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LaTeX Math Block
anchorMatBal
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 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)


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


where

LaTeX Math Inline
bodyp_i = p(0)

initial formation pressure

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body\Delta Q (t)

cumulative reservoir fluid balance

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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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bodyQ^{\uparrow}_t(t)

cumulative offtakes by the time moment

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bodyt

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bodyc_t(p)

total compressibilityas function of formation pressure 

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bodyp(t)
 

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bodyQ^{\downarrow}_t(t)

cumulative intakes by the time moment

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bodyt

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bodyA_e

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bodyQ^{\downarrow}_{GC}(t)

cumulative volumetric inflow from gas cap expansion

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bodyh_e

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bodyQ^{\downarrow}_{AQ}(t)

cumulative volumetric inflow from aquifer expansion

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