Modeling Bacteria Transport Using Fractional Derivatives

Usually contaminant transport through porous media is modeled through the advection-dispersion equation (ADE), while the heterogeneities in the system are modeled stochastically. Unfortunately, stochastic models are computationally intensive. An alternative is to use fractional ADEs, which are capable of capturing the greater variation in particle locations that are seen in various breakthrough curve data. We model bacteria transport through porous media using fractional ADEs, and solve the resulting fractional initial value problem with forcing functions numerically.