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Driving equationInitial condition

Homogeneous Aquifer reservoir with

LaTeX Math Inline
body\chi(r)= \rm const

Initial Aquifer pressure is considered to be the same as Net Pay Area
LaTeX Math Block
anchorRC
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\frac{\partial p_a}{\partial t} = \chi \cdot \left[ \frac{\partial^2 p_a}{\partial r^2} + \frac{1}{r}\cdot \frac{\partial p_a}{\partial r} \right]
LaTeX Math Block
anchor1
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p_a(t = 0, r)= p(0)



Inner Aquifer boundaryOuter Aquifer boundary is one of the two below:
Pressure variation at the contact with Net Pay Are"No-flow" outer Aquifer boundary Full pressure support outer Aquifer boundary 
LaTeX Math Block
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p_a(t, r=r_e) = p(t)
LaTeX Math Block
anchorp1_PSS
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\frac{\partial p_a}{\partial r} 
\bigg|_{(t, r=r_a)} = 0
LaTeX Math Block
anchorgradp
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 p_a(t, r = \infty) = 0

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