Two-phase Lattice Boltzmann Simulations Research Articles

Surface wetting characterization in pore-scale multiphase flow simulations: A Ketton carbonate case study

Direct numerical simulations are commonly applied to X-ray computed microtomography images of porous rocks to measure petrophysical properties, such as relative permeability. To complement and/or expand laboratory data with useful simulations, such simulations need to reflect the true wetting condition of reservoir rock. It is therefore important to investigate approaches for assigning surface wetting conditions in pore-scale multiphase flow simulations. Two-phase Lattice-Boltzmann simulations are conducted on a Ketton carbonate image using different effective wetting models and then compared to pore-scale experimental data on the same rock, which is published elsewhere in (Scanziani et al., 2018). Two different wetting models are established based on the aging of the Ketton sample with crude oil at connate water saturation. Model 1 provides uniform wetting on all oil treated surfaces. Model 2 attempts to capture the multiscale nature of carbonate by allowing for spatially varying wetting conditions on oil treated surfaces based on local microporosity. Assessment criteria are based on pore-scale morphological measures, which include oil surface area coverage, oil phase topology, fluid/fluid curvatures, and contact angles. Overall, Model 1 with an assigned contact angle of greater than +10° above the geometrically measured contact angle from the experimental data provided the best results based on our assessment criteria.

Competition between main meniscus and corner film flow during imbibition in a strongly wetting square tube

Imbibition in a strongly wetting square tube with corner flow can be described by an interacting capillary bundle model, where the first sub-capillary describes the main meniscus flow while the others describe corner film flow. In this work, an advanced modified interacting capillary bundle model (MICBM) is developed to simulate imbibition dynamics in a strongly wetting square tube incorporating the viscous coupling effect. The flow conductances of each sub-capillary are obtained from two-phase lattice Boltzmann simulations with different viscosity ratios considering the viscous coupling effect. After verifying its accuracy, MICBM is used to analyze the imbibition dynamics of main meniscus and corner film flows under different conditions. The results show that, with increasing viscosity ratio between wetting and non-wetting fluids and increasing driving force, the wetting corner film development tends to be less significant compared with main meniscus flow. Interestingly, the corner film length first increases then decreases when the wetting fluid is less viscous than the non-wetting fluid in a long square tube. A phase diagram of dimensionless corner film length versus driving force and viscosity ratio is proposed to characterize the competition between main meniscus and corner film flow. Gravity and smaller contact angle make the corner film development more obvious. In addition, the tube length and width are shown to influence the interaction between main meniscus and corner film flow for a low viscosity ratio. The underlying physics of the above phenomena are explained in detail.

Two-phase lattice Boltzmann simulation of nanofluid conjugate heat transfer in a microchannel

Two-phase lattice Boltzmann simulation of nanofluid conjugate heat transfer in a microchannel

Modified curved boundary scheme for two-phase lattice Boltzmann simulations

The lattice Boltzmann (LB) method has gained much success in a variety of fields involving fluid flow and/or heat transfer. In this method, the bounce-back scheme is a popular technique for the treatment of nonslip boundaries. However, this scheme leads to a staircase representation of curved walls. Therefore many curved boundary schemes have been proposed, but mostly have detrimental effects such as mass leakage. Several correction schemes have been suggested for simulating single-phase flows, but very few discussions or studies have been made for two-phase LB simulations with curved boundaries. In this paper, the performances of three well-known schemes for dealing with curved boundaries in two-phase LB simulations are investigated through modeling a droplet resting on a circular cylinder. For all of the investigated schemes, the results show that the simulated droplet rapidly “evaporates” under the nonslip and isothermal condition, owing to the imbalance between the mass streamed out of the system by outgoing distribution functions and the mass streamed into the system by incoming distribution functions at each boundary node. Based on the numerical investigation, we formulate two modified mass-conservative curved boundary schemes for two-phase LB simulations. The accuracy of the modified curved boundary schemes and their capability of conserving mass in two-phase LB simulations are numerically demonstrated.

