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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 |
while the latter is related to the reservoir pore volume
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V_o = s_o \, V_\phi = (1-s_{wi}) \, V_\phi |
so that
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V_o = B_o \, V_O = (1-s_{wi}) \, V_\phi \quad \Rightarrow \quad V_\phi = \frac{B_o \, V_O}{(1-s_{wi})} |
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\delta V_\phi = Q_O \, B_o |
thus leading to
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c_t = \frac{1}{V_{\phi}} \frac{\partial V_{\phi}}{\partial p} =
\frac{1-s_{wi}}{B_o \, V_O} \frac{B_o \, Q_O}{\delta p} =\frac{1-s_{wi}}{\delta p} \frac{Q_O}{V_O} = \frac{1-s_{wi}}{\delta p} \cdot {\rm EUR_O} |
where
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\delta p = p_i - p_{wf}
pressure reduction due to pore volume reduction caused by offtakes.
For
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\frac{1-s_{wi}}{(p_i - p_{wf \, min})} \cdot {\rm EUR_O} = c_t = \rm const |
and
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{\rm EUR}_O = \frac{ (p_i - p_{wf \, min}) \, c_t}{(1-s_{wi})} |
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 ]
