Vapor-liquid Equilibrium Model Research Articles

Parameter estimation in vapor-liquid equilibrium modeling of compounds related to biodiesel production using opposite point-based differential evolution algorithm.

Biodiesel stands out as the most favorable alternatives to fossil-derived diesel, offering a multitude of environmental benefits. At various stages of biodiesel production, the separation processes necessitate thermodynamic models with the capability to correlate and predict phase equilibria of mixtures. In this study, application of the classical differential evolution (DE) and its new enhanced version, the OPDE algorithm, for modeling vapor-liquid equilibrium (VLE) associated with components related to biodiesel production is presented. The algorithms were analysed and contrasted in terms of their performance, in estimating parameters for Wilson, NRTL and UNIFAC models. Additionally, classical least-squares (LS) and error-in-variable (EIV) approaches were examined and compared. Also, VLE datasets for a specific system have been merged, and parameters have been estimated. The findings suggest that parameters obtained through LS approach align with those reported in literature, indicating faster convergence in all problems. In contrast, the EIV approach achieved a higher objective function value compared to the LS approach, exhibiting low deviation. OPDE outperformed DE in terms of performance. The enhancement in RMSTD value has been found within range 91%-99% for EIV approach. Further, novel findings derived from some of the studied VLE datasets are presented.

Rotating cylinder electrode in reactive CO2 capture: Identifying active C species via transport, VLE models and kinetics

AbstractThis article explores technical challenges and potential methodologies for understanding electrochemical Reactive CO Capture (RCC) mechanisms. RCC offers potential energy cost advantages by directly converting captured CO into fuels and chemicals, unlike traditional carbon capture and utilization (CCU) processes that require sequential capture, concentration, and compression. However, direct conversion of captured CO introduces complexity due to additional equilibrium buffer reactions, making it challenging to identify active species for reduction in electrochemical studies. This article discusses methods to integrate transport, thermodynamics, and kinetics concepts to identify active carbon sources in RCC. Vapor‐Liquid Equilibrium (VLE) and transport models are validated against experimental results obtained in a gastight rotating cylinder electrode reactor and are shown as useful tools for studying RCC in heterogeneous electrocatalysts across different capture agents, solvents, and temperatures. This article establishes an experimental framework for advancing research in electrochemical RCC.

Artificial neural network aided vapor–liquid equilibrium model for multi-component high-pressure transcritical flows with phase change

In this work, an artificial neural network (ANN) aided vapor–liquid equilibrium (VLE) model is developed and coupled with a fully compressible computational fluid dynamics (CFD) solver to simulate the transcritical processes occurring in high-pressure liquid-fueled propulsion systems. The ANN is trained in Python using TensorFlow, optimized for inference using Open Neural Network Exchange Runtime, and coupled with a C++ based CFD solver. This plug-and-play model/methodology can be used to convert any multi-component CFD solver to simulate transcritical processes using only open-source packages, without the need of in-house VLE model development. The solver is then used to study high-pressure transcritical shock-droplet interaction in both two- and four-component systems and a turbulent temporal mixing layer (TML), where both qualitative and quantitative agreement (maximum relative error less than 5%) is shown with respect to results based on both direct evaluation and the state-of-the-art in situ adaptive tabulation (ISAT) method. The ANN method showed a 6 times speed-up over the direct evaluation and a 2.2-time speed-up over the ISAT method for the two-component shock-droplet interaction case. The ANN method is faster than the ISAT method by 12 times for the four-component shock-droplet interaction. A 7 times speed-up is observed for the TML case for the ANN method compared to the ISAT method while achieving a data compression factor of 2881. The ANN method also shows intrinsic load balancing, unlike traditional VLE solvers. A strong parallel scalability of this ANN method with the number of processors was observed for all the three test cases. Code repository for 0D VLE solvers, and C++ ANN interface—https://github.com/UMN-CRFEL/ANN_VLE.git.

