A Mathematical Model Development for Simulating Nitrate Pollutant Transport along a River

2021 ◽  
Vol 57 ◽  
pp. 149-168
Author(s):  
Kayode O. Olowe ◽  
Muthukrishnavellaisamy Kumarasamy
Keyword(s):  
Mathematical Model ◽  
Water Quality ◽  
Surface Water ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Nitrate Concentration ◽  
Pollutant Transport ◽  
Spatial And Temporal Variation ◽  
Wide Range ◽  
Natural Rivers

Contamination of surface water bodies by a wide range of organic and inorganic pollutants has been a serious problem in the recent time, these have an effect on human and aquatic animals. The water quality deterioration calls for regular monitoring of the water quality in order to maintain the health and sustainability of the aquatic ecosystems. Accurate monitoring of discharged pollutants into the rivers may be time taking and labour intensive. Water quality models are significant tools for simulating water quality and controlling the surface water pollution. The purpose of this study is to develop a simplified mathematical model which is hybrid cells in series model (HCIS) to simulate the spatial and temporal variation of nitrate concentration in natural rivers. The HCIS model was formulated to serve as an alternative method to the Fickian based models. Analytical solutions for the first order reaction kinetics of nitrate with the advection and dispersion process were derived using Laplace transformation technique. The model considered the effect of nitrate concentration at several points along the river downstream by considering the transformation of nitrite to nitrate through nitrification process. In addition, the uptake of nitrate by algae for its growth and conversion of nitrate to nitrogen gas due to denitrification process were considered. The HCIS-NO3 model was applied to uMgeni River, South Africa to investigate the nitrate concentration along the river. Furthermore, the quantitative measures based on the coefficient of determination (R2) and standard errors (SE) were used to evaluate the performance of the model. The result shows that the simulated values agreed with the measured values of nitrate concentration in the river which resulted in a R2 value of 0.72 and a low standard error. Analytical solutions of HCIS - NO3 model were compared with the numerical solutions of the Fickian based ADE model for hypothetical problems. Comparison of the responses indicates that the HCIS - NO3 and ADE- NO3 models were in good agreement. The study shows that the hybrid model is a simple and effective tool for simulating pollutant transport in natural rivers.

An Approximate Method for Transient Radial Flow

1962 ◽  
Vol 2 (03) ◽  
pp. 225-256 ◽  
Author(s):  
G. Rowan ◽  
M.W. Clegg
Keyword(s):  
Infinite Series ◽  
Analytical Solutions ◽  
Radial Flow ◽  
Numerical Solutions ◽  
Basic Theory ◽  
Variable Pressure ◽  
Flow Problems ◽  
Disturbed Zone ◽  
Approximate Analytical Solutions ◽  
Wide Range

Abstract The basic equations for the flow of gases, compressible liquids and incompressible liquids are derived and the full implications of linearising then discussed. Approximate solutions of these equations are obtained by introducing the concept of a disturbed zone around the well, which expands outwards into the reservoir as fluid is produced. Many important and well-established results are deduced in terms of simple functions rather than the infinite series, or numerical solutions normally associated with these problems. The wide range of application of this approach to transient radial flow problems is illustrated with many examples including; gravity drainage of depletion-type reservoirs; multiple well systems; well interference. Introduction A large number of problems concerning the flow of fluids in oil reservoirs have been solved by both analytical and numerical methods but in almost all cases these solutions have some disadvantages - the analytical ones usually involve rather complex functions (infinite series or infinite integrals) which are difficult to handle, and the numerical ones tend to mask the physical principles underlying the problem. It would seem appropriate, therefore, to try to find approximate analytical solutions to these problems without introducing any further appreciable errors, so that the physical nature of the problem is retained and solutions of comparable accuracy are obtained. One class of problems will be considered in this paper, namely, transient radial flow problems, and it will be shown that approximate analytical solutions of the equations governing radial flow can be obtained, and that these solutions yield comparable results to those calculated numerically and those obtained from "exact" solutions. It will also be shown that the restrictions imposed upon the dependent variable (pressure) are just those which have to be assumed in deriving the usual diffusion-type equations. The method was originally suggested by Guseinov, whopostulated a disturbed zone in the reservoir, the radius of which increases with time, andreplaced the time derivatives in the basic differential equation by its mean value in the disturbed zone. In this paper it is proposed to review the basic theory leading to the equations governing the flow of homogeneous fluids in porous media and to consider the full implications of the approximation introduced in linearising them. The Guseinov-type approximation will then be applied to these equations and the solutions for the flow of compressible and incompressible fluids, and gases in bounded and infinite reservoirs obtained. As an example of the application of this type of approximation, solutions to such problems as production from stratified reservoirs, radial permeability discontinuities; multiple-well systems, and well interference will be given. These solutions agree with many other published results, and in some cases they may be extended to more complex problems without the computational difficulties experienced by other authors. THEORY In order to review the basic theory from a fairly general standpoint it is proposed to limit the idealising assumptions to the minimum necessary for analytical convenience. The assumptions to be made are the following:That the flow is irrotational.That the formation is of constant thickness.Darcy's Law is valid.The formation is saturated with a single homogeneous fluid. SPEJ P. 225^

scholarly journals Spatial and temporal variation of salt ions in the surface water of Shule River Valley in Gansu Province, China

