Predicting NRTL parameters for binary hydrocarbon mixtures for calculating liquid—vapor equilibriums of multicomponent systems

The parameters of the NRTL method are fitted, for binary hydrocarbon systems, on the activity coefficients calculated by the Flory—Hildebrand method with binary coefficients l_ij of deviation from the geometric mean assumption for cohesive energy densities (NRTL-FH parameters). For aromatic saturated hydrocarbon mixtures, the l_ij coefficients are correlated to the products δ_iδ_j of solubility parameters. The predicted NRTL-FH parameters are used in calculations of bubble pressures and vapor phase compositions of binary hydrocarbon mixtures and of ternary mixtures with at least two hydrocarbon components. The NRTH-FH method is compared to the Chao—Seader and the zero l_ij-Flory-Hildebrand methods for many hydrocarbon systems, and gives the best results among these three predictive methods. The introduction of the non zero l_ij coefficients is an improvement in regards to the case with zero l_ij coefficients, particularly for the cycloparaffin-aromatic hydrocarbon mixtures. The NRTL-FH method is also compared to the NRTL-EXP method (parameters fitted on experimental data), and results obtained with the two methods are satisfactory for binary and ternary mixtures.     

Interaction model for the critical pressures of aliphatic hydrocarbon mixtures

An interaction model is proposed for the prediction of the critical pressures of multicomponent aliphatic hydrocarbon mixtures which may include methane. This model utilizeg a series consisting of terms of increasing order which has been truncated beyond the fifth interaction term. After a number of algebraic manipulations, the excess critical pressure for these multicomponent mixtures has been represented as follows The nonmethane interaction coefficients A_ij, B_ij, C_ij and β_ijk and the methane interaction coefficients A_1j, B_1j, C_1j, D_1j and β_1jk have been expressed as functions of the critical pressure parameter, π_ij. The resulting relationships permit the evaluation of these interaction coefficients for a multicomponent system and from its composition, the critical pressure of the mixture is calculated. The critical pressures of several binary and multicomponent aliphatic hydrocarbon mixtures have been calculated and have been compared with experimental values. For 99 binary methane-free mixtures representing 11 systems, the average deviation is 3.23%. For 46 binary mixtures representing six methane systems, the average deviation becomes 4.41 %. For 36 multicomponent aliphatic hydrocarbon mixtures containing from three to six components, the average deviation is found to be 3.18%.     

Diffusion and electrical conduction in molten salts of the type AZ + BZ. The phenomenological coefficients in the system LiNO3 + AgNO3 at 533 K

By superposing diffusion and electrical conduction the ionic phenomenological coefficients (l_ij) have been solved as functions of the measureable transport coefficients in the molten salt systems of the type AZ + BZ. A clear difference has been made between the entropy producing processes, diffusion and electrical conduction, and the reversible transport of matter with electric current. In the treatment the Onsager reciprocal relations of the ionic form appear as a result of the superposition and the ionic forces become functions of the gradient of the component chemical potential, the transport number, the electric current density, and the conductivity. The quantitative concentration dependences of the ionic l_{i + j +} s have been calculated for the system LiNO₃+ AgNO₃ at 533 K for the entire range of the composition. The relations between the l_{i + j +} s and the interfriction coefficients have also been given. Differing from aqueous electrolyte solutions the cross coefficient (l_{i + j +}/x_ix_j) (i ≠ j) does not vanish in approaching a pure molten salt component. Therefore the Nernst—Planck equations cannot be applied to these molten salts.     

Programmed polymer light-scattering data

An ALGOL computer program has been devised to manipulate light-scattering data from the Brice-Phoenix photometer. The input consist of experimental values of the galvanometer deflections and filter factors used for each concentration c and angle of measurement θ. These are transformed to the appropriate variables in the fundamental equation including the particle scattering factor, viz: c/Qθ = (W/K^*)M?_w^?1[1 + (16/3) × π²n₁²λ〈S²〉 sin² (θ/2)] + (W/K^*)2A₂c + (W/K^*)3A₃c² in which Qθ is a corrected from of the Rayleigh ratio and (W/K^*) is a composite constant term for the instrument and polymer–solvent system. By writing X?_ij for the variable c/Q_θ at θ_i and c_j, a function X is found by least squares to fit X?_ij, thus X = l + m sin (θ/2) + nc_j + bc_j². The equations arising from minimizing Σ_i^K=1 Σ_j^L=1 (X_ij ? X?_ij)² are solved by the computer to yield the best-fitting coefficients l, m, n, and b. These can then be related simply to the molecular weight, root-mean-square radius of gyration, second and third virial coefficients, respectively. The final portion of the program is designed to check the fit of these coefficients. It yields a table of the differences between all experimental c/Qθ values and the coressponding ones obtained by inserting the derived l, m, n, and b into the fundamental equation. The procedure has been tested satisfactorily by using a well-standardized sample of polystyrene in toluene at 30°C. and a wavelength of 436 mμ.     

