In this paper we propose and analyse a mathematical model for preflush treatment in an oil reservoir. The model is based on two phase flow in which both phases are fully miscible. For the case of constant injection rate condition, fully implicit solutions can be constructed. Saturation profiles consist of shocks and fingering zones. For constant pressure conditions we construct a semi-explicit relation for the shock position and the gel penetration depth. The model predicts diversion behaviour of polymer-gel treatment from low permeability layers and hence viscous preflush improves the efficiency of polymer-gel treatment.

Free boundary problems (msc 35R35), Flows in porous media; filtration; seepage (msc 76S05)
Modelling, Analysis and Simulation [MAS]

Vermolen, F.J, Pieters, G.-J, Zitha, P.L.J, & Bruining, J. (1999). A mathematical model for preflush treatment in an oil reservoir using a fully miscible fluid. Modelling, Analysis and Simulation [MAS]. CWI.