Particle deposition onto solid surfaces with microscopic charge heterogeneity: the "bump effect"

In the laboratory, partially water-wet systems are often mistaken for completely oil-wet systems, because imbibition only starts after removal of the oil layer, which originally covers the grains. The (long) time required to remove the oil film will be referred to as delay time. Incorporation of delay time in a more general description of capillary pressure and relative permeability functions is called the non-equilibrium effect. No attempt has yet been made to model non-equilibrium effects in fractured reservoirs for a field-scale problem and this is the main innovative aspect of this paper. We apply homogenization to derive an upscaled model for fractured reservoirs and include delay time effects. Furthermore, we develop a computationally efficient numerical approach to solve the upscaled model. The upscaled model overcomes limitations of the dual-porosity model including the use of a transfer function and shape factor. This paper examines various aspects of wettability behavior in fractured reservoirs, viz., the contact angle, mixed wetting, and non-equilibrium effects in capillary pressure. The main characteristic that determines reservoir behavior is the Peclet number that expresses the ratio of the average imbibition time divided by the residence time of the fluids in the fractures.At low Peclet numbers and thus high gravity numbers, under-riding is aggravated by large contact angles and longer delay times. However, for low Peclet and low gravity numbers, the effect of contact angle and delay time for the non-equilibrium effects can be ignored without appreciable loss of accuracy. For low Peclet numbers, the recovery for the mixed-wet fracture/mixed-wet matrix case is more than for the water-wet fracture/mixed-wet matrix case because a combination of capillary imbibition and gravity drainage occurs in the former case. For low Peclet numbers, the ultimate oil recovery for the water-wet fracture/mixed-wet matrix case is about the matrix Amott index times the recovery obtained for completely water-wet reservoirs. For residence times of water in the fractured reservoir much longer than the delay time, the delay time (non-equilibrium effect) does not influence the oil recovery qualitatively. Conversely, for high Peclet numbers, the residence time of water in the fractures is short and the relatively longer delay times reduce the cumulative oil production considerably as expected. Furthermore, at high Peclet numbers, after water breakthrough, the oil recovery appears to be approximately proportional to the cosine of the contact angle. It is important to distinguish between truly oil-wet systems and systems that are water-wet with long delay times. The efficiency of waterflooding in naturally fractured oil reservoirs decreases in the sequence of completely water-wet, mixed-wet fracture/mixed-wet matrix, water-wet fracture/mixed-wet matrix, and completely oil-wet, respectively. For the same amount of injected water, the recovery at low Peclet numbers is larger than the recovery at high Peclet numbers.

Analytical and numerical methods are employed to investigate species transport by electrophoretic or electroosmotic motion in the curved geometry of a two-dimensional turn. Closed-form analytical solutions describing the turn-induced diffusive and dispersive spreading of a species band are presented for both the low and high Peclet number limits. We find that the spreading due to dispersion is proportional to the product of the turn included angle and the Peclet number at low Peclet numbers. It is proportional to the square of the included angle and independent of the Peclet number when the Peclet number is large. A composite solution applicable to all Peclet numbers is constructed from these limiting behaviors. Numerical solutions for species transport in a turn are also presented over a wide range of the included angle and the mean turn radius. On the basis of comparisons between the analytical and numerical results, we find that the analytical solutions provide very good estimates of both dispersive and diffusive spreading provided that the mean turn radius exceeds the channel width. These new solutions also agree well with data from a previous study. Optimum conditions minimizing total spreading in a turn are presented and discussed.

