Single-stage Equilibrium Research Articles

Quasi-single-stage optimization for permanent magnet stellarators

Advanced stellarators are typically optimized in two stages. The plasma equilibrium is optimized first, followed by the design of coils/permanent magnets. However, the coils/permanent magnets in the second stage may become too complex to achieve the desired equilibrium. To address this problem, a quasi-single-stage optimization method has been proposed. In this paper, we introduce this method for designing permanent magnet (PM) stellarators. The new approach combines straightforward PM metrics to penalize the maximum required PM thickness and the mismatch between the fixed-boundary equilibrium and the free-boundary one, along with typical physical targets. Since the degrees of freedom of the PMs are not included and directly used to minimize the objective function in this method, so we call it ‘quasi-single-stage’ optimization. We apply this quasi-single-stage optimization method to find a new quasi-axisymmetric PM design. The new design starts from MUSE, which was initially designed using a two-stage optimization approach. The resulting design, MUSE++, exhibits an order of magnitude lower quasi-symmetric error and a one-order reduction in normal field error. We show that MUSE++ has approximately 30% fewer magnets compared to a proxy model ‘MUSE-0’ that uses the same FAMUS optimization without the benefit of a single-stage equilibrium optimization. These results demonstrate that the new single-stage optimization method can concurrently improve plasma properties and simplify permanent magnet complexity.

Fractionation and purification of a high-impurity, alkaline-pretreated, corn stover lignin with simple renewable solvents

Corn stover has been identified as a key resource in the transition from petrochemicals to sustainably sourced energy and materials; however, the as-recovered lignin from alkaline pretreatment contains unusually high levels of residual impurities, which must be removed to maximize potential application. Thus, the Aqueous Lignin Purification using Hot Agents (ALPHA) process was applied to a corn stover lignin containing ∼10 % carbohydrates and ∼3 % ash. Lignin fractions ∼100 times cleaner than the feed lignin and of controlled molecular weight (i.e., as low as one-fifth and as high as triple the absolute molecular weight (Mw) of the feed) were obtained. The ALPHA solvent was a hot (60 or 75 °C) solution of 80 % ethanol combined with the feed lignin at an unusually low, 3:1 solvent-to-feed lignin ratio – conditions that create the liquid–liquid equilibrium (LLE) phase split needed to practice ALPHA. Lignin fractionation then commenced by adding water to the original solution, decreasing the ethanol content in increments of 3–4 wt%. Surprisingly, the highest Mw fractions did not precipitate until the solution contained just below 50 % ethanol, by which point almost half of the starting lignin of near-average Mw had already precipitated. Another unexpected result was that the lignin waste stream from the initial purification step could be increased from 40 to 98 % lignin in a single equilibrium stage simply by re-processing that waste with another 80 % ethanol solution at the conditions given above. In summary, the efficacy of ALPHA for purifying and fractionating an impurities-laden corn stover lignin to ultraclean levels in a scalable manner requiring only aqueous bioethanol solutions has been demonstrated.

Development of a continuous evaporation system for an API solution stream prior to crystallization

AbstractA bubble column was investigated as a method to achieve a desired and controllable rate of evaporation of a pharmaceutical solution. Applying a thermodynamic model to predict the rate of evaporation, all predicted values were observed to have accuracies within the bounds of instrumentation errors (<5% absolute). The developed model accounted for the measured effect of reduced vapor pressure, caused by the dissolved solids as a function of their concentration. A general method to obtain accurate measurement of this effect is introduced and applied, improving the accuracy of model predictions. Consistent and repeatable evaporation rates ranging from 0.7 to 6.9 g/min were achieved experimentally, and errors between predicted rates and observed ranged from 0.219% to 4.19% absolute. This demonstrates a controllable and flexible method for the evaporation of process streams which can be compared to harsher conventional methods such as boiling. The column was configured in a continuous mode and coupled to a downstream crystallizer (MSMPR). Using the column as a controllable concentrator, the concentration of a dilute feed stream of paracetamol in methanol was increased in a single equilibrium stage. The column demonstrated the ability to concentrate the solution in flow by 179%, delivering a flow of 2 ml/min of concentrated liquor to the MSMPR. The MSMPR achieved steady‐state of control, measured by offline dissolved concentration analysis and particle count by FBRM in situ, highlighting the applicablity of the column to perform reliably in a continuous tandem.

