100 likes | 207 Views
K is a tensor with 9 components. K xx K xy K xz K yx K yy K yz K zx K zy K zz. K =. K xx , K yy, K zz are the principal components of K. q = - K grad h. K xx K xy K xz K yx K yy K yz K zx K zy K zz. q x q y q z. = -. global. local. z. z’. x’.
E N D
K is a tensor with 9 components Kxx Kxy Kxz KyxKyy Kyz Kzx KzyKzz K = Kxx ,Kyy, Kzz are the principal components of K
q = - Kgrad h Kxx Kxy Kxz Kyx Kyy Kyz Kzx Kzy Kzz qx qy qz = -
global local z z’ x’ x Kxx Kxy Kxz Kyx Kyy Kyz Kzx Kzy Kzz K’x 0 0 0 K’y 0 0 0 K’z [K] = [R]-1 [K’] [R]
Assume that there is no flow across the bedding planes z local global z’ grad h q x’ Kz’=0 x
General governing equation for steady-state, heterogeneous, anisotropic conditions, without a source/sink term with a source/sink term
2D horizontal flow; homogeneous and isotropic aquifer with constant aquifer thickness, b, so that T=Kb. Poisson Eqn.
C.E. Jacob’s Island Recharge Problem L y 2L ocean ocean well R= 0.00305 ft/d T= 10,000 ft2/day L = 12,000 ft x ocean
C.E. Jacob’s Island Recharge Problem R h datum groundwater divide ocean ocean b x = - L x = 0 x = L We can treat this system as a “confined” aquifer if we assume that T= Kb.