Prediction of Tracer Concentration and Mixing in CFSTRs with Mean Age Distribution

Abstract

Three-dimensional time-dependent tracer concentration distributions in nonideal continuous flow stirred tank reactors with pulse input are studied computationally. Both the steady transport equation for mean age and the time-dependent transport equation for tracer concentration are solved. It is found that the time-dependent tracer concentration history can be divided into two stages: an initial stage, in which the concentration is highly location-dependent, and a stationary stage, in which the concentration decays with a location-independent, constant exponential rate. This rate is found to be the inverse of the volume-averaged mean age. The length of the initial stage is found to be very short, on the same order of magnitude as the batch blend time. It is also found that the scaled concentration distribution in the stationary stage is almost identical to the scaled mean age distribution. The spatial and temporal concentration distribution in the stationary stage can be determined once the initial stage and the mean age solution are obtained. Thus, the CPU time required is orders of magnitude smaller than that for the full time integration of the unsteady concentration equation. With the solution of tracer concentration distribution known, mixing time and other quantitative measures for the tracer mixing can be easily calculated.