Excess enthalpy data for the ternary system methane—ethylene—carbon dioxide by flow calorimetry

Excess enthalpy data for the ternary system methane – ethylene – carbon dioxide was obtained utilizing an isothermal flow calorimeter. The measurements were made at three temperatures: 293.15, 305.15 and 313.15 K and pressures of 1.114, 1.520 and 3.445 MPa (11, 15 and 34 atm). The determination of excess enthalpies for the binary systems methane—ethylene, ethylene—carbon dioxide and methane—carbon dioxide has been reported in three preceeding articles, respectively: Gagné et al., 1985; Ba et al., 1979 and Barry et al., 1982a. The binary interaction coefficients k_ij obtained for these systems have been utilized as initial values for the optimization procedure leading to the k_ij for the ternary system. For the case of the ternary system studied in this investigation, two types of binary interaction coefficients k_ij have been determined from experimental data: k_ij independent of temperature and pressure and k_ij adjusted as function of temperature and pressure. Experimental data were compared with the predictions from Benedict—Webb—Rubin and Redlich—Kwong equations of state. In both cases, the coefficients k_ij dependent on temperature and pressure led to better prediction of excess enthalpies.     

Prediction of Multi-Target Networks of Neuroprotective Compounds with Entropy Indices and Synthesis,Assay, and Theoretical Study of New Asymmetric 1,2-Rasagiline Carbamates

In a multi-target complex network, the links (L_ij) represent the interactions between the drug (d_i) and the target (t_j), characterized by different experimental measures (K_i, K_m, IC₅₀, etc.) obtained in pharmacological assays under diverse boundary conditions (c_j). In this work, we handle Shannon entropy measures for developing a model encompassing a multi-target network of neuroprotective/neurotoxic compounds reported in the CHEMBL database. The model predicts correctly >8300 experimental outcomes with Accuracy, Specificity, and Sensitivity above 80%–90% on training and external validation series. Indeed, the model can calculate different outcomes for >30 experimental measures in >400 different experimental protocolsin relation with >150 molecular and cellular targets on 11 different organisms (including human). Hereafter, we reported by the first time the synthesis, characterization, and experimental assays of a new series of chiral 1,2-rasagiline carbamate derivatives not reported in previous works. The experimental tests included: (1) assay in absence of neurotoxic agents; (2) in the presence of glutamate; and (3) in the presence of H₂O₂. Lastly, we used the new Assessing Links with Moving Averages (ALMA)-entropy model to predict possible outcomes for the new compounds in a high number of pharmacological tests not carried out experimentally.     

Phase behaviour of CO2 -bitumen fractions

The phase behaviour of Cold Lake bitumen and its five fractions (or “cuts”) saturated with carbon dioxide is examined. The two lightest fractions (bp < 510°C) were clear liquids, whereas the third and fourth fractions were dark and viscous, i.e. much like the whole bitumen. The fifth fraction was a glass-like solid, with a softening temperature of approximately 100°C. The vapour-liquid equilibrium (VLE) data for the bitumen and bitumen fractions saturated with CO₂ were collected at temperatures from 25 to 150°C and pressures up to 10 MPa. Experiments were also performed at conditions under which pure CO₂ exists as a liquid. The VLE and LLE data were correlated with the Peng-Robinson equation of state by modeling each bitumen fraction as one pseudocomponent whose critical properties and acentric factor were estimated from correlations available in the literature. The CO₂-solubility and density data were used to develop generalized correlations for the critical pressure and the binary interaction parameter (k_ij) in terms of molar mass and critical temperature. The model was subsequently used to predict the solubility of CO₂ in the whole bitumen which was represented as a 5-component mixture. A correlation for Cut i-Cut j binary interaction parameter (k_ij) was developed in terms of temperature and the difference in hydrocarbon molar masses. The average deviation in the predicted and experimental CO₂-solubility in the whole Cold Lake bitumen was less than 7%.     

