Binary Equilibrium Research Articles

Correlation of water-chlorohydrocarbon mutual solubilities using a modified non-quadratic mixing rule and the Cubic-Two-State equation of state

The Cubic Two-State equation of state was employed to correlate the measured mutual solubilities of water and 23 chlorinated hydrocarbons (CHCs). Following the scheme framework laid out by Medeiros and Brindis-Flores, a nonquadratic Kabadi-Danner type mixing rule is used, where the water-water dispersive parameter is corrected due to the presence of a hydrophobic solute. The model’s three parameters were adjusted to correlate experimental binary liquid-liquid equilibrium data to relatively high accuracy. The observed minimum in CHC solubility in water near ambient conditions is reproduced reliably. Overall deviations from experimental data were 7.8% for CHC solubility in the aqueous phase and 13% for water solubility in the organic phase.

Calculation of the Phase Equilibrium of CO2–Hydrocarbon Binary Mixtures by PR-BM EOS and PR EOS

The phase equilibrium data of CO2–hydrocarbon binary mixtures are important for the design and operation of CO2 flooding, coal liquefaction, and supercritical extraction processes. Numerous pieces of binary phase equilibrium data have been obtained. Thus, models for the accurate calculation of binary and multicomponent mixtures must be developed on the basis of existing data. In this work, 3578 vapor–liquid phase equilibrium data points for 10 CO2–hydrocarbon binary mixtures, including CO2–butane, CO2–pentane, CO2–isopentane, CO2–hexane, CO2–benzene, CO2–heptane, CO2–octane, CO2–nonane, CO2–decane, and CO2–undecane, were collected. The PR and PR-BM equations of state (EOS) in combination with relevant mixing rules were used to calculate the phase equilibrium data of the CO2–hydrocarbon binary mixtures. The binary interaction parameter kij in the PR EOS was temperature independent, whereas parameters in the PR-BM EOS were functions of temperature. Thus, the phase equilibrium data and other thermodynamic properties of the binary and multicomponent mixtures at different temperatures and pressures can be calculated by using the parameters obtained in this work. The PR-BM EOS performed better than the PR EOS, and the average absolute deviations over the temperature range of 255.98–408.15 K calculated by the PR EOS and PR-BM EOS were less than 5.74% and 3.36%, respectively. The results calculated by the two EOS were compared with those calculated by other models, such as PPR78, PR + LCVM + UNIFAC, KIE + PR EOS + HV, and PSRK. The phase equilibrium data of CO2–butane–decane, CO2–hexane–decane, and CO2–octane–decane ternary mixtures were calculated by the two EOS. The average overall deviations for the CO2 mole fractions calculated by the two EOS were less than 7.66%.

Ion Exchange Modeling of the Competitive Adsorption of Cu(II) and Pb(II) Using Chemically Modified Solid Waste Coffee

The presence of potentially toxic metals such as Cu(II) and Pb(II) in aquifers and industrial effluents represents a serious health problem due to their high toxicity, non-biodegradability, and ability to bioaccumulate. In this study, the removal of these pollutants individually and as a binary mixture has been studied, using solid coffee waste modified with 0.6 M citric acid as the adsorbent, and a mathematical model based on the ion exchange mechanism was implemented to elucidate the adsorption equilibrium. The characterization of modified coffee waste showed a pH value at the point of zero charge of 2.97 and a high concentration of carboxylic groups, which are susceptible to ion exchange. Furthermore, the quantification of interchangeable ions confirmed that the main mechanism of adsorption is the ion exchange of metal ions with the protons present on the adsorbent’s surface. The experimental data of the individual and binary adsorption equilibrium using a model based on a phenomenological approach was analyzed. The phenomenological model was compared with the Freundlich and Langmuir empirical solid-liquid adsorption models. The results showed that the adsorption capacities of Cu(II) and Pb(II) individually were 1.46 and 1.18 meq/g, and in a binary mixture were 1.43 and 1.24 meq/g, respectively, at pH 5 and 30 °C. In addition, the separation coefficients from ion exchange model revealed the predominance of protons as an exchangeable ion, which is in accordance with the experimental evidence. Finally, the correlation coefficient showed that the proposed model predicts accurately the adsorption equilibrium.

