A mathematical model for predicting oil-water separation efficiency in a de-oiling hydrocyclone

The de-oiling hydrocyclone is among the most effective devices to recover oil from oily wastewater. In this work, a new model is theoretically developed to predict the separation efficiency of oil droplets in hydrocyclones. According to the analysis of the flow pattern, the droplet dynamics, and oil concentration distribution in the de-oiling hydrocyclone, the differential equation for the new model is established based on the principle of the mass balance of oil droplet. The proposed model can be finally expressed as a simple explicit function including the main geometrical dimensions and operating parameters. The availability of this model is validated by comparison of the calculated grade efficiency with experimental data and other theoretical separation model.     

CFD and Population Balance Modeling of Crude Oil Emulsions in Batch Gravity Separation—Comparison to Ultrasound Experiments

Water-in-oil emulsion destabilization and separation in a batch gravity separator was investigated experimentally and by numerical modeling. A multiphase computational fluid dynamics (CFD) was used with a population balance model (PBM) to model separation behavior of crude oil emulsions. The inhomogeneous discrete method is used to solve the population balance equations. Closure kernels are applied to model droplet–droplet coalescence. To describe the increase in emulsion viscosity with water concentration, an emulsion viscosity model was selected that predicted emulsion stability and the denser emulsion layer forming above the coalescing interface, otherwise known as the dense packed zone or layer (DPZ). The results from a commercial CFD code are compared to experimental data of the water fraction vertical distribution measured by low-power ultrasound in the batch separator. The predicted time-dependent profiles of water fraction in the separator were found to be in good agreement with the experimental measurements for the range of water content from 6 to 50%. The model predicts the effect of water fraction on the separation kinetics and the evolution of the DPZ. Further studies are underway to apply the models to emulsions from different types of crude oils.     

Numerical simulation of deformation behavior of droplet in gas under the electric field and flow field coupling

The water droplets in the process of electrostatic coalescence are important when studying electrohydrodynamics. In the present study, the electric field and flow field are coupled through the phase field method based on the Cahn–Hilliard formulation. A numerical simulation model of single droplet deformation under the coupling field was established. It simulated the deformation behavior of the movement of a droplet in the continuous phase and took the impact of droplet deformation into consideration which is affected by two-phase flow velocity, electric field strength, the droplet diameter, and the interfacial tension. The results indicated that under the single action of the flow field, when the flow velocity was lower, the droplet diameter was greater as was the droplet deformation degree. When the flow velocity was increased, the droplet deformation degree of a small-diameter droplet was at its maximum size, the large-diameter droplet had a smaller deformation degree, and the middle-diameter droplet was at a minimum deformation degree. When the flow velocity was further increased, the droplet diameter was smaller, and the droplet deformation degree was greater. Under the coupled effect of the electric field and flow field, the two-phase flow velocity and the electric field strength were greater, and the degree of droplet deformation was greater. While the droplet diameter and interfacial tension were smaller, the degree of droplet deformation was greater. Droplet deformation degree increased along with the two-phase flow velocity. The research results provided a theoretical basis for gas–liquid separation with electrostatic coalescence technology.     

Application experiment and numerical simulation analysis of oil–water separator with two-oriented corrugated coalescence plate

The new structure of two-oriented corrugated plate is developed in an oil–water separator. The surface of the corrugated plate is modified so that one side is provided with a hydrophobic property and the other side is provided with a hydrophilic property. The effect of feed flow rate and composition on the separation efficiency of the separator is analyzed by experiments. A three-dimensional model of the separator is established for simulation by using the fluent software. The separation effect is characterized by the maximum concentration and thickness of the two constituents. The simulation results are in good agreement with the experimental results. The feed composition and feed flow rate can be worked together in the coalescence process. Both in the experiment and in the simulation, the concentration of the outlet of this polynode separator can reach more than 99% in the treatment of oil-bearing rate from 30% to 60% and inlet flow rate at 800?L/h～2000?L/h, which confirms the high separation efficiency of the device structure. At the same time, it also can be concluded that the lower oil phase concentration is suitable for larger inlet flow, while higher oil phase concentration is more applicable for lower flow rate in the appropriate range.     

