(142ax) Stability of a Two-Phase Column Bioreactor for Algae Growth

Stability of a Two-Phase Column Bioreactor for Algae Growth

Justin Smith, Daniel Crunkleton, Selen Cremaschi

Department of Chemical Engineering, University of Tulsa, 800 South
Tucker Drive, Tulsa, OK 74104, USA

We perform a linear stability analysis of algae growth in
a two-phase air-water bubble column.  To
accomplish this, the 2D, Cartesian, Navier-Stokes equations for fluid flow are
coupled using the Boussinesq approximation with the reactive concentration balance
for algae growth.  A system of seven
equations is obtained and a normal mode perturbation of the horizontal and
vertical components of the velocity of both the continuous and dispersed phases,
the gas volume fraction, pressure, and algae concentration is performed.  The equations are linearized by setting any
product of multiple perturbations equal to zero under the assumption that as
the perturbation size is small, the size of a product of multiple perturbations
is negligible.  A stability matrix is then
constructed, the determinant of which gives a dispersion relation with roots that
can be analyzed for stability as a function of several values of key process parameters,
including initial algae concentration, and reaction rate, defined here as algae
growth rate. By varying the size of both the horizontal and vertical wave
vector components of the perturbation, the stability of the bioreactor is determined
by observing changes to the amplitude and sign of the real parts of the roots.  The stability characteristics of the system
indicate that for base case force parameters in a system with drag and virtual
mass forces, bubble induced turbulence, and bubble pressure forces, algae
growth is most stable with small values for algae growth rate and initial algae
concentration and becomes less stable as the initial algae concentration is
increased.  The asymptotic behavior of
the current study compares favorably with previous linear
stability results that considered the two-phase system in the absence of a reactive
concentration balance.