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The EUR during the natural oil depletion can be assessed with the following formulaequation (see NDR @model for derivation):
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{\rm EUR}_O = \frac{Q_O}{V_O} = \frac{ (p_i - p_{wf}) \, c_t}{(1-s_{wi})\, B_o} =
\frac{ (p_i - p_{wf}) }{(1-s_{wi})\, B_o} \, \big( c_r + s_{wi} c_w + (1-s_{wi})c_o \big) |
where
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minimal flowing bottom-hole pressure |
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initial formation pressure |
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formation volume factor for oil, |
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cumulative oil production |
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initial water saturation in oil pay |
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V_O = V_o/B_o = s_o \, V_\phi = (1-s_{wi}) \, V_\phi |
so that
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V_\phi = \frac{B_o \, Q_O}{(1-s_{wi})} |
The pore volume reduction due to offtakes is:
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\delta V_\phi = Q_O \, B_o |
thus leading to
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where
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\delta p = p_i - p_{wf} |
pressure reduction due to pore volume reduction caused by offtakes.
For low compressible oil, the total compressibility can be assumed constant
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becomes:...
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\frac{1-s_{wi}}{\delta p} \cdot {\rm EUR_O} = c_t \, (p_i - p_{wf \, min})
and
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{\rm EUR}_{\rm NDR} = \frac{Q_o}{V_o} = \frac{ (p_i - p_{wf \, min}) \, c_t}{(1-s_{wi})\, B_o} |
For the naturally flowing wells the bottom hole pressure under flowing conditions can be roughly assed by homogeneous multiphase pipe flow model assessed as:
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Petroleum Industry / Upstream / Production / Field Development Plan / Recovery Methods
[ Waterflood Recovery (WF) ]
[ NDR @model ]