Physical analysis and modeling of the Falcon concentrator for beneficiation of ultrafine particles

A predictive model of the Falcon enhanced gravity separator has been derived from a physical analysis of its separation principle, and validated against experimental data. After summarizing the previous works that led to this model and the hypotheses on which they rely, the model is extended to cover a wide range of operating conditions and particle properties. The most significant development presented here is the extension of the analytical law to concentrated suspensions, which makes it applicable to actual plant operating conditions. Two examples of industrial use cases are described and studied by interrogation of the model: dredged sediment waste reduction and coal recovery from fine tailings. Comparisons with empirical studies available in the literature show a good agreement between model predictions and industrial data. The model is then used to identify separation efficiency limitations as well as possible solutions to overcome them. These two examples serve to show how this predictive model can be used to obtain valuable information to improve physical separation processes using a Falcon concentrator, or to evaluate Falcon separator’s abilities for new applications

Deterministic ratchets for suspension fractionation

Driven by the current insights in sustainability and technological development in biorefining natural renewable resources, the food industry has taken an interest in fractionation of agrofood materials, like milk and cereal crops. The purpose of fractionation is to split the raw material in several functional ingredients. For example, milk can be split in fractions containing milk fat, casein micelles, and whey proteins. Traditionally, separation processes in food industry are mainly aimed at separating fluid from a suspension stream. Frequently membrane technology is used this type of separation; membranes seem an obvious choice because they are able to sieve components during mild fractionation of many foods, which are suspensions by nature, like milk, or are suspended in liquid during processing (such as starch granule suspensions). However, membrane separation is hindered by fouling of the pores by the food ingredients and accumulation of these components in front of the pore, which makes fractionation with membranes more challenging than plain separation of fluid and solids. That is why we have investigated the possibilities of alternative technologies such as microfluidic devices, and evaluated them under conditions required for food applications. Microfluidic devices are currently investigated for fractionation in biological applications, like sorting of DNA or cells. Due to the large degree of freedom in design, these devices are very suited for innovative fractionation technologies. First, we have evaluated various designs available in literature in chapter 2, which concludes that so-called deterministic ratchets are the most promising technology for fractionation of food suspensions. This conclusion is based on the high yield, compactness of equipment, and high selectivity that can be reached with such devices. In chapters 3 6, we report on detailed investigations on deterministic ratchets through 2D simulation (chapter 3), image analysis in comparison with simulation results (chapter 4), and full 3D simulations in combination with the previously mentioned methods (chapter 5). In the last chapter, our findings are summarized in classification and design rules, and an outlook for future developments is given. Deterministic ratchets are microchannels, containing a regularly spaced array of obstacles, through which the particle suspension flows. The essential property of these ratchets is that each obstacle row is displaced slightly laterally with respect to the previous row. Small particles follow the streamlines of the fluid, and zigzag around the obstacles, while particles larger than a certain critical size bump into the obstacles, and are consequently displaced from their streamline. The larger particles will continuously be displaced in a direction in which the obstacles are placed, and have a certain angle with the flow direction. The small particles are moving in the direction of the liquid flow, which implies under an angle of zero degrees. Via the difference in migration angle of the zigzag and displacement motion, particles can be fractionated, and collected from different outlets. An important property of deterministic ratchets is the size of the particles relative to the width of the so-called flow lane, which determines whether it will show zigzag motion or not. This we have investigated intensively in chapter 3 by means of 2-D flow field simulation. The critical particle size is related to the width of the flow lanes, within which the zigzagging particles will move, and we have determined the flow lane widths for various designs. The distribution of the flow lane width is found to depend strongly on the design of the ratchets. For a limited number of designs the original hypothesis of the inventors of the deterministic ratchets holds, and the flow lanes are symmetrically distributed over the space in between obstacles in one single row. In general, ratchets have an asymmetric flow lane distribution, and typically, ratchet designs suitable for food applications show a strong asymmetric flow lane distribution. An asymmetric flow lane distribution implies that there is not one critical flow lane width but two that determine the type of motion of particles inside the ratchets. As a first approach we have taken these as the first and last (and largest) flow lane width, df,1 and df,N. Consequently, particles are expected to show alternative motions that are in between zigzag and displacement motion. Its existence has become evident in the experiments described in chapter 4, and we have named it mixed motion. The mixed motion is irregular, in contrast to the zigzag and displacement motion, and has a migration angle which is intermediate between the angles corresponding to zigzag and displacement motion, 0 tracked by high speed recording, and the migration angle were quantified through tailor-made image analysis. As expected, the transitions between the different types of particle motion seem to occur on the basis of the critical length scales, df,1 and df,N. However, this conclusion can not be stated with high certainty because of the large experimental error due to the wide particle size distribution of the used suspensions. Because the ratchets used in chapter 4 has not been specifically designed to investigate various particle behaviors, we have designed new ratchets based on the critical length scales, df,1 and df,N, via 2D flow simulations, in order to allow detailed investigation. Although these critical length scales do not take all aspects that play a role during particle movement in a ratchet into account, we have stated that they can be used as an initial guideline for ratchet designs. Next, we have performed detailed and computationally intensive, 3D simulations, that include the particles. These 3D simulations are performed to check the validity of the classification rules, derived from the 2D simulations, that only include fluid flow. The simulation results show that the transition between zigzag and mixed motion occurs indeed at the critical length scale, df,1, being the width of the first flow lane. However, the length scale determining the occurrence of displacement motion is larger than the last lane width, df,N, and might even be uncorrelated with it. We have concluded that this second critical length scale, df,c, can only be determined via 3D simulations. The thus obtained classification rules are investigated experimentally and we have been able to correlate the migration angle of many observed particles exhibiting mixed motion, to the critical length scales. This makes us confident, that we now have identified the relevant critical length scales in deterministic ratchets. In the concluding chapter, we discuss the approach that we chose to ultimately derive the classification rules, and discuss the implications of the corrected length scales on the key performance indicators of ratchets, that are relevant to food applications. We find that obtaining the correct critical length scales requires computationally intensive 3D simulations. Specifically for compact ratchet designs, which are relevant for food application, the critical lane width df,c is not much different from df,N, obtained via 2D flow simulations - and 2D simulation may thus offer a more time-efficient way of estimating df,c. Further, we have discussed the existence of mixed motion in terms of selectivity during fractionation for polydisperse suspensions, and have found that the yield, compactness, and selectivity, all decrease, but at the same time it also opens possibilities for fractionation in multiple streams in one step. <br/

