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The value of cumulative aquifer influx 

LaTeX Math Inline
body--uriencoded--Q%5e%7B\downarrow%7D_%7BGCAP%7D
 is modelled as in Aquifer Drive Models (most popular being Carter-Tracy model).

The value of 

LaTeX Math Inline
body\gamma_n
 can be linked to the Dynamic drainage volume of a well
LaTeX Math Inline
body--uriencoded--V_%7B\phi, n%7D
 as:

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LaTeX Math Block
anchorIKI6E
alignmentleft
\gamma_n = c_{t,n} \cdot V_{\phi, n} = (c_r + s_{w,n} \cdot c_w + s_{o,n} \cdot c_o + s_{g,n} \cdot c_g) \cdot  \phi_n \cdot V_n

...

LaTeX Math Block
anchorIKI6E
alignmentleft
s_{w,n} + s_{o,n} + s_{g,n} = 1


In case of Water Injector 

LaTeX Math Inline
body--uriencoded-- s_%7Bo,n%7D = s_%7Bor%7D, \quad s_%7Bg,n%7D = 0, \quad s_%7Bw,n%7D = 1 - s_%7Bor%7D
.

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In regular case , the initial formation pressure at datum is the same for all wells: 

LaTeX Math Inline
body--uriencoded-- p_%7Bnr%7D(0) = p_i = %7B\rm const%7D, \ \forall n
.


The value of 

LaTeX Math Inline
body\gamma_n
 can be linked to the Dynamic drainage volume of a well
LaTeX Math Inline
body--uriencoded--V_%7B\phi, n%7D
 as:

LaTeX Math Block
anchorIKI6E
alignmentleft
\gamma_n = c_{t,n} \cdot V_{\phi, n} = (c_r + s_{w,n} \cdot c_w + s_{o,n} \cdot c_o + s_{g,n} \cdot c_g) \cdot  \phi_n \cdot V_n
LaTeX Math Block
anchorIKI6E
alignmentleft
s_{w,n} + s_{o,n} + s_{g,n} = 1


See Also

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Petroleum Industry / Upstream /  Production / Subsurface Production / Field Study & Modelling / Production Analysis / Capacitance Resistance Model (CRM)

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