Post on 11-Mar-2018
Effects of Turbulence on Hydraulic Heads and Parameter Sensitivities in Preferential
Ground-Water Flow Layers
Barclay Shoemaker and Eve Kuniansky U.S. Geological Survey
Preferential flow layer
Diffuse flow layer
Project Funded by USGS Ground-Water Resources ProgramKevin Dennehy, Program Manager
Contributors / Collaborators:Kevin Cunningham (USGS)
Joann Dixon (USGS)Keith J. Halford (USGS)
Preferential flow layer
Diffuse flow layer
Streamlines trace out the path of a ‘mass-less’ particle moving within the ground-water flow system.
WHAT IS TURBULENT GROUND-WATER FLOW ?
Fluid Inertial Forces > Viscous Forces
Reynolds numbers indicate whether flow is laminar or turbulent
forcesviscousforcesinertialqdRe ==
μρ
Flow is turbulent when the critical Reynolds number (NRe) is exceeded
turbulentisflowNRe ,Re>
WHAT IS TURBULENT GROUND-WATER FLOW ?
Darcy’s Law is not valid for turbulent flow
Notice turbulencedecreases Specific Discharge, energy is lost to eddies
Δh/ΔxGradient
Specific Discharge
α
Laminar Flow
Turbulent Flow
Dashed line, flow laminar for entire range of graph (Darcian flow)
critical Reynolds number
WHAT IS TURBULENT GROUND-WATER FLOW ?
WHY STUDY TURBULENT FLOW ?•It’s fundamental hydrology
• Could explain most groundwater movement in karst
• Implications for:• Fate of injected waters
• ASR• Wastewater
• Saltwater intrusion• Nutrient loading (from submarine
groundwater discharge)• Contaminate transport
Streamlines trace out the path of a ‘mass-less’ particle moving within the ground-water flow system.
CFPM2 Governing Flow Equation
thSW
zhKlam
zyhKlam
yxhKlam
x szzyyxx ∂∂=+⎟
⎠⎞
⎜⎝⎛
∂∂
∂∂+⎟⎟
⎠
⎞⎜⎜⎝
⎛∂∂
∂∂+⎟
⎠⎞
⎜⎝⎛
∂∂
∂∂
Traditional MODFLOW with Darcy’s Law and laminar hydraulic conductivity
CFP Mode 2 computes horizontal turbulent flow using turbulent hydraulic conductivity.
thSW
zhKlam
zyhKturb
yxhKturb
x szzyyxx ∂∂=+⎟
⎠⎞
⎜⎝⎛
∂∂
∂∂+⎟⎟
⎠
⎞⎜⎜⎝
⎛∂∂
∂∂+⎟
⎠⎞
⎜⎝⎛
∂∂
∂∂
lamadjturb KFK =
Turbulent horizontal hydraulic conductivity (Kturb) is a non-linear function of the Reynolds Number (Re)
after critical Reynolds number (NRe) is exceeded.
11 −− ΔΔ=
kiterkiterturb
critlamkiteradj hK
hKF
porelamcrit dK
lvNh Δ=Δ Re
CFPM2 Turbulent K
Derived by Kuniansky and Halford, 2008
SPECIFIC DISCHARGE, IN METERS PER DAY
0 50 100 150 200 250 300
HYD
RA
ULI
C G
RA
DIE
NT,
UN
ITLE
SS
0.000
0.001
0.002
0.003
0.004
0.005
0.006
Darcy WeisbachDarcy's LawCFPM2 Approach
Critical head difference is exceeded
SPECIFIC DISCHARGE, IN METERS PER DAY
0 50 100 150 200 250 300
HYD
RA
ULI
C G
RA
DIE
NT,
UN
ITLE
SS
0.000
0.001
0.002
0.003
0.004
0.005
0.006
Darcy WeisbachDarcy's LawCFPM2 Approach
Critical head difference is exceeded
CFPM2 Benchmark Testing
Permeameter Data Verify New Turbulence Process for MODFLOW
By Eve L. Kuniansky and others.
