General governing equation for transient heterogeneous and anisotropic

General governing equation for transient, heterogeneous, and anisotropic conditions Specific Storage Ss = V / ( x y z h)

OUT – IN = x y z = change in storage = - V/ t Ss = V / ( x y z h) V = Ss h ( x y z) t t

OUT – IN = = - V t

Law of Mass Balance + Darcy’s Law = Governing Equation for Groundwater Flow -------------------------------div q = - Ss ( h t) +R* (Law of Mass Balance) q = - K grad h (Darcy’s Law) div (K grad h) = Ss ( h t) –R*

2 D confined: 2 D unconfined: Storage coefficient (S) is either storativity or specific yield. S = Ss b & T = K b

1 D, transient, homogeneous, isotropic, confined, no sink/source term • Explicit solution (with stability criterion) • Implicit solution

Reservoir Problem t=0 Confined Aquifer 1 D, transient t>0

t=0 t>0 datum 0 L = 100 m BC: h (0, t) = 16 m; t > 0 h (L, t) = 11 m; t > 0 IC: h (x, 0) = 16 m; 0 < x < L (represents static steady state) Modeling “rule”: Initial conditions should represent a steady state configuration of heads. x

h 1 h 2 datum 0 L = 100 m At t = tss the system reaches a new steady state: h(x) = ((h 2 –h 1)/ L) x + h 1 x (Eqn. 4. 12 W&A)

Explicit Solution

Water Balance IN OUT t>0 Storage IN + change in storage = OUT + Flow in Storage Flow out Convention: Water coming out of storage goes into the aquifer (+ column). Water going into storage comes out of the aquifer (- column).