Influence of Discrete Particle Diameter and Separating Velocity on the Separation Efficiency of Wave-Plate Separator Including Coalescence and Breakup Model

Wave-plate separators are widely used to remove fine liquid droplet entrained in gas flow based on the inertia force difference of gas and liquid phase. The CFD method is adopted to simulate the separating process of wave-plate separator, the models and parameters used in the simulation were verified through comparing with the experimental data. It is validated that including the droplet coalescence and breakup model, which take place during the separating process, can depict the separating process better. The results indicate that the separation efficiency of wave-plate separator presents two peaks with the increasing of the separating velocity, the first peak is caused by gravity and the second peak is formed for the inertia separation, whereas with the increasing of the droplet diameter, the two peaks are no longer distinct. In addition, the separation efficiency is changed little with droplet diameter variation if the wave-plate separator is worked on the corresponding velocities of the two peaks, and changed a lot at other velocity. Researching results about droplet breakup also showed that only large diameter droplet will break up at lower flow velocity, and the droplet breakup diameter became smaller and smaller with the increasing of the flowing velocity.     

Numerical simulation of droplet coalescence behavior in gas phase under the coupling of electric field and flow field

The coalescence behavior of droplets in an electric field belongs to the important research contents of electrohydrodynamics. Based on the phase field method of the Cahn–Hilliard equation, the electric field and the flow field are coupled to establish the numerical model of twin droplet coalescence in a coupled field. The effects of flow rate, electric field strength, droplet diameter, and interfacial tension on the coalescence behavior of droplets during the coalescence process were investigated. The results show that the dynamic behavior of the droplets is divided into coalescence, after coalescence rupture, and no coalescence under the coupling of electric field and flow field. The proper increase of the electric field strength will accelerate the coalescence of the droplets, and the high electric field strength causes the droplets to burst after coalescence. Excessive flow rates make droplets less prone to coalescence. Under the coupling field, the larger the droplet interface tension, the smaller the droplet diameter, the smaller the flow rate, and the shorter the droplet coalescence time. The results provide a theoretical basis for the application of electrostatic coalescence in gas–liquid separation technology.     

Homogenization Efficiency of Two Immiscible Fluids in Static Mixer Using Droplet Tracking Technique

Comprehensive understanding of the mechanism of two-phase flow agitation is essential to control the mixing performance in chemical processes. The aim of the present study is to understand mixing behavior of two phase flow emulsification process in details by utilizing a three-dimensional computational fluid dynamics (CFD) scheme and predicting the flow characteristics of O/W emulsion in a Kenics static mixer (KSM) operating as an in line continuous homogenizer. The overall study is carried out in three steps: (a) a turbulent flow analysis, to obtain an overall characteristic of the emulsion resulting in CFD model and (b) comparing theoretical data of model with those of experimental studies in order to validate the CFD approach; (c) a droplet tracking step, to extensively study the distribution of marked droplets during the mixing procedure. To achieve this goal, the individual droplets being numerically labeled and visually colored regarding their droplet size; a quantitatively scrutiny of mixing for the droplet distribution was introduced. As a result, the droplet tracking using CFD has successfully evaluated the mixing performance and is proposed as a practical numerical scheme for predicting the KSM behavior.     

Spreading and sorption of droplets on layered porous substrates

In this paper spreading and sorption of a droplet on an anisotropic, layered porous substrate are investigated numerically. Flow in the saturated part of the porous material is governed by Darcy's law, assuming a sharp wetting front separating the saturated regions from the dry regions. Numerical results are presented for spreading and sorption of droplets in their dependence on the material and process parameters for axisymmetric configurations. Limiting cases of sorption into infinitely thick and very thin porous layers are considered. For an analytical sorption model for thin substrates fed by an infinite reservoir a correction term taking into account the flow resistance in the inlet region is derived and the consistence of the modified model with numerical and experimental results is shown. For two-layer substrates, numerical results on the influence of the layer permeabilities on the sorption kinetics are presented.     

