Review Of Basic Hydrogeology Principles

Types of Terrestrial Water Groundwater SoilMoisture Surface Water

Unsaturated Zone – Zone of Aeration Pores Full of Combination of Air and Water Zone of Saturation Pores Full Completely with Water

Porosity Primary Porosity Secondary Porosity Sediments Sedimentary Rocks Igneous Rocks Metamorphic Rocks

Porosity n = 100 (Vv / V) n = porosity (expressed as a percentage) Vv = volume of the void space V = total volume of the material (void + rock)

= Porosity Permeability VS Ability to hold waterAbility to transmit water Size, Shape, Interconnectedness Porosity  Permeability Some rocks have high porosity, but low permeability!!

Vesicular Basalt Porous But Not Permeable ClayPorous High Porosity, but Low Permeability Interconnectedness Small Pores Sand Porous and Permeable

The Smaller the Pore Size The Larger the Surface Area The Higher the Frictional Resistance The Lower the Permeability High Low

Darcy’s Experiment He investigated the flow of water in a column of sand He varied: Length and diameter of the column Porous material in the column Water levels in inlet and outlet reservoirs Measured the rate of flow (Q): volume / time

K = constant of proportionality Q = -KA (  h / L) Darcy’s Law Empirical Law – Derived from Observation, not from Theory Q = flow rate; volume per time (L 3 /T) A = cross sectional area (L 2 )  h = change in head (L) L = length of column (L)

L 3 x L T x L 2 x L What is K? K = Hydraulic Conductivity = coefficient of permeability K = QL / A (-  h) / // LT What are the units of K? = The larger the K, the greater the flow rate (Q) K is a function of both: Porous medium The Fluid

Clay10 -9 – Silt10 -6 – Silty Sand10 -5 – Sands10 -3 – Gravel10 -2 – 1 Sediments have wide range of values for K (cm/s) Clay Silt Sand Gravel

Not a true velocity as part of the column is filled with sediment Q = -KA (  h / L) Rearrange QA q = = -K (  h / L) q = specific discharge (Darcian velocity) “apparent velocity” –velocity water would move through an aquifer if it were an open conduit if it were an open conduit

Average linear velocity = v = True Velocity – Average Mean Linear Velocity? QA q = = -K (  h / L) Only account for area through which flow is occurring Flow area = porosity x area Water can only flow through the pores QnAqn =

Aquifers Aquifer – geologic unit that can store and transmit water at rates fast enough to supply reasonable amounts to wells Confining Layer – geologic unit of little to no permeability Aquitard, Aquiclude Gravels Clays / Silts Sands

Water table aquifer Confined aquifer Types of Aquifers Unconfined Aquifer high permeability layers to the surface overlain by confining layer

Homogeneity – same properties in all locations Homogeneous vs Heterogenous Variation as a function of Space Heterogeneity hydraulic properties change spatially

Anisotropic changes with direction Isotropy vs Anisotropy Variation as a function of direction Isotropic same in direction

In Arid Areas: Water table flatter In Humid Areas: Water Table Subdued Replica of Topography Regional Flow

Subdued replica of topography Discharge occurs in topographically low spots Water Table Mimics the Topography Need gradient for flow If water table flat – no flow occurring Sloping Water Table – Flowing Water Flow typically flows from high to low areas Q = -KA (  h / L)

Discharge vs Recharge Areas Recharge Downward Vertical Gradient Discharge Upward Vertical Gradient

Discharge Topographically High Areas Deeper Unsaturated Zone Flow Lines Diverge Recharge Topographically Low Areas Shallow Unsaturated Zone Flow Lines Converge

Equations of Groundwater Flow Fluid flow is governed by laws of physics Any change in mass flowing into the small volume of the aquifer must be balanced by the corresponding change in mass flux out of the volume or a change in the mass stored in the volume or both Law of Mass Conservation Continuity Equation Matter is Neither Created or Destroyed Darcy’s Law

Balancing your checkbook $ My Account

Let’s consider a control volume dx dy dz Area of a face: dxdz Confined, Fully Saturated Aquifer

dx dy dz qxqx qyqy qzqz q = specific discharge = Q / A

dx dy dz qxqx qyqy qzqz  w = fluid density (mass per unit volume) Apply the conservation of mass equation

