281977 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.