scholarly journals Impact of Dual Substrate Limitation on Biodenitrification Modeling in Porous Media

Processes ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 890
Author(s):  
Mostafa Abaali ◽  
Jérôme Harmand ◽  
Zoubida Mghazli
Keyword(s):  
A Priori ◽  
Growth Function ◽  
Single Type ◽  
A Priori Error Estimate ◽  
Single Substrate ◽  
Spatially Distributed ◽  
Dual Substrate Limitation ◽  
Diffusion Convection ◽  
Reaction Equations ◽  
Dual Substrate

In this work, we consider a model of the biodenitrification process taking place in a spatially-distributed bioreactor, and we take into account the limitation of the kinetics by both the carbon source and the oxidized nitrogen. This model concerns a single type of bacteria growing on nitrate, which splits into adherent bacteria or free bacteria in the liquid, taking all interactions into account. The system obtained consists of four diffusion-convection-reaction equations for which we show the existence and uniqueness of a global solution. The system is approximated by a standard finite element method that satisfies an optimal a priori error estimate. We compare the results obtained for three forms of the growth function: single substrate limiting, “multiplicative” form, and “minimum” form. We highlight the limitation of the ‘ single substrate limiting model”, where the dependency of the bacterial growth on the nitrate is neglected, and find that the “minimum” model gives numerical results closer to the experimental results.

Modelling of the Transient Behaviour of a Membrane-Attached Biofilm Reactor under Successive Pulses of a Synthetic Wastewater Substrate

2008 ◽  
Vol 6 (1) ◽  
Author(s):  
Margarita Mercedes González-Brambila ◽  
Felipe Lopez-Isunza
Keyword(s):  
Biofilm Reactor ◽  
Synthetic Wastewater ◽  
Residual Water ◽  
Monod Kinetics ◽  
Heterogeneous Model ◽  
Transient Behaviour ◽  
Relative Contribution ◽  
Dual Substrate Limitation ◽  
Diffusion Convection ◽  
Dual Substrate

This work deals with the theoretical and experimental study of the transient behaviour of a membrane-attached biofilm reactor (MARB) when it is exposed to a series of pulse injections of concentrated solutions of sodium acetate, used as a synthetic wastewater. The MARB is connected to a reservoir tank with full recirculation containing the synthetic wastewater, and oxygen permeates through the wall membrane to the biofilm attached to it. For the two experiments reported in this work air is also sparged into the residual water in the tank providing an extra source of oxygen that diffuses simultaneously from the membrane and from the liquid into the biofilm. A pseudo-heterogeneous model using Monod kinetics with dual substrate limitation was employed to predict the observed evolution of substrate and dissolved oxygen concentrations in the MABR. The model accounts for the counter-diffusion of substrate and oxygen as well as for the reaction within the biofilm. It also predicts biomass growth and the production of extra cellular polymers, which in turn causes the biofilm to grow. Transport and kinetic parameters previously estimated, are used in the model to predict the growth rates in the biofilm and allow the analysis of the relative contribution of the rates of mass transport by diffusion, convection and growth reaction.

scholarly journals A priori and a posteriori error analysis for a hybrid formulation of a prestressed shell model.

2021 ◽  
Author(s):  
Serge Nicaise ◽  
Ismail Merabet ◽  
Rayhana REZZAG BARA
Keyword(s):  
Shell Model ◽  
A Priori ◽  
Functional Space ◽  
Finite Element Approximation ◽  
Posteriori Error ◽  
Error Estimator ◽  
Element Approximation ◽  
A Posteriori ◽  
A Posteriori Error ◽  
A Priori Error Estimate

This work deals with the finite element approximation of a prestressed shell model using a new formulation where the unknowns (the displacement and the rotation of fibers normal to the midsurface) are described in Cartesian and local covariant basis respectively. Due to the constraint involved in the definition of the functional space, a penalized version is then considered. We obtain a non robust a priori error estimate of this penalized formulation, but a robust one is obtained for its mixed formulation. Moreover, we present a reliable and efficient a posteriori error estimator of the penalized formulation. Numerical tests are included that confirmthe efficiency of our residual a posteriori estimator.

