MODELING AND ANALYSIS OF THE DEPLETION OF ORGANIC POLLUTANTS BY BACTERIA WITH EXPLICIT DEPENDENCE ON DISSOLVED OXYGEN

In this paper, a nonlinear mathematical model is proposed and analyzed to study the depletion of dissolved oxygen caused by interactions of organic pollutants with bacteria in a water body, such as lake. The system is assumed to be governed by three dependent variables, namely, the cumulative concentration of organic pollutants, the density of bacteria and the concentration of dissolved oxygen. In the model, the coefficient of interaction of organic pollutants with bacteria depends upon the concentration of dissolved oxygen nonlinearly and explicitly, which is the main focus of this paper, has never been studied before. The stability theory of differential equations is used to analyze the model and to confirm the analytical results numerical simulation is performed. The model analysis shows that if the coefficient of interaction mentioned above depends upon dissolved oxygen explicitly, the decrease in its concentration is more than the case when the interaction does not depend on dissolved oxygen and consequently the depletion of organic pollutants is also more in such a case.     

Mathematical modeling and analysis of the depletion of dissolved oxygen in eutrophied water bodies affected by organic pollutants

In this paper, an ecological type nonlinear mathematical model is proposed to study the simultaneous effect of water pollution and eutrophication on the concentration of dissolved oxygen (DO) in a water body. It is assumed that the organic pollutants and the nutrients are discharged into water body from outside with constant rates. The system is modeled by considering the variables such as cumulative concentration of organic pollutants, the densities of bacteria, nutrients, algae, detritus and the concentration of DO. The analysis of the model shows that the decrease in the concentration of DO due to simultaneous effect of water pollution and eutrophication is much more than when only single effect is present in the water body, thus leading to more uncertainty about the survival of DO-dependent species.     

Modeling the depletion of dissolved oxygen in a water body located near a city

Water bodies located nearby cities are much prone to pollution, especially in the developing countries, where effluents treatment facilities are generally lacking. The main reason for this phenomenon is the increasing population in the cities, and the large number of industries located near them. This leads to generation of huge amounts of domestic and industrial sewage that is discharged into the water bodies, increasing their organic pollutant load and resulting in the depletion of dissolved oxygen. In this paper, we propose a mathematical model for this situation, focusing especially on the resulting quality of the water, determined by the level of dissolved oxygen. The model also accounts for resources needed for the population survival and for the industrial operations. In addition, we describe also the decomposition of organic pollutants by bacteria in the aquatic medium. Feasibility conditions and stability criteria of the system's equilibria are determined analytically. The results show that human population and industries are relevant influential factors responsible for the increase in organic pollutants and the decrease in dissolved oxygen in the water body, in the sense that they may exert a destabilizing effect on the system. The numerical simulations confirm the analytical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Modeling and analysis of the removal of an organic pollutant from a water body using fungi

In this paper, a non linear mathematical model for removing an organic pollutant such as a dye from a water body is proposed and analyzed. In the modeling process four variables are considered, namely, (i) the concentration of the dye, (ii) the density of fungus population, (iii) the concentration of a nutrient and (iv) the concentration of dissolved oxygen (DO). It is assumed that an organic pollutant is present in water with given concentration or discharged with a constant rate in water. It is assumed further that fungus population is kept alive and active due to supply of a nutrient. It is considered that nutrient and oxygen are supplied to the water body from outside with constant rates. The model is analyzed by using the stability theory of differential equations. The model analysis shows that organic pollutant can be removed from the water body by fungus population and the level of degradation depends upon the concentration of organic pollutant, the density of fungal population and the interaction processes involved.The simulation analysis of the proposed model confirms the analytical results. It is also found that these results are qualitatively in line with the experimental observations of one of the authors (Sanghi).     

