Mudcake growth equation - Formation invasion

Input(s)

$f_{s}$: Mud Solid Fraction (fraction)

$\varnothing_{c}$: Mudcake Porosity (fraction)

$v_{N}$: Darcy Velocity of the Filtrate through the cake and past the paper (in./s)

Output(s)

$\frac{d x_{c}(t)}{d t}$: Mudcake Growth by time (in./s)

Formula(s)

$$ \frac{d x_{c}(t)}{d t}=\left(\frac{f_{s}}{\left(1-f_{s}\right)\left(1-\emptyset_{c}\right)}\right)\left|v_{n}\right| $$

Reference(s)

Chin, W. C. (1995). Formation Invasion, Page: 39.