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

Beteta, Alan; Skauge, Arne

doi:10.3390/polym14194159

Cited by 11 publications

(10 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Tchelepi, 2006a and2006b;Erandi et al, 2015;Mostaghimi et al, 2016;Adam et al, 2017;Hamid and Muggeridge, 2018;Kampitsis et al, 2019Kampitsis et al, , 2020 or more conventional numerical approaches (Berg and Ott, 2012;de Loubens et al, 2018;Bakharev et al, 2020;Chaudhuri and Vishnudas, 2018). It is in this area that the current work is located, and follows some previous papers from the authors where direct numerical simulation does lead to very detailed fingers which agrees well with experiment (Sorbie, et al, 2020;Salmo, et al, 2022;Beteta et al, 2022a).…”

Section: Viscous Fingering (Vf) Literaturesupporting

confidence: 71%

“…Unstable waterfloods (and tertiary polymer floods) were performed on 2D slabs of Bentheimer sandstone, and the full dataset of oil recovery, watercut and pressure drop profiles and in situ x-ray images of the finger patterns (all vs. PV injected) were reported. In our previous work, all of this data was used to test our simulation methodology (Sorbie, et al, 2020) to model immiscible viscous fingering with oil/water viscosity ratios over the range, (o/w) ~ 400 to 7000 (Salmo, et al, 2022;Beteta et al, 2022a). The agreement between the experiment and direct simulations were all between very good and excellent.…”

Section: Viscous Fingering (Vf) Literaturementioning

confidence: 98%

“…The second school, to which the authors broadly subscribe, believes the problem is more likely to be with the physics and formulation of the viscous fingering problem or the algorithmic approach to the solution of the VF problem. An approach to the solution of the immiscible VF problem was proposed by the authors recently (Sorbie et al, 2020), and is described in detail in that paper and applied in subsequent work to model viscous fingering experiments in 2D slabs referred to above (Salmo et al, 2022;Beteta et al, 2022a). In brief, this approach starts from the "observed" fractional flow (denoted 𝑓 𝑤 * (𝑆 𝑤 )) as the main input to the numerical simulation.…”

Section: The Problem Of Modelling Viscous Fingering By Direct Numeric...mentioning

confidence: 99%

“…However, this only specifies a ratio of relative permeabilities, (𝑘 𝑟𝑜 /𝑘 𝑟𝑤 ), and the correct choice of these is the one that maximises the total mobility, 𝜆 𝑇 (𝑆 𝑤 ), where , 𝜆 𝑇 (𝑆 𝑤 ) = 𝜆 𝑜 (𝑆 𝑤 ) + 𝜆 𝑤 (𝑆 𝑤 ); or at least maximises 𝜆 𝑇 (𝑆 𝑤 ) within the constraints of the end point relative permeabilities. Extensive discussion of this method and its application to modelling viscous dominated 2D viscous fingering floods is given in previous publications (Sorbie et al, 2020;Salmo et al, 2022;Beteta et al, 2022a). A paper on the application of this approach to model field scale viscous fingering and the effect of polymer flooding is currently in press (Beteta et al, 2023).…”

Section: The Problem Of Modelling Viscous Fingering By Direct Numeric...mentioning

confidence: 99%

See 3 more Smart Citations

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

Beteta¹,

Sorbie²,

Skauge³

et al. 2023

Preprint

Self Cite

View full text Add to dashboard Cite

Realistic immiscible viscous fingering, showing all of the complex finger structure observed in experiments, has proved 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 displacement where viscosity ratio$\left({\mu }_{o}/{\mu }_{w}\right)$>> 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 non-linear diffusion term in the two-phase flow equations, denoted here as $D\left({S}_{w}\right)$. Therefore, the addition of capillary pressure, ${P}_{c}\left({S}_{w}\right)$, into the equations acts as a damping or stabilization term on viscous fingering, where it is the derivative of the of this quantity that is important, i.e. $D\left({S}_{w}\right)\tilde\left(d{P}_{c}\left({S}_{w}\right)/d{S}_{w}\right)$. 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 ${P}_{c}=0$). Since we already have a good method for numerically generating complex realistic immiscible fingering for the ${P}_{c}=0$ 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 2 cases (WW and OW) are important in how the value of corresponding $D\left({S}_{w}\right)$ functions, relate to the (Buckley-Leverett, BL) shock front saturation, ${S}_{wf}$, of the viscous dominated (${P}_{c}=0$) 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, ${C}_{VC1}$, (and a corresponding “shape group”, ${C}_{S1}$), 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 2 experiments in a lab scale bead pack where $\left({\mu }_{o}/{\mu }_{w}\right)$=100; no fingering is seen in the WW case whereas clear developed immiscible fingering is observed in the OW case.