Sequential optimal experimental design for vapor-liquid equilibrium modeling

We propose a general methodology of sequential locally optimal design of experiments for explicit or implicit nonlinear models, as they abound in chemical engineering and, in particular, in vapor-liquid equilibrium modeling. As a sequential design method, our method iteratively alternates between performing experiments, updating parameter estimates, and computing new experiments. Specifically, our sequential design method computes a whole batch of new experiments in each iteration and this batch of new experiments is designed in a two-stage locally optimal manner. In essence, this means that in every iteration the combined information content of the newly proposed experiments and of the already performed experiments is maximized. In order to solve these two-stage locally optimal design problems, a recent and efficient adaptive discretization algorithm is used. We demonstrate the benefits of the proposed methodology on the example of the parameter estimation for the non-random two-liquid model for narrow azeotropic vapor-liquid equilibria. As it turns out, our sequential optimal design method requires substantially fewer experiments than traditional factorial design to achieve the same model precision and prediction quality. Consequently, our method can contribute to a substantially reduced experimental effort in vapor-liquid equilibrium modeling and beyond.

Effects of non-equilibrium phase behavior in nanopores on multi-component transport during CO2 injection into shale oil reservoir

Injecting CO2 into shale oil reservoirs is one of the most effective methods for enhancing oil recovery (EOR) while simultaneously facilitating CO2 capture, utilization, and storage (CCUS). However, it is not always that gas dissolution or condensate evaporation reaches equilibrium instantaneously during the CO2 injection process. In cases where equilibrium is not attained instantaneously, conventional vapor-liquid equilibrium models will have certain limitations in characterizing phase transition hysteresis. These limitations will affect the accuracy of simulating multi-component transport in porous media. In this paper, a robust and generic vapor-liquid non-equilibrium thermodynamic model considering nano-confinement effects (NC) was established by introducing component mass transfer rates proportional to the chemical potential difference. The established model was then used to modify the fully-compositional, projection-based embedded discrete fracture model (pEDFM). Furthermore, C++ hybrid programming and the Graphics Processing Unit (GPU) parallel method were both used to accelerate both the nonlinear and linear solvers. By comparing with results from MATLAB Reservoir Simulation Tools (MRST), Eclipse, and tNavigator, the accuracy and advantages of our solver were demonstrated. The results show that if the underground fluid undergoes a phase transition from a vapor-liquid two-phase state to a single-phase state, non-equilibrium thermodynamic effects need to be considered, and the simulation results show a larger two-phase zone, higher bottom hole pressure, and lower cumulative liquid production. But the nano-confinement effects will weaken the non-equilibrium thermodynamic effects.

Open access, thermodynamically consistent, electrolyte NRTL model for piperazine, AMP, water, CO2 systems on Aspen Plus

This study developed a comprehensive, open-access, thermodynamically consistent, validated vapour-liquid equilibrium model for CO2 absorption into aqueous solutions of piperazine (PZ) activated 2-amino-2-methyl-1-propanol (AMP) on Aspen Plus. This solves a two-decade-old problem of inconsistent specification of PZ, and lacking AMP/PZ, thermodynamic models on Aspen Plus, supporting robust process modelling of AMP/PZ-based CO2 capture systems, considered the contemporary benchmark. The model coverage is wide: total amine concentrations from 30 wt% to 50 wt%, AMP/PZ mole ratios from 0.46 to 23.1, CO2 loadings from 0.04 to 1.07 mol CO2/mol amine, and temperatures from 20 °C to 160 °C. The significance lies in the model’s innovative treatment of the zwitterion PZH+CO2–, leading to accurate VLE predictions and closed charge balances. Absolute average relative deviations (AARD) are 16.6 % to 22.3 % for CO2 partial pressure predictions and 6.3 % to 7.7 % for absorption heats. Gibbs-Helmholz and flash calculated absorption heats consistently compare within 1.5 % to 7.0 %, signalling the model’s thermodynamic consistency.

