Review Of Basic Hydrogeology Principles Types of Terrestrial

Review Of Basic Hydrogeology Principles

Types of Terrestrial Water Surface Water Soil Moisture Groundwater

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

Porosity Primary Porosity Sediments Sedimentary Rocks Secondary Porosity 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 water Ability to transmit water Size, Shape, Interconnectedness Porosity = Permeability Some rocks have high porosity, but low permeability!!

Vesicular Basalt Clay Interconnectedness Small Pores Porous But Not Permeable High Porosity, but Low Permeability 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

Darcy’s Law Q = -KA ( h / L) 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) K = constant of proportionality

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

Clay Silt Sediments have wide range of values for K (cm/s) Clay 10 -9 – 10 -6 Silt 10 -6 – 10 -4 Silty Sand 10 -5 – 10 -3 Sands 10 -3 – 10 -1 Gravel 10 -2 – 1 Sand Gravel

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

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

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

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

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

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

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

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

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

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

Equations of Groundwater Flow Fluid flow is governed by laws of physics Darcy’s Law of Mass Conservation Continuity Equation Matter is Neither Created or Destroyed 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

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

dz qx qy dy dx qz q = specific discharge = Q / A

dz qx qy dy dx qz w = fluid density (mass per unit volume) Apply the conservation of mass equation

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. Change in Mass in Control Volume = Mass Flux In – Mass Flux Out dz ( wqx) dydz dy dx - ( wqx) dxdydz x - ( wqy) dxdydz y - ( wqz) dxdydz z - ( wqx + wqy + wqz ) dxdydz x y z

Change in Mass in Control Volume = Mass Flux In – Mass Flux Out n dz dy dx 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) M = [( )(n)(dx)(dy)(dz)] t t w

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

- ( x qx+ y qy + z qz ) Remember Darcy’s Law qx = - Kx( h/ x) dz qy = - Ky( h/ y) dy dx qz = - Kz( h/ z) h (K x x x ) h ( + y Ky y 1 [( )(n)] h = x( Kx x w t w ) ) + z ( Kz h z ) h + y( Ky y ) + z ( Kz h z )

1 [( )(n)] w t w After Differentiation and Many Substitutions ( wg + n wg) h t = aquifer compressibility = compressibility of water ( wg + n wg) h h ( = x Kx x t ) h + y( Ky y ) + z ( Kz h z ) But remember specific storage Ss = wg ( + n )

h (K x x x ) h + y( Ky y ) + z ( Kz h z ) = Ss h t 3 D groundwater flow equation for a confined aquifer heterogeneous anisotropic transient Transient – head changes with time Steady State – head doesn’t change with time If we assume a homogeneous system Homogeneous – K doesn’t vary with space h h Kx x( x ) + Ky y( y ) + Kz ( h ) = Ss h z z t If we assume a homogeneous, isotropic system Isotropic – K doesn’t vary with direction: Kx = Ky = Kz = K 2 h + 2 h = S h ) K ( x 2 s 2 2 y z t

Let’s Assume Steady State System 2 h + 2 h = 0 x 2 y 2 z 2 Laplace Equation Conservation of mass for steady flow in an Isotropic Homogenous aquifer

2 h 2 h = S h K ( x 2 + y 2 + z 2 ) s t If we assume there are no vertical flow components (2 D) 2 h + 2 h Kb ( x 2 y 2 ) = Ssb h t 2 h + 2 h = S h x 2 y 2 T t

h (K x x x Heterogeneous ) h + y( Ky y ) + z ( Kz h z ) Anisotropic =0 Steady State 2 h + 2 h = S h ) K ( x 2 s 2 2 y z t Homogeneous Isotropic Transient 2 h + 2 h = 0 x 2 y 2 z 2 Homogeneous Isotropic Steady State

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

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

Remember the Confined System h (K x x x ) h + y( Ky y ) + ( Kz h z z ) = Ss h t Let’s look at Unconfined Equivalent h (h. Kx x x h ) + y(h. Ky y ) = Sy h t Assume Isotropic and Homogeneous h (h x x h ( ) + y h y ) Sy h = K t Boussinesq Equation Nonlinear Equation

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