Study of Fingering Dynamics of Two Immiscible Fluids in a Homogeneous Porous Medium with Considering Wettability Effects Using a Pore-Scale Multicomponent Lattice Boltzmann Model

2021 ◽  
Author(s):  
Eslam Ezzatneshan ◽  
Reza Goharimehr
Keyword(s):  
Porous Medium ◽  
Dynamic Viscosity ◽  
Lattice Boltzmann ◽  
Capillary Number ◽  
Viscosity Ratio ◽  
Viscous Fingering ◽  
Immiscible Fluids ◽  
Pore Scale ◽  
Homogeneous Porous Medium ◽  
Wetting Fluid

In the present study, a pore-scale multicomponent lattice Boltzmann method (LBM) is employed for the investigation of the immiscible-phase fluid displacement in a homogeneous porous medium. The viscous fingering and the stable displacement regimes of the invading fluid in the medium are quantified which is beneficial for predicting flow patterns in pore-scale structures, where an experimental study is extremely difficult. Herein, the Shan-Chen (S-C) model is incorporated with an appropriate collision model for computing the interparticle interaction between the immiscible fluids and the interfacial dynamics. Firstly, the computational technique is validated by a comparison of the present results obtained for different benchmark flow problems with those reported in the literature. Then, the penetration of an invading fluid into the porous medium is studied at different flow conditions. The effect of the capillary number (Ca), dynamic viscosity ratio (M), and the surface wettability defined by the contact angle (θ) are investigated on the flow regimes and characteristics. The obtained results show that for M<1, the viscous fingering regime appears by driving the invading fluid through the pore structures due to the viscous force and capillary force. However, by increasing the dynamic viscosity ratio and the capillary number, the invading fluid penetrates even in smaller pores and the stable displacement regime occurs. By the increment of the capillary number, the pressure difference between the two sides of the porous medium increases, so that the pressure drop Δp along with the domain at θ=40∘ is more than that of computed for θ=80∘. The present study shows that the value of wetting fluid saturation Sw at θ=40∘ is larger than its value computed with θ=80∘ that is due to the more tendency of the hydrophilic medium to absorb the wetting fluid at θ=40∘. Also, it is found that the magnitude of Sw computed for both the contact angles is decreased by the increment of the viscosity ratio from Log(M)=−1 to 1. The present study demonstrates that the S-C LBM is an efficient and accurate computational method to quantitatively estimate the flow characteristics and interfacial dynamics through the porous medium.

scholarly journals Lattice Boltzmann Simulation of Immiscible Two-Phase Displacement in Two-Dimensional Berea Sandstone

2018 ◽  
Vol 8 (9) ◽  
pp. 1497 ◽  
Author(s):  
Qingqing Gu ◽  
Haihu Liu ◽  
Yonghao Zhang
Keyword(s):  
Interfacial Tension ◽  
Lattice Boltzmann ◽  
Viscosity Ratio ◽  
Immiscible Fluids ◽  
Lattice Boltzmann Model ◽  
Immiscible Fluid ◽  
Two Dimensional ◽  
Berea Sandstone ◽  
Fluid Saturation ◽  
Wetting Fluid

Understanding the dynamic displacement of immiscible fluids in porous media is important for carbon dioxide injection and storage, enhanced oil recovery, and non-aqueous phase liquid contamination of groundwater. However, the process is not well understood at the pore scale. This work therefore focuses on the effects of interfacial tension, wettability, and the viscosity ratio on displacement of one fluid by another immiscible fluid in a two-dimensional (2D) Berea sandstone using the colour gradient lattice Boltzmann model with a modified implementation of the wetting boundary condition. Through invasion of the wetting phase into the porous matrix, it is observed that the viscosity ratio plays an important role in the non-wetting phase recovery. At the viscosity ratio ( λ ) of unity, the saturation of the wetting fluid is highest, and it linearly increases with time. The displacing fluid saturation reduces drastically when λ increases to 20; however, when λ is beyond 20, the reduction becomes less significant for both imbibition and drainage. The front of the bottom fingers is finally halted at a position near the inlet as the viscosity ratio increases to 10. Increasing the interfacial tension generally results in higher saturation of the wetting fluid. Finally, the contact angle is found to have a limited effect on the efficiency of displacement in the 2D Berea sandstone.