CO2 solubility and amine volatility data for low-concentration solutions of MEA, AMP, PZ and CESAR-1 blend (AMP/PZ)

Water-wash section(s) effectively reduce amine compound emissions in amine-based carbon capture processes. Reliable predictions of the behavior of these emission control technologies depend on detailed understanding of the vapor-liquid equilibrium (VLE) of water wash system. However, existing vapor-liquid equilibrium data in the literature focus primarily on solvent-like amine concentrations in amine–CO2–H2O systems; hence, new low-concentration VLE data are needed. In this work, the CO2 solubility in low-concentration solutions of monoethanolamine (MEA), piperazine (PZ), 2-amino-2-methyl-1-propanol (AMP), and AMP/PZ blend (CESAR-1) was investigated for temperatures between 303 and 353 K at atmospheric pressure. Additionally, amine volatility measurements for CO2-loaded low-concentration solutions of MEA, PZ, AMP and CESAR-1 were performed in the range of 313–373 K and 8–96 kPa. Overall, the data show that the CO2 partial pressure increases with increasing CO2 loading and temperature. Similarly, the amine partial pressure increases with increasing pressure and temperature. The new experimental data were compared with two existing VLE models using electrolyte non-random two-liquid activity coefficient models to evaluate the ability of the latter to predict vapor-liquid equilibrium behavior. Both CO2 solubility and amine volatility predictions by the models tend to show significant deviations. The comparison highlight the need for such low-concentration data for all systems studied. This data shall serve to improve existing water-wash modeling tools.

Population Balance Equations for Reactive Separation in Polymer Upcycling.

Many polymer upcycling efforts aim to convert plastic waste into high-value liquid hydrocarbons. However, the subsequent cleavage of middle distillates to light gases can be problematic. The reactor often contains a vapor phase (light gases and middle distillates) and a liquid phase (molten polymers and waxes with a suspended or dissolved catalyst). Because the catalyst resides in the liquid phase, middle distillates that partition into the vapor phase are protected against further cleavage into light gases. In this paper, we consider a simple reactive separation strategy, in which a gas outflow removes the volatile products as they form. We combine vapor-liquid equilibrium models and population balance equations (PBEs) to describe polymer upcycling in a two-phase semibatch reactor. The results suggest that the temperature, headspace volume, and flow rate of the reactor can be used to tune selectivity toward the middle distillates, in addition to the molecular mechanism of catalysis. We anticipate that two-phase reactor models will be important in many polymer upcycling processes and that reactive separation strategies will provide ways to boost the yield of the desired products in these cases.

Retracted: Modeling of Vapor-Liquid Equilibrium for Electrolyte Solutions Based on COSMO-RS Interaction

Retracted: Modeling of Vapor-Liquid Equilibrium for Electrolyte Solutions Based on COSMO-RS Interaction

Entrainer assisted production of high purity 2-phenyl ethyl acetate by reactive distillation

Reactive distillation (RD) is a promising alternative for the processes involving reversible reactions. In this work, we examine its potential for the esterification of a heavy alcohol (2-phenyl ethyl alcohol) with acetic acid in the presence of an ion exchange resin (Amberlyst-15) as the catalyst. The proposed RD process facilitates separation of the desired product, 2-phenyl ethyl acetate, in the pure form and provides a cost-effective and compact alternative to the conventional batch process. We determine the feasibility of this approach by conducting experiments in a laboratory-scale hybrid reactive distillation column having structured packings filled with Amberlyst-15. The experimental results are compared with the predicted values from an equilibrium-staged RD model. The model uses reaction kinetics developed in our earlier studies and the vapor–liquid equilibrium model is based on the experimental data generated in the present work and data available in literature. The experimentally validated model is further used to identify the best possible operating and design parameters to achieve high purity, high conversion and longer catalyst life. All in all, entrainer-based reactive distillation was found to be feasible in this case. The methodology followed here can be easily extended to similar reactions of heavy alcohols with lower carboxylic acids like acetic acid.

