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Understanding Tensor Components in Anisotropic Conditions with Jacob's Island Recharge Problem

Explore the principles of tensors, anisotropic conditions, and Jacob's Island Recharge Problem in hydrogeology. Study the Poisson equation, homogeneous aquifers, and steady-state conditions without source/sink terms.

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Understanding Tensor Components in Anisotropic Conditions with Jacob's Island Recharge Problem

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  1. K is a tensor with 9 components Kxx Kxy Kxz KyxKyy Kyz Kzx KzyKzz K = Kxx ,Kyy, Kzz are the principal components of K

  2. q = - Kgrad h Kxx Kxy Kxz Kyx Kyy Kyz Kzx Kzy Kzz qx qy qz = -

  3. 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]

  4. Assume that there is no flow across the bedding planes z local global z’ grad h q x’ Kz’=0  x

  5. General governing equation for steady-state, heterogeneous, anisotropic conditions, without a source/sink term with a source/sink term

  6. 2D horizontal flow; homogeneous and isotropic aquifer with constant aquifer thickness, b, so that T=Kb. Poisson Eqn.

  7. 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

  8. 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.

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