Aquifer Nomenclature Aquifer a geologic unit that can

Aquifer Nomenclature • Aquifer - a geologic unit that can store and transmit water at rates sufficient enough to supply exploitable quantities of water • Confining Layer - a geologic unit having little or no intrinsic permeability – Don’t Use • Aquifuge - no water transmission • Aquitard - stores water, little transmission • Aquiclude - aquifuge that forms upper boundary to aquifer • Leaky Confining Layer - a confining layer that leaks

Types of Aquifers Unconfined Clay K’<10 -7 Sand K>>K’ Sand Rock Semi-Confined Semi-Unconfined Clay K’<<K Clay K’<K K Sand Leaky Confining Layer - Storage Ignored K Sand Real Leaky Confining Layer - Storage cannot be ignored • K = Horizontal Hydraulic Conductivity • K’ = Vertical Hydraulic Conductivity

Perched Water Table

Water Table Potentiometric Surface Water Table Well Artesian Well Unconfined Flowing Well Confined The same aquifer can be both confined and unconfined.

Basic Hydraulic Parameters Soil Va = Vol of Air Total Vol. (Vt) Water Vw = Vol. of Water Vs = Vol of Solids Solid Va + Vw = Vv = Vol of Voids = Pore Space Variable No. 1 Porosity (n) = (Vv/Vt)x 100 Expressed as %

Determining Porosity Saturate Known Volume of Dry Soil Volume of Water Added = Vol of Voids Example: 100 cm 3 soil, add 42 cm 3 water = 42% porosity Example: 10 m column 1 m 2 Add 3 m of water to saturate soil What is porosity?

Variable No. 2 - Specific Yield Saturate Known Volume of Dry Soil Volume Water Drained by Gravity Total Volume Sample = Specific Yield (Sy) Drain x 100

Variable No. 3 – Specific Retention Volume Remaining on Soil Particles Total Volume = Specific Retention (Sr) Note: Specific Yield Dictates water bearing properties not porosity n = Sy + Sr

Typical Values of n and Sy Unconsolidated Deposits Gravel n% Sy % 25 - 40 22 - 25 Sand 25 - 50 Silt 35 - 50 18 Clay 40 - 70 2 Rocks sandstone shale crystalline 20 - 27 Primary n % Secondary n % 5 - 30 0 - 10 <5 Fractures increase overall n 2 to 5 % or more if weathered

Key Points • Specific Yield is the Important Property for Flow • Smaller the grain size – lower the Specific Yield • n = Sy + specific retention • Values usually estimated • Porosity varies only over two orders of magnitude

Distribution of Water in Earth Materials Fluid Pressure: a. closed tube w/ sand b. saturated & sealed c. under pressure d. no flow - static hp A Water in pore space exerts pressure on grains around pore space Define fluid pressure - P kg m/sec 2 P º Force/Unit Area = m 2 = N/m 2 = Pa Place Piezometer into tube to measure pressure “Water will rise in tube a height hp until Force produced by the weight of water in piezometer balances P being exerted in the pore space”

P = rghp hp r = density of water g = accel. of gravity hp= ht. of water in well Unit Weight Define - rg as unit weight - Force exerted by one unit volume of water g = rg For water: gw = 9820 N/m 3 (metric) = 62. 4 pcf (English)

Typical Application surface P@A = gwhp clay hp A Note: taking measurements of water levels in in a well provides more than P Unit Weight can be determined for anything - gd = dry unit weight - solids gb = bulk unit weight - solids + moisture gs = saturated unit weight - solids + water Typical Values Pierre shale - 90 -100 pcf Sandy Gravel 8% moisture - 125 -135 pcf Limestone - 165 pcf at saturation

Hydraulic Conductvity constant head reservoir Darcy’s Experiment (1857) Dh D Sand L h 1 h 2 datum Measure Q Q µ Dh Q µ 1/L Qµ A

