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Modelling facility for formation pressure 

LaTeX Math Inline
bodyp(t)
 at any time moment 
LaTeX Math Inline
bodyt
 as response to production flowrates history:

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anchorMatBal
alignmentleft
\phi_e (p_i) \, c_t(p_i) \, p_i - \phi_e(p) \, c_t(p) \, p(t)  = \frac{Q^{\uparrow}_t(t) - Q^{\downarrow}_t(t)}{A_e \cdot h_e}

where

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LaTeX Math Inline
bodyp(t)

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LaTeX Math Inline
bodyp_i = p(0)

initial formation pressure

LaTeX Math Inline
body\phi_e

effective porosity

LaTeX Math Inline
bodyA_e

drainage area

LaTeX Math Inline
bodyh_e

effective formation thickness

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

cumulative offtakes by the time moment

LaTeX Math Inline
bodyt

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

cumulative intakes by the time moment

LaTeX Math Inline
bodyt

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