A single particle approach for analyzing flow systems. Part III: Multiple fluids

This paper provides a stochastic model for general flow systems with several inlets and outlets, where different fluids are fed through the various inlets. Several process characteristics are derived and discussed. They include the distribution, mean, and variance of the number of visits and total residence time of the various fluid elements to flow regions and the fraction of each fluid that avoids a flow region or a group of flow regions. It is shown that for any fluid and any specified region, the local flow rate through the region is equal to the product of the net flow rate through the system and the mean number of visits to the region by a fluid element of this type. Expressions are also derived for the compositions of material at the outlet streams and at individual flow regions exits, as well as for the composition of material inside each flow region. These results may be employed to verify flow models of physical systems and to determine model parameters.