# Research

* Stability* is a long-lasting topic in particulate flows. Theoretical models for particulate flows often treat particles and fluid as two interpenetrating continua; closure relations that describe particle-fluid interactions usually assume that particles are homogeneously distributed in the fluid, which, as we know today, is usually not true.

Particle clusters arise because 1) particle-particle collisions can be inelastic; 2) viscous dissipation of particles' fluctuating motion increases nonlinearly with solid volume fraction; 3) particle-fluid drag increases nonlinearly with solid volume fraction. Mechanisms 1) and 2) can be isolated and studied using simulations of granular and gas-solid system with no gravity. In such systems, the initial fluctuating motion of particles is gradually dissipated by inelastic collisions between particles and the viscosity. The reduction of fluctuations with time leads to the name "homogeneously cooling system" (HCS). In fluidization and sedimentation, all three mechanisms are present.

In HCS (HCS=homogeneously cooling system), the leading mode of instability is in the velocity field in the form of vortices. Formation of particle cluster always follows the formation of vortices. In sedimentation, particle cluster in the form of a steady horizontal traveling wave is formed when particle-fluid density ratio is increased to beyond 50-100.

## Cluster formation in HCS

## Cluster formation in sedimentation

Relevant publication:

- Yin, Zenk, Mitrano, Hrenya, Impact of collisional vs. viscous dissipation on flow instabilities in gas-solid systems, J. Fluid Mech. 727, R2, 2013.
- Garzo, Fullmer, Hrenya, Yin, Transport coefficients of solid particles immersed in a viscous gas, Phys. Rev. E 93:012905, 2016.

* Heat and mass transfers* in low-Reynolds-number particulate flows are strongly assisted by particles-generated velocity disturbances on the length scale of d especially at high Peclet numbers. Experiments conducted at IUSTI with shear flow show that the enhancement in heat transfer can be several fold of the molecular heat transfer when Pe is O(10-100). For mass transfer in liquid, the enhancement in can be thousands fold when Pe is on the order of millions. The enhancement comes from the chaotic motion of the particles, which acts to advect heat / mass and help mixing. Our simulation of heat transfer in sheared suspensions achieved very good agreement with experimental measurements.

Relevant Publication:

- Metzger, Rahli, Yin, Heat transfer across sheared suspensions: role of the shear-induced diffusion, J. Fluid Mech. 724:527-552, 2013.
- Souzy, Yin, Villermaux, Abid, Metzger, Super-diffusion in sheared suspensions, Phys. Fluids 27:041705, 2015.

We conduct direct numerical simulation of fluid flow and transport through porous media using the lattice Boltzmann method. The lattice Boltzmann method solves the Navier-Stokes equation through simulation of the evolution of a fluid particle velocity distribution. Multicomponent extensions of the lattice Boltzmann method can be used to simulate multiphase flow through porous media. Lattice Boltzmann method coupled with random-walk particle tracking can be used to simulate solute and colloidal transport. The following table lists our group's computational capabilities.

TOPIC | METHOD | APPLICATIONS |
---|---|---|

Porous Media Reconstruction | Voronoi-based porous media models | Effect of pore geometry on flow / transport properties3 |

Single-Phase Flow | Lattice Boltzmann method
Lattice Boltzmann method with slip boundary condition Random walk particle tracking Particle tracking with colloidal interactions D(iscrete) E(element) M(ethod)-LBM coupling |
Characterization of permeability from images
Characterization of apparent permeability with surface slip Simulation of solute transport in porous media Simulation of colloidal transport in porous media and filtration Permeability of deformable porous media |

Multiphase Flow | Multiphase, multicomponent lattice Boltzmann method | Simulation of multiphase displacement in porous media |

High-Performance Computing | MPI-parallelized lattice Boltzmann and particle-tracking simulators | Solve problems of meaningful size 10003 voxels with nearly perfect scaling up performance |

** Geometric reconstruction** using two- and three-dimensional Voronoi diagrams is quick, efficient, and all-analytical. It allows easy implementations of essential geometric features, such as structure, anisotropy and heterogeneity, while maintaining the stochastic nature of porous medium.

Pore network constructed from a two-dimensional Voronoi diagram.

From left to right: porous medium model with fracture-like pores, porous medium model with network of tubular pores, porous medium model with embedded vugs.

