Modelling facility for field-average formation pressure p(t) and Bottom-Hole Pressure ( p^{\uparrow}_{wf}(t) for producers and p^{\downarrow}_{wf}(t) for injectors) at any time moment t as response to production flowrates history:
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where
A_e | drainage area | h_e | effective formation thickness averaged over drainage area |
p_i = p(0) | initial formation pressure | \Delta Q (t) | full-field cumulative reservoir fluid balance |
J^{\uparrow}_k | productivity index of k-th producer | Q^{\uparrow}_t(t) | cumulative offtakes from k-th producer by the time moment t |
J^{\downarrow}_i | injectivity Index of i-th injector | Q^{\downarrow}_t(t) | cumulative intakes to i-th injector by the time moment t |
p^{\uparrow}_{wf}(t) | field-average BHP in producers | Q^{\uparrow}_t(t) | full-field cumulative offtakes by the time moment t |
p^{\downarrow}_{wf}(t) | field-average BHP in injectors | Q^{\downarrow}_t(t) | full-field cumulative intakes by the time moment t |
\phi_e(p) | effective porosity as function of formation pressure p(t) | Q^{\downarrow}_{GC}(t) | full-field cumulative volumetric inflow from gas cap expansion |
c_t(p) | total compressibility as function of formation pressure p(t) | Q^{\downarrow}_{AQ}(t) | full-field cumulative volumetric inflow from aquifer expansion |
In practice there is no way to measure the external influx Q^{\downarrow}_{GC}(t) and Q^{\downarrow}_{AQ}(t) so that one need to model them and use model parameters to fit (1) – (3).
There is a list of various analytical aquifer and gas cap models which are normally based on the relations:
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Variations
In some specific cases equation (1) can be explicitly integrated:
Low compressibility rocks and fluids | Ideal dry gas | ||||
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\{ \phi_e = {\rm const}, \ c_t = {\rm const} \} | c_t = c_r + \frac{1}{p} \sim \frac{1}{p} | ||||
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where
V_e = A_e \, h_e \, \phi_e | drainage volume |
See Also
Petroleum Industry / Upstream / Production / Subsurface Production / Field Study & Modelling / Production Analysis