Analysis of gas-solid flow using particle-resolved direct numerical simulation: flow physics and modeling

Gas-solid flows are encountered in many industrial processes such as pneumatic conveying, fluid catalytic cracking, CO2 capture and fast pyrolysis process. In spite of several experimental and numerical studies performed to understand the physics governing observed phenomena in gas-solid flows, and to propose accurate closure models for computational fluid dynamics (CFD) simulations using the averaged conservation equations, there are several challenges in gas-solid flows that yet need to be addressed. In many of the industrial processes, the solid-to-fluid density ratio is of the order of 100 to 1000, and the particle diameter ranges from 50 to 500 micron. The interaction of heavy and large particles with the carrier phase leads to the formation of a boundary layer around each particle that in turn gives rise to interphase momentum transfer at the fluid-solid interface. The rate of work done by the carrier flow to sustain the interphase transfer of momentum leads to generation of velocity fluctuations in both the gas phase and the solid phase. Gas-phase velocity fluctuations enhance gas-particle heat transfer and the mixing of chemical species. Additionally, fluctuating motion of solid particles together with microscale hydrodynamic instabilities give rise to formation of mesoscopic particle clusters in gas-solid flows. The particle clusters then modify the hydrodynamic field and then the interconnected phenomena mentioned above dynamically modify the response of the system. Furthermore, if there exists a particle size distribution in the dispersed phase, the differences in the gas-particle and particle-particle drag forces lead to the segregation phenomenon. In this study, particle-resolved direct numerical simulation (PR-DNS) is used to address some aspects of the challenges noted above, and to propose closure models for device-scale CFD calculations. First, the level of gas-phase velocity fluctuations is quantified, and its dependence on flow parameters is explained. An algebraic Reynolds stress model is proposed by decomposing the Reynolds stress into isotropic and deviatoric parts. Also the influence of solid particles with isotropic turbulent flow has been addressed using PR-DNS. In addition, in this study the slip velocity between two particle size classes in a bidisperse mixture is quantified, which is the key signature of segregation of particle size classes. The predictive capability of two-fluid closure models in predicting the slip velocity between particle size classes is also assessed. PR-DNS is used to propose a bidisperse gas-particle drag model that improves the prediction of the mean slip velocity between the two particle size classes. In addition, the mechanism of transfer of kinetic energy from the mean flow to fluid-phase and particle velocity fluctuations in a homogeneous bidisperse suspension is explained. This mechanism of transfer of energy is important because particle velocity fluctuations affect the particle-particle drag, which jointly with the gas-particle drag on each particle class determines the mean slip velocity between the two particle classes. In this study we have also used PR-DNS to quantify the mean drag force on particle clusters that are statistically consistent with those observed in experiments. A clustered particle drag model has been proposed based on our PR-DNS results. To address the effect of filtering the hydrodynamic field on flow statistics, which is used in LES of gas-solid flows, we have shown that the source and sink of kinetic energy in particle velocity fluctuations obtained from the PR-DNS are different from those predicted by the LES approach. These differences lead to a different level of kinetic energy in the solid phase obtained from the two approaches, and thus the flow characteristics that depend on solid-phase kinetic energy, such as formation and evolution of particle clusters, may not be comparable between the PR-DNS and LES approaches. In this study we have also used PR-DNS to quantify the growth rate of mixing length in a particle-laden mixing layer, and the corresponding mechanism is identified by using a scaling analysis

