CEE 370 Environmental Engineering Principles Lecture #22 Water - - PowerPoint PPT Presentation

David Reckhow CEE 370 L#22 1

CEE 370 Environmental Engineering Principles

Lecture #22 Water Resources & Hydrology II: Wells, Withdrawals and Contaminant Transport

Reading: Mihelcic & Zimmerman, Chapter 7

Updated: 5 November 2019

Print version

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Darcy’s Law

 Groundwater flow, or flow through

porous media

 Used to determine the rate at which water

• r other fluids flow in the sub-surface

region

 Also applicable to flow through engineered

system having pores

 Air Filters  Sand beds  Packed towers

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Groundwater flow

 Balance of forces, but frame of reference

is reversed

 Water flowing though a “field” of particles

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 Head

 Height to which water rises within a well

 At water table for an “unconfined” aquifer  Above water table for “confined” aquifers

 Hydraulic Gradient

 The difference in head between two points in a

aquifer separated in horizontal space

dx dh Gradient Hydraulic 

Terminology

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Terminology

 Porosity

 The fraction of total volume of

soil or rock that is empty pore space

 Typical values

 5-30% for sandstone rock  25-50% for sand deposits  5-50% for Karst limestone formations  40-70% for clay deposits

volume total pores

• f

volumes  

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Darcy’s Law

 Obtained theoretically by setting drag forces equal to

resistive forces

 Determined experimentally by Henri Darcy (1803-

1858)

                   L h K A L h K dx dh KA Q

L

Flow per unit cross- sectional area is directly proportional to the hydraulic gradient

L, or

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Hydraulic Conductivity, K

 Proportionality constant between hydraulic

gradient and flow/area ratio

 A property of the medium through which

flow is occurring (and of the fluid)

 Very High for gravel: 0.2 to 0.5 cm/s  High for sand: 3x10-3 to 5x10-2 cm/s  Low for clays: ~2x10-7 cm/s  Almost zero for synthetic barriers: <10-11 for

high density polyethylene membranes

 Measured by pumping tests

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Hydraulic Conductivity - Table

 Compare with M&Z Table 7.23

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Darcy Velocity

 re-arrangement of Darcy’s Law gives the Darcy Velocity, ʋ  Not the true (or linear or seepage) velocity of groundwater flow

because flow can only occur in pores

 combining

         dx dh K A Q vd

A Q V QL L L v

Q V a true

   



1     

d a true

v v   1   v va  1 

• r

          L h K A Q v

• r

M&Z

M&Z Equ #7.20 M&Z Equ #7.21

Velocities Illustrated

 Pipe with soil core

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 v v

Distance Water Velocity

v

Q Q Soil

Empty Empty

Darcy Velocity Darcy Velocity “True” Velocity

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Alternative illustration

Example C



An aquifer material of coarse sand has piezometric surfaces of 10 cm and 8 cm above a datum and these are spaced 10 cm apart. If the cross sectional area is 10 cm2, what is the linear velocity of the water?



Hydraulic gradient:



From the prior table, K for coarse sand is 5.2 x 10-4, so the Darcy velocity is:



Assuming that the porosity is 30% or 0.3 (prior Table):

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cm cm cm cm cm L h 2 . 10 8 10    

 

s m x cm cm s m x L h K v

4 4

10 04 . 1 2 . 10 2 . 5

 

    s m x s m x v vwater

4 4 '

10 47 . 3 3 . 10 04 . 1

 

   

See M&Z, example 7.9, part a

Definitions

 Specific Yield – the fraction of water in an

aquifer that will drain by gravity

 Less than porosity due to capillary forces  See Table 7-5 in D&M for typical values

 Transmissivity (T) – flow expected from a 1 m

wide cross section of aquifer (full depth) when the hydraulic gradient is 1 m/m.

