modeling equation is... 

The following details mathematical expressions for instantaneous (point or local) or overall (integral) selectivity in series and parallel reactions at constant density and isothermal conditions. An instantaneous selectivity is defined as the ratio of the rate of formation of one product relative to the rate of formation of another product at any point in the system. The overall selectivity is the ratio of the amount of one product formed to the amount of some other product formed in the same period of time. 

Table 7-2 and Figs. 7-3 and 7-4 show the analytical solution of the integrals for two simple first-order reaction systems in an isothermal constant-volume batch reactor or plug flow reactor. Table 7-3 shows the analytical solution for the same reaction systems in an isothermal constant-density CSTR. 

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