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LaTeX Math Block
anchorMatBal
alignmentleft
 A_e \, h_e \int_{p_i}^p \phi_e(p) \, c_t(p) \, dp  = \Delta Q (t) =  Q^{\downarrow}_t(t) - Q^{\uparrow}_t(t) + Q^{\downarrow}_{GC}(t) + Q^{\downarrow}_{AQ}(t)

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


For low compressibility rocks and fluids 

LaTeX Math Inline
body\{ \phi_e = {\rm const}, \ c_t = {\rm const} \}
the MatBal equation 
LaTeX Math Block Reference
anchorMatBal
can be explicitly integrated:

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