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 Optimal Wetting Angles in Lattice Boltzmann Simulations of Viscous Fingering

2021 ◽  
Author(s):  
Peter Mora ◽  
Gabriele Morra ◽  
Dave A. Yuen ◽  
Ruben Juanes
Keyword(s):  
Oil Recovery ◽  
Lattice Boltzmann ◽  
Viscous Fingering ◽  
High Viscosity ◽  
Wetting Angle ◽  
Flow In Porous Media ◽  
Unexpected Result ◽  
Two Phase ◽  
Low Viscosity ◽  
Lattice Boltzmann Simulations

AbstractWe conduct pore-scale simulations of two-phase flow using the 2D Rothman–Keller colour gradient lattice Boltzmann method to study the effect of wettability on saturation at breakthrough (sweep) when the injected fluid first passes through the right boundary of the model. We performed a suite of 189 simulations in which a “red” fluid is injected at the left side of a 2D porous model that is initially saturated with a “blue” fluid spanning viscosity ratios $$M = \nu _\mathrm{r}/\nu _\mathrm{b} \in [0.001,100]$$ M = ν r / ν b ∈ [ 0.001 , 100 ] and wetting angles $$\theta _\mathrm{w} \in [ 0^\circ ,180^\circ ]$$ θ w ∈ [ 0 ∘ , 180 ∘ ] . As expected, at low-viscosity ratios $$M=\nu _\mathrm{r}/\nu _\mathrm{b} \ll 1$$ M = ν r / ν b ≪ 1 we observe viscous fingering in which narrow tendrils of the red fluid span the model, and for high-viscosity ratios $$M \gg 1$$ M ≫ 1 , we observe stable displacement. The viscous finger morphology is affected by the wetting angle with a tendency for more rounded fingers when the injected fluid is wetting. However, rather than the expected result of increased saturation with increasing wettability, we observe a complex saturation landscape at breakthrough as a function of viscosity ratio and wetting angle that contains hills and valleys with specific wetting angles at given viscosity ratios that maximize sweep. This unexpected result that sweep does not necessarily increase with wettability has major implications to enhanced oil recovery and suggests that the dynamics of multiphase flow in porous media has a complex relationship with the geometry of the medium and the hydrodynamical parameters.

scholarly journals Influence of Wetting on Viscous Fingering Via 2D Lattice Boltzmann Simulations

2021 ◽  
Author(s):  
Peter Mora ◽  
Gabriele Morra ◽  
Dave A. Yuen ◽  
Ruben Juanes
Keyword(s):  
Phase Space ◽  
Oil Recovery ◽  
Lattice Boltzmann ◽  
Field Studies ◽  
Viscous Fingering ◽  
Wetting Angle ◽  
Water Flooding ◽  
Two Phase ◽  
Fluid Displacement ◽  
Porous Model

AbstractWe present simulations of two-phase flow using the Rothman and Keller colour gradient Lattice Boltzmann method to study viscous fingering when a “red fluid” invades a porous model initially filled with a “blue” fluid with different viscosity. We conducted eleven suites of 81 numerical experiments totalling 891 simulations, where each suite had a different random realization of the porous model and spanned viscosity ratios in the range $$M\in [0.01,100]$$ M ∈ [ 0.01 , 100 ] and wetting angles in the range $$\theta _w\in [180^\circ ,0^\circ ]$$ θ w ∈ [ 180 ∘ , 0 ∘ ] to allow us to study the effect of these parameters on the fluid-displacement morphology and saturation at breakthrough (sweep). Although sweep often increased with wettability, this was not always so and the sweep phase space landscape, defined as the difference in saturation at a given wetting angle relative to saturation for the non-wetting case, had hills, ridges and valleys. At low viscosity ratios, flow at breakthrough is localized through narrow fingers that span the model. After breakthrough, the flow field continues to evolve and the saturation continues to increase albeit at a reduced rate, and eventually exceeds 90% for both non-wetting and wetting cases. The existence of a complicated sweep phase space at breakthrough, and continued post-breakthrough evolution suggests the hydrodynamics and sweep is a complicated function of wetting angle, viscosity ratio and time, which has major potential implications to Enhanced Oil Recovery by water flooding, and hence, on estimates of global oil reserves. Validation of these results via experiments is required to ensure they translate to field studies.

