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