GCA-EOS extension to mixtures of phenol ethers and derivatives with hydrocarbons and water

Anisol and its derivatives are typically used in the flavoring and fragrance industry, and they are also considered as additives for fuels and solvents for separation processes. Despite their growing importance, due to the development of biomass conversion routes, only few authors have modeled their phase behavior, which is required to assess industrial applications. In this work, we extend the Group Contribution with Association Equation of State (GCA-EOS) to multiphase equilibria of phenol ethers. We investigate pure anisole and its derivatives, as well as their mixtures with linear and cyclic alkanes, alkenes, aromatic hydrocarbons, and water. To fit the model parameters and assess its predictive capacity, we assemble an experimental database with the vapor pressure of 8 phenol ethers and 283 binary equilibrium datapoints. The parameterization procedure aims to reduce the required number of binary interaction parameters, avoiding to over correlate the model. The results show that GCA-EOS predicts the pure vapor pressure data with an average deviation of 3%, as well as the VLE of binary mixtures with similar accuracy. On the other hand, the model is also able to describe the mutual solubility of methoxy aromatic compounds with water.

Predicting Mole-Fraction-Dependent Dissociation for Weak Acids.

We demonstrate for formic and acetic acid dissolved in water as examples that the binary quantum cluster equilibrium (bQCE) approach can predict acid strengths over the whole range of acid concentrations. The acid strength increases in a complex rather than a simple way with increasing mole fraction of the acid from 0 to 0.7, reflecting the complex interplay between the dissociated ions or conjugate bases available as compared to the acid and water molecules. Furthermore, our calculated ion concentrations meet the experimental maximum of the conductivity with excellent agreement for acetic acid and satisfactorily for the formic acid/water mixture. As only a limited number of simple quantum-chemical calculations are required for the prediction, bQCE is clearly a valuable approach to access these quantities also in non-aqueous solutions. It is a highly valuable asset for predicting ionization processes in highly concentrated solutions, which are relevant for biological and chemical systems, as well as technological processes.

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.

A Cluster Approach for Activity Coefficients: General Theory and Implementation

In the framework of the binary quantum cluster equilibrium theory, we introduce a cluster approach to access activity coefficients of binary mixtures. This approach allows derivation of activity coefficients based on quantum chemically calculated clusters. The cluster sets in this work comprise clusters ranging in size from one to six molecules of either a single or two species. For each cluster size up to five conformers if detectable are considered such that important liquid motifs are included. Via self-consistent-field calculations the binary quantum cluster equilibrium theory gives the Gibbs energies and thus the excess Gibbs energies of mixing. Derivation with respect to the particle number allows access to activity coefficients. To achieve an analytical expression, we apply the standard approach of fitting a Redlich–Kister polynomial to the excess Gibbs energy and calculate its derivative, which leads to good results for the binary mixture cases of acetonitrile/benzene and methanol/ethanol, as well...

Simulation of CO2/CH4 high pressure separation on microporous activated carbon

Pure component adsorption equilibrium of CH4 and CO2 on activated carbon have been studied at three different temperatures, 298, 323, and 348 K within a pressure range of 10–2000 kPa. Binary adsorption equilibrium isotherm was described using extended Sips equation and ideal adsorbed solution theory (IAST) model. Experimental breakthrough curves of CO2/CH4 (40:60 in a molar basis) were performed at four different pressures (300, 600, 1200, and 1800 kPa). The experimental results of binary isotherms and breakthrough curves have been compared to the predicted simulation data in order to evaluate the best isotherm model for this scenario. The IAST and Sips models described significantly different results for each adsorbed component when higher pressures are set. These different results cause a significant discrepancy in the estimation of the equilibrium selectivity. Simulated and experimental equilibrium selectivity data provided by IAST presented values of around 4, for CO2/CH4, and extended Sips presented values of around 2. Also, simulated breakthrough curves showed that IAST fits better to the experimental data at higher pressures. According to the simulations, in a binary mixture at total pressure over 800 kPa, extended Sips model underestimated significantly the CO2 adsorbed amount and overestimated the CH4 adsorbed amount.