Global uncertainty assessments by high dimensional model representations (HDMR)

A general set of quantitative model assessment and analysis tools, termed high-dimensional model representations (HDMR), have been introduced recently for high dimensional input-output systems. HDMR are a particular family of representations where each term in the representation reflects the independent and cooperative contributions of the inputs upon the output. When data are randomly sampled, a RS(random sampling)-HDMR can be constructed, which is an efficient tool to provide a fully global statistical analysis of a model. The individual RS-HDMR component functions have a direct statistical correlation interpretation. This relation permits the model output variance σ² to be decomposed into its input contributions σ²=∑_iσ_i²+∑_i<jσ_ij²+? due to the independent variable action σ_i², the pair correlation action σ_ij², etc. The information gained from this decomposition can be valuable for attaining a physical understanding of the origins of output uncertainty as well as suggesting additional laboratory/field studies or model refinements to best improve the quality of the model. To reduce sampling effort, the RS-HDMR component functions are approximately represented by orthonormal polynomials. Only one randomly sampled set of input-output data is needed to determine all σ_i, σ_ij, etc. and a few hundred samples may give reliable results. This paper presents its methodology and applications on an atmospheric photochemistry model and a trace metal bioremediation model.     

Measurement of enthalpies of mixing in gaseous phase for the binary system carbon dioxide – hydrogen sulphide by an isothermal flow calorimeter

Enthalpies of mixing for the binary system carbon dioxide – hydrogen sulphide were measured by means of an isothermal flow calorimeter at temperatures of 293.15. 305.15 and 313.15 K. For the first isotherm, excess enthalpy measurements were made at pressures of 0.507, 1.013 and 1.419 MPa. For the last two isotherms, these measurements were performed at pressures of 0.507, 1.013 and 1.520 MPa. The experimental data were treated by the same techniques described for the systems previously studied (Barry et al., 1982a, 1982b, 1982c). Two types of binary interaction coefficients k_ij have been utilized for the prediction of experimental data from equations of state: coefficients k_ij independent of temperature and pressure, and k_ij's adjusted as function of temperature and pressure. A better prediction of the excess enthalpy experimental data was obtained from the latter series of binary interaction coefficients.     

Potential-pH diagrams for complex systems

A generalized thermodynamic analysis and a geometric interpretation of potential-pH diagrams for multi-element systems are presented. The presence of reactive gases, e.g. CO₂ and SO₂, and complex-forming species, e.g. NH₃ and Cl^–, are expressly considered. The equilibrium state is described by a set of independent formation reactions of all species containing the active redox element, M. The formation reactions are written in terms of a user-specified set of primitive species, e.g. M, H₂O, H⁺,e, X and Y, where X and Y could be CO₂ and Cl^– for example. Some of these primitive species, e.g. M ande, may be virtual species, that is, they do not have an independent existence as separate entities in the reaction mixture. This procedure permits an explicit algebraic solution for the potential-pH diagram. Examples of Pourbaix and predominance diagrams for complex uranium and chromium systems are given. A defined by Equation 41 - a activity - a _M overall activity of redox element M - D maximum dimensionality of diagram - E electrochemical potential - F Faraday's constant - f degrees of freedom - G _f.n ⁰ standard free energy of formation of speciesn - h _i stoichiometric coefficient for H⁺ in generalized formation reaction - M symbol for redox element - M _i symbol forith species containing redox element M - M _X molal concentration of species M _i - [M]_T total dissolved concentration of redox element M - n number of species containing redox element M - P number of phases - P_j symbol for primitive species - p pressure - p _ij stoichiometric coefficient for species P_j in generalized formation reaction - r number of independent reactions - R gas constant - s number of species - t number of primitive species - w _i stoichiometric coefficient for H₂O in generalized formation reaction - [X] molal concentration of X - x _i stoichiometric coefficient for species X in generalized formation reaction - y _i stoichiometric coefficient for species Y in generalized formation reaction - z _i stoichiometric coefficient for electrons in generalized formation reaction - _i atoms of redox element in species M _i (_i v_i ^–1) - activity coefficient - chemical potential - v_i stoichiometric coefficient for species M _i in generalized formation reaction (v_{i i} ^–1) - aq aqueous phase - b, c, d dissolved species (M_b, M_c, M_d) containing redox element M - i ith species, M_i (gaseous, solid or dissolved) containing redox element M - j primitive species - M redox element M - s, t, u, v solid phases (M_s, M_t, M_u, M_v) containing redox element M - o standard state - reference electrode     

