Bubble Modeling

   Bubble mediated gas transfer modelling is used to determine the gas exchanged by the bubble with the surrounding fluid as it rises within and is advected by fluid motions. Normally, each bubble is considered unaffected by other bubbles. The model will also predict the lifetime for bubbles.

   Calculations by bubble models are of interest to scientists trying to determine oceanic uptake of gases of geophysical interest, such as CO2 and dimethyl sulfide, geologists attempting to predict the fate of methane released from oceanic seeps, chemical engineers looking at mass trasnfer within chemical reactors, biologists looking at bubbles in biological systems such as divers blood, aquaculture specialists looking at oxygen loss in fish ponds, and sewage treatment engineers looking at the productivity of bacteria used to reduce human wastes, to name a few. Added to this list might be food engineers looking at beverage carbonation. Image a cold beer with no bubbles!

   A bubble model combines the equations that describe the behavior of a bubble as it rises in the water with equations of motion, and mass transfer. The differential equations are then solved for the specific bubble size distribution and environmental conditions, inlcuding ambient fluid motions being simulated. To save on computation time, look up tables are calculated for various parameter, such as the gas transfer coefficient with respect to radius. Details of the model can be found in Leifer and Patro (2002) and Leifer and Judd (2002).

How the bubble model works

a. The first step is to initialize necessary parameters. These include temperature, salinity, and the presence of surfactants, parameters related to bulk fluid motions, model spatial limits, and gas parameters including aqueous concentrations, partial pressures, solubilities, and Schmidt numbers. If the bubbles originate sufficiently deep (more than 100 meters) then that pressure effects need to be considered, including compressibility (or the Van der Waals force) and pressure effects on solubility.

b. If necessary, the model must calculate the flux distribution. For a hydrocarbon seep, i.e., a steady stream, this is the flux distribution and is the number of bubbles per second in each radius increment. If the simulation if for a bubble plume, the initial (creation) distribution is needed, and is the number of bubbles per size increment at each depth created in a bubble plume.

c. The third step is to create look up tables for speed of bubble rise velocity and Reynolds number as a function of bubble size, bulk fluid velocities, gas transfer efficiency, and partial pressures.

The following steps are applied to each bubble size (and depth) class.

d. Based on the lookup table fluid motions the vector sum fluid motions for the bubble are calculated.

e. The coupled differential equations describing bubble size change, molar change, and position change are integrated numerically until the bubble either surfaces or dissolves. A third-fourth order Runge-Kutta numerical integration scheme is used to solve the stiff equations describing bubble time and spatial evolution.

f. The results of the integration (molar content, size, position) are interpolated to a smooth time and spatial grid where they are stored. Gas flux is determined from the derivative of the molar content change in time.

The model loops back to D. to simulate the next bubble size class (and/or the next depth).

Bubble model flowchart

Model Flow chart
G. Global results for the simulation, such as aqueous concentration change and total gas flux from all bubbles in the plume or stream are calculated.

H. Results of the calculation are archived.


References

  Leifer I., and A. Judd, 2002. Oceanic Methane Layers : A Bubble Deposition Mechanism from Marine Hydrocarbon Seepage. Terra Nova, 16, 471-485.

  Leifer I., and R. Patro, 2002. The bubble mechanism for transport of methane from the shallow sea bed to the surface :
A review and sensitivity study. Cont. Shelf Res., 22, 2409-2428.

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