Novel viscoelastic model for predicting the synthetic polymer’s viscoelastic behavior in porous media using direct extensional rheological measurements

Abstract

High molecular weight, flexible polymers used for heavy oil recovery exhibits viscoelasticity that causes the thickening of apparent viscosity which could not be predicted by the conventional shear thinning rheological models. Unified apparent viscosity model (UVM) developed at UT-Austin based on the postulation that the apparent viscosity of polymer solutions is the sum of shear and elongational viscosity accounts for the viscoelastic thickening in the extensional part through relaxation time, maximum elongational viscosity and strain hardening index. Although UVM addresses the other limitation of the previous viscoelastic models, its dependence on the core flood data to predict maximum elongational viscosity and strain hardening index limits its commercial independent usage for preliminary screening.These limitations are addressed in our novel viscoelastic model named as Azad Trivedi Viscoelastic Model (AT-VEM), which could predict the apparent viscosity in the shear thickening region using the extensional parameters measured by capillary breakup extensional rheometer (CaBER) through the combination of Upper Convected Maxwell (UCM), finite extensible nonlinear elasticity (FENE) and power law theories. CaBER set up uses a step-strain to stretch the drop of polymeric liquid placed between the two plates and monitor its midpoint diameter during filament drainage. The relaxation time is determined by fitting the filament diameter from the region representing the balance between the elastic stress and surface tension into UCM. As per FENE theory, fluid relaxes at the rate two-third of its strain rate and the extensional viscosity around the critical Deborah number of 0.66 corresponds to the maximum elastic limit and would be the maximum elongational viscosity. Filament during drainage gets strained and the corresponding increment in extensional viscosity is fitted with power law to determine the strain hardening index.A series of core flood data (performed using partially hydrolyzed polyacrylamide (HPAM) polymers) from the UT-Austin that validated the UVM model was used extensively. Other reported literature data were also used. Extensional rheology was performed on those polymers at the similar conditions to determine the relaxation time, maximum elongational viscosity, and strain hardening index. These parameters along with the shear parameters were used to match the reported apparent viscosity. All the experiments fairly match well with the average downscaling power factor of 0.35 to the maximum elongational viscosity and subtrahend of 1.2 to the strain hardening index. Downscaling and subtrahend factor is essential to scale down the pure elongation in the extensional bulk field to the combination of shear and elongation experienced in the porous media.AT-VEM can be incorporated into commercial numerical simulators for predicting the injectivity and recovery due to viscoelastic thickening independently and thereby assist in quick screening polymers for oil recovery applications.