Fugacity Coefficients Research Articles

Comparative Study of Cocurrent and Countercurrent Modes of Operation for a Thermal Hydrolyzer in an Industrial Urea Wastewater Treatment Loop

In this work, a comparison of cocurrent and countercurrent modes of operation for an industrial wastewater treatment loop of an industrial urea plant has been carried out. In both modes of operation, a loop with a thermal hydrolyzer is used for urea decomposition, and two desorbers are used for the removal of ammonia and carbon dioxide. In the proposed model, the extended electrolytic UNIQUAC equation is used to describe the nonideality of the liquid phase of the NH3−CO2−H2O−urea system, and the perturbed-hard-sphere (PHS) equation of state is applied to predict the vapor fugacity coefficients. Also, the urea hydrolysis reactors are divided into several continuously stirred tank reactors (CSTRs) and the equilibrium-stage model is applied for modeling of both kinds of reactors and of the desorbers. The simulation results show that countercurrent mode of operation is necessary to achieve new environmental standards and complete treatment. The data predicted using the model were consistent with available plant data, indicating the validity of the model. The impact of different parameters on the performance of the urea wastewater treatment loops has been examined. Overall, this study results in beneficial information about the use of the cocurrent and countercurrent hydrolysis reactors in the urea wastewater treatment process.

Isobaric vapor–liquid equilibria for the n-heptane + ethylene glycol monopropyl ether and n-octane + ethylene glycol monopropyl ether systems

Vapor–liquid equilibria (VLE) for the n-heptane + ethylene glycol monopropyl ether and n-octane + ethylene glycol monopropyl ether systems were measured. Isobaric VLE measurements of the associating fluid mixtures were conducted at several pressures (60 kPa, 80 kPa and 100 kPa) using Fischer VLE 602 equipment. The experimental data were correlated using a two-term virial equation for vapor-phase fugacity coefficients and the three suffix Margules equation, Wilson, NRTL, and UNIQUAC models for liquid-phase activity coefficients. The results show good agreement with the variety of models.

Investigating the Effects of Mass Transfer and Mixture Non-Ideality on Multiphase Flow Hydrodynamics Using CFD Methods

A numerical framework has been proposed to model the interacting effects of mixture non-ideality and mass transfer on hydrodynamics of a multiphase system using CFD methods. Mass transfer during condensation and vaporization is modeled by chemical potential at the liquid-vapor interface. Species mass transfers are related to the diffusion at the interface which in turn is related to the concentration gradients at the interface. A finite volume scheme is used to solve the equations of motion. Since the thermodynamic non-ideality of the system has been taken into account, the equilibrium calculations were performed using the fugacity coefficient definition for both the liquid and gas phases. The obtained results and their comparison against experimental data show that the proposed framework can simulate the hydrodynamic behavior of multi-component multi-phase systems with thermodynamic non-ideality.

CO2Absorption into Mixed Aqueous Solutions of 2-Amino-2-hydroxymethyl-1,3-propanediol and Piperazine

Solubility data of CO2 in aqueous mixtures of 2-amino-2-hydroxymethyl-1,3-propanediol (AHPD) and piperazine (Pz) were measured over a range of temperature from 288.15 to 333.15 K and for total amine concentrations up to 3.1 kmol·m−3. The CO2 partial pressure was kept within 0.21−2 637 kPa using a vapor−liquid equilibrium (VLE) apparatus based on a static-analytic method. The solubility of N2O in the Pz−AHPD aqueous solutions was also performed in order to determine, with the N2O analogy, the Henry’s law constant of CO2 in these solutions. The experimental data for the ternary system AHPD−CO2−H2O were correlated using a modified Pitzer’s thermodynamic model for the activity coefficients combined with the virial equation of state for representing the fugacity coefficients. The solubility of carbon dioxide in aqueous solutions of mixed amine (Pz + AHPD) was predicted by supposing that the parameters characterizing the single amine systems are essential for describing the quaternary system behavior.