Management strategies for the control of eutrophication processes in Fogliano lagoon (Italy): a long-term analysis using a mathematical model

Models are developed and used to analyse and test different management strategies aimed at limiting eutrophication processes in Fogliano Lagoon: modification of lagoon hydrodynamics by tidal flow regulation, harvest of algae biomass, reclaim of sediments. Mathematical models, which have been constructed and proposed, simulate, on a multiyear time scale, the main ecological processes responsible for the most important effects of eutrophication: vegetal blooms, summer anoxia. For different management strategies, hydrodynamic fields produced by wind and tide, and three-dimensional concentration fields of significant species in the ecological phenomena, in water and into sediments, are quantified and compared. The species simulated are: in the water column dissolved oxygen, phytoplanktonic biomass, macrophytic biomass, orthophosphate, dissolved organic carbon, particulate organic carbon and hydrogen sulphide; in sediments dissolved oxygen, dissolved organic carbon, particulate organic carbon, orthophosphate, adsorbed phosphorous and hydrogen sulphide. On the basis of the results of the simulations carried out, the best management strategy limiting eutrophication processes in Fogliano lagoon has been pointed out.     

Dynamic modelling of dissolved oxygen in the creeks of Sagar island,Hooghly–Matla estuarine system,West Bengal,India

Hooghly–Matla estuarine ecosystem is one of the largest estuarine ecosystems of the world. Sagar island is the largest delta in this estuarine complex. This island is criss-crossed by small and large creeks with mangrove vegetation and all are connected to the principal estuarine water. Decomposition of mangrove litter in soil is major source of inorganic nutrient to phytoplankton of the adjacent creeks. Deforestation of mangrove affects the primary production, which in turn reduces the availability of dissolved oxygen for the organisms residing in the estuary. Considering the importance of dissolved oxygen in various aspects of aquatic life, a dynamic model of dissolved oxygen at Sagar island of Hooghly–Matla estuarine complex with the help of single dimension differential equation is proposed in the present paper. Different physical, chemical and biological factors such as solar irradiance, temperature, salinity of water, particulate organic matter, re-aeration, wind velocity, phytoplankton and zooplankton, which control the fluctuation of dissolved oxygen, are included in the present model. Most of the parameter values are collected directly from the field surveys. The parameter values which are not able to collect from the field, obtained from literatures are calibrated. To make the model realistic it is properly validated with observed data and to know the statistical significance, chi square goodness fit test is performed. Field surveys are performed over two years. During calibration and validation, two sets of data (first year and second year data) are used. Chi-square values are 5.97 and 6.17 for first and second sets of data respectively (p < 0.05). Sensitivity analysis reveals that optimal light intensity is the most sensitive parameter for dissolved oxygen dynamics. Results also show that wind velocity, solar irradiation, salinity of water and temperature are important factors for controlling the dynamics of dissolved oxygen. Macrophytes have very little contribution to oxygen production in the creeks of Sagar island. Model reveals that low dissolved oxygen in the creek water is one of the causes of decline in fish population of the estuary.     

Modeling the depletion of dissolved oxygen due to algal bloom in a lake by taking Holling type-III interaction

In this paper a non-linear mathematical model for depletion of dissolved oxygen due to algal bloom in a lake is proposed and analyzed. The model is formulated by considering four variables namely, cumulative concentration of nutrients, density of algal population, density of detritus and concentration of dissolved oxygen. In the modeling process it is assumed that nutrients are continuously coming with a constant rate to the lake through water runoff from agricultural fields and domestic drainage. The Holling type-III interaction between nutrients and algal population is considered. Equilibrium values have been obtained and their stability analysis has also been performed. Numerical simulations are carried out to explain the mathematical results.     

Random signal analysis in an environmental sciences problem

Two major difficulties are encountered in the identification of wastewater treatment plant and river water quality dynamics: process behaviour can neither be easily observed, nor easily experimented upon, and the underlying biological nature of the processes involved is only partially understood. This paper describes the derivation of a model for the interaction between dissolved oxygen (DO), biochemical oxygen demand (BOD), and algae in a freshwater river. Noisy measurements from a stretch of the River Cam downstream of Cambridge are analysed using various techniques of identification, parameter estimation and filtering. An important feature of the paper is the interpretation of system identification as a hypothesis testing/decision making procedure.     

An Arbitrary Lagrangian Eulerian formulation for a 3D eutrophication model in a moving domain

This work analyzes a realistic mathematical model that governs eutrophication (an ecological process involving nutrients, phytoplankton, zooplankton, organic detritus and dissolved oxygen) into a moving aquatic domain. As a main result, we obtain existence-uniqueness results for the solution of the system within the general framework of non-cylindrical domains (based on studying the properties of a generic parabolic problem). The fact of dealing with moving domains, and the lack of regularity, preclude the use of standard semigroup approach, forcing us towards the utilization of Arbitrary Lagrangian Eulerian techniques.     

