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.