Linking continuum-scale state of wetting to pore-scale contact angles in porous media

HypothesisWetting phenomena play a key role in flows through porous media. Relative permeability and capillary pressure-saturation functions show a high sensitivity to wettability, which has different definitions at the continuum- and pore-scale. We hypothesize that the wetting state of a porous medium can be described in terms of topological arguments that constrain the morphological state of immiscible fluids, which provides a direct link between the continuum-scale metrics of wettability and pore-scale contact angles. ExperimentsWe perform primary drainage and imbibition experiments on Bentheimer sandstone using air and brine. Topological properties, such as Euler characteristic and interfacial curvature are measured utilizing X-ray micro-computed tomography at irreducible air saturation. We also present measurements for the United States Bureau of Mines (USBM) index, capillary pressure and pore-scale contact angles. Additional studies are performed using two-phase Lattice Boltzmann simulations to test a wider range of wetting conditions. FindingsWe demonstrate that contact angle distributions for a porous multiphase system can be predicted within a few percent difference of directly measured pore-scale contact angles using the presented method. This provides a general framework on how continuum-scale data can be used to describe the geometrical state of fluids within porous media.

Two-phase lattice Boltzmann simulation of natural convection in a Cu-water nanofluid-filled porous cavity: Effects of thermal boundary conditions on heat transfer and entropy generation

The present work investigates the effect of four different thermal boundary conditions on natural convection in a fluid-saturated square porous cavity to make a judicious choice of optimal boundary condition on the basis of entropy generation, heat transfer and degree of temperature uniformity. Four different heating conditions- uniform, sinusoidal and two different linear temperature distributions are applied on the left vertical wall of the cavity respectively, while maintaining the right vertical wall uniformly cooled and the horizontal walls thermally insulated. The two-phase thermal lattice Boltzmann (TLBM) model for nanofluid is extended to simulate nanofluid flow through a porous medium by incorporating the Brinkman–Forchheimer-extended Darcy model. The close agreement between present LBM solutions with the existing published results lends validity to the present findings. The current results indicate that the uniform and bottom to top linear heating are found to be efficient heating strategies depending on Rayleigh number (103 ≤ Ra ≤ 105) and Darcy number (10−1 ≤ Da ≤ 10−6). It is observed that the nanofluid improves the energy efficiency by reducing the total entropy generation and enhancing the heat transfer rate although its augmentation depends on the optimal volume fraction of nanoparticles.

Dynamic behavior of binary water droplets approaching each other in cloud by the improved two-phase lattice Boltzmann simulation

Dynamic behavior of binary water droplets approaching each other in cloud by the improved two-phase lattice Boltzmann simulation

Two-phase lattice Boltzmann simulation of the effects of base fluid and nanoparticle size on natural convection heat transfer of nanofluid

The effects of two kinds of base fluid (H2O and Ga) and three different nanoparticle radiuses (20nm, 40nm and 80nm) on the natural convection heat transfer of a rectangular enclosure filled with Al2O3–H2O and Al2O3–Ga nanofluid at different Rayleigh numbers (Ra=103 and Ra=105) are discussed based on a two-phase lattice Boltzmann method in this paper. It is found that Al2O3–Ga nanofluid shows a better heat transfer enhancement than Al2O3–H2O nanofluid. Al2O3–Ga and Al2O3–H2O nanofluid with the same smallest radius (r=20nm) can enhance the heat transfer by 86.0% and 24.5% compared with water respectively. It is also found that Al2O3–Ga nanofluid at low Rayleigh number (Ra=103) shows the biggest heat transfer enhancement (shows a 4.4% increase for every nanoparticle radius decreasing 20nm) compared with Al2O3–H2O nanofluid. The enhancement ratio at low Rayleigh number is about 3–10.8% and 23.5–28.8% more than that at high Rayleigh number for Al2O3–water and Al2O3–Ga nanofluid respectively. In addition, the nanoparticle fraction distributions in the enclosure are also investigated.

Numerical Simulation of Natural Convection of a Nanofluid in an Inclined Heated Enclosure Using Two-Phase Lattice Boltzmann Method: Accurate Effects of Thermophoresis and Brownian Forces.

Laminar natural convection in differentially heated (β = 0°, where β is the inclination angle), inclined (β = 30° and 60°), and bottom-heated (β = 90°) square enclosures filled with a nanofluid is investigated, using a two-phase lattice Boltzmann simulation approach. The effects of the inclination angle on Nu number and convection heat transfer coefficient are studied. The effects of thermophoresis and Brownian forces which create a relative drift or slip velocity between the particles and the base fluid are included in the simulation. The effect of thermophoresis is considered using an accurate and quantitative formula proposed by the authors. Some of the existing results on natural convection are erroneous due to using wrong thermophoresis models or simply ignoring the effect. Here we show that thermophoresis has a considerable effect on heat transfer augmentation in laminar natural convection. Our non-homogenous modeling approach shows that heat transfer in nanofluids is a function of the inclination angle and Ra number. It also reveals some details of flow behavior which cannot be captured by single-phase models. The minimum heat transfer rate is associated with β = 90° (bottom-heated) and the maximum heat transfer rate occurs in an inclination angle which varies with the Ra number.