Change in Mass in Control Volume = Mass Flux In – Mass Flux Out Conservation of Mass The conservation of mass requires that the change in mass stored in a control volume over time (t) equal the difference between the mass that enters the control volume and that which exits the control volume over this same time increment. dx dy dz - (  w q x ) dxdydz - ( xx wqxwqx + yy wqywqy + zz wqzwqz ) dxdydz xx - (  w q y ) dxdydz yy - (  w q z ) dxdydz zz (  w q x ) dydz

Volume of control volume = (dx)(dy)(dz) Volume of water in control volume = (n)(dx)(dy)(dz) Mass of Water in Control Volume = (  w )(n)(dx)(dy)(dz) Change in Mass in Control Volume = Mass Flux In – Mass Flux Out dx dy dz n [(  w )(n)(dx)(dy)(dz)] MtMt tt =

tt = Change in Mass in Control Volume = Mass Flux In – Mass Flux Out - ( xx wqxwqx + yy wqywqy + zz wqzwqz ) dxdydz Divide both sides by the volume [(  w )(n)] tt = - ( xx wqxwqx + yy wqywqy + zz wqzwqz ) If the fluid density does not vary spatially [(  w )(n)] tt = - ( xx qxqx + yy qyqy + zz qzqz ) 1w1w

q x = - K x (  h/  x) q y = - K y (  h/  y) q z = - K z (  h/  z) xx qxqx + yy qyqy + zz qzqz Remember Darcy’s Law xx ( KxKx hxhx ) yy ( KyKy hyhy ) zz ( KzKz hzhz ) ++ dx dy dz xx ( KxKx hxhx ) yy ( KyKy hyhy ) zz ( KzKz hzhz ) ++ [(  w )(n)] tt 1w1w = ( - )

tt 1w1w After Differentiation and Many Substitutions (  w g + n  w g) htht  = aquifer compressibility  = compressibility of water xx ( KxKx hxhx ) yy ( KyKy hyhy ) zz ( KzKz hzhz ) ++ = (  w g + n  w g) htht S s =  w g (  + n  ) But remember specific storage

xx ( KxKx hxhx ) yy ( KyKy hyhy ) zz ( KzKz hzhz ) ++ = SsSs htht 3D groundwater flow equation for a confined aquifer If we assume a homogeneous system K SsSs htht 2hx22hx2 ++ 2hy22hy2 2hz22hz2 = ( ) transientanisotropicheterogeneous xx ( KxKx hxhx ) yy ( KyKy hyhy ) zz ( KzKz hzhz ) ++ = SsSs htht If we assume a homogeneous, isotropic system Transient – head changes with time Steady State – head doesn’t change with time Homogeneous – K doesn’t vary with space Isotropic – K doesn’t vary with direction: K x = K y = K z = K

Let’s Assume Steady State System Laplace Equation Conservation of mass for steady flow in an Isotropic Homogenous aquifer 2hx22hx2 ++ 2hy22hy2 2hz22hz2 = 0

If we assume there are no vertical flow components (2D) Kb SsbSsb htht 2hx22hx2 + 2hy22hy2 = ( ) STST htht 2hx22hx2 + 2hy22hy2 = K SsSs htht 2hx22hx2 ++ 2hy22hy2 2hz22hz2 = ( )

xx ( KxKx hxhx ) yy ( KyKy hyhy ) zz ( KzKz hzhz ) ++ = 0 HeterogeneousAnisotropicSteady State K SsSs htht 2hx22hx2 ++ 2hy22hy2 2hz22hz2 = ( ) HomogeneousIsotropicTransient 2hx22hx2 ++ 2hy22hy2 2hz22hz2 = 0 HomogeneousIsotropicSteady State

Unconfined Systems Water is derived from storage by vertical drainage Sy Pumping causes a decline in the water table

In a confined system, although potentiometric surface declines, saturated thickness (b) remains constant In an unconfined system, saturated thickness (h) changes And thus the transmissivity changes Water Table

xx ( KxKx hxhx ) yy ( KyKy hyhy ) zz ( KzKz hzhz ) ++ = SsSs htht Remember the Confined System xx ( hK x hxhx ) yy ( hK y hyhy ) + = SySy htht Let’s look at Unconfined Equivalent Assume Isotropic and Homogeneous xx ( h hxhx ) yy ( h hyhy ) + = SyKSyK htht Boussinesq Equation Nonlinear Equation

Let v = h 2 For the case of Island Recharge and steady State