Pulling Terms Together Q µ (Dh/L) A Hydraulic Gradient (Slope of the fluid pressure term) Slope Dh = Hyd raulic Gradie nt L ft/ft or unitless Dh/L = I = dh/d. L = i Q/A slope = K = Hydraulic Conductivity gradient

Rewrite, Q= - KIA Darcy’s Law sometimes see it written with negative sign b/c flow is in the direction of decreasing fluid pressure Units - m/sec, cm/sec, m/day, ft/day gpd/ft 2 Conceptually, Gradient = 1 1 Unit Volume 1 1 K = Flow in gpd per unit area under unit hydraulic gradient @ 25 C°

Typical Values sandy gravel silty clay 10 -2 to 102 cm/sec 10 -6 to 10 -9 cm/sec Important Points to Remember: K varies over 12 to 14 orders of magnitude Major control on rate at which contaminants move in subsurface Main parameter needed in modeling Varies spatially in response to geology Need to know how depositional/tectonic processes might influence spatial heterogeneity of K K 1 K 2 K 3 contaminant K 2 > K 3 > K 1

Intrinsic Permeability Repeat Darcy’s Experiment Add Non-aqueous phase liquid Dh D L Sand h 1 h 2 datum Measure Q Hold Dh, L and A constant Q = KIA Q for water ¹ Q for NAPL K must vary with fluid properties -

K µ unit weight (g) unit wt. = Force/unit volume = rg K µ r (density) K µ 1/m (viscosity of fluid) Pulling terms together: K µ rg/ m or K = ki rg/ m Property of medium Property of fluid ki = intrinsic permeability - property of just the medium K = hydraulic conductivity - property of the medium and of fluid

Units for Intrinsic Permeability cm 2, ft 2, etc Typical Values Material ki (cm 2) K (cm/sec) Clay 10 -12 to 10 -15 10 -6 to 10 -9 Silt or Till 10 -10 to 10 -12 10 -4 to 10 -6 Fine Sand 10 -9 to 10 -11 10 -3 to 10 -5 Well Sorted Sand 10 -7 to 10 -9 10 -1 to 10 -3 Well Sorted Gravel 10 -6 to 10 -8 100 to 10 -2 Define intrinsic permeability with lower case k with subscript i Hydraulic conductivity defined with a capital K Darcy’s Law Q = ki(rg/ m) (Dh/L) A K

Key Points ki property of the medium only K a property of the medium and fluid K through identical material will vary with density, viscosity and temperature of fluid

Define Specific Storage Ss = r w g ( a + nb ) rw = initial density of water g = acceleration due to gravity a = aquifer compressibility n = porosity b= fluid compressibility Ss = Specific Storage The volume of water either released from or taken into storage per unit volume of confined aquifer per unit change in fluid pressure

Conceptual meaning of Ss Vol Out or In surface 1 unit vol clay aquifer Ss = Volume of water released or taken into storage per unit volume of confined aq. per unit head change in fluid pressure Units - m 3/m = 1/m so units of 1/L

Storage Coefficient Vol Out or In 1 unit area of aquifer surface 1 unit clay 1 unit vol Ss x b b = aquifer thickness aquifer b S = Ss x b Volume of water released or taken into storage from a vertical column of aquifer of height b, and unit basal area when subjected to a unit change in fluid pressure S is dimensionless

Transmissivity (T) surface clay I=1 1 unit vol I=1 K K T b aquifer K = volumetric flow per unit time per unit area of aquifer under a hydraulic gradient of one at 25 °C T = volumetric flow per unit time per one unit width of the aquifer extended over the entire thickness of the aquifer at 25 °C K x b = T Units are: gpd/ft or m 3/sec/m or m 2/sec

Pumping a Confined Aquifer Q drop clay aquifer Aquifer is still saturated - how can this be?