CFD simulation of oil–water separation characteristics in a compact flotation unit by population balance modeling

Huge amounts of produced water are generated in offshore oil production. The Compact Flotation Unit (CFU) is an excellent pretreatment technology of produced water with high separation efficiency, low residence, and small split ratio. The Computational Fluid Dynamics-population balance model (CFD-PBM) method is used in the present work to study the oil–water separation characteristics in the self-developed Beijing Institute of Petrochemical Technology Compact Flotation Unit (BIPTCFU) at both micro-scale and macro-scale, which would help us gain more insights into the mechanism and the influence of flow field on the oil–water separation process such as the oil droplets’ diameter distribution and separation efficiency. The effects of the inlet diameter, the height of the preliminary separation zone, and the width of the annular space on the oil–water separation characteristics of CFU were discussed systematically. It is illustrated that the appropriate increase of inlet velocity, decrease of annular gap width, and increase of the height in the preliminary separation zone can effectively promote the collision and coalescence process of oil droplets. However, the overlarge height of the preliminary separation zone and the too narrow width of the annular space will both have a significant negative effect on the migration and separation of oil and water and lead to the decrease of separation efficiency.     

CFD Simulation of Droplet Formation in a Wide-Type Microfluidic T-Junction

Droplet formation in a wide-type microfluidic T-junction was studied using the computational fluid dynamics (CFD) method. Two distinct regimes of droplet formation were confirmed: dripping and jetting; and, at both regimes, droplet size decreases with an increase in capillary number. CFD simulation demonstrated that droplet formation in the T-junction can be divided into three steps: droplet emergence and growing up; separation with the disperse phase; and detachment from the channel wall. The wettability of the channel wall significantly affects the process of droplet detachment from the channel wall; also, the simulation clearly showed that droplets can be formed only when the continuous phase fluid preferentially wets the channel wall, that is, its contact angle on the wall is smaller than 90°. Finally, the CFD study verified that the disperse phase flow rate can significantly affect the droplet size as well as the mechanism of droplet formation.     

The effect of interfacial viscosity on the droplet dynamics under flow field

The effects of interfacial viscosity on the droplet dynamics in simple shear flow and planar hyperbolic flow are investigated by numerical simulation with diffuse interface model. The change of interfacial viscosity results in an apparent slip of interfacial velocity. Interfacial viscosity has been found to have different influence on droplet deformation and coalescence. Smaller interfacial viscosity can stabilize droplet shape in flow field, while larger interfacial viscosity will increase droplet deformation, or even make droplet breakup faster. Different behavior is found in droplet coalescence, where smaller interfacial viscosity speeds up film drainage and droplet coalescence, but larger interfacial viscosity postpones the film drainage process. This is due to the change of film shape from flat‐like for smaller interfacial viscosity to dimple‐like for larger interfacial viscosity. The film drainage time still scales as Ca⁰ at smaller capillary number (Ca), and Ca^1.5 at higher capillary number when the interfacial viscosity changes. The interfacial viscosity only affects the transition between these limiting scaling relationships. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1505–1514, 2008     

Modeling Injection of Dense Liquid Sprays in Radio Frequency Inductively Coupled Plasmas

A spray model and a droplet collision model are implemented into a radio frequency inductively coupled plasma model. The discrete parcel technique combined with the stochastic Monte Carlo method is used to solve the spray equation and determine the outcomes of droplet collisions in dense sprays. Plasma--spray interactions are considered by adding source terms to the conservation equations of mass, momentum and energy of the plasma phase. Two types of the outcomes of water droplets collisions, coalescence and grazing, are predicted and compared to the experimental and analytical results. The agreement is quite good. The effects of droplet collisions on droplet size distribution of the spray and the spray evaporation are investigated. It is found that the droplet collisions can increase the average droplets size of the spray. For the mono-disperse spray, the collisions can lead to a delay on the spray evaporation. However, for the poly-disperse spray, the effect of droplet collisions on the spray evaporation could not be predicted before the calculation due to the randomness of droplet collisions.     

