  The multiphase flow mechanism in miscible displacement through porous media
is an important topic in various applications, such as petroleum engineering,
low Reynolds number suspension flows, dusty gas dynamics, and fluidized beds.
To simulate such flows, volume averaging spatial operators are considered to
incorporate pressure drag and skin friction experienced by a porous medium. In
this work, a streamline-based Lagrangian methodology is extended for an
efficient numerical approach to handle dispersion and diffusion of solvent
saturation during a miscible flow. Overall pressure drag on the diffusion and
dispersion of solvent saturation is investigated. Numerical results show
excellent agreement with the results obtained from asymptotic analysis. The
present numerical simulations indicate that the nonlinear effects due to skin
friction and pressure drag cannot be accurately captured by Darcy's method if
the contribution of the skin friction dominates over that of the pressure drag.
Moreover, mass conservation law is investigated, which is an important feature
for enhanced oil recovery, and the results help to guide a good agreement with
theory. This investigation examines how the flow regime may be optimized for
enhanced oil recovery methods.