CACHAÇA PRODUCTION IN A LAB‐SCALE ALEMBIC: MODELING AND COMPUTATIONAL SIMULATION

ABSTRACT This work presents the application of a differential distillation model for the simulation of cachaça production in a pot still (alembic). The vapor–liquid equilibria of the multicomponent mixture were described in a rigorous way, using the nonrandom two‐liquid model for the liquid phase activity coefficients and the virial equation with the chemical theory for the vapor phase fugacity coefficients. Two experimental trials were performed in order to validate the simulation results. The boiling points of the wine and the ethanol concentration of the distillate were measured at fixed time intervals. The concentrations of acetaldehyde, ethyl acetate, methanol, n‐propanol, isobutanol and isoamyl alcohol, and the volatile acidity were analyzed in the head, heart and tail fractions of the distillate. In general, a good agreement was achieved between the experimental and the simulation results, in terms of the temperature and the alcoholic graduation profiles, and also a satisfactory similitude in terms of the concentrations of the main congeners.PRACTICAL APPLICATIONSSpirit's sensorial quality depends on the ethanol and main congener concentrations, which should be controlled by dividing the distillate in appropriate cuts (head, heart and tail fractions) during the distillation. A correct simulation procedure of the pot still distillation allows improving the policy of distillate cuts, considering the product quality, the maximal recovery of ethanol in the heart fraction (spirit) and the energy consumption. It can as well help to define a policy of distillate cuts more appropriate to different types of wine, i.e., wines containing, for instance, larger concentrations of light components (acetaldehyde, methanol, etc.), or of those containing larger contents of heavy compounds, such as acetic acid. So this work goal was to indicate that computational simulation, based on a careful modeling of the system, could be an important tool to investigate the effect of processing variables in the final product quality, also in terms of minor compounds.

Dissolution Potential of SO2 Co-Injected with CO2 in Geologic Sequestration

Sulfur dioxide is a possible co-injectant with carbon dioxide in the context of geologic sequestration. Because of the potential of SO2 to acidify formation brines, the extent of SO2 dissolution from the CO2 phase will determine the viability of co-injection. Pressure-, temperature-, and salinity-adjusted values of the SO2 Henry's Law constant and fugacity coefficient were determined. They are predicted to decrease with depth, such that the solubility of SO2 is a factor of 0.04 smaller than would be predicted without these adjustments. To explore the potential effects of transport limitations, a nonsteady-state model of SO2 diffusion through a stationary cone-shaped plume of supercritical CO2 was developed. This model represents an end-member scenario of diffusion-controlled dissolution of SO2, to contrast with models of complete phase equilibrium. Simulations for conditions corresponding to storage depths of 0.8-2.4 km revealed that after 1000 years, 65-75% of the SO2 remains in the CO2 phase. This slow release of SO2 would largely mitigate its impact on brine pH. Furthermore, small amounts of SO2 are predicted to have a negligible effect on the critical point of CO2 but will increase phase density by as much as 12% for mixtures containing 5% SO2.

Simultaneous Removal of Urea, Ammonia, and Carbon Dioxide from Industrial Wastewater Using a Thermal Hydrolyzer−Separator Loop

In this work, simultaneous removal of urea, ammonia, and carbon dioxide from industrial wastewater was studied via modeling and simulation of a hydrolyzer−separator loop. The extended electrolytic UNIQUAC equation has been used to describe the nonideality of the liquid phase and the perturbed-hard-sphere (PHS) equation of state has been applied to predict the vapor fugacity coefficients. This work also uses a multistage well-mixed model for the liquid and vapor flows with a nonideal rate-based model for urea thermal hydrolyzer. Our study incorporates the reaction rate of urea hydrolysis and takes into account the effects of solution nonideality and backmixing on the reactor performance. The rates of urea reaction are written in terms of activity of reactants. The model provides temperature and flow rate distributions of different components along the height of the hydrolysis reactor and the desorbers. The simulation results have been found to be in good agreement with the plant data indicating the validity of the model. The impact of different parameters on the performance of the wastewater treatment loop has been examined. The results of this work showed that an increase in the inlet temperature of the wastewater and steam flow rate and also decrease the reflux ratio would improve the urea and ammonia removal efficiency.

Prediction of sublimation pressures from SCO2+hydrocarbon systems using a particle swarm optimization

A method to predict the sublimation pressures of solid hydrocarbons using a biologically-deriver algorithm is presented. Seven binary gas-solid phase systems of supercritical carbon dioxide with hydrocarbons are considered in this study. The Peng-Robinson equation of state with the Wong-Sandler mixing rules are used to evaluate the fugacity coefficient on the systems. Then, particle swarm optimization is used for minimize the difference between calculated and experimental solubility, and the sublimation pressures are calculated from solubility data. The results show that the method presented is reliable enough and can be used with confidence to estimate the sublimation pressure of other hydrocarbons.

