Reservoir simulation

Numerical Modeling of Unstable Waterfloods and Tertiary Polymer Floods for Viscous Oils

This paper addresses the challenges in modeling highly unstable waterflooding, using both a conventional Darcy-type simulator and an adaptive dynamic prenetwork model, by comparing the simulated results with experimental data including saturation maps.


The saturation distribution after unstable waterflooding for highly viscous oil may have a decisive effect on the efficiency of tertiary polymer flooding, in particular because of hysteresis effects associated with oil banking. This paper addresses the challenges in modeling highly unstable waterflooding, using both a conventional Darcy-type simulator and an adaptive dynamic prenetwork model, by comparing the simulated results with experimental data including saturation maps. It also highlights the important role of relative permeability hysteresis in the tertiary recovery of viscous oils by polymer injection.


Waterflooding into viscous oils can lead to severe viscous fingering of the injected water—a well-known type of instability in porous-media flow that is intrinsically related to the viscosity contrast between the displaced fluid (oil) and the displacing fluid (water). A direct consequence of this phenomenon is a significant bypassing of the oil in place and a low recovery factor, as observed at both laboratory scale and field scale. Viscous instabilities between two immiscible ­fluids are dependent not only on the viscosity ratio but also on the capillary number and rock wettability. In particular, experimental studies have shown that the effect of viscous fingering strongly increases when the displacing fluid gets less wetting than the displaced fluid (i.e., when going from imbibition to drainage). In order to reduce or eliminate hydrodynamic instabilities, polymer flooding can be implemented as a secondary or tertiary recovery mechanism.

This work considers three waterflood and tertiary-polymer-flood experiments conducted on Bentheimer sandstone slabs with heavy oils with viscosity of approximately 2,000 and 7,000 cp, under nonwater-wet conditions. These experiments belong to a series of heavy-oil-displacement experiments whose objective was to investigate the effect on oil recovery of various parameters, such as oil viscosity, slab length, and injection pattern. Besides standard measurements of fluid production and differential pressures, an X-ray scanner was used to visualize the spatial distribution of the fluids as a function of time.

A set of three experiments is considered with different oil viscosities (7,000 and 2,000 cp) and different flow patterns (linear and quarter five-spot). A first attempt is made to reproduce qualitatively the waterflood X-ray images before breakthrough time by use of 2D high-resolution Darcy-type simulations with capillary pressure and relative permeability curves inferred from a 3D quasi­static pore-network model. A second attempt uses an adaptive dynamic pore-network model that is based on a 2D pore network constructed from the statistics of the 3D network. Finally, a simultaneous history matching of the tertiary polymer floods is conducted with a Darcy-type simulation model initialized at the end of the waterflood. Results show that relative permeability hysteresis during oil banking allows a rapid propagation of the oil bank while the high incremental oil recovery at the end of polymer injection is mostly because of the favorable mobility ratio.

The comparison of X-ray data and simulated saturation maps (Fig. 1), consistent with previous observations, shows that the characteristics of the oil bank (saturation, velocity) are reproduced better by the hysteresis model. The propagation of the polymer front is quite well-predicted by both models, although the irregular shape is not reproduced. When subtracting the X-ray image at the end of waterflooding from the X-ray images acquired during polymer flooding, it is clear that a significant amount of oil is driven into previously established water channels. In the simulation model that does not account for hysteresis, oil invasion into water channels is clearly overestimated, notably before the arrival of the oil bank, and the oil-bank saturation is almost uniform. With the hysteresis model, oil invasion remains limited and the memory effects observed experimentally are reproduced qualitatively. However, the saturation contrasts along previously established water channels after propagation of the oil bank are not captured correctly.

Fig. 1—Simulated oil-saturation maps without hysteresis (a) and with hysteresis (b) and experimental X-ray oil-saturation maps (c). PVI=pore volumes injected.


By simply reducing the water mobility during oil banking, the hysteresis model allows the rapid propagation of the oil bank observed experimentally and accounts reasonably well for the oil in­vasion into previously established water channels. Hysteresis has a strong effect on the oil-recovery profile, notably in terms of breakthrough time for the oil bank. However, it should be noted that the incremental oil recovery after polymer breakthrough and stabilization of the water cut, reaching approximately 40% of the original oil in place in both cases, is mostly governed by the mobility ratio and the shape of the relative permeability curves close to residual oil saturation.