Transient Deposition of Colloidal Particles in Heterogeneous Porous Media

Laminar cross-flow convective heat transfer of a finned cylindrical tube in the presence of particle deposition and deposit erosion

A finite element analysis of the fluid flow and the colloidal particle transport equations near a micropatterned charged substrate under radial impinging jet flow conditions is presented to investigate the charge heterogeneity effects on particle deposition. The particle Sherwood number representing the dimensionless particle deposition flux is obtained as a function of the radial distance from the stagnation point. The charge heterogeneity is modeled as concentric bands bearing positive and negative charges on the substrate. When a negatively-charged particle approaches such a charge heterogeneous substrate, it experiences an alternating attractive and repulsive force due to the presence of different charges on the substrate. Consequently, as the particle moves radially outward from the stagnation point, it experiences a periodic array of favorable (attractive) and unfavorable (repulsive) regions on the substrate, giving rise to an oscillatory trajectory. The numerical results obtained from the finite element model are in excellent agreement with existing theoretical and experimental values of deposition rates on homogeneous collector surfaces. However, the results for particle deposition over a heterogeneous substrate depict a significant deviation from those predicted by the patchwise heterogeneity model due to the coupled influence of hydrodynamic interactions and the surface chemical heterogeneity of the collector. The particles that do not deposit over an unfavorable repulsive band are convected to the next favorable band by the tangential velocity. This increases the particle concentration at the leading edge of each favorable band resulting in an increase in particle deposition over the favorable bands and the overall deposition rate on to the collector. Application of this phenomenon will be discussed in context of developing micropatterned surfaces with engineered particle capture properties.

Dry powder inhalation (DPI) has attracted much attention as a treatment for respiratory diseases owing to the large effective absorption area in a human respiratory system. Understanding the drug particle motion in the respiratory system and the deposition behavior is necessary to improve the efficiency of DPI. We conducted computer simulations using a model coupling a discrete element method and a computational fluid dynamics method (DEM-CFD) to evaluate the particle deposition in human respiratory system. A simple artificial respiratory model was developed, which numerically investigated the effect of particle properties and inhalation patterns on the particle deposition behavior. The DEM-CFD simulations demonstrated that the smaller- and lower-density particles showed higher reachability into the simple respiratory model, and the particle arrival ratio to the deep region strongly depended on the aerodynamic diameter. The particle arrival ratio can be described as an exponential function of the aerodynamic diameter. Furthermore, the exponential relationship between the particle reachability into the depth of the simple respiratory model and the aerodynamic diameter predicted the particle aerodynamic diameter based on the required reachability. The particle shape also had an impact on the particle deposition behavior. The rod-like particles with a larger aspect ratio indicated higher reachability into the depth of the simple respiratory model. This was attributed to the high velocity motion of the particles whose long axis was in the direction of the deep region.

The mechanisms and causes of deviation from the classical colloid filtration theory (CFT) in the presence of repulsive Derjaguin-Landau-Verwey-Overbeek (DLVO) interactions were investigated. The deposition behavior of uniform polystyrene latex colloids in columns packed with spherical soda-lime glass beads was systematically examined over a broad range of physicochemical conditions, whereby both the fluid-phase effluent particle concentration and the profile of retained particles were measured. Experiments conducted with three different-sized particles in a simple (1:1) electrolyte solution reveal the controlling influence of secondary minimum deposition on the deviation from CFT. In a second series of experiments, sodium dodecyl sulfate (SDS) was added to the background electrolyte solution with the intent of masking near-neutrally charged regions of particle and collector surfaces. These results indicate that the addition of a small amount of anionic surfactant is sufficient to reduce the influence of certain surface charge inhomogeneities on the deviation from CFT. To verify the validity of CFT in the absence of surface charge heterogeneities, a third set of experiments was conducted using solutions of high pH to mask the influence of metal oxide impurities on glass bead surfaces. The results demonstrate that both secondary minimum deposition and surface charge heterogeneities contribute significantly to the deviation from CFT generally observed in colloid deposition studies. It is further shown that agreement with CFT is obtained even in the presence of an energy barrier (i.e., repulsive colloidal interactions), suggesting that it is not the general existence of repulsive conditions which causes deviation but rather the combined occurrence of "fast" and "slow" particle deposition.

