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### Prof. S. N. PandaHead, School of Water Resources

### Modelling Process

### Modelling Process

### Ganga River Basin, India

Groundwater Modelling of Ganga Basin – Opportunities and Challenges

Physiography and groundwater flow of Ganga basin

(Source: Ministry of Environment and Forests, Government of India)

Annual groundwater draft in comparison with net annual availability in Ganga basin

(Source: Ministry of Environment and Forests, Government of India)

Annual replenishable groundwater in comparison with annual draft in Ganga basin

(Source: Ministry of Environment and Forests, Government of India)

Schematic illustration for evaluating stream-aquifer interaction

Reach inflow

Evaporation

Change in storage

Groundwater inflow

Inflow or leakage to/from groundwater

Stream inflow

Rainfall

Reach Outflow

Stream Reach

Recharge to groundwater

Evapotranspiration

Groundwater outflow

Stream outflow

Problems with groundwater in the Ganga Basin

- Imbalance in groundwater draft
- Waterlogging and salinity in canal commands
- Groundwater pollution

Movement of water through the hydrologic cycle

(Source: usgs.gov)

Gaining stream

Losing stream with shallow watertable

Base flow

Losing stream with deep watertable

Water Balance Concept

The basic concept of groundwater balance is:

Input to the system ‑ outflow from the system = change in storage of the system (over a period of time)

Flow components for assessing groundwater balance

ET

Overland Flow

Pr

Ir

Boundary

Seepage

Pumping well

Per

Cap

Boundary

Watertable

Qper

Sgrw

Qdr

Qlsi

Qlso

Qup

Qdo

Clay

Considering the various inflow and outflow components in a given study area, the groundwater balance equation can be written as:

Rr + Rc + Ri + Rt + Si + Ig = Et + Tp + Se + Og + S

where,

Rr = recharge from rainfall

Rc = recharge from canal seepage

Ri = recharge from field irrigation

Rt = recharge from tanks

Si = influent seepage from rivers

Ig = inflow from other basins

Et = evapotranspiration from groundwater

Tp = draft from groundwater

Se = effluent seepage to rivers

Og = outflow to other basins; and

S = change in groundwater storage

Groundwater Survey and Investigation

Water table contour map showing a local mound and depression in water table and direction of groundwater flow

Water table contour map

Flow net

Flow net technique for estimation of subsurface horizontal flow

Components of a Mathematical Model

- Governing Equation
- (Darcy’s law + water balance equation) with head (h) as the dependent variable
- Boundary Conditions
- Initial conditions (for transient problems)

for steady-state, heterogeneous, anisotropic conditions, without a source/sink term

with a source/sink term

chemical species

Dispersion

Chemical

Reactions

Advection

Source/sink term

Change in concentration

with time

- is porosity

D is dispersion coefficient

v is velocity

Update Model

Mathematical Model

Unsatisfactory Results

Computation

Poor Fit

Compare Model and Field

Calibrate Model

Satisfactory Results

Conclude study

(Decisions & Recommendations)

Opportunities and Challenges in the Ganga Basin

- Wide variation in climate from semi-arid to sub-humid/sub-tropical regions
- Large-scale spatial variation in
- Soil texture and land-use
- Type of aquifers and its properties
- Spatio-temporal variation in

- meteorological parameters associated with uncertainties

- groundwater recharge and discharge components

- Groundwater level monitoring is not being done regularly and intensively
- Setting up/optimising monitoring networks and setting up groundwater protection zones
- Groundwater resources too need to be planned and managed for maximum basin-level efficiency.

Diversified geological climatological and topographic set-up, giving rise to divergent ground water situations

- Excessive use of our rivers, are causing downstream problems, of water quality and ecological stress.
- Climate change impacts directly on the availability of water resources both in space and time.
- The precarious balance between growing demands and supplies brings forth the importance of maintaining quality of both surface and ground water.

Application of existing groundwater models include water balance (in terms ofwater quantity)

- gaining knowledge about the quantitative aspects of the unsaturated zone
- simulating of water flow and chemical migration in the saturated zone including river-groundwater relations
- assessing the impact of changes of the groundwater regime on the environment

State-wise distribution of the drainage area of Ganga river

(Source: Status paper on river Ganga, NRCD, MoEF, 2009)

Soil types in Ganga basin

(Source: Central Pollution Control Board, National River Conservation Directorate (MoEF) (2009))

Data requirement for groundwater balance study over a given time period:

- Precipitation
- River
- Canal
- Tank
- Water table
- Groundwater draft
- Aquifer parameters
- Land use and cropping patterns

Management of a groundwater system, means making such decisions as:

- The total volume that may be withdrawn annually from the aquifer.
- The location of pumping and artificial recharge wells, and their rates.
- Decisions related to groundwater quality.
- Groundwater contamination by:
- Hazardous industrial wastes
- Leachate from landfills
- Agricultural activities such as the use of fertilizers and pesticides

