Modeling the Effect of Filtration of Pre-Gel Aggregates on Gel Placement in Layered Reservoirs with Crossflow
Authors: Midha V. , Green D.W. , McCool C.S. , Willhite G.P. 
Published: December 2007

Abstract
Flow experiments with the polyacrylamide-chromium gel system have shown that a build-up of resistance occurs in a localized region some distance behind the front of the injected gel solution. The age of the solution at the point of development of resistance is less than the beaker gel time. This resistance has been described as being due to the filtration of pre-gel aggregates, and a linear model based on this mechanism was shown to match experimental data.
This paper describes the extension of the filtration model for the polyacrylamide-chromium gel to the simulation of permeability modification treatments in a well penetrating a layered reservoir in which there is crossflow The effects on treatment viability of several parameters were investigated. The parameters include permeability contrast, vertical permeability and layer thickness, injection pressure, gel solution viscosity and zonal isolation.
The injection behavior can be divided into three sequential flow regimes, the last of which is dominated by relatively more flow into the low-permeability zone and should be avoided. Treatment is enhanced by a high permeability contrast, low viscosity gel solution and zonal isolation. Filtration of pre-gel aggregates, under proper conditions, reduces crossflow into the low-permeability zone and thus works to improve gel placement.

Introduction
Flow experiments with the polyacrylamide-chromium system show a build-up of resistance in a localized region some distance behind the front of the gelant. Several pore volumes of gelant flow through this region till complete plugging of the sandpack occurs. The age of solution flowing through the zone of flow resistance is significantly lower than the "gel time" of the solution in a beaker. These trends suggest that the build-up of flow resistance during in situ gelation does not result from a simple bulk gelation at the displacement front. On increasing the flowrate, the gelant penetrates further into sandpacks, but also plugs the sandpacks at a faster rate.
Previous models simulate in situ gelation of polyacrylamide-chromium system in porous media by relating a lumped "resistance factor" to the kinetics of the redox reaction. These models do not predict the characteristic features of the experimental results with the polyacrylamide system. More importantly, these models do not show the effect of flow rate on the rate of build-up of flow resistance. This dependance is essential for an accurate scale-up of laboratory experiments to field-scale conditions.
Todd et al. proposed a model based on the hypothesis that build-up of resistance for the polyacrylamide-chromium system is due to the filtration of pre-gel polymer aggregates by the porous medium. The crosslinking ions released by the redox reaction are attached to the polymer molecules and lead to the formation of aggregates of crosslinked polymer molecules. The attached chromium ions enhance the filtration properties of the aggregates by their ability to form crosslinks with polymer deposited on the walls of the pores. The zone of flow resistance is characterized by a rapid reduction in porosity and permeability of the porous medium well before a gel structure is formed.
Since the redox reaction is a slow, kinetically-controlled process, at high flow rates it is possible to inject the gelling solution deep into a porous medium before significant amounts of crosslinking ions are released. Once chromium-ions are attached to the polymer molecules, the rate of filtration is a function of the interstitial velocity of the aggregates through the pores. Higher interstitial velocities lead to faster rates of filtration and plugging. The model of Todd et al. successfully matched experimental results over a range of flow rates suggesting the validity of the underlying filtration mechanism.
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