Two Ways Water is Removed from Storage in a Confined Aquifer 1. Pumping decreases fluid pressure, so …. . . rw P , water expands as it is released Vw Water Compressibility Component 2. Pumping decreases fluid pressure, so …… P se Vt n storage Aquifer Compressibility Summary - In a confined aquifer, water is released from storage by: 1. Expansion of water 2. Compression of the Aquifer , water expelled by compression of aquifer

S is unitless Typical Values of S are 10 -3 to 10 -6 Removal of Water From Storage in an Unconfined Aquifer Surface P=0 drop When you pump water out from an unconfined aquifer - you literally dewater the pore spaces Water drains by gravity - in accordance w/ Sy

Typical Values for Sy = 10 -1 to 10 -3 Note: Storage actually = Sy + (Ss x b) Usually neglect any aquifer compression or water expansion b/c Sy is so much larger so, S = Sy for an Unconfined Aquifer Key Points About Storage 1. Water released from storage in a confined aquifer by a) expansion of water and b) consolidation of aquifer material and is governed by S 2. Water is released from storage in an unconfined aquifer by dewatering the aquifer pores and is governed dominantly by Sy

Specific Capacity (SC) Q drop clay aquifer • Pump well until steady drawdown in well is achieved • Pumping Rate, Q / drawdown = Specific Capactiy • Units are L 3/T/L, eg. , gal/day/ft,

General Relationship Between Specific Capacity and Transmissivity can be estimated by two empirical relationships and making some assumptions For a confined aquifer T = SC x 2000 Where, well radius = 0. 5 feet pumping period = 1 day Initial T estimate = 30, 000 gpd. ft Storage estimate = 10 -3 For an unconfined aquifer T = SC x 1500 Where, same as above except storage is 7. 5 x 10 -2 Note: the effect of assuming a T value to estimate a T Value using this formula is not really a problem because It is derived from the Jacob modified non-equilibrium Equation and appears in a log term. So large variations In the assumed T has very little affect on the result.

Bedrock Aquifers Hydraulic Conductivity and Transmissivity of bedrock wells can also be determined through pumping tests • Average K values can be determined for entire borehole • T is determined by multiplying the average K value by the length of saturated uncased borehole length • You can also set up packers and isolate individual water-bearing fractures to determine the K for an individual fracture

Example Problem: Pump Well at 10 m 3/min for 1 day Water Level drops 7 m over 1 ha What is the specific yield?

Example Problem: Pump Well at 10 m 3/min for 1 day Water Level drops 7 m over 1 ha What is the specific yield? 1. 10 m 3/min x 60 min/hr x 24 hr/day x 1 day = 14400 m 3 2. 14400 m 3/10000 m 2 = 1. 44 m 3/m 2 = 1. 44 m = Volume of water extracted 3. Change in water level was 7 m or 7 m 3/m 2 which is the total over which the change occurred 4. Therefore, 1. 44/7 = 21 %

Tectonic Alluvial Valley Alternating layers of Sand, Silt, Clay

General Sequence Recent Deposits Lacustrine Deposits Sand Gravel Till veneer (lodgement or ablation or both polished bedrock

surface soil-water (root) zone Unsaturated Zone (Aeration or Vadose Zone) P<0 Capillary Zone Water Table Phreatic Surface P=0 Saturated Zone intermediate zone P>0 Groundwater Capillary Zone - combination of molecular attraction and surface tension between water and air capillarity Capillary zone can be saturated or nearly saturated but fluid pressure is negative

Typical Water Profile in Soil Saturation 0 100% root zone Depth (m) intermediate zone Recharge Happens Capillary Zone P=0 Tension Saturated Zone AWC PWP Field Capacity (Specific Retention) Soil Moisture Water Table

Importance of K and ki Distinction 1. Different fluids will travel at different rates Water and Non-Aqueous phase liquids will move at different rates due to differences in density and viscosity 2. Brines and highly saline solutions will move at different rates due to higher density of saline waters over fresh water. 3. Low temperature fluids will move at different rate than high temperature fluids Recall, viscosity and density are temperature dependent

