Evaluation of mixing performance based on transition response method

3 Evaluation of mixing performance based on transition response method 

There have been several attempts to use the transition response method for the evaluation of the mixing performance of operations/equipment. In the transition response method for the flow system, a tracer is injected into the inlet and the change in its concentration at the outlet with time is measured. On the other hand, in the case of the batch system, the tracer is injected into some specific position, and the change in the spatial distribution of the concentration in the equipment with time is measured. In the following discussion, a method based on information entropy to evaluate the mixing operations/equipment on the basis of the transient response method is discussed. 

When one tracer element is observed at the inlet, the mixing performance of the operation/equipment is evaluated from the viewpoint of information entropy based on the uncertainty regarding the amount of time taken by the tracer element to reach the outlet. The time the tracer is injected is set as the origin. The definite integral from zero to infinity of the RTD function of the dimensionless residence time (r(= t/T, T = V/Q, V volume of equipment, Q flow rate)) should be unity. Additionally, by considering the definition of dimensionless time, its average value is fixed at unity. Therefore, the standardized and restrictive conditions can be written as 

This amount of uncertainty disappears when the residence time of the observed tracer element is known. Next, the RTD function for the maximum and minimum values of H(t) are discussed mathematically. Since the variable t takes a positive value and the average of t is fixed at unity, according to Section 1.6, H(t) assumes maximum and minimum values as 

The correspondence of the conditions for the maximum and minimum values of H( t) with the practical mixing phenomena is considered. The condition under which H(t) takes the maximum value is realized when the perfect mixing flow is established in the equipment, that is, when the concentration of tracer in the equipment is perfectly homogeneous every time and the concentration of tracer at the outlet decreases exponentially. On the other hand, the condition under which H t) takes the minimum value is realized when a piston flow is established in the equipment, that is, when the tracer does not disperse in the 

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