Viscous fingering in porous media occurs when the (miscible or immiscible) displacing fluid has a lower viscosity than the displaced fluid. For example, immiscible fingering is observed in experiments where water displaces a much more viscous oil. Modelling the observed fingering patterns in immiscible viscous fingering has proven to be very challenging, which has often been identified as being due to numerical issues. However, in a recent paper (Sorbie et al. in Transp. Porous Media 133:331–359, 2020) suggested that the modelling issues are more closely related to the physics and formulation of the problem. They proposed an approach based on the fractional flow curve, $${f}_{w}^{*}$$f w ∗ , as the principal input, and then derived relative permeabilities which give the maximum total mobility. Sorbie et al. were then able to produce complex, well-resolves immiscible finger patterns using elementary numerical methods. In this paper, this new approach to modelling immiscible viscous fingering is tested by performing direct numerical simulations of previously published experimental water/oil displacements in 2D sandstone porous media. Experiments were modelled at adverse viscosity ratios ( $${\mu }_{o}/{\mu }_{w}$$μ o / μ w ), with oil viscosities ranging from μ_o = 412 to 7000 cP, i.e. for a viscosity ratio range, ( $${\mu }_{o}/{\mu }_{w}$$μ o / μ w ) $$\sim$$∼ 400–7000. These experiments have extensive production data as well as in situ 2D immiscible fingering images, measured by X-ray scanning. In all cases, very good quantitative agreement between experiment and modelling results is found, providing a strong validation of the new modelling approach. The underlying parameters used in the modelling of these unstable immiscible floods, the $${f}_{w}^{*}$$f w ∗ functions, show very consistent and understandable variation with the viscosity ratio, ( $${\mu }_{o}/{\mu }_{w}$$μ o / μ w ).

Several experimental studies have shown significant improvement in heavy oil recovery with polymers displaying different types of rheology, and the effect of rheology has been shown to be important. These experimental studies have been designed to investigate why this is so by applying a constant flow rate and the same polymer effective viscosity at this injection rate. The types of rheology studied vary from Newtonian and shear thinning behavior to complex rheology involving shear thinning and thickening behavior. The core flood experiments show a significantly higher oil recovery with polyacrylamide (HPAM), which exhibits shear thinning/thickening behavior compared to biopolymers like Xanthan, which is purely shear thinning. Various reasons for these observed oil recovery results have been conjectured, but, to date, a clear explanation has not been conclusively established. In this paper, we have investigated the theoretical rationale for these results by using a dynamic pore scale network model (DPNM), which can model imbibition processes (water injection) in porous media and also polymer injection. In the DPNM, the polymer rheology can be shear thinning, shear thinning/thickening, or Newtonian (constant viscosity). Thus, the local effective viscosity in a pore within the DPNM depends on the local shear rate in that pore. The predicted results using this DPNM show that the polymer causes changes in the local flow velocity field, which, as might be expected, are different for different rheological models, and the changes in the velocity profile led to local diversion of flow. This, in turn, led to different oil recovery levels in imbibition. However, the critical result is that the DPNM modelling shows exactly the same trend as was observed in the experiments, viz. that the shear thinning/thickening polymer gave the highest oil recovery, followed by the Newtonian Case and the purely shear thinning polymer gave the lowest recover, but this latter case was still above the waterflood result. The DPNM simulations showed that the shear-thinning/thickening polymer show a stabilized frontal velocity and increased oil mobilization, as observed in the experiments. Simulations for the shear-thinning polymer show that, in high-rate bonds, the average viscosity is greatly reduced, and this causes enhanced water fingering compared to the Newtonian polymer case. No other a priori model of the two-phase fluid physics of imbibition, coupled with the polymer rheology, has achieved this degree of predictive explanation, of these experimental observations, to our knowledge.