Estimation of solid vapor pressures from supercritical CO 2 + biomolecule systems using a PSO algorithm

A method to estimate the solid vapor pressures of biomolecules using a biologically deriver algorithm is presented. The solid vapor pressure is usually small for most solid compounds and in many cases available experimental techniques cannot be used to obtain accurate values. Therefore, estimation methods must be used to obtain these data. Five binary gas–solid phase systems of supercritical CO 2 + biomolecule containing caffeine, artemisinin, capsaicin, cholesterol, and β-carotene are considered in this study. Particle swarm optimization is used for minimize the difference between calculated and experimental solubility. Then, the solid vapor pressures of biomolecules are calculated from solubility data. The Peng–Robinson equation of state with the Wong–Sandler mixing rules are used to evaluate the fugacity coefficient on the systems. The results show that the method presented is reliable enough and can be used with confidence to estimate the solid vapor pressure of any organic biomolecule.

A Phase-Partitioning Model for CO2–Brine Mixtures at Elevated Temperatures and Pressures: Application to CO2-Enhanced Geothermal Systems

Correlations are presented to compute the mutual solubilities of CO2 and chloride brines at temperatures 12–300°C, pressures 1–600 bar (0.1–60 MPa), and salinities 0–6 m NaCl. The formulation is computationally efficient and primarily intended for numerical simulations of CO2-water flow in carbon sequestration and geothermal studies. The phase-partitioning model relies on experimental data from literature for phase partitioning between CO2 and NaCl brines, and extends the previously published correlations to higher temperatures. The model relies on activity coefficients for the H2O-rich (aqueous) phase and fugacity coefficients for the CO2-rich phase. Activity coefficients are treated using a Margules expression for CO2 in pure water, and a Pitzer expression for salting-out effects. Fugacity coefficients are computed using a modified Redlich–Kwong equation of state and mixing rules that incorporate asymmetric binary interaction parameters. Parameters for the calculation of activity and fugacity coefficients were fitted to published solubility data over the P–T range of interest. In doing so, mutual solubilities and gas-phase volumetric data are typically reproduced within the scatter of the available data. An example of multiphase flow simulation implementing the mutual solubility model is presented for the case of a hypothetical, enhanced geothermal system where CO2 is used as the heat extraction fluid. In this simulation, dry supercritical CO2 at 20°C is injected into a 200°C hot-water reservoir. Results show that the injected CO2 displaces the formation water relatively quickly, but that the produced CO2 contains significant water for long periods of time. The amount of water in the CO2 could have implications for reactivity with reservoir rocks and engineered materials.

Predicting the extraction yield of nimbin from neem seeds in supercritical CO 2 using group contribution methods, equations of state and a shrinking core extraction model

The purpose of this paper is to present the predicted extraction of nimbin from neem seeds using supercritical CO 2 when only the molecule structure of nimbin is known. Group contribution methods (GCM) were used to estimate pure component properties, equations of state (EoS) to estimate the pressure/volume/temperature (PVT) behaviour and fugacity coefficient of solute in the solute–solvent mixture. Transport properties were estimated using available correlations and a shrinking core model was used to predict the extraction yield. The model predictions were compared with experimental data; the effect of CO 2 flow rate (0.24–1.24 mL/min), temperature (308–333 K), pressure (10–26 MPa), particle size (0.575–1.850 mm) and weight of neem kernel powder (1.0–2.5 g) were investigated. The predicted results were found to agree well with the measured results and the model was able to explain the presence of optimum yields that were observed experimentally.