Fluctuation Theory in Chemical Kinetics

In this research, we study the stability properties of chemical reactions of arbitrary orders. In a given chemical experiment, we focus on the formation of a chemical equilibrium by optimizing the reaction rate. Under infinitesimal simultaneous variations of the concentrations of reacting species, the binary component equilibrium is achieved when either one of the orders or concentrations of reactants vanishes. The chemical concentration capacities of the components are calculated to describe the local stability of the equilibrium. The correlation between the components is obtained as the mixed second-order derivative of the rate with respect to concentrations. The global stability analysis is performed by introducing a symmetric matrix with its diagonal components as the chemical capacities and off-diagonal components as the local correlation. We find that the local chemical stability requires the orders of the reactants to be either negative or larger than unity. The corresponding global stability requires the positivity of a cubic factor over the orders of the reactants. In short, our consideration illustrates how a chemical reaction takes place by attaining its activation state and asymptotically approaches the equilibrium when two components are mixed with arbitrary orders. Qualitative discussions are provided to support our analysis towards the formation of an optimized equilibrium. Finally, along with future directions, we discuss verification of our model towards the formation of carbon-based reactions, formation of organic/inorganic chemical equilibria and catalytic oxidation of C O − H 2 mixtures in presence of Pt.

Expounding the role of interference on the recovery of nutrient fractions from aqua matrix using calcined gastropod shell

The need to elucidate the influence of the presence of the major components (i.e. organic matter phosphate and nitrate) of nutrient-rich wastewater on the process of nutrient recovery, using calcined gastropod shell (CGS), necessitated this study. The time–concentration profiles of the recovery of organic matter, phosphate and nitrate were studied in synthetic feed water that contained single adsorbate of interest. Both the single and binary component equilibrium isotherm parameters were derived to explicate and quantify the impact of the presence of each constituent of the nutrient rich wastewater on the process of resource recovery. The time-concentration profiles of all the recovery processes showed that the process of nitrate recovery is the rate limiting step in the use of CGS as the reactive material. The pseudo second order kinetic equation gave the best description of both the nutrient and organic matter recovery but the processes were described by different equilibrium isotherm equations. The determination of the efficiency of interference on nutrient recovery showed that nitrate and organic matter exhibited minimal influence on phosphate recovery but the presence of phosphate and organic matter significantly impacted nitrate recovery. The recovery of organic matter was not vitiated by the presence of either phosphate or nitrate. The real life implications of the findings from this study showed that the use of CGS as a reactive material in resource recovery from a nutrient-rich wastewater would provide a double-pronged approach for resource recovery and appreciable treatment of wastewater for reuse.

Simultaneous removal of binary dye from textile effluent using cobalt ferrite-alginate nanocomposite: Performance and mechanism

The rapid removal of dye effluent containing two or more dyes is in demand due to its significant environmental issues. The present communication deals with the simultaneous adsorption of Reactive red 195 (RR195) and Reactive yellow 145 (RY145) from a textile dye effluent in a binary component system. Cobalt ferrite-alginate nanocomposite synthesized by ex-situ polymerization was employed as an adsorbent for the removal of binary dye effluent. The first order derivative spectrophotometric method was applied for the simultaneous quantification of RR195 and RY145 in binary solutions. The binary adsorption equilibrium could be achieved within 60 min, and the adsorption process followed pseudo second order kinetics. The removal efficiency could be maintained in a wide pH range of 3–6. The presence of amine, hydroxyl, carbonate and ferrite groups on the adsorbent surface played a vital role in the removal of RR195 and RY145 from their binary mixture. The continuous adsorption experiments revealed that the breakthrough time and exhaustion time increases with an increase in the bed height. The experimental results present new sustainable, cost effective biocompatible nanocomposite as a potential adsorbent for the removal of real-time dye effluent. Moreover, it is magnetically separable and reusable. The cobalt ferrite-alginate as a sole nanocomposite is capable of eliminating the whole dye content from a mixture and serves as a better solution for effective water remediation.

