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LaTeX Math Inline
bodyA_e

drainage area

LaTeX Math Inline
bodyh_e

effective formation thickness averaged over drainage area

LaTeX Math Inline
bodyp_i = p(0)

initial formation pressure

LaTeX Math Inline
body\Delta Q (t)

full-field cumulative reservoir fluid balance

LaTeX Math Inline
bodyJ^{\uparrow}_k

productivity index of

LaTeX Math Inline
bodyk
-th producer

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

cumulative offtakes from

LaTeX Math Inline
bodyk
-th producer by the time moment
LaTeX Math Inline
bodyt

LaTeX Math Inline
bodyJ^{\downarrow}_i

injectivity Index of

LaTeX Math Inline
bodyi
-th injector

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

cumulative intakes to

LaTeX Math Inline
bodyi
-th injector by the time moment
LaTeX Math Inline
bodyt

LaTeX Math Inline
bodyp^{\uparrow}_{wf}(t)

field-average BHP in producers

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

full-field cumulative offtakes by the time moment

LaTeX Math Inline
bodyt

LaTeX Math Inline
bodyp^{\downarrow}_{wf}(t)

field-average BHP in injectors

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

full-field cumulative intakes by the time moment

LaTeX Math Inline
bodyt

LaTeX Math Inline
body\phi_e(p)

effective porosity as function of formation pressure 

LaTeX Math Inline
bodyp(t)
 

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

full-field cumulative volumetric inflow from gas cap expansion

LaTeX Math Inline
bodyc_t(p)

total compressibilityas function of formation pressure 

LaTeX Math Inline
bodyp(t)
 

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

full-field cumulative volumetric inflow from aquifer expansion



In practice there is no way to measure the external influx   

LaTeX Math Inline
bodyQ^{\downarrow}_{GC}(t)
 and 
LaTeX Math Inline
bodyQ^{\downarrow}_{GC}(t)
 so that one need to model them and use model parameters to fit 
LaTeX Math Block Reference
anchorMatBal
 – 
LaTeX Math Block Reference
anchorBHP_INJ
.

There is a list of various analytical aquifer and gas cap models which are normally based on the relations:


LaTeX Math Block
anchor1
alignmentleft
Q^{\downarrow}_{GC}(t) = F_{GC}(p(t), p_{wf}(t))



LaTeX Math Block
anchor1
alignmentleft
Q^{\downarrow}_{GC}(t) = F_{AQ}(p(t), p_{wf}(t))



Variations

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In some specific cases equation 

LaTeX Math Block Reference
anchorMatBal
can be explicitly integrated:

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