3-Phase Bioreactor Lack of Mass Conservation
 

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I am simulating a 2L bioreactor (1L liquid volume) at 500 RPMs, so the headspace is in included. Air (1 mm dispersed phase) is sparged through the reactor by a sparger on the bottom of the reactor per a specified VVM. The air inlet (specified with a 1 volume fraction for air and 0 for oil and water) is specified onto the holes of the sparger as a normal speed mass and momentum boundary condition calculated via expression. A similar expression, based on the reactor VVM, is used to calculate the air (1 volume fraction, 0 for oil and water) on the outlet. The intent of using expressions is to ensure the vessel is mass balanced. Within the 1L liquid phase 75% is water (continuous phase) and 25% is oil (a polydispersed MUSIG phase). The reactor has two impellers and is baffled.
I have been using a high performance cluster and running the simulations for 2 weeks and generally get around 150,000 iterations. The simulations usually do not come to a standard (1E-4) convergence criteria. The problem I have with the results is the lack of mass conservation. Water will usually increased from the 37.5% original specification to around 47.5% volumeAve of the assembly. At the same time oil will generally increase 2-4% with air decreasing. With 100% mass conservation, oil and water would remain and air should be mass balanced from the inlet/outlet expressions.
Based on some previous reading of Ansys CFX Modeling Guide:
1. Multi Phase Modeling 7.1.6 Volume Fraction –
Multiphase modeling employs the notion of interpenetrating continua. Although phases are mixed at length scales much larger than molecular, they are also assumed to be mixed at length scales smaller than you want to resolve. Thus, each phase is assumed to be present in principle in each control volume, and assigned a volume fraction equal to the fraction of the control volume occupied by that phase. This variable appears as .Volume Fraction in the results file. The variable .Conservative Volume Fraction is also available but should not usually be used for postprocessing. The conservative 297 Release 2021 R2 - © ANSYS, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates. Multiphase Terminology volume fraction is used by the CFX-Solver; it may exceed 1 and may not sum to unity over all fluids during the solution. However, these criteria are enforced in a converged solution.

If there are areas of all oil and or air, ANSYS CFX is assuming water is there, which would artificially increase the amount of water in the domain correct? I am assuming also, if there is foam or oil/air bubbles, CFX can’t handle this and will over predict coalescence resulting in water in that location. Any thoughts, comments of corrections would be much appreciated?

2. The lack of mass conservation is a function of convergence. There are simplifications made in the solution to help approximate a steady-state solution for a dynamic, multiphase system. Some of these dynamic events include changing liquid shape, level undulations, splashing, foam, and liquid entrainment in the air exiting the reactor (w/ no oil/water makeup specified within the reactor).


Thank you so much for your help!