Vapor-liquid Equilibrium Model Research Articles

Experimental and theoretical investigation of solubility of carbon dioxide in concentrated aqueous solution of 2-amino-2-methyl-1-propanol and piperazine

In this work, new experimental results for the (vapour+liquid) equilibrium (VLE) of CO2 in piperazine (PZ)-activated concentrated aqueous 2-amino-2-methyl-1-propanol (AMP) are presented for the temperature range of (303 to 328)K and PZ concentration range of (2 to 8)wt.%, keeping the total amine concentration in the solution at 40% and 50wt.%. The partial pressures of CO2 are in the range of (0.2 to 1500)kPa. The electrolyte non-random two-liquid (ENRTL) theory has been used to develop the VLE model for the quaternary system (CO2+AMP+PZ+H2O) to describe the equilibrium behaviour of the solution. The CO2 cyclic capacity of these solvents is determined between the rich and lean CO2 loadings. It is found that the CO2 cyclic capacity increases with the addition of PZ in aqueous AMP and also with the increase in AMP concentration in the aqueous solution. However, solid precipitation has been observed for 50wt.% total amine concentration below T=318K for all relative compositions of AMP and PZ in the solvent at higher CO2 loading. The model results of equilibrium composition, pH of the loaded solution and amine volatility of the mixed solvent system, are also presented.

A vapor–liquid equilibrium thermodynamic model for a Fischer–Tropsch reactor

Caldwell and van Vuuren (1986) [1] were the first to realize the importance of vapor–liquid equilibrium (VLE) considerations in the Fischer–Tropsch (FT) synthesis modeling. They used Raoult's law to describe VLE. Recently, a variety of VLE thermodynamic models have been used to model FT products. Thus the aim of this study was to conduct an experiment to measure actual vapor and liquid compositions of long chains hydrocarbons under FT reaction conditions to ascertain whether Raoult's law is sufficient or other elaborate VLE models are required. The results obtained show that VLE is attained inside an FT reactor. The measured vapor and liquid compositions ( K-values) can be sufficiently described by Raoult's law. Hydrocarbons with carbon number greater than 18 deviates from Raoult's law. The deviations from Raoult's law are due to diffusion limitations. Elaborate thermodynamic models could be used given the pure component parameters with relevant mixing rules for a higher degree of accuracy.

Characterization of ammonia-based CO 2 capture process using ion speciation

Carbon dioxide absorption process using an ammonia solution provides many advantages including higher absorption capacity, no degradation and lower regeneration energy requirement. In this study, the ammonium ion species were identified and measured at various experimental conditions using a 13C NMR. Carbamate was the main species at the early stage of the absorption process due to the excessive presence of ammonia molecules. In contrast, bicarbonate prevailed at the final stage when most of ammonia molecules reacted with CO 2 molecules. As temperature increased, the amount of carbonate dramatically decreased, while that of bicarbonate and carbamate increased. From the thermodynamic simulation using the vapor–liquid equilibrium model (VLE), it was found that the ammonium speciation data generally agreed with the experimental results. In conclusion, we proposed a reasonable and straightforward method for the determination of the ion concentrations in aqueous ammonia for CO 2. This work will improve the understanding of solution behavior associated with absorption and regeneration reactions and finally will be used for the monitoring, evaluation and optimization of the ammonia-based CO 2 capture process.

The role of vapour–liquid equilibrium in Fischer–Tropsch product distribution

This work uses vapour–liquid equilibrium (VLE) to explain the observed two-alpha product distribution in Fischer–Tropsch (FT) reactors. We discuss three possible scenarios or cases of Anderson–Schulz–Flory (ASF) product distribution and VLE. The three cases assume the following: (1) the reaction sets up a single alpha ASF distribution in the total (vapour+liquid) products, (2) the vapour phase follows a single alpha distribution and (3) a single alpha distribution is set up in the liquid phase. We then look at the consequences of these assumptions in conjunction with a simple Raoult's law VLE model on the exit product distributions. We find that only Case 3 gives rise to a two-alpha model in accordance with experimental results that is frequently observed in FT reactors. This model further predicts a relationship between the two values of alpha that are consistent with the measured experimental results.

