GROUNDWATER CONTAMINANT
TRANSPORT MODELING FOR RIVER
BASINS
Suresh A Kartha
Assistant Professor
Department of Civil Engineering
IIT Guwahati



This presentation is an academic exercise, where we intended to generate interest in you on groundwater contaminant transport modeling.
I am sure such a presentation should help some students in their future research.
2


Water present in the subsurface environment of earth is called groundwater.

It extends vertically and aerially on the subsurface of the earth.

It requires certain type of soils to bear water in the subsurface that are called aquifers.
Ground Level
Water Table Line
Aquifer
Impermeable Strata
3

Figure taken from the document “ Some Critical issues on Groundwater in India” Centre for
Water Policy (2005) (www.sandrp.in/groundwater/crisugrdwtr.pdf)

Ground water is an integral part of
Hydrologic Cycle
4

Distribution of water on earth
Courtesy: Corbett Foundation
5

How Groundwater is formed in the subsurface?

Rainfall water percolates into the subsurface.

It gets accumulated over impermeable layers forming GW formations.

From the National Commission on Integrated
Water Resources Development data, 432 billion cubic metre volume of GW is estimated.
6




Ground water is part of hydrologic cycle.
Similarly one can think of ground water as part of large river basins.
For example River Ganga also encompasses a large underground water reservoir along
7

8

Groundwater runoff in some river basins in India
Source:
(www.sandrp.in/groundwater/crisu grdwtr.pdf)
9

In India,

Groundwater is used for drinking, irrigation, and other domestic purposes.


Even many industries extracts GW for their use.
A conjunctive mechanism is therefore required in many regions for sustainable extraction.
10


Therefore, groundwater aquifers are closely linked with rivers.

Here the groundwater is feeding the river.
River
11


In this case, the river is feeding the groundwater.
River

Therefore, any effect of quality or quantity on one may affect the other.
12

Groundwater can get contaminated?

GW is prone to contamination by various means.
 landfill leaching, radio-nuclide dumping, subsurface chemical reactions, etc.
Rainfall
Ground Level
Percolation of leached liquid
Unsaturated zone
Ground Water Table
Radio-nucleic waste
Water Table
13



The process of dissolution of harmful chemicals (or materials) from landfills formed from dumping of wastes is called leaching.
The migration of these toxic dissolved chemicals from landfills into the natural resources like river, groundwater, etc. is a major urban environmental problem referred as landfill leaching.
14


Landfills are dumps or heaps formed from dumping of wastes.

Wastes are of the following types

Foods

Plastics

Electronic goods

Industrial wastes

Hospital and medicinal wastes

Biological wastes, etc
15

This photograph is taken from the following website http://www.otobeygir.com/
This photograph is taken from the following website http://www.nunukphotos.com/Pollution-photos/Waste-landfill-site
16

This photograph is taken from the following website http://www.landfill-site.com/html/good_landfilling_practise_1.html
17







These wastes acts as huge reactors of formation of toxic products.
Amount of wastes generated in urban areas are large and wide.
Therefore, urban areas has unique problems like landfill leaching
These landfills also breeds harmful insects and organisms.
Spreads contagious diseases
Groundwater pollution
18




One can use the laboratory experiments and on field data measuring equipments to measure the contaminant concentrations in groundwater. Then plot them and infer.
Can use remote sensing equipments to trace the movement of contaminants in the subsurface and map them.
Can use mathematical models to express the contaminant movement in subsurface.
19





The subsurface water system – i.e. the groundwater is considered as porous medium.
Using the continuum mechanics approach, the fundamental principles on mass, momentum, and energy can be applied on the porous continuum.
Principles of conservation of mass of the contaminant in the fluid
Conservation of linear momentum
20

Porous Media dx dz dy
White coloured area is solid domain q
Grey coloured area is liquid or gas domain


Pores may be partially or fully filled with water in the subsurface.
Groundwater regions below the surface of earth are in fully saturated conditions.
21

As contaminant transport in groundwater involves
 the flow of water and
 Migration or transport of contaminants through porous media,
An integrated approach of fluid flow and solute transport through porous media has to be taken for analysing contamiant transport.
22

Flow of liquids



Flows of liquids - analyzed by determining the liquid pressure and liquid saturation in the entire porous media.
They are mathematically described using the principles of conservation of liquid mass.
This principle suggests - Mass of water is conserved in the porous media (the landfills, unsaturated subsurface below, and the groundwater).
    l

 t
  .
     S l
23

Flow analyses





Darcy’s velocity is function of hydraulic conductivity and hydraulic gradient.
In variably saturated (unsaturated) conditions the hydraulic conductivity is related to the intrinsic permeability of soil and the viscosity of the liquid.
u l
  k
 p l

