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

2. 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.

3. What is Groundwater?
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

4. You are aware of Hydrologic Cycle
Figure taken from the document “Some Critical issues on Groundwater in India” Centre for Water Policy (2005) (
Ground water is an integral part of Hydrologic Cycle

5. Distribution of water on earth
Courtesy: Corbett Foundation

6. 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.

7. Groundwater as part of River Basin
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

9. Groundwater runoff in some river basins in India
Source: (

10. 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.

11. Link of GW with Rivers
Therefore, groundwater aquifers are closely linked with rivers.
Here the groundwater is feeding the river.
Ground Surface
Groundwater Table
River

12. Link of GW with Rivers
In this case, the river is feeding the groundwater.
Therefore, any effect of quality or quantity on one may affect the other.
Ground Surface
River
Groundwater Table

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

14. What is Landfill Leaching?
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.

15. 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

16. Some Photographs of Landfill sites
This photograph is taken from the following website
This photograph is taken from the following website

17. Some Photographs of Landfill sites
This photograph is taken from the following website

18. 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

19. How will you then study contaminant transport for subsurface water system?
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.

20. How will you then model contaminant transport for subsurface water system
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

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

22. 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.

23. 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).

24. 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.
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.

25. Conservation of mass for the contaminant
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 = +

26. 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.

27. Mathematical Formulations
These phenomena in transport can be described mathematically using again the principles of conservation of mass.
Conservation of mass equation is developed for concerned contaminant specie.
The transport equation for contaminant transport in the groundwater is:
Change in contaminant mass
Change due to dispersive effects
Change due to advection
Change due to consumption
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

28. Conservation of mass for the contaminant
Advective fluxes through the boundary surfaces of the volume =
Dispersive flux through boundary surfaces
Inside the above volume mass may be generated or destroyed. This is given by
This process consist of sorption, degradation, chemical reactions, etc.

29. Mathematical Formulations…
The transport equations can also be extended to include:
Instantaneous sorption
Rate-limited sorption
Ca is the concentration of pollutant specie in the flowing liquid
ρb is the bulk density of porous media or the mine
Sm1 is the concentration of pollutant in the instantaneously sorbed state
Sm2 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

30. Numerical methods for model development
Domain discretised into rectangular grids. Here two-dimensional case is described
i,j+1
Z-direction
Y-direction
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:
Divergence theorem application gives:

31. Numerical methods for model development
Approximating the above equation by implicit finite-difference scheme, we get
A residual equation of the above can be obtained as such:

32. 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.
The fertilisers may dissolve and reach the groundwater first and from their it may flow to the river.
River
Agricultural Plot

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

34. 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.

35. 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.

36. Thank You