A new model in correlating and calculating the solid–liquid equilibrium of salt–water systems

In this work, a new activity coefficient model was deduced for the correlation of solid–liquid equilibrium(SLE) in electrolyte solutions. The new excess Gibbs energy equation for SLE contains two parts: the single electrolyte item and the mixed electrolyte item. Then a new hypothesis for the reference state of activity coefficients was proposed in the work. Literature data for single electrolyte solution and mixed electrolyte solution systems,with temperature spanning from 273.15 to 373.15 K, were successfully correlated using the developed model.     

Observations of solid–liquid systems in anchor agitated vessels

Although process development is often done in well agitated vessels (e.g. with a retreat curve, pitched blade turbine etc.), there are a sizeable number of contract manufacturers’ still deploying a significant number of anchor agitated process units. For the purpose of observing the Zwietering constant value ‘S’ and few industrially important solid–liquid systems, we conducted extensive suspension experiments with anchor agitated vessels for varying D/T ratios (0.74 and 0.73). In this study, Zwietering's N_js (just suspension speed) and the corresponding ‘S’ factor were obtained for each system over a range of solid loadings. We found that the Zwietering constant was strongly dependent on the nature of the solid–liquid system; i.e. different systems had different ‘S’ values for the same geometrical configuration.     

Experimental investigation and CFD simulation of liquid–solid–solid dispersion in a stirred reactor

For understanding the monosodium aluminate hydrate crystallization from the supersaturated aluminate solution containing red mud as the leaching liquor of bauxite, the liquid–solid–solid dispersion of a simulant system, i.e. glycerite, red mud and sand, in a stirred reactor has been experimentally investigated as well as simulated using computational fluid dynamics model (CFD) for the first time. The computational model is based on the Eulerian multi-fluid model along with RNG k–ε turbulence model, where Syamlal–obrien-symmetric drag force model (Syamlal, 1987) of the inter-phase momentum transfer between two dispersed solid phases is taken into account. A good agreement is obtained between the experimental data of solid distributions and the simulation results in the flow fields of liquid–solid–solid as well as liquid–solid systems. The solid suspension qualities of both liquid–solid and liquid–solid–solid systems in the stirred reactors with and without draft tube were also studied in detail based on mixing time, the standard deviation of solid concentration proposed by Bohnet and Niesmak (1980), the flow pattern and power number. The influence of the interaction between two dispersed solid phases on the suspension of red mud is found significantly greater than that of sand. The holdup of sand below the impeller is considerably larger than that above the impeller and the red mud dispersion approaches homogeneous in the reactor. The mixing time of liquid–solid–solid suspension is longer than that of liquid–solid suspension under the same conditions, and the mixing times of both systems in the stirred reactor with draft tube are longer than that in the reactor without draft tube. Furthermore, the distributions of sand and red mud in the reactor with draft tube were found less homogeneous than those without draft tube in most cases.     

Development and verification of coarse-grain CFD-DEM for nonspherical particles in a gas–solid fluidized bed

Computational fluid dynamics coupled with discrete element method (CFD-DEM) has been widely used to understand the complicated fundamentals inside gas–solid fluidized beds. To realize large-scale simulations, CFD-DEM integrated with coarse-grain model (CG CFD-DEM) provides a feasible solution, and has led to a recent upsurge of interest. However, when dealing with large-scale simulations involving irregular-shaped particles such as biomass particles featuring elongated shapes, current CG models cannot function as normal because they are all developed for spherical particles. To address this issue, a CG CFD-DEM for nonspherical particles is proposed in this study, and the morphology of particles is characterized by the super-ellipsoid model. The effectiveness and accuracy of CG CFD-DEM for nonspherical particles are comprehensively evaluated by comparing the hydrodynamic behaviors with the results predicted by traditional CFD-DEM in a gas–solid fluidized bed. It is demonstrated that the proposed model can accurately model gas–solid flow containing nonspherical particles, merely the particle dynamics are somewhat lost due to the scaleup of particle size. Finally, the calculation efficiency of CG CFD-DEM is assessed, and the results show that CG CFD-DEM can largely reduce computational costs mainly by improving the calculation efficiency of DEM. In general, the proposed CG CFD-DEM for nonspherical particles strikes a good balance between efficiency and accuracy, and has shown its prospect as a high-efficiency alternative to traditional CFD-DEM for engineering applications involving nonspherical particles.     

