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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) + V^{\downarrow}_{GC}(t) + V^{\downarrow}_{AQWAQ}(t)



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



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anchorBHP_INJ
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p^{\downarrow}_{wf, k}(t) = p(t) -  {J^{\downarrow}_i}^{-1} \cdot \frac{dQ^{\downarrow}_k}{dt}


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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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bodyp_i = p(0)

initial formation pressure

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body\Delta Q (t)

full-field cumulative reservoir fluid balance

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bodyJ^{\uparrow}_k

productivity index of

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bodyk
-th producer

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bodyQ^{\uparrow}_t(t)

cumulative offtakes from

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bodyk
-th producer by the time moment
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bodyt

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bodyJ^{\downarrow}_i

injectivity Index of

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bodyi
-th injector

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bodyQ^{\downarrow}_t(t)

cumulative intakes to

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bodyi
-th injector by the time moment
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bodyt

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bodyp^{\uparrow}_{wf}(t)

field-average BHP in producers

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bodyQ^{\uparrow}_t(t)

full-field cumulative offtakes by the time moment

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bodyt

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bodyp^{\downarrow}_{wf}(t)

field-average BHP in injectors

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bodyQ^{\downarrow}_t(t)

full-field 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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bodyQ^{\downarrow}_{GC}(t)

full-field cumulative volumetric inflow from gas cap expansion

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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}_{AQWAQ}(t)

full-field cumulative volumetric inflow from aquifer expansion

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