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

Const PI expansion:

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

Finite-volume reservoir PSS depletion:

bar p = p_i - \frac{Q_{WAQ}}{V_{WAQ} c_t}