Immiscible Viscous Fingering: Modelling Unstable Water–Oil Displacement Experiments in Porous Media

Salmo, Iselin Cecilie; Sorbie, Kenneth Stuart; Skauge, Arne; Alzaabi, Mohamed Adel

doi:10.1007/s11242-022-01847-8

Cited by 19 publications

(24 citation statements)

References 56 publications

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“…As shown here, and discussed previously in Salmo et al (2022) [ 15 ], going from the lowest to highest oil viscosity, then clearly the viscosity ratio, (µ o /µ w ), and the (conventional end-point) mobility ratio, M , both increase. This is actually anti-correlated with the value of the local mobility ratio M(S wf ) at the shock front, where S w = S wf (see Table 1 ).…”

Section: Discussionsupporting

confidence: 87%

“…In this work, the 2D simulation grid is generated with a dimensionless correlation length (

) of 0.03 with 500 × 500 grid cells. This was established in previous work for the water displacements [ 15 ]. The base case simulation permeability field is shown in Figure 1 .…”

Section: Methodsmentioning

confidence: 87%

“…Permeability distribution ranges from 0.01 to 10 D with an average of ~3 D. The effect of this permeability range of (k max /k min ) is examined below. Sensitivities to grid resolution and correlation length have been previously presented, and as such are not repeated here [ 15 , 16 , 31 ].…”

Section: Methodsmentioning

confidence: 99%

“…The classical review of viscous fingering by Homsy (1987) [ 13 ] has recently been updated by Pinilla et al (2021) [ 14 ]. Additionally, a recent review of viscous fingering relating more closely to the present work is given in Salmo et al, (2022) [ 15 ]. This review shows that many of the methodologies put forward in the literature are either unable to reproduce all aspects of the fingering process at a range of length scales (i.e., oil/water production, pressure drop and finger patterns) or are not compared directly against experiments for full validation.…”

Section: Introductionmentioning

confidence: 99%

“…In the current paper the new simulation methodology presented by Sorbie et al (2020) [ 16 ] is applied to a series of unstable immiscible displacement experiments from the literature [ 25 , 26 ] where a viscous oil (µ o = 412 mPa.s–7000 mPa.s) is displaced first by water (µ w = 0.9 mPa.s–1.0 mPa.s) then by a water phase viscosified by the addition of a hydrolysed polyacrylamide, HPAM (µ p = 18 mPa.s–60 mPa.s). A previous paper applied our approach to the viscous unstable waterfloods in these experiments [ 15 ], and here this work is extended to the modelling of the tertiary polymer flooding (i.e., polymer injection following some period of water injection). Using this approach, we show in this paper that all stages of these experiments are captured (oil recovery, water cut, and pressure drop vs. PV injected), including representative finger patterns.…”

Section: Introductionmentioning

confidence: 99%

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Immiscible Viscous Fingering: The Simulation of Tertiary Polymer Displacements of Viscous Oils in 2D Slab Floods

Beteta

Skauge

2022

Polymers

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Immiscible viscous fingering in porous media occurs when a high viscosity fluid is displaced by an immiscible low viscosity fluid. This paper extends a recent development in the modelling of immiscible viscous fingering to directly simulate experimental floods where the viscosity of the aqueous displacing fluid was increased (by the addition of aqueous polymer) after a period of low viscosity water injection. This is referred to as tertiary polymer flooding, and the objective of this process is to increase the displacement of oil from the system. Experimental results from the literature showed the very surprising observation that the tertiary injection of a modest polymer viscosity could give astonishingly high incremental oil recoveries (IR) of ≥100% even for viscous oils of 7000 mPa.s. This work seeks to both explain and predict these results using recent modelling developments. For the 4 cases (µo/µw of 474 to 7000) simulated in this paper, finger patterns are in line with those observed using X-ray imaging of the sandstone slab floods. In particular, the formation of an oil bank on tertiary polymer injection is very well reproduced and the incremental oil response and water cut drops induced by the polymer are very well predicted. The simulations strongly support our earlier claim that this increase in incremental oil displacement cannot be explained solely by a viscous “extended Buckley-Leverett” (BL) linear displacement effect; referred to in the literature simply as “mobility control”. This large response is the combination of this effect (BL) along with a viscous crossflow (VX) mechanism, with the latter VX effect being the major contributor to the recovery mechanism.

