Is FracPro leakoff model lumped?

In the FracPro notes (slide 24) they have a leakoff model defined by three coefficients:

$C_v = 0.0469 \sqrt{\frac{k_i \Delta p \phi}{\mu_a}}$

$C_c = 0.0374 \Delta p \sqrt{\frac{k_r C_r \phi}{\mu_r}}$

$C_w = 0.0164 \frac{m}{A}$

Here $\Delta p$ is a pressure difference, $\phi$ is a porosity, and the $\mu$s are viscosities of various types. Are these models all heuristic or are any of them related to an actual solution of the Navier-Stokes eqn, suitably lumped or averaged?