Accounting for interface behaviour in multi-stage aqueous two-phase extraction

Aqueous two-phase extraction (ATPE) is an alternative, cheaper and continuous protein purification technique. For ATPE to be used in industry, it must compete with current batch purification procedures, which can be achieved using multi-stage operation. To design extraction processes using ATPE appropriate process models must be developed. In this study, experimentally determined single-stage equilibrium data was used to generate a model to describe the behaviour of protein in multi-stage counter-current ATPE. Two distribution systems are considered: liquid–liquid (LL) and liquid-interface-liquid (LIL) distribution. The LIL model considers material which precipitates at the interface of the system. These models were then both compared against a three-stage experimental case study ATPE. The LIL model described the case study system better than the LL model, reducing the error from 40% to 11%. With this significant increase in accuracy, the LIL model represents an important tool with which to design multi-stage ATPE processes.

A horizontal axis rotating disc contactor combining narrow mixing space and oil-wet slits

Rotating disc contactor (RDC) is one of the most important extraction columns for liquid-liquid extraction. A single-stage horizontal axis RDC (HRDC) was developed and used for extraction of emulsion system. The extractor composed characteristics of narrow mixing space of 1 mm and oil-wet slits. For ethanol/water/2-ethyl-hexanol system, both mass transfer and phase separation were enhanced simultaneously, and the extraction efficiency was higher than single equilibrium stage. The results showed the sufficient mass transfer achieved at low-rotation speed in a short time. Extract phase separation was enhanced by crossing the narrow oil-wet slits repeatedly to make oil droplets coalescence. The circulation flow played a key factor for the higher efficiency. The extractor was simulated with Aspen Plus©.

Deep neural network learning of complex binary sorption equilibria from molecular simulation data.

We employed deep neural networks (NNs) as an efficient and intelligent surrogate of molecular simulations for complex sorption equilibria using probabilistic modeling. Canonical (N 1 N 2 VT) Gibbs ensemble Monte Carlo simulations were performed to model a single-stage equilibrium desorptive drying process for (1,4-butanediol or 1,5-pentanediol)/water and 1,5-pentanediol/ethanol from all-silica MFI zeolite and 1,5-pentanediol/water from all-silica LTA zeolite. A multi-task deep NN was trained on the simulation data to predict equilibrium loadings as a function of thermodynamic state variables. The NN accurately reproduces simulation results and is able to obtain a continuous isotherm function. Its predictions can be therefore utilized to facilitate optimization of desorption conditions, which requires a laborious iterative search if undertaken by simulation alone. Furthermore, it learns information about the binary sorption equilibria as hidden layer representations. This allows for application of transfer learning with limited data by fine-tuning a pretrained NN for a different alkanediol/solvent/zeolite system.

Nanoporous Block Polymer Thin Films Functionalized with Bio-Inspired Ligands for the Efficient Capture of Heavy Metal Ions from Water.

Heavy metal contamination of water supplies poses a serious threat to public health, prompting the development of novel and sustainable treatment technologies. One promising approach is to molecularly engineer the chemical affinity of a material for the targeted removal of specific molecules from solution. In this work, nanoporous polymer thin films generated from tailor-made block polymers were functionalized with the bio-inspired moieties glutathione and cysteamine for the removal of heavy metal ions, including lead and cadmium, from aqueous solutions. In a single equilibrium stage, the films achieved removal rates of the ions in excess of 95%, which was consistent with predictions based on the engineered material properties. In a flow-through configuration, the thin films achieved an even greater removal rate of the metal ions. Furthermore, in mixed ion solutions the capacity of the thin films, and corresponding removal rates, did not demonstrate any reduction due to competitive adsorption effects. After such experiments the material was repeatedly regenerated quickly with no observed loss in capacity. Thus, these membranes provide a sustainable platform for the efficient purification of lead- and cadmium-contaminated water sources to safe levels. Moreover, their straightforward chemical modifications suggest that they could be engineered to treat sources containing other recalcitrant environmental contaminants as well.

