Modelling facility for 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 |
Q^{\uparrow}_t(t) | cumulative offtakes by the time moment t |
Q^{\downarrow}_t(t) | cumulative intakes by the time moment t |
(2) | \phi_e (p_i) \, c_t(p_i) \, p_i - \phi_e(p) \, c_t(p) \, p(t) = \frac{Q^{\uparrow}_t(t) - Q^{\downarrow}_t(t)}{A_e \cdot h_e} |
See Also
Petroleum Industry / Upstream / Production / Subsurface Production / Field Study & Modelling / Production Analysis