Direct simulation of pore-scale two-phase visco-capillary flow on large digital rock images using a phase-field lattice Boltzmann method on general-purpose graphics processing units

Alpak, Faruk O.; Zacharoudiou, Ioannis; Berg, Steffen; Dietderich, Jesse; Saxena, Nishank

doi:10.1007/s10596-019-9818-0

Cited by 40 publications

(17 citation statements)

References 87 publications

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“…The method was also shown to correctly predict fluid connectivity in imbibition in Gildehauser sandstone and simulate relative permeability data in close agreement with results from Darcy-scale core flooding experiments (Alpak et al, 2018). Further validation of the method investigating snap-off in constricted capillary tubes, Haines jumps, and capillary desaturation on real-rock systems is reported in (Alpak et al, 2019).…”

Section: Discussionsupporting

confidence: 52%

“…The hydrodynamic equations of motion, continuity (7), Navier-Stokes (8), and convection diffusion equation (9) can be obtained by performing a Chapman-Enskog expansion (Luo, 2000) on the discretized Boltzmann equations (Equation A4), while the following restrictions have to be imposed on the distribution functions: Finally, we would like to point out that the free energy lattice Boltzmann method is capable of handling high-viscosity ratios up to 10 3 . For validation of the numerical method we refer the reader to the work reported in Zacharoudiou and Boek (2016), Zacharoudiou et al (2017), and Alpak et al (2019). This covers the dynamics of capillary filling, demonstrating that the method can capture the correct dynamics of imbibition in the limits of short and long time scales (different regimes for the imbibition length vs. time), as well as for varying viscosity ratio (we considered viscosity ratios M = nw / w in the range 10 −3 ≤ M ≤ 1) (Zacharoudiou & Boek, 2016).…”

Section: Discussionmentioning

confidence: 99%

“…the diffusive term M ∇ 2 in the convection-diffusion Equation 9 can be written as D∇ 2 with D = M (a + 3b 2 eq ) the diffusion coefficient. We note here that it is also possible to define the mobility coefficient M to be a function of the order parameter in such a way that is restricting diffusion to the vicinity of fluid-fluid interfaces (Alpak et al, 2019).…”

Section: Appendix A: Lattice Boltzmann Methodsmentioning

confidence: 99%

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Pore‐Scale Modeling of Drainage Displacement Patterns in Association With Geological Sequestration of CO₂

Zacharoudiou

Boek

Crawshaw

2020

Water Resources Research

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We investigate the immiscible displacement (drainage) of a wetting fluid in a porous medium by a nonwetting fluid using multi-graphics processing unit (GPU) lattice Boltzmann simulations with the aim of better understanding the pore-scale processes involved in the geological sequestration of CO 2. Correctly resolving the dynamics involved in multiphase flow in permeable media is of paramount importance for any numerical scheme. Generally, the average fluid flow is assumed to be at low Reynolds numbers Re av. Hence, by neglecting inertial effects, this immiscible displacement should be characterized by just two dimensionless numbers, namely, the capillary number Ca av and the viscosity ratio, which quantify the ratio of the relevant forces, that is, the viscous and capillary forces. Our investigation reveals that inertial effects cannot be neglected in the range of typical capillary numbers associated with multiphase flow in permeable media. Even as the average Ca av and Re av decrease away from the injection point, inertial effects remain important over a transient amount of time during abrupt Haines jumps, when the nonwetting phase passes from a narrow restriction to a wider pore space. The local Re l at the jump sites is orders of magnitude higher than the average Re av , with the local dynamics being decoupled from the externally imposed flow rate. Therefore, a full Navier-Stokes solver should be used for investigating pore-scale displacement processes. Using the Ohnesorge number to restrict the parameter selection process is essential, as this dimensionless number links Ca av and Re av and reflects the thermophysical properties of a given system under investigation.

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Section: Discussionsupporting

confidence: 52%

Section: Discussionmentioning

confidence: 99%

Section: Appendix A: Lattice Boltzmann Methodsmentioning

confidence: 99%

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Pore‐Scale Modeling of Drainage Displacement Patterns in Association With Geological Sequestration of CO₂

Zacharoudiou

Boek

Crawshaw

2020

Water Resources Research

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“…It is likely that the front morphology becomes less sensitive to interstitial velocity distributions (which have a finger lengthening effect) and more impacted by the capillary entry pressure distributions (which has a front smoothening effect due to its spatial homogeneity) as the subpore-scale surface roughness disorder increases. An exact explanation of why surface roughness reduces capillary fingering at low capillary numbers requires further visualization of the pressure and interstitial velocity fields through direct numerical modeling (Alpak et al, 2019). Overall, we can conclude that at low capillary numbers, the role of global bypass trapping begins to diminish when Ω > 6%.…”

Section: 1029/2019wr025170mentioning

confidence: 73%

Capillary Trapping Following Imbibition in Porous Media: Microfluidic Quantification of the Impact of Pore‐Scale Surface Roughness

Mehmani¹,

Kelly

Torres‐Verdín³

et al. 2019

Water Resources Research

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Due to diagenesis, pores in subsurface rocks such as sandstones exhibit varying degrees of surface roughness in the forms of authigenic cement coatings and mineral dissolution. Previous work describing capillary trapping in porous media has primarily focused on pore‐space geometry, wettability, and fluid viscosity contrast, while acknowledging, but not quantifying, the potential impact of surface roughness. We introduce a method to implement surface roughness with controlled variation of hillock density and heights into glass microfluidic chips and investigate surface roughness impacts on gas trapping following imbibition of water into air. We demonstrate that surface roughness with hillock height‐to‐pore‐depth ratios (herein called Ω) less than a media‐dependent threshold (Ω = 6%–10% in the micromodels) does not promote nonwetting phase (gas) trapping. By contrast, rougher micromodels with Ω values larger than the aforementioned roughness threshold show a dramatic increase in the saturation of trapped gas (gas saturation values up to 64%) due to an observed change in imbibition dynamics from binary filling to pendular‐ring formation within pore throats as well as capillary pinning within pore bodies. Furthermore, when the micromodel intermediate capillary number results are compared to Land's model, only the roughest microfluidics chips (Ω > 10%) fall within the literature‐described values of the characteristic trapping constant, C, implying that surface roughness is also a key gas trapping control, independent of or in addition to pore‐space geometry and wettability. An a priori menisci stability criterion and a heuristic explanation based on local contact angle variations are proposed to explain surface roughness‐induced trapping.