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.

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

Effects of Inertia and Viscosity on Single Droplet Deformation in Confined Shear Flow

2013 ◽  
Vol 13 (3) ◽  
pp. 706-724 ◽  
Author(s):  
Samaneh Farokhirad ◽  
Taehun Lee ◽  
Jeffrey F. Morris
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Viscous Fluid ◽  
Lattice Boltzmann ◽  
Viscosity Ratio ◽  
Diffuse Interface ◽  
Single Droplet ◽  
Droplet Deformation ◽  
Droplet Dynamics ◽  
Lattice Boltzmann Simulations

AbstractLattice Boltzmann simulations based on the Cahn-Hilliard diffuse interface approach are performed for droplet dynamics in viscous fluid under shear flow, where the degree of confinement between two parallel walls can play an important role. The effects of viscosity ratio, capillary number, Reynolds number, and confinement ratio on droplet deformation and break-up in moderately and highly confined shear flows are investigated.

Two-Phase Flow (Oil-Water) in Petroleum Reservoir with Irregular Geometry Including Water Injection: Effect of Porosity on the Oil Recovery Factor

2012 ◽  
Vol 326-328 ◽  
pp. 181-186 ◽  
Author(s):  
F. Alves Batista ◽  
B. Gonçalves Coutinho ◽  
Severino Rodrigues de Farias Neto ◽  
Antônio Gilson Barbosa de Lima
Keyword(s):  
Oil Recovery ◽  
Two Phase Flow ◽  
Water Injection ◽  
Recovery Factor ◽  
Phase Flow ◽  
Petroleum Reservoir ◽  
Two Phase ◽  
Fully Implicit ◽  
Irregular Geometry ◽  
Black Oil Model

The aim of this work is to study theoretically the effect of porosity of an oil reservoir with arbitrary geometry on the oil recovery factor. A two-dimensional mathematical modeling (Black-oil model) and numerical solution applied to two-phase flow (water-oil) into the reservoir with irregular geometry including water injection is presented. The conservation equations written in generalized coordinates are solved using the finite volume method, with a fully implicit technique. Results of the pressure and saturation distributions and oil recovery factor over time are presented and evaluated for different values of porosity of the reservoir.

scholarly journals Color-gradient lattice Boltzmann modeling of immiscible two-phase flows on partially wetting surfaces

2017 ◽  
Vol 232 (3) ◽  
pp. 416-430 ◽  
Author(s):  
Yuan Yu ◽  
Haihu Liu ◽  
Yonghao Zhang ◽  
Dong Liang
Keyword(s):  
Lattice Boltzmann ◽  
Capillary Number ◽  
Viscosity Ratio ◽  
High Viscosity ◽  
Contact Angles ◽  
Displacement Velocity ◽  
Two Dimensional ◽  
Change Rate ◽  
Finger Length ◽  
Color Gradient

A zero-interfacial-force condition is derived and implemented to improve the wetting boundary scheme for a lattice Boltzmann color-gradient model. This new wetting boundary scheme is validated by two static problems, i.e. a droplet resting on a flat surface and a cylindrical surface, and one dynamic problem, i.e. the capillary filling in a two-dimensional channel. In these simulations, we observe that non-physical mass transfer is suppressed and spurious velocities become smaller. Meanwhile, accurate results including dynamic contact line movement are achieved for a broad range of contact angles. The model is then applied to study the displacement of immiscible fluids in a two-dimensional channel. Both the displacement velocity and the change rate of finger length are found to exhibit a linear dependence on the contact angle at the viscosity ratio of unity. The displacement velocity decreases but the change rate of finger length increases with increasing capillary number, while the displacement velocity tends to be constant, i.e. two-thirds of the maximum inlet velocity, at high viscosity ratios or low capillary numbers. In contrast to the displacement velocity, the change rate of finger length is negligible at high viscosity ratios or low capillary numbers, where the finger length is in an equilibrium state, while the equilibrium finger length itself is smaller at a higher viscosity ratio or a lower capillary number.

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.

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