Effective Stress & Storage Block of cement s s = Total Stress (psf) Spring = soil matrix Spring z A Now let’s place the spring in a cell

imaginary piezometer s 1. fill to base of block closed h cell 2. water represents fluid in pore spaces 3. no load carried by fluid A Water rises in piezometer under its own weight Hydrostatic Pressure P@A = rgh

Place additional load on spring Ds s Excess fluid pressure Start a Test z h A 1. Load applied matrix wants to consolidate and realign 2. Sealed tube, fluid has no where to go so additional load is borne by the fluid spring does not compress 3. Additional load on fluid manifested in an increase in fluid pressure > hydrostatic

Drain Ds s z h h z’ 1. As water drains, excess fluid pressure dissipates 2. Load slowly transferred from fluid to matrix 3. Matrix responds by compressing - system consolidates and porosity decreases

Ds Fluid pressure returns to hydrostatic s h z’’ Aquifer is consolidated Total Stress, st (s + D s ) on system will resolve into 2 parts: P = Fluid Pressure load borne by the fluid se = Effective Stress load borne by the solids We write, st = se + P

During the Test Ds s Excess Fluid Pressure h z’ Total Stress is balanced by load borne by the solids (se) and the load borne by the fluid (P) - At start of test, load borne by fluid - At completion of test load borne by solids - In between, load was shared by solids and fluid

Behavior in Confined Aquifers Train surface clay aquifer Fluid Pressure rise + static 0 fall Time

Train surface clay aquifer Train Stops Fluid Pressure rise + Train leaves static 0 fall Time

Real Aquifers In real aquifers - st (total stress) is constant Total stress never really changes so, if you increase P (fluid pressure) then you must reduce se (effective stress) and vice versa P + se = constant so, DP = - D se So P and se are the only parameters changing Two Processes 1. Aquifer Compression place load on aquifer, matrix consolidates, reduces porosity, expells water se , Vt , n , Storage

Aquifer Compressibility is: a = - (DVt / Vto) / Dse 2. Water Compressibility increase pressure on water, volume will decrease, water will contract, density increases, more water can be stored P r Vw storage Water Compressibility is: b = - (DVw / Vwo) / DP or since Mass is conserved, M = r w Vw then b = (Drw / rwo) / DP

Train Stops Fluid Pressure rise + Train leaves static 0 fall Time 1. Train approaches - total stress goes up - initially load carried by fluid - increase P 2. Train stops - fluid pressure declines by draining rapid transfer from fluid to solids support aquifer compresses by reducing porosity 3. Train leaves - effective stress on solids released aquifer rebounds elastically and increases porosity - increase in pore volume lowers fluid pressure 4. Water flows back to low P zone - static

Geotechnical Application surface 10 ft 5 ft A clay gb = 100 pcf sand gs = 125 pcf Total Stress (Pressure) @ A = (100 pcf x 10 ft) + (125 pcf x 5 ft) = 1625 psf

Distribution of Water in Earth Materials – Saturated vs. Unsaturated surface water table 1. Take spot at 10 ft below water table Total P = Force/unit area from water + force/unit area atmosphere By convention, pressure at earth’s surface set is zero P = gw h p = 62. 4 pcf x 10 ft Formal definition of the saturated zone P>0 Void space 100% saturated Vw/Vv = 1

surface water table 2. Take spot at 10 ft above water table Install tensiometer - surface tension and molecular attraction creates vacuum Soil Exerts tension which is negative Formal definition of the unsaturated zone P<0 Vw/Vv < 1 Voids do not have to be 100% saturated

surface water table 3. Take spot on the water table There is no column of water inside the piezometer exerting a force at water table Soil is saturated at the water table Formal definition of the water table P=0 Uniquely defines the water table

Storage Coefficient (S) Vol Out or In 1 unit area of aquifer surface 1 unit clay 1 unit vol b = aquifer thickness b aquifer S = volume of water a confined aquifer releases or takes into storage per unit surface area of aquifer per unit change in fluid pressure normal to that surface extended over the entire thickness of of the aquifer