A Mathematical Model of In-Situ Gelation of Polyacrylamide by a Redox Process

Abstract

Summary Recent displacement data conclusively show that the initial permeability reduction during in-situ gelation processes does not result from a bulk gelation of the injected fluid. This paper presents a filtration-based model that correctly accounts paper presents a filtration-based model that correctly accounts for all physical phenomena occurring during in-situ gelation displacements. Introduction Permeability modification treatments are used to improve waterflood Permeability modification treatments are used to improve waterflood sweep efficiency in mature waterfloods. These treatments consist of injecting a polymer solution combined with a crosslinking agent into a water-injection well. It is envisioned that the viscous gelling solution enter shigh-permeability, water-swept regions of the reservoir and plugs these channels, forcing subsequent water injection into regions of the reservoir that have not been swept by water. Previous investigators represented the in-situ permeability reduction mechanism as simple bulk gelation of the injection solution. However, displacement data show that flow resistance developed in sandpacks before the injected polymer solution could get in bulk. McCool and McCool et al. proposed that the initial permeability was reduced by filtration of Cr+3/polyacrylamide permeability was reduced by filtration ofCr+3/polyacrylamide aggregates from the gelling solution, well before a true" gel" could form. This paper presents a new numerical model based on the filtration hypothesis. The model consists of a mass-transport equation for10 species coupled with kinetic models of the gelation process and porousmedium and with filtration models from the process and porous medium and with filtration models from the literature. The model successfully matches Marty et al. five in-situ gelation displacements. Model formulation and simulation results are presented here. Background Permeability modification treatments for injection wells are Permeability modification treatments for injection wells are designed by choosing a treatment radius around the wellbore and calculating the volume of gelling solution required to displace the water saturated PV in this region. It is assumed that the gelling solution forms a bulk gel throughout this region after injection. Laboratory displacement data show that high flow resistance developed in sandpacks before the polymer solution could gel in bulk. Large pressure drops caused by this region of high flow resistance limited the amount of gel solution that could be injected into the sandpacks. Although a bulk get formed in the region bounded by this zone of high flow resistance, the treatment depth was limited and was significantly less than predicted from formation of a bulk gel. Previous investigators assumed that an in-situ permeability reduction mechanism resulted from simple bulk gelation of the injected solution. However, McCool et al. hypothesized that the permeability reduction resulted because the porous medium filtered permeability reduction resulted because the porous medium filtered aggregates of chromium/polyacrylamide from the gelling solution well before a true"get" could form. None of the models in the literature include the mechanisms needed to simulate correctly the in-situ gelation behavior of gelling systems studied by McCool, McCool et al., and Marty et al. The model developed in this paper is based on the filtration of gel aggregates from agelling solution. Model Description This section describes a conceptual model of in-situ gelation and develops mathematical equations to model the process. The model was developed by combining transport equations for the various chemical species in porous media with models of gelation kinetics and filtration processes. Equations describing chemical reaction kinetics and filtration mechanisms are taken from the literature. The porous medium consists of a linear sandpack of known permeability and porosity. A solution of thiourea, dichromate, and permeability and porosity. A solution of thiourea, dichromate, and polyacrylamide is injected into one end of the sandpack and polyacrylamide is injected into one end of the sandpack and progresses through the porous medium. Initially, nopolymer chains progresses through the porous medium. Initially, no polymer chains are chemically crosslinked, although the solution has a beginning level of entanglement "crosslinks," giving the solution an initial shear modulus, G', and defining an initial size distribution of "pregelclusters." Polyacrylamide solutions used in gelation displacements typically exceed the polymer entanglement concentration. Pregel clusters oraggregates first form when individual polymer chains become physically entangled with other polymer chains. Chemical crosslinking in the polyacrylamide/redox system begins when thiourea reacts with dichromate to produce CT +3 ions, which then attach to polymer chains. Attached CT +3 ions participate in crosslink formation, joining polymer chains and small clusters to form larger pregel clusters. During gelation processes, these pregel clusters steadily increase in size as small clusters combine pregel clusters steadily increase in size as small clusters combine to form larger ones. In the absence of shear, the largest aggregates ultimately form an "infinite" gel molecule throughout the volume of gelling solution. We believe that permeability reduction during in-situ gelation displacements results largely from the filtration of these large polymer aggregates before the infinite gel network is formed. Polymer is retained in the porous medium in two ways. When injected polymer first contacts the porous medium, a layer of polymer adsorbs on to the surface of the sand grains. This thin, polymer adsorbs onto the surface of the sand grains. This thin, dense initial layer is attached to the surface of the sand grain by physical entrapment and surface attractions and has little effect physical entrapment and surface attractions and has little effect on permeability. As polymer aggregates increase in size, some are filtered out and attach to previously deposited polymer. The filtration rate increases with polymer concentration, aggregate size, and attached Cr+3concentration. Porosity and permeability of the porous medium decrease as filtration progresses, causing the zone of high flow resistance observed during laboratory in-situ gelation displacements.

Aperture-Tolerant, Chemical-Based Methods to Reduce Channeling

“…12,14,[120][121][122][123] However, after gel aggregates form and grow to the size of pore throats, gel filtration can radically increase the resistance to flow. [120][121][122] The literature indicates that gelants can penetrate a significant distance into porous rock before gelation, but after gelation, gel propagation is extremely slow or negligible. 12,14,[120][121][122][123] Alternatively, if gelation is stopped sufficiently early or if gels are sufficiently sheared so that gel particles remain significantly smaller than pore throats, the gel suspensions can propagate through porous rock; however, the level of mobility reduction is generally small (less than 2).…”

“…[120][121][122] The literature indicates that gelants can penetrate a significant distance into porous rock before gelation, but after gelation, gel propagation is extremely slow or negligible. 12,14,[120][121][122][123] Alternatively, if gelation is stopped sufficiently early or if gels are sufficiently sheared so that gel particles remain significantly smaller than pore throats, the gel suspensions can propagate through porous rock; however, the level of mobility reduction is generally small (less than 2). 16 Also, suspensions of gel particles and adsorbed polymers provide resistance factors and residual resistance factors that increase with decreasing permeability.…”

“…12,14,[120][121][122][123] Early in the gelation process, it propagates through sandstone like a polymer solution without crosslinker. After some point (presumably when gel aggregates grow to the size of pore throats), gel propagation is extremely slow or negligible.…”

“…Consider how crosslinked polymer gels perform in porous media during conformance-improvement treatments. 12,14,[120][121][122][123] Early in the gelation process, most gelants behave like clean fluids that do not contain suspended particulate matter. 12,14,[120][121][122][123] However, after the first gel aggregates form and grow to the size of pore throats, filtration of the gel aggregates (within the porous rock) can radically increase the resistance to flow.…”

“…12,14,[120][121][122][123] Early in the gelation process, most gelants behave like clean fluids that do not contain suspended particulate matter. 12,14,[120][121][122][123] However, after the first gel aggregates form and grow to the size of pore throats, filtration of the gel aggregates (within the porous rock) can radically increase the resistance to flow. [120][121][122] Gelants (e.g., polymer-crosslinker solutions prior to significant polymer crosslinking) can penetrate a significant distance into porous rock before gelation, but after gelation, gel propagation is extremely slow or non existent.…”