# 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.