Multiscale Modelling of De Novo Anaerobic Granulation

Abstract

A multiscale mathematical model is presented to describe de novo granulation, and the evolution of multispecies granular biofilms, in a continuously fed bioreactor. The granule is modelled as a spherical free boundary domain with radial symmetry. The equation governing the free boundary is derived from global mass balance considerations and takes into account the growth of sessile biomass as well as exchange fluxes with the bulk liquid. Starting from a vanishing initial value, the expansion of the free boundary is initiated by the attachment process, which depends on the microbial species concentrations within the bulk liquid and their specific attachment velocity. Nonlinear hyperbolic PDEs model the growth of the sessile microbial species, while quasi-linear parabolic PDEs govern the dynamics of substrates and invading species within the granular biofilm. Nonlinear ODEs govern the evolution of soluble substrates and planktonic biomass within the bulk liquid. The model is applied to an anaerobic, granular-based bioreactor system, and solved numerically to test its qualitative behaviour and explore the main aspects of de novo anaerobic granulation: ecology, biomass distribution, relative abundance, dimensional evolution of the granules and soluble substrates, and planktonic biomass dynamics within the bioreactor. The numerical results confirm that the model accurately describes the ecology and the concentrically layered structure of anaerobic granules observed experimentally, and that it can predict the effects on the process of significant factors, such as influent wastewater composition; granulation properties of planktonic biomass; biomass density; detachment intensity; and number of granules.

Multiscale modelling of heavy metals adsorption on algal-bacterial photogranules

“…The bioreactor volume V is assumed constant and equal to 400 m 3 . The number of granules N G has been selected through an iterative procedure varying the detachment coefficient λ [24], with the aim to obtain a 25% filling ratio by considering granules with a steady-state radius of about 1 mm (an average size representative of OPGs [16,27]). After the reaction phase, the solid-liquid separation occurs in the reactor, whereby perfect settling has been considered for granules (no granule is removed from the reactor during the emptying phase).…”

“…Granule mesoscale model. The mathematical model describing the de novo granulation process derived by Tenore et al [24] has been here extended to model the biosorption process of heavy metals on granular biofilms matrix. The granule mesoscale consists of a fixed number of biofilm granules (N G ) immersed within the bulk liquid and assumed to be identical at each instant.…”

“…Based on the continuum approach introduced in Wanner and Gujer [30] for one-dimensional planar biofilms, the model equations for granular biofilms were derived in Tenore et al [24] under the assumption of radial symmetry from mass balance considerations in a differential volume of a spherical domain.…”

“…This multiscale approach leads to model the formation and ecology of the biofilm granules and the performances of the SBR system, considering the interaction between the granules and bulk liquid. The granular biofilm model, derived in Tenore et al [24], is formulated as a spherical free boundary value problem under the assumption of radial symmetry. Processes of microbial growth, attachment, and detachment are included to describe the formation and expansion of granules.…”

“…Experimental observations show that each biofilm component is characterized by the presence of specific number of adsorption sites, which are able to adsorb the contaminants present in the wastewater. For this purpose, model equations describing the variation of free binding sites, and diffusion and adsorption of metals have been here derived for the first time in the case of granular biofilm, by following the approach proposed by Tenore et al [24]. The variation of free binding sites is assumed to depend on the biofilm growth and adsorption process, and is modelled through a system of hyperbolic partial differential equations (PDEs) [7].…”