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The general form of non-linear single-phase pressure diffusion model@model is given by:
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\beta({\bf r},p) \, \frac{\partial p}{\partial t} = \nabla \Big( M({\bf r},p, \nabla p) \cdot \nabla p \Bigphi \cdot c_t \cdot \partial_t p - \nabla \left( M \cdot ( \nabla p - \rho \cdot \mathbf{g} ) \right) - c \cdot M \cdot (\nabla p)^2 = \sum_k q({\bf r}) \cdot \delta({\bf r}-{\bf r}_k) |
with non-linear dependence of fluid mobility
on
reservoir pressure and spatial
pressure gradient
:
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Below is the list of popular physical phenomena and their mathematical models which can be covered by
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model.
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Pressure diffusion equation is going to be:
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с_t \phi_e \frac{\partial p}{\partial t} = \nabla ( \frac{k(\nabla p)}{\mu} \nabla p) |
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