Numerical Modeling of the Effects of Disproportionate Permeability Reduction Water-Shutoff Treatments on Water Coning

Abstract

In the present paper, we analyze numerically the disproportionate permeability reduction (DPR) water-shutoff (WSO) treatments in oil production well, i.e., the ability to reduce relative permeability (RP) to water more than to oil. The technique consists of bullhead injection of polymer solutions (gelant) into the near-wellbore formation without zone isolation. By assuming the low dissolution of polymer in oil and the low mobility of the gel in porous medium, we reduced the compositional model of the process to a simple two-phase model, with RP and capillary pressure (PC) dependent on the water and gel saturation. We proposed the extension of the LET correlations used to calculate RP and PC for the case of three phases (oil–water–gel). The problem is divided into two stages: the polymer injection and the post-treatment production. Both of these processes are described by the same formal mathematical model, which results from incompressible two-phase flow equations formulated in terms of normalized saturation and global pressure. The thermal effects caused by the injection of a relatively cold aqueous solution are taken into account. The numerical solution shows favorable results for the DPR WSO treatments. Other techniques, such as the creation of impermeable barrier and downhole water sink (DWS) technology, are also tested in order to check the validity of the developed numerical model with experimental data.