Designing Experiments for Model Identification of the Nitrification Process

1991 ◽  
Vol 24 (6) ◽  
pp. 9-16 ◽  
Author(s):  
P. J. Ossenbruggen ◽  
H. Spanjers ◽  
H. Aspegren ◽  
A. Klapwijk
Keyword(s):  
Mechanistic Model ◽  
Nonlinear Differential Equations ◽  
Model Identification ◽  
Reaction Rates ◽  
Variable Coefficients ◽  
Model Specification ◽  
First Order ◽  
Interactive Behavior ◽  
Batch Tests ◽  
Nitrification Process

A series of batch tests were performed to study the competition for oxygen by Nitrosomonas and Nitrobacter in the nitrification of ammonia in activated sludge. Oxygen uptake rate (OUR) and dynamic (compartment) models describing the process are proposed and tested. The OUR model is described by a Monod relationship and the biogradation process by a set of first order nonlinear differential equations with variable coefficients. The results show a mechanistic model and ten reaction rates are sufficient to capture the interactive behavior of the nitrification process. Methods for model specification, calibrating, and testing the model and the design of additional experiments are described.

scholarly journals On the Generalized Simplest Equations: Toward the Solution of Nonlinear Differential Equations with Variable Coefficients

2021 ◽  
Author(s):  
Gunawan Nugroho ◽  
Purwadi Agus Darwito ◽  
Ruri Agung Wahyuono ◽  
Murry Raditya
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Riccati Equation ◽  
Nonlinear Differential Equation ◽  
Nonlinear Differential Equations ◽  
Variable Coefficients ◽  
Higher Order ◽  
First Order ◽  
Generalized Riccati Equation ◽  
Polynomial Differential Equation

The simplest equations with variable coefficients are considered in this research. The purpose of this study is to extend the procedure for solving the nonlinear differential equation with variable coefficients. In this case, the generalized Riccati equation is solved and becomes a basis to tackle the nonlinear differential equations with variable coefficients. The method shows that Jacobi and Weierstrass equations can be rearranged to become Riccati equation. It is also important to highlight that the solving procedure also involves the reduction of higher order polynomials with examples of Korteweg de Vries and elliptic-like equations. The generalization of the method is also explained for the case of first order polynomial differential equation.

CHARACTERISATION OF THE NITRIFICATION PROCESS FOR DESIGN PURPOSES

1994 ◽  
Vol 30 (4) ◽  
pp. 47-56 ◽  
Author(s):  
O. Sinkjær ◽  
L. Yndgaard ◽  
P. Harremoës ◽  
J. L. Hansen
Keyword(s):  
Kinetic Theory ◽  
Nitrification Rate ◽  
Experimental Basis ◽  
Batch Tests ◽  
Mode Of Operation ◽  
Nitrification Process ◽  
Aerobic Reactor ◽  
The City ◽  
Specific Evaluation ◽  
Aerobic Sludge

Pilot plant experiments have been performed over a period of four years in order to establish an experimental basis for the upgrading of the treatment plants of the city of Copenhagen to nitrogen removal. The design chosen is based on the alternating mode of operation. Nitrification rates have been determined in batch tests on activated sludge extracted from the pilot plants and through the measuring of transient concentrations during the alternating mode of operation in the aerobic reactor. The data have been nonnalised to standard conditions by correcting them according to the kinetic theory. By monitoring the normalised nitrification rate it could be established that the nitrification process was occasionally inhibited. The aerobic sludge age required to maintain nitrification has been estimated. A specific evaluation has been made of the sensitivity of the required sludge age to the oxygen concentration and temperature.

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

The effect of the textile industry dye bath additive EDTMPA on colour removal characteristics by ozone oxidation

2007 ◽  
Vol 55 (10) ◽  
pp. 145-153 ◽  
Author(s):  
T. Ölmez ◽  
I. Kabdaşlı ◽  
O. Tünay
Keyword(s):  
Organic Matter ◽  
Textile Industry ◽  
Reaction Rates ◽  
Textile Dye ◽  
Pseudo First Order Reaction ◽  
Ozone Oxidation ◽  
Reactive Dyeing ◽  
First Order ◽  
Organic Matter Oxidation ◽  
Pseudo First Order

