Contact dynamic modeling of a liquid droplet between two approaching porous materials

A computational fluid dynamics model based on a finite difference solution to mass and momentum conservation equations (Navier–Stokes equations) for a liquid droplet transport between two porous or nonporous contacting surfaces (CSs) is developed. The CS dynamic (equation of motion) and the spread of the incompressible liquid available on the primary surface for transfer are coupled with the Navier–Stokes equations. The topologies of the spread dynamic between and inside both surfaces (primary and CSs) are compared with experimental data. The amount of mass being transferred into the CS, predicted by the model, is also compared to the experimental measurements. The impact of the initial velocity on the spread topology and mass transfer into the pores is addressed. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2346–2353, 2014     

Visualizing multiphase flow and trapped fluid configurations in a model three‐dimensional porous medium

We report an approach to fully visualize the flow of two immiscible fluids through a model three‐dimensional (3‐D) porous medium at pore‐scale resolution. Using confocal microscopy, we directly image the drainage of the medium by the nonwetting oil and subsequent imbibition by the wetting fluid. During imbibition, the wetting fluid pinches off threads of oil in the narrow crevices of the medium, forming disconnected oil ganglia. Some of these ganglia remain trapped within the medium. By resolving the full 3‐D structure of the trapped ganglia, we show that the typical ganglion size, as well as the total amount of residual oil, decreases as the capillary number Ca increases; this behavior reflects the competition between the viscous pressure in the wetting fluid and the capillary pressure required to force oil through the pores of the medium. This work thus shows how pore‐scale fluid dynamics influence the trapped fluid configurations in multiphase flow through 3‐D porous media. © 2013 American Institute of Chemical Engineers AIChE J, 59:1022‐1029, 2013     

Experimental study of the role of the Weber and capillary numbers on Mesler entrainment

Mesler entrainment is the formation of a very large number of very small bubbles by a relatively low velocity drop impacting a liquid surface. The role of the Weber number in Mesler entrainment has received significant attention. However, the effect of the capillary number, which quantifies the relative importance of viscous and surface tension forces, has not been explored. This is due primarily to the fact that virtually all Mesler entrainment research has used a single liquid, water, as the working fluid. This, combined with certain experimental restrictions, makes difficult an independent variation of the Weber and capillary numbers. To address this problem, Mesler entrainment was investigated using two silicone oils, having kinematic viscosities of 0.65 cSt and 10.0 cSt, respectively, revealing the effect of the capillary number on Mesler entrainment, a result which has not been obtained heretofore. The silicone oils give extremely repeatable results when compared to water. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

Flow through porous media of a shear-thinning liquid with yield stress

Darcy's law for the laminar flow of Newtonian fluids through porous media has been modified to a more general form which will describe the flow through porous media of fluids whose flow behavior can be characterized by the Herschel-Bulkley model. The model covers the flow of homogeneous fluids with a yield value and a power law flow behavior. Experiments in packed beds of sand were carried out with solutions of paraffin wax in two oils and with a crude oil from the Peace River area of Canada. The model fitted the data well. A sensitivity analysis of the fitting parameters showed that the model fit was very sensitive to errors in the flow behavior index, n , of the Herschel-Bulkley model. A comparison of the “n” values calculated from viscometer measurements and from flow measurements agreed well. A more general Reynolds number for flow through porous media, which includes a fluid yield value, was developed. The data were fitted to a Kozeny-Carman type equation using this Reynolds number. The constant in the Kozeny-Carman equation was determined for the two packed beds studied using Newtonian oils. The data could all be represented, within the experimental error, by the relationship f^* = 150/Re^*. Since the mean volume to surface diameter of the packing was determined by the measurement of its permeability to a Newtonian oil, assuming C' = 150, the new definition of the Reynolds number allows the direct use of the Kozeny-Carman equation with Herschel-Bulkley type fluids.     

