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The poroelastic models like - Biot theory- are built on the continuum approach. But I am not able to understand, how this heterogeneous media can be considered as a continuum.

However, If the porous material is anisotropic and tortuous, I think we cannot apply the continuum approach to model the flow inside the porous media. If this is true, then how to model the same?

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You should use continuum mechanics laws and approaches based on axiomatics of continuum mechanics:

  1. Euclidean space. The space in which body motion is considered is three-dimensional
  2. Absolute time $t$. The time does not depend on the choice of reference system.
  3. Hypothesis of continuity. The material body is a continuous medium
  4. The law of conservation of mass. Every material body $V$ has a scalar non-negative characteristic - mass $M$, which: a) does not change with any body movements if the body consists of the same material points, b) is an additive value: $M (V) = M (V_ {1}) + M (V_ {2})$, where $V = V_ {1} + V_ {2}$.
  5. The law of conservation of momentum (change in the amount of motion).
  6. The law of conservation of angular momentum (changes in angular momentum).
  7. The law of conservation of energy (the first law of thermodynamics).
  8. The existence of absolute temperature (the third law of thermodynamics).
  9. The law of entropy balance (second law of thermodynamics).
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  • $\begingroup$ Any reason for "Euclidean space" to appear twice? $\endgroup$
    – nicoguaro
    Commented Jun 13, 2019 at 15:34

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