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Introduction to

Water Quality Modeling

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BackgroundUsing Raw water for domestic/Industrial purposes needsTREATMENT.

The DEGREE of THIS treatment may vary from

Simple sedimentation to Costly biological /chemical treatment

Degree of treatment is DECIDED based on producing acceptablelevel of water quality in receiving waters

ACCEPTABLE LEVEL is decided by predicting water quality ofreceiving waters

The predicting is generally done by using WATER QUALITYMODELLING

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Water treatment

plant

Waste water

treatment plant

City 

Stream

Waste loading (W) [MT-1]

Critical Concentration (C) [ML-3]

Water Quality Modeling

Water quality Modeling describes the linkage between “C” and “W” 

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Water Quality Management Process

Drainage Basin Water QualityModel

Treatment

Desirable water

use

C < C goal

Desired concentration goal

Yes

No

“C” “W” 

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Fundamental Quantities of WQM

Mass : Amount of pollutant is ‘Mass’ Such property is referred as Extensive

Property

Additive in natureConcentration : It is a Normalized quantitity and

referred as an Intensive

PropertyIntensive property represents the Strength

rather than the quantity of the pollution

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Example

One, two, three spoons of sugar will sweeten

your tea with varying degree depending up on

the size of your ‘mug’ [Mug= Receiving System]

Number of spoons :Analogous to mass

Sweetness: Concentration

Organism is more concerned to “Sweetness” 

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RATESProperties that are normalized  to time are commonly referred toRates.

1. Mass loading rate : Waste discharges are typicallyrepresented by MASS LOADING RATE (W)

W= m/ t

Where m= mass of pollutant

t= time period

If W enters the receiving waters as “point source” i.e. throughconduits, pipes or channels

For such point source , loading rate (W) is determined by measuringconcentrations along with volumetric flow rate(Q , L3T-1),

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2. Volumetric flow rate : For steady Conditions,

the flow rate is often calculated with continuity

equation

Q= U AC

Where U= Velocity of water in conduit [LT-1]

Ac = Cross Sectional area of conduit [L2] 

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3. Mass flux rate

What is flux ?

It is used to designate “RATE OF MOVEMENT OF

AN EXTENSIVE QUANTITY LIKE MASS OR HEAT

NORMALIZED TO AREA” 

Mass flux rate through a conduit can be

calculated as

J = (m/t Ac )  = W/ Ac

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Basic Concepts and Relationships

Relating “C” and “W” by the Physical, Chemical

and biological characteristics of receiving waters

and the waste.

C= f { W, Physics, Chemistry and biology} (1)

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To employ a linear relationship,

The equation (1) is modified as

C= W/a (2)

Where a= assimilation factor (L3T-1)

represents physics, chemistry and

biology of receiving water.

Equation 2 is a linear equation as C α  W

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Algorithms for WQM

1. Simulation model

C= W/a (2)

The above model simulates “concentration”

(system response) as a function of stimuli

(loading) and system characteristics(assimilation factor )

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2. Assimilative Capacity based WQM

W= aC (3)

The value of W can be determined from themodel for a desirable concentration level for

different assimilative capacities estimated from

physics, biology and chemistry of the recieving.

This Model is useful in design of treatment plant

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3. Environmental Modifications

based WQM

a = W/C (4)

How the system environment (Physical, chemical

and biological parameters) can be modified to

meet the required C for a given waste load W

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ReferencesChapra,S.C. et al (1983), “Engineering approaches for lake

management”, Volume 2: Mechanistic modelling, butterworth,USA.

Thomann R.V.(1963), “Mathematical model for D.O” J.San.Engr.Div.ASCE 89(SA5): 1-30

Thomann R.V (1981), “Equilibrium model of fate of microcontaminants in diverse aquatic food chains” Can. J. Fish Aquat.Sci.38:280-296.

Thomann R.V. et al (1983) “Physico-chemical model of toxicsubstances in the great lakes”, J. Great Lakes Res. 9(4), 474-496.

Thomann R.V.et al (1964) “Estuarine water quality management andforecasting” J.San. Engr.Division ASCE 90(SA5):9-36.

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