EES215

Lecture 11

Global hydrologic cycle; components
Isolation of component of interest
Groundwater - definitions

Darcy's Law - observation that flow is proportional to diameter of pipe:

Q/A = v = - K(h₁- h₂)/l = - K¶h/¶l

h - hydraulic head
¶h/¶l - hydraulic gradient
K - hydraulic conductivity
Q - Darcy flux (Volume/time)
v - specific discharge (length/time)
A - area of pipe

Definition of porosity: ratio of void volume over total volume (in percent)

Heterogeneous hydraulic permeability:
Horizontal component:   K_x = S (d_i K_i)/ S (d_i)
Vertical component:    K_z = S (d_i)/ S (d_i/K_i)
With d_i thickness of individual layers with conductivity K_i

In most situations, layers are reasonably parallel to the surface so that the horizontal component is to be used for flow estimates (exceptions are related to considerations of infiltration such as the likelihood of groundwater reaching a waste repository)

Porosity: void space/total volume; usually given in percent
relation to rock type; history of rock; formation of porosity
distribution of rock types

Permeability – degree of interconnectedness of pore space

K hydraulic conductivity - dependent on characteristics of fluid and rock
Dependence:  K = kr_wg/m
Proportional to product of density and grav. acceleration; and inversely proportional to viscosity of fluid involved - proportionality constant is called intrinsic permeability - function of medium alone with units of L². All these parameters together are called hydraulic conductivity or, in older textbooks, the coefficient of permeability
Units of permeability: 1 Darcy = 1.01x10^-8 cm²
Hydraulic conductivity: cm/s; m/s; gal/day/ft²
Examples   Fig. 1

Groundwater terms:

• aquifers: formation which allow the flow of water (sandstone; gravel)
• aquitards: formations with sizable porosity which are saturated with water but do not allow the flow of water (high porosity; low permeability; ex: shale)
• aquicludes: formations which have low porosity and low permeability (granite and similar igneous rocks; salt layers)

Changes in porosity, permeability
Porosity reduction: compaction; pressure solution
Compaction: grain to grain rearrangement into closer contacts - no chemical reaction involved
Pressure solution: dissolution of outer rims of grains where strain is greatest
Dependence of porosity on depth
Chemical water-rock interaction - increase in porosity due to dissolution of minerals; decrease in porosity due to deposition

Measurement of permeability: In the lab – apparatus based on Darcy’s Law
In situ (field measurements) pump tests etc.
Large differences between lab and in-situ measurements, especially in igneous rocks due to the presence of fractures

Origin of fractures: folding and faulting
Deep erosion with differential stress
Shrinkage cracks (shales; shaley sands)

Conjugate fractures - originated from same event
Orthogonal fractures - from sequential events
Regional fractures - large scale features