Modified expressions for substrate flux into biofilm

Biofilms are a common microbial ecosystem of microbial organisms and their extracellular polymeric substances or any sorbed substances. The biofilm is using wastewater, waste gas cleaning or reactants into harmless or valuable products. Purpose of study is to give as simple as possible, mathematical expression for description of the substrates transport through a homogeneous and heterogeneous biofilm with or without external mass transfer resistances. The investigation is focusing on the transport of the substrates. The substrate transfer rate will be expressed in limiting cases of the Monod kinetics in closed mathematical forms. It will be discussed the mass transfer rates for homogeneous and heterogeneous biofilms It will be analysed the substrate transfer rate and the concentration distribution in all three cases and the effectiveness factor as a function of the reaction rate.

Water Research, 2005

Biofilm modeling is often considered as a complex mathematical subject. This paper evaluates simple equations to describe the basic processes in a biofilm system with the main aim to show several interesting applications. To avoid mathematical complexity the simulations are carried out in a simple spreadsheet. Frequently, only the solution for zeroorder reaction kinetics of the reaction-diffusion equation is used (better known as half-order kinetics). A weighted average of the analytical solutions for zero-and first-order reactions is proposed as basic and useful model to describe steady-state (in biofilm composition) biofilm reactors. This approach is compared with several modeling approaches, such as the simple solution for zero-order reaction and more complex ones (i) direct numerical solution for the diffusion equations, (ii) 1-D AQUASIM and (iii) 2-D modeling. The systems evaluated are single and multiple species biofilms. It is shown that for describing conversions in biofilm reactors, the zero-order solution is generally sufficient; however, for design purposes large deviations of the correct solution can occur. Additionally, the role of diffusion in flocculated and granular sludge systems is discussed. The relation between the measured (apparent) substrate affinity constant and diffusion processes is outlined. r

Water Science and Technology, 2010

Mathematical models are critical to modern environmental biotechnology—both in research and in the engineering practice. Wastewater treatment plant (WWTP) simulators are used by consulting engineers and WWTP operators when planning, designing, optimizing, and evaluating the unit processes that comprise municipal and industrial WWTPs. Many WWTP simulators have been expanded to include a submerged completely-mixed biofilm reactor module that is based on the mathematical description of a one-dimensional biofilm. Leading consultants, equipment manufacturers, and WWTP modelling software developers have made meaningful contributions to advancing the use of biofilm models in engineering practice, but the bulk of the engineering community either does not use the now readily available biofilm reactor modules or utilizes them as ‘black-box’ design tools. The latter approach results in the mathematical biofilm models being no more useful than the empirical design criteria and formulations that...

Enzyme and Microbial Technology, 1982

The fluidized bed biofilm reactor is a novel biological wastewater treatment process. The use of small, fluidized particles in the reactor affords growth support surface an order of magnitude greater than conventional biofilms systems, while avoiding clogging problems which would be encountered under fixed bed operation. This allows retention of high biomass concentration within the reactor. This high biomass concentration, in turn, translates to substrate conversion efficiencies an order of magnitude greater than possible in conventional biological reactors. The primary objective of this research has been the development of a mathematical model of the fluidized bed biofilm reactor. The mathematical model has two major subdivisions. The first predicts biomass holdup and biofilm thickness within the reactor using drag vi TABLE OF CONTENTS

Applied Water Science, 2016

Biofilm process is widely used for the treatment of a variety of wastewater especially containing slowly biodegradable substances. It provides resistance against toxic environment and is capable of retaining biomass under continuous operation. Development of kinetics is very much pertinent for rational design of a biofilm process for the treatment of wastewater with or without inhibitory substances. A simple approach for development of such kinetics for an aerobic biofilm reactor has been presented using a novel biofilm model. The said biofilm model is formulated from the correlations between substrate concentrations in the influent/effluent and at biofilm liquid interface along with substrate flux and biofilm thickness complying Monod's growth kinetics. The methodology for determining the kinetic coefficients for substrate removal and biomass growth has been demonstrated stepwise along with graphical representations. Kinetic coefficients like K, k, Y, b t , b s , and b d are determined either from the intercepts of X-and Y-axis or from the slope of the graphical plots.

Water Research, 1999

AbstractÐA simple dynamic model is presented for fast simulation of the removal of multiple substrates by dierent bacterial species growing in a bio®lm reactor. The model is an extension to the well-known half-order reaction concept that combines a zero-order kinetic dependency on substrate concentration with diusion limitation. The basic idea behind this model implementation is to decouple the calculations of the two major processes in the bio®lm: substrate diusion and biochemical conversion. The separate assessment of substrate diusion allows to relate the penetration depth of substrates to a fraction of biomass that is active in conversion. The conversion is then calculated considering only the active fraction of the biomass. The model is compared to experimental data from the literature and is found to be able to closely replicate the overall dynamics in a bio®lm system. The major advantage of the proposed model is the simple structure which leads to a reduction of the computational eort as compared to state-of-the-art mixed-culture bio®lm models. #

Water science and technology : a journal of the International Association on Water Pollution Research, 2017

