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Introduction to groundwater modeling

Giovanni Formentin

giovanni.formentin@gmail.com

mailto:giovanni.formentin@gmail.com

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Topics

1. What is a model

2. Main types of groundwater models

3. Purpose of a model

4. Implementation of a flow model

5. Example of a MODFLOW model

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1.What is a model

A model is a simplified representation of the real world

Can be physical…

Rarely used, almost only for didactical purposes

http://groundwater.unl.edu/Groundwater.shtml

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What is a model

A model is a simplified representation of the real world

… or mathematical:

solves the equations governing groundwater flow and the interactions with

- the surface (RAIN, EVAPOTRANSPIRATION, IRRIGATION…)

- surficial water bodies (RIVERS, LAKES, SEA…)

- structures (WELLS, DRAINAGE SYSTEMS, UNDERGROUND WORKS…)

Mathematical models

ANALYTICAL

• models representing simple conditions, not needing to be solved by numerical methods

• e.g. homogeneous and isotropic medium, time-constant boundary conditions, no complex overlapping of hydraulic effects

NUMERICAL

• the representation (generally in 2D or 3D) of a domain is discretised in space and time

• e.g. representation of real, existing settings with different layers, varying properties and time-varying conditions

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Based on two equations:

- Continuity equation (flux IN – flux OUT = change in storage)

- Darcy equation (q = - K * i)

Space and time need to be discretized

Space: cells, nodes, elements

Time: time-steps

Numerical models can manage:

– geological heterogeneity

– aquifer thickness variation

– complex boundary conditions

– stationary and transient conditions

Numerical models

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Ky

Kz

Kx

q= -k grad h

qx = -K dh/dx

Flux in - flux out = change in fluid mass stored

Representative Element Volume (REV)

V = x·y·z

y

porous material element, big enough to

represent the aquifer properties and small

enough to represent a homogeneous part

of aquifer

x

Mathematical combination of continuity and

Darcy equationqy = -K dh/dy

qz = -K dh/dz

storage

Numerical models

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The equations can be solved basing on different assumptions and

discretization strategies

- FINITE DIFFERENCES (e.g. MODFLOW)

- FINITE ELEMENTS (e.g. SUTRA, FEFLOW)

- FINITE VOLUMES

Every formulation has pros and cons in terms of simplicity, flexibility, accuracy,

computational time

Numerical models

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• Space is discretized through a grid

Mesh-centered gridBlock-centered grid

• Each cell is given a property (K, s…) value and may host

one or more boundary conditions

• Two types of grids: block-centered grid or mesh-

centered grid

M. AndersonM. Anderson

Finite differences

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Finite differences block-centered

MODFLOW (2-3D; McDonald e Harbaugh):developed by the USGS in 1988, is the most

widespread code for GW flow simulation.

Combined with MT3D, RT3D and SEAWAT,

simulates transport, degradation and density-

dependent problems

PLASM (2D)M. Anderson

M. Anderson

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Sutra (Voss, 1984)

Feflow (Diersch, 1996): a 2-3Dcode for flow, transport and heat

simulation

Mathematical Conditions and properties are assigned to nodes of 2D

elements (triangles or quadratic) or 3D elements (tetrahedral, etc.)

M. Anderson

Finite elements

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Finite

Differences

Finite Elements

M. Anderson

M. Anderson

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STEADY-STATE

Time is not considered as a variable

flux IN – flux OUT = 0 no variation in aquifer storage

Good to assess the average condition

TRANSIENT

Simulates the evolution of a system over time

Time is divided into steps (“stress periods” in MODFLOW)

Boundary conditions may vary (e.g. different recharges depending

on monthly rainfall, different pumping periods, tidal levels in coastal

models)

Steady-state and transient models

2. Main types of gw models

• Groundwater flow (saturated / unsaturated)

• Solute transport into groundwater

• Heat transport into groudwater

• Interaction between freshwater and saltwater(saltwater intrusion)

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Groundwater flow model

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modified from U.S.G.S.

Solute transport

• Simulates the movement of solutes (metals, ions, organic compounds…) into groundwater

• Coupling of a flow model with a transport model (e.g. MODFLOW + MT3D)

• Transport by advection, diffusion, dispersion

• Degradation can also be simulated

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Solute transport

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modified from http://www.rgc.ca/

Heat transport

• Simulates the transport of heat into groundwater

• Coupling of a density-dependent flow model and a transport model (e.g. MODFLOW + SEAWAT)

• Typical application: simulation of geothermal heatpumps – heating or cooling systems usinggroundwater as heat source or sink

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Heat transport

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dT (°C)

Withdrawal well

Re-immission well

MODFLOW 2000 + SEAWAT v. 4

Saltwater intrusion

• Simulates the transport of dissolved salt intogroundwater

• Coupling of a density-dependent flow model and a transport model (e.g. MODFLOW + SEAWAT)

• Typical application: simulation of saltwater intrusioninto coastal aquifers

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Saltwater – unconfined aquifer

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(CUSTODIO E., LLAMAS M.R., 1996)