Joint incremental learning network for flexible modeling of carbon dioxide solubility in aqueous mixtures of amines

Vapor-liquid equilibrium (VLE) modeling is one of the most essential tasks for rigorous estimations of thermodynamic properties in chemical process design and analysis. To realize any commercially feasible carbon dioxide (CO2) capture scheme using a carefully chosen aqueous amine solution, the accurate model of CO2 solubility in this water-amine system plays a vital role. However, the experimental data of various mixtures of amine solvents are insufficient and expensive to acquire. In view of this problem, a novel joint incremental learning network (JILN) structure is proposed for modeling equilibrium solubility of CO2 in various bi-solvent aqueous amine mixtures. With the proposed method, the knowledge embedded in the well-trained mono-solvent models can be extracted and effectively transferred to their related multi-solvent models. By adopting the proposed modeling method, the numerical experimental results showed that the mean absolute percentage errors (MAPEs) for various bi-solvent models were 2.1–4.9%, which indicates a maximum of 68% reduction in prediction blunders if compared with their ANN counterparts.

Study of isobaric vapor–liquid equilibria of diethyl carbonate + ethylene carbonate for lithium-ion battery electrolyte solvent recycling

The limited life-cycle of lithium-ion batteries (LIBs) remains a significant issue for the industry. Recycling electrolytes from the batteries is one crucial aspect of LIBs recycling, which can conserve resources and reduce environmental pollution. The vapor–liquid equilibrium (VLE) data and models for the currently widely used carbonates, such as ethylene carbonate (EC), dimethyl carbonate (DMC), propylene carbonate (PC), diethyl carbonate (DEC), and ethyl methyl carbonate (EMC), can play an important role in designing the recycling process. In this work, the VLE data of DEC and EC is measured for the first time. A sophisticated equation of state, the Perturbed-Chain Polar Statistical Associating Fluid Theory, is used to establish the VLE model, not only for the newly measured DEC and EC system but also for other carbonates and their mixtures. Through the discussion of how the molecular characteristics of carbonates influence the VLE behavior, the dipolar character of linear carbonate molecules has been revealed. This demonstrates the power and importance of sophisticated modelling approaches in investigating molecular behavior of electrolyte solvents in the context of LIB recycling. Hence, this work provides valuable experimental and model data for designing recycling processes of electrolyte solvents and offers molecular insight into carbonates.

Vapor-liquid equilibrium modeling for binary system of R152a/R1234ze(E)

At present, the environment impact of refrigerants has been given attention. The binary mixture R152a/R1234ze(E) is an environmentally friendly refrigerant, which solves problems of poor cooling performance of the R1234ze(E) cycle and flammability of R152a. In order to obtain its basic thermal and physical parameters, it is necessary to carry out vapor–liquid equilibrium (VLE) research, and the cubic equation of states (EOS) is often used in the calculation of the thermodynamic properties of mixtures. In this paper, the VLE predicted models for R152a/R1234ze(E) in the temperature range of 298.15–328.15 K were constructed using Soave-Redlich-Kwong (SRK), Peng-Robinson (PR) equations of state (EOS) combined with van der Waals (vdW), Huron-Vidal (HV) mixing rules, respectively. The equilibrium pressures and vapor-phase mole fractions of the models were obtained by calculation, and all four models presented an extreme correlation with the experimental data. And it can be concluded that the calculated results of the PR + HV model are closer to the experimental data than those of the other three models, with the average absolute deviation of 0.0027 for vapor-phase mole fraction (AAD(ycal)) and the average absolute relative deviation of 0.243% for equilibrium pressure (AARD(pcal)), which provides a basis for accurately calculating the thermophysical properties of the mixture R152a/R1234ze (E).

