Unit 01 : Advanced Hydrogeology

Review of Groundwater Flow

Malcolm ReevesCivil and Geological Engineering

What is hydrogeology?

• Hydrogeology is the study of the laws governing the movement of subsurface water,

• the mechanical, chemical and thermal interaction of this water with the porous solid,

• and the transport of energy, chemical constituents and particulates by the flow.

Domenico and Schwartz, 1997

Laws governing movementDarcy’s Law• Q = -A.K dh/dx

Q is the flow, K is the hydraulic conductivity, dh/dx is the head gradient and A is the cross sectional area normal to x.

• Q/A = q = -K dh/dxq is called the specific discharge

• v = q/n = -(K/n) dh/dxv is the advective (flow) velocityn is the porosity

Mechanical, Thermal and Chemical Interactions

• Mixing caused by– Hydraulic (mechanical) gradients (dh/dx)– Thermal gradients (dT/dx)– Chemical gradients (dC/dx)

• Interactions of fluids with the porous medium

Groundwater Transport

• Groundwater transports fluids. The process is called advection.

• Advection of fluid also carries:– Solutes (metals, organics, nutrient, etc)– Particulates (colloids, bacteria, etc)– Energy (mainly heat)

Hydrologic Cycle

Elements of the Hydrologic Cycle• Condensation• Precipitation• Evaporation• Transpiration• Interception (Interception refers to

precipitation that does not reach the soil, but is instead intercepted by the leaves and branches of plants and the forest floor.

• Infiltration• Percolation• Runoff

Water Profile

Bound Water in Minerals

Capillary Water

Intermediate Vadose Water

Water in Unconnected Pores

Groundwater

Soil Water

Inte

rsti

tial

Zo

ne

Sa

tura

ted

Un

sat

ura

ted

Subsurface Flow

• Infiltration• flow entering at the ground surface

• Percolation• vertical downward unsaturated flow

• Interflow• sub-horizontal unsaturated and perched saturated flow

• Groundwater flow• sub-horizontal saturated flow

Soil Moisture

J F M A M J J A S O N D

Mil

lim

etre

s o

f W

ater

Spring Recharge Fall

Recharge

Soil MoistureDepletion

PotentialEvaporation

AdjustedPrecipitation

Infiltration Capacity

• Water supplied to the soil surface at an increasing rate will eventually runoff.

• Water supplied to the soil surface at a constant rate infiltrates at a rate that decreases with time to a limiting rate.

• This limiting rate (when the soil is saturated) is called the infiltration capacity of the soil surface.

Field Capacity

• Flow of water in an unsaturated soil cannot take place until a limiting moisture content is reached.

• This limiting moisture content is called the field capacity of the soil in soil science and the residual water saturation in hydrogeology.

InfiltrationIn

filt

rati

on

Rat

e

0% Moisture Content 100%

Infiltration Capacity

Fie

ld

Ca

pac

ity

Infiltration Capacity [ LT-1 ]Field Capacity [ % ]

Hydrograph Components

• Stream flow hydrographs can be broken down into three components:– Runoff (overland flow)– Interflow (unsaturated sub-horizontal flow)– Baseflow (groundwater flow)

• Each component has a characteristic recession (decay) rate.

Baseflow

• The decline of the flow in a stream in the absence of input is called recession

• Empirically, recession curves are exponential decay functions Q = Qoe-kt.

• After long periods without precipitation, the recession rate is called baseflow and is characteristic of the groundwater system feeding the stream.

• The groundwater recession constant is given by the equation k = ln(Qo/Q)/t

Hydrograph Analysis

• Point A is minimum Q gradient is determined from recession rate

• Point B is maximum Q• Point C is Q at time T*

after the peak:T* = An

where A is the drainage area and n

is an empirical power.If A is in km2, n = 0.14

If A is in mile2, n = 0.20Time

Dis

char

ge

AB

C

T*

Global Hydrological Equation

Input – Output = Change in Storage

P – E –T – Ro = DS

P precipitation

E evaporation

T transpiration

Ro runoff

DS change in groundwater storage

P = I (DS) + R (Ro) + E (T+E)

Elements of the Basin Cycle

Surface

Soil

Aquifer

F

P ETs

Rs Ta

Str

eam

Ch

ann

els

Ro

Qo

Qi

Qs

Qa

For the groundwater sub-systemRs + Qi – Ta – Qa = DS

Aquifer Types

• Unconfined - storage LARGE depends on specific yield• Confined - storage SMALL depends on compressibilities

=κρεμάμενος υδροφόρος

Porosity

Material Porosity(%)

well-sorted sand or gravel 25-50sand and gravel, mixed 20-35glacial till 10-20silt 35-50clay 33-60

Specifics of Aquifer Storage

Unconfined

Sy = n - Sr

n porosity

Sy specific yield (gravity drainage)

Sr specific retention (like field capacity)

Confined

S = b.Ss

b thickness

Ss specific storage

Ss = g.(a + n. b )g specific weight

a matrix compressibility

b water compressibility

Specific YieldMaterial Specific Yield

(%)Max Min Mean

coarse gravel 25 12 22medium gravel 26 13 23fine gravel 30 21 25gravelly sand 35 20 25coarse sand 35 20 27medium sand 32 15 26fine sand 28 10 21silt 19 4 18sandy clay 12 3 7clay 5 0 2

Hydraulic Conductivity

MaterialHydraulic

Conductivity(m/s)

well-sorted gravel 10-4 to 10-2

well-sorted sand 10-5 to 10-3

silty sands, fine sands 10-7 to 10-5

silt, clayey sand, till 10-8 to 10-6

clay 10-11 to 10-8

Steady-State Flow• q = -K dh/dx

K is hydraulic conductivity [ LT-1 ]h is hydraulic head [ L ]

• q = -(kg/m) dh/dxk is intrinsic permeability [ L2 ]m is absolute viscosity [ FL-2T ]

g is specific weight [ FL-3 ]

For horizontal flow gdh/dx = dp/dx• q = -(k/m) dp/dx

p is fluid pressure [ FL-2 ]

Vertical Flow

• For vertical flow

q = -K dh/dz

h = p/g + z

dh/dz = (1/g) dp/dz

q = -(kg/m) dh/dz

q = -(k/m)(dp/dz + 1)

Steady-State Flow Systems

Density-Dependent Flow

• For density-dependent flow

q = K dh/dz

h = p/g + z

dh/dz = (1/g)(dp/dz – (p/g)dg/dz + 1)

q = -(kg/m) dh/dz

q = -(k/m)(dp/dz + 1 – (p/g)dg/dz)

Unsaturated Flow

For unsaturated flowq = -K(y) dh/dz h = y + z y is the pressure head

z is the elevation headh is the total hydraulic head

The pressure head, , y depends on saturation. At full saturation, y increases with depth. In the unsaturated zone, y is negative and is called suction pressure.

Soil Water Characteristic Curve

- Pressure +

Dep

th WaterTable

0% Saturation 100%

+

P

ress

ure

-

WaterTable

Hyd

raulic C

on

du

ctivity

Steady-State and Transient FlowSteady-State

Inflow = Outflowdq/dx = d(K dh/dx)/dx = 0

TransientInflow - Outflow = Change in Storage

dq/dx = d(K dh/dx)/dx = S.dh/dtK is hydraulic conductivity [ LT-1 ]S is storage coefficient [ ]h is hydraulic head [ L ]