Fractionation of magnetic microspheres in a microfluidic spiral: interplay between magnetic and hydrodynamic forces

Magnetic forces and curvature-induced hydrodynamic drag have both been studied and employed in continuous microfluidic particle separation and enrichment schemes. Here we combine the two. We investigate consequences of applying an outwardly directed magnetic force to a dilute suspension of magnetic microspheres circulating in a spiral microfluidic channel. This force is realized with an array of permanent magnets arranged to produce a magnetic field with octupolar symmetry about the spiral axis. At low flow rates particles cluster around an apparent streamline of the flow near the outer wall of the turn. At high flow rates this equilibrium is disrupted by the induced secondary (Dean) flow and a new equilibrium is established near the inner wall of the turn. A model incorporating key forces involved in establishing these equilibria is described, and is used to extract quantitative information about the magnitude of local Dean drag forces from experimental data. Steady-state fractionation of suspensions by particle size under the combined influence of magnetic and hydrodynamic forces is demonstrated. Extensions of this work could lead to new continuous microscale particle sorting and enrichment processes with improved fidelity and specificity

Bifurcation of solutions through a contact manifold in bidisperse models

This research focuses on a hyperbolic system that describes bidisperse suspensions, consisting of two types of small particles dispersed in a viscous fluid. The dependence of solutions on the relative position of contact manifolds in the phase space is examined. The wave curve method serves as the basis for the first and second analyses. The former involves the classification of elementary waves that emerge from the origin of the phase space. Analytical solutions to prototypical Riemann problems connecting the origin with any point in the state space are provided. The latter focuses on semi-analytical solutions for Riemann problems connecting any state in the phase space with the maximum packing concentration line, as observed in standard batch sedimentation tests. When the initial condition crosses the first contact manifold, a bifurcation occurs. As the initial condition approaches the second manifold, another structure appears to undergo bifurcation, although it does not represent an actual bifurcation according to the triple shock rule. The study reveals important insights into the behavior of solutions in relation to these contact manifolds. This research sheds light on the existence of emerging quasi-umbilic points within the system, which can potentially lead to new types of bifurcations as crucial elements of the elliptic/hyperbolic boundary in the system of partial differential equations. The implications of these findings and their significance are discussed