Groundwater Modelling

- The only effective way to test effects of groundwater management strategies
- Conceptual model Steady state model Transient model
- Processes

Groundwater flow (calculate both heads and flow)

Solute transport – requires information on flow (calculate concentrations)

Model Design

- Conceptual Model
- Selection of Computer Code
- Model Geometry
- Grid
- Boundary array
- Model Parameters
- Boundary Conditions
- Initial Conditions
- Stresses

Update Model

Mathematical Model

Unsatisfactory Results

Computation

Poor Fit

Compare Model and Field

Calibrate Model

Satisfactory Results

Conclude study

(Decisions & Recommendations)

General governing equation for transient, heterogeneous, and anisotropic conditions

Kx, Ky, Kz are components

of the hydraulic conductivity

Specific Storage

Ss = V / (x y z h)

Types of Solutions of Mathematical Models

- Analytical Solutions: h= f(x, y, z, t)
- Numerical Solutions
- Finite difference methods
- Finite element methods

Model Design

- Conceptual Model
- Selection of Computer Code
- Model Geometry
- Grid
- Boundary array
- Model Parameters
- Boundary Conditions
- Initial Conditions
- Stresses

Suitability of groundwater in increasing dry season productivity in the coastal region of the Ganga basin

- How the recharge mechanisms can be used to reduce salinity.
- Climate change impact on groundwater.

Management of Excess Rainwater

- Mismatch between water supply and demand

- Possible solutions

- Rainwater conservation and recycling

- Multiple use of harvested water

- Managed aquifer recharge

- Management of stagnant water in lowland areas

Rainwater Conservation

a. Storage of rainwater on surface reservoir

b. Recharge to ground water

- Pits
- Trenches
- Dug wells
- Hand pumps
- Recharge wells
- Recharge shafts
- Lateral shafts with bore wells
- Spreading techniques

Methods of Rainwater Storage

- Infiltration
- Injection

Benefits

- Ideal solution to water problems in water stress areas
- Capture and storage of water in monsoon when rainwater is abundant
- More water will be available for summer use
- Rise in groundwater level - Improves declining aquifers
- May increase base flow to streams
- Mitigates the effects of drought
- Reduces the runoff which chokes the storm water drains
- Flooding of roads and low land areas are reduced
- Quality of water improves
- Soil erosion will be reduced
- Saving of energy per well for lifting of ground water – 1 m rise in water level saves about 0.40 KWH of electricity

What is Managed Aquifer Recharge (MAR)?

- Managed Aquifer Recharge is:
- The infiltration or injection of water into an aquifer
- Water can be withdrawn at a later date but also left in the aquifer (e.g. to benefit the environment)

Why Consider MAR?

- Allows storage of water in wet seasons
- Improvement in groundwater quality
- Allows increased use of groundwater from other parts of the aquifer systems
- To stop seawater intrusion in coastal areas
- To maintain or increase available water supplies for use in agriculture, drinking water supply, and industry

The point of origin of the Ganga, known as the Gangotri (left) and Devprayag, the point of confluence of the Alaknanda (from right) and Bhagirathi (from left) to form the Ganga (right).

The river systems in India are grouped into four broad categories:

The Himalayan rivers

The Peninsular rivers

The Coastal rivers

The Inland rivers

The Ganga River (length: 2525 km long; catchment area: 861404 km2) is fed by runoff from

Vast land area bounded Himalaya in the north.

Peninsular highlands and the Vindhya Range in the south.

The states of Haryana, Rajasthan, Uttar Pradesh and West Bengal, comprising 50% of the basin area.

The basin spreads over four countries: India, Nepal, Bangladesh and China.

Soil and rainfall (isohyetal) map of Ganga Basin(Source: Ministry of Environment and Forests, Government of India)

Vegetation Types of Ganga Basin(Source: Ministry of Environment and Forests, Government of India)

- An important component of water resource systems and source of clean water.
- More abundant than Surface Water
- Extracted from aquifers through pumping wells and supplied for domestic use, industry and agriculture.
- With increased withdrawal of groundwater, the quality of groundwater has been continuously deteriorating.
- Linked to Surface Water systems and sustains flows in streams

Groundwater in Hydrologic Cycle

(Source: physicalgeography.net)

Dynamic Groundwater Resources of India

- Total replenishable groundwater in the country = 433 BCM
- 5,723 units (blocks, talukas, mandals, districts) assessed –
- 15% over-exploited
- 4% critical
- 10% semi-critical
- Delhi, Haryana, Punjab, Rajasthan are overusing their groundwater resources.
- Andhra Pradesh has the highest number of over-exploited units.
- The agricultural (tube-well dependent) state of Punjab has developed (usage compared to availability) its groundwater upto 145%.
- Delhi is mining 170% of its groundwater.
- Countrywide percentage of groundwater development is 58%.

