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 A_e \, h_e \int_{p_i}^p \phi_e(p) \, c_t(p) \, dp  =  Q^{\uparrowdownarrow}_t(t) - Q^{\downarrowuparrow}_t(t)

where

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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

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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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bodyA_e

drainage area

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bodyh_e

effective formation thickness averaged over drainage area

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p(t)  = p_i -+ \frac{Q^{\uparrowdownarrow}_t(t) - Q^{\downarrowuparrow}_t(t)}{V_e \cdot c_t}

where

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p(t)  = p_i - \exp \left[ \frac{Q^{\uparrowdownarrow}_t(t) - Q^{\downarrowuparrow}_t(t)}{V_e \cdot c_t} \right]


See Also

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

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