Determination of dynamic contact angles in solid–liquid–liquid systems using the Wilhelmy plate apparatus

The purpose of this work was to carry out a systematic study of the effects of brine composition and rock mineralogy on rock-oil-brine interactions taking place in petroleum reservoirs. These terms are generally lumped into a single term called wettability in petroleum engineering. The extent of wetting of the rock surface by water or oil depends on the dynamic contact angles measured in such a mode as to enable movements of the three-phase contact line. The Wilhelmy plate technique has been used in this study to measure adhesion tension (which is the product of interfacial tension and cosine of the contact angle) at the solid-liquid interface. The water-advancing and water-receding contact angles have been calculated from the adhesion tensions by making independent measurements of the liquid-liquid interfacial tensions using a du Noüy ring tensiometer. The water-advancing and receding angles have been measured in this study for pure hydrocarbons against synthetic brines of different concentrations. Polished surfaces of glass slides and dolomite have been used to simulate the reservoir rock surfaces. A nonionic surfactant (ethoxy alcohol), which is being used in Yates reservoir in West Texas for enhancing oil recovery, was used to quantify its wettability effects. The results of the systematic experimental investigation of the effects of practical variables on wettability are presented. It is found that interactions between surface-active agents at the interface of two liquids have an effect on wettability alteration. The composition and concentrations of different organic and inorganic chemical species have a major effect in making a reservoir oil-wet or water-wet.     

In situ UV–Vis spectroscopy in gas–liquid–solid systems

This paper presents the use of ultraviolet–visible spectroscopy (UV–Vis) spectroscopy in a slurry of particles, a packed bubble column, and a trickle bed to assess the changes in the state of an active component on the surface of the solid support. As a model system, insoluble pH indicators deposited on the particles and on a solid foam packing (used as the packing material in the packed bubble column and the trickle bed) are used which fluoresce different UV–Vis spectra according to the liquid pH. The experimental results indicate that for the slurry the UV–Vis spectra obtained from the moving particles can be used to characterize the state of the pH indicator and to determine the transition point. The UV–Vis spectra can also be used to characterize the concentration of particles. Bubbles in the packed bubble column result in disturbances in the UV–Vis spectra collected from the pH indicator adsorbed to the solid surface and this interference is removed successfully with a newly developed tolerance-and-averaging method. In the trickle bed the liquid film flowing over the solid surface does not disturb the UV–Vis spectra. An abrupt change in the state of the pH indicator is therefore observed successfully.     

Modeling of dynamic systems with a variable number of phases in liquid–liquid equilibria

Modeling of dynamic systems with a variable number of phases is still a challenge, especially for multiple liquid phases. A common approach from literature derives first-order Karush–Kuhn–Tucker (KKT) conditions of the Gibbs free energy minimization and relaxes these if a phase does not exist. It aims at enabling dynamic simulation in all phase regimes of systems in vapor–liquid equilibrium by following a nonphysical continuous solution. In this work, we demonstrate that this continuous solution is not always possible in liquid–liquid equilibrium problems. The demonstration is done both theoretically and for illustrative examples. To overcome the demonstrated issues, we review the use of negative flash approach that allows negative molar amounts of nonexisting phases and propose a hybrid continuous formulation that explicitly assigns phase variables in the single-phase regime and solves flash equations otherwise. Various dynamic case studies demonstrate the applicability and limitations of all three approaches. © 2018 American Institute of Chemical Engineers AIChE J, 65: 571–581, 2019     

Development of a filtered reaction rate model for reactive gas–solid flows based on fine-grid simulations

The filtered reaction rate for the coarse-grid simulations of reactive gas–solid flows can be obtained via a correction to its microscopic reaction rate. The correction term is defined as the mesoscale effectiveness factor η_Δ , which is the ratio of the reaction rate obtained from the fine-grid simulations to that obtained from the coarse-grid simulations. The considered reaction is an isothermal, solid-catalyzed surface reaction with a power law reaction rate model. The simulation results show that the mean η_Δ is almost invariant with the reaction orders at the same Damköhler number. A closure correlation for the mean η_Δ is formulated. However, the standard deviation of η_Δ is found to be quite large. A presumed probability density function model is proposed to capture the fluctuating properties of η_Δ . The predictability of the closure correlations are evaluated via performing the filtered two fluid model simulations in circulating fluidized beds of ozone decomposition.     