Recovery of Butanol by Counter-Current Carbon Dioxide Fractionation with its Potential Application to Butanol Fermentation.

A counter-current CO2 fractionation method was applied as a mean to recover n-butanol and other compounds that are typically obtained from biobutanol fermentation broth from aqueous solutions. The influence of operating variables, such as solvent-to-feed ratio, temperature, pressure and feed solution composition was experimentally studied in terms of separation efficiency, butanol removal rate, total removal and butanol concentration in the extract at the end of the continuous cycle. With respect to the temperature and pressure conditions investigated, results show that the highest separation efficiency was obtained at 35 °C and 10.34 MPa. At these operating conditions, 92.3% of the butanol present in the feed solution was extracted, and a concentration of 787.5 g·L−1 of butanol in the extract was obtained, starting from a feed solution of 20 g·L−1. Selectivity was calculated from experimental data, concluding that our column performs much better than a single equilibrium stage. When adding ethanol and acetone to the feed solution, ethanol was detected in the water-rich fraction (raffinate), whereas the highest concentration of acetone was found in the butanol rich fraction (extract).

New soluble octakis-substituted Co(II) phthalocyanines: Synthesis, spectra, supramolecular chemistry

The synthesis of (Octakis(3,5-di-tert-butylphenoxy)phthalocyaninato) cobalt(II) (CoPc(3,5-di-tBuPhO)8) was reported. The new phthalocyanine complex was characterized by UV–vis, IR, 1H NMR and mass spectra and elemental analysis. The supramolecule formation reactions of CoPc(3,5-di-tBuPhO)8 with pyridine (Py) and 2′-(4-pyridyl)-5′-(2-pyridyl)-1′-(3-pyridylmethyl)pyrrolidino[3′,4′:1,2][60]fullerene (Py3F) were studied in toluene by methods of chemical kinetics and thermodynamics, UV, visible, IR and 1H NMR spectroscopy. The addition of pyridine results in single-stage equilibrium between the donor-acceptor complex 1:1 and the initial cobalt phthalocyanine. The reaction with the substituted fullerene goes to the formation of phthalocyanine - fullerene 1:1 supramolecule in the kinetic mode. The product of supramolecular complexation were identified by spectral methods.

Experiment on the continuous recovery of H2 from hydrogenation plant off-gas via hydrate formation in tetra-n-butyl ammonium bromide solution

Here, an approach toward for continuous H2 recovery from hydrogenation plant off-gas based on hydrate formation in the presence of tetra-n-butyl ammonium bromide (TBAB) is proposed. Firstly, we explored the conditions to form the CH4/H2/TBAB hydrate through pressure search method in the single-stage equilibrium separation experiments toward CH4/H2 mixture. The influence of initial pressure, temperature, and initial gas–liquid volume ratio were systematically optimized in the context of 10 wt% TBAB solution. Then, we conducted the continuous separation experiments of CH4/H2 binary mixture and hydrogenation plant off-gas using a set of laboratory-scale continuous stirred reactor according to the optimized conditions, in which the effects of pressure and liquid flow rate upon continuous separation were further studied. The experimental results that the H2 concentration in the unhydrated gas (the recovered gas) is up to 89 mol% and the yield of H2 recovery is more than 58.68% indicate the efficiency to recover H2 using continuous hydrate separation, which lays the foundation for further industrial application.