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“…Pore scale experiments (DiCarlo et al, 2003;Moebius and Or, 2012;Berg et al, 2013Berg et al, , 2014Armstrong et al, 2014a;Reynolds et al, 2017;Lin Q. et al, 2018;Lin et al, 2019a) and numerical simulations (Lenormand et al, 1983;Raeini et al, 2014;Armstrong et al, 2015;Guédon et al, 2017;Alpak et al, 2019;Berg C. F. et al, 2020;Winkler et al, 2020) also exhibit fluctuations in pressure and saturation (Ramstad and Hansen, 2006;Pak et al, 2015), which are caused by pore scale displacement events, such as Haines jumps and coalescence (Rücker et al, 2015b), where the non-wetting phase replaces the wetting phase and snap-off and pistonlike displacement (Lenormand et al, 1983;Dixit et al, 1998), where the wetting phase replaces the non-wetting phase. These events lead to interruption and rearrangement of the connected pathways the respective phases flow through (Tuller and Or, 2001) and are described by a rigorous theoretical framework of pore-scale thermodynamics (Morrow, 1970).…”

Section: Introductionmentioning

confidence: 99%

The Origin of Non-thermal Fluctuations in Multiphase Flow in Porous Media

et al. 2021

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Core flooding experiments to determine multiphase flow in properties of rock such as relative permeability can show significant fluctuations in terms of pressure, saturation, and electrical conductivity. That is typically not considered in the Darcy scale interpretation but treated as noise. However, in recent years, flow regimes that exhibit spatio-temporal variations in pore scale occupancy related to fluid phase pressure changes have been identified. They are associated with topological changes in the fluid configurations caused by pore-scale instabilities such as snap-off. The common understanding of Darcy-scale flow regimes is that pore-scale phenomena and their signature should have averaged out at the scale of representative elementary volumes (REV) and above. In this work, it is demonstrated that pressure fluctuations observed in centimeter-scale experiments commonly considered Darcy-scale at fractional flow conditions, where wetting and non-wetting phases are co-injected into porous rock at small (<10−6) capillary numbers are ultimately caused by pore-scale processes, but there is also a Darcy-scale fractional flow theory aspect. We compare fluctuations in fractional flow experiments conducted on samples of few centimeters size with respective experiments and in-situ micro-CT imaging at pore-scale resolution using synchrotron-based X-ray computed micro-tomography. On that basis we can establish a systematic causality from pore to Darcy scale. At the pore scale, dynamic imaging allows to directly observe the associated breakup and coalescence processes of non-wetting phase clusters, which follow “trajectories” in a “phase diagram” defined by fractional flow and capillary number and can be used to categorize flow regimes. Connected pathway flow would be represented by a fixed point, whereas processes such as ganglion dynamics follow trajectories but are still overall capillary-dominated. That suggests that the origin of the pressure fluctuations observed in centimeter-sized fractional flow experiments are capillary effects. The energy scale of the pressure fluctuations corresponds to 105-106 times the thermal energy scale. This means the fluctuations are non-thermal. At the centimeter scale, there are non-monotonic and even oscillatory solutions permissible by the fractional flow theory, which allow the fluctuations to be visible and—depending on exact conditions—significant at centimeter scale, within the viscous limit of classical (Darcy scale) fractional flow theory. That also means that the phenomenon involves both capillary aspects from the pore or cluster scale and viscous aspects of fractional flow and occurs right at the transition, where the physical description concept changes from pore to Darcy scale.

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Direct simulation of pore-scale two-phase visco-capillary flow on large digital rock images using a phase-field lattice Boltzmann method on general-purpose graphics processing units

Cited by 40 publications

References 87 publications

Pore‐Scale Modeling of Drainage Displacement Patterns in Association With Geological Sequestration of CO₂

Pore‐Scale Modeling of Drainage Displacement Patterns in Association With Geological Sequestration of CO₂

Capillary Trapping Following Imbibition in Porous Media: Microfluidic Quantification of the Impact of Pore‐Scale Surface Roughness

The Origin of Non-thermal Fluctuations in Multiphase Flow in Porous Media

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Direct simulation of pore-scale two-phase visco-capillary flow on large digital rock images using a phase-field lattice Boltzmann method on general-purpose graphics processing units

Cited by 40 publications

References 87 publications

Pore‐Scale Modeling of Drainage Displacement Patterns in Association With Geological Sequestration of CO2

Pore‐Scale Modeling of Drainage Displacement Patterns in Association With Geological Sequestration of CO2

Capillary Trapping Following Imbibition in Porous Media: Microfluidic Quantification of the Impact of Pore‐Scale Surface Roughness

The Origin of Non-thermal Fluctuations in Multiphase Flow in Porous Media

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Pore‐Scale Modeling of Drainage Displacement Patterns in Association With Geological Sequestration of CO₂

Pore‐Scale Modeling of Drainage Displacement Patterns in Association With Geological Sequestration of CO₂