Integrated Differential Evolution for Global Optimization and Its Performance for Modeling Vapor–Liquid Equilibrium Data

Parameter estimation in thermodynamic models has been of great interest in chemical engineering because of its complex nature, including nonlinearity, flat objective function in the neighborhood of the global optimum, badly scaled model, and nondifferential term(s) in the equations. In this article, a stochastic global optimization algorithm called integrated differential evolution (IDE) is introduced to solve the parameter estimation problems for modeling vapor–liquid equilibrium (VLE) data. In IDE, the choice of mutation strategy and associated parameters are adapted according to the learning experience from previous generations. The tabu list used in IDE can avoid revisiting the same area and avoid unnecessary function evaluations. A novel and effective stopping criterion based on the number of rejected points during the generation of a trial vector is tested and compared with other criteria. Furthermore, IDE uses a local optimizer after the global search to find the optimum accurately and efficiently. The performance of IDE for benchmark functions and VLE modeling is compared with that of other stochastic algorithms such as DE, DE with tabu list, particle swarm optimization, simulated annealing, and the deterministic algorithm Branch and Reduce Optimization Navigator (BARON). IDE is shown to be better than or comparable to these algorithms for parameter estimation in modeling VLE data.

Solubility of carbon dioxide in aqueous solution of 2-amino-2-methyl-1-propanol and piperazine

In this work, new experimental results of the vapour–liquid equilibrium (VLE) of CO 2 in aqueous 2-amino-2-methyl-1-propanol (AMP) and piperazine (PZ) have been presented in the temperature range of 298–328 K and PZ concentration range of 2–8 mass%, keeping the total amine concentration in the solution at 30 mass%. The partial pressures of CO 2 were in the range of 0.1–1450 kPa. A thermodynamic model was developed to correlate and predict the VLE of CO 2 in aqueous AMP + PZ. The electrolyte nonrandom two liquid (ENRTL) theory has been used to develop the VLE model for the quaternary system (CO 2 + AMP + PZ + H 2O) to describe the equilibrium behaviour of the solution. The experimental data from this work and data available in the literature were used to regress the ENRTL interaction parameters. The model predictions are in good agreement with the experimental data of CO 2 solubility in aqueous blends of this work as well as those reported in the literature. The current model can also predict speciation, heat of absorption, pH of the CO 2 loaded solution, and amine volatility.

Examining the effect of binary interaction parameters on VLE modelling using cubic equations of state

Vapor–liquid equilibrium (VLE) data are important in the optimization of thermodynamic cycles. As energy concerns continue to grow, improving the efficiencies of power and refrigeration cycles is increasingly important. Numerical simulations using empirical equations of state provide an excellent alternative to time consuming experimental measurement of VLE data. However, it is important to understand the limitations of using correlative equations for data prediction. In this study, a water–ethanol mixture is simulated with various VLE models. Non-optimal binary interaction parameters are considered and model accuracy is evaluated in terms of average absolute percent deviation (%AAD) between simulated and experimental bubble and dew point pressures. For this system, it is found that as the correlative accuracy of a model increases, the predictive ability decreases. Specifically, the temperature dependence of the binary interaction parameters is shown to be an important consideration for the water–ethanol system when more complex combining rules are implemented.

Validation of CFD simulation for ammonia emissions from an aqueous solution

In order to model and predict ammonia emissions from animal houses, it is important to determine the concentration on the emission surface correctly. In the current literature, Henry's law is usually used to model the mass transfer through the gas–liquid surface (e.g. manure or aqueous solution). The objective of this study is to investigate the accuracy of three models for Henry's law constant (HLC) as well as functions derived from experimental vapor–liquid equilibrium (VLE) properties of ammonia water to determine the concentration on the liquid ammonia solutions surface in order to be used as boundary condition for CFD prediction of ammonia emission. The accuracy of CFD simulation depends on many factors. In this study, the effects of appropriate geometry model, inlet turbulent parameters and three turbulence models (low-Reynolds number k– ɛ model, renormalization group k– ɛ model and Shear Stress Transport k– w model) on ammonia emissions are investigated and discussed. Then the concentration boundary condition determined by different HLC models and the VLE model is validated by ammonia emissions and concentration profiles measured in the boundary layer. The results indicate that the current HLC models generally over-predict the ammonia emissions from aqueous solution in this study whereas VLE gives better agreement between simulated and measured results. A linear relation is observed between ammonia mass transfer coefficient obtained from the VLE relation and those from HLC models.