Fluid‐particle drag in inertial polydisperse gas–solid suspensions

In this article, we extend the low Reynolds number fluid‐particle drag relation proposed by Yin and Sundaresan for polydisperse systems to include the effect of moderate fluid inertia. The proposed model captures the fluid‐particle drag results obtained from lattice‐Boltzmann simulations of bidisperse and ternary suspensions at particle mixture Reynolds numbers ranging from 0 ≤ Re_mix ≤ 40, over a particle volume fraction range of 0.2 ≤ ? ≤ 0.4, volume fraction ratios of 1 ≤ ?_i/?_j ≤ 3, and particle diameter ratios of 1 ≤ d_i/d_j ≤ 2.5. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

The effect of electrolytically formed gas bubbles on ionic mass transfer at a plane vertical electrode

The mechanism which explains the increase in the rate of mass transfer through bubble evolution is not completely established. Three models have been proposed. The present work reports experimental results obtained with a cell design which can separate the contribution of the parameters defining each model.The results obtained allow one to conclude that the main contribution to the increase in the mass transfer rate is due to the macroscopic motion of the fluid caused by the ascending bubbles. A competition between the size and the number of the bubbles at different current densities would be the cause of the constant mass transfer current over a range of gas evolution rates.Nomenclature I _g total constant current applied to the generator electrode (mA) - I _i current related to the electrochemical gas evolution (mA) - I _m mass transport current (mA) - j _g total constant current density (mAcm^–2) - j _i gas evolution current density (mAcm^–2) - j _{H 2} hydrogen evolution current density (mAcm^–2) - j _i,m mass transfer current density for the i electrode (mAcm^–2) - j _m mass transfer current density (mAcm^–2) - j _l free convection limiting current density (mAc^–2) - x the distance from the origin of the hydrogen boundary layer to the test electrode (mm) - h ₁ height of the generator electrode (mm) - h ₂ height of the inert gap between electrodes (mm) - h _i height of the n electrodes (mm) - h height of the single electrode (mm) - a electrode width (mm) - diffusional boundary layer thickness (cm) - j _im difference betweenj _im.     

Aggregation of Alcohols Ethoxylates in n-Heptane

The solubility and aggregation process of polyethoxylated non-ionic surfactants, of general formula C _i H_2i+1–(O–CH₂–CH₂) _j –OH with i = 6, 8, 10 and j = 3–6 (C _i EO _j ), in heptane were studied. The aggregation of C _i EO _j surfactants in heptane was investigated by using methylene blue (MB) as an absorption probe. In solutions of MB in the presence of these surfactants in heptane, at concentrations larger than the re-dissolution concentration, the UV bands associated to free MB (A ₁) and MB–EO complex (A ₂) were detected. The ratio of these intensities A ₂/A ₁, was used to study the kinetics of the complex formation in pure surfactant. The value of A ₂/A ₁ depends on the surfactant structure and the media wherein MB is dissolved, being larger in the pure surfactant than in heptane solutions. These results are explained in terms of solvent effect and aggregate structures on the complex formation.

A model for SOFC anode performance

A model for anode performance of a planar anode-supported SOFC is developed. The model includes Butler–Volmer relation for the hydrogen oxidation, Ohm’s law for ionic current and equation of hydrogen mass balance in the anode channel. We show that the regime of anode operation depends on the relation between the cell current density j and the critical current density j_crit. Analytical solutions to the system of governing equations for the case of “low” (j<j_crit) and “high” (jj_crit) currents are derived. In the “low-current” regime the anode polarization voltage is proportional to cell current, which justifies the notion of anodic activation resistivity R_a. Full hydrogen utilization increases the value of R_a by a factor of 2. In the “high-current” regime polarization voltage depends on cell current logarithmically, with the effective Tafel slope being twice the kinetic value (doubling of Tafel slope). In this regime 100% hydrogen utilization leads to a constant 230-mV shift of polarization curve as a whole.     

Characterization of styrene–methyl methacrylate–n-butyl acrylate terpolymers. I. Average diad concentration determined by 1H-NMR

The average diad concentrations of methyl methacrylate (MMA) unit, P ₂{M_iM_j}, of the title terpolymer prepared by radical polymerization with various conversions were studied by ¹H-NMR measurements. Several methoxy proton peaks of MMA resolved by the diamagnetic shielding effects of styrene were assigned to the individual microstructures of MMA-centered triads. The P ₂{M_iM_j} were determined from these peak ratios according to the terminal copolymerization model and the Ham's assumption of statistical simplification for a multicomponent copolymer (P₂{M_iM_j} = P₂{M_jM_i}), The observed values, P ₂{M_iM_j}, agreed with the values calculated from the monomer reactivity ratios for each conversions, and agreement with the copolymerization theory was evident.     