Assessing uncertainty in geochemical models for core formation in Earth

Unraveling the conditions at which Earth's metallic iron core formed yields important information about Earth's early accretion and differentiation history. Multi-variable statistical modeling of siderophile element partitioning between core-forming metallic liquids and silicate melts form the basis for physical models of core formation. While it seems clear that core segregation in a deep peridotitic magma ocean is generally consistent with many mantle siderophile element abundances, there is considerable disparity among extant physical models in terms of the key parameters of pressure, temperature and oxygen fugacity at which the core formed. Moreover, there is ongoing debate over whether simple single-stage equilibrium or more complex multi-stage accretion models are required by the partitioning data. Here we consider how variations in the statistical regression of partitioning data affect the outcomes of physical models for core formation. Taking extant experimental data sets for four well-studied siderophile elements (Ni, Co, W and V) as examples, we find that the regression model exerts a fundamental control on physical model outcomes. Further, the experimental data are currently too imprecise to discriminate among various single-stage and continuous core formation scenarios. Progress in the development of physical models requires better isolation of the independent variables that affect partition coefficients and verification of activity models at high pressure and temperature in order to reduce the global uncertainty in multi-variable statistical models.

Experimental Study on the Separation of CH4 and N2 via Hydrate Formation in TBAB Solution

In order to reduce the emission of coal bed methane mixed with air (can be regarded as a CH4 and N2 mixture), which will be helpful to adequately utilize the natural resources and protect environment, the separation of CH4 and N2 via hydrate formation in tetra-n-butylammonium bromide (TBAB) solution was systematically studied in this work. The CH4−N2 hydrate formation conditions were determined in TBAB solution first, and then the separation experiments were carried out in TBAB and TBAB−sodium dodecyl sulfate (SDS) solution, respectively. The experimental results show that CH4 and N2 form a hydrate much easier after adding TBAB to water. The composition of CH4 in the hydrate after single-stage equilibrium separation in TBAB solution can be increased from 46.25 mol % to 67.86 mol %. At the same conditions, the composition of CH4 after separation in TBAB−SDS solution is 68.66 mol % and the reaction time shortens greatly. Besides, the recovery of CH4 is more than 47%, and the gas storage capacity of hydrate ...

Application of aqueous two-phase systems to antibody purification: A multi-stage approach

The single-stage equilibrium aqueous two-phase extraction (ATPE) of human antibodies from a Chinese hamster ovary (CHO) cells supernatant was investigated. The performance of polyethylene glycol 3350 (PEG 3350)/phosphate aqueous two-phase systems (ATPS) was evaluated by studying several experimental conditions, such as pH, ionic strength, volume ratio and initial antibody concentration in the feed stock. The conditions that favoured the extraction of human immunoglobulin G (IgG) were low pH values, high NaCl concentration and high volume ratios. The percentage of contaminants removal did not depend on the pH value and NaCl concentration, increasing, however, as the volume ratio decreased. About 66% of total contaminants were removed when a volume ratio of 0.4 was used. The multi-stage equilibrium ATPE was also investigated by simulating a four stages cross-current operation in test tubes. According to the IgG equilibrium curves and respective McCabe Thiele diagrams, a predicted optimised scheme of a counter-current multi-stage ATPE was described. An IgG recovery yield of 89% and a protein purity of 75% can be achieved using a PEG/phosphate ATPS containing 10% (w/w) NaCl, five stages and a volume ratio of 0.4. This represents significant improvements in the recovery yield and purity when compared to a single-stage trial performed at the same experimental conditions, where a 61% recovery yield and 55% protein purity were attained. Based on the CHO cells supernatant components equilibrium curves, it was observed that IgG can be completely purified from the higher molecular weight (MW) components and partially purified from the lower MW components.

