Motivation

Inputs & Outputs

Inputs		Outputs
	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 relaxation time

Detailing Inputs
	aquifer Productivity Index
	aquifer transmissibility
	oil pay area
	aquifer area
	aquifer relaxation time
	aquifer total compressibility
	aquifer pore compressibility
	aquifer water compressibility
	aquifer volume
	aquifer effective thickness
	aquifer porosity

p_{AQ}(t) = p_i - \frac{Q_{AQ}(t)}{V_{AQ} \cdot c_t}

\frac{d Q^{\downarrow}_{AQ}}{dt} + \frac{1}{\tau} Q^{\downarrow}_{AQ} = J \cdot ( p_i - p(t))

q^{\downarrow}_{AQ}(t)=\frac{d Q^{\downarrow}_{AQ}}{dt}

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

p_{AQ}(t) = p_i - \frac{Q_{AQ}}{V_{AQ} c_t}

Eliminating one arrives to .