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anchorMatBal
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 VA_e \, h_e \int_{p_i}^p \phi_e(p) \, c_t(p) \, dp  = Q^{\uparrow}_t(t) - Q^{\downarrow}_t(t)

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V_e = \, h_{eff} volume

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bodyp_i = p(0)

initial formation pressure

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bodyQ^{\uparrow}_t(t)

cumulative offtakes by the time moment

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bodyt

LaTeX Math Inline
bodyQ^{\downarrow}_t(t)

cumulative intakes by the time moment

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bodyt

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body\phi_e(p)

effective porosity as function of formation pressure 

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bodyp(t)
 

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bodyc_t(p)

total compressibility as function of formation pressure 

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bodyp(t)
 

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body

A_e

drainage

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bodyA_e

drainage area

LaTeX Math Inline
bodyh_{eff}e

effective formation thickness averaged over drainage area

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LaTeX Math Block
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p(t)  = p_i - \frac{Q^{\uparrow}_t(t) - Q^{\downarrow}_t(t)}{V_e \cdot \phi_e \cdot c_t}c_t}

where

LaTeX Math Inline
bodyV_e = A_e \, h_e \, \phi_e

drainage volume



See Also

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Petroleum Industry / Upstream /  Production / Subsurface Production / Field Study & Modelling / Production Analysis

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