Determination of ammonium salt/ion speciation in the CO2 absorption process using ammonia solution: Modeling and experimental approaches

Abstract Ammonia solution has received special attention as an effective absorbent in CO 2 capture process because of its higher CO 2 absorption capacity and lower chemical cost rather than amine solution such as monoethanolamine. In ammonia based CO 2 capture process, various ammonium salts/ions would be formed reacting with ammonia and CO 2 . The ammonium speciation in the liquid phase greatly affected the overall process efficiency, the energy requirement of ammonia regeneration or CO 2 recovery process. In this study, we examined the ammonium speciation in ammonia solution during the CO 2 absorption reaction using a 13 C-NMR (nuclear magnetic resonance) spectrometry and identified bicarbonate (HCO 3 − ), carbonate (CO 3 2− ) and carbamate (NH 2 COO − ) ions. Moreover VLE (vapor-liquid equilibrium) model which is thermodynamic model in vapor-liquid phase was also applied to simulate ammonium speciation. The simulation results for the ammonium speciation were generally well-agreed with the experimental results, even though some discrepancies were observed as the absorbed amount of CO 2 increased. In conclusion, a combined approach utilizing both ( 13 C-NMR analysis and VLE model) can help to understand the reactions between ammonia and CO 2 and optimize the CO 2 capture process using ammonia solution.

Application of a New Gibbs Energy Equation to Model a Distillation Tower for Production of Pure Ethanol

AbstractA steady‐state equilibrium‐stage model based on MESH equations was proposed to simulate saline extractive distillation columns. The interaction parameters between each component of water‐CaCl2 and ethanol‐water were obtained from mean ionic activity coefficients and vapor‐liquid equilibrium (VLE) experimental data. Additionally, the interaction coefficients for the ethanol‐CaCl2 pair were fitted to experimental VLE data which were reported by Nishi for the ethanol‐water‐CaCl2 system. It should be noted that adjustable parameters between each pair were considered to be temperature dependent. The results confirmed that the proposed model could accurately predict the experimental vapor‐liquid equilibrium data for ethanol‐CaCl2‐water systems. Finally, the validated model was coded using MATLAB software and was solved using the Wang‐Henke method, including the VLE and enthalpy models.

Novel bare-bones particle swarm optimization and its performance for modeling vapor–liquid equilibrium data

Parameter estimation in models plays a significant role in developing mathematical models which are used for understanding and analyzing physical, chemical and biological systems. Parameter estimation problems for vapor–liquid equilibrium (VLE) data modeling are very challenging due to the high non-linearity of thermodynamic models. Recently, stochastic global optimizations and their applications to these problems have attracted greater interest. Of the many stochastic global optimization methods, Bare-bones particle swarm optimization (BBPSO) is attractive since it has no parameters to be tuned by the user. In this study, modifications are introduced to the original BBPSO using mutation and crossover operators of differential evolution algorithm to update certain particles in the population. The performance of the resulting algorithm is tested on 10 benchmark functions and applied to 16 VLE problems. The performance of the proposed BBPSO for VLE modeling is compared with that of other stochastic algorithms, namely, differential evolution (DE), DE with tabu list, genetic algorithm and simulated annealing in order to identify their relative strengths for VLE data modeling. The proposed BBPSO is shown to be better than or comparable to the other stochastic global optimization algorithms tested for parameter estimation in modeling VLE data.

Composition Estimation of Reactive Batch Distillation by Using Adaptive Neuro-Fuzzy Inference System

Composition estimation plays very important role in plant operation and control. Extended Kalman filter (EKF) is one of the most common estimators, which has been used in composition estimation of reactive batch distillation, but its performance is heavily dependent on the thermodynamic modeling of vapor-liquid equilibrium, which is difficult to initialize and tune. In this paper an inferential state estimation scheme based on adaptive neuro-fuzzy inference system (ANFIS), which is a model base estimator, is employed for composition estimation by using temperature measurements in multicomponent reactive batch distillation. The state estimator is supported by data from a complete dynamic model that includes component and energy balance equations accompanied with thermodynamic relations and reaction kinetics. The mathematical model is verified by pilot plant data. The simulation results show that the ANFIS estimator provides reliable and accurate estimation for component concentrations in reactive batch distillation. The estimated states form a basis for improving the performance of reactive batch distillation either through decision making of an operator or through an automatic closed-loop control scheme.