The accuracy of a biofilm reactor model depends on the extent to which physical system conditions (particularly bulk-liquid hydrodynamics and their influence on biofilm dynamics) deviate from the ideal conditions upon which the model is based. It follows that an improved capacity to model a biofilm reactor does not necessarily rely on an improved biofilm model, but does rely on an improved mathematical description of the biofilm reactor and its components. Existing biofilm reactor models typically include a one-dimensional biofilm model, a process (biokinetic and stoichiometric) model, and a continuous flow stirred tank reactor (CFSTR) mass balance that [when organizing CFSTRs in series] creates a pseudo two-dimensional (2-D) model of bulk-liquid hydrodynamics approaching plug flow. In such a biofilm reactor model, the user-defined biofilm area is specified for each CFSTR; thereby, Xcarrier does not exit the boundaries of the CFSTR to which they are assigned or exchange boundaries w...

Biochemical Engineering Journal, 2002

Step changes in inlet concentration has been introduced into the completely mixed three-phase fluidized bed biofilm reactor treating simulated domestic wastewater to study the dynamic behavior of the system and to establish the suitable kinetic model from the response curve. Three identical reactors having different biomass volumes were operated in parallel. It was found that the response curves showed second-order characteristics, and thus at least two first-order differential equations are necessary to simulate the substrate and biomass response curves. Nonlinear regression analysis was performed using different types of rate equations and their corresponding kinetic parameters were used to simulate the theoretical response curve using the Runge-Kutta numerical integration method. As a result, although various types of conventional biokinetic models such as Monod, Haldane and Andrew types were examined, all the theoretical substrate response curves underestimated time constants compared to the actual substrate response plots. On the other hand, the theoretical curve of the kinetic model that incorporates adsorption term has best fit to the actual response in most of the cases. Thus, it was concluded that adsorption of substrate onto biofilm and carrier particles has significant effect on the dynamic response in biofilm processes.

Biotechnology and Bioengineering, 2012

We present a novel analytical approach to describe biofilm processes considering continuum variation of both biofilm density and substrate effective diffusivity. A simple perturbation and matching technique was used to quantify biofilm activity using the steady-state diffusionreaction equation with continuum variable substrate effective diffusivity and biofilm density, along the coordinate normal to the biofilm surface. The procedure allows prediction of an effectiveness factor, h, defined as the ratio between the observed rate of substrate utilization (reaction rate with diffusion resistance) and the rate of substrate utilization without diffusion limitation. Main assumptions are that (i) the biofilm is a continuum, (ii) substrate is transferred by diffusion only and is consumed only by microorganisms at a rate according to Monod kinetics, (iii) biofilm density and substrate effective diffusivity change in the x direction, (iv) the substrate concentration above the biofilm surface is known, and (v) the substratum is impermeable. With this approach one can evaluate, in a fast and efficient way, the effect of different parameters that characterize a heterogeneous biofilm and the kinetics of the rate of substrate consumption on the behavior of the biological system. Based on a comparison of h profiles the activity of a homogeneous biofilm could be as much as 47.8% higher than that of a heterogeneous biofilm, under the given conditions. A comparison of h values estimated for first order kinetics and h values obtained by numerical techniques showed a maximum deviation of 1.75% in a narrow range of modified Thiele modulus values. When external mass transfer resistance, is also considered, a global effectiveness factor, h 0 , can be calculated. The main advantage of the approach lies in the analytical expression for the calculation of the intrinsic effectiveness factor h and its implementation in a computer program. For the test cases studied convergence was achieved quickly after four or five iterations. Therefore, the simulation and scale-up of heterogeneous biofilm reactors can be easily carried out.

Brazilian Journal of Chemical Engineering, 2009

This work presents an experimental and theoretical investigation of anaerobic fluidized bed reactors (AFBRs). The bioreactors are modeled as dynamic three-phase systems. Biochemical transformations are assumed to occur only in the fluidized bed zone. The biofilm process model is coupled to the system hydrodynamic model through the biofilm detachment rate; which is assumed to be a first-order function of the energy dissipation parameter and a second order function of biofilm thickness. Non-active biomass is considered to be particulate material subject to hydrolysis. The model includes the anaerobic conversion for complex substrate degradation and kinetic parameters selected from the literature. The experimental setup consisted of two mesophilic (36±1ºC) labscale AFBRs (R1 and R2) loaded with sand as inert support for biofilm development. The reactor start-up policy was based on gradual increments in the organic loading rate (OLR), over a four month period. Step-type disturbances were applied on the inlet (glucose and acetic acid) substrate concentration (chemical oxygen demand (COD) from 0.85 to 2.66 g L-1) and on the feed flow rate (from 3.2 up to 6.0 L d-1) considering the maximum efficiency as the reactor loading rate switching. The predicted and measured responses of the total and soluble COD, volatile fatty acid (VFA) concentrations, biogas production rate and pH were investigated. Regarding hydrodynamic and fluidization aspects, variations of the bed expansion due to disturbances in the inlet flow rate and the biofilm growth were measured. As rate coefficients for the biofilm detachment model, empirical values of 4 3.73 10 ⋅ and 4 0.75 10 ⋅ s 2 kg-1 m-1 for R1 and R2, respectively, were estimated.