Optimizing Geometric Parameters in Hydrocyclones for Enhanced Separations: A Review and Perspective

Hydrocyclones have been extensively applied for solid–liquid or liquid–liquid separations in various industries. However, the exact mechanisms underlying the enhanced separation technologies based on the optimization of geometric parameters of hydrocyclones remain unclear, and a number of research teams have performed numerous studies to enlarge the application scope of hydrocyclones by optimizing geometric parameters. This review provides a comprehensive state-of-the-art review of hydrocyclone enhanced-separation technologies. The enhanced-separation technologies are categorized into ten groups: cylindrical section, inlet, vortex finder, underflow pipe, conical section, hydrocyclone inclination angle, hydrocyclone insertion, conical-section/apex water injection, reflux device, and multi-hydrocyclone arrangement. These enhanced-separation technologies were analyzed and summarized according to the key separation-performance parameters of hydrocyclones, such as separation efficiency, cut size, split ratio, energy consumption, and capacity. It is expected that both the reviewed contents and the proposed challenges and future methodologies and technologies may provide research fellows working in this field with an improved understanding of enhanced separation technologies of hydrocyclones.     

Dynamics of alternating current electric field–assisted non-Newtonian droplet formation with geometry confinement

Recently, microfluidic techniques have been widely applied for biomaterial droplet manipulations due to their precision and efficiency. Many biosamples such as deoxyribonucleic acid and blood samples are non-Newtonian fluids with complex rheology, which brings challenges in control over them. The electric field is characterized by fast response and excellent adaptation to control microscale fluid flow. Here, we systematically investigate the alternating current electric field–assisted formation of non-Newtonian droplet in a flow-focusing microchannel with different sizes of channel orifice. The dependencies of flow conditions, microchannel geometries and electric parameters on the dynamics of non-Newtonian droplet formation are thus elucidated. An effective capacitance electric model is developed to reveal and predict the interaction between the fluid flow and the electric field. Furthermore, the flow field of non-Newtonian droplet formation is captured via the high-speed microparticle image velocimetry system. The characteristics of the regimes of droplet formation and the influences of the channel orifice are revealed quantitatively. Our work offers elaborate references to the control of non-Newtonian droplet formation, which benefits a wide range of applications in biology and chemistry.     

Dynamics of water droplets detached from porous surfaces of relevance to PEM fuel cells

The detachment of liquid droplets from porous material surfaces used with proton exchange membrane (PEM) fuel cells under the influence of a cross-flowing air is investigated computationally and experimentally. CCD images taken on a purpose-built transparent fuel cell have revealed that the water produced within the PEM is forming droplets on the surface of the gas-diffusion layer. These droplets are swept away if the velocity of the flowing air is above a critical value for a given droplet size. Static and dynamic contact angle measurements for three different carbon gas-diffusion layer materials obtained inside a transparent air-channel test model have been used as input to the numerical model; the latter is based on a Navier–Stokes equations flow solver incorporating the volume of fluid (VOF) two-phase flow methodology. Variable contact angle values around the gas–liquid–solid contact-line as well as their dynamic change during the droplet shape deformation process, have allowed estimation of the adhesion force between the liquid droplet and the solid surface and successful prediction of the separation line at which droplets loose their contact from the solid surface under the influence of the air stream flowing around them. Parametric studies highlight the relevant importance of various factors affecting the detachment of the liquid droplets from the solid surface.     