Evaluation of stochastic global optimization methods for modeling vapor–liquid equilibrium data

Parameter estimation for vapor–liquid equilibrium (VLE) data modeling plays an important role in design, optimization and control of separation units. This optimization problem is very challenging due to the high non-linearity of thermodynamic models. Recently, several stochastic optimization methods such as Differential Evolution with Tabu List (DETL) and Particle Swarm Optimization (PSO) have evolved as alternative and reliable strategies for solving global optimization problems including parameter estimation in thermodynamic models. However, these methods have not been applied and compared with respect to other stochastic strategies such as Simulated Annealing (SA), Differential Evolution (DE) and Genetic Algorithm (GA) in the context of parameter estimation for VLE data modeling. Therefore, in this study several stochastic optimization methods are applied to solve parameter estimation problems for VLE modeling using both the classical least squares and maximum likelihood approaches. Specifically, we have tested and compared the reliability and efficiency of SA, GA, DE, DETL and PSO for modeling several binary VLE data using local composition models. These methods were also tested on benchmark problems for global optimization. Our results show that the effectiveness of these stochastic methods varies significantly between the different tested problems and also depends on the stopping criterion especially for SA, GA and PSO. Overall, DE and DETL have better performance for solving the parameter estimation problems in VLE data modeling.

Vapor–Liquid Equilibrium for Binary Systems of 2,3-Pentanedione with Diacetyl and Acetone

2,3-Pentanedione and diacetyl are byproducts of sugar manufacture and have many food related uses. Vapor−liquid equilibrium (VLE) data for the systems presented in this paper are required to determine thermodynamic model parameters which will be used to simulate the design of a purification process. A vapor and liquid recirculating still was used to measure data for diacetyl + 2,3-pentanedione at 333.15 K, 343.15 K, 353.15 K, and 40 kPa, as well as for acetone + 2,3-pentanedione at 323.15 K, 30 kPa, and 40 kPa. The γ−φ correlation approach for VLE modeling was used to correlate the data with excess Gibbs energy models. The vapor phase nonideality was computed using the truncated (two-term) virial equation of state. The Wilson, NRTL, and UNIQUAC excess Gibbs energy models were used to account for liquid phase departure from ideal behavior. The data are shown to be thermodynamically consistent by both the Van Ness point and direct tests.

Experimental and Numerical Study on Vapor Condensation of Wet Flue Gas in Chimney

Increase of the emission of CO2, which is mostly the result of the combusted fossil fuels into the atmosphere, exponentially increases. Through increased energy efficiency there is lower CO2 emission. There is a tendency to reduce exhaust gases temperatures down from their original value referred to as “acid dew point”, 115-160°C. A result is vapor condensation of wet flue in chimney. Condensation occurs when the surface temperature is below the dew point of the vapor-gas mixture. Therefore, Vapor-Liquid Equilibrium models are required in order to determine the dew point of the mixture. Wet flue gas is simulated with vapor-air mixture. A numerical model was presented to calculate the velocity and thermal field of turbulent vapor-air mixture flow trough a chimney. The momentum and temperature field were calculated via a finite-volume CFD code, using the k – e turbulence model. The validation of this calculation was conducted employing an experimental set for heat and mass transfer in vertical upward vapor-air mixture. Measurements were done using a stainless steel tube of 13.2 mm I.D. (internal diameter) and 70 I.D. lengths. Flow rates of steam and air were varied as the experimental parameters. The experiment involves two-phase, two-component, heat and mass transfer. Comparisons of wall temperature and condensate rate were made and the model was shown to give an acceptable results.

Prediction of equilibrium solubility of CO2 in aqueous alkanolamines using differential evolution algorithm

AbstractThe design of sour‐gas treating processes with alkanolamine solvents requires knowledge of the vapour–liquid equilibrium (VLE) of the aqueous acid gas–alkanolamine systems. Representation of the experimental data with a thermodynamically rigorous model is required, so that one can systematically correlate and predict the VLEs of these systems. The modified Clegg–Pitzer equations have been used to correlate and predict the VLE of CO2 in the aqueous N‐methyldiethanolamine (MDEA) and 2‐amino‐2‐methyl‐1‐propanol (AMP) systems. Differential evolution (DE), an evolutionary computational technique, has been used for parameter estimation of the developed VLE model in an effort to predict the VLE of CO2 in aqueous MDEA and AMP solutions with a comparable accuracy to that by using the non‐traditional simulated annealing (SA) and deterministic technique like Levenberg–Marquardt (LM), if not better. In this work, the DE/rand‐best/1/bin strategy has been used for finding near global minimum solutions to the multivariable optimization problem as a part of the numerical solution of the developed model.