 T=K*D

 Where D is the aquifer depth and K is hydraulic conductivity

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Drawdown I

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 Unconfined aquifer

 D&M: Figure 7-31a

 Showing cone of depression

Drawdown II

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 Confined aquifer

 D&M: Figure 7-31b

Cones of Depression

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 Conductivity

 Low K

 Deep, shallow

cone

 overlapping

Flow Model

 Well in confined aquifer  In an unconfined aquifer

 D is replaced by average height of water table

(h2+h1)/2, so:

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   

1 2 1 2

/ ln 2 r r h h KD Q   

 

 

1 2 2 1 2 2

/ ln r r h h K Q   

Where: hx is the height of the piezometric surface at distance “rx” from the well See examples: 7-10 and 7-11 in D&M

Contaminant Flow

 Separate Phase flow – low solubility

compounds

 Low density:

 LNAPL – light non-aqueous phase liquid

 High density: HNAPL

 Dissolved contaminant

 Flows with water, but subject to

retardation

 Caused by adsorption to aquifer materials

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See D&M section 9-7, pg.389-393

Adsorption in Groundwater

 Based on relative affinity of contaminant for aquifer to

water

 Defined by partition coefficient, Kp:  And more fundamentally the Kd can be related to the soil organic

fraction (foc) and an organic partition coefficient (KOC):

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) / ( ) / ( water L moles C soil kg moles C K

dissolved w adsorbed s p

  

• c
• c

p

f K K 

See also pg 392 in D&M 2nd ed. Similar to Equ 3.33, pg 95 in M&Z Equ 2-89, pg 76 in D&M 2nd ed. Similar to Equ 3.32, pg 95 in M&Z

Relative Velocities

 The retardation coefficient, R, is defined as

the ratio of water velocity to contaminant velocity

 And since only the dissolved fraction of the

contaminant actually moves

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' ' cont water f

R   

         

adsorbed dissolved dissolved water cont

moles moles moles

' '

 

Equ 9-42, pg 391 in D&M 2nd ed.

Relating R to Kd

 So  And therefore  And we can parse the last term:

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         

adsorbed dissolved dissolved water cont

moles moles moles

' '

 

dissolved adsorbed dissolved adsorbed dissolved cont water f

moles moles moles moles moles R      1

' '

 

               ) / ( ) / ( ) / ( ) / ( soil kg aquifer L X water L aquifer L Y water L moles C soil kg moles C moles moles

dissolved w adsorbed s dissolved adsorbed

cont

 Note that the fundamental partition

coefficient is:

 So:  And then

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) / ( ) / ( water L moles C soil kg moles C K

dissolved w adsorbed s p

   X Y K R

p f

 1

             ) / ( ) / ( soil kg aquifer L X water L aquifer L Y K moles moles

p dissolved adsorbed

cont

 where:

 Where:

 ρs is density of soil particles without pores

 usually ~2-3 g/cm3

 ρb is the bulk soil density with pores

 So, then

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 

 1 

  water L aquifer L

Y  

b s soil kg aquifer L

X    1 1   

 

 

                         

b p s p f

K K R 1 1 1

Compare to Equ 9-43, pg 391 in D&M 2nd ed.

M&Z Equ #7.23

See M&Z, example 7.9, part b

Estimation of partition coefficients

 Relationship to organic fraction  and properties of organic fraction  combining, we get:

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• c
• c

p

K f K 

• w
• c

K x K

7

10 17 . 6





Octanol:water partition coefficient

• w
• c

p

K f x K

7

10 17 . 6





Karickhoff et al., 1979; Wat. Res. 13:241

                      C g m

• r

m tox mg C g tox mg

3 3

. .                 O H m tox mg Oct m tox mg

2 3 3

. . .

m K f

p d

  1 1

Octanol:water partitioning

 2 liquid phases in a separatory

funnel that don’t mix

 octanol  water

 Add contaminant to flask  Shake and allow contaminant to

reach equilibrium between the two

 Measure concentration in each (Kow

is the ratio)

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cont

 Retardation in Groundwater & solute

movement

p b f

K R    1 =Soil bulk mass density = void fraction

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