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 = Q^{\uparrow}_t(t) - Q^{\downarrow}_t(t) |
where
p_i = p(0) | initial formation pressure |
\phi_e(p) | effective porosity as function of formation pressure p(t) |
c_t(p) | total compressibility as function of formation pressure p(t) |
A_e | drainage area |
h_e | effective formation thickness averaged over drainage area |
Q^{\uparrow}_t(t) | cumulative offtakes by the time moment t |
Q^{\downarrow}_t(t) | cumulative intakes by the time moment t |
For low compressibility rocks and fluids \{ \phi_e = {\rm const}, \ c_t = {\rm const} \} the MatBal equation (1) can be explicitly integrated:
(2) | p(t) = p_i - \frac{Q^{\uparrow}_t(t) - Q^{\downarrow}_t(t)}{A_e \cdot h_e \cdot \phi_e \cdot c_t} |
See Also
Petroleum Industry / Upstream / Production / Subsurface Production / Field Study & Modelling / Production Analysis