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}) |
| LaTeX Math Block |
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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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