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.     

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 model for thin-film stability and spreading in solid–liquid–liquid systems

The presence of thin aqueous films and their stability has a profound effect on reservoir rock–fluids interactions involved in spreading and adhesion. The stability of thin wetting aqueous films on rock surfaces is governed by several variables including pH, brine and crude oil compositions, and capillary pressure. These variables govern the wetting states in the solid–liquid–liquid systems. The wetting states influence the residual oil saturation and the oil-water relative permeabilities and, consequently, the oil recovery. The objective of this study was to deduce a functional dependence of thin-film stability on the above parameters by considering intermolecular and surface interactions in rock–crude oil–brine systems. The surface forces are manifested as disjoining pressure in thin films. The disjoining pressure isotherms for the selected solid–liquid–liquid systems have been computed in terms of the bulk properties of the media. The equilibrium contact angles have also been computed from the integration of the Young–Laplace equation, which relates contact angle to the capillary pressure and disjoining pressure isotherm of the system. The contact-angle data obtained from sessile-drop experiments have been compared with the calculated results, as well as with other published results. Adhesion maps, which relate the film stability to brine pH and molarity, have been developed. The rock–fluids systems considered for this study consisted of smooth glass, quartz and Yates reservoir fluids. The DLVO theory has been used to model the intermolecular forces. The structural forces are incorporated to overcome the limitations of the DLVO theory. A charge regulation model has been used to analyze the crude oil–brine and glass–brine interfaces. The effects of multivalent ions have been incorporated using an equivalent molarity concept. The overall computational model developed in this study is aimed at providing a priori prediction capability of rock-fluids interactions in petroleum reservoirs for inclusion in reservoir simulators.     

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.     

The gap between the measured and calculated liquid–liquid interfacial tensions derived from contact angles

We present our new findings about the causes of discrepancies between the measured and calculated liquid-liquid interfacial tensions derived from contact angles. The calculated ones are based on either the equation developed by Fowkes or that by van Oss, Chaudhury and Good (VCG), while the measured ones are based on the sessile drop, weight-volume by Jańzuk et al. and the axisymmetric drop shape analysis (ADSA) by Kwok and Neumann. Indeed, there are deviations between the calculated and measured results. For an immiscible liquid-liquid or liquid-solid interface, we prefer to employ Harkins spreading model, which requires the interfacial tension to be constant. However, for the initially immiscible liquid-liquid pairs, we propose an adsorption model, and our model requires the interfacial tension to be varying and the surface tensions of bulk liquids at a distance from the interface to remain unchanged. Thus, the difference between the initial and final interfacial spreading coefficients (S_i) equals the equilibrium interfacial film pressure (π_i)_e. According to our findings, the calculated interfacial tension represents the initial value (γ₁₂)_o, which differs from the equilibrium value (γ₁₂)_e obtained experimentally after some time delay. This expected gap at a reasonable time frame is chiefly caused by the equilibrium interfacial film pressure between the two liquids. The initial (or calculated) interfacial tension can be positive or negative, while the equilibrium (or measured) one can reach zero. In fact, the former is shown to have more predictive value than the latter. A negative initial interfacial tension is described to favor miscibility or spontaneous emulsification but it tends to revert to zero instantaneously. Thus, a miscible liquid mixture should have zero interfacial tension. In response to recent papers by Kwok et al., we show that the disagreements between the calculated and measured interfacial tensions are definitely not caused by the failure of the VCG approach. Correct interfacial tensions are calculated for liquid pairs containing formamide or dimethyl sulfoxide (DMSO) by using the dispersion components cited in Fowkes et al.'s later publication. With the corrected surface tension components, the equilibrium interfacial film pressures (π_i)_e's for at least 34 initially immiscible liquid pairs have been calculated. These values are generally lower than the corresponding spreading pressures π_e's obtained by others using the Harkins model. Recently, we established a relationship between these two film pressures with the Laplace equation and found a new criterion for miscibility to be (π_i)_e = π_e.     

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.     

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.     

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.     

Determination of the ash content of solid fuel using annihilation γ-rays

The possibility of the instrumental determination of the ash content of solid fuel using annihilation γ-rays was demonstrated. Analytical expressions for the evaluation of sensitivities were obtained. The method was recommended for the analysis of high-ash coals in large masses without special sample preparation.     

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.     

Prediction of curved oil–water interface in horizontal pipes using modified model with dynamic contact angle

In this study, interface shapes of horizontal oil–water two-phase flow are predicted by using Young-Laplace equation model and minimum energy model. Meanwhile, the interface shapes of horizontal oil–water twophase flow in a 20 mm inner diameter pipe are measured by a novel conductance parallel-wire array probe(CPAP). It is found that, for flow conditions with low water holdup, there is a large deviation between the model-predicted interface shape and the experimentally measured one. Since the variation of pipe wetting characteristics in the process of fluid flow can lead to the changes of the contact angle between the fluid and the pipe wall, the models mentioned above are modified by considering dynamic contact angle. The results indicate that the interface shapes predicted by the modified models present a good consistence with the ones measured by CPAP.     

Investigations of mass transfer with chemical reactions in two-phase liquid–liquid systems

A new method based on experimental determination of the product distribution of a set of complex test reactions has been introduced and applied to study mass transfer in liquid–liquid systems. The test reactions consist of two parallel reactions, one of them being instantaneous and the second fast relative to mass transfer. Two reactants are transferred from the dispersed, organic phase (phase volume 1% vol) to the continuous aqueous phase, where the third reactant is present. Experiments were carried out in a batch system agitated with either a six-blade paddle impeller or a high-shear rotor–stator LR4 Silverson mixer to disperse drops and increase the mass transfer rate. The product distribution and the drop size distribution were measured using gas chromatography–mass spectroscopy and Malvern MasterSizer, respectively with pH variation recorded during the process. The results show that the focused supply of energy in the Silverson mixer is effective for the short term irreversible drop break-up process producing smaller droplets than the six-blade paddle impeller. However for the long term mass transfer process the paddle impeller is more effective due to more uniform supply of energy and better mixing throughout the tank compared to the more localized mixing of the Silverson.     