Unified model for the prediction of consecutive solid–liquid filtration and expression at the constant pressure

Unified nonlinear model is proposed for the prediction of consecutive solid–liquid filtration and expression at the constant pressure. This model is based on the Darcy–Terzaghi filtration-consolidation equations modified to consider power-law pressure dependence of the specific cake resistance, and transforming Darcy law to the linear form. The model considers nonuniform structure of compressible filter cakes obtained by filtration and following expression. The profiles of local compressive pressure and local cake characteristics are simulated and compared for different moderately and highly compressible filter cakes (H.K. kaolin, CaCO₃, silica, activated sludge) based on the analytical and numerical solutions of the model. It is shown that the behavior of solid–liquid expression depends from the initial structure of compressed materials. Consolidation ratio U of the filter cakes with initially nonuniform structure formed by filtration differs from that of semi-solid materials with initially uniform structure. Different methods of determination of consolidation coefficient are analyzed and compared for nonuniformly structured filter cakes.     

Analysis of concentration polydispersity in mixed liquid–liquid systems

Inter-phase mass transfer for each chemical component is typically modelled with one material balance for the continuous and one for the dispersed phase. This approach contains inherently an assumption that the phases are well mixed at least locally. For the dispersed phase, this assumption requires that breakage and coalescence are significantly faster compared to the mass transfer, which is not necessarily true. It is important to carry out preliminary assessment whether the dispersed phase segregation is important and should be considered in subsequent modelling efforts, before embarking heavy multidimensional simulations where all possible dispersed phase variations are considered. In this work, relevant time scales are first defined and used for analyzing dispersed phase mixedness in liquid–liquid systems with mass transfer between the phases. Then appropriate dispersed phase modelling tools for the purpose are evaluated. Simple droplet number density based analysis is shown to estimate mixedness reasonably well. Furthermore, the drop number density approach is also shown to predict the average drop sizes with almost comparable accuracy than the full population balances.     

Experimental solid–liquid equilibria and solid formation kinetics for carbon dioxide in methane for LNG processing

In cryogenic liquefaction processes, CO₂ poses a solid-formation risk even in trace concentrations. We present solid–fluid equilibrium (SFE) data for CO₂ in liquid methane at CO₂ concentrations from (52 to 500) ppm, extending the available data and indicating that models tuned to existing data over predict the solubility of CO₂ at LNG storage temperatures (~112 K) by nearly a factor of 3. The new data are used to improve the SFE model in the ThermoFAST software package. The formation kinetics of CO₂ solids in liquid methane are elucidated at conditions relevant to cryogenic gas processing. Repeated, ramped-temperature formation measurements provide a statistical basis for quantifying solidification risk. Nucleation rates extracted from the ramped-temperature data, consistent with those measured at fixed temperature, were used to extract parameters describing CO₂ solid formation in methane. These results significantly improve the ability to predict CO₂ solid formation risk in cryogenic natural gas processing.     

Measurement of real-time flow structures in gas–liquid and gas–liquid–solid flow systems using electrical capacitance tomography (ECT)

The real-time cross-sectional distributions of the gas holdups in gas–liquid and gas–liquid–solid systems are measured using electrical capacitance tomography. For the gas–liquid system, air as the gas phase and both Norpar 15 (paraffin) and Paratherm as the liquid phases are used. Polystyrene beads whose permittivity is similar to that of Paratherm are used as the solid phase in the gas–liquid–solid system. The three-phase system is essentially a dielectrically two-phase system enabling measurement of the gas holdup in the gas–liquid–solid system independent of the other two phases. A new reconstruction algorithm based on a modified Hopfield dynamic neural network optimization technique developed by the authors is used to reconstruct the tomographic data to obtain the cross-sectional distribution of the gas holdup. The real-time flow structure and bubbles flow behavior in the two- and three-phase systems are discussed along with the effects of the gas velocity and the solid particles.     