show abstract

Section: Viscous Fingering (Vf) Literaturesupporting

confidence: 71%

Section: Viscous Fingering (Vf) Literaturementioning

confidence: 98%

Section: The Problem Of Modelling Viscous Fingering By Direct Numeric...mentioning

confidence: 99%

Section: The Problem Of Modelling Viscous Fingering By Direct Numeric...mentioning

confidence: 99%

See 2 more Smart Citations

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

Beteta¹,

Sorbie²,

Skauge³

et al. 2023

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…However, the underlying mechanism of all three of the above effects is viscous cross ow (VX). For the rst effect above, the role of VX in improving the areal 2D ngering is already very well established and discussed in our previous publications (Beteta et al, 2022b(Beteta et al, , 2022aSorbie et al, 2020;Sorbie & Skauge, 2019). However, the second two effects are also due to the VX mechanism, here the viscous effect operates to overcome the gravitational effect (water slumping) and cause the upward ow of injected polymer and the downward ow of oil and the subsequent recovery of the attic oil.…”

Section: Discussionmentioning

confidence: 80%

Immiscible Viscous Fingering at the Field Scale: Numerical Simulation of the Captain Polymer Flood

Beteta¹,

Sorbie²,

Johnson³

2023

Preprint

Self Cite

View full text Add to dashboard Cite

Immiscible fingering in reservoirs results from the displacement of a resident high viscosity oil by a significantly less viscous immiscible fluid, usually water. During oil recovery processes, where water is often injected for sweep improvement and pressure support, the viscosity ratio between oil and water (µo/µw) can lead to poor oil recovery due to formation of immiscible viscous fingers resulting in oil bypassing. Polymer flooding, where the injection water is viscosified by the addition of high molecular weight polymers, is designed to reduce the impact of viscous fingering by reducing the µo/µw ratio. A considerable effort has been made in the past decade to improve the mechanistic understanding of polymer flooding as well as in developing the numerical simulation methodologies required to model it reliably. Two key developments have been (i) the understanding of the viscous crossflow mechanism by which polymer flooding operates in the displacement of viscous oil; and (ii) the simulation methodology put forward by Sorbie et al. (2020), whereby immiscible fingering and viscous crossflow can be simply matched in conventional reservoir simulators. This publication extends the work ofBeteta et al. (2022) to conceptual models of a field case currently undergoing polymer flooding – the Captain field in the North Sea. The simulation methodology is essentially “upscaled” in a straightforward manner using some simple scaling assumptions. The effects of polymer viscosity and slug size are considered in a range of both 2D and 3D models designed to elucidate the role of polymer in systems both with and without “water slumping”. Slumping is governed by the density contrast between oil and water, the vertical communication of the reservoir and the fluid velocity and, when it occurs, the injection water channels along the bottom of the reservoir directly to the production well(s). It is shown that polymer flooding is very applicable to a wide range of reservoirs, with only modest injection viscosities and bank sizes return significant volumes of incremental oil. Indeed, oil incremental recoveries (IR) of between 29–89% are predicted in the simulations of the various 2D and 3D cases, depending on the slug design for both non-slumping and slumping cases. When strong water slumping is present the performance of the polymer flood is significantly more sensitive to slug design, as alongside the viscous crossflow mechanism of recovery, a further role of the polymer is introduced – sweep of the ‘attic’ oil by the viscous polymer flood, which is able to overcome the gravity driven slumping and we also identify this mechanism as a slightly different form of viscous crossflow. In slumping systems, it is critical to avoid disrupting the polymer bank before sweeping of the attic oil has been performed. However, as with the non-slumping system, modest injection viscosities and bank sizes still have a very significant impact on recovery. The conceptual models used here have been found to be qualitatively very similar to real field results. Our simulations indicate that there are few cases of viscous oil recovery where polymer flooding would not be of benefit.

show abstract

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

Beteta,

Sorbie,

Skauge

et al. 2023

Transp Porous Med

View full text Add to dashboard Cite

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.

show abstract

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

Cited by 11 publications

References 41 publications

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

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

Immiscible Viscous Fingering at the Field Scale: Numerical Simulation of the Captain Polymer Flood

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

Contact Info

Product

Resources

About