Concentration of hydrofluoric acid during processing columbite and loparite concentrates

The results of modeling the concentration of hydrofluoric acid on the example of processing columbite and loparite concentrates are presented. It is shown that when optimizing the rectification process, it is necessary to use the electrolyte NRTL vapor-liquid equilibrium model and use the total energy consumption going to the separation of the mixture as an optimization criterion. The information about the work on the extraction of anhydrous hydrogen fluoride from hydrofluoric acid is presented.

Investigation and optimization of polyolefin elastomers polymerization processes using multi-objective genetic algorithm

The aim of this research is to develop continuous reactor network models to determine the reactor configuration and corresponding optimal operating conditions of a polyolefin elastomers polymerization process. To achieve this objective, a modified vapor-liquid equilibrium model is integrated with both the continuous stirred tank reactor (CSTR) model and the plug flow reactor (PFR) model to accurately predict the vaporization rates of liquid. The multi-objective problem is formulated to maximize the monomer conversion and minimize the total annualized cost simultaneously. To solve the multi-objective problem, the genetic algorithm is utilized to identify the optimal operating conditions. Furthermore, the impact of the reactor combination mode is analyzed by varying the number and sequence of CSTR or PFR. The research findings reveal that a multi-phase CSTR without circulating stream followed by a PFR is the optimal reactor configuration. The proposed configuration can enhance reactor productivity and reduce the total annualized cost simultaneously while meeting the desired polymer properties.

Multicomponent vapor-liquid equilibrium measurements and modeling of triethylene glycol, water, and natural gas mixtures at 6.0, 9.0 and 12.5 MPa

Triethylene glycol (TEG) is commonly used for natural gas dehydration, and with subsea processing facilities on the rise, an increasing interest is being shown in complex phase equilibria involving petroleum fluids and polar compounds. In this study, examples of such phase equilibria have been studied. New measurements for multicomponent vapor-liquid equilibrium (VLE) of TEG/Water/Natural Gas systems have been performed at pressures ranging from 6.0 MPa to 12.5 MPa and temperatures in the range 15 °C to 40 °C. Two types of natural gas, a Synthetic Gas (xCH4=0.62) and a Real Gas (xCH4=0.92), were mixed with an aqueous TEG solution, with TEG weight percentages ranging from 95 wt.% to 99 wt.%. Glycol in gas (y1), water in gas (y2), and gas solubility in liquid (xNG) were measured with relative experimental uncertainties below 32%. Since the systems are highly associating, the Cubic-Plus-Association (CPA) equation of state (EoS) was selected to model their phase behavior . Different association schemes (4C, 4F, 5F, 6F and 5C) were tested for TEG, and the classical 4C scheme is shown to perform best. The CPA EoS performed in general terms well, considering the number of components in the systems, the associated complexities, and high measurement uncertainty for such low concentrations (<1 ppm) in the gas phase. Furthermore, the content of N2, CO2, CH4 and ethane were modelled in the liquid phase at various conditions.

Evaluation of cubic, PC-SAFT, and GERG2008 equations of state for accurate calculations of thermophysical properties of hydrogen-blend mixtures

Hydrogen (H2) is a clean fuel and key enabler of energy transition into green renewable sources and a method of achieving net-zero emissions by 2050. Underground H2 storage (UHS) is a prominent method offering a permanent solution for a low-carbon economy to meet the global energy demand. However, UHS is a complex procedure where containment security, pore-scale scattering, and large-scale storage capacity can be influenced by H2 contamination due to mixing with cushion gases and reservoir fluids. The literature lacks comprehensive investigations of existing thermodynamic models in calculating the accurate transport properties of H2-blend mixtures essential to the efficient design of various H2 storage processes. This work benchmarks cubic equations of state (EoSs), namely Peng–Robinson (PR) and Soave Redlich–Kwong (SRK) and their modifications by Boston–Mathias (PR-BM) and Schwartzentruber–Renon (SR-RK), for their reliability in predicting the thermophysical properties of binary and ternary H2-blend mixtures, including CH4, C2H6, C3H8, H2S, H2O, CO2, CO, and N2, in addition to Helmholtz-energy-based EoSs (i.e., PC-SAFT and GERG2008). The benchmarked models are regressed against the experimental data for vapor–liquid equilibrium (VLE) that covers a wide range of pressures (0.01 to 101 MPa), temperatures (92 K to 367 K), and mole fractions (0.001 to 0.90) of H2. The novelty of this work is in benchmarking and optimizing the parameters of the mentioned EoSs to study VLE envelopes, densities, and other critical transport properties, such as heat capacity and the Joule–Thomson coefficient of H2 mixtures in a wide range of associated conditions. The results highlight the significant effect of the temperature-dependent binary interaction parameters on the calculations of thermophysical properties. The SR-RK EoS demonstrated the highest agreement with VLE data among the cubic EoSs with a low root mean square error and absolute average deviation. The PC-SAFT VLE models demonstrated results comparable to the SR-RK. The sensitivity analysis highlighted the high influence of impurity on changing the thermophysical behavior of H2-blend streams during the H2 storage process.