Effect of Particle Size on the Kinetics of Particle Deposition under Attractive Double Layer Interactions

Enhancement of heat or mass transport in a spherical drop of a dielectric fluid translating in another dielectric fluid in the presence of uniform electric field is investigated. The internal problem or the limit of the majority of the transport resistance being in the dispersed phase is considered. The transient energy conservation equation is solved using a fully implicit finite volume method. In the literature, there is a plenty of studies that had been carried out when the electric field acts in the same plane of translation. In this paper, considering creeping flow regime, numerical computations have been conducted when the electric field acts perpendicular to the plane at which translation acts. As such the flow is no longer a two dimensional flow as a third component velocity comes to picture. At the first glance, thoughts of transport enhancement come to mind on the presence of a third velocity component that might promote mixing and consequently enhance transport effectiveness. Results are expressed in terms of the Nusselt number. Nusselt numbers are plotted in terms of Peclet number, Fourier number and the parameter L which is defined as the ratio of the maximum electric-field-induced surface velocity to translation-induced surface velocity. The code was validated by comparing, results for Peclet numbers of 500 and 1000 to corresponding cases available in literature. Results showed good agreement with previous results. A 3-D grid of 20×40×60 has been considered to cover the computational domain. A grid independence study has been carried out by doubling the whole grid. Results show acceptable results compromising accuracy and code running time. The effect of electric field is expressed in terms of parameter L. For low Peclet numbers (Pe ≤ 250), the application of electric field perpendicular to the plane at which translation acts leads to enhancement of heat/mass transport compared to that in pure translation. Such enhancement is about the same when the electric field and translation act in the same plane. On the other hand, for moderate Peclet numbers (Pe= 250∼1000), the transport enhancement is significant when compared to the enhancement obtained by an electric field acts in the same plane of action of translation as well as pure translation. These results can be understood by comparing time scales for diffusion and convection. When Peclet number is low the convection time scale is very large and hence mixing is not that effective in promoting heat / mass transfer. Whereas for moderate Peclet number, when the convection time scale gets smaller, heat/mass transfer is considerably enhanced compared to low Peclet numbers.

Particle deposition under the influence of an electrostatic force is very common but is usually ignored as a factor in many indoor environments and controlled chamber studies. A new model accounting for Brownian and turbulent diffusion, inertia effect, Coulombic (field) and image forces has been formulated. Electrostaticenhanced deposition velocity was quantitatively investigated and compared with the experimental results. An experimental test chamber facility of 1.8m3 was designed to study particle deposition under the influences of electrostatic forces using monodisperse tracer particles in the size range of 3.5–9.0μm. The test sample surfaces were acetate sheet, plain smooth glass plate and thin copper coil. In another set of experiments, the surfaces were treated with commercial anti-electrostatic spray. The results reveal that deposition velocity onto the acetate sheet is significantly higher than that onto the plain glass and copper surfaces showing that the electrostatic attraction force must be taken into account. The key mechanism for deposition onto acetate sheet is by electrostatic attraction. Deposition onto the acetate sheet pre-treated with an anti-static spray shows deposition significantly reduced by 93%. The results also shows that glass surfaces should be first pre-treated to reduce static before deposition velocity measurements. By treating the glass surface with the spray, the deposition velocity was reduced by 68%. A similar reduction was observed for copper foil samples.

Experimental data obtained for particle transport in downward and upward flows in smooth and rough porous media are analyzed at various flow rates. The data analysis and interpretation are aided through an analytical model with linear kinetics that assumes two sites for particle deposition within a medium, namely, reversible and irreversible, together with a dual mode of irreversible deposition. The bimodal particle transport model is obtained using the Green's function method and is capable of fitting, with reasonable accuracy, the observed transport and deposition behavior of particles. Approximations for advection‐dominated flows are also obtained that could represent a simplified modeling tool. Expressions of the temporal moments are developed and algebraic equations are derived that express the model parameters in terms of the moments of the measured particle concentration distributions. The transport models helped define the relationship of the modeled parameters to flow velocity and media roughness. The fitting results show that the parameters for rough and smooth media vary in a systematic way with the pore fluid velocity. The results also reveal that flow direction has a significant influence on the mode and magnitude of irreversible particle deposition for the conditions investigated. For the same seepage velocity, the rate of particle deposition is greater for upward flows than for downward flows. Moreover, roughness effects increase the irreversible particle deposition in downward flows but have little effect in upward flows.

