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The EUR during the natural oil depletion can be assessed with the following formulaequation (see NDR @model for derivation):
| LaTeX Math Block |
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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
The STOIIP
is related to reservoir oil volume as:...
| 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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| STOIIP |
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| initial water saturation in oil pay |
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| total compressibility |
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...
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V_O = V_o/B_o
...
...
| LaTeX Math Block |
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V_o = s_o \, V_\phi = (1-s_{wi}) \, V_\phi |
so that
| LaTeX Math Block |
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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}} |
...
...
| LaTeX Math Block |
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\delta V_\phi = B_o \, Q_O |
and this can be related to total compressibility
as:...
...
where
...
...
...
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The pressure reduction due to pore volume reduction caused by offtakes is going to be a difference between initial formation pressure and minimal bottom-hole flowing pressure :
| LaTeX Math Block |
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\delta p = p_i - p_{wf} |
For low compressible oil, the total compressibility can be assumed constant
and | LaTeX Math Block Reference |
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becomes:| LaTeX Math Block |
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\frac{1-s_{wi}}{(p_i - p_{wf \, min})} \cdot {\rm EUR_O} = c_t = \rm const |
and
| LaTeX Math Block |
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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 ]