Flow of viscoelastic surfactants through porous media

We compare the flow behavior of viscoelastic surfactant (VES) solutions and Newtonian fluids through two different model porous media having similar permeability: (a) a 3D random packed bed and (b) a microchannel with a periodically spaced pillars. The former provides much larger flow resistance at the same apparent shear rate compared to the latter. The flow profile in the 3D packed bed cannot be observed since it is a closed system. However, visualization of the flow profile in the microchannel shows strong spatial and temporal flow instabilities in VES fluids appear above a critical shear rate. The onset of such elastic instabilities correlates to the flow rate where increased flow resistance is observed. The elastic instabilities are attributed to the formation of transient shear induced structures. The experiments provide a detailed insight into the complex interplay between the pore scale geometry and rheology of VES in the creeping flow regime. © 2017 American Institute of Chemical Engineers AIChE J, 64: 773–781, 2018     

Viscous flow in a channel partially filled with a porous medium and with wall suction

In this paper, we consider a coupled two-dimensional flow of a Newtonian fluid, both above and through a porous medium. In the fluid-only region, the two-dimensional flow field is governed by the Navier-Stokes equation. We consider the Brinkman-extended Darcy law relationship in the porous medium. Inertial terms are retained in the formulation and the interface conditions between the two domains are those as outlined by Ochoa-Tapia and Whitaker (Int. J. Heat Mass Transfer 38 (1995) 2635). It should be noted that these interface conditions are formulated with an empirical constant β that is unknown a priori. The model equations were solved using two independent methods. In the first method, we pose a similarity variable and reduce the governing equations to two, coupled, non-linear ordinary differential equations. In the second approach, the governing equations were re-posed as a one-domain problem, using the procedure outlined by Basu and Khalili (Phys. Fluids 11 (1999) 1031), so that the conditions at the interface need not be considered. The resulting equation was solved directly, in primitive variable form, using a finite volume formulation. This enabled us to determine β by comparing the resulting solutions.     

Jamming of cellulose ether solutions in porous medium

The flow of aqueous cellulose ether solutions through a bead packing is investigated using magnetic resonance imaging and filtration measurements. A rather complex behavior dominated by jamming (clogging) and unjamming phenomena in time is observed. With the help of several characterization techniques (laser grain sizing, dynamic light scattering, optical microscopy, and rheometry), we find that the particular methyl(hydroxyethyl) cellulose prepared with a specific protocol, tends to form aggregates in water, even at the lowest achievable concentration. These aggregates are highly polydisperse, ranging from 100 nm to 100 μm in size, and are deformable. Their origin appears to be the hydrophobic links among molecules and the related local crystallization. It is suggested that these features play a key role in the observed jamming/unjamming during filtration tests. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3923–3935, 2015     

Dynamic effects on capillary pressure–Saturation relationships for two‐phase porous flow: Implications of temperature

Work carried out in the last decade or so suggests that the simulators for multiphase flow in porous media should include an additional term, namely a dynamic coefficient, as a measure of the dynamic effect associated with capillary pressure. In this work, we examine the dependence of the dynamic coefficient on temperature by carrying out quasi‐static and dynamic flow simulations for an immiscible perchloroethylene–water system. Simulations have been carried out using a two‐phase porous media flow simulator for a range of temperatures between 20 and 80^°C. Simulation domains represent 3‐D cylindrical setups used by the authors for laboratory‐scale investigations of dynamic effects in two‐phase flow. Results are presented for two different porous domains, namely the coarse and fine sands, which are then interpreted by examining the correlations between dynamic coefficient(s) and temperature, time period(s) required for attaining irreducible water saturation, and the dynamic aqueous/nonaqueous phase saturation and capillary pressure plots. The simulations presented here maintain continuity from our previous work and address the uncertainties associated with the dependency of dynamic coefficient(s) on temperature, thereby complementing the existing database for the characterization of dynamic coefficients and subsequently enabling the users to carry out computationally economical and reliable modeling studies. © 2012 The Authors. AIChE Journal, published by Wiley on behalf of the AIChE. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. AIChE J, 58: 1951–1965, 2012     

Characteristic time scales for predicting the scalar flux at a free surface in turbulent open‐channel flows