Simulations of slip flow on nanobubble-laden surfaces

On microstructured hydrophobic surfaces, geometrical patterns may lead to the appearanceof a superhydrophobic state, where gas bubbles at the surface can have a strongimpact on the fluid flow along such surfaces. In particular, they can stronglyinfluence a detected slip at the surface. We present two-phase lattice Boltzmannsimulations of a flow over structured surfaces with attached gas bubbles anddemonstrate how the detected slip depends on the pattern geometry, the bulkpressure, or the shear rate. Since a large slip leads to reduced friction, our resultsgive assistance in the optimization of microchannel flows for large throughput.

Two-Phase Lattice Boltzmann Simulation of Behavior of a Body with a Viscoelastic Membrane in Fluid Flows (Effect of Internal Fluid Viscosity on Body Behavior)

The behavior of a deformable body with a viscoelasitc membrane in fluid flows is numerically investigated by the two-phase lattice Boltzmann method. In the calculations, the internal fluid of the body is distinguished from the surrounding fluid so that the viscosities of these fluids can be separately specified. Using this method, the deformation of the body under a shear flow is simulated by changing the viscosity ratio η, which is defined as the ratio of the viscosity of the internal fluid to that of the surrounding fluid. It is found that as the viscosity ratio increases, the deformability of the body remains almost constant for 0.1 ≤ η ≤ 1, whereas it decreases linearly for 1 < η ≤ 10. In addition, the behavior of the body in a square pipe flow is simulated for various viscosity ratios. The velocity near the centerline of the pipe decreases with increasing the viscosity ratio, and thus the flow rate becomes reduced. In the case of lower viscosity ratio (0.1 ≤ η ≤ 1), the body becomes a parachute-like shape and approaches toward the centerline of the pipe; that is, axial accumulation is observed. In the case of higher viscosity ratio (e.g., η = 6), the body forms into a slipper-like shape, migrating laterally toward a certain equilibrium position between the wall and the centerline of the pipe.

Simulation of Two-Phase Flow in Reservoir Rocks Using a Lattice Boltzmann Method

SummaryWe present results from simulations of two-phase flow directly on digitized rock-microstructure images of porous media using a lattice Boltzmann (LB) method. The implemented method is performed on a D3Q19 lattice with fluid/fluid and fluid/solid interaction rules to handle interfacial tension and wetting properties. We demonstrate that the model accurately reproduces capillary and wetting effects in pores with a noncircular shape. The model is applied to study viscous coupling effects for two-phase concurrent annular flow in circular tubes. Simulated relative permeabilities for this case agree with analytical predictions and show that the nonwetting-phase relative permeability might greatly exceed unity when the wetting phase is less viscous than the nonwetting phase.Two-phase LB simulations are performed on microstructure images derived from X-ray microtomography and process-based reconstructions of Bentheimer sandstone. By imposing a flow regulator to control the capillary number of the flow, the LB model can closely mimic typical experimental setups, such as centrifuge capillary pressure and unsteady- and steady-state relative permeability measurements. Computed drainage capillary pressure curves are found to be in excellent agreement with experimental data. Simulated steady-state relative permeabilities at typical capillary numbers in the vicinity of 10−5 are in fair agreement with measured data. The simulations accurately reproduce the wetting-phase relative permeability but tend to underpredict the nonwetting-phase relative permeability at high wetting-phase saturations. We explain this by pointing to percolation threshold effects of the samples. For higher capillary numbers, we correctly observe increased relative permeability for the nonwetting phase caused by mobilization and flow of trapped fluid. It is concluded that the LB model is a powerful and promising tool for deriving physically meaningful constitutive relations directly from rock-microstructure images.

Slip Flow Over Structured Surfaces with Entrapped Microbubbles

On hydrophobic surfaces, roughness may lead to a transition to a superhydrophobic state, where gas bubbles at the surface can have a strong impact on a detected slip. We present two-phase lattice Boltzmann simulations of a Couette flow over structured surfaces with attached gas bubbles. Even though the bubbles add slippery surfaces to the channel, they can cause negative slip to appear due to the increased roughness. The simulation method used allows the bubbles to deform due to viscous stresses. We find a decrease of the detected slip with increasing shear rate which is in contrast to some recent experimental results implicating that bubble deformation cannot account for these experiments. Possible applications of bubble surfaces in microfluidic devices are discussed.