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  =  Q^{\downarrow}_t(t) - Q^{\uparrow}_t(t)

where

	initial formation pressure
	cumulative offtakes by the time moment
	cumulative intakes by the time moment
	effective porosity as function of formation pressure
	total compressibility as function of formation pressure
	drainage area
	effective formation thickness averaged over drainage area

For low compressibility rocks and fluids the MatBal equation can be explicitly integrated:

p(t)  = p_i + \frac{Q^{\downarrow}_t(t) - Q^{\uparrow}_t(t)}{V_e \cdot c_t}

where

For ideal dry gas:

p(t)  = p_i \exp \left[ \frac{Q^{\downarrow}_t(t) - Q^{\uparrow}_t(t)}{V_e \cdot c_t} \right]

See Also