Mathematical analysis of a three-dimensional eutrophication model

In this paper we present and analyze a nutrient-phytoplankton-zooplankton-organic detritus-dissolved oxygen mathematical model simulating eutrophication processes into aquatic media. As a main result, we obtain existence and uniqueness results for the solution of the system, under realistic hypotheses of non-smooth coefficients (in particular, a non-regular water velocity). This lack or regularity prevent us from using the standard semigroup approach, forcing us towards the utilization of more refined techniques.     

Numerical modeling for compartment fire environment under a solid-cone water spray

A mathematical model was developed for simulating the fire environment of a compartment under the action of a solid-cone water spray such as those discharged from a water mist fire suppression system. A smoke layer was induced by a fire in the compartment. The solid-cone water spray was discharged to act on the smoke layer, but not on the burning object. Under this condition of having a stable smoke layer, the compartment was divided into three regions. Region 1 is the upper hot smoke layer, Region 2 is the lower cool air layer and Region 3 is the solid-cone spray. The effects on the smoke layer development due to spray-induced flow were considered on the basis of mass, momentum and heat conservation. Water droplets of the solid-cone spray were divided into four typical classes based on the droplet distribution function.

The parameters including the smoke layer interface height, smoke temperature and air temperature, smoke flow rate through the opening and oxygen concentration in the air layer were investigated under various heat release rates, water application rates and volume mean diameters of the solid-cone spray. Effective hot gas entrainment and water vapor production suggested that the water spray should contain a variety of droplet size. In this way, a compartment fire can be controlled effectively through indirect interaction such as oxygen concentration depletion.     

A multiphase finite element simulation of biological conversion processes in landfills

Worldwide, landfills are the most common way to dispose of waste, but have an impact on the environment as a result of harmful gas and leachate production. Estimating the long-term behaviour of a landfill in regard to this gas production and organic degrading, as well as to settlement and waste water production, is of high importance. Therefore, a model has been developed to simulate these processes. This constitutive model is based on the multiphase Theory of Porous Media. The body under investigation consists of an organic and an inorganic phase as well as a liquid and a gas phase. The equations of the model are developed on the basis of a consistent thermo-mechanical approach including the momentum balance for the solid phase and the mixture, the energy balance for the mixture and the mass balance for the gas phase. All interactions between the constituents such as mass transfers, interaction forces and energy fluxes are taken into consideration. The strongly coupled set of partial differential equations is implemented in the finite element code FEAP. The theoretical framework and the results of meantime successfully performed simulation of a real landfill body will be shown. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Application of nonlinear optimization to water quality

Two formulations for nonlinear optimization (minimize variance and fractile programming formulations) are presented for the solution of water quality planning problems. The optimization algorithms are applied to the problem of determining the optimal waste removal to mitigate the deleterious impacts of the waste discharges on the dissolved oxygen concentration in a water body. The pollutant loading and transport in the stream are considered as random variables with the first two moments of the resulting distributions included in the models.     

Modeling the removal of gaseous pollutants and particulate matters from the atmosphere of a city

In this paper, a nonlinear mathematical model is proposed and analyzed to study the removal of gaseous pollutants and particulate matters from the atmosphere of a city by precipitation. The atmosphere consists of four interacting phases i.e. the raindrops phase, the gaseous pollutants phase, the phase of gaseous pollutants absorbed (dissolved) in rain drops and the phase of particulate matters. The dynamics of these phases is assumed to be governed by ordinary differential equations with source, interaction, removal and recycle terms. The proposed model is analyzed by using stability theory of differential equations. It is shown that the pollutants can be removed from the atmosphere and their removal rates depend mainly upon the rates of emission of the pollutants, rate of rain drops formation and the rate of falling rain drops on the ground. If the rate of precipitation is very high, the pollutants may be removed completely from the atmosphere.     