Study of vapor–hydrate two-phase equilibria

In recent years, the technology of separating gas mixtures by forming hydrate has received increasing recognition, particularly the separation of light-gas mixtures. We performed an experimental and modeling study of systems containing hydrogen, methane, ethane and ethylene, both with and without the thermodynamic promoter tetrahydrofuran (THF) in water. Vapor–hydrate equilibrium data ( P– T– x– y data) were measured for (H 2 + CH 4), (H 2 + N 2 + CH 4) and (CH 4 + C 2H 4) gas mixtures in the absence and presence of THF. A relatively simple algorithm was used to calculate vapor–hydrate two-phase equilibria. The Patel–Teja equation of state, coupled with a van der Waals–Platteeuw-type hydrate model, was applied to calculate the equilibrium flash of vapor–hydrate phases. The parameters in the hydrate model were determined by correlating the experimental data of hydrate formation conditions. In addition, we predicted the composition of gas mixture in the hydrate phase when structure I and structure II hydrates coexisted in a (CH 4 + C 2H 6) gas mixture. The test results indicated that proposed algorithm is adequate for predicting vapor–hydrate equilibria. Accurate predictions of single-stage equilibrium between the vapor and the hydrate phases are important for developing separation technology via hydrate formation.

Experimental and simulation of single equilibrium stage separation of (methane + hydrogen) mixtures via forming hydrate

To separate gas mixture through forming hydrate is a new technology, which might be applicable in recovering economically valuable gas components, such as hydrogen and ethylene from refinery gases. A set of equipment was designed and constructed for the experimental study of gas mixtures separation efficiency via forming hydrate. Batch operation method with/without gas–liquid circulating can be adopted. The separation efficiency for hydrogen + methane gas mixtures in pure water, 1, and 6 mol% tetrahydrofuran (THF) in initial aqueous solution were examined at different temperature, pressure, and feed gas composition conditions. The results showed that high operation pressure is needed for separation from pure water, which is only used to the initial hydrogen enriched. With the existence of THF in aqueous solution, hydrogen was remarkably enriched in vapor phase by a single equilibrium stage, especially when 6 mol% THF added. Based on the extended Chen-Guo hydrate model, an algorithm for vapor-hydrate flash calculation was developed to simulate the single equilibrium stage separation of gas mixtures. Good predict precision can be obtained by the simulating algorithm, which was then extended to simulate the experimental conditions that cannot be achieved by the limit of device.

The origin of the depletions of V, Cr and Mn in the mantles of the Earth and Moon

Abstract The reasons for the similarity of the depleted abundances of V, Cr and Mn in the mantles of the Earth and Moon, which may throw light on the origin of the Moon, have been controversial. In order to test if a single-stage equilibrium core formation model can explain these depletions in the Earth, we investigated the partitioning of V, Cr, Mn, Ni and Co between liquid metal and magnesiowustite, an important liquidus phase of the peridotite mantle at high pressure. The experiments were performed mostly at 2200°C, 5–23 GPa and constrained oxygen fugacities. Metal–magnesiowustite partition coefficients for V, Cr and Mn increase very weakly with increasing pressure, indicating only a slight increase in siderophile behaviour, whereas temperature has a relatively large effect on their partitioning. Ni and Co partition coefficients decrease as a function of pressure as previously reported. Because magnesiowustite/silicate melt partition coefficients are close to unity, these results can be applied to metal/silicate partition coefficients. The results demonstrate that high pressure alone during core formation cannot explain the depleted mantle abundances of V, Cr and Mn, in contrast to those of Ni and Co. However, taking all variables into account enables the mantle abundances of V, Cr, Mn, Ni and Co to be explained by metal segregation in a deep magma ocean above ∼3300°C, 35 GPa and an oxygen fugacity that is consistent with the present FeO content of the Earth’s mantle. Such conditions can be reached in a magma ocean on a giant impactor, if it is large enough (i.e. several times the mass of Mars), or on the Earth. Therefore, the Moon is likely to have formed largely from material that was ejected either from the mantle of a large impactor or from the Earth’s mantle.

MULTISTAGE SEPARATION OF QUINOLINE AND ISO-QUINOLINE BY DISSOCIATION EXTRACTION

ABSTRACT The separation of quinoline and iso-quinoline by dissociation extraction has been studied using toluene and aqueous hydrochloric acid as solvents. A laboratory scale multistage countercurrent mixer-settler unit was employed. Details are presented for the design and operation of this equipment The results for the separation of the quinoline and iso-quinoline mixture using a ten stage extractor are presented. Single stage equilibrium data and equilibrium equations reported previously have been used to develop a stage to stage calculation procedure and applied to determine flow rates and conjugate phase compositions in a ten stage unit. Experimental and calculated results for the concentrations of quinoline and iso-quinoline are compared and found to give good agreement.