Relevant publication:

Xiao, Yin, Geometry models of porous media based on Voronoi tessellations and their porosity-permeability relations, Comput. Math. Appl. 72:328-348, 2016

** Flows with surface slip** are usually observed when a fluid flows over a non-wetting or rough surface, or when a gas flows through a narrow restriction, the size of which is getting close to the dimension of the mean free path, but not so small that it only allows free molecular flow. In terms of the Knudsen number (mean free path over the dimension of the restriction), gas slip flow regime is generally defined as Kn < 0.1. Such flows are still governed by the Navier-Stokes equation, but the boundary condition at the solid surface is the slip type. The effect of this slip boundary condition on the permeability of fluid through porous medium can be solved by using a lattice Boltzmann method with slip boundary condition.

Flows with no-slip boundary condition (left) and with slip boundary condition (right). These two flows were driven by the same body force and the difference in the velocity is observed in the colors - more reds in the slip case.

Relevant publication:

Wang, Yin, Apparent permeability of flow through periodic arrays of spheres with first-order slip, Powder Tech. 311:313-327, 2017.

** Particle-tracking method** is an effective way to simulate transport of solute of actual particulates in porous media. When it is used for solute transport, the particle motion typically includes a Brownian component to simulate diffusion. When it is used for particulate transport, an equation of motion is generally formulated to account for particle weight, size, and its interactions with pore surface as well as with other particles.Solute transport through porous media is often described, on the Darcy scale, by the advection-diffusion equation. However, the validity of the equation is often challenged, as the velocity distribution of pore fluid is seldom Gaussian, especially in the direction of the mean flow. Transport of particulates through porous media is more complex than transport of solutes, because particles, due to their finite sizes and/or interactions with pore surface, do not sample the same flow field as solutes do. In some circumstances, transport of particulates through porous media may be significantly accelerated; in other circumstances, particles may be trapped, leading to reduced permeability of the porous medium.

We conduct pore-scale simulations of solute and particle transport, in an attempt to establish physically based Darcy level descriptions. As natural porous media are often both physically and chemically heterogeneous, proper "average" of the effect of heterogeneities is needed.

Transport of particles through a porous medium.

Relevant publication:

Guo, Huang, Xiao, Yin, Chun, Um, Neeves, Wu, Bead-based microfluidic sediment analogues: Fabrication and colloid transport. Langmuir 32:9342-9350, 2016.

** Combination of DEM and LBM** can be used to simulate deformation of porous medium under stress. DEM stands for discrete element method. Using DEM, we simulated the compaction of a porous medium made up by 25,000 particles. The porous medium made up by these particles is resolved by a lattice Boltzmann mesh consisting of 1000

^{3}voxels. As the porous medium was compacted, the particles changed their positions, and the voxel map was changed. The change in the porosity was registered, and the change in the permeability was obtained by a direct simulation of fluid flow through the deformed porous medium. This study establishes a power-law scaling relation between porosity and permeability during compaction and show that the pore geometry has a significant effect on the porosity-permeability relation.

A porous medium with a center hole is being stressed in the vertical direction. DEM modeling performed by Labra and Sun @ University of Edinburgh. Flow simulations were conducted to characterize the change in permeability.

Relevant publication:

Petunin, Labra, Xiao, Tutuncu, Sun, Yin, Porosity and permeability change under stress and correlation to rock texture. 5th Biot Conference in Poromechanics, 2013.

** Dynamics of multiphase flow** through porous medium is very important for improved and enhanced oil recovery. We use multicomponent lattice Boltzmann methods to simulate displacement processes and study the effect of pressure, viscosity, wettability and capillary forces on the superficial velocities of phases. Multiphase flow through porous media can be driven by a variety of means - gravity, pressure difference, wettability - these flows cannot and should not be all described by the relative permeability curve. There are also situations involving three phases - oil, gas, and water - the gradient-flux law for three phases requires fundamental study.

Collaborators: Dongxiao Zhang (Peking University)

Relevant publication:

Huang, Xiao, Yin, Lattice Boltzmann simulation of immiscible displacement using a pressure boundary condition. Under review.

** Parallel computing** is critical for porous media flow simulations. Porous media are often highly heterogeneous. Simulations that are conducted in limited number of pores often do not reflect the complexity of flow on the larger scale that are often controlled by variations in the pore size and wettability. In order to accommodate these variations, computations must admit large domains and parallelization computing is indispensable. Our lattice Boltzmann programs were tested on Titan and Mira, the second and fifth largest super computers in the world (as of June 2014), and showed very high parallel efficiency at 262,144 processors.

