Spatial distribution of mean age and higher moments of unsteady and reactive tracers: Reconstruction of residence time distributions

•A new moment generation transport equation has been derived with almost full generality.•The equation is tested with different examples of use.•RTD can be reconstructed through this equation and reconstruction methods.•The equation provides excellent computational features and accuracy.

The purpose of this investigation is to study the spatial distribution of mean age and higher moments of unsteady and reactive tracers. This objective has been achieved by deriving a moment generation transport equation with full generality. Using this equation, it is possible to derive the age and moment equations for other models previously presented in the literature. The novelty of this method relies on a completely general mathematical framework that permits density, velocity or any other fluid variable to be space and time dependent, and the inclusion of multiple inlets to a computational domain. In addition, if a kinetic expression for the appearance/disappearance of the tracer is supplied, the corresponding moments can also be computed accurately. The main results show how the use of this equation along with a reconstruction method for the Residence Time Distribution allows for a decrease of four orders of magnitude in the computational cost required for the obtaining of such distributions in some cases. This result implies that a better understanding of flow features inside vessels and can be gained, and the optimization of such vessels from the viewpoint of the moments of the RTD is possible.