Network models for two-phase flow in porous media Part 1. Immiscible microdisplacement of non-wetting fluids

1986 ◽  
Vol 164 ◽  
pp. 305-336 ◽  
Author(s):  
Madalena M. Dias ◽  
Alkiviades C. Payatakes
Keyword(s):  
Porous Medium ◽  
Capillary Number ◽  
Viscosity Ratio ◽  
Linear Equations ◽  
Small Time ◽  
Creeping Flow ◽  
Flow In Porous Media ◽  
Two Phase ◽  
Unit Cells ◽  
Wetting Fluid

A theoretical simulator of immiscible displacement of a non-wetting fluid by a wetting one in a random porous medium is developed. The porous medium is modelled as a network of randomly sized unit cells of the constricted-tube type. Under creeping-flow conditions the problem is reduced to a system of linear equations, the solution of which gives the instantaneous pressures at the nodes and the corresponding flowrates through the unit cells. The pattern and rate of the displacement are obtained by assuming quasi-static flow and taking small time increments. The porous medium adopted for the simulations is a sandpack with porosity 0.395 and grain sizes in the range from 74 to 148 μrn. The effects of the capillary number, Ca, and the viscosity ratio, κ = μo/μw, are studied. The results confirm the importance of the capillary number for displacement, but they also show that for moderate and high Ca values the role of κ is pivotal. When the viscosity ratio is favourable (κ < 1), the microdisplacement efficiency begins to increase rapidly with increasing capillary number for Ca > 10−5, and becomes excellent as Ca → 10−3. On the other hand, when the viscosity ratio is unfavourable (κ > 1), the microdisplacement efficiency begins to improve only for Ca values larger than, say, 5 × 10−4, and is substantially inferior to that achieved with κ < 1 and the same Ca value. In addition to the residual saturation of the non-wetting fluid, the simulator predicts the time required for the displacement, the pattern of the transition zone, the size distribution of the entrapped ganglia, and the acceptance fraction as functions of Ca, κ, and the porous-medium geometry.

The investigation of the viscous fingering phenomenon of immiscible fluids displacement by the Lattice Boltzmann method

2020 ◽  
Vol 98 (7) ◽  
pp. 650-659
Author(s):  
Peisheng Li ◽  
Chengyu Peng ◽  
Peng Du ◽  
Ying Zhang ◽  
Boheng Dong ◽  
...  
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Viscosity Ratio ◽  
Viscous Fingering ◽  
Immiscible Fluids ◽  
Lattice Boltzmann Model ◽  
Fluid Accumulation ◽  
Sweep Efficiency ◽  
Fingering Phenomena ◽  
Boltzmann Method

In this paper, the viscous fingering phenomena of two immiscible fluids with a large viscosity ratio was simulated by the Lattice Boltzmann method. The Rothman–Keller Lattice Boltzmann model was applied to study the viscous fingering phenomena in a microchannel where the high viscosity fluids were displaced by low viscosity fluids. We have investigated the influences of parameters such as viscosity ratio (M), surface wettability, capillary number (Ca), and Reynolds number (Re) on finger structures, breakthrough time (Ts), and areal sweep efficiency (Se). In particular, the effects of surface tension and large viscosity ratio on the phenomenon of fluid accumulation were intensively studied. The simulation results showed that the fluid accumulation became more obvious gradually with the increase of M, which led to more serious displacement effects. Moreover, Se increased as the contact angle increased. Besides, as the viscous fingering phenomenon weakened, the phenomenon of fluid accumulation became more evident. Furthermore, the finger pattern had a tendency to increase as the value of Ca and Re increased, and the phenomenon of fluid accumulation decreased with the decrease of Ts and Se.

Study of the Effect of Wetting on Viscous Fingering Before and After Breakthrough by Lattice Boltzmann Simulations

2021 ◽  
Author(s):  
Peter Mora ◽  
Gabriele Morra ◽  
Dave Yuen ◽  
Ruben Juanes
Keyword(s):  
Reynolds Number ◽  
Oil Recovery ◽  
Lattice Boltzmann ◽  
Capillary Number ◽  
Viscosity Ratio ◽  
Viscous Fingering ◽  
Wetting Angle ◽  
Recovery Factor ◽  
Transition To Turbulence ◽  
Two Phase

