Simulation of the Hydrodynamic Behaviour of a Biological Packed Bed

Biological filtration through submerged packed bed is a technology that has been recently integrated in control and management of water and soil pollution. Scaled-up packed bed reactors, however, bring lower yields than expected. One of the main causes of lower performance of filters is related to poor liquid distribution which affects the distribution of both incoming substrates and reaction products. The main factors involved in flow maldistribution is the presence of immobile areas, dead volumes, short-circuiting, internals recirculation, and dispersion. A study on the hydraulic characteristics of a submerged packed bed is an accurate procedure to get information about the presence of these flow disturbances.

The hydraulic characteristics of a laboratory submerged packed bed, filled with a volcanic stone (pozzuolana), have been experimentally investigated through tracer tests. Sets of essays at flow rates from 1 to 2.5 l/h in clean conditions were performed. The results showed a considerable amount of dispersion through the filter as the hydraulic loading was changed, indicating a multiplicity of hydrodynamic states and approaching its behavior to plug flow.

The difficulties in the computed simulation seem to be related to the existence of an inflow boundary condition.

Moreover, a proper formulation of the boundary condition for the analysis of column displacements experiments in the laboratory is determinant for the interpretation of the observed data and for the subsequent extrapolation of the experimental results.

Additionally, we are interested in the evolutionary problem, including the behavior at short time. Therefore, the influence of the inflow boundary condition needs to be considered carefully, since it can be crucial for the numerical simulation.

Another computational challenge is to use an accurate method that is stable under the presence of numerical boundary conditions. Stability, more than accuracy, is usually affected by the presence of numerical boundary conditions.

Lastly, to extract the hydraulic characteristics of the flow, we need to invert the experimental data, estimating the values for the advection and dispersion coefficients.

A numerical procedure to solve the advection-dispersion equation model for a semi-infinite system is being developed considering a boundary condition with appropriate physical meaning.

The numerical simulation uses finite difference schemes and takes into account this particular boundary condition (which changes according to the flow rates and the organic loadings).

A derivative-free optimization solver is being used to extract the hydraulic characteristics of the flow (i.e., the advection and dispersion coefficient values) from the experimental data.

[1] A. Albuquerque, A. Araújo, and E. Sousa, Application of the advection-dispersion equation to characterize the hydrodynamic regime in a submerged packed bed reactor, A. Tadeu and S.N. Atluri (eds), Proceedings of the 2004 International Conference on Computational & Experimental Engineering & Sciences, pp. 548-553, Tech Science Press, 2004. pdf file

António Albuquerque, Department of Civil Engineering and Architecture, UBI
Adérito Araújo, LCM-CMUC
Ercília Sousa, LCM-CMUC
Luís Nunes Vicente, LCM-CMUC