Chapter 10 - Experimental techniques in particle deposition kinetics

The microscale simulation of ultrafine particle transport and deposition in fibrous filtration media was achieved with a novel particle tracking model using a 3D Monte Carlo model. The particle deposition process is governed by the convection–diffusion field. Simulations were performed by considering the fibrous filtration media as an array of identical parallel fibers, in which the flow field was accurately described by an analytical solution. The model of particle movement was described by the random probability distribution characterized by a dimensionless factor, the Peclet number (Pe), based on a convection–diffusive equation of particle transport in fluid. The influence of the particle Peclet number (Pe) on the particle deposition process and the resulting deposition morphology was investigated. The results were analyzed in terms of dust layer growth, particles’ trajectories and dust layer porosity for a vast range of Peclet numbers. The development of distinct deposition morphologies was found by varying the Peclet number (Pe). With a small Peclet number, diffusion dominated deposition and led to the formation of a more open and looser dust layer structure, while with larger Peclet numbers, convection dominated deposition and was found to form compact deposits. According to the change in the location of the packing densities along the dust layer height direction, the dust layer structure could be divided into three typical parts: the substructure, main profile and surface layer. In addition, the deposit morphologies observed for a high Pe were in good agreement with the experimental results found in the literature.

Owing to its fundamental nature, convection-diffusion flows are researched in a number of engineering, scientific, and aeronautical applications. The right meshing approaches are necessary for convection-diffusion simulations. Major meshes in computational fluid dynamics that are used to find the solutions to discretized governing equations include uniform, piecewise-uniform, graded, and hybrid meshes. Unintentionally applying the meshes might lead to poor solutions including numerical oscillations, over- or under-predictions, and lengthy computing time. Accentuating the effectiveness of exponentially graded mesh finite-difference scheme, this paper takes the simulation of a 2D steady scalar convection-diffusion into account. The problem was solved by assigning certain mesh expansion factor to the mesh according to Peclet number. The factor was determined based on its previously derived logarithmically linear relationship with low Peclet number. Based on the values of Peclet number and the source, eight groups of test cases are presented in this paper. It was found that given a Peclet and a mesh number, simulation error percentage was surprisingly constant regardless the source values. The rates of convergence for the scheme, however, were comparable with respect to source values. Uniform convergence rate was also found to be achievable in all test cases corresponding to Peclet number of interests. This work successfully assessed the validity range of the generalized logarithmically linear model between exponentially graded mesh expansion factor and Peclet number for the simulation.

Axial dispersion of a tracer in a two-dimensional gas-liquid flow is studied computationally using a finite-volume/front-tracking method. The effects of Peclet number, capillary number, and segment size are examined. At low Peclet numbers, the axial dispersion is mainly controlled by the convection through the liquid films between the bubbles and channel walls. In this regime, the computational results are found to be in a very good agreement with the existing model due to Pedersen and Horvath [Ind. Eng. Chem. Fundam. 20, 181 (1981)]. At high Peclet numbers, the axial dispersion is mainly controlled by the molecular diffusion, with some convective enhancement. In this regime, a new model is proposed and found to agree well with the computational results. These Peclet number regimes are shown to persist for different slug lengths. The axial dispersion is found to depend weakly on the capillary number in the diffusion-controlled regime. Finally, computational simulations are performed for the cases of six bubbles to mimic bubble trains, and results are compared with the theoretical models.