Annual replenishable groundwater in comparison with annual draft in Ganga basin

Ground Water and Surface Water Interaction

- Ground water and surface water contained in the hydrological system are closely interrelated
- The studies examines the processes of ground water flow generation and estimation of ground water discharge including ground water discharge to rivers (base flow)
- In a ground water basin, it is common to identifyseveral aquifers separated either by less permeable orimpermeable layers

the upper aquifer is recharged through the bed and banksof the river. The lower aquifer is recharged through theintervening aquitard

- finite difference equations describes the response of the aquifer system to appliedstresses
- quasi three-dimensional model simulates a ground water system having any number of aquifers

The studies on the ground water/surface waterinterrelationship made it possible to solve a number of importantscientific and practical problems :

- to estimate base flow and, therefore, sustained low riverdischarges of different probabilities
- to estimate the ground water contribution to total waterresources and the water balance of regions
- to evaluate quantitatively the natural ground water resourcesfor determining the prospects of their use within large areasand as a component of the safe ground water yield

The methods for estimating the ground water dischargeof the upper hydrodynamic zone are fairly well developed as compared to deep artesianaquifers and their contribution to surface runoff

- A natural process that occurs in virtually all coastal aquifers.
- Defined as movement of seawater inland into fresh groundwater aquifers, as a result of
- higher seawater density than freshwater
- groundwater withdrawal in coastal areas

- In the coastal margins of ground water basin, the lowering of water level or potentiometric head results in the intrusion of sea water
- Inland gradient for saline intrusion result from pumping at rate higher than the recharge to the ground water basin
- wedge-shaped intrusion occurs as sea water is approximately 1.025 times heavier than fresh water

Field surveys (geophysical and geochemical studies) can only reveal the present state of seawater intrusion but can not make impact assessment and prediction into the future

- Mathematical models are needed for these purposes
- Ghyben-Herzberg relation is a highly simplified model
- Dynamic movement of groundwater flow and solute transport needs to be considered
- A density-dependent solute transport model including advection and dispersion is needed for the modelling

Advection-Dispersion Equation

Flow Equation

Distribution of Head

Velocity Field

Concentration distribution in time and space

- Restoration to the original, non-polluted state of polluted ground water is more difficult than surface water
- Geologic and hydrogeologic setting along with magnitude of the pollution hazard for a specific incident must be evaluated.
- Movement of contaminants and its control largely depends on the hydrogeologic environment
- Processes of migration and alterations present in ground water are also present in the unsaturated zone

Remedial action can be classified into three broad categories

- Physical containment measures, including slurry trench cutoff walls, grout curtains, sheet piling, and hydrodynamic control
- Aquifer rehabilitation, including withdrawal, treatment, reinjection (or recharge), and in-situ treatment such as chemical neutralization and biological neutralization
- Withdrawal, treatment and use

use of models provide more appropriate and rigorous method for integrating all the available data together

- It evaluates the response of the aquifer system to a contamination event
- The models are derived from the expression of the flow and transport processes in terms of mathematical equations
- Equations are solved by incorporating appropriate parameter values and boundary conditions

Before extensive pumping

After extensive pumping by many wells

Pumping causes a cone of depression and draws the salt water upwards into the well.

- An important component of water resource systems.
- Extracted from aquifers through pumping wells and supplied for domestic use, industry and agriculture.
- With increased withdrawal of groundwater, the quality of groundwater has been continuously deteriorating.
- Water can be injected into aquifers for storage and/or quality control purposes.

MANAGEMENT means making decisions to achieve goals without violating specified constraints.

- Once contamination has been detected in the saturated or unsaturated zones, requires the prediction of the path and the fate of the contaminants, in response to the planned activities.
- Any monitoring or observation network must be based on the anticipated behavior of the system.
- The tool for understanding the system and its behavior and for predicting the response is the model.
- Usually, the model takes the form of a set of mathematical equations, involving one or more partial differential equations. We refer to such model as a mathematical model.
- The preferred method of solution is the analytical solution.

For most practical problems we transform the mathematical model into a numerical one, solving it by means of computer programs.

What is a “model”?

- Any “device” that represents approximation to field system
- Physical Models
- Mathematical Models (Analytical and Numerical)

Modeling begins with formulation of a concept of a hydrologic system and continues with application of, for example, Darcy\'s Law to the problem, and may culminate in a complex numerical simulation.

