# Physical Properties of Aquifers Groundwater Hydraulics Daene C.

Physical Properties of Aquifers Groundwater Hydraulics Daene C. McKinney 1 Outline Porous Medium Porosity Moisture Content Particle Size Distribution of water in subsurface Capillary Pressure Soil Moisture Characteristic Curves Specific Yield and Retention Piezometric head in aquifers Aquifer Types Aquifer Storage 2 Porous Medium

Groundwater All waters found beneath the ground surface Occupies pores (void space space not occupied by solid matter) Porous media Numerous pores of small size Pores contain fluids (e.g., water and air) Pores act as conduits for flow of fluids Type of rocks and their Number, size, and arrangement of pores Affect the storage and flow through a formation.

Pores shapes are irregular Differences in the minerals making up the rocks Geologic processes experienced by them. 3 Continuum Approach to Porous Media Pressure, density etc. apply to fluid elements that are large relative to molecular dimensions, but small relative to the size of the flow problem We adopt a Representative Elementary Volume (REV) approach REV must be large enough to contain enough pores to define the average value of the variable in the fluid phase and to ensure that the pore-to-pore fluctuations are smoothed out REV must be small enough that larger scale heterogeneities do not get averaged out (layering, etc.) 4 Porosity

Soil volume V (Saturated) Por e with wat er solid 5 Porosity Property of the voids of the porous medium % of total volume occupied by voids Cubic Packing Soil volume V (Saturated)

Por e with wat er solid Rhombo Packing 6 Porosity Porosity: total volume of soil that can be filled with water V f= i V Soil volume V (Saturated)

V - Vs f= V V = Total volume of element Vi = Volume of Pores Vs = Volume of solids Por e with wat er solid r - r r f = m d =1- d rm rm rm = particles density (grain density) Void Ratio: V

f e= i = rd = bulk density Vs 1- f 7 Typical Values of Porosity Material Porosity (%) Peat Soil 60-80 Soils 50-60 Clay 45-55

Silt 40-50 Med. to Coarse Sand 35-40 Uniform Sand 30-40 Fine to Med Sand 30-35 Gravel 30-40 Gravel and Sand 30-35

Sandstone 10-20 Shale 1-10 Limestone 1-10 8 Volumetric Water Content Soil volume V (Unsaturated) 9 Saturation Soil volume V (Unsaturated)

10 Particle Size of Some Soils 11 Particle Size Distribution Poorly sorted silty fine to medium sand Well sorted fine sand Particle size distribution curves Soil classification standards Soil texture

Relative % of grain sizes 12 Particle Size Distribution Sand 49% Clay 40% Soil Characteristics of Cyprus Soil Sample 13 Occurrence of Groundwater

Ground water occurs when water recharges the subsurface through cracks and pores in soil and rock Shallow water level is called the water table 14 Distribution of Water in Subsurface Moisture Profile Water moves down (up) during infiltration (evaporation) Capillary fringe

Water held by capillary forces, water content near field capacity except during infiltration Soil zone depend on % of pore space filled with water Unsaturated Zone

Description Different zones Soil Profile Saturated ar base Field capacity at top Saturated Zone Fully saturated pores Field capacity - Water remaining after gravity drainage Wilting point - Water remaining after gravity drainage & evapotranspiration 15

Saturation Soil volume V (Unsaturated) Saturation Water Content Water Saturation 16 Surface Tension Below interface Forces act equally in all directions At interface Some forces are missing Pulls molecules down and together

Like membrane exerting tension on the surface Curved interface Higher pressure on concave side Pressure increase is balanced by surface tension s = 0.073 N/m (@ 20oC) Interface water air

Net force inward No net force Capillary pressure Relates pressure on both sides of interface 17 Surface Tension sgl gas ssg b < 90o - liquid is wetting the solid b > 90o - liquid is non-wetting the solid b solid air

liquid ssl air solid solid b Hg b water Mercury nonwetting solid Water wetting solid 18 Capillary Pressure

Two immiscible fluids in contact exhibit a discontinuity in pressure across the interface separating them. This pressure difference is capillary pressure pc It depends on the curvature of the interface. pnw is the pressure in the nonwetting fluid (air, say) pw is the pressure in the wetting fluid (water, say) 19 Capillary Pressure Air pair z pair y p pc