Abstract We present a suite of numerical simulations of two-phase flow through a 2D model of a porous medium using the Rothman-Keller Lattice Boltzmann Method to study the effect of viscous fingering on the recovery factor as a function of viscosity ratio and wetting angle. This suite involves simulations spanning wetting angles from non-wetting to perfectly wetting and viscosity ratios spanning from 0.01 through 100. Each simulation is initialized with a porous model that is fully saturated with a "blue" fluid, and a "red" fluid is then injected from the left. The simulation parameters are set such that the capillary number is 10, well above the threshold for viscous fingering, and with a Reynolds number of 0.2 which is well below the transition to turbulence and small enough such that inertial effects are negligible. Each simulation involves the "red" fluid being injected from the left at a constant rate such in accord with the specified capillary number and Reynolds number until the red fluid breaks through the right side of the model. As expected, the dominant effect is the viscosity ratio, with narrow tendrils (viscous fingering) occurring for small viscosity ratios with M ≪ 1, and an almost linear front occurring for viscosity ratios above unity. The wetting angle is found to have a more subtle and complicated role. For low wetting angles (highly wetting injected fluids), the finger morphology is more rounded whereas for high wetting angles, the fingers become narrow. The effect of wettability on saturation (recovery factor) is more complex than the expected increase in recovery factor as the wetting angle is decreased, with specific wetting angles at certain viscosity ratios that optimize yield. This complex phase space landscape with hills, valleys and ridges suggests the dynamics of flow has a complex relationship with the geometry of the medium and hydrodynamical parameters, and hence recovery factors. This kind of behavior potentially has immense significance to Enhanced Oil Recovery (EOR). For the case of low viscosity ratio, the flow after breakthrough is localized mainly through narrow fingers but these evolve and broaden and the saturation continues to increase albeit at a reduced rate. For this reason, the recovery factor continues to increase after breakthrough and approaches over 90% after 10 times the breakthrough time.

scholarly journals Modeling Immiscible Fluid Displacement in a Porous Medium Using Lattice Boltzmann Method

Fluids ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 89
Author(s):  
Magzhan Atykhan ◽  
Bagdagul Kabdenova (Dauyeshova) ◽  
Ernesto Monaco ◽  
Luis R. Rojas-Solórzano
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Lattice Boltzmann ◽  
Capillary Number ◽  
Viscosity Ratio ◽  
Penetration Rate ◽  
Surface Wettability ◽  
Gas Viscosity ◽  
Boltzmann Method ◽  
Gas Penetration

The numerical investigation of the interpenetrating flow dynamics of a gas injected into a homogeneous porous media saturated with liquid is presented. The analysis is undertaken as a function of the inlet velocity, liquid–gas viscosity ratio (D) and physical properties of the porous medium, such as porous geometry and surface wettability. The study aims to improve understanding of the interaction between the physical parameters involved in complex multiphase flow in porous media (e.g., CO2 sequestration in aquifers). The numerical simulation of a gaseous phase being introduced through a 2D porous medium constructed using seven staggered columns of either circular- or square-shaped micro-obstacles mimicking the solid walls of the pores is performed using the multiphase Lattice Boltzmann Method (LBM). The gas–liquid fingering phenomenon is triggered by a small geometrical asymmetry deliberately introduced in the first column of obstacles. Our study shows that the amount of gas penetration into the porous medium depends on surface wettability and on a set of parameters such as capillary number (Ca), liquid–gas viscosity ratio (D), pore geometry and surface wettability. The results demonstrate that increasing the capillary number and the surface wettability leads to an increase in the effective gas penetration rate, disregarding porous medium configuration, while increasing the viscosity ratio decreases the penetration rate, again disregarding porous medium configuration.

Equation of State’s Crossover Enhancement of Pseudopotential Lattice Boltzmann Modeling of CO2 Flow in Homogeneous Porous Media

Fluids ◽  
2021 ◽  
Vol 6 (12) ◽  
pp. 434
Author(s):  
Assetbek Ashirbekov ◽  
Bagdagul Kabdenova ◽  
Ernesto Monaco ◽  
Luis R. Rojas-Solórzano
Keyword(s):  
Porous Medium ◽  
Lattice Boltzmann ◽  
Multiphase Flows ◽  
Equations Of State ◽  
Density Ratio ◽  
Narrow Channel ◽  
Lattice Boltzmann Model ◽  
High Density Ratio ◽  
Homogeneous Porous Medium ◽  
Density Ratios

