A new radial model of in situ gelation of Polyacrylamide by Cr(III) produced by a redox reaction has been developed based on reaction kinetics describing the crosslinking and aggregation in the gelling solution, coupled with filtration equations governing the deposition of polymer on the porous medium. The gel system is based on the reaction of Cr(VI) with thiourea to produce Cr (III). Gelation occurs when Cr (III) reacts with Polyacrylamide. The radial model is an extension of a linear displacement model (SPE 20215). The linear model was tested against displacement data and matching parameters in the model were determined by regression. These parameters were then used in the radial model to simulate cases of practical importance.
The radial model describes gelation behavior during the period of gel solution injection and the subsequent shut-in period. During the injection phase, a buildup of flow resistance occurs in the presence of radial flow, i.e., a variable shear field. After shut-in, continued reaction of the gelling solution is simulated under conditions of zero shear. These features allow simulation of a complete gelation treatment from the injection phase through the shut-in period. Using this model, ranges of injection rates, pH, and injection and shut-in times are investigated. The pH history of the gel solution was found to be an important variable in the gelation process. If reservoir pH is in the vicinity of 8.0, gelation is retarded and long shut-in periods are required to develop adequate gel properties for permeability modification. The effects of reservoir pH can be offset by increasing the pH and the concentration of the reducing agent in the gel solution.
A simulation of a three-layer system maintained at constant pressure drop was conducted to illustrate the capability of the model. Permeabilities of the three layers varied from 0.035 to 3.5 darcies. For the gel system simulated, all layers became plugged to some extent during the injection phase. Depth of gel penetration was dependent upon the permeability of the interval. In the lowest permeability zone, the affected region was within the range where remedial treatment after gelation might remove the gelled zone. These results suggest that isolation of high permeability zones is required for in-depth permeability modification using the gel system examined in this study.