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The major difference between cumulative offtakes and cumulative production is that cumulative offtakes accounts for the shrinkage factors and cross-phase exchange coefficients  which depend on formation pressure 

LaTeX Math Inline
bodyp_e(t)
 and formation temperature 
LaTeX Math Inline
bodyT(\tau)
 
and may vary over time:


Cumulative offtakes

(no reference to the fluid)

Cumulative production

(no reference to the fluid)

LaTeX Math Inline
bodyQ Q^{\uparrow}_{off} = \int_0^t B(p(\tau), T(\tau)) qq^{\uparrow}(\tau) d\tau

LaTeX Math Inline
bodyQ Q^{\uparrow}_p = \int_0^t qq^{\uparrow}(\tau) d\tau