Consider a system of net hydrocarbon pay and finite or infinite volume Aquifer as a radial composite reservoir with inner composite area being a Net Pay Area and outer composite area an Aquifer
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The Aquifer's outer boundary may be "no-flow" for finite-volume Aquifer or full pressure support, thus implementing the case of the constant pressure for infinite-volume Aquifer.
The transient pressure diffusion in the outer (Aquifer) composite area is going to honour the following equation:
| Driving equation | Initial condition |
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Homogeneous Aquifer reservoir with | Initial Aquifer pressure is considered to be the same as Net Pay Area |
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| LaTeX Math Block |
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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 |
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| p_a(t = 0, r)= p(0) |
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| Inner Aquifer boundary | Outer Aquifer boundary is one of the two below: |
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| Pressure variation at the contact with Net Pay Are | "No-flow" outer Aquifer boundary Full pressure support outer Aquifer boundary | "Constant pressure" |
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| p_a(t, r=r_e) = p(t) |
| | LaTeX Math Block |
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| anchor | p1_PSS |
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| alignment | left |
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| \frac{\partial p_a}{\partial r}
\bigg|_{(t, r=r_a)} = 0 |
| | LaTeX Math Block |
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| anchor | pconst |
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| alignment | left |
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| p_a(t, r = \infty) = 0 |
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| LaTeX Math Block |
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| \frac{\partial p_1}{\partial t_D} = \frac{\partial^2 p_1}{\partial r_D^2} + \frac{1}{r_D}\cdot \frac{\partial p_1}{\partial r_D} |
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| p_1(t_D = 0, r_D)= 0 |
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| p_1(t_D, r_D=1) = 1 |
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| \frac{\partial p_1(t_D, r_D)}{\partial r_D}
\Bigg|_{r_D=r_{aD}} = 0 |
or | LaTeX Math Block |
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| \quad {\rm or} \quad p_1(t_D, r_D = \infty) = 0 |
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