2018 ◽  
Vol 19 (2) ◽  
pp. 662-670 ◽  
Author(s):  
Quan en Guo ◽  
Bao guo Li ◽  
Li li Nan ◽  
Zhong nan Nie ◽  
Shi yu Cao
Keyword(s):  
Water Quality ◽  
Surface Water ◽  
River Water ◽  
Total Dissolved Solids ◽  
Quality Parameters ◽  
Gansu Province ◽  
Spatial And Temporal Variation ◽  
Dissolved Solids ◽  
Lower Region ◽  
Water Ph

Abstract The objective of the study was to assess the quality of the Shule River water for irrigational purposes. Surface water samples were collected along the course of the river in May and October 2012. The samples were analyzed for pH, electrical conductivity (EC), bicarbonate, chloride, sulphate, sodium, potassium, calcium and magnesium. Surface water was generally alkaline (average pH 8.17) and water pH and total dissolved solids in May were higher than those in October. EC ranged from 0.24 to 2.15 mS cm−1. Sodium was identified as the dominant cation, sulphate was identified as the dominant anion in May for both samples of river water but, in October, the dominant anions are respectively sulphate, bicarbonate and chloride from the upper region to the lower region. The total dissolved solids, chloride and sodium were found to exceed the permissible limits for irrigation water in the lower region. According to the principal factor analysis results, among water quality parameters measured in this study, chloride is the best indicator for monitoring water quality. The results revealed a deteriorating water quality in the lower region of the river.

Progress in Analytical Modeling of Water Hammer

2021 ◽  
Author(s):  
Kamil Urbanowicz ◽  
Haixiao Jing ◽  
Anton Bergant ◽  
Michał Stosiak ◽  
Marek Lubecki
Keyword(s):  
Analytical Solutions ◽  
Numerical Solutions ◽  
Dynamic Pressure ◽  
Complete Solution ◽  
Water Hammer ◽  
Inverse Transformation ◽  
Mathematical Form ◽  
Dimensionless Time ◽  
Wide Range ◽  
Analytical Formulas

Abstract In this paper analytical formulas of water hammer known from the literature are simplified to the shortest possible mathematical form based on dimensionless parameters: dimensionless time, water hammer number, etc. Novel formulas are determined, for example for the flow velocity and wall shear stress in the Muto and Takahashi solution. A complete solution in the Laplace domain is presented and the problem of its inverse transformation is discussed. A series of comparative studies of analytical solutions with numerical solutions and the results of experimental research were carried out. The compared analytical solutions, taking into account the frequency-dependent nature of the hydraulic resistances, show very good agreement with the experimental results in a wide range of water hammer numbers, in particular when Wh ≤ 0.1. On the other hand, it turned out that the analytical model based on the quasi-steady friction in great detail simulates dynamic pressure response in systems characterized by a high value of the water hammer number Wh ≥ 0.5.

Advanced oxidation technologies for the degradation of pesticides in ground water and surface water

2002 ◽  
Vol 2 (1) ◽  
pp. 129-138 ◽  
Author(s):  
G.F. Ijpelaar ◽  
M. Groenendijk ◽  
R. Hopman ◽  
Joop C. Kruithof
Keyword(s):  
Water Quality ◽  
Water Treatment ◽  
Surface Water ◽  
Advanced Oxidation Processes ◽  
Nitrate Concentration ◽  
Advanced Oxidation ◽  
Fenton Process ◽  
Practical Application ◽  
Oxidation Processes ◽  
By Products

An overview of the Advanced Oxidation Processes (AOP) studied for the degradation of pesticides combined with the formation of by-products is presented. It was found that the degree of conversion of pesticides is about the same with the Fenton process and UV/H2O2 within the margin of practical application, but slightly different with ozone/H2O2. Bentazone is readily degraded by the latter process, but more persistent during water treatment with the Fenton process and UV/H2O2, whilst atrazine is difficult to convert with all of these processes. Although bromate formation cannot be avoided completely with ozone/H2O2, it can be realized with the Fenton process and UV/H2O2. Upon degradation of pesticides with UV/H2O2 nitrite is produced, the amount depending on the water quality with respect to the nitrate concentration. Based on the a-selective nature of the hydroxyl radical AOC is formed out of DOC, which indicates that ozone/H2O2, the Fenton process as well as UV/H2O2 should be applicable for the development of biological GAC filtration.