In this study, the effects of the phosphonic acid based sequestering agent EDTMPA used in the textile dye baths on colour and organic matter removal by ozone oxidation was experimentally investigated. Procion Navy HEXL dyestuff that has been commonly used for the reactive dyeing of cellulose fibers was selected as the model component. The organic matter oxidation by ozone was determined to obey the pseudo-first order kinetics as they are treated singly or in combination. COD removal rates obtained from pseudo-first order reaction kinetics showed that oxidation of Navy HEXL alone (0.0947 L/min) was faster than that of EDTMPA (0.0171 L/min) and EDTMPA with dye (0.0155 L/min) at pH 3.0. It was also found that reaction rates of single EDTMPA removal and EDTMPA and dye mixture removal increased as the reaction pH was increased from 3.0 to 10.5.

scholarly journals Some Further Results on Oscillations for Neutral Delay Differential Equations with Variable Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Fatima N. Ahmed ◽  
Rokiah Rozita Ahmad ◽  
Ummul Khair Salma Din ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Variable Coefficients ◽  
Oscillatory Behaviour ◽  
Neutral Delay ◽  
Neutral Equations ◽  
First Order ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

We study the oscillatory behaviour of all solutions of first-order neutral equations with variable coefficients. The obtained results extend and improve some of the well-known results in the literature. Some examples are given to show the evidence of our new results.

Elasticity Solution for a Radially Nonhomogeneous Hollow Circular Cylinder

1999 ◽  
Vol 66 (3) ◽  
pp. 598-606 ◽  
Author(s):  
Xiangzhou Zhang ◽  
Norio Hasebe
Keyword(s):  
Circular Cylinder ◽  
Continuous Functions ◽  
Variable Coefficients ◽  
Circular Cylinders ◽  
Explicit Solutions ◽  
Elasticity Solution ◽  
First Order ◽  
Hollow Circular Cylinder ◽  
Homogeneous Elasticity ◽  
Ordinary Differential Equation Systems

An exact elasticity solution is developed for a radially nonhomogeneous hollow circular cylinder of exponential Young’s modulus and constant Poisson’s ratio. In the solution, the cylinder is first approximated by a piecewise homogeneous one, of the same overall dimension and composed of perfectly bonded constituent homogeneous hollow circular cylinders. For each of the constituent cylinders, the solution can be obtained from the theory of homogeneous elasticity in terms of several constants. In the limit case when the number of the constituent cylinders becomes unboundedly large and their thickness tends to infinitesimally small, the piecewise homogeneous hollow circular cylinder reverts to the original nonhomogeneous one, and the constants contained in the solutions for the constituent cylinders turn into continuous functions. These functions, governed by some systems of first-order ordinary differential equations with variable coefficients, stand for the exact elasticity solution of the nonhomogeneous cylinder. Rigorous and explicit solutions are worked out for the ordinary differential equation systems, and used to generate a number of numerical results. It is indicated in the discussion that the developed method can also be applied to hollow circular cylinders with arbitrary, continuous radial nonhomogeneity.

scholarly journals Reactivity of Phenol and Aniline towards Quinolinium Chloro Chromate: A Comparative Oxidation Kinetic Study

2015 ◽  
Vol 59 ◽  
pp. 81-92
Author(s):  
Seplapatty Kalimuthu Periyasamy ◽  
H. Satham Hussain ◽  
R. Manikandan
Keyword(s):  
Oxidation Kinetic ◽  
Activation Parameters ◽  
Dipole Interaction ◽  
Reaction Rates ◽  
Hydrogen Ion ◽  
Aqueous Acetic Acid ◽  
Acetic Acid Medium ◽  
First Order ◽  
Different Temperatures ◽  
Kinetics Of

The kinetics of Oxidation of Phenol and aniline by quinolinium Chlorochromate (QCC) in aqueous acetic acid medium leads to the formation of quinone and azobenzene respectively. The reactions are first order with respect to both Phenol and aniline. The reaction is first order with respect to quinolinium chlorochromate (QCC) and is catalyzed by hydrogen ion. The hydrogen-ion dependence has the form: kobs = a+b [H+]. The rate of oxidation decreases with increasing dielectric constant of solvent, indicating the presence of an ion-dipole interaction. The reaction does not induced the polymerization of acrylonitrile. The retardation of the rate by the addition of Mn2+ ions confirms that a two electron transfer process is involved in the reaction. The reaction rates have been determined at different temperatures and the activation parameters have been calculated. From the above observations kinetic results a probable mechanism have been proposed.

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