Motivation

Inputs & Outputs

Inputs
	field-average formation pressure at time moment	Cumulative subsurface water influx from aquifer
	initial formation pressure	Subsurface water flowrate from aquifer
	aquifer Productivity Index
	aquifer transmissibility
	aquifer relaxation time
Detailing Inputs
	aquifer volume
	aquifer area
	pay area

Pseudo Steady State Flow		Oil field performs as single well with cross-sectional area in
	Aquifer pressure is constant
	Aquifer Productivity Index is constant

\frac{d Q_{AQ}}{dt} + \frac{1}{\tau} Q_{AQ} = J \cdot ( p_i - p(t))

J_{AQ} = \frac{2 \pi \sigma}{\ln \frac{A_{AQ}}{A_e} - \frac{3}{4} }

q_{AQ}=\frac{d Q_{AQ}}{dt}

where

	water influx from aquifer at time moment		aquifer transmissibility
	aquifer productivity index		aquifer relaxation time
	initial formation pressure		aquifer area
	field-average formation pressure at time moment		pay area

Const PI expansion:

q_{AQ} = \frac{d Q_{WAQ}}{dt} = J \cdot ( p_{AQ} - p(t))

Finite-volume reservoir PSS depletion:

p_{AQ} = p_i - \frac{Q_{WAQ}}{V_{WAQ} c_t}