Experimental determination of the (vapor + liquid) equilibrium data of binary mixtures of fatty acids by differential scanning calorimetry

(Vapor + liquid) equilibrium (VLE) data for three binary mixtures of saturated fatty acids were obtained by differential scanning calorimetry (DSC). However, changes in the calorimeter pressure cell and the use of hermetic pans with holes ( ϕ = 250 mm) in the lids were necessary to make it possible to apply this analytical technique, obtaining accurate results with smaller samples and shorter operational times. The systems evaluated in this study were: myristic acid (C 14:0) + palmitic acid (C 16:0), myristic acid (C 14:0) + stearic acid (C 18:0), and palmitic acid (C 16:0) + stearic acid (C 18:0), all measured at 50 mm Hg and with mole fractions between 0.0 and 1.0 in relation to the most volatile component of each diagram. The fugacity coefficients for the components in the vapor phase were calculated using the Hayden and O’Connell method [J.G. Hayden, J.P. O’Connell, Ind. Eng. Chem. Process Design Develop. 14 (3) (1975) 209–216] and the activity coefficients for the liquid phase were correlated with the traditional g E models (NRTL [H. Renon, J.M. Prausnitz, Aiche J. 14 (1968) 135–144], UNIQUAC [D.S. Abrams, J.M. Prausnitz, Aiche J. 21 (1975) 116–128], and Wilson [J.M. Prausnitz, N.L. Linchtenthaler, E.G. Azevedo, Molecular Thermodynamics of Fluid-phase Equilibria, River-Prentice Hall, Upper Saddle, 1999]). The sets of parameters were then compared in order to determine which adjustments best represented the VLE.

Calculation of Solid−Liquid−Gas Equilibrium for Binary Systems Containing CO2

Two equations typically used for the pure-solid fugacity proved to be identical by selecting an appropriate relation for the pure-solid vapor pressure and the pure-liquid vapor pressure. On the basis of the pure-solid fugacity, a semipredictive model using solubility data (SMS) and a calculation model combining with GE models (CMG) were developed to calculate the solid−liquid−gas (SLG) coexistence lines of pure substances in the presence of CO2. For the SMS model, the Peng−Robinson equation of state (PR-EoS) with the van der Waals one-fluid mixing rule is used to correlate the solute solubility in CO2 to obtain the interaction parameter k12, which is further employed to predict the SLG coexistence lines by two methods: one adopts the fugacity coefficient of the solute in the liquid phase by an equation of state calculation (SMS-φ); the other uses the activity coefficient of the solute in the liquid phase calculated from the UNIFAC model (SMS-γ). For the CMG model, the PR-EoS with the linear combination of...

Investigation on isobaric vapor–liquid equilibrium for acetic acid + water + methyl ethyl ketone + isopropyl acetate

Isobaric vapor–liquid equilibrium (VLE) data for acetic acid + water, acetic acid + methyl ethyl ketone (MEK), MEK + isopropyl acetate, acetic acid + MEK + water and acetic acid + MEK + isopropyl acetate + water are measured at 101.33 kPa using a modified Rose cell. The nonideal behavior in vapor phase of binary systems measured in this work is analyzed through calculating fugacity coefficients since mixture containing acetic acid deviates from ideal behavior seriously in vapor phase due to the associating effect of acetic acid. Combined with Hayden–O’Connell (HOC) equation, the VLE data of the measured binary systems for acetic acid + water, acetic acid + MEK and MEK + isopropyl acetate are correlated by the NRTL and UNIQUAC models. The NRTL model parameters obtained from correlating data of binary system are used to predict the VLE data of the ternary and quaternary systems, and the predicted values obtained in this way agree well with the experimental values.

Treatment of wastewater polluted with urea by counter-current thermal hydrolysis in an industrial urea plant

In this paper, the removal of urea from industrial wastewater by thermal hydrolysis was studied via modeling and simulation of counter-current urea thermal hydrolysis reactor. The features of our proposed model are (1) the use of Nakamura equation of state to predict the vapor fugacity coefficients and UNIQUAC equation to describe the non-ideality of liquid phase, (2) the use of multi-stage well-mixed model for the liquid and vapor flows with non-ideal rate-based model for urea thermal hydrolyser, (3) the reactions are assumed to take place in the liquid phase. The model incorporates reaction rates of urea hydrolysis and takes into account the effects of solution non-ideality and back mixing on the urea thermal hydrolyser performance. The rates of reaction are written in terms of activity of reactants which are determined using a thermodynamic framework for system of NH 3–CO 2–H 2O–urea mixture. The model provides temperature and concentrations distribution of different components in the liquid and vapor phases along the height of urea thermal hydrolyser. The predicted data of the model were consistent with the plant data indicating validity of the model. Also the effects of key parameters on the performance of urea thermal hydrolyser such as the temperature and flow rate of the steam and wastewater were examined. The results of this work show each parameter that causes an increase in temperature level along the urea thermal hydrolyser improves the urea removal efficiency.