Thermodynamic analysis of biodiesel production systems at supercritical conditions

This work reports thermodynamic analysis of systems involved in the biodiesel production using ethanol at supercritical conditions. PC-SAFT equation of state was used from ASPEN Plus simulator for modeling all investigated systems. Binary and ternary phase equilibrium data at high pressure and temperature were used to assess the PC-SAFT capability of predicting the thermodynamic behavior of the complex mixture of interest in this work. The results showed that the PC-SAFT is a reliable tool to represent the phase behavior of mixtures involving ethanol, vegetable oil, fatty acid, ethyl esters of fatty acid and glycerol. Phase behavior of the reaction system was evaluated under specified experimental conditions and considering different reaction conversions. Pressure-temperature diagrams demonstrated that the two-phase region for the reaction mixture decreases as the extension of reaction is increased. The PC-SAFT equation of state was used to estimate the density of the reactant mixture and the effect of this parameter over the residence of the reaction was assessed, where it was clearly demonstrated that the density of the mixture greatly affects the residence time calculation for the reactions of biodiesel production at high pressure conditions.

Single and Binary Mixture Adsorption Behaviors of C6–C8 Hydrocarbons on Silica–Alumina Gel

To ensure the technical use of natural gas, heavy hydrocarbons and other components must be separated. Therefore, in this work the adsorption of C6–C8 hydrocarbons n-hexane, n-heptane, n-octane, benzene, toluene, and cyclohexane on a commercial silica–alumina gel (Sorbead H) was investigated in experiments and dynamic simulations. Single and binary mixture equilibrium isotherms were determined from cumulative breakthrough curve experiments on a fixed bed adsorber at 25–75 °C and 1.3 bar (abs) in the trace range up to approximately 5000 ppmmol. The adsorption behavior is interpreted on the basis of the molecular structure of the adsorptive, the surface chemistry, and the pore structure of the adsorbents. Binary mixture isotherms were calculated using the theory of the ideal adsorbed solution (IAST). The results were in good agreement with experimental data. The adsorption dynamics was investigated by breakthrough curve experiments and simulated dynamically using an isothermal model based on mass balances a...

Adsorption equilibrium of xylene isomers and ethylbenzene on MIL-125(Ti)_NH2: the temperature influence on the para-selectivity

The separation of xylene isomers feedstock containing ethylbenzene is still a relevant industrial challenge. The increase in p-xylene consumption worldwide promotes the search for more efficient separation processes. One possible way to achieve such a goal is to upgrade the existing SMB units with selective adsorbents operating at lower temperatures. Therefore, new adsorbents such as the functionalized metal–organic framework MIL-125(Ti)_NH2 appear as strong candidates. The MIL-125(Ti)_NH2 was tested in this work for the selective adsorption and separation of xylene isomers, including ethylbenzene, in liquid phase and using n-heptane as eluent. In this way, a detailed experimental study of binary and multicomponent adsorption equilibrium of xylene isomers in MIL-125(Ti)_NH2, at three temperatures (299 K, 313 K and 343 K) in liquid phase, was performed and is reported in this manuscript. Ternary breakthrough experiments indicate competitive adsorption between p-xylene over the two other isomers. Indeed the selectivity values range from 1.4 to 1.9 and 1.5 to 2.3 for the p-xylene/m-xylene and p-xylene/o-xylene pairs, respectively, increasing with the temperature. Similar trends are observed for the quaternary mixtures, where p-xylene and ethylbenzene are adsorbed preferentially. However, the MIL-125(Ti)_NH2 does not discriminate between the two more linear molecules at lower temperatures. Yet, when temperature is increased to 343 K, the adsorption of p-xylene becomes more favorable than ethylbenzene, presenting a selectivity of 1.3. Therefore, within the studied temperature range a temperature, 343 K is the most favorable temperature to operate the SMB process, for the p-xylene production from mixtures containing ethylbenzene.

