Front displacement of a particle in the reservoir - Formation invasion

Input(s)

$x_{o}$: Initial Marked Position (ft)

$k$: Permeability $(\mathrm{mD})$

$\mu$: Viscosity $(\mathrm{cP})$

Ø: Porosity (fraction)

$P_{r}$: Constant "Reservoir" Pressure at $\mathrm{x}=\mathrm{L}$ (psi)

$P_{l}$: Pressure at $\mathrm{x}=0$ location (psi)

$t$: time (days)

$L$: Length $(\mathrm{ft})$

Output(s)

$x(t)$: Front Displacement of an Initially Marked Particle in the Reservoir (ft)

Formula(s)

$$ x(t)=x_{o}-\left(\frac{k}{\mu \varnothing}\right)\left(\frac{\left(P_{r}-P_{l}\right) t}{L}\right) $$

Reference(s)

Chin, W. C. (1995). Formation Invasion, Page: 30.