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LaTeX Math Block
anchorBHP_PROD
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PP^{\uparrow}_{wf}(t) = p(t) - J^{-1} \frac{dQ^{\uparrow}}{dt}


LaTeX Math Block
anchorBHP_INJ
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P^{\downarrow}_{wf}(t) = p(t) - J^{-1} \frac{dQ^{\downarrow}}{dt}

where

LaTeX Math Inline
bodyp_i = p(0)

initial formation pressure

LaTeX Math Inline
body\Delta Q (t)

cumulative reservoir fluid balance

LaTeX Math Inline
body\phi_e(p)

effective porosity as function of formation pressure 

LaTeX Math Inline
bodyp(t)
 

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

cumulative offtakes by the time moment

LaTeX Math Inline
bodyt

LaTeX Math Inline
bodyc_t(p)

total compressibilityas function of formation pressure 

LaTeX Math Inline
bodyp(t)
 

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

cumulative intakes by the time moment

LaTeX Math Inline
bodyt

LaTeX Math Inline
bodyA_e

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

cumulative volumetric inflow from gas cap expansion

LaTeX Math Inline
bodyh_e

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

cumulative volumetric inflow from aquifer expansion

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