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

Print version Updated: 5 November 2019 CEE 370 Environmental Engineering Principles Lecture #22 Water Resources & Hydrology II: Wells, Withdrawals and Contaminant Transport Reading: Mihelcic & Zimmerman, Chapter 7 David Reckhow CEE 370 L#22 1

Darcy’s Law  Groundwater flow, or flow through porous media  Used to determine the rate at which water or other fluids flow in the sub-surface region  Also applicable to flow through engineered system having pores  Air Filters  Sand beds  Packed towers 2 CEE 370 L#23 David Reckhow

Groundwater flow  Balance of forces, but frame of reference is reversed  Water flowing though a “field” of particles 3 CEE 370 L#23 David Reckhow

Terminology  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 dh  Hydraulic Gradient dx 4 CEE 370 L#23 David Reckhow

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 volumes of pores   total volume 5 CEE 370 L#23 David Reckhow

Darcy’s Law  Obtained theoretically by setting drag forces equal to resistive forces  Determined experimentally by Henri Darcy (1803- 1858) L, or      dh h h          L  Q KA K A K dx  L   L  Flow per unit cross- sectional area is directly proportional to the hydraulic gradient 6 CEE 370 L#23 David Reckhow

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 7 CEE 370 L#23 David Reckhow

Hydraulic Conductivity - Table  Compare with M&Z Table 7.23 8 CEE 370 L#23 David Reckhow

Darcy Velocity  re-arrangement of Darcy’s Law gives the Darcy Velocity, ʋ M&Z Equ #7.20      Q dh Q h           v d K v K or A  dx  A  L   Not the true (or linear or seepage) velocity of groundwater flow because flow can only occur in pores M&Z L L QL 1 Q       v true a     V V A  combining Q 1 1     v a v v v or true a d   M&Z Equ #7.21 9 CEE 370 L#23 David Reckhow

Velocities Illustrated  Pipe with soil core Soil Empty Empty Q Q Darcy “True” Velocity Darcy Velocity Velocity v  v v Water Velocity Distance 10 CEE 370 L#22 David Reckhow

Alternative illustration 11 CEE 370 L#23 David Reckhow

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 cm 2 , what is the linear velocity of the water?   Hydraulic gradient: h 10 cm 8 cm cm    0 . 2 cm L 10 cm From the prior table, K for coarse sand is 5.2 x 10 -4 , so the Darcy velocity is:     h m cm m      4 4 v K 5 . 2 x 10 0 . 2 1 . 04 x 10 s cm s L Assuming that the porosity is 30% or 0.3 (prior Table):  m  4 1 . 04 x 10 v s m      ' 4 v water 3 . 47 x 10 s 0 . 3 See M&Z, example 7.9, part a 12 CEE 370 L#22 David Reckhow

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 13 CEE 370 L#22 David Reckhow

Drawdown I  Unconfined aquifer  D&M: Figure 7-31a  Showing cone of depression 14 CEE 370 L#22 David Reckhow

Drawdown II  Confined aquifer  D&M: Figure 7-31b 15 CEE 370 L#22 David Reckhow

Cones of Depression  Conductivity  Low K  Deep, shallow cone  overlapping 16 CEE 370 L#22 David Reckhow

Flow Model  Well in confined aquifer Where: h x is the height of the   piezometric surface at distance    2 KD h h “r x ” from the well Q 2 1   ln r / r 2 1  In an unconfined aquifer  D is replaced by average height of water table (h 2 +h 1 )/2, so:      2 2 K h h See examples: 7-10 and Q 2 1   7-11 in D&M ln r / r 2 1 17 CEE 370 L#22 David Reckhow

Contaminant Flow  Separate Phase flow – low solubility compounds See D&M section 9-7, pg.389-393  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 18 CEE 370 L#22 David Reckhow

Adsorption in Groundwater  Based on relative affinity of contaminant for aquifer to water  Defined by partition coefficient, K p : Equ 2-89, pg 76 in D&M 2 nd ed.  C ( moles / kg soil ) Similar to Equ 3.32,  s adsorbed K pg 95 in M&Z p  C ( moles / L water ) w dissolved  And more fundamentally the Kd can be related to the soil organic fraction (f oc ) and an organic partition coefficient (K OC ): K  K f See also pg 392 in D&M 2 nd ed. p oc oc Similar to Equ 3.33, pg 95 in M&Z 19 CEE 370 L#22 David Reckhow

Relative Velocities  The retardation coefficient, R, is defined as the ratio of water velocity to contaminant velocity  '  Equ 9-42, pg 391 in R water D&M 2 nd ed. f  ' cont  And since only the dissolved fraction of the contaminant actually moves   moles      ' ' dissolved   cont water  moles moles   dissolved adsorbed 20 CEE 370 L#22 David Reckhow

Relating R to K d    So  moles '    dissolved cont    '  moles moles   water dissolved adsorbed  And therefore   ' moles moles moles     R water dissolved adsorbed 1 adsorbed f  ' moles moles cont dissolved dissolved  And we can parse the last term:      moles C ( moles / kg soil ) Y ( L aquifer / L water )    adsorbed s adsorbed      moles C ( moles / L water ) X ( L aquifer / kg soil )   dissolved w dissolved 21 CEE 370 L#22 David Reckhow

cont  Note that the fundamental partition coefficient is:  C ( moles / kg soil )  K s adsorbed p  C ( moles / L water ) w dissolved  So:     moles Y ( L aquifer / L water )    adsorbed K   p   moles X ( L aquifer / kg soil )   dissolved  And then Y  1  R K f p X 22 CEE 370 L#22 David Reckhow

cont  where:     1 1   1      Y L aquifer X L aquifer   kg soil    L water s b  Where:  ρ s is density of soil particles without pores  usually ~2-3 g/cm 3  ρ b is the bulk soil density with pores  So, then               R 1 K s 1 K b       f p p     1     M&Z Equ #7.23 Compare to Equ 9-43, pg 391 in D&M 2 nd ed. See M&Z, example 7.9, part b 23 CEE 370 L#22 David Reckhow

1  1 f d  K m p Estimation of partition coefficients  Relationship to organic fraction   mg tox .  K    f K    3 m g C     or   p oc oc  mg tox .  g C     3  m   and properties of organic fraction Octanol:water   7 K 6 . 17 x 10 K oc ow partition  combining, we get: coefficient      7 mg tox . K 6 . 17 x 10 f K    3 m Oct .   p oc ow  mg tox .     3  m H O   2 Karickhoff et al., 1979; Wat. Res. 13:241 24 CEE 577 #30 David Reckhow

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 (K ow is the ratio) 25 CEE 577 #30 David Reckhow

cont  Retardation in Groundwater & solute movement   1  R b K f p   =Soil bulk mass density  = void fraction 26 CEE 370 L#29 David Reckhow

27 CEE 370 L#23 David Reckhow

 To next lecture 28 CEE 370 L#22 David Reckhow