Mathematical Model of In-Situ Gelation of Polyacrylamide by a Redox Process
- B.J. Todd (U. of Kansas) | G.P. Willhite (U. of Kansas) | D.W. Green (U. of Kansas)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Engineering
- Publication Date
- February 1993
- Document Type
- Journal Paper
- 51 - 58
- 1993. Society of Petroleum Engineers
- 2.4.3 Sand/Solids Control, 4.1.5 Processing Equipment, 5.5.2 Core Analysis, 6.5.2 Water use, produced water discharge and disposal, 1.2.3 Rock properties, 4.1.2 Separation and Treating, 5.3.4 Integration of geomechanics in models, 4.3.4 Scale, 5.4.1 Waterflooding, 5.1 Reservoir Characterisation, 5.4.7 Chemical Flooding Methods (e.g., Polymer, Solvent, Nitrogen, Immiscible CO2, Surfactant, Vapex)
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Recent displacement data conclusively show that the initial permeabilityreduction during in-situ gelation processes does not result from a bulkgelation of the injected fluid. This paper presents a filtration-based modelthat correctly accounts paper presents a filtration-based model that correctlyaccounts for all physical phenomena occurring during in-situ gelationdisplacements.
Permeability modification treatments are used to improve waterfloodPermeability modification treatments are used to improve waterflood sweepefficiency in mature waterfloods. These treatments consist of injecting apolymer solution combined with a crosslinking agent into a water-injectionwell. It is envisioned that the viscous gelling solution entershigh-permeability, water-swept regions of the reservoir and plugs thesechannels, forcing subsequent water injection into regions of the reservoir thathave not been swept by water. Previous investigators represented the in-situpermeability reduction mechanism as simple bulk gelation of the injectionsolution. However, displacement data show that flow resistance developed insandpacks before the injected polymer solution could get in bulk. McCool andMcCool et al. proposed that the initial permeability was reduced by filtrationof 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 onthe 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 withfiltration models from the literature. The model successfully matches Marty etal. five in-situ gelation displacements. Model formulation and simulationresults are presented here.
Permeability modification treatments for injection wells are Permeabilitymodification treatments for injection wells are designed by choosing atreatment radius around the wellbore and calculating the volume of gellingsolution required to displace the watersaturated PV in this region. It isassumed that the gelling solution forms a bulk gel throughout this region afterinjection. Laboratory displacement data show that high flow resistancedeveloped in sandpacks before the polymer solution could gel in bulk. Largepressure drops caused by this region of high flow resistance limited the amountof gel solution that could be injected into the sandpacks. Although a bulk getformed in the region bounded by this zone of high flow resistance, thetreatment depth was limited and was significantly less than predicted fromformation of a bulk gel. Previous investigators assumed that an in-situpermeability reduction mechanism resulted from simple bulk gelation of theinjected solution. However, McCool et al. hypothesized that the permeabilityreduction resulted because the porous medium filtered permeability reductionresulted because the porous medium filtered aggregates ofchromium/polyacrylamide from the gelling solution well before a true"get" could form. None of the models in the literature include themechanisms needed to simulate correctly the in-situ gelation behavior ofgelling systems studied by McCool, McCool et al., and Marty et al. The modeldeveloped in this paper is based on the filtration of gel aggregates from agelling solution.
This section describes a conceptual model of in-situ gelation and developsmathematical equations to model the process. The model was developed bycombining transport equations for the various chemical species in porous mediawith models of gelation kinetics and filtration processes. Equations describingchemical reaction kinetics and filtration mechanisms are taken from theliterature. The porous medium consists of a linear sandpack of knownpermeability and porosity. A solution of thiourea, dichromate, and permeabilityand porosity. A solution of thiourea, dichromate, and polyacrylamide isinjected into one end of the sandpack and polyacrylamide is injected into oneend of the sandpack and progresses through the porous medium. Initially, nopolymer chains progresses through the porous medium. Initially, no polymerchains are chemically crosslinked, although the solution has a beginning levelof entanglement "crosslinks," giving the solution an initial shearmodulus, G', and defining an initial size distribution of "pregelclusters." Polyacrylamide solutions used in gelation displacementstypically exceed the polymer entanglement concentration. Pregel clusters oraggregates first form when individual polymer chains become physicallyentangled with other polymer chains. Chemical crosslinking in thepolyacrylamide/redox system begins when thiourea reacts with dichromate toproduce CT +3 ions, which then attach to polymer chains. Attached CT +3 ionsparticipate in crosslink formation, joining polymer chains and small clustersto form larger pregel clusters. During gelation processes, these pregelclusters steadily increase in size as small clusters combine pregel clusterssteadily increase in size as small clusters combine to form larger ones. In theabsence of shear, the largest aggregates ultimately form an "infinite"gel molecule throughout the volume of gelling solution. We believe thatpermeability reduction during in-situ gelation displacements results largelyfrom the filtration of these large polymer aggregates before the infinite gelnetwork is formed. Polymer is retained in the porous medium in two ways. Wheninjected polymer first contacts the porous medium, a layer of polymer adsorbsonto the surface of the sand grains. This thin, polymer adsorbs onto thesurface of the sand grains. This thin, dense initial layer is attached to thesurface of the sand grain by physical entrapment and surface attractions andhas little effect physical entrapment and surface attractions and has littleeffect on permeability. As polymer aggregates increase in size, some arefiltered out and attach to previously deposited polymer. The filtration rateincreases with polymer concentration, aggregate size, and attached Cr+3concentration. Porosity and permeability of the porous medium decrease asfiltration progresses, causing the zone of high flow resistance observed duringlaboratory in-situ gelation displacements.
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