Modelling facility for field-average formation pressure p(t) at any time moment t as response to production flowrates history:
(1) | 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) + Q^{\downarrow}_{GC}(t) + Q^{\downarrow}_{AQ}(t) |
(2) | P_{wf}(t) = p(t) - J^{-1} \frac{dQ^{\uparrow}}{dt} |
where
p_i = p(0) | initial formation pressure | \Delta Q (t) | cumulative reservoir fluid balance |
\phi_e(p) | effective porosity as function of formation pressure p(t) | Q^{\uparrow}_t(t) | cumulative offtakes by the time moment t |
c_t(p) | total compressibility as function of formation pressure p(t) | Q^{\downarrow}_t(t) | cumulative intakes by the time moment t |
A_e | Q^{\downarrow}_{GC}(t) | cumulative volumetric inflow from gas cap expansion | |
h_e | effective formation thickness averaged over drainage area | Q^{\downarrow}_{AQ}(t) | cumulative volumetric inflow from aquifer expansion |
For low compressibility rocks and fluids \{ \phi_e = {\rm const}, \ c_t = {\rm const} \} the MatBal equation (1) can be explicitly integrated:
(3) | p(t) = p_i + \frac{\Delta Q(t)}{V_e \cdot c_t} |
where
V_e = A_e \, h_e \, \phi_e | drainage volume |
For ideal dry gas:
(4) | p(t) = p_i \exp \left[ \frac{\Delta Q(t)}{V_e \cdot c_t} \right] |
See Also
Petroleum Industry / Upstream / Production / Subsurface Production / Field Study & Modelling / Production Analysis