scholarly journals Approximate Models of Microbiological Processes in a Biofilm Formed on Fine Spherical Particles

Processes ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 48
Author(s):  
Szymon Skoneczny ◽  
Monika Cioch-Skoneczny
Keyword(s):  
Method Of Lines ◽  
Approximate Model ◽  
Spherical Particles ◽  
Biofilm Growth ◽  
Biofilm Reactors ◽  
Microbiological Processes ◽  
Approximate Models ◽  
The Method Of Lines ◽  
Homotopy Analysis ◽  
Air Lift

This paper concerns the dynamical modeling of the microbiological processes that occur in the biofilms that are formed on fine inert particles. Such biofilm forms e.g. in fluidized-bed bio-reactors, expanded bed biofilm reactors and biofilm air-lift suspension reactors. An approximate model that is based on the Laplace–Carson transform and a family of approximate models that are based on the concept of the pseudo-stationary substrate concentration profile in the biofilm were proposed. The applicability of the models to the microbiological processes was evaluated following Monod or Haldane kinetics in the conditions of dynamical biofilm growth. The use of approximate models significantly simplifies the computations compared to the exact one. Moreover, the stiffness that was present in the exact model, which was solved numerically by the method of lines, was eliminated. Good accuracy was obtained even for large internal mass transfer resistances in the biofilm. It was shown that significantly higher accuracy was obtained using one of the proposed models than that which was obtained using the previously published approximate model that was derived using the homotopy analysis method.

scholarly journals Hydraulic properties of subglacial sediment determined from the mechanical response of water-filled boreholes

1995 ◽  
Vol 41 (137) ◽  
pp. 112-124 ◽  
Author(s):  
Brian S. Waddington ◽  
Garry K. C. Clarke
Keyword(s):  
Hydraulic Properties ◽  
Mechanical Response ◽  
Method Of Lines ◽  
Approximate Model ◽  
Analytic Solutions ◽  
Pressure Effects ◽  
Yield Information ◽  
The Method Of Lines ◽  
Nonlinear Transient ◽  
Pressure Changes

AbstractFreezing of water-filled boreholes drives water into the subglacial bed and the associated pressure effects yield information about subglacial hydraulic properties. A numerical model describing the mechanical response of an unconnected borehole and the bed beneath it to this freezing forcing was developed, using a nonlinear transient visco-elastic ice-flow law and an approximate model of top-down freezing. The resulting system of equations was solved using the method of lines. Results agreed well with analytic solutions, when parameters were correctly chosen. Forward modelling of pressure records from three 1992 boreholes and three from other years indicated that the till underlying Trapridge Glacier has a hydraulic conductivity of 1.35-7.0 × 10−9m s−1. The model was also used to investigate the response of a borehole to sudden pressure changes. The response is very fast compared to pressure-sensor sampling rates; thus, the true basal signal is essentially unaffected by the presence of the borehole, except during the initial freeze-in.

scholarly journals Hydraulic properties of subglacial sediment determined from the mechanical response of water-filled boreholes

1995 ◽  
Vol 41 (137) ◽  
pp. 112-124 ◽  
Author(s):  
Brian S. Waddington ◽  
Garry K. C. Clarke
Keyword(s):  
Hydraulic Properties ◽  
Mechanical Response ◽  
Method Of Lines ◽  
Approximate Model ◽  
Analytic Solutions ◽  
Pressure Effects ◽  
Yield Information ◽  
The Method Of Lines ◽  
Nonlinear Transient ◽  
Pressure Changes

AbstractFreezing of water-filled boreholes drives water into the subglacial bed and the associated pressure effects yield information about subglacial hydraulic properties. A numerical model describing the mechanical response of an unconnected borehole and the bed beneath it to this freezing forcing was developed, using a nonlinear transient visco-elastic ice-flow law and an approximate model of top-down freezing. The resulting system of equations was solved using the method of lines. Results agreed well with analytic solutions, when parameters were correctly chosen. Forward modelling of pressure records from three 1992 boreholes and three from other years indicated that the till underlying Trapridge Glacier has a hydraulic conductivity of 1.35-7.0 × 10−9m s−1. The model was also used to investigate the response of a borehole to sudden pressure changes. The response is very fast compared to pressure-sensor sampling rates; thus, the true basal signal is essentially unaffected by the presence of the borehole, except during the initial freeze-in.

SOLUTION OF THE RICHARDS EQUATION IN A SOIL PROFILE WITH TWO LAYERS USING THE METHOD OF LINES

2020 ◽  
Author(s):  
Diego Sousa Lopes ◽  
Augusto Cezar Cordeiro Jardim ◽  
Diego Estumano ◽  
Emanuel Macêdo ◽  
João Quaresma
Keyword(s):  
Soil Profile ◽  
Method Of Lines ◽  
Richards Equation ◽  
The Method Of Lines

TRAVELLING WAVES AND OSCILLATIONS IN SAL’NIKOV’S COMBUSTION REACTION IN A COMPRESSIBLE GAS

2015 ◽  
Vol 56 (3) ◽  
pp. 233-247 ◽  
Author(s):  
RHYS A. PAUL ◽  
LAWRENCE K. FORBES
Keyword(s):  
Asymptotic Solution ◽  
Multiple Scales ◽  
Travelling Waves ◽  
Method Of Lines ◽  
Travelling Wave ◽  
Reaction Scheme ◽  
Compressible Viscous Gas ◽  
The Method Of Lines ◽  
Temperature Waves ◽  
Parameter Values

We consider a two-step Sal’nikov reaction scheme occurring within a compressible viscous gas. The first step of the reaction may be either endothermic or exothermic, while the second step is strictly exothermic. Energy may also be lost from the system due to Newtonian cooling. An asymptotic solution for temperature perturbations of small amplitude is presented using the methods of strained coordinates and multiple scales, and a travelling wave solution with a sech-squared profile is derived. The method of lines is then used to approximate the full system with a set of ordinary differential equations, which are integrated numerically to track accurately the evolution of the reaction front. This numerical method is used to verify the asymptotic solution and investigate behaviours under different conditions. Using this method, temperature waves progressing as pulsatile fronts are detected at appropriate parameter values.

Enhanced Reactor Performance with Pressure and Vacuum Swing Reaction

2004 ◽  
Vol 2 (1) ◽  
Author(s):  
Vincent G Gomes
Keyword(s):  
Method Of Lines ◽  
Fixed Bed ◽  
Downstream Processing ◽  
Operating Conditions ◽  
Reactor Performance ◽  
Orthogonal Collocation ◽  
The Method Of Lines ◽  
Dynamic Experiments ◽  
Product Separation ◽  
Pressure Swing

Product separation and regeneration of sorbent was accomplished in a novel pressure swing reactor through pressurisation, adsorption, blowdown and purge steps. The switching from sorption to reaction to regeneration was tested in a two bed sorption/reaction apparatus. Models developed for the mass and momentum transfer in the catalyst bed and sorber, were solved using orthogonal collocation within the method of lines. The effects of operating conditions and cycle configurations on performance were assessed. The results from dynamic experiments with propene metathesis to produce ethene and 2-butene in a fixed-bed catalytic reactor were in agreement with model predictions. Both pressure and vacuum swing demonstrated that conversion and product quality can be enhanced by periodic cycling with greater separation obtained with vacuum swing. The separation of products help reduce the downstream processing costs of exit mixtures, enable reactant utilisation by recycling and improve product handling at subsequent stages. The efficacy of the periodic separating reactor in terms of conversion, product purity and recovery were investigated.

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