Water Resources System Modeling
Water Quality Modeling
Water Resources Planning and Management: M8L4
D Nagesh Kumar, IISc
Objectives
 To discuss about water quality parameters and standards
 To discuss
about river water quality modeling, its
components and governing equations
 To model dissolved oxygen in rivers
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Water Resources Planning and Management: M8L4
D Nagesh Kumar, IISc
Introduction
 Water quality maintaining and monitoring has become an important part of
sustainable development
 Quality problems in water arise mainly due to its molecular structure itself which
makes it a universal dissolvent
 Water quality is expressed as a function of space and time
 Quality of water body shows rapid variations
 Variations are more in a river, less in lakes and much less in aquifers.
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Water Resources Planning and Management: M8L4
D Nagesh Kumar, IISc
Water Quality Monitoring
 Monitoring indicates the long term, standardized measurement and observation of
the environment
 Location of sampling station depends on the purpose of study
 Sampling stations can be divided into
i. Basic stations which are located usually at the mouth of main streams, major tributaries,
downstream of river development projects, at hydrometric stations, gauge discharge sites,
industrial and urban centers and at points of water use
ii. Auxiliary stations which are meant to analyse the effect of pollutants discharged into a stream,
determination of assimilation capacity of stream etc
 Stream quality is assessed by interpolating the data collected at these stations.
 Samples for water quality should be taken at places where composition is uniform
across the cross-section.
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Water Resources Planning and Management: M8L4
D Nagesh Kumar, IISc
Water Quality Monitoring…
 Sampling points in rivers should be away from any disturbing influences
 Sampling frequency depends on the purpose and relative importance of the station,
variability of data and accessibility of station
 Basic stations usually collect at a sampling frequency of 3 - 4 months per year
 Atleast one sample should be taken in one season
 Stations located downstream of a waste outlet, should take samples weekly or bi-
weekly
 If the purpose is recreational, sampling can be restricted to the season of use.
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Water Resources Planning and Management: M8L4
D Nagesh Kumar, IISc
Water Quality Parameters
 Many organic constituents may present in water
 Measurement of all of them may be practically difficult
 Organic pollution is indicated by the non-parametric tests
 Carbon Oxygen Demand (COD) or
 Total Organic Carbon (TOC).
 Parameters to be measured are the following:
 Total organic carbon, biochemical oxygen demand (BOD), cyanide, pesticides, suspended
solids, nitrogen, fluoride, cadmium, chromium, copper, lead, nickel, zinc, mercury, boron,
dissolved oxygen (DO), pH value, and coliform bacteria.
 Additional information such as total hardness, alkalinity, calcium hardness, sulphate,
phosphate, sodium, potassium etc may be also needed if the objective is to evaluate the
influence of pollution control measures on the cost of water treatment.
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Water Resources Planning and Management: M8L4
D Nagesh Kumar, IISc
Water Quality Standards
 Usage of water depends on its quality
 Permissible limits depend on the intended use
 For example, water from a particular source may be good for irrigation, but may
not be advisable for drinking
 Guidelines for drinking water quality were issued by WHO in 1996
(www.who.int/water_sanitaion_health/Water_quality/drinkwat.htm)
Bacteriological quality of drinking water
Organisms
All water intended for drinking
E. coli or thermotolerant coliform bacteria
Treated water entering the distribution system
E. coli or thermotolerant coliform bacteria
Total coliform bacteria
Treated water in the distribution system
E. coli or thermotolerant coliform bacteria
Total coliform bacteria
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Water Resources Planning and Management: M8L4
Guideline
Must not be detectable in any 100 ml sample
Must not be detectable in any 100 ml sample
Must not be detectable in any 100 ml sample
Must not be detectable in any 100 ml sample
Must not be detectable in any 100 ml sample
D Nagesh Kumar, IISc
River Water Quality Modeling
 Water quality can be divided into five categories based on the colour of discharge:
Category
Colour
Amount of pollution
I
Blue
No/ Slight
II
Green
Moderate
III
Yellow
Heavy
IV
Red
Excessive
V
Black
Zone of devastation
 Two components for river water quality modeling:
 Forecasting the developments in the basin and subsequent effects in the water quality
 Forecasting of pollution concentration changes within the stream which includes
prediction of solute concentration at various points at various times taking solute
concentration at specified point as input and finding the dominant processes controlling
the solute concentration.