- CONCEPTUAL MODEL
- MATHEMATICAL MODEL
- ANALOG MODEL
- PHYSICAL MODEL

Line diagram of the Ganga with major tributaries

(Source: Status paper on river Ganga, NRCD, MoEF, 2009)

Importance of ground water flow models

- Construct representations and helps understanding the interrelationships between elements of hydrogeological systems
- Efficiently develop a sound mathematical representation
- Make reasonable assumptions and simplifications
- Understand the limitations of the mathematical representation and interpretation of the results

Groundwater models can be used :

- To predict or forecastexpected artificial or natural changes in the system.
- To describe the system in order to analyse various assumptions
- To generatea hypothetical system that will be used to study principles of groundwater flow associated with various general or specific problems.

- Groundwater flow
- Transport
- Particle tracking: requires velocities and a particle tracking code. calculate path lines
- (b)Full solutetransport: requires velocites and a solute transport model. calculate concentrations

- Processes we need to model
- Groundwater flow
- calculate both heads and flows (q)
- Solute transport – requires information on flow (velocities)
- calculate concentrations

Requires a flow model and a solute transport model.

Modelling Process

- Establish the Purpose of the Model
- Develop Conceptual Model of the System
- Select Governing Equations and Computer Code
- Model Design
- Calibration
- Calibration Sensitivity Analysis
- Model Verification
- Prediction
- Predictive Sensitivity Analysis
- Presentation of Modeling Design and Results
- Post Audit
- Model Redesign

Mathematical model:

Simulates ground-water flow and/or solute fate and transport indirectly by means of a set of governing equations thought to represent the physical processes that occur in the system.

(Anderson and Woessner, 1992)

2D confined:

2D unconfined:

Storage coefficient (S) is either storativity or specific yield.

S = Ss b & T = K b

Groundwater flow is described by Darcy’s law.

This type of flow is known as advection.

Linear flow paths

assumed in Darcy’s law

True flow paths

The deviation of flow paths from

the linear Darcy paths is known

as dispersion.

Figures from Hornberger et al. (1998)

with chemical reaction terms.

In addition to advection, we need to consider two other processes in transport problems.

- Dispersion
- Chemical reactions

groundwater flow equation

groundwater flow equation

1D, transient flow; homogeneous, isotropic,

confined aquifer; no sink/source term

Transport Equation:

Uniform 1D flow; longitudinal dispersion;

No sink/source term; retardation

1D, transient flow; homogeneous, isotropic,

confined aquifer; no sink/source term

Transport Equation:

Uniform 1D flow; longitudinal dispersion;

No sink/source term; retardation

Adescriptive representation of a groundwater system that incorporates an interpretation of the geological & hydrological conditions.

Selection of Computer Code

Depends largely on the type of problem(Flow, solute, heat, density dependent etc. along with 1D, 2D, 3D)

Model geometry

It defines the size and the shape of the model. It consists of model boundaries, both external and internal, and model grid.

Grid

In Finite Difference model, the grid is formed by two sets of parallel lines that are orthogonal. In the centre of each cell is the node

Boundaries

- Physical boundaries are well defined geologic and hydrologic features that permanently influence the pattern of groundwater flow (faults, geologic units, contact with surface water etc.)
- Hydraulic boundaries are derived from the groundwater flow net and therefore “artificial” boundaries set by the model designer. They can be no flow boundaries or boundaries with known hydraulic head.

Model Parameters

- Time, Space (layer top and bottom), Hydrogeologic characteristics (hydraulic conductivity, transmissivity, storage parameters and effective porosity)

Initial Conditions

- Values of the hydraulic head for each active and constant-head cell in the model.

- Calibration parameters are uncertain parameters whose values are adjusted during model calibration.
- Typical calibration parameters include hydraulic conductivity and recharge rate.
- Model validation is to determine how well the mathematical representation of the processes describes the actual system behavior.

- MODFLOW
- (Three-Dimensional Finite-Difference Ground-Water Flow Model)
- When properly applied, MODFLOW is the recognized standard model.
- Ground-water flow within the aquifer is simulated in MODFLOW using a block-centered finite-difference approach.
- Layers can be simulated as confined, unconfined, or a combination of both.
- Flows from external stresses such as flow to wells, areal recharge, evapotranspiration, flow to drains, and flow through riverbeds can also be simulated.

- MT3D (A Modular 3D Solute Transport Model)
- FEFLOW (Finite Element Subsurface Flow System)
- HST3D (3-D Heat and Solute Transport Model)
- SEAWAT (Three-Dimensional Variable-Density Ground-Water Flow)
- SUTRA (2-D Saturated/Unsaturated Transport Model)
- SWIM (Soil water infiltration and movement model)
- VISUAL HELP(Modeling Environment for Evaluating and Optimizing Landfill Designs)
- Visual MODFLOW (Integrated Modeling Environment for MODFLOW and MT3D)

Several methods to control saline intrusion

- Reduction of ground water extraction
- Artificial recharge by spreading
- Physical barrier
- Mathematical modelling of unsteady flow of saline and fresh water in aquifer

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