The original Shan-Chen’s pseudopotential Lattice Boltzmann Model (LBM) has continuously evolved during the past two decades. However, despite its capability to simulate multiphase flows, the model still faces challenges when applied to multicomponent-multiphase flows in complex geometries with a moderately high-density ratio. Furthermore, classical cubic equations of state usually incorporated into the model cannot accurately predict fluid thermodynamics in the near-critical region. This paper addresses these issues by incorporating a crossover Peng–Robinson equation of state into LBM and further improving the model to consider the density and the critical temperature differences between the CO2 and water during the injection of the CO2 in a water-saturated 2D homogeneous porous medium. The numerical model is first validated by analyzing the supercritical CO2 penetration into a single narrow channel initially filled with H2O, depicting the fundamental role of the driving pressure gradient to overcome the capillary resistance in near one and higher density ratios. Significant differences are observed by extending the model to the injection of CO2 into a 2D homogeneous porous medium when using a flat versus a curved inlet velocity profile.

Capillary Impregnation of Viscous Fluids in a Multi-Layered Porous Medium

2019 ◽  
Author(s):  
Shabina Ashraf ◽  
Jyoti Phirani
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Oil Recovery ◽  
Viscous Fluids ◽  
Spontaneous Imbibition ◽  
Lab On Chip ◽  
Capillary Impregnation ◽  
Relative Placement ◽  
Homogeneous Porous Medium ◽  
Wetting Fluid

Abstract Capillary impregnation of viscous fluids in porous media is useful in diagnostics, design of lab-on-chip devices and enhanced oil recovery. The impregnation of a wetting fluid in a homogeneous porous medium follows Washburn’s diffusive law. The diffusive dynamics predicts that, with the increase in permeability, the rate of spontaneous imbibition of a wetting fluid also increases. As most of the naturally occurring porous media are composed of hydrodynamically interacting layers having different properties, the impregnation in a heterogeneous porous medium is significantly different from a homogeneous porous medium. A Washburn like model has been developed in the past to predict the imbibition behavior in the layers for a hydrodynamically interacting three layered porous medium filled with a non-viscous resident phase. It was observed that the relative placement of the layers impacts the imbibition phenomena significantly. In this work, we develop a quasi one-dimensional lubrication approximation to predict the imbibition dynamics in a hydrodynamically interacting multi-layered porous medium. The generalized model shows that the arrangement of layers strongly affects the saturation of wetting phase in the porous medium, which is crucial for oil recovery and in microfluidic applications.

Visualization of a Surfactant Flood of an Oil-Saturated Porous Medium

1984 ◽  
Vol 24 (03) ◽  
pp. 325-327 ◽  
Author(s):  
L. Paterson ◽  
V. Hornof ◽  
G. Neale
Keyword(s):  
Porous Medium ◽  
Oil Recovery ◽  
Capillary Number ◽  
Saturated Porous Medium ◽  
Surfactant Solution ◽  
Viscous Fingering ◽  
Water Flooding ◽  
Alkyl Aryl Sulfonate ◽  
Oil Viscosity ◽  
Paraffin Oil