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Water Resources Planning and Management: M8L4
D Nagesh Kumar, IISc
River Water Quality Modeling…
 Forecasting of concentration depends on the stability of contaminants
 Contaminants are stable if the concentration changes only through dilution and
evaporation
 However, precipitation, sedimentation, adsorption etc also act as forcing factors to
change the concentrations of many organic and inorganic substances
 Such processes are influenced by factors such as pH, temperature, bed
characteristics etc, which need to be treated separately
 Pollutants may enter the river through a
 Point source: If the source is a well-defined outlet such as industrial outlet or municipal
sewers
 Non-point source: If the source is distributed along the water course such as runoff from
land
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Water Resources Planning and Management: M8L4
D Nagesh Kumar, IISc
River Water Quality Modeling…
 Source of pollutants can also be classified as continuous and instantaneous source
 Continuous sources: Dump pollutants over a long period of time (eg. municipal waste
water plant)
 Instantaneous sources: Dump pollutants for a very short interval of time (eg. Spill from a
tanker).
 Pollutograph: A plot of pollute concentration with respect to time
 Loadograph: Graph of the product of pollutant concentration and flow rate/time
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Water Resources Planning and Management: M8L4
D Nagesh Kumar, IISc
Components of a River Water Quality Model
 Governing dynamic equations of a river water quality model consider
 various hydrologic, thermal and biochemical processes that take place within the system
 These equations are basically conservation of mass, momentum and energy.
 Biochemical and chemical processes in a river are influenced by hydraulic and
thermal conditions
 Main influencing hydraulic variables are flow velocity, depth and discharge
 An increase in flow velocity decreases the self-purification
 It also results in increased turbulence
 Aids in proper mixing of oxygen
 Increases reaeration.
 Greater depths block penetration of sunlight – Slows down the photosynthetic
process
 Pollutant concentration is inversely proportional to discharge since an increased
discharge increases the dilution rate.
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Water Resources Planning and Management: M8L4
D Nagesh Kumar, IISc
Components of a River Water Quality Model…
 River water quality model can be divided into three components
 Hydraulic
 Thermal and
 Biochemical submodels
Hydraulic and thermal models:
 Considering one-dimensional unsteady flow, the influencing variables are flow
depth and cross-section of flow
 Influencing equations are conservation of mass and momentum.
 Thermal model has only one variable i.e., temperature. This submodel can be
skipped by directly inputting the variable to the biochemical model.
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Water Resources Planning and Management: M8L4
D Nagesh Kumar, IISc
Components of a River Water Quality Model…
Biochemical model:
 Real life interactions may lead to a large number of variables
 Make the model complex
 One may reduce the number of variables by substitution or grouping of similar
variables
 Pertinent indicator of water quality: Dissolved oxygen (DO)
 BOD: Amount of oxygen needed for biochemical oxidation of matter in a unit
volume of water
 Most of the biochemical models are simplified versions of the real processes
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Water Resources Planning and Management: M8L4
D Nagesh Kumar, IISc
Components of a River Water Quality Model…
Geochemical processes
 In addition to the physical processes, chemical and biological processes also
influence the solute transport
 These geochemical reactions can be either
 Homogenous: Dissolved species interact with species of same phase (eg. Hydrolysis) or
 Heterogenous: Species from different phases are involved (eg. Reaction between
dissolved oxygen and atmospheric oxygen)
Sorption
 Process which controls the pollute concentration
 Process in which a dissolved species called sorbate becomes associated with a
solid surface called sorbent
 Absorption: Sorbate penetrate the sorbent
 Adsorption: When sorbate interacts with surface or intersurface of sorbent
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Water Resources Planning and Management: M8L4
D Nagesh Kumar, IISc
Components of a River Water Quality Model…
Pollutant concentration
Concentration C: Measure of the quantity of a constituent
C=M/V
where M is the mass of the constituent and V is the volume of fluid.
Transport of pollutant in rivers
 Transport of a constituent is measured in terms of flux
 Flux is the rate of flow of mass or energy per unit area normal to the direction of
flow
 Unit: Quantity per unit area per unit time.
 Pollutant is transferred through two important mechanisms:
 Advection and
 Dispersion.
