In continuous processes, the properties and quality of the products depend on the residence time of different feed substances, and feed materials may not spend the same amount of time in a reactor. When designing equipment for continuous processes, it is essential to have information about the residence time distribution (RTD) of the reactants that are introduced into a reactor. Added reactants could include solids, liquids, gases or a multiphase combination). This one-page reference reviews concepts associated with determining RTD for a continuous stirred-tank reactor (CSTR).
Ideal and non-ideal reactors
Ideal CSTRs can be thought of as theoretical models in which mixing and transport processes are well known and predictable. Real-world reactors are non-ideal systems, where mixing is not perfect, and where stagnant zones and other phenomena can lead to a range of different residence times in the reactor.
The RTD is the probability distribution of the time that a given sample of feed material is likely to spend inside the reactor. Determining residence times for ideal reactors involves relatively straightforward calculations, because it is assumed that the reactor contents are perfectly mixed and the concentration of reactants is uniform throughout the volume of the reactor. For an ideal CSTR, the mean residence time can be calculated by dividing the reactor volume by the volumetric flowrate.
For non-ideal reactors, the RTD usually must be determined experimentally using real-world data. Steady-state flow coming into the reactor and leaving the reactor, as well as the volume of the reactor, are assumed to be fixed (constant).
Tracer experiments
Tracer experiments can be used to determine the RTD for a reactor to determine how far the reactor deviates from the behavior of an ideal reactor. A tracer is a material designed to behave in the same way within the reactor as the regular process media normally flowing through the reactor. In a CSTR, common tracer materials include salts (such as NaCl and LiCl) because of their low-cost and ability to be detected using conductivity probes. Dyes and radioactive isotopes are also used as tracers.
Ideal characteristics of the tracer material include the following: inertness, so as not to react with the process fluid; similar physical properties (such as density and viscosity) to the material entering the reactor; having the ability to be readily detectable, so it can be measured accurately at high and low concentrations; and stability under the process conditions.
The objective of tracer experiments for RTD is to inject the tracer material into the inlet of a reactor, then measure the amount of tracer leaving the reactor at the reactor outlet over time. The concentration change of tracer per unit time is graphed.
Tracer response techniques
Methods for injecting a tracer into a reactor are generally categorized into two groups, as follows:
Pulse input. In a pulse-input experiment, a fixed amount of tracer is introduced into the inlet of a reactor (or a series of reactors) all at once over the briefest possible time interval (Figure 1A, pulse injection).
A detector then records the concentration of tracer as it leaves the reactor over time. The concentration of tracer at the outlet is proportional to the RTD. The detector will begin to detect small amounts of tracer exiting the reactor, and the concentration of tracer will gradually increase to a maximum concentration, and then decline back to zero once all the tracer passes through the reactor (Figure 1A, pulse response).
Step input. In a step-input tracer experiment, tracer is introduced at a given time, then the tracer concentration is kept constant by continuously adding tracer material into the reactor. In this case, the response increases from zero to a maximum tracer concentration, where the value then plateaus (Figure 1, Diagram B).
FIGURE 1. There are two common methods for introducing tracer materials into a reactor to measure RTD. In the pulse method, tracer is added all at once in a brief time period. For the step-input method, tracer is added, and the concentration maintained at a constant level with continuous addition
References
1. Tibbet, M., Practical Training on Residence Time Distribution, ETH-Zurich Macromolecular Engineering Lab, macro.ethz.ch.
2. Dudokovic, M. and Felder, R., Mixing effects in chemical reactors: Models for non-ideal reactors, AIChE Chemical Engineering Modular Instruction Series, Module E4.5.