HOLDUP AND DISPERSION - TRACER RESIDENCE TIMES, MOMENTS AND INVENTORY MEASUREMENTS

The inventory function is the quantity of tracer remaining in a continuous-flow system at elapsed time t when steady flow of the tracer is replaced by untraced flow at t = 0. The relations between residence-time distributions, moments and changes in inventory when a tracer is flushed from a system are established. It is shown that inventory measurements could be an attractive way of measuring moments. In particular, the mean residence time is given by the intercept on the baseline of the initial tangent to the inventory curve, and the variance by the area between the inventory curve, the initial tangent and the baseline. It is proposed that dispersion be defined in terms of the variance of the residence-time distribution. This would allow experimentalists to record their results independently of models or theories in addition to comparing their results with the predictions of theories. Methods based on inventory measurements are potentially more accurate than the traditional step- and pulse-response methods. Ways in which inventory measurements might be made are suggested. It is timely that the theory should be presented now because tomographic methods that could be used to measure inventory are starting to appear.