Upscaling hydraulic conductivity for GW flow models - Victor
18 important questions on Upscaling hydraulic conductivity for GW flow models - Victor
General spatial scales that describe flow and transport at a certain scale (4). Pore, core, local and regional scales occur.
- Pore scale (10^-6 - 10^-2 m): Navier-Stokes equations for GW flow
- Core scale (10^-1 - 10^0 m: Darcy, not yet K
- Local scale (10^2 - 10^3 m): 3D, pollution problems, pumping test could be done, heterogeneity is visible
- Regional scale (horizontal dim 10^3-10^5 m: might have geology & model is based upon this; aquifers(horizontal GW flow) and aquitards(vertical GW flow) occur
Pore scale: Navier-Stokes
What is the REV - Representative Elementary Volume?
At the representative elementary volume, a porous medium can be considered to have uniform properties so that simplified flux equations such as Darcy’s Law can be applied that contain a single value for the
hydraulic properties of the medium (ie. K – hydraulic conductivity).
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Which equations are used at pore scale and which parameters are used for these equations?
u = fluid velocity
h = hydraulic head
v = viscosity
Study of solute transport and effect of pore scale processes and/or geometry
Give the formula for Hydraulic Conductivity (K)?
k: intrinsic permeability/pore space (m^2)
rho: density of fluid (kg/m3)
mu: viscosity of fluid (kg/(ms))
What can be done at core scale to measure K?
Using a permeameter, using Darcy's Law, to evaluate a core scale value of K of a sedi sequence.
Give the formula for Darcy's Law
What K measurement value can be used on dry outcrops?
What metric do pumping tests yield?
How can upscaling by model calibration be done?
- Adjust regional scale hydraulic properties so that observed hydraulic heads match those simulated
- Also include observed residence times or GW fluxes (recharge)
How can upscaling by averaging K be done?
- Geostatistical/math techniques based upon characteristics (eg heterogeneity and anisotropy) of K field to come to Transmissivity based models
When upscaling from fine to coarse scale cells, there are two basic techniques
that can be used:
1) geostatistical techniques based upon statistical properties
observed on the small scale (e.g., mean, standard deviation etc. of K field).
2) flow based upscaling in which the flow through the larger cell is matched to the simulated flow through the fine scale cells by adjusting the effective hydraulic conductivity (calibration).
1 and 2 can be combined.
How is K often distributed?
Very heterogenic surface uses which mean to approach K?
Which mean is calculated in stratified deposits serial flow (flow perpendicular to layers or vertical)
Occurs in aquifers
What is the rule of thumb for vertical flow in aquifers?
a values: 1/1, 1/3, 1/10
How to calculate resistance(units of time)?
How to approach flow in aquifers and aquitards?
Predominantly horizontal flow
Arithmetic mean of K: *by D for Transmissivity
Aquitard:
Predominantly vertical flow
Harmonic mean of K: D/K to obtain resistance
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