A fractal-like kinetics equation to calculate landfill methane production

Landfill appears as a convenient choice to get rid of municipal solid waste while providing energy, due to methane generated through anaerobic fermentation. However, without capture and treatment landfill gas is considered an important source of atmospheric methane. The control and use of this gas require knowledge of both, current yield and long-term accumulative production. These values are usually calculated with mathematical expressions that consider 100% of conversion, and homogeneous chemical reactivity inside the fill. Nevertheless, fermentation in landfills is erratic and spatially heterogeneous. This work introduces a fractal-like chemical kinetics equation to calculate methane generation rate from landfill, Q_CH4 (m³/year), in the way: where fermentable wastes are partitioned in readily, moderately and slowly biodegradable categories, L₀ is the potential of methane yield of refuse (m³/tonne under standard conditions), d_s is the solid-phase fracton dimension, k_i is the reaction kinetics constant of waste category i (year⁻¹), and t_j is the time from the year of burying j (year), C_ij⁰ (kg/tonne) and M_ij (kg) are the initial concentration and the mass of waste category i landfilled in year j, respectively. The idea behind this equation is that methane production kinetics is limited by the diffusion of hydrolyzed substrate into a heterogeneous solid-phase towards discrete areas, where methanogenesis occurs. A virtual study for a hypothetical case is developed. The predictions from this fractal approach are contrasted with those coming from two equations broadly used in the industrial work. The fractal-like kinetics equation represents better the heterogeneous nature of the fermentation in landfills.     

Predicting the phase equilibria of synthetic petroleum fluids with the PPR78 approach

The PPR78 approach is a group contribution‐based thermodynamic model which combines at constant packing fraction the Peng–Robinson equation of state and a Van Laar‐type g^E model. This article demonstrates that, using classical mixing rules (linear on b and quadratic on a), the PPR78 model may also be seen as a group contribution method for the estimation of the temperature‐dependent k_ij of the widely used PR EoS. Our model is endowed of 15 groups and it is possible to predict the k_ij for any mixture containing alkanes, aromatics, naphthenes, CO₂, N₂, H₂S, and mercaptans. This study exhibits the capability of this approach to predict the phase behavior of synthetic petroleum fluids containing components of different volatilities. The many comparisons between calculated and experimental data on natural gases, crude oils, and gas condensates allow concluding that the PPR78 approach is a successful model for phase equilibria calculations of this kind of mixtures. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Sensitivity analysis of catalytic conversion of n-C6

The present paper is a case study of an application of sensitivity analysis in chemical kinetics. Emphasis is laid upon chemical interpretation of sensitivity information and on identification of the most important model important model parameters. The kinetic model for reforming of C₆ hydrocarbons proposed by Mobil [14] is extended to the analysis of the behavior of n-hexane conversion in an adiabatic reactor. The importance of six initial conditions (feed composition and initial temperature) is analyzed by the computation of normalized first order sensitivity gradients (y/y) (δy_i/δy). The relative importance of 21 model parameters α_j is estimated by the computation of normalized sensitivity gradients of the type (α_j/y_i) (δy_i/δα_j). The influence of the decisive model parameters ΔH and ΔH (activation enthalpies of benzene hydrogenation and methyl cyclopentane isomerization, respectively) as well as operating parameters is presented. The problem of uncertainly in the value of ΔH and its influence on the model solution is also sown. Finally, some advantages of the application of normalized gradients of the explanation of process behavior are discussed.     

Adsorption of dyes on chitin. I. Equilibrium studies

Equilibrium isotherms have been studied for the adsorption of four dyestuffs, namely, Acid Blue 25, Acid Blue 158, Mordant Yellow 5, and Direct Red 84, onto chitin. Langmuir and Freundlich constants have been determined and the effects of chitin particle size and solution temperature have been investigated. Theoretical isotherms have been compared with experimental data and good agreement was obtained using a composite isotherm of the general form: Y_e = iC_e/(1 + jC_e^m), where i,j, and m are constants.     

Binary interaction coefficients of the Redlich—Kwong equation of state

A direct relationship between the binary interaction coefficients, k_ij and c_ij proposed by Chueh and Prausnitz, and Zudkevitch, for modifying the original mixing rules of the Redlich—Kwong equation of state is presented. Values of k_ij are evaluated by means of two methods for binary vapor—liquid equilibrium data for five systems at a total of thirty-two isothermal conditions. The calculated results from k_ij value obtained by minimizing Σ|ΔP| values are preferable to those obtained by minimizing Σ|Δy| values. The effect of temperature on k_ij for the systems investigated is shown and discussed.