P l
 l g

Again, hydraulic conductivity as well as the liquid pressure in the medium can be related with the liquid saturation in unsaturated conditions.
This gives you a partial differential equation (pde) either in terms of pressure or saturation.
Solving this pde gives you pressure distribution or saturation distribution.
24


In a porous medium control volume, the conservation of mass of the contaminant can be expressed
The Material Derivative
Or
Time Derivative of Mass of Contaminant
=
The amount of mass of contaminant generated or destroyed inside the CV
Net mass outflow of
+ Contaminant mass through the surfaces of CV
25

Transport analyses




Dissolved toxic chemicals or contaminants are transported in porous media by advection, dispersion, sorption, and degradation.
Advection of contaminants is the movement caused along with flowing groundwater at the seepage velocity in porous media.
Dispersion is a mixing process, in which the solute is seen to spread out from the flow path.
Sorption describes the chemical processes in which the contaminant mass is either entrained into soil or leaches out from the soil.
26

Mathematical Formulations
 These phenomena in transport can be described mathematically using again the principles of conservation of mass.
 Conservation of mass equation is
The transport equation for developed for concerned contaminant specie.
R

C
 t
 
.

D C
 contaminant transport in the groundwater is:
 
.
vC
Change in contaminant mass
Change due to Change due Change due to dispersive to advection consumption effects
• where C is concentration of contaminant in the liquid flowing through the pores of ground water sources,
• D is hydrodynamic dispersion coefficient
• R is retardation factor
27

Advective fluxes through the boundary surfaces of the volume = uC
 x
 y
Dispersive flux through boundary surfaces
D

C
 x
 x
 y
Inside the above volume mass may be generated or destroyed. This is given by

C
 t
This process consist of sorption, degradation, chemical reactions, etc.
28

Mathematical Formulations…
The transport equations can also be extended to include:

S m 1
 t


 t
  l
FKC a


S
 t m 2
 k
 
1

F
  l
KC a

S m 2

Instantaneous sorption Rate-limited sorption
• C a
• ρ b is the concentration of pollutant specie in the flowing liquid is the bulk density of porous media or the mine
• S m1
• S m2 is the concentration of pollutant in the instantaneously sorbed state is the concentration of pollutant in the rate-limited sorbed state
• F is the fraction of total sorption that is instantaneous
• k is the rate of sorption or the rate at which the acid extracts the pollutant specie
29

Numerical methods for model development
• Domain discretised into rectangular grids. Here twodimensional case is described i,j+1 i-1,j i,j i+1,j i,j-1
X-direction
For a 2D case, the width or thickness in the y-direction is assumed as unity
The conservation of mass for acid in the flowing liquid is:




    l
C a
 t
 
 d   



.

D C a

  l
  .
u C a
  C a



Divergence theorem application gives:

  l



  l
C a

 t

 d     l

 a
.
  l

 l a


 C d  


 

30

Numerical methods for model development
Approximating the above equation by implicit finite-difference scheme, we get
  l
 n  1



C a
 n  1


 t
C a

  
0
   l
 q

 d u l q


C
 n  1
 a q

 x q
C a
 n  1
 
 A q
  b  u C q
 n  1
 a q
A q
  b


   l
 n  1   C
 n  1  a

A residual equation of the above can be obtained as such:
R
 n

1

C a





  l l
 n

1

  l
 q 







C a
 n

1


 t
C a d u l q




C
 n

1
 a q

 x q
C





S C l 0




  a
 n

1




 b
A q





 l
 q
 u C l q a
 n

1
 q
  b
  l l
 n

1
 
C a
 n

1


A q

31


How will you apply such mathematical models for contaminant transport

For example, if there is a river and the banks consist of agricultural plots filled with harmful fertilisers.
River
 The fertilisers may dissolve and reach the groundwater first and from their it may flow to the river.
32


To apply such mathematical models for contaminant transport

The boundary condition in such a situation will be
River
 Constant hydraulic head on the river boundary. The concentration boundary can be given as zero gradient.
33

To apply such mathematical models for contaminant transport





Different types of boundary conditions you need to incorporate as per the physical situation demands.
Such mathematical studies are essential for analysing ground water pollution in river basins
Because these will help in better understanding of the process.
It will also help in better preparation for experimental studies.
We can also plan experiments in a better as we are aware of the physical processes.
34

CONCLUSIONS







Groundwater essential component in hydrologic cycle.
Most groundwater aquifers are inter linked with river bodies.
Groundwaters are susceptible to contamination from rivers or top soil.
Similarly groundwater may also contaminate rivers.
Conceptual modeling of contaminant migration in groundwater bodies are essential for better understanding of the processes prior to experimentation.
The processes that cause transport or migration of contaminants are advection, dispersion, sorption, etc.
Any planning at river basin level should also include groundwater modeling.
35

36