Mean age theory in multiphase systems

• Mean age theory was extended here to multiphase systems.
• Computational results were well validated against experimental results.
• This technique is applicable to any combination of phases.
• This technique is applicable to advective and diffusive processes.
• Key novelty is for multiphase applications with very long residence times or ages.

Conventional residence time distributions reveal system mixing and dispersion characteristics but are limited to discrete sampling locations, typically at the exit. Mean age theory extends the usefulness of the concept by providing spatial distributions of the mean age of material inside a system using an innovative steady-state approach that incorporates time as a passive scalar, but has been limited to single phase systems. Mean age theory was extended here to multiphase systems by defining the scalar tracer concentration independently for individual phases, which allows mean age to be solved at steady-state for each phase independently within a multiphase system. The theory was well validated by comparing residence time distributions extracted from spatial mean age distributions determined computationally at two locations where RTDs were experimentally measured in a water–oil flow system. Mean residence times from MMA theory were within 1–3% of experimental values and variances were within 3–11%. Means and variances derived from MMA theory matched experimental values more closely than did values derived from the conventional transient solutions, indicating better accuracy due to the steady-state solution. This technique is widely applicable to multiphase systems of any phase type (liquids, solids, and gases), and since it can be solved at steady-state, is advantageous for applications with extraordinary long residence times or ages.