Solid pure component property effects on modeling upper crossover pressure for supercritical fluid process synthesis: A case study for the separation of Annatto pigments using SC-CO 2

In this work a new method to predict upper crossover pressure based on equations of state is developed and applied to systems containing supercritical CO 2 and Annatto ( Bixa orellana) pigments. The calculation of the solubility of bixin in supercritical carbon dioxide is done using the Peng–Robinson–LCVM–UNIFAC equation of state and the effect of any uncertainty of some solid pure component properties on the upper crossover pressure is also investigated. The calculation of the solubility of norbixin in supercritical CO 2 is also done but in a completely predictive way using only solubility parameter data and group contribution since no experimental data of solubility is available. For both systems pure component parameters are initially estimated by group contribution and subsequently tuned by the model. It is also shown that the slope of sublimation pressure curve plays a major role in the accuracy of the upper crossover pressure determination. Furthermore, the present method can be used for upper crossover pressure analysis regardless of the equation of state and mixing rules adopted to calculate the fugacity coefficient of solid solute in the fluid phase. The results for solubility and crossover pressure calculated with this method are in good agreement with experimental data for CO 2–bixin available in literature. The method described here can be useful to any solid–fluid system of interest in supercritical fluid extraction process synthesis.

IMPLEMENTATION OF MATHEMATICA FOR DEVELOPMENT AND APPLICATION OF EOS MODELS. II: DERIVATION OF THE GENERALIZED EXPRESSION FOR THE FUGACITY COEFFICIENTS OF COMPOUNDS IN A MIXTURE

This work discusses an implementation of the computer program Mathematica for derivation of the generalized expression for the fugacity coefficients of compounds in a mixture. This expression may substantially simplify the systematic comparison between predictions of fluid phase equilibria yielded by different EOS models. Simple algorithms for the vapor pressure, VLE, and LLE calculations are also presented.

Isobaric vapor–liquid equilibria for the n-hexane + 2-isopropoxyethanol and n-heptane + 2-isopropoxyethanol systems

Vapor–liquid equilibria (VLE) for the n-hexane + 2-isopropoxyethanol and n-heptane + 2-isopropoxyethanol (at 60, 80, and 100 kPa) systems were measured. Two systems present positive deviations from ideal behavior. And the system n-heptane + 2-isopropoxyethanol shows a minimum boiling azeotrope at all pressures. Experimented data have been correlated with the two term virial equation for vapor-phase fugacity coefficients and the three suffix Margules equation, Wilson, NRTL, and UNIQUAC equations for liquid-phase activity coefficients. Experimental VLE data show excellent agreements with models.

Extractive rectification of the benzene fraction of reformer naphtha using N-methylpyrrolidone-N-formylmorpholine mixtures

Extractive rectification of the benzene fraction of reformer naphtha was studied, and the relative fugacity coefficients of the heptane-benzene system in the presence of N-methylpyrrolidone-N-formylmorpholine mixtures of various compositions were determined. A synergistic effect was revealed for a mixed selective solvent containing 29–30 wt % iV-formylmorpholine, 68–69% N-methylpyrrolidone, and 2–3 wt % water.

Thermodynamic modeling of vapor–liquid equilibrium of binary systems ionic liquid + supercritical {CO 2 or CHF 3} and ionic liquid + hydrocarbons using Peng–Robinson equation of state

Vapor–liquid equilibrium (VLE) data from literature for binary systems involving several ionic liquids were correlated. The Peng–Robinson equation of state, coupled with the van der Waals and Wong–Sandler mixing rules, was used as the thermodynamic model to evaluate the fugacity coefficients. The UNIQUAC and NRTL models were used to calculate the excess Gibbs free energy in the Wong–Sandler mixing rule. A molecular modeling strategy using the software ChemOffice was used to calculate the volume and surface area parameters of ionic liquids for UNIQUAC, while the binary interaction energy parameters for UNIQUAC and NRTL models, as well as the binary interaction parameter of the van der Waals and Wong–Sandler mixing rules were estimated through a method based on the genetic algorithm. The results show that, as expected, the Wong–Sandler mixing rules represented better the data, with both activity coefficient models showing high accuracy. However, in one case, NRTL predicted an erroneous azeotropic condition, while UNIQUAC was able to correlate the data without this error.