Abstract This paper discusses the viscous fingering that occurs when water or a surfactant solution displaces oil in a porous medium. Such floods were visualized in an porous medium. Such floods were visualized in an oil-wet porous medium composed of fused plastic particles. The flow structure changed significantly within the range of capillary numbers between 10 -4 and 10 -3 . The addition of surfactant resulted in narrower fingers, which developed in a more dispersive fashion. Introduction In describing fluid/fluid displacements in porous media, a useful dimensionless quantity is the capillary number, (1) which corresponds to the ratio of viscous forces to capillary forces. Here, v is the specific fluid discharge or Darcy velocity, it is viscosity, and o is interfacial tension (IFT). It has been shown that the recovery of oil from an underground reservoir increases significantly if the capillary number can be increased beyond the range of 1 × 10 -4 to 2 × 10 -3 during water flooding (see Larson et al. 1 ). To this end, surfactants are used extensively in tertiary oil recovery operations with the objective of reducing IFT and consequently mobilizing the oil ganglia which otherwise would remain trapped. This paper is concerned with the viscous fingering that occurs when water displaces oil in a porous medium, and we present a brief consideration on the effects that surfactants have on fingering. Noting that Peters and Flock have visualized fingering within the range of capillary numbers between 1.6 × 10 -6 and 7.2 × 10 -4, we present here visualizations at capillary numbers of 7.7 × 10 5 and 1.0 × 10 -3. Both our visualizations and the experiments of Peters and Flock involve large viscosity ratios so that only the viscosity of the more viscous fluid is considered when determining the capillary number. In particular, it is observed that as the capillary number increases, ganglia or blobs of displacing fluid are created at the displacement front in correspondence with the capillary numbers at which trapped ganglia are mobilized. This creation of ganglia at capillary numbers above 10 -3 was noted briefly in a previous paper 3 in which heptane displacing glycerine previous paper 3 in which heptane displacing glycerine was described. A secondary objective of this work was to test the Chuoke et al. theory for predicting the wavelength of fingers, wavelength being the peak-to-peak distance between adjacent well-developed fingers. Experimental Procedure The apparatus for these studies was described in Ref. 3. Basically, it consists of a slab of consolidated plastic particles 1.34 × 0.79 × 0.0 1 8 ft [0.44 × 0.26 × 0.006 m] with particles 1.34 × 0.79 × 0.0 1 8 ft [0.44 × 0.26 × 0.006 m] with a porosity of 0.43 and a permeability of 7, 100 darcies. This high permeability, when compared with that of reservoir rocks, should not be important for this study since capillary numbers and residual saturations are independent of pore size. Water (viscosity 1 cp [1 mPa s]) was used to displace paraffin oil (viscosity 68 cp 168 mPa s] at 77F [25C]). The water was dyed with methylene blue (which acts as a mild surfactant). Without the dye, the oil/water IFT was 42 dyne/cm [42 mN/m]. The addition of dye lowered this value to 36 dyne/cm [36 mN/m] for the concentration of dye used. For the surfactant flood, a 1 % sodium alkyl aryl sulfonate solution was used, giving a surfactant-solution/paraffin-oil IFT of 3.0 dyne/cm [3.0 mN/m]. Water Displacing Oil To compare our experiments with previous investigations of fingering, the displacement of paraffin oil by water at an average specific fluid discharge of 1.34 × 10–4 ft/sec [4.1 × 10 -5 m/s], corresponding to a capillary number of 7.7 × 10 -5, was studied (Fig. 1). Chuoke et al .4 and later Peters and Flock 2 have presented a formula for predicting the wavelength of presented a formula for predicting the wavelength of finger, lambda m : (2) where k is permeability, C is a dimensionless parameter which Peters and Flock call the wettability number and suggest would have the value 25 for an oil-wet porous medium, and mu o and mu ware viscosities of the displaced oil and displacing water, respectively. It was observed that the plastic particles of the porous medium considered here were oil wet because of adsorption of oil. SPEJ P. 325

Pore scale evaluation of thermal conduction anisotropy in granular porous media using Lattice Boltzmann method

2017 ◽  
Vol 27 (4) ◽  
pp. 867-888 ◽  
Author(s):  
R. Askari ◽  
M.F. Ikram ◽  
S. H. Hejazi
Keyword(s):  
Surface Roughness ◽  
Porous Medium ◽  
Lattice Boltzmann ◽  
Thermal Conduction ◽  
Pore Scale ◽  
Deviation Angle ◽  
Content Type ◽  
Boltzmann Method ◽  
Fitting Parameters ◽  
Conduction Anisotropy

Purpose Thermal conduction anisotropy, which is defined by the dependency of thermal conductivity on direction, is an important parameter in many engineering and research studies such as the design of nuclear waste depositional sites. In this context, the authors aim to investigate the effect of grain shape in thermal conduction anisotropy using pore scale modeling that utilizes real shapes of grains, pores and throats to characterize petrophysical properties of a porous medium. Design/methodology/approach The authors generalize the swelling circle approach to generate porous media composed of randomly arranged but regularly oriented elliptical grains at various grain ratios and porosities. Unlike previous studies that use fitting parameters to capture the effect of grain–grain thermal contact resistance, the authors apply roughness to grains’ surface. The authors utilize Lattice Boltzmann method to solve steady state heat conduction through medium. Findings Based on the results, when the temperature field is not parallel to either major or minor axes of grains, the overall heat flux vector makes a “deviation angle” with the temperature field. Deviation angle increases by augmenting the ratio of thermal conductivities of solid to fluid and the aspect ratios of grains. In addition, the authors show that porosity and surface roughness can considerably change the anisotropic properties of a porous medium whose grains are elliptical in shape. Originality/value The authors developed an algorithm for generation of non-circular-based porous medium with a novel approach to include grain surface roughness. In previous studies, the effect of grain contacts has been simulated using fitting parameters, whereas in this work, the authors impose the roughness based on the its fractal geometry.

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