Copper(II) Removal from Aqueous Solutions by Chelation in Supercritical Carbon Dioxide Using Fluorinated β-Diketones

Copper removal from aqueous solutions by chelation in supercritical carbon dioxide was investigated. The chelating agents were 1,1,1-trifluoroacetylacetone (TFA) and 2,2-dimethyl-6,6,7,7,8,8,8-heptafluoro-3,5-octanedione (FOD). Extraction efficiencies were determined for a single equilibrium stage in the temperature range 308−328 K and the pressure range 9.9−24.0 MPa and ranged from 4% to 84%. The extraction efficiencies increased with increasing the initial amount of chelating agent and with decreasing the initial copper concentration. No significant changes in extraction efficiencies were observed with temperature and pressure at a fixed initial amount of chelating agent. A thermodynamic model based on combined reaction and phase equilibria was also developed for prediction of extraction efficiencies.

Thermodynamics of Extraction of Copper(II) from Aqueous Solutions by Chelation in Supercritical Carbon Dioxide

The primary goal of this research was to investigate the feasibility of removing heavy metals from wastewater by chelation in supercritical carbon dioxide. Copper was used as the model contaminant. Extraction efficiency was determined as a function of temperature, pressure, initial moles of chelating agent, and initial moles of copper in a 300-cm3 autoclave. Results indicated that 60% removal of copper can be achieved in a single equilibrium stage with an initial copper concentration of 100 ppm and hexafluoroacetylacetone (HFA), present in excess, as the chelating agent. Experimental extraction efficiencies ranged from 14 to 60% and increased with increasing initial chelate concentration and CO2 density and with decreasing initial copper concentration. A thermodynamic model based on combined reaction and phase equilibria was developed for the prediction of extraction efficiencies. Five aqueous-phase reactions and four phase equilibrium relations were considered in the development of the model. Equilibrium constants and phase distribution coefficients were either drawn from the available literature or measured. The distribution coefficient of the copper−chelate complex was estimated as the ratio of the solubility of the complex in the supercritical phase to its solubility in the aqueous phase. The model successfully predicted the effects of tem perature, pressure, and initial amounts of chelating agent and metal contaminant on extraction efficiencies without the use of any adjustable parameters.

In Situ Determination of the Rate of Unassisted Degradation of Saturated-Zone Hydrocarbon Contamination

Abstract A method to measure the in situ degradation rate of dissolved hydrocarbon contamination has been developed and applied at two locations at a field site. The method uses the rates of downward diffusion of oxygen and upward diffusion of carbon dioxide through the unsaturated zone, as calculated from vertical soil-gas concentration gradients, combined with stoichiometry to obtain two degradation rates in hydrocarbon mass per water table surface area per time. Values of 0.385 gram per m2 per day and 0.52 gram per m2 per day (based upon oxygen data) and 0.056 gram per m2 per day and 0.12 gram per m2 per day (based upon carbon dioxide data) were calculated at a field site with dissolved fuel contamination. This result of lower values from ground-air carbon dioxide concentrations is consistent with a significant fraction of the carbon dioxide produced being lost to the aqueous phase. Based upon a single-stage equilibrium phase-transfer model, gas/water volume ratios of 0.02 and 0.2 for the capillary fringe were calculated. Groundwater carbon dioxide fugacities and soil-gas carbon dioxide concentrations were used at the two locations and a third to determine whether the source of elevated soil carbon dioxide concentrations were unsaturated-zone hydrocarbon degradation or a saturated-zone process. This technique has potential applicability in setting risk-based remedial criteria and in allowing inclusion of the contribution of in situ degradation in remedial design. This can result in major remedial cost savings.