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### Unit 03a : Advanced Hydrogeology

Basin Hydrogeologic Cycle

Groundwater Basin

- A groundwater basin is a hydrologic unit of groundwater storage defined as an area more or less separate from neighboring groundwater storage areas.
- Basins are normally delimited by natural physical boundaries such as rivers, flow divides, and flow barriers.

Driving Forces

- The principal driving forces for groundwater flow were recognized very early by Chamberlin (1895) and King (1899):
- Topographic (gravitational)
- Thermal
- Capillary
- Later tectonic strain (compaction) was recognized as an additional driving force.

Topographic Driving Forces

Chamberlin and later King defined and documented the confined and unconfined behaviour of groundwater systems over 100 years ago.

- Thomas S. Chamberlin (1885) identified elevation differences as the topographic drive for groundwater movement
- “the pressure-producing mechanism is the hydrostatic weight of the body of water….”

T.C. Chamberlin

- Franklin H. King (1899) stated that the water table everywhere is a subdued replica of the topography and that water moves from topographically high areas to topographically low areas
- “the dynamic mechanism required to maintain flow is continuous replenishment by precipitation….”

F.H.King

Conceptual Model of Regional Flow

- M. King Hubbert (1940) was the first to publish a conceptual model for a flow field based on head potential
- Hubbert’s model predicts the characteristics of the flow net in both recharge and discharge areas and is consistent with the water table as a subdued replica of the topographic surface

M. King Hubbert

Hubbert’s model is essentially a 2D solution of Laplace’s equation where all boundaries except the upper surface are specified as no flow. The upper surface can be specified as any function representing the form of the water table. A general solution is:

f(x,z) = ao + S an cosh(npz/L).cos(npx/L)

n =1

where f is the hydraulic potential and L is the length of the flow cell

Hubbert’s Model

One specific solution when the water table (upper surface boundary condition) is a simple cosine function:

f(x,zo) = A – B cos(npx/L)

has the form:

f(x,zo) = A – B cosh(npz/L).cos(npx/L)

cosh(npzo/L)

Multi-Cell Model of Regional Flow

- J. Tóth (1962, 1963) was the first to significantly extend the conceptual work of Hubbert
- Tóth investigated a more complex flow system with a sinusoidal water table superimposed on a regional slope
- Tóth identified local, intermediate and regional flow systems based on this simple topographic model.

Tóth’s solution uses a slightly more complex boundary condition than Hubbert:

f(x,zo) = B’x/L – b sin(2px/l)

The first (B’) term represents the regional slope and the second (b) term the more local sinusoidal relief. The parameter b is the amplitude of the topography and L/l is the number of flow cells

Tóth’s Model

- If b=0 (no local-scale topography) only a regional flow system develops
- If B’=0 (no regional-scale topography) only local flow systems develop
- If b=B’=0 (no topography) waterlogged conditions will develop with the water table near the surface discharging by evapotranspiration
- If B’ and b > 0 and L/l >> 0 then regional, intermediate and local flow systems will develop.

Later Developments

- Joe Tóth only considered an isotropic homogeneous aquifer in his early work and used simple analytical models.
- Freeze and Witherspoon (1966,1967) used Tóth’s basic model but extended it’s application to layered systems using numerical models.
- Freeze and Witherspoon dealt primarily with the role of permeability contrasts in influencing flow lines in layered systems.
- These effects are important in understanding regional flow.

k1

k1

k2

k2

k2

Flow Line Refraction- If k decreases with depth, equipotentials crowd together and flow becomes more vertical
- If k increases with depth, equipotentials spread apart and flow becomes more horizontal
- If k increases significantly with depth, equipotentials become more widely spaced and flow becomes sub-horizontal

k1> k2

k1< k2

k1<< k2

k2

k1<< k2

Aquitard and Aquifer- For regional flow systems where k2 /k1 or kaquifer/kaquitard tends to be 100 or greater
- Flows in aquitards (k1) are subvertical
- Flows in aquifers (k2) are subhorizontal
- The spacing of flow lines is a measure of flux so that the aquifer is acting as a collector, concentrating flow.

