Some useful upper bounds for the selection of optimal profiles

In enhanced oil recovery by chemical flooding within tertiary oil recovery, it is often necessary to choose optimal viscous profiles of the injected displacing fluids that reduce growth rates of hydrodynamic instabilities the most thereby substantially reducing the well-known fingering problem and improving oil recovery. Within the three-layer Hele–Shaw model, we show in this paper that selection of the optimal monotonic viscous profile of the middle-layer fluid based on well known theoretical upper bound formula [P. Daripa, G. Pasa, A simple derivation of an upper bound in the presence of a viscosity gradient in three-layer Hele–Shaw flows, Journal of Statistical Mechanics (2006) 11. http://dx.doi.org/10.1088/1742-5468/2006/01/P01014] agrees very well with that based on the computation of maximum growth rate of instabilities from solving the linearized stability problem. Thus, this paper proposes a very simple, fast method for selection of the optimal monotonic viscous profiles of the displacing fluids in multi-layer flows.