Equilibrium study of binary mixture biosorption of Cr(III) and Zn(II) by dealginated seaweed waste: investigation of adsorption mechanisms using X-ray photoelectron spectroscopy analysis.

The alginate extraction residue (RES) from the Brazilian Sargassum filipendula was successfully employed as biosorbent in this binary equilibrium study, revealing a greater affinity and selectivity for Cr(III) than for Zn(II). Experimental results also revealed that the process is of endothermic nature and well adjusted by Langmuir-Freundlich binary model. The X-ray photoelectron spectroscopy (XPS) analysis revealed that coordination with hydroxyl groups of RES prevailed in Cr removal, followed by carboxyl-metal complexation. As far as Zn(II) is concerned, ion exchange with carboxylate groups of RES was the largest contributor. Nevertheless, scanning electron microscopy coupled with Fourier transform infrared spectroscopy indicated the participation of sulfate functions in a minor degree.

Construction and evaluation of ternary solid-liquid phase diagram of pyraclostrobin (form IV) and its intermediate in ethanol and N,N-dimethylformamide

Abstract In order to improve the purity of target product and reduce the cost of industrial production, the phase diagrams of pyraclostrobin and its intermediate (pheny N-methoxy-N- (2- ((N′-pyrazinyl) pyrazolyl-3′-oxymethyl) -phenyl) carbamate) in binary and ternary systems was studied. In each ternary phase diagram, there were three crystallization regions (pure pyraclostrobin intermediate, pure pyraclostrobin, and mixture of pyraclostrobin and its intermediate), two co-saturated curves, and one co-saturated point. The crystallization region of pyraclostrobin intermediate was larger than that of pyraclostrobin in ethanol and N, N-dimethylformamide (DMF) at three temperatures. In order to extend application of the obtained binary and ternary systems, the NRTL model and Wilson model were used to describing the solubility behaviour of pyraclostrobin and its intermediate in binary and ternary systems, the value of root-mean-square deviation (RMSD) was no more 9.01 × 10−3, the value of relative average deviation (RAD) was a little large, and no more than 5.84%. The calculated results via two models were all acceptable for the binary and ternary solid-liquid phase equilibrium. Ethanol and DMF in different temperature can be applied to separate the mixture of pyraclostrobin and its intermediate.

Archaeological Arsenical Bronzes and Equilibrium in the As-Cu System

Understanding the effects of impurities, segregation, undercooling, and solidification velocity is necessary to reconstruct prehistoric As-Cu alloy manufacturing processes and practices. Moreover, these alloys often contain a wide variety of minor and trace elements such that the binary As-Cu equilibrium phase diagram does not adequately represent arsenical bronze artifacts as-cast in ancient molds. Furthermore, the variable cooling rates present in as-cast alloys of predominantly arsenic and copper, due to the thermal properties of differing mold materials, would have had profound effects on the formation of inversely segregated arsenic. Alloys with 1 to 15 wt pct arsenic were prepared and studied using differential thermal analysis, metallography, and scanning electron microscopy with energy-dispersive X-ray spectroscopy. Equilibrium diagrams were established and the potential influence of trace elements discussed. A new liquidus curve for the equilibrium diagram in this compositional range, measuring slightly higher in temperature, was established.

