Lecture 9.5 & 10 Storage in confined aquifers Specific storage & storage coefficient

Storage in confined aquifers & 1-D flow equation

Moisture distribution & water retention curve Water pressure is GT atmospheric Pores remain full Where would the water come from ?

Examine storage changes in a finite element in a confined aquifer Consider the shown element ( size Δx, Δy, Δz ) This element contains a mass of water M = ρ φ Δx Δy Δz Change in water mass dM = d(ρ φ Δx Δy Δz ) = Δx Δy d(ρ φ Δz ) Or dM = Δx Δy [Δz φ d(ρ) + ρ d(φ Δz )]

Change in mass due to water compressibility dM = Δx Δy [Δz φ d(ρ) + ρ d(φ Δz )] Define water compressibility Relate β to dρ ρ= m/Vfor constant mass dρ = -m/V 2 dV Therefore dρ/ρ = -dV/V Use in equation for β to get dρ = ρ β dP

Change in mass due to aquifer compressibility dM = Δx Δy [Δz φ d(ρ) + ρ d(φ Δz ) ] substituting dM = Δx Δy [Δz φ ρ β dP + ρ α p φΔz dP ] Define bulk volume compressibility Relate α to d(φΔz) Vp (pores) = φΔz ΔxΔy d (φΔz) = α p φΔz dP

Storage/ confined aquifer dM = Δx Δy Δz ρ φ [ β + α p ] dP dM / ρ = dV = (Δx Δy Δz) φ [ β + αp ] dP dV/V = φ [ β + αp ] dP = φ [ β + αp ] dh * γ Specific storage or storativity [1/L]

Specific storage & storage coefficient S volume of water released per unit aquifer volume per unit decline in head Can define S c if the aquifer have a constant thickness B = S B S c volume of water released per unit aquifer area per unit decline in head (analogus to S y )

Flow in confined aquifers

Flow equation Darcy law Mass balance (1-d flow) ROMA= net mass flux in notice units Volume/time/volume 3d flow

The governing equation is obtained by using DL in CE

If the confined aquifer has a constant thickness then we can integrate over the vertical neglecting vertical flow (h not h(z)): Define new parameters (i.e. storage coef & transmissivity) The resulting equation w/out source term is:

For homogeneous isotropic aquifer with constant thickness the GPDE is For axisymmetric problems:

Air flow in porous media

Air flow through porous media The applicable form of Darcy law is : Neglecting gravity and considering 1-D flow in x-d : Therefore mass flow rate is:

Example (Bear, 1972 page 192)