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

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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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