Experimental and Mathematical Simulation of Noncompetitive and Competitive Adsorption Dynamic of Formic Acid–Levulinic Acid–5-Hydroxymethylfurfural from Single, Binary, and Ternary Systems in a Fixed-Bed Column of SY-01 Resin

Levulinic acid (LA) is a versatile platform chemical in the modern concept of the biorefinery and can be used to synthesize a broad range of desirable chemicals and fuel additives. Unfortunately, because LA released from biomass hydrolysate is accompanied by formic acid (FA) and 5-hydroxymethylfurfural (5-HMF), it is also important to investigate the binary and ternary adsorption equilibrium, as well as competitive dynamic fixed-bed column adsorption from the viewpoint of industrial application. Batch adsorption experiments showed that the affinity of SY-01 resin toward FA–LA–5-HMF were in the order of 5-HMF > LA > FA under noncompetitive and competitive systems. The highest adsorption capacity were 7.54 mg/g wet resin for FA, 103.51 mg/g wet resin for LA, and 107.73 mg/g wet resin for 5-HMF. Interestingly, the presence of FA has a synergistic effect on the adsorption of LA and 5-HMF onto SY-01 resin in a binary- or ternary-mixtures system, leading to a slight increase in adsorption uptakes. Furthermore, ...

Studies of Metallic and Trace Minerals of the Tiegelongnan Cu‐Au Deposit, Central Tibet, China

Electron probe micro‐analysis (EPMA) and scanning electron microscopy (SEM) equipped with energy dispersive spectrometry (EDS) have been used to investigate the principal ore minerals and coexisting metallic mineral inclusions in polished thin sections from the Tiegelongnan deposit, which consists of a high‐sulfidation epithermal system (HSES) and a porphyry system (PS). Molybdenite, chalcopyrite, bornite, tennantite, enargite, digenite, anilite, covellite, and tetrahedrite have been identified by EPMA. Intergrowth, cross‐cutting and replacement relationships between the metallic minerals suggest that molybdenite formed first (stage 1), followed by chalcopyrite ± bornite ± hematite (stage 2), then bornite ± Cu‐sulfides ± Cu‐Fe‐sulfoarsenides (stage 3), and lastly Cu‐Fe‐ sulfoarsenides ± Cu‐ sulfides (stage 4). Pyrite is developed throughout all the stages. Droplet‐like inclusions of Au‐Te minerals commonly occur in tennantite but not in the other major sulfides (molybdenite, chalcopyrite and bornite), implying that tennantite is the most important Au telluride carrier. The pervasive binary equilibrium phases of calaverite and altaite constrain fTe2 in the range from ∼−6.5 to ∼−8 and fS2 < −11. The intergrowth of bornite and chalcopyrite and the conversion from bornite to digenite suggest fluctuated and relatively low precipitation temperature conditions in the HSES relative to the PS. Contrastingly, the dominance of chalcopyrite in the PS, with minor bornite, suggests relatively high temperature conditions. These new results are important for further understanding the mineral formation processes superimposed by HSES and PS systems.

Binary adsorption equilibrium and breakthrough of toluene and cyclohexane on macroporous and hypercrosslinked polymeric resins

Adsorption-based separation is one of the most widely used methods in treating gasoline vapor. For effective control of gasoline vapor emission, the total concentration of non-methane hydrocarbons (NMHC) and the specific component such as toluene must meet the emission limit values. In this study, hypercrosslinked polymeric resin (Hyper-resin) and macroporous polymeric resin (Macro-resin) were selected as adsorbents. Toluene and cyclohexane were chosen as the representative of alkanes and aromatic hydrocarbons components of gasoline vapor. Pure and binary component adsorption isotherms of toluene and cyclohexane on two resins were measured by head space analysis method. Breakthrough data for binary system were obtained at the different concentrations of toluene (12–46 mg/L) and cyclohexane (15 mg/L and 102 mg/L) using a fixed-bed reactor. The results indicate that adsorption equilibria of binary component can be predicted by ideal adsorbed solution theory (IAST) with the average relative error lower than 15% using the pure component adsorption isotherm data. Hyper-resin provides higher selectivity to toluene than Macro-resin in binary equilibrium and breakthrough system. Moreover, the breakthrough adsorption capacities of pure component (toluene and cyclohexane) and their mixture on Hyper-resin are higher than those on Macro-resin, suggesting Hyper-resin would be a promising adsorbent for treating gasoline vapor.