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Section: Discussionsupporting

confidence: 87%

“…In this work, the 2D simulation grid is generated with a dimensionless correlation length (

) of 0.03 with 500 × 500 grid cells. This was established in previous work for the water displacements [ 15 ]. The base case simulation permeability field is shown in Figure 1 .…”

Section: Methodsmentioning

confidence: 87%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Immiscible Viscous Fingering: The Simulation of Tertiary Polymer Displacements of Viscous Oils in 2D Slab Floods

Beteta

Skauge

2022

Polymers

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The Role of Immiscible Fingering on the Mechanism of Secondary and Tertiary Polymer Flooding of Viscous Oil

et al. 2022

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Immiscible viscous fingering in porous media occurs when a low viscosity fluid displaces a significantly more viscous, immiscible resident fluid; for example, the displacement of a higher viscosity oil with water (where μo > > μw). Classically, this is a significant issue during oil recovery processes, where water is injected into the reservoir to provide pressure support and to drive the oil production. In moderate/heavy oil, this leads to the formation of strong water fingers, bypassed oil and high/early water production. Polymer flooding, where the injected water is viscosified through addition of high molecular weight polymers, has often been applied to reduce the viscosity contrast between the two immiscible fluids. In recent years, there has been significant development in the understanding of both the mechanism by which polymer flooding improves viscous oil recovery, as well as in the methodologies available to directly simulate such processes. One key advance in modelling the correct mechanism of polymer oil recovery in viscous oils has been the development of a method to accurately model the “simple” two-phase immiscible fingering (Sorbie in Transp Porous Media 135:331–359, 2020). This was achieved by first choosing the correct fractional flow and then deriving the maximum mobility relative permeability functions from this. It has been proposed that central to the polymer oil recovery is a fingering/viscous crossflow mechanism, and a summary of this is given in this paper. This work seeks to validate the proposed immiscible fingering/viscous crossflow mechanism experimentally for a moderately viscous oil (μo = 84 mPa.s at 31 °C; μw = 0.81 mPa.s; thus, (μo/μw) ~ 104) by performing a series of carefully monitored core floods. The results from these experiments are simulated directly to establish the potential of our modified simulation approach to capture the process (Sorbie, et al., 2020). Both secondary and tertiary polymer flooding experiments are presented and compared with the waterflood baselines, which have been established for each core system. The oil production, water cut and differential pressure are then matched directly using a commercial numerical reservoir simulator, but using our new “fractional flow” derived relative permeabilities. The use of polymer flooding, even when applied at a high water cut (80% after 0.5 PV of water injection), showed a significant impact on recovery; bringing the recovery significantly forward in time for both tertiary and secondary polymer injection modes—a further 13–16% OOIP. Each flood was then directly matched in the simulator with excellent agreement in all experimental cases. The simulations allowed a quantitative visualisation of the immiscible finger propagation from both water injection and the banking of connate water during polymer flooding. Evidence of a strong oil bank forming in front of the tertiary polymer slug was also observed, in line with the proposed viscous crossflow mechanism. This work provides validation of both polymer flooding’s viscous crossflow mechanism and the direct simulation methodology proposed by Sorbie et al. (Transp Porous Media 135:331–359, 2020). The experimental results show the significant potential for both secondary and tertiary polymer flooding in moderate/heavy oil reservoirs.

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Immiscible Viscous Fingering: The Effects of Wettability/Capillarity and Scaling