On the Diffusion-Convection-Reaction Equations

1999 ◽  
Vol 60 (3) ◽  
pp. 207-210 ◽  
Author(s):  
S A El-Wakil ◽  
A Elhanbaly ◽  
M A Abdou
Keyword(s):  
Diffusion Convection ◽  
Reaction Equations

scholarly journals How Can Spatially Distributed Uncertainties Be Included in FEA and in Parameter Estimation for Model Updating?

2003 ◽  
Vol 10 (1) ◽  
pp. 15-25 ◽  
Author(s):  
M.W. Zehn ◽  
A. Saitov
Keyword(s):  
Parameter Estimation ◽  
Model Updating ◽  
A Priori ◽  
Estimation Methods ◽  
Parameter Distribution ◽  
Fe Model ◽  
Weighting Matrix ◽  
Spatially Distributed ◽  
Updating Procedure ◽  
Parameter Estimation Methods

Owing to manufacturing composite materials and others show considerable uncertainties in wall-thickness, fluctuations in material properties and other parameter, which are spatially distributed over the structure. These uncertainties have a random character and can therefore not being reduced by some kind of mesh refinement within the FE model. What we need is a suitable statistical approach to describe the parameter changing that holds for the statistics of the process and the correlation between the parameter spatially distributed over the structure. The paper presents a solution for a spatial correlated simulation of parameter distribution owing to the manufacturing process or other causes that is suitable to be included in the FEA. The parameter estimation methods used in updating algorithms for FE-models, depend on the choice of a priori to be determined weighting matrices. The weighting matrices are in most cases assumed by engineering judgement of the analyst carrying out the updating procedure and his assessment of uncertainty of parameters chosen and measured and calculated results. With the statistical description of the spatial distribution at hand, we can calculate a parameter weighting matrix for a Baysian estimator. Furthermore, it can be shown in principle that with model updating it is possible to improve the probabilistic parameter distribution itself.

scholarly journals Areal parameter estimates from multiple datasets

2019 ◽  
Vol 475 (2231) ◽  
pp. 20190352 ◽  
Author(s):  
B. L. N. Kennett
Keyword(s):  
Significant Contribution ◽  
A Priori ◽  
Relative Weight ◽  
Parameter Estimates ◽  
Multiple Datasets ◽  
Wide Range ◽  
Spatially Distributed ◽  
Data Points ◽  
Spatial Terms ◽  
Weighted Combination

A wide range of methods exist for interpolation between spatially distributed points drawn from a single population. Yet often multiple datasets are available with differing distribution, character and reliability. A simple scheme is introduced to allow the fusion of multiple datasets. Each dataset is assigned an a priori spatial influence zone around each point and a relative weight based on its physical character. The composite result at a specific location is a weighted combination of the spatial terms for all the available data points that make a significant contribution. The combination of multiple datasets is illustrated with the construction of a unified Moho surface in part of southern Australia from results exploiting a variety of different styles of analysis.

scholarly journals A priori error for unilateral contact problems with Lagrange multipliers and isogeometric analysis

2018 ◽  
Vol 39 (4) ◽  
pp. 1627-1651 ◽  
Author(s):  
Pablo Antolin ◽  
Annalisa Buffa ◽  
Mathieu Fabre
Keyword(s):  
Isogeometric Analysis ◽  
A Priori ◽  
Contact Problems ◽  
Unilateral Contact ◽  
Spline Space ◽  
Three Dimensions ◽  
B Spline ◽  
A Priori Error Estimate ◽  
The Stability ◽  
Unilateral Contact Problems

Abstract In this paper we consider a unilateral contact problem without friction between a rigid body and a deformable one in the framework of isogeometric analysis. We present the theoretical analysis of the mixed problem. For the displacement, we use the pushforward of a nonuniform rational B-spline space of degree $p$ and for the Lagrange multiplier, the pushforward of a B-spline space of degree $p-2$. These choices of space ensure the proof of an inf–sup condition and so on, the stability of the method. We distinguish between contact and noncontact sets to avoid the classical geometrical hypothesis of the contact set. An optimal a priori error estimate is demonstrated without assumption on the unknown contact set. Several numerical examples in two and three dimensions and in small and large deformation frameworks demonstrate the accuracy of the proposed method.

Sign in / Sign up

Export Citation Format

Share Document