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.     

Analysis of dilute solid–liquid suspensions in turbulent stirred tanks

In this work, dilute suspensions of solid particles in stirred tanks are investigated by Particle Image Velocimetry measurements, which were specifically designed to determine the effects of the dispersed phase on mean velocity and turbulence levels of the continuous phase and the local solid–liquid slip velocity. In order to determine the effect of particle size and concentration, glass particles of narrow size distribution were selected; the particle content was increased stepwise up the maximum of 0.2 vol.%. Overall, moderate dampening of liquid turbulent fluctuations was found with the smaller particles, while turbulence enhancement was observed with the bigger ones. Continuous phase turbulence was found to affect the local map of the particle settling velocity, which was also discussed on the basis of a force balance analysis. The reduction of particle settling velocity due to free stream turbulence under specific conditions is confirmed.     

Defluidized zones in liquid–solid fluidized beds

Defluidized zones often appear on the distributor plates of liquid–solid fluidized beds. They can lead to hot spots, the formation of undesirable side products or the degradation of products or reactants. In some cases, a solid residue forms and plugs the distributor.Two different techniques were developed to detect defluidized zones. The first technique uses a specially designed collision probe to monitor local particle motion. The second technique is aimed at the on-line detection of defluidized zones in industrial bioreactors. It uses local bed conductivity fluctuations.Defluidized zones were measured in beds of 3 or 5 mm diameter glass beads fluidized by an aqueous saline solution. Special experiments established the importance of horizontal liquid flow and distributor plate roughness on the formation of defluidized zones.A model describes how a defluidized zone can be eliminated. It considers that a defluidized zone is broken by the drag force on its particles of downward and sideways liquid flow. This liquid flow is induced by suction from the liquid jets issuing from the distributor holes. The resulting drag force is resisted by friction between particles or between particles and the distributor surface.     

Experimental determination of the Hamaker constants for solid–water–oil systems

The van der Waals interaction (vdW) is a fundamental interaction in colloid and interface science. Regardless of the methods used in deriving the vdW interaction between two bodies as a function of their separation distance, the Hamaker constant is always an essential parameter involved. In this paper, a simple experimental method is presented to determine the Hamaker constant. As an example, the Hamaker constant of a solid-water-oil system is related to its surface and interfacial energies, which can be measured accurately. Based on the proposed method, the effects of two typical solid surfaces and three kinds of aqueous solutions on the Hamaker constant and wettability of the solid-water-oil system are studied. It is found that hydrophilic and hydrophobic solid surfaces will lead to rather different Hamaker constants and wettability behaviour. The detailed experimental results also show that the ionic surfactant solutions have a strong influence, whereas the pH value of the aqueous phase has a limited effect on the Hamaker constant. In addition, the electrolyte solutions do not strongly affect the Hamaker constant for the oil phase interacting with the solid surface across an electrolyte solution. Such determined Hamaker constants are in reasonable agreement with the reported Hamaker constants for oils (dodecane and hexadecane), mica, and metals (Ag, Au, and Cu) interacting across a pure water phase.     

Developments in the understanding of gas–solid contact efficiency in the circulating fluidized bed riser reactor:A review

In the last several decades, circulating fluidized bed reactors have been studied in many aspects including hydrodynamics, heat and mass transfer and gas–solid two phase contacting. However, despite the abundance of review papers on hydrodynamics, there is no summary paper on gas–solid contact efficiency to date, especially on high density circulating fluidized beds(CFBs). This paper gives an introduction to, and a review of the measurement of contact efficiency in circulating fluidized bed riser. Firstly, the popular testing method of contact efficiency including the method of heating transfer experiment and hot model reaction are discussed, then previous published papers are reviewed based on the discussed methods. Some key results of the experimental work are described and discussed. Gas–solid contact efficiency is affected by the operating conditions as well as the particle size distribution. The result of the contact efficiency shows that the CFB riser is far away from an ideal plug flow reactor due to the characteristics of hydrodynamics in the riser. Lacunae in the available literature have been delineated and recommendations have been made for further work.     

Investigation of turbulence modulation in solid–liquid suspensions using parallel competing reactions as probes for micro-mixing efficiency

The Bourne and the Villermaux competitive reaction chemistries were applied to study the effects of suspended particles on the yield of an undesired product and hence to infer their effects on local dissipation rates. Two-phase micro-mixing experiments were carried out in a 1 l stirred vessel, agitated by a pitched-blade turbine, using four particle size ranges: 70–100, 250–300, 700–750 and 1000 μm. Experiments were carried out with up to 1.75 vol% particles in the Bourne scheme and 3 vol% in the Villermaux scheme. Both reaction schemes gave qualitatively similar results, although stronger effects of added particles were obtained with the Bourne chemistry. The effect of 700–750 μm particles could not be distinguished from experimental error, but the other size ranges gave increased by-product yields and suppressed the dissipation rates. These results confirmed earlier two-phase PIV observations: smaller particles (70–100 and 250–300 μm) gave maximum suppression at ∼1 vol%. Above this volume fraction, the level of suppression decreased and in some cases turbulence augmentation occurred, indicating that particle concentration, as well as size, is an important factor.