The stability of miscible displacement in porous media: Nonmonotonic viscosity profiles

The stability of miscible displacement in porous media is analyzed theoretically. By considering the nonmonotonic viscosity variation effects, new stability equations are derived in a similar domain with and without the quasi-steady state approximations (QSSA). An analytical approach to solve the newly driven stability equations is proposed and its validity is confirmed by comparing its solutions with numerically obtained ones. Through the growth rate analysis without the QSSA, it is shown analytically that the system is unconditionally stable for the long-wave disturbance regardless of the viscosity profile. The present growth rate obtained for small time without the QSSA is quite different from the previous analyses based on the QSSA where the growth rate of the disturbance depends strongly on the viscosity profile. Through the stability characteristics for the finite time case, the validity of the QSSA is discussed. The present stability condition explains the system more reasonably than the previous results based on the conventional QSSA. (C) 2011 American Institute of Physics. [doi:10.1063/1.3624620]