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The pore-saturating fluid volume is related to total rock volume and reservoir porosity as: | LaTeX Math Block |
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| V_f = V_r \phi |
The total reservoir compressibility is going to be: | LaTeX Math Block |
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| c_t = -\frac{1}{V_r} \, \frac{\partial V_r}{\partial p} = - \frac{\phi}{V_f} \, \frac{\partial}{\partial p} \left( \frac{V_f}{\phi} \right)
= - \frac{\phi}{V_f} \, \left( V_f \, \frac{\partial}{\partial p} \frac{1}{\phi} + \frac{1}{\phi} \frac{\partial V_f}{\partial p} \right)
= \frac{1}{\phi} \, \frac{\partial \phi}{\partial p} - \frac{1}{V_f} \, \frac{\partial V_f}{\partial p} = c_r + c_f |
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Some applications (like multi-phase pressure diffusion) account for the impact of cross-phase fluid exchange on the total compressibility which require some corrections to equation
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c_t(s,P) = c_r + c_w s_w + c_o s_o + c_g s_g + s_o [ R_{sp} + (c_r + c_o) R_{sn} ] + s_g [ R_{vp} + R_{vn}(c_r + c_g) ] |
where
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See Non-linear multi-phase pressure diffusion @model for derivation of
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.See also
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[Compressibility] [Total Compressibility]