scholarly journals Arsenic occurrence in water bodies in Kharaa river basin

2018 ◽  
Vol 18 (44) ◽  
pp. 12-19
Author(s):  
Azzaya T ◽  
Burmaa G ◽  
S Alen ◽  
Narangarav T ◽  
Nyamdelger Sh
Keyword(s):  
Heavy Metals ◽  
Water Quality ◽  
Surface Water ◽  
River Basin ◽  
Gold Mining ◽  
Quality Standard ◽  
Anthropogenic Sources ◽  
Water Quality Standard ◽  
Permissible Level ◽  
Wide Range

Distribution of arsenic (As) and its compound and related toxicology are serious concerns nowadays. Gold mining activity is one of the anthropogenic sources of environmental contamination regarding As and other heavy metals. In Mongolia, the most productive gold mining sites are placed in the Kharaa river basin. A hundred water samples were collected from river, spring and deep wells in this river basin. Along with total As and its species-As(III) and As(V), examination of concentration levels of other key parameters, 21 heavy metals with pH, total hardness, electric conductivity, anion and cations, was also carried out. In respect to the permissible limit formulated by the Mongolian National Drinking water quality standard (MNS 0900:2005, As10 µg/l), the present study showed that most of samples were found no contamination. In Kharaa river basin, an average concentration of total As in surface water was 4.04 µg/l with wide range in 0.07−30.30 µg/l whereas it was 2.24 µg/l in groundwater. As analysis in surface water in licensed area of Gatsuurt gold mining showed a mean concentration with 24.90 µg/l presenting higher value than that of value in river basin by 6 orders of magnitude and it was 2 times higher than permissible level as well. In Boroo river nearby Boroo gold mining area, As concentration in water was ranged in 6.05−6.25 µg/l. Ammonia pollution may have present at estuary of Zuunmod river in Mandal sum with above the permissible level described in national water quality standard. Geological formation of the rocks and minerals affected to change of heavy metal concentration, especially As and uranium (U) at spring water nearby Gatsuurt-Boroo improved road.

Analytical Solution of Temperature Field in Micro-Poiseuille Flow With Constant Wall Temperature

2008 ◽  
Author(s):  
Masoud Darbandi ◽  
Salman SafariMohsenabad ◽  
Shidvash Vakilipour
Keyword(s):  
Temperature Field ◽  
Wall Temperature ◽  
Analytical Solutions ◽  
Analytical Study ◽  
Numerical Solutions ◽  
Experimental Studies ◽  
Constant Wall Temperature ◽  
Power Series Method ◽  
The Past ◽  
Wide Range

The analytical study of microchannels has been considered as a preliminary approach to alleviate the difficulties which are normally encountered in numerical and experimental studies. Among the analytical solutions, those with high robustness and low complexities are certainly more attractive. In this work, we present a theoretical approach to predict the temperature field in micro-Poiseuille channel flow with constant wall temperature. The use of power series method simplifies the solution in the current analytical approach. The current analytical derivations are examined for channels with both hot-wall and cold-wall conditions. The current solutions agree well with the numerical solutions for a wide range of Knudsen numbers. Contrary to the past analytical solutions and in spite of using a simple and robust approach, the current formulations predict the temperature field in the channel readily.

Magnetoencephalography inverse problem in the spheroid geometry

2019 ◽  
Vol 27 (2) ◽  
pp. 159-169 ◽  
Author(s):  
Petr I. Karpov ◽  
Tatyana Zakharova
Keyword(s):  
Inverse Problem ◽  
Exact Solution ◽  
Magnetic Fields ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Approximate Analytical Solutions ◽  
Wide Range ◽  
Ill Posed ◽  
The Brain

AbstractThe inverse problem of magnetoencephalography is ill-posed and difficult for both analytical and numerical solutions. Additional complications arise from the volume (passive) currents and the associated magnetic fields, which strongly depend on the brain geometry. In this paper, we find approximate analytical solutions for the forward and the inverse problems in the spheroid geometry. We compare the obtained results with the exact solution of the forward problem and deduce that for a wide range of parameters our approximation is valid. The analysis sheds new light on the role of the volume magnetic fields for solving the inverse problem of magnetoencephalography.

AN EVALUATION OF SUB-SURFACE WATER QUALITY AROUND BHARUCH-SURAT INDUSTRIAL REGION, GUJARAT, INDIA

2019 ◽  
Vol 38 (2) ◽  
pp. 200-220
Author(s):  
SOMNATH SAHA ◽  
◽  
SUKANTA KUMAR SAHA ◽  
TATHAGATA GHOSH ◽  
ROLEE KANCHAN ◽  
...  
Keyword(s):  
Water Quality ◽  
Surface Water ◽  
Surface Water Quality ◽  
Industrial Region
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