Modeling and measurement of vapor-liquid equilibrium of In–Pb and In–Pb–Sn alloy systems in vacuum distillation

This study reports the measurement and modeling of vapor-liquid equilibrium (VLE) in In–Pb and In–Pb–Sn alloys subjected to vacuum distillation at a system pressure of 5–10 Pa in the temperature range of 1100–1280 K. Pb and In was satisfactorily separated by a single-stage distillation at 1180 K. Pb was thoroughly removed from In–Pb–Sn alloy by a single-stage distillation at 1220 K. Molecular interaction volume model (MIVM) was used to calculate the activities of components of In–Pb alloy. The deviations were small. The activities of components of In–Pb–Sn alloy were also predicted by MIVM. The VLE of In–Pb and In–Pb–Sn alloy systems were predicted by MIVM and VLE theory. The calculated results agree well with VLE data determined from experiments, which indicates that the calculated VLE is reliable. The VLE can be used to guide the separation of indium-based alloys by vacuum distillation. In this study, the model prediction was combined with vacuum distillation experiments, which not only verified the reliability of MIVM for indium-based alloys, but also optimized the process parameters of vacuum distillation of indium-based alloys, providing theoretical guidance for the separation and purification of indium-based alloys by vacuum distillation or the treatment of indium-containing complex materials.

Modeling of Vapor-Liquid Equilibrium for Electrolyte Solutions Based on COSMO-RS Interaction

The modeling of phase equilibrium for electrolyte solutions plays an important role in chemical thermodynamics. Modeling and calculation of the vapor-liquid equilibrium (VLE) for an electrolyte solution are studied in this paper. The influence mechanism for the microscopic interaction on the macroscopic VLE is further studied by COSMOtherm. Then, a developed model is proposed. The interaction parameters in the model are linked to the COSMO interaction energy (H_int). The interaction equations are remodeled using 1stopt software, and components are used to replace the “interaction parameters” used in a previous model. The developed model can be used to successfully predict VLE data for electrolyte solutions based on the α and hi parameters.

Distillation behavior of the system (formaldehyde + water + isoprenol)

Isoprenol (3-methyl-3-buten-1-ol) is produced industrially from aqueous formaldehyde and isobutene. In the process, mixtures of formaldehyde, water, and isoprenol are separated by distillation. As formaldehyde reacts with both water and isoprenol, these mixtures are reactive multicomponent systems. Information on the distillation behavior of these mixtures is lacking in the literature. We have therefore carried out single-stage batch distillation experiments to determine residue curves in the system (formaldehyde + water + isoprenol) at pressures between 5 and 80 kPa. Furthermore, we have used a physico-chemical vapor–liquid equilibrium model, in which the complex reactions in the studied system are explicitly considered, to calculate residue curve maps for the system (formaldehyde + water + isoprenol). They reveal a complex, strongly pressure-dependent topology with several azeotropes. The results from the batch distillation experiments confirm the predicted residue curves.