scholarly journals Bifurcation Analysis of an Impulsive System Describing Partial Nitritation and Anammox in a Hybrid Reactor

2021 ◽  
Vol 55 (3) ◽  
pp. 2099-2109
Author(s):  
Matthew J. Wade ◽  
Gail S. K. Wolkowicz
Keyword(s):  
Bifurcation Analysis ◽  
Impulsive System ◽  
Hybrid Reactor ◽  
Partial Nitritation

scholarly journals Bifurcation analysis of an impulsive system describing Partial Nitritation and Anammox in a hybrid reactor

2020 ◽  
Author(s):  
Matthew J. Wade ◽  
Gail S. K. Wolkowicz
Keyword(s):  
Batch Reactor ◽  
Mechanistic Model ◽  
Impulsive System ◽  
Hybrid Reactor ◽  
Partial Nitritation ◽  
Discrete Parameter ◽  
Consistent Manner ◽  
Mapping Process ◽  
Oxygen Requirements

AbstractLow-energy deammonification under mainstream conditions is a technology that has received significant attention in recent years as the water industry drives towards long-term sustainability goals. Simultaneous partial nitritation-Anammox (PN/A) is one process that can provide substantial energy reduction and lower sludge yields. Mathematical modelling of such a process offers engineers insights into the conditions for maximising the potential of PN/A. Laureni et al., Water Res. (2019) have recently published a reduced mechanistic model of the process in a sequencing batch reactor, which indicates the effect of three key operating parameters (Anammox biofilm activity, dissolved oxygen concentration and fraction of solids wasted) on performance. The analysis of the model is limited, however, to simulation with relatively few discrete parameter sets. Here, we demonstrate through the use of bifurcation theory applied to an impulsive system, that a phase space can be generated describing the continuous separation of system equilibria. Mapping process performance data onto these spaces allows engineers to target suitable operating regimes for specific objectives. Here, for example, we note that the nitrogen removal efficiency is maximised close to the trans-critical bifurcation curve denoting nitrite oxidising bacteria washout, but control of solids washout and Anammox biofilm activity can also reduce oxygen requirements whilst maintaining an appropriate Hydraulic Retention Time. The approach taken is significant given the possibility for using such a methodology for models of increasing complexity, which will enable engineers to probe the entire parameter space of systems of higher dimensionality and realism in a consistent manner.

scholarly journals Bifurcation Analysis and Application for Impulsive Systems with Delayed Impulses

2017 ◽  
Vol 27 (12) ◽  
pp. 1750186 ◽  
Author(s):  
Kevin E. M. Church ◽  
Xinzhi Liu
Keyword(s):  
Bifurcation Analysis ◽  
Disease Transmission ◽  
Impulsive System ◽  
Impulsive Systems ◽  
Center Manifold Reduction ◽  
Delayed Impulse ◽  
Special Cases ◽  
Manifold Reduction ◽  
Delayed Impulses ◽  
Impulsive Harvesting

In this article, we present a systematic approach to bifurcation analysis of impulsive systems with autonomous or periodic right-hand sides that may exhibit delayed impulse terms. Methods include Lyapunov–Schmidt reduction and center manifold reduction. Both methods are presented abstractly in the context of the stroboscopic map associated to a given impulsive system, and are illustrated by way of two in-depth examples: the analysis of a SIR model of disease transmission with seasonality and unevenly distributed moments of treatment, and a scalar logistic differential equation with a delayed census impulsive harvesting effort. It is proven that in some special cases, the logistic equation can exhibit a codimension two bifurcation at a 1:1 resonance point.

Anaerobic Thermophilic (55°C) Treatment of TMP Whitewater in Reactors Based on Biomass Attachment and Entrapment

1999 ◽  
Vol 40 (11-12) ◽  
pp. 67-75 ◽  
Author(s):  
Sigrun J. Jahren ◽  
Jukka A. Rintala ◽  
Hallvard Ødegaard
Keyword(s):  
Granular Sludge ◽  
Biofilm Reactor ◽  
Upflow Anaerobic Sludge Blanket ◽  
Hybrid Reactor ◽  
Anaerobic Sludge ◽  
Loading Rates ◽  
Anaerobic Reactors ◽  
Multi Stage ◽  
Degradation Rates ◽  
Thermomechanical Pulping

Thermomechanical pulping (TMP) whitewater was treated in thermophilic (55°C) anaerobic laboratory-scale reactors using three different reactor configurations. In all reactors up to 70% COD removals were achieved. The anaerobic hybrid reactor, composed of an upflow anaerobic sludge blanket (UASB) and a filter, gave degradation rates up to 10 kg COD/m3d at loading rates of 15 kg COD/m3d and hydraulic retention time (HRT) of 3.1 hours. The anaerobic multi-stage reactor, consisting of three compartments, each packed with granular sludge and carrier elements, gave degradation rates up to 9 kg COD/m3d at loading rates of 15-16 kg COD/m3d, and HRT down to 2.6 hours. Clogging and short circuiting eventually became a problem in the multi-stage reactor, probably caused by too high packing of the carriers. The anaerobic moving bed biofilm reactor performed similar to the other reactors at loading rates below 1.4 kg COD/m3d, which was the highest loading rate applied. The use of carriers in the anaerobic reactors allowed short HRT with good treatment efficiencies for TMP whitewater.

Bifurcation Analysis for Physiological Flow of a Nanofluid: Application of Biomechanics

2018 ◽  
Vol 14 (6) ◽  
pp. 481-502 ◽  
Author(s):  
Anber Saleem ◽  
Sadia Waheed ◽  
Sohail Nadeem
Keyword(s):  
Bifurcation Analysis ◽  
Physiological Flow

Two-parameter bifurcation analysis of longitudinal flight dynamics

2003 ◽  
Vol 39 (3) ◽  
pp. 1103-1112 ◽  
Author(s):  
Der-Cherng Liaw ◽  
Chau-Chung Song ◽  
Yew-Wen Liang ◽  
Wen-Ching Chung
Keyword(s):  
Bifurcation Analysis ◽  
Flight Dynamics ◽  
Two Parameter ◽  
Parameter Bifurcation
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