Measurement and correlation of solid–liquid phase equilibria for binary and ternary systems consisting of N-vinylpyrrolidone, 2-pyrrolidone and water

The solid–liquid equilibria(SLE)for binary and ternary systems consisting of N-Vinylpyrrolidone(NVP),2-Pyrrolidone(2-P)and water are measured.The phase diagrams of NVP(1)+2-P(2),NVP(1)+water(2),NVP(1)+2-P(2)+1 wt%water(3)and NVP(1)+2-P(2)+2 wt%water(3)are identified as simple eutectic type with the eutectic points at 263.75 K(x_(1E)=0.5427),251.65 K(x_(1E)=0.3722),260.25 K(x_(1E)=0.5031)and256.55 K(x_(1E)=0.4684),respectively.The phase diagram of 2-P(1)+water(2)has two eutectic points(x_(1E)=0.1236,T_E=259.15 K and x_(1E)=0.7831,T_E=286.15 K)and one congruent melting point(x_(1C)=0.4997,T_C=303.55 K)because of the generation of a congruently melting addition compound:2-P·H_2O.The ideal solubility and the UNIFAC models were applied to predict the SLE,while the Wilson and NRTL models were employed in correlating the experimental data.The best correlation of the SLE data has been obtained by the Wilson model for the binary system of NVP+2-P.The UNIFAC model gives more satisfactory predictions than the ideal solubility model.     

Modified COSMO-UNIFAC model for ionic liquid–CO2 systems and molecular dynamic simulation

A new predictive molecular thermodynamic model (i.e., modified COSMO-SAC-UNIFAC) was first proposed and extended to predict the solubility of CO₂ in pure and mixed ionic liquids (ILs) at the temperatures down to 263.2 K. It is interesting to discover that with equimolar amounts, the solubility of CO₂ in such 1:1 IL pairs, that is, [A₁][B₁] + [A₂][B₂] and [A₁][B₂] + [A₂][B₁], was consistent at the same temperature and pressure in the case of exchanging their respective cations and anions. The molecular dynamic (MD) simulation for CO₂ + mixed ILs was performed to deeply analyze and explain this intriguing phenomenon. Not only the CO₂ gas drying experiment with the ILs ([C2mim][OAc], [C2mim][dca], and [C2mim][OAc] + [C2mim][dca]) as absorbents but also the corresponding process simulation and optimization were made to stress the effectiveness and applicability of the new thermodynamic model. Thus, this work ranges from molecular level to systematic scale.     

Transient gas–liquid mass transfer model for thin liquid films on structured solid packings

This paper describes a model for gas–liquid mass transfer through thin liquid films present on structured packings for gas–liquid operations under dispersed gas flow regime. The model has been derived for two cases: the absorption (or desorption) of a gaseous component into the liquid film and the transfer of the gaseous component through the liquid film to the packing surface where an infinitely fast reaction takes place. These cases have been solved for three bubble geometries: rectangular, cylindrical, and spherical. For Fourier numbers below 0.3, the model corresponds to Higbie’s penetration theory for both cases. The Sherwood numbers for cylindrical and spherical bubbles are 20% and 35% higher, respectively, than for rectangular bubbles. In case of absorption and Fourier numbers exceeding 3, the effect of bubble geometry becomes more pronounced. The Sherwood numbers for cylindrical and spherical bubbles now are 55% and 100% higher, respectively, than for rectangular bubbles. In case of an infinitely fast reaction at the packing surface, the Sherwood number corresponds to Whitman’s film theory (Sh=1$Sh=1$) for all bubble geometries. In this paper also practical approximations to the derived Sherwood numbers are presented. The approximations for both cases and all bubble geometries describe all the model data within an error of 4%. The application of the model has been demonstrated for three examples: (1) gas–liquid mass transfer for a structured packing; (2) gas–liquid mass transfer in a microchannel operated with annular flow; (3) gas–liquid mass transfer in a microchannel with Taylor flow.     

Numerical optimization for blades of Intermig impeller in solid–liquid stirred tank

The multiphase flow in the solid-liquid tank stirred with a new structure of Intermig impeller was analyzed by computational fluid dynamics(CFD).The Eulerian multiphase model and standard k-ε turbulence model were adopted to simulate the fluid flow,turbulent kinetic energy distribution,mixing performance and power consumption in a stirred tank.The simulation results were also verified by the water model experiments,and good agreement was achieved.The solid-liquid mixing performances of Intermig impeller with different blade structures were compared in detail.The results show that the improved Intermig impeller not only enhances the solid mixing and suspension,but also saves more than 20% power compared with the standard one.The inner blades have relatively little influence on power and the best angle of inner blades is 45°,while the outer blades affect greatly the power consumption and the optimized value is 45°.     