Relevant Publication

Xiao, Yin, Geometry models of porous media based on Voronoi tessellations and their porosity-permeability relations, Comput. Math. Appl. 72:328-348, 2016

** Microfluidics and nanofluidics porous media models** are used to visualize multiphase flows and to provide "ground truth" to verify the simulations. The microfluidic chips are fabricated on polymer substrates and are inexpensive. Their pore size can be made to vary from a few micrometers to hundreds of micrometers. The geometry of the chips can be designed to mimic the texture of a real porous medium. The graph below shows water flooding and surfactant flooding experiments conducted in two microfluidic models. One has a nearly uniform channel width (6 μm); another has a wider channel width (8 μm) and have many embedded large pores to simulate vugs.

From top to bottom: water flooding in a porous medium model with nearly uniform pore sizes; surfactant flooding in the same porous medium; water flooding in a porous medium model with vugs; surfactant flooding in the same porous medium. Water (dark color) is the non-wetting phase. Flow direction is from left to right.

Movie 3 - Dynamics of water-oil displacement (without surfactan)

Movie 4 - Dynamics of water-oil displacement (with surfactant)

Movie 5 - Dynamics of water-oil displacement in a vuggy medium

Although microfluidic porous media models are powerful research tools, their pore size are still too large when compared to many reservoir rocks. Pores of carbonates are often hundreds of nanometers; pores of oil-bearing Bakken and Eagle Ford rocks are often tens of nanometers in size; many organic pores in the kerogen are several nanometers in size. To create experimental models that can directly reflect the critical dimension of these rocks, we use nanofluidic models. These models contains channels that are tens of nanometers in size, etched on silicon substrates. We are nanofluidic models to study phase transition in nanopores and single- and multiphase flows.

Left: Nanochannels 3 μm wide and 300 nm deep etched into a silicon substrate. Right: Nanochannels 3 μm wide and 30 nm deep.

Movie 6 - Dynamics of air-water displacement across a nanofluidic channel network.

Relevant Publications:

- Wu, Xiao, Johnson-Paben, Retterer, Yin, Neeves, Single- and two-phase flow in microfluidic porous media analogs based on Voronoi tessellation, Lab Chip 12:253-261, 2012 (Cover)
- Xu, Ok, Xiao, Neeves, Yin, Effect of pore geometry and interfacial tension on water-oil displacement efficiency in oil-wet microfluidic porous media analogs, Phys. Fluids 26:093102, 2014.
- Wu, Bai, Ma, Ok, Neeves, Yin, Optic imaging of two-phase-flow behavior in 1D nanoscale channels, SPE J. 19:793-802, 2014.
- He, Xu, Gao, Yin, Neeves, Visual evaluation of surfactant performance for enhanced well productivity in the unconventional reservoirs using rock-on-a-chip approach, J. Petro. Sci. Eng. 135:531-541, 2015.

** **

Effect of pore size on the phase state and transition of hydrocarbon fluids is a problem of significant interest for unconventional reservoirs. As is well recognized, when liquid and gas coexist in a porous medium, liquid is usually the wetting phase. The pressure of gas is higher than that of the liquid by the capillary pressure, whose magnitude is determined by the Young-Laplace equation. As pore size decreases to tens of nanometers, the capillary pressure between the gas and the liquid phases can be as high as several atm. As a result, the formation of the gas phase (bubble point) in a depressurization process is typically delayed, the degree of which depends on the temperature and the composition of the fluid. We write thermodynamic phase equilibrium models to describe the process of depressurization and phase change in porous media. In addition to modeling, we also conduct nanofluidic experiments to generate data for validation.

** **

Initial Condition - Liquid fully saturates the porous medium.

As piston moves to the right, pressure is reduced and gas is generated in the porous medium.

Critical gas saturation is reached and gas is produced from the porous medium.

Relevant Publications:

- Wang, Yin, Neeves, Ozkan, Effect of pore-size distribution on phase transition of hydrocarbon mixtures in nanoporous media, SPE J. 21:1981-1995, 2016.
- Zhu, Yin, Ozkan, Theoretical investigation of the effect of membrane properties of nanoporous reservoirs on the phase behavior of confined light oil. SPE-175536, 2015.
- Parsa, Yin, Ozkan, Direct observation of the impact of nanopore confinement on petroleum gas condensation. SPE-175118, 2015.