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Water Resources Planning and Management: M8L4
D Nagesh Kumar, IISc
Components of a River Water Quality Model…
Advection (or Convection):
 Transfer of a constituent due to the motion of the carrying fluid
 The constituent moves with the fluid velocity
 Flux F due to advection is the product of velocity U and concentration C
F= UC
 Volume of the constituent remains same, while the location changes
Dispersion:
 As the constituent moves downstream, the volume increases and the concentration
decreases due to mixing up
 Dispersion can be due to molecular diffusion and velocity variations
 In natural streams, the main forcing factor is velocity variations
 Flux due to diffusion is given by Flick’s law
 Flux in the x direction is
C
Fx  E x
x
where Ex is the longitudinal dispersion coefficient or diffusivity.
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Water Resources Planning and Management: M8L4
D Nagesh Kumar, IISc
Components of a River Water Quality Model…
Effects of advection and dispersion
Time, t
Time, t+1
Advection
Dispersion
Advection + Dispersion
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Water Resources Planning and Management: M8L4
D Nagesh Kumar, IISc
Governing Advective – Diffusion Equation
 Basic equation behind the effects of advection and dispersion on solute
concentration is the conservation of mass
Time rate of change of mass = mass inflow – mass outflow
 One-dimensional form commonly applied in streams
C  UC  1  
C 


 AEL
  KC
t
x
A x 
x 
where U is the average longitudinal velocity
A cross-sectional area and
EL is the longitudinal dispersion coefficient.
 Advection-dispersion equation assuming constant U and EL
C
C 
 2C
 U
 EL 2
t
x
x
 Above equations can be solved analytically
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Water Resources Planning and Management: M8L4
D Nagesh Kumar, IISc
Modeling of Oxygen in Rivers
Dissolved oxygen
 Depends on temperature, pressure, dissolved solids turbulence etc.
 DO in freshwaters at 1 atmospheric pressure ranges from 15 mg/L at 00C to 6 mg/L at
400C
 DO level is used as an indicator of pollution by organic matter
Biochemical oxygen demand (BOD)
 Amount of oxygen required for aerobic micro-organisms to oxidize the organic matter to a
stable inorganic form
 A measure of the amount of biochemically degradable organic matter present in the water
 Concentrations in rivers vary from 2 to 15 mg/L
 BOD in unpolluted water is less than 2 mg/L
 Raw sewage has a BOD of about 600 mg/L which may come down to 20 – 100 mg/L after
treatment.
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Water Resources Planning and Management: M8L4
D Nagesh Kumar, IISc
Modeling of Oxygen in Rivers…
Chemical oxygen demand (COD)
 A measure of the oxygen equivalent of organic matter that is susceptible to oxidation by a
strong oxidizing agent
 In natural water, it is the amount of oxygen required for oxidation of a waste to carbon
dioxide and water
 COD of surface water ranges from 20 mg/L (for unpolluted waters) to 200 mg/L (for
effluent added waters)
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Water Resources Planning and Management: M8L4
D Nagesh Kumar, IISc
Modeling of Oxygen in Rivers…
 Mass balance of BOD and oxygen deficit in a stream with constant flow and
geometry can be expressed as
dL
 kr L
dx
dD
U
 ka D  kd L
dx
U
where
U is the average stream velocity,
L is the carbonaceous BOD concentration,
x is the distance downstream from the discharge point,
kr is the total removal rate,
D is the dissolved oxygen deficit,
ka is the aeration rate and
kd is the removal rate of BOD
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Water Resources Planning and Management: M8L4
D Nagesh Kumar, IISc
Modeling of Oxygen in Rivers…
 cs is the saturation concentration for DO
 c is the oxygen concentration
 Then deficit D = cs – c
 Above equations can be solved for BOD and DO concentration for a single point
source whose BOD concentration is L0 and oxygen deficit is D0 and can be
expressed as
 k  
L  L0 exp  r  x 
 U  
 k     k  
  k  
k L
c  cs  D0 exp  a  x   exp  r  x   exp  a  x   d 0
 U     U  
  U   k a  k r 
 Water quality models for catchments, lakes , reservoirs and ground water differ
from those of rivers in terms of sources, biological considerations etc.
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Water Resources Planning and Management: M8L4
D Nagesh Kumar, IISc
Thank You
Water Resources Planning and Management: M8L4
D Nagesh Kumar, IISc