(a) Cube 6 Vertical Axis
0
10
20
30
40
CRITICAL VELOCITYMEASUREDSIMULATED
Klam = 48 m/dNRe = 1.44RMS = 0.70 m/d
(b) Cube 6 Horizontal Axis 1
0
10
20
30
40
Klam = 61 m/dNRe = 1.44RMS = 0.35 m/d
(c) Cube 6 Horizontal Axis 2
0
10
20
30
40
0.00 0.25 0.50 0.75 1.00
?H/?L, DIMENSIONLESS
Klam = 36 m/dNRe = 1.44RMS = 0.57 m/d
SPEC
IFIC
VEL
OC
ITY,
IN M
ETER
S PE
R D
AY
CFPM2 Testing
ET Station
Broward CountyMiami-Dade County
Bisc
ayne
Bay
Water Conservation Area No. 3A
Water Conservation Area No. 3B
Everglades National
Park
L-67A
L-67C
L-29
L-31N
C-4
C-6
C-2
0 2 4 6 Kilometers
0 2 4 6 Miles
80°30' 80°20'
26°00'
25°50'
25°40'
CFPM2 APPLICATION TO BISCAYNE AQUIFER
Hydrogeologic conceptualization of Lake Belt area from:Cunningham and Dixon, written communication
Preferential flow layer
Diffuse flow layer
CFPM2 APPLICATION TO BISCAYNE AQUIFER
A
θ⎟⎟⎠
⎞⎜⎜⎝
⎛=
vgdKlam 32
2
To estimate Klam, one could use the resistance terms in the Darcy-Weisbach equation, limited by effective porosity. Limiting
by effective porosity accounts for the resistance offered by “dead end” voids.
CFPM2 APPLICATION TO BISCAYNE AQUIFER
Derived by Eve Kuniansky, 2008
Table 1. Initial estimates of laminar horizontal hydraulic conductivity for preferential flow layers
Layer Source Data NumberWells
MeanEffectivePorosity(%)
Number ofMeasurementOn cores orimages
MeanVugDiameter(cm)
Laminar HorizontalHydraulic Conductivity(meters per day)
2 DirectMeasurementon cores
23 11.8 240 0.9 200,000
5 DirectMeasurementon cores
6 18.3 65 0.8 300,000
8 MostlyMeasurementsfrom digitalborehole wallimages
22 14.8 438 3.5 5,000,000
Data from Kevin Cunningham and others, 2006
Broward CountyMiami-Dade County
Bisc
ayne
Bay
Water Conservation Area No. 3A
Water Conservation Area No. 3B
Everglades National
Park
L-67A
L-67C
L-29
L-31N
C-4
C-6
C-2
Explanation
Flow vector
1
2
3
4
Canal or stream
Turbulence Codes
Flow to right and front are laminar
Flow to right is turbulant
Flow to front is turbulant
Flow to right and front are turbulant
0 2 4 6 Kilometers
0 2 4 6 Miles
Preliminary Run—layer 8
Upper critical Reynolds Number equals 55
Model parameter
rch hk1 vk1 hk2 vk2 hk3 vk3 hk4 vk4 hk5 vk5 hk6 vk6 hk7 vk7 hk8 vk8 T v1 v2 v3
Com
posi
te-s
cale
d se
nsiti
vity
, uni
tless
0.00
0.01
0.02
0.03
0.04
Scenario 1Scenario 2Scenario 3Scenario 4Scenario 5
CFPM2 APPLICATION TO BISCAYNE AQUIFER
1. Extent of turbulent flow increases with increasing hydraulic conductivity, mean void diameter, groundwater temperature, and decreasing critical Reynolds numbers.
2. When turbulence was active (occurring in about 56% of preferential flow model cells), head differences from laminar elevations ranged from about 18 to +27 cm.
3. The composite-scaled sensitivities of horizontal hydraulic conductivities decreased by as much as 70% when turbulence was essentially removed.
4. This study highlights potential errors in model calculations based on the equivalent porous media assumption, which assumes laminar flow in uniformly distributed void spaces
Summary
Limitations
• Macro-scale simplification of impacts of turbulent flow
• Vast uncertainty in aquifer hydraulic properties and boundaries
• Theory is sound, but applications on systems with uncertainty may produce unreliable predictions
Thanks !For more information,bshoemak@usgs.gov
Picture taken by Eve Kuniansky of field trip to Fish River Cave near Yangshuo, China,
Shoemaker, W. B., K. J. Cunningham, E. L. Kuniansky, and J. Dixon (2008), Effects of turbulence on hydraulic heads and parameter sensitivities in preferential groundwater flow layers, Water Resour. Res., 44, W03501, doi:10.1029/2007WR006601.