EFFECT OF ACETIC ACID ON CO2 CORROSION OF CARBON STEEL IN VAPOR-WATER TWO-PHASE HORIZONTAL FLOW

The effect of acetic acid on the corrosion behavior of X 65 and C 1018 carbon steel in vapor-water two-phase stratified flow (Vsg: 2 m/s; Vsl: 0.1 m/s) at 2 bars total pressure, 1.54 bars CO2 partial pressure, pH 5.5, and 80°C was studied in a low pressure-high temperature multiphase flow horizontal loop using electrochemical and mass loss techniques. The liquid phase is composed of 1% NaCl aqueous solution containing different concentrations of acetic acid (500 to 5000 ppm total acetic acid), and the gas phase is composed of CO2-acetic acid-water vapor mixture. The corrosion rates, on both the top and bottom of the line, increase with increase in acetic acid concentration, which was attributed to the contribution of hydrogen ions by the free acetic acid to the cathodic reaction. Partial coverage of the metal surface by FeCO3 on both the top and bottom of the line is reported to be responsible for the observed localized corrosion. Surface analysis investigated with SEM and XRD is reported. A vapor-liquid equilibrium model was developed for the system studied.

The performance of simulated annealing in parameter estimation for vapor-liquid equilibrium modeling

In this paper we report the application and evaluation of the simulated annealing (SA) optimization method in parameter estimation for vapor-liquid equilibrium (VLE) modeling. We tested this optimization method using the classical least squares and error-in-variable approaches. The reliability and efficiency of the data-fitting procedure are also considered using different values for algorithm parameters of the SA method. Our results indicate that this method, when properly implemented, is a robust procedure for nonlinear parameter estimation in thermodynamic models. However, in difficult problems it still can converge to local optimums of the objective function.

Estimation of the particle and gas scavenging contributions to wet deposition of organic nitrogen

We estimated the wet deposition flux of dissolved organic nitrogen (DON) to Tampa Bay, Florida, using 24-h integrated aerosol and rainwater samples collected simultaneously on days with rainfall between July and September 2005. In rainwater, dissolved inorganic nitrogen (DIN) and DON average concentrations were 54.7±44.0 and 4.7±2.7 μM-N, respectively, and DON represented 8.9±5.8% of the total dissolved nitrogen (TDN=DIN+DON). Our estimates of wet deposition fluxes for NH 4 + , NO 3 - and DON were 1.40, 3.18 and 0.34 kg-N ha −1 yr −1, respectively. In aerosols (PM 10), DIN and DON concentrations were 78.5±56.2 and 6.3±2.6 nmol m −3, respectively, and DON represented 10.3±7.3% of TDN. Particle scavenging rates were calculated assuming a lognormal size distribution for particles and lognormal, gamma and Marshall–Palmer size distributions for raindrops. For the range of precipitation rates and measured aerosol concentrations, below-cloud scavenging of aerosol-phase DON contributed only 1±0.7% to rainwater N concentrations. Dimethylamine (DMA) was observed in aqueous extracts of fine (PM 2.5) and coarse (PM 10−2.5) aerosol samples, but could be quantitatively measured only in fine particles with an average concentration of 688±615 pmol-N m −3, representing an average contribution of 12.8±6.7% of the total DON concentration measured in the same particle fraction. AIM 2 vapor–liquid equilibrium modeling predicted an average gas-phase DMA concentration of 107.4±176.9 pmol-N m −3. Although DMA concentrations were below our analytical detection limit on all rainwater samples, the average modeled gas and particle DMA contribution to DON concentration in rainwater was 0.4±0.7%.

Objective functions analysis in the minimization of binary VLE data for asymmetric mixtures at high pressures

Five different objective functions were studied with the purpose of analyzing their performance for parameters estimation of vapor–liquid equilibrium models for a series of 13 non-polar and 13 polar asymmetric binary mixtures at high pressures. Peng–Robinson equation of state coupled with the Wong–Sandler mixing rules were used for modeling the VLE in all cases. The first two objective functions are based on the calculation of the distribution coefficients for each component in the mixture and the remaining objective functions involve additional calculations of other quantities such as the bubble point pressure. In general, the optimal parameters obtained from all objective functions showed a good prediction capacity of the behavior of the vapor phase. It is also demonstrated that a good prediction of the pressure depends on the form of the objective function. It was found that one objective function has slight advantages over the other analyzed objective functions: first, it does not involve additional iterative calculations as the bubble point or isothermal flash for each data point; second, the optimal second virial coefficient interaction parameter shows to be in concordance with the statistical thermodynamic postulates; and finally, VLE predictions using the optimal parameters obtained with the help of this objective function show very good representations of both the vapor phase and pressure.