The numerical modeling of the unstable waterfloods was first attempted with a conventional Darcy-type simulator, using capillary pressure and relative permeability curves inferred from a 3D quasistatic pore-network model. On the basis of realistic hypotheses concerning the system wettability, a screening study was performed to generate a large set of relative permeability and oil/water capillary pressure curves that were all tested against experimental data by running 2D high-resolution Darcy-type simulations. Those were initialized using an early-time X-ray image, thus imposing a strongly favorable perturbation to trigger the viscous fingers. Nevertheless, none of the tested relative permeability and oil/water capillary pressure functions could match the measured water­flood data; in particular, the water-breakthrough time was strongly overestimated and the dendritic structure of the viscous fingers observed qualitatively in the X-ray images was not reproduced. Several hypotheses can be formulated to explain the failure of the multiphase extension of Darcy’s law in the present case, the most convincing one being a violation of the continuum and local capillary equilibrium assumptions upon which the concept of a representative elementary volume for the definition of relative permeability and oil/water capillary pressure functions is based.

In a second attempt, the unstable-waterflood experiments were simulated with an adaptive dynamic pore-network model code on a representative 2D pore network. In order to simulate the full-scale geometry efficiently, the algorithm adaptively chooses regions that require a fully dynamic treatment, while treating other regions as quasistatic. The simulated saturation maps were found to be in very good qualitative agreement with the experimental data, although water-breakthrough times were still overestimated. This mismatch can be attributed to the limitations of 2D modeling in the sense that, by allowing an additional dimension for the propagation of viscous fingers, 3D modeling should lead to faster water breakthrough. If the limitations of the continuum Darcy-type formulation might be overcome by the use of an adaptive pore-network model, further improvements of the computational performance are still required to tackle realistic 3D networks within reasonable computation time.

The history matching of the tertiary polymer floods was conducted from the end of the waterfloods; however, here, only the two experiments with identical oil viscosity but different flow patterns were considered. In both experiments, the mobility ratio was improved significantly, leading to a quasistable polymer front. The conventional polymer-flood model based on a simple generalization of Darcy’s law was applied to verify whether a multiexperiment history match could be obtained. The first history-matching strategy was simply based on the unsteady-state relative permeabilities inferred from a 1D interpretation of the waterflood experiment conducted in a linear-flow configuration. The second strategy used the same set of relative permeabilities for increasing water saturations, but hysteresis scanning curves were added to the water relative permeability to account for a reduction of water mobility during oil banking.

As indicated by the history-matching results, the oil-bank characteristics can be reproduced correctly only by the hysteresis model. In this case, the overall agreement with production and pressure data is quite good, although certain aspects are not reproduced correctly, such as the strong effect of chase water fingering in the long-slab experiment. The agreement with X-ray data is qualitatively acceptable in terms of average front positions; however, certain features are not captured well, such as the irregular shape of the polymer front or the saturation contrasts along previously established water channels after propagation of the oil bank. Nevertheless, it is quite remarkable that a simultaneous history match of this quality could be obtained with only a small number of tuning parameters (four in total). The authors suggest that a more-advanced hysteresis model (e.g., accounting for a dependency upon local capillary number), or inclusion of oil relative permeability hysteresis, could be used to improve the match.

This history-matching exercise has shown that the proposed hysteresis model is quite robust with respect to flow pattern—here, linear vs. quarter five-spot—which represents a novel contribution compared with previous work. As suggested by this laboratory-scale study, the hysteresis phenomenon associated with oil banking may have a strong effect on the breakthrough time of the oil bank. Such a phenomenon is likely to play an important role at larger scales, and the interaction with heterogeneities also could be investigated by 3D sector-model simulations with different permeability distributions. Further work is required to investigate the effect of the fluid distribution after unstable waterflooding on the performance of tertiary polymer flooding.

This article, written by Special Publications Editor Adam Wilson, contains highlights of paper SPE 182638, “Numerical Modeling of Unstable Waterfloods and Tertiary Polymer Floods For Highly Viscous Oils,” by R. de Loubens, SPE, G. Vaillant, M. Regaieg, J. Yang, A. Moncorgé, SPE, C. Fabbri, and G. Darche, SPE, Total, prepared for the 2017 SPE Reservoir Simulation Conference, Montgomery, Texas, USA, 20–22 February. The paper has not been peer reviewed.