Mudcake growth equation 2 - Formation invasion

Input(s)

$\varnothing_{\text {eff: }} \quad$ Effective Porosity (fraction)

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

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

$x_{f}$: Transient Invasion Front (in.)

$x_{f, o}$: Initial Displacement, i.e., Spurt (in.)

Output(s)

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

Formula(s)

$$ x_{c}(t)=\left[\varnothing_{e f f} f_{s} /\left\{\left(1-\varnothing_{c}\right)\left(1-f_{s}\right)\right\}\right]\left(x_{f}-x_{f, o}\right) $$

Reference(s)

Chin, W. C. (1995). Formation Invasion, Page: 45.