Soli d pw Soli d Wat er r Rise of water in a capillary tube. Capillary forces must balance the weight of water Capillary pressure head 20 Capillary Pressure Air pair z B Negative

pressure y p Positive pressure Solid pair A pw Solid Water pc r (A) Below the water level

(B) Above the water level Difference in pressure across the interface is 21 Drainage Drainage occurs when the water pressure in the pores becomes less than the air pressure Interfacial tension prevents displacement of water in the left pore solid Pore water press. = -p r Pore air press. = 0 solid If pc increases, radius must decrease, or water occupies smaller pores. Water recedes into pores small enough to support the interface with a radius required 22

to balance the capillary force. Water drains from the large pores first. Energy in Flow Systems v2/(2g) Velocity head p/g Pressure head z Elevation head v2/(2g) EGL HGL p/g v2/(2g) z Hydraulic grade line (HGL) height of water in piezometer tube

datum Energy grade line (EGL) Height of water in pitot tube 23 Piezometric Head Confined aquifer p h= z g Unconfined aquifer p h= z g Pressure p =0 head = 0

p g h =z z 24 Piezometric Head in Unsaturated Flow Soil volume V (Unsaturated) Saturated Zone q = f y<0 pw > 0 Water Table y=0 pw = 0 Unsaturated Zone

q < f y>0 pw < 0 25 Subsurface Pressure Distribution z Capillary pressure head in zone above water table Ground surface Pressure is negative above water table y =y (q ) Hydrostatic pressure distribution exists below the water table (p = 0).

p =- g z Unsaturated zone y Water table Pressure is positive below water table Saturated zone p<0 z =0; p =0 d1 P =gd1 0 p =0

p 0 26 Soil Water Characteristic Curves y Vadose Zone Porosity y =y (q ) Capillary Zone yb Critacal Head (Bubbling Press.)

Capillary pressure head Function of: Pore size distribution Moisture content qo Irreducible Water content f Porosity y =y (q ) 27 Capillary Rise in Soils 28 Aquifer Types

Confined aquifer Under pressure Bounded by impervious layers Unconfined aquifer Phreatic or water table Bounded by a water table Aquifer

Store & transmit water Unconsolidated deposits sand and gravel, sandstones etc. Aquitard Transmit dont store water Shales and clay 29 Aquifer Storage Storativity (S) - ability of an aquifer to store water Change in volume of stored water due to change in piezometric head. Volume of water released (taken up) from aquifer per unit decline (rise) in piezometric head. Unit area

Unit decline in head Released water 30 Aquifer Storage Fluid Compressibility (b) Aquifer Compressibility (a) Confined Aquifer Water produced by 2 mechanisms 1. Aquifer compaction due to increasing effective stress 2. Water expansion due to decreasing pressure Unconfined aquifer Water produced by draining pores

V =arg S =r g(a fb ) S =Sy 31 Unconfined Aquifer Storage Storativity of an unconfined aquifer (Sy, specific yield) depends on pore space drainage. Some water will remain in the pores - specific retention, Sr Sy = f Sr Unit area Unit decline in head

Released water 32 Porosity, Specific Yield, & Specific Retention S r =f - S y 33 Confined Aquifer Storage Storativity of a confined aquifer (Ss) depends on both the compressibility of the water (b) and the compressibility of the porous medium itself (a). Unit area Unit decline in head

Released water 34 Example Storage in a confined sandstone aqufier f = 0.1, a = 4x10-7 ft2/lb, b = 2.8x10-8 ft2/lb, g = 62.4 lb/ft3 ga = 2.5x10-5 ft-1 and gbf = 1.4x10-7 ft-1 Solid Fluid 2 orders of magnitude more storage in solid b = 100 ft, A = 10 mi2 = 279,000,000 ft2 S = Ss*b = 2.51x10-3

If head in the aquifer is lowered 3 ft, what volume is released? V = SAh = 2.1x106 ft3 35 Summary Porous Medium Porosity Moisture Content Particle Size Distribution of water in subsurface Capillary Pressure Soil Moisture Characteristic Curves Specific Yield and Retention Piezometric head in aquifers Aquifer Types Aquifer Storage 36

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