Deviations from ideal flow conditions

In principle, if the temperatures, velocities, flow patterns, and local rates of mixing of every element of fluid in a reactor were known, and if the differential material and energy balances could be integrated over the reactor volume, one could obtain an exact solution for the composition of the effluent stream and thus the degree of conversion that takes place in the reactor. However, most of this information is lacking for the reactors used in laboratory or commercial practice. Consequently, it has been necessary to develop approximate methods for treating 

Except for the case of an ideal plug flow reactor, different fluid elements will take different lengths of time to flow through a chemical reactor. In order to be able to predict the behavior of a given piece of equipment as a chemical reactor, one must be able to determine how long different fluid elements remain in the reactor. One does this by measuring the response of the effluent stream to changes in the concentration of inert species in the feed stream—the so-called stimulus-response technique. In this section we will discuss the analytical form in which the distribution of residence times is cast, derive relationships of this type for various reactor models, and illustrate how experimental data are treated in order to determine the distribution function. 

The mathematical relations expressing the different amounts of time that fluid elements 

Since F(t + dt) represents the volume fraction of the fluid having a residence time less than t + dt, and F(t) represents that having a residence time less than r, the differential of F(t dF(t will be the volume fraction of the effluent stream having a residence time between t and t + dt. Hence dF(t) is known as the residence time distribution function. From the principles of probability the average residence time (t) of a fluid element is given by 

Determination of average residence time from residence time distribution function. 

---

It is convenient to classify deviations from ideal flow conditions into two categories. 

Chapter 11 Deviations from Ideal Flow Conditions... 

Chapter 11 Deviations from Ideal Flow Conditions equation (11.1.59) may be rewritten as... 

The main problems related to the use of the tubular-flow reactor are caused by the deviations from ideal flow conditions, entrance and exit effects, heating and cooling rates and effects of heat of reaction on the temperature profiles and on the temperature difference between the reactants and the reactor wall. The heat transfer limitations can be very significant if the reactor diameter is not very small and if temperatures above 600°C are employed. Another problem arises from the difficulty in the evaluation of the actual reaction time, because of the increase in volume of the reacting mixture with temperature and conversion. 

---