Micro-computed tomography for the investigation of stationary liquid–liquid and liquid–gas interfaces in capillaries

For better understanding and optimization of multiphase flow in miniaturized devices, micro-computed tomography (μCT) is a promising visualization tool, as it is nondestructive, three-dimensional, and offers a high spatial resolution. Today, computed tomography (CT) is a standard imaging technique. However, using CT in microfluidics is still challenging, since X-ray related artifacts, low phase contrast, and limited spatial resolution complicate the exact localization of interfaces. We apply μCT for the characterization of stationary interfaces in thin capillaries. The entire workflow for imaging stationary interfaces in capillaries, from image acquisition to the analysis of interfaces, is presented. Special emphasis is given to an in-house developed segmentation routine. For demonstration purposes, contact angles of water, liquid polydimethylsiloxane, and air in FEP, glass, and PMMA are determined and the influence of gravity on interface formation is discussed. This work comprises the first steps for a systematic 3D investigation of multiphase flows in capillaries using μCT.     

Flow regimes in a gas–liquid–solid three-phase moving bed

The gas–liquid–solid three-phase moving beds could supply a potential solution for multiphase reactions with catalyst easily deactivated, and the flow regimes in it were studied by optical method and pressure drop measurement. Results showed that taking the trickle flow as the initial flow regime, the flow channels were more obvious as the particle velocity increased. When the initial flow regimes were pulse flow and bubble flow respectively, the pulse-to-trickle and bubble-to-pulse flow transitions mainly occurred at moderate-to-high particle velocities (0.01–0.04 m s⁻¹ under conditions used in this work). Moreover, the flow regime map in the three-phase moving bed was constructed and shown that the region of trickle flow increased and the region of bubble flow decreased. Finally, the application of three-phase moving beds was discussed, and it could be suitable for those reactions, which had to operate in the pulse flow, bubble flow, and transition zone.     

Numerical simulation of micro-mixing in gas–liquid and solid–liquid stirred tanks with the coupled CFD-E-model

The coupled CFD-E-model for multiphase micro-mixing was developed, and used to predict the micro-mixing effects on the parallel competing chemical reactions in semi-batch gas–liquid and solid–liquid stirred tanks. Based on the multiphase macro-flow field, the key parameters of the micro-mixing E-model were obtained with solving the Reynolds-averaged transport equations of mixture fraction and its variance at low computational costs. Compared with experimental data, the multiphase numerical method shows the satisfactory predicting ability. For the gas–liquid system, the segregated reaction zone is mainly near the feed point, and shrinks to the exit of feed-pipe when the feed position is closer to the impeller. Besides, surface feed requires more time to completely exhaust the added H⁺ solution than that of impeller region feed at the same operating condition. For the solid–liquid system, when the solid suspension cloud is formed at high solid holdups, the flow velocity in the clear liquid layer above the cloud is notably reduced and the reactions proceed slowly in this almost stagnant zone. Therefore, the segregation index in this case is larger than that in the dilute solid–liquid system.     

Evaporative liquid jets in gas–liquid–solid flow system

Some aspects of the fundamental characteristics of evaporative liquid jets in gas–liquid–solid flows are studied and some pertinent literature is reviewed. Specifically, two conditions for the solids concentration in the flow are considered, including the dilute phase condition as in pneumatic convey and the dense phase condition as in bubbling or turbulent fluidized beds. Comparisons of the fundamental behavior are made of the gas–solid flow with dispersed non-evaporative as well as with evaporative liquids.For dilute phase conditions, experiments and analyses are conducted to examine the individual phase motion and boundaries of the evaporative region and the jet. Effects of the solids loading and heat capacity, system temperature, gas flow velocity and liquid injection angle on the jet behavior in gas and gas–solid flows are discussed. For dense phase conditions, experiments are conducted to examine the minimum fluidization velocity and solids distribution across the bed under various gases and liquid flow velocities. The electric capacitance tomography is developed for the first time for three-phase real time imaging of the dense gas–solid flow with evaporative liquid jets. The images reflect significantly varied bubbling phenomenon compared to those in gas–solid fluidized beds without evaporative liquid jets.