Optimized heavy oil-in-water emulsions for flow in pipelines

Oilfield operations such as drilling, reservoir management, and production require the injection and/or production of complex fluids to improve the extraction of crude oils. Some of these complex fluids such as drilling muds, fracking fluids, foams, emulsions, surfactants, and polymers, fall under the classification of colloidal suspensions which is one substance of microscopically dispersed insoluble particles suspended throughout another substance. These colloidal suspensions show complex rheological properties that are dependent on the suspension properties, flow conditions, and flow conduit dimensions. Rheology of colloidal suspensions is a complex subject that is still being investigated. The focus of this study is on heavy oil-in-water emulsions. Heavy oil and bitumen resources account for approximately 70% of the remaining oil discovered to date in the world. Heavy crude oils are costly to produce, transport, and refine compared to light crude oils due to the high viscosity of heavy crude oils. To improve the economic viability of producing heavy oils, especially in a time with low crude oil prices, operational expenses must be reduced. One of the main areas to improve is the cost associated with transporting produced heavy oils from production wells to refineries. Currently, heavy oils are diluted with low viscosity diluents such as condensates and light crude oils to lower the mixture viscosity below 350 cSt before heavy oils can be transported through pipelines. The diluted mixtures require up to 50% (vol.) diluents to lower the heavy oil viscosity. High demand and low supply of condensates and constrained pipeline capacities have resulted in pipeline transportation costs of up to $22/bbl of diluted heavy oil from Canada to refineries in the U.S. An alternative method of transporting heavy oils is to transport heavy oils in an emulsified form, heavy oil-in-water emulsions, which can show orders of magnitude lower viscosities compared to the viscosity of heavy oils. In this study, a simple, one-step method of preparing heavy oil-in-water emulsions was developed. The physical properties of heavy oil-in-water emulsions are controlled and modified by optimizing the chemical formulation used to prepare emulsions. Stable heavy oil-in-water emulsions can be prepared with chemical formulations that are tailored to the type of heavy oils and available water sources which can range from freshwater to softened seawater. The rheology of heavy oil-in-water emulsions has been characterized with a rotational viscometer. Heavy oil-in-water emulsions, especially concentrated emulsions, showed complex rheological properties such as shear thinning behavior, two-step yield stresses, two-step wall slips, and rheopexy. A rheological equation and a wall slip equation have been developed to model the rheology of heavy oil-in-water emulsions over a range of shear rates and flow conduit dimensions. Heavy oil-in-water emulsions characterized with capillary tube viscometers showed drastically different viscosity measurements compared to the viscosity measurements obtained with a rotational viscometer. This is important because the flow of emulsions in pipelines are similar to the flow of emulsions in capillary tube viscometers, not rotational viscometers. The lower viscosities measured with capillary tube viscometers are attributed to oil droplet migration away from the tube walls due to the shear heterogeneity observed in Poiseuille (tube) flow. A scaling equation was proposed to relate the viscosity measurements of emulsions with a rotation viscometer to the viscosity measurements of emulsions with capillary tube viscometers. The rheological measurements of heavy oil-in-water emulsions are used to estimate the flow of emulsions in crude oil pipelines with various radii. Viscosity measurements of optimized heavy oil-in-water emulsions with a rotational viscometer showed that heavy oil-in-water emulsions with up to 75$1-3/bbl of emulsion. Heavy oil-in-water emulsions also showed drag reduction properties which can significantly increase the maximum flow capacity of crude oil pipelines. Transporting heavy oils as concentrated heavy oil-in-water emulsions appeared to be a competitive if not a better method of lowering heavy oil viscosity compared to the diluent method in terms of cost and flow performance in pipelines.Petroleum and Geosystems Engineerin

A Continuous Mathematical Model of the One-Dimensional Sedimentation Process of Flocculated Sediment Particles

A new continuous one-dimensional sedimentation model incorporating a new continuous flocculation model that considers aggregation and fragmentation processes was derived and tested. Additionally, a new procedure to model sediment particle size distribution (PSD) was derived. Basic to this development were three different parametric models: Jaky, Fredlund and the Gamma probability distribution (GPD) were chosen to fit three different glass micro-spheres PSDs having average particle sizes of 7, 25 and 35 microns. The GPD provided the best fit with the least parameters. The bimodal GPD was used to fit ten sediment samples with excellent results (\u3c 5% average error). A continuous flocculation model was derived using the method of moments for solving the continuous Smoluchowski coagulation equation with fragmentation. The initial sediment PSD was modeled using a bimodal GPD. This new flocculation model resulted in a new general moments’ equation that considers aggregation and fragmentation processes, which is represented by a system of ordinary differential equations. The model was calibrated using a genetic algorithm with initial and flocculated PSDs of four sediment samples and four anionic polyacrylamides flocculants. The results show excellent correlation between predicted and observed values (R2 \u3e 0.9878). A new continuous one-dimensional sedimentation model that resulted in a scalar hyperbolic conservation law was derived from the well-known Kynch kinematic sedimentation model. The model was calibrated using column tests results with glass micro-spheres particles. Two different glass microspheres particle size distributions (PSDs) were used with average diameters of 7 and 37 microns. Excellent values of coefficient of determination (R2 \u3e 0.89, except for one test replicate) were obtained for both the small and large glass micro-spheres PSDs. These results suggest that the proposed sedimentation model can be expanded to model the sedimentation process inside a sediment pond