MODELING THE EVOLUTION OF NATURAL ORGANIC MATTER IN THE ENVIRONMENT WITH AN AGENT‐BASED STOCHASTIC APPROACH

ABSTRACT. Natural organic matter (NOM) is ubiquitous in terrestrial and aquatic ecosystems, and it plays a crucial role in the evolution of soils, the transport of pollutants, and the global carbon cycle. NOM is a complex mixture of molecules and is thus heterogeneous in structure and composition. As NOM passes through an ecosystem, it is acted upon by a variety of processes, such as microbial degradation, adsorption to mineral surfaces, and photochemical reactions that can change its properties and reactivity. The evolution of NOM in space and time thus is an important research area in biology, geochemistry, ecology, soil science, and water resources. Due to its complex structural and chemical heterogeneity, new simulation approaches are needed to help better understand the evolution of NOM properties and reactivity as it passes through an ecosystem. We present a new stochastic model, which explicitly treats NOM as a large number of discrete heterogeneous molecules (“agents”) with different probabilities of transformations or reactions. The NOM, the microorganisms, and their environment are taken together as a complex system, with the NOM interactions within this system simulated using an agent‐based stochastic modeling approach. The initial users of the NOM simulations include a geographically separated group of NSF‐sponsored scientists and engineers from different research disciplines, including both academics and U.S. government scientists. A Web‐based interface serves as a prototype NOM “collaboratory” designed to promote collaboration among the various researchers and to allow them to share their data, model results, and suggested approaches or improvements across distributed sites. This Web‐based interface has been designed to allow researchers to access the simulation model remotely from a standard Web browser. The Web‐based interface thus allows researchers at distant locations to provide parameters for their simulations, to start and stop simulations, and to plot and view results, all remotely.     

Velocity Vector Field Optimization in Bioventing

Bioventing is a technology used to remove some kinds of pollutants from the subsoil and it is based on the capability of some bacteria species to biodegrade contaminants. The biochemical reaction requires, among other things, oxygen and, therefore, oxygen is inflated into the subsoil by wells. The mathematical model describes the movement of the different fluids which are present in the subsoil – air, water, pollutants, oxygen and so on – and the bacteria population dynamics. The presence of source reactive terms in the continuity equations allows the contaminant biodegradation to be described. The design of a subsoil decontamination intervention concerns bioavailability problems and, in particular, the oxygen concentration. Therefore, in order to enhance the biodegradation phenomenon, the optimization of the subsoil oxygen velocity field in the polluted area is required, by an appropriate choice of the well positions and of the well air inflating rates. In mathematical terms, the goal is to obtain the decontamination of the subsoil with an optimal value of an objective function by acting on some control variables which, in this case, are the well positions and the inflating rates. In this paper several kind of objective function are proposed. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

System dynamics of euthrophication processes in lakes

Eutrophication is the phenomenon observed in the bodies of water that receive large influxes of nutrients due to agricultural runoff or urban waste disposal. It is characterized by blooms of either green or blue-green algae (often noxious smelling) and by a drastic reduction in dissolved oxygen and often makes it impossible for many species of fish and zooplankton to live in the water. The objective was to examine the effects of eutrophication on plankton seasonal dynamics. Simulation models have been used primary tool in the study of eutrophication in lakes. Many eutrophication models have been developed both to predict the effect of nutrient additions on lake biota and to examine how effective various nutrient diversions alternatives might be improved water quality. Systems dynamics was studied using the model, which is expressed as a series of four differential equations as its state variables for the rates of change of phytoplankton, zooplankton, nitrogen and phosphorus. Influence of the phosphorus concentration on eutrophication was treated and studied as the one of the most important process in the lake ecosystem.     

Numerical study of sediment transport in turbulent two-phase flows around an obstacle

This paper numerically investigates the transport of dissolved and particulate pollutants in turbulent channel flows. We present a predictive hydrodynamic model in order to explore the dispersion phenomenon of a pollutant injected at a free surface around an obstacle. The air/water interface was modeled using the volume of fluid method (VOF). Numerical results agree well with experimental data and the penetration of pollutant released at different inlet positions of the channel is studied. The Lagrangian tracking of individual particles was performed, and the transport and deposition of various particle size, density and velocity in the channel were analyzed. The standard k–ε turbulence model was chosen for this simulation.We found that large particles with a density of 1600 kg/m³, a velocity of 2 m/s and a diameter higher than 70 mm are deposited around the obstacle and near the end sill of the channel, while particles of very small size (lower than 5 mm) remain suspended in the flow and arrive at the outlet of the channel without any deposition rate. This factor must be taken into account during the discharge of effluents and pollutants in coastal water.