Saltwater – Multi-aquifer

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Seawater Intrusion

Coastal Aquifer - No Pumping

Modified from: WRD – Water Replenishment District of Southern California

Seawater Intrusion

Coastal Aquifer - With Pumping

Modified from: WRD – Water Replenishment District of Southern California

Brackish WaterFresh Water

Sea Level

Seawater Intrusion

Coastal Aquifer - Intrusion Advancing

Modified from: WRD – Water Replenishment District of Southern California

Brackish WaterFresh Water

Sea Level

Seawater Intrusion – injection well

Coastal Aquifer - Pumping and Injection

Modified from: WRD – Water Replenishment District of Southern California

Brackish WaterFresh Water

Sea Level

Seawater Intrusion – injection well

Coastal Aquifer - Pumping and Injection

Modified from: WRD – Water Replenishment District of Southern California

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3. Purpose of a model

PREDICTION

and DESIGNRESEARCHSYSTEM

UNDERSTANDING and

INTERPRETATION

A flow or transport model can be built for different purposes

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System understanding and interpretation

Implemented to represent and understand the behavior of a hydrogeological system.

Helpful to:

– Organize data: while studying the dynamics of a wide regional system, data

collection and organization in a model allows to create and improve the

conceptual model, optimizing further data collection.

– Understand system dynamics: through the implementation of models

representing theoretical scenarios, it is possible to understand the system

behavior and GW dynamics

– Validate the conceptual site model: a numerical model could help to select

among different conceptual models or to reduce the starting assumptions

through comparison between real data and model results

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Numerical models are a powerful tool to assist in groundwater managing and in the

design of remediation systems

Prediction models are implemented to predict GW flow/transport changes caused by

new stresses applied to the hydrogeological system

They need a calibration and a validation process, i.e. the comparison between

simulation results and real data (heads, fluxes, concentrations, temperatures…).

After calibration/validation assess the ability of the model to represent the real

system, it can be applied to predict new scenarios:

– forecast of system evolution deriving from natural changes in water

balance (climate change, river levels…..) or from human intervention

(wells, irrigation…)

– prediction of the effects of remediation actions in contaminated sites

(e.g. design of a pump & treat system and forecast of its effect on

contaminant distribution over time)

Prediction and design

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GW resource management

• To assess and understand system dynamics and mass balance

• To evaluate GW cross-flow between aquifers

• To assess interactions between surficial waters and groundwater

• To authorize new GW exploitations

• To assess existing aquifer exploitation activities

assessment of withdrawal impact on GW resources

and identification of policies of sustainable use

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MS

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MS

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MS

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MS

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MS

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MS

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MS

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Sector Flow rate (l/s)

West 12,1

29,4Central 15,5

East 1,8

Salt water intrusion

Hydraulic

barrier

Mass balance

Injection wells

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= 1° aquifer

= aquitard/aquiclude

= 2° aquifer

= lake

QUARRY UNDERGROUND TUNNEL

water pressure

SLOPE INSTABILITY

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4. Implementation of a flow model

Anderson & Woessner

Model purpose definition

Prediction or interpretation purpose?

Which ANSWERS we are looking for?

SCALE OF THE MODEL? Regional or local?

FLOW OR TRANSPORT? Is fluid density important?

Can an ANALYTICAL model give good results?

Are the AVAILABLE DATA enough to support a

numerical model?

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The conceptual model tries to represent in a simplified, but comprehensive, way

the real flow system

Simplification is unavoidable: there’s no limit to the complexity of the real world

Need to find an equilibrium between simplification and detail in order to represent

just the relevant phenomena

Some basic rules

- Analyze the data assessing their reliability

- Organize the data (better in a GIS)

- Build a “solid” conceptual model

- Start simple, adding complexity only if needed

The conceptual model

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Anderson & Woessner

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The choice of the code depends on model purposes and hydrogeological site

characteristics:

-complexity of the hydrogeological structure

-flow-transport-density dependent problem etc….

E E'

SEZIONE LITOSTRATIGRAFICA E-E'

E E'

SEZIONE LITOSTRATIGRAFICA E-E'

Code selection and model design

Model design

• Model domain

• Layering and mesh refining where necessary

• Input of the hydrogeological layers

• Input of the aquifer properties (hydraulic conductivity K, storage coefficient s…)

• Input of the boundary conditions (sea, rivers, lakes, wells…)

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Variation of properties and boundary conditions to obtain the best agreement

between measures and model outputs (heads, flow rates, concentrations,

temperatures…)

Calibration

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After the previous steps it is possible to use the model to understand the system

dynamics or to predict flow and heads linked to new stress

The model reliability is evaluated by the simulation of flow/stress conditions

different from those used in calibration: e.g. different recharge, pumping tests

etc…

7. Prediction

Check of a prediction scenario after the real application of new stresses

8. Postaudit

9. Model update

Collection of relevant data may drive updates in the model structure

Further steps6. Validation

Modflow GUIs

Modflow is usually run in a Graphical User Interface (GUI)

ModelMuse (free)

Groundwater Vistas

Visual Modflow

GMS

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