Breakage rate of colloidal aggregates in shear flow through stokesian dynamics

We study the first breakage event of colloidal aggregates exposed to shear flow by detailed numerical analysis of the process. We have formulated a model, which uses stokesian dynamics to estimate the hydrodynamic interactions among the particles in a cluster, van der Waals interactions and Born repulsion to describe the normal interparticle interactions, and the tangential interactions through discrete element method to account for contact forces. Fractal clusters composed of monodisperse spherical particles were generated using different Monte Carlo methods, covering a wide range of cluster masses (N(sphere) = 30-215) and fractal dimensions (d(f) = 1.8-3.0). The breakup process of these clusters was quantified for various flow magnitudes (γ), under both simple shear and extensional flow conditions, in terms of breakage rate constant (K(B)), mass distribution of the produced fragments (FMD, f(m,k)), and critical stable aggregate mass (N(c)), defined as the largest cluster mass that does not break under defined flow conditions. The breakage rate K(B) showed a power law dependence on the product of the aggregate size and the applied stress, with values of the corresponding exponents depending only on the aggregate fractal dimension and the type of flow field, whereas the prefactor of the power law relation also depends on the size of the primary particles comprising a cluster. The FMD was fitted by Schultz-Zimm distribution, and the parameter values showed an analogous dependence on the product of the aggregate size and the applied stress similar to the rate constant. Finally, a power law relation between the applied stress and corresponding largest stable aggregate mass was found, with an exponent value depending on the aggregate fractal dimension. This unique and detailed analysis of the breakage process can be directly utilized to formulate a breakage kernel used in solving population balance equations.     

Evaluation of a mathematical model using experimental data and artificial neural network for prediction of gas separation

In recent times, membranes have found wide applications in gas separation processes. As most of the industrial membrane separation units use hollow fiber modules, having a proper model for simulating this type of membrane module is very useful in achieving guidelines for design and characterization of membrane separation units. In this study, a model based on Coker, Freeman, and Fleming＇s study was used for estimating the required membrane area. This model could simulate a multicomponent gas mixture separation by solving the governing differential mass balance equations with numerical methods. Results of the model were validated using some binary and multicomponent experimental data from the literature. Also, the artificial neural network （ANN） technique was applied to predict membrane gas separation behavior and the results of the ANN simulation were compared with the simulation results of the model and the experimental data. Good consistency between these results shows that ANN method can be successfully used for prediction of the separation behavior after suitable training of the network     

Experimental study of the relative effect of pressure drop and flow rate on the droplet size downstream of a pipe restriction

An experimental setup consisting of a 100?mm inner diameter pipeline, a butterfly valve with inner diameter of 100?mm, and oil and water pumping capacities of up to 20?m³/h were used to study droplet breakup in two-phase oil–water flow. The tests were performed at atmospheric pressure and under ambient temperatures. A particle-sizing camera was used to quantify droplet sizes. Combinations of different flow rates, water cuts, and pressure drops were tested to determine the relative effects of flow rate and pressure drop over a valve on the droplet breakup process. The test matrix was designed so that it should be possible to determine if the droplet sizes produced were independent of the flow rate. The fluid system consisted of a water phase and a mineral oil with viscosity of 4?mPa?·?s. Two different droplet breakup models were compared against the measured droplet sizes. The two models considered turbulence and droplet acceleration through the restriction respectively as the main contributor for droplet breakup.     

Passive droplet trafficking at microfluidic junctions under geometric and flow asymmetries

When droplets enter a junction they sort to the channel with the highest flow rate at that instant. Transport is regulated by a discrete time-delayed feedback that results in a highly periodic behavior where specific patterns can continue to cycle indefinitely. Between these highly ordered regimes are chaotic structures where no pattern is evident. Here we develop a model that describes droplet sorting under various asymmetries: branch geometry (length, cross-section), droplet resistance and pressures. First, a model is developed based on the continuum assumption and then, with the assistance of numerical simulations, a discrete model is derived to predict the length and composition of the sorting pattern. Furthermore we derive all unique sequences that are possible for a given distribution and develop a preliminary estimation of why chaotic regimes form. The model is validated by comparing it to numerical simulations and results from microfluidic experiments in PDMS chips with good agreement.