Beteta,

Sorbie,

Skauge

et al. 2023

Transp Porous Med

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Realistic immiscible viscous fingering, showing all of the complex finger structure observed in experiments, has proven to be very difficult to model using direct numerical simulation based on the two-phase flow equations in porous media. Recently, a method was proposed by the authors to solve the viscous-dominated immiscible fingering problem numerically. This method gave realistic complex immiscible fingering patterns and showed very good agreement with a set of viscous unstable 2D water → oil displacement experiments. In addition, the method also gave a very good prediction of the response of the system to tertiary polymer injection. In this paper, we extend our previous work by considering the effect of wettability/capillarity on immiscible viscous fingering, e.g. in a water → oil displacements where viscosity ratio $$\left( {\mu_{{\text{o}}} /\mu_{{\text{w}}} } \right) \gg 1$$ μ o / μ w ≫ 1 . We identify particular wetting states with the form of the corresponding capillary pressure used to simulate that system. It has long been known that the broad effect of capillarity is to act like a nonlinear diffusion term in the two-phase flow equations, denoted here as $$D(S_{w} )$$ D ( S w ) . Therefore, the addition of capillary pressure, $$P_{c} (S_{w} )$$ P c ( S w ) , into the equations acts as a damping or stabilisation term on viscous fingering, where it is the derivative of this quantity that is important, i.e. $$D(S_{w} )\sim\left( {dP_{c} (S_{w} )/dS_{w} } \right)$$ D ( S w ) ∼ d P c ( S w ) / d S w . If this capillary effect is sufficiently large, then we expect that the viscous fingering to be completely damped, and linear stability theory has supported this view. However, no convincing numerical simulations have been presented showing this effect clearly for systems of different wettability, due to the problem of simulating realistic immiscible fingering in the first place (i.e. for the viscous-dominated case where $$P_{c} = 0$$ P c = 0 ). Since we already have a good method for numerically generating complex realistic immiscible fingering for the $$P_{c} = 0$$ P c = 0 case, we are able for the first time to present a study examining both the viscous-dominated limit and the gradual change in the viscous/capillary force balance. This force balance also depends on the physical size of the system as well as on the length scale of the capillary damping. To address these issues, scaling theory is applied, using the classical approach of Rapport (1955), to study this scaling in a systematic manner. In this paper, we show that the effect of wettability/capillarity on immiscible viscous fingering is somewhat more complex and interesting than the (broadly correct) qualitative description above. From a “lab-scale” base case 2D water → oil displacement showing clear immiscible viscous fingering which we have already matched very well using our numerical method, we examine the effects of introducing either a water wet (WW) or an oil wet (OW) capillary pressure, of different “magnitudes”. The characteristics of these two cases (WW and OW) are important in how the value of corresponding $$D(S_{w} )$$ D ( S w ) functions, relate to the (Buckley–Leverett) shock front saturation, $$S_{wf}$$ S wf , of the viscous-dominated ($$P_{c} = 0$$ P c = 0 ) case. By analysing this, and carrying out some confirming calculations, we show clearly why we expect to see much clearer immiscible fingering at the lab scale in oil wet rather than in water wet systems. Indeed, we demonstrate why it is very difficult to see immiscible fingering in WW lab systems. From this finding, one might conclude that since no fingering is observed for the WW lab-scale case, then none would be expected at the larger “field” scale. However, by invoking scaling theory—specifically the viscous/capillary scaling group, $$C_{{{\text{VC1}}}}$$ C VC1 , (and a corresponding “shape group”, $$C_{{{\text{S}}1}}$$ C S 1 ), we demonstrate very clearly that, although the WW viscous fingers do not usually appear at the lab scale, they emerge very distinctly as we “inflate” the system in size in a systematic manner. In contrast, we demonstrate exactly why it is much more likely to observe viscous fingering for the OW (or weakly wetting) case at the lab scale. Finally, to confirm our analysis of the WW and OW immiscible fingering conclusions at the lab scale, we present two experiments in a lab-scale bead pack where $$\left( {\mu_{{\text{o}}} /\mu_{{\text{w}}} } \right) = 100$$ μ o / μ w = 100 ; no fingering is seen in the WW case, whereas clear developed immiscible fingering is observed in the OW case.

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Immiscible Viscous Fingering: Modelling Unstable Water–Oil Displacement Experiments in Porous Media

Cited by 19 publications

References 56 publications

Immiscible Viscous Fingering: The Simulation of Tertiary Polymer Displacements of Viscous Oils in 2D Slab Floods

Immiscible Viscous Fingering: The Simulation of Tertiary Polymer Displacements of Viscous Oils in 2D Slab Floods

The Role of Immiscible Fingering on the Mechanism of Secondary and Tertiary Polymer Flooding of Viscous Oil

Immiscible Viscous Fingering: The Effects of Wettability/Capillarity and Scaling

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