The purpose of this study is to predict the turbulent scalar flux at a free surface subject to a fully developed turbulent flow based on a hydrodynamic analysis of turbulence in the region close to the free surface. The effect of the Reynolds number on turbulent scalar transfer mechanisms is extensively examined. A direct numerical simulation technique is applied to achieve the purpose. The surface‐renewal approximation is used to correlate the free‐surface hydrodynamics and scalar transport at the free surface. Two types of characteristic time scales have been examined for predicting turbulent scalar flux. One is the time scale derived from the characteristic length and velocity scale at the free surface. The other is the reciprocal of the root‐mean‐square surface divergence. The results of this study show that scalar transport at the free surface can be predicted successfully using these time scales based on the concept of the surface‐renewal approximation. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

Effect of confinement on the bubble points of hydrocarbons in nanoporous media

The bubble point of reservoir petroleum fluids in nanoporous media is an important parameter in shale oil production. We present experimental results on the bubble points of octane and decane confined in controlled‐pore glasses (CPGs) with pore sizes of 4.3 and 38.1 nm. Differential scanning calorimetry (DSC) is used to measure the temperature at which the vapor phase begins to form (i.e., the bubble point). We find that the bubble point is dramatically affected by pore diameter: at 38.1 nm the confinement effect is insignificant, but at 4.3 nm two distinct bubble points appear, suggesting two distinct populations of evaporating fluid. Deviations are as great as ±15 K for both peaks relative to the bulk bubble point for 4.3 nm CPGs. Thermogravimetric analysis is consistent with DSC, supporting the validity of these results. Based on these experiments and previous simulations, we propose a two‐state model for the nanoconfined hydrocarbons. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1772–1780, 2016     

Water and methane in shale rocks: Flow pattern effects on fluid transport and pore structure

Using molecular dynamics simulations, the two‐phase flow of water and methane through slit‐shaped nanopores carved from muscovite is studied. The simulations are designed to investigate the effect of flow patterns on fluids transport and on pore structure. The results indicate that the Darcy's law, which describes a linear relation between flow rate and pressure drop, can be violated when the flow pattern is altered. This can happen when the driving force, that is, the pressure drop, increases above a pore‐size dependent threshold. Because the system considered here contains two phases, when the fluid structure changes, the movement of methane with respect to that of water changes, leading to the violation of the Darcy's law. Our results illustrate the importance of the capillary force, due to the formation of water bridges across the model pores, not only on the fluid flow, but also on the pore structure, in particular its width. When the water bridges are broken, perhaps because of fast fluid flow, the capillary force vanishes leading to significant pore expansion. Because muscovite is a model for illite, a clay often found in shale rocks, these results advance our understanding regarding the mechanism of water and gas transport in tight shale gas formations. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2993–2999, 2015     

Snap‐off of a liquid drop immersed in another liquid flowing through a constricted capillary

Emulsions are encountered at different stages of oil production processes, often impacting many aspects of oilfield operations. Emulsions may form as oil and water come in contact inside the reservoir rock, valves, pumps, and other equipments. Snap‐off is a possible mechanism to explain emulsion formation in two‐phase flow in porous media. Quartz capillary tubes with a constriction (pore neck) served to analyze snap‐off of long (“infinite”) oil droplets as a function of capillary number and oil‐water viscosity ratio. The flow of large oil drops through the constriction and the drop break‐up process were visualized using an optical microscope. Snap‐off occurrence was mapped as a function of flow parameters. High oil viscosity suppresses the breakup process, whereas snap‐up was always observed at low dispersed‐phase viscosity. At moderate viscosity oil/water ratio, snap‐off was observed only at low capillary number. Mechanistic explanations based on competing forces in the liquid phases were proposed. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Anisotropic convective heat transfer in microlattice materials