Regional Flow

- To predict flow patterns in regional flow systems the data requirements include:
- Permeability distributions
- Geometry of basin boundaries (including the surface topography)
- The most influential factors on flow patterns are:
- Ratio of basin depth to lateral extent
- Configuration of the water table (topography)
- Permeability distribution
- Major valleys collect flow and concentrate discharge
- Deep permeable aquifers act as conduits and control recharge rates and the location of recharge areas
- Stratigraphic pinchouts at depth exert an influence the location of recharge and discharge areas

Effect of Topography on Flow Patterns

Low relief topography

Moderate relief topography

High relief topography

Effect of Dip on Flow Patterns

Dip towards discharge area – low relief

Dip towards recharge area – high relief

Mountainous Terrain

- 20% of global flow systems
- K distribution dominated by fracturing
- Deep circulation –relatively high Kv for fractured rock
- Water circulates to depths where elevated temperatures exist
- Water table free surface relatively unrelated to topography
- Relationship between K and infiltration has strong influence on flow patterns

Carbonate Terrain

- 10% of global systems supplying >25% global population with water supply
- Self-organized networks of solution enlarged fractures
- Dual porosity systems – matrix dominates storage – fractures dominate flow
- Tracer velocities up to 21 km/d (0.25 m/s) have been measured
- A few springs integrate flow from large areas

Groundwater in Coastal Regions

- Freshwater flow limits saltwater encroachment
- Development disturbs natural balance and can lead to major seawater intrusion
- Control of saline intrusion achieved by:
- Artificial recharge of freshwater
- Reduction and rearrangement of wells
- Development of coastal trough to limit intrusion
- Development of coastal pressure ridge
- Installation of subsurface flow barriers

Small seawater wedge balanced by net outflow to ocean

Seawater wedge advances inland as a result of pumping

Mixing as a result of fluctuations in aquifer recharge

Saline IntrusionInterface assumed rigid

Fluids assumed immiscible

Segregated flow

Pressures for fluid columns onshore and offshore are assumed to balance

gsz =gf(hf + z)

z = hfgf / (gs - gf)

Assuming gf = 1000 kN/m3 and gs = 1025 kN/m3 the depth to the saline interface

z 40 hf

This is called the Ghyben-Hertzberg formula.

hf

z

z

Ghyben-HertzbergSeepage face below sea level

(x,z) is point on interface

Q’ = Q/L is discharge per unit length of coast

z2 = 2Q’xrf + { Q’rf } 2

K(rs – rf) K(rs - rf)

The depth to the interface at the coast (x=0) is:

z = Q’rf

K(rs – rf)

The height of the water table for any x is:

hf = 2Q’x (rs – rf)

K rf

The greater the flow, the deeper the interface and the greater the gap x.

Glover Analysisx

hf

z

m

Interface

Fresh water

Salt water

When pump wells lower the head above a saline interface, the interface rises. This is phenomenon is called “upconing”.

There is an analytical solution that estimates the rise due to upconing for small perturbations of the saline interface.

z = Q’rf _

2pdK(rs – rf)

The displacement process is unstable and premature breakthrough of salt water at the pump well occurs if z/d is greater than about 0.5.

d

z

UpconingSurface Features

- Surface features of groundwater flow (mainly discharge) include:
- Springs
- Seeps
- Saline Soils
- Permanent and Ephemeral Streams
- Marshes, Swamps, Bogs and Fens (Wetlands)
- Ponds, Sloughs and Lakes

Prairie Profile

Recharge

Recharge

Saline

Seepage

Saline

Seepage

- A central topographic high bounded by areas of natural discharge (Meyboom, 1966)
- Geology is generaly low-K tills over higher-K intertill sands and gravels
- No streams - most discharge occurs by evapotranspiration

Groundwater and Vegetation

- Willow rings occur around recharge sloughs and local discharge sloughs – phreatophytes with low alkali tolerance
- Saline soils associated with intermediate to regional discharge systems – halophytes with high salt tolerance (foxtails, salicornia)
- Discharge sloughs associated with region flow systems have high TDS and precipitate salts

Bogs are characterized by spongy peat deposits, acidic waters, and a floor covered by a thick carpet of sphagnum moss.

Bogs receive all or most of their water from precipitation rather than from runoff, groundwater or streams.

Fens are peat-forming wetlands that receive nutrients from sources other than precipitation: usually from upslope drainage from soils and from groundwater.

Fens differ from bogs because they are less acidic and have higher nutrient levels. They support a much more diverse ecology.

Bogs and FensSlough and Lake Interactions

Recharge

Flow-through

Discharge

Sloughs can provide recharge or receive discharge or act as both source and sink.

Water entering the ground in recharge areas is transmitted to distant points and results in a soil moisture deficit in the soils overlying the recharge area

Water entering the soil in a discharge areas cannot overcome the upward gradient and is returned to the surface by evapotranspiration locally.

Recharge and Discharge Areassoil salinization

dry

Basin Hydrologic Cycle

- How much groundwater participates in the basin hydrologic cycle?
- Tóth estimates 90% of recharge never penetrates deeper than about 80 m.
- Tritium studies confirm this theoretical estimate.
- Many streams receive much of their baseflow component from the area within the nearest topographic high
- Regional flow components are small compared with locally derived flows.

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