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Natural Depletion
The Expected Estimated Ultimate Recovery
Natural Depletion
during the natural depletion can be assessed with the following formula:
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EUR = \frac{Q_o}{V_o} = \frac{ (p_i - p_{wf \, min}) \, c_t}{(1-s_{wi})\, B_o} =
\frac{ (p_i - p_{wf \, min}) }{(1-s_{wi})\, B_o} \, \big( c_r + s_{wi} c_w + (1-s_{wi})c_o \big) |
where
is flowing bottom-hole pressure, – initial formation pressure, – formation volume factor for oil, – cumulative oil production, – STOIIP, – initial water saturation in oil pay.
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The definition of total compressibility | LaTeX Math Block |
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| c_t = \frac{1}{V_{\phi}} \frac{\partial V_{phi}}{\partial p} = c_r + s_{wi} c_w + (1-s_{wi})c_o \big |
and can be split into rock, water, oil components: | LaTeX Math Block |
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| c_t = c_r + s_{wi} c_w + (1-s_{wi})c_o \big |
For low compressible oil compressibility can be assumed constant and the volume reduction can be related to pressure decline as:| LaTeX Math Block |
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| \frac{\delta V_\phi}{V_\phi} = c_t \, \delta p = c_t \, (p_i - p_{wf \, min}) |
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| \delta V_\phi = Q_o \, B_o |
and | LaTeX Math Block |
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| V_o = s_o \, V_\phi = (1-s_{wi}) \, V_\phi |
hence | LaTeX Math Block |
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| \frac{Q_o \, B_o \, (1-s_{wi})}{V_o} = c_t \, (p_i - p_{wf \, min}) |
and | LaTeX Math Block |
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| EUR = \frac{Q_o}{V_o} = \frac{ (p_i - p_{wf \, min}) \, c_t}{(1-s_{wi})\, B_o} |
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p_{wf \, min} = p_s + \rho_g \, g\, h + \bigg( 1- \frac{\rho_g}{\rho_o} \bigg) \, p_b |
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