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The STOIIP can be written as:| LaTeX Math Block |
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| V_O = V_o/B_o = s_o \, V_\phi = (1-s_{wi}) \, V_\phi |
so that | LaTeX Math Block |
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| V_\phi = \frac{B_o \, Q_O}{(1-s_{wi})} |
The pore volume reduction due to offtakes is: | LaTeX Math Block |
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| \delta V_\phi = Q_O \, B_o |
thus leading to | LaTeX Math Block |
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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 | LaTeX Math Block |
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| c_t = c_r + s_{wi} c_w + (1-s_{wi})c_o |
is total compressibility of oil saturated formation and
| LaTeX Math Block |
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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 and | LaTeX Math Block Reference |
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becomes:| LaTeX Math Block |
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| \frac{1-s_{wi}}{\delta p(p_i - p_{wf \, min})} \cdot {\rm EUR_O} = c_t \, (p_i - p_{wf \, min})= \rm const |
and | LaTeX Math Block |
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| {\rm EUR}_{\rm NDR} = \frac{Q_o}{V_o}O = \frac{ (p_i - p_{wf \, min}) \, c_t}{(1-s_{wi})\, B_o} |
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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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