Fluid dynamics and heat transfer of flow through periodic open‐cellular microlattice structures are characterized for varying superficial flow orientations and flow rates to investigate heat transfer and pressure loss anisotropy. For given Reynolds number, friction factor is lowest when flow is aligned with the largest straight‐through passages in the microlattice. A maximum friction factor, over twice the optimally aligned friction factor, exists for flow orientations between π/8 and π/4 rad off the optimal alignment, with little variation in friction factor for π/8 and π/4 rad. Heat transfer is maximized at π/4 rad off axis from the largest straight‐through passages; however, less angular variation occurs in Nusselt number than in friction factor. Empirical correlations involving superellipses yield analytical equations describing Nusselt number dependence on flow angle and Reynolds number. This work enables selection of optimal flow orientations and optimal cellular architecture in convective heat transfer implementations of microlattice materials for lightweight and multifunctional applications. © 2012 American Institute of Chemical Engineers AIChE J, 59: 622–629, 2013     

Modeling drying in thin porous media after coupling pore-level drying dynamics with external flow field

This article uses a novel, fully coupled method to solve the isothermal slow drying of porous media in laminar flow. The film effect is included and a novel logistic equation is used to relate the pore network variables with the external field variables. The model is used to simulate the drying of several thin porous media with different aspect ratios in a flow. One, two, or all sides of the pore network are opened to the flow. The studies show that the higher exposed area vs. total volume ratio leads to faster drying while the orientation of the porous media is immaterial.     

Characterization of Taylor vortex flow in a short liquid column

We present a study on Taylor vortex flow in the annulus between a rotating inner cylinder and a stationary outer cylinder, featured with a wide gap (radius ratio is 0.613) and a short column (aspect ratio is 5.17). A particle image velocimetry (PIV) system was used to determine the position, shape, and velocity distribution of the vortices, by which the flow was also confirmed to lie in the nonwavy Taylor vortex regime for all operating conditions explored in this study. Our results suggest that end boundary effects are important, in which the vortex number decreases with decreasing column length. For a system with an aspect ratio of 5.17, six vortices appear in the gap with their position, size, and shape varying at different Reynolds numbers. The fluid velocities show an asymmetric feature with respect to the vortex centers, while the maximum axial and radial velocities increase almost linearly with the increasing reduced Reynolds number (Re ? Re_c). In addition, computational fluid dynamics study was employed under the same conditions, and its results agree well with the PIV measurements. Overall, this study provides a quantitative understanding of the formation of Taylor vortices in a constrained space. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Effects of flow history on oil entrapment in porous media: An experimental study

The effect of flow history on fluid phase entrapment during immiscible two‐phase flow in Hele‐Shaw cells packed with spherical and crushed glass beads is investigated. The wetting fluid is injected into an initially oil saturated cell at a well‐defined capillary number. It is observed that the size and shape of the trapped clusters strongly depend on the history of flooding such that less oil was trapped in the medium when the injecting capillary number gradually increased to the final maximum capillary number compared to the case when the injection was started and maintained constant at the maximum capillary number. In addition, a comprehensive series of experiments were conducted to delineate the effects of the capillary number on the phase entrapment. Contrary to previously published data, our experimental data reveal that the residual oil saturation depends on capillary number nonmonotonically. A physically based relationship to scale the capillary desaturation curve is proposed. © 2014 American Institute of Chemical Engineers AIChE J, 61: 1385–1390, 2015     

The flow and displacement in porous media of fluids with yield stress

We study the mobilization and subsequent flow in a porous medium of a fluid with a yield stress, modeled as a Bingham plastic. We use single-capillary expressions for the mobilization and flow in a pore-throat, and a pore-network model that accounts for distributed yield-stress thresholds. First, we extend the statistical physics method of invasion percolation with memory, which models lattice problems with thresholds, to incorporate dynamic effects due to the viscous friction following the onset of mobilization. Macroscopic relations between the applied pressure gradient and the flow rate for single-phase flow are proposed as a function of the pore-network microstructure and the configuration of the flowing phase. Then, the algorithm is applied to model the displacement of a Bingham plastic by a Newtonian fluid in a porous medium. The results find application to a number of industrial processes including the recovery of oil from oil reservoirs and the flow of foam in porous media.