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%.     

Simulation of the composition and proportions of anions in polymerized silicate melts

A new statistical model is proposed for describing an equilibrium structure of polymer complexes in a silicate melt. The model makes it possible to calculate the molecular-mass distributions of polyanions of the general formula (Si _i O_{3i + 1 ? j} )^{2(i + 1 ? j} )^?, where i is the number of silicon atoms and j is the number of intramolecular closures of bridging bonds. The proposed model is implemented as the STRUCTON computer program (version 1.1, 2006) intended for calculating the composition and proportions of polyanions at different degrees of polymerization of the system. The executable code is implemented on personal computers. The distributions of Q ⁿ structons, which are obtained experimentally from Raman and NMR spectroscopic data or evaluated theoretically, are used as input parameters for the computer program. The testing calculations are performed with the STRUCTON program for three arbitrary distributions of Q ⁿ particles corresponding to different degrees of polymerization 0.25 ≤ α ≤ 0.49 for the model system containing 104 initial structons. The results of the statistical simulation have demonstrated that a limited ensemble of polymer complexes is formed in the system, so that the mean number of different types of complexes varies from 46 to 141. This result correlates with an increase in the mean size of anions from 1.87 to 8.60 and with a decrease in the total number of polymer particles from 5320 to 1166 in the aforementioned range of degrees of polymerization α.     

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.     

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.     

Effective conductivities of an FeS positive in LiCl-KCl eutectic electrolyte at different states of charge

The effective conductivities of an FeS positive electrode in an Li-Al/FeS cell were determined for different states of charge and discharge in LiCl-KCl eutectic electrolyte at 450° C. The data obtained experimentally were compared with those obtained in 67.4 mol% LiCl-KCl electrolyte and theoretically predicted profiles. The electrode resistance profiles indicate that precipitation of KC1, in addition to formation of Li₂S, in the positive electrode causes high internal resistance and limits the discharge capacity.Nomenclature C _i,b Bulk concentration of speciesi outside the electrode (mol cm^–3) - C _i,p Concentration of speciesz in the pore solution (mol cm^–3) - D _i Diffusion coefficient of speciesi (cm² sec^–1) - F Faraday's constant (96 487 C equiv^–1) - I Current density (A cm^–1) - k _j Conductivity ratio defined ask _j /k _c - K _m,j Conductivity ratio defined asK _m,j /k _c - L Electrode thickness per unit volume (cm) - R _i,diffu Rate of concentration change of speciesi due to diffusion (mol s^–1cm^–3) - R _i,migra Rate of concentration change of speciesi due to migration (mol s^–1 cm^–3) - R _i,precip Rate of concentration change of speciesi due to precipitation (mol s^–1cm^–3) - R _i,reac Rate of concentration change of speciesi due to reaction (mol s^–1cm^–3) - t Time (s) - t _i ^Cl Transference number of speciesi relative to Cl^– - ¯ _j Molar volume ofj (cm³mol^–1) - w _LiCl Mass fraction of LiCl - x _i Mole fraction of speciesi - (x _LiCl)_KCl,sat Mole fraction of LiCl in LiCl-KCl electrolyte saturated with KC1 - (x _LiCl)_LiCl,sat Mole fraction of LiCl in LiCl-KCl electrolyte saturated with LiCl - _i Rate constant of production or consumption of speciesi - Void fraction or porosity - _j Volume fraction of solid phasej - _ps Volume fraction of precipitated salt - K _c Conductivity of continuous phase, e.g. electrolyte (^–1 cm^–1) - k _j Conductivity of solid phasej (^–1 cm^–1) - K _m,j Effective conductivity for a mixture of conductive solid phasej and the electrolyte at a given volume fraction of phasej (^–1 cm^–1) - Density of electrolyte (g cm^–3) - Effective conductivity of FeS electrode at a state of discharge (^–1 cm^–1) - Effective resistivity of FeS electrode at a state of discharge ( cm)     

Introduction to powder surface area : By S. Lowell,Wiley, New York, 1979; pp 189; £11.00.

The values of first-order specific rates of breakage, S_i, and primary daughter fragment distributions, B_i,j, of quartz were determined in a laboratory ball mill. It was concluded that B_i,j values were constant for all conditions and that the specific rates of breakage fitted the relation S_i = ax^α_i, x_i being sieve size. The value of α was 0.80 for normal filling conditions but decreased to 0.53 for values of U < 0.3, U being defined by f_c/0.4J, f_c and J being the fractional volume filling of the mill by powder and balls respectively (based on a formal porosity of 0.4 for powder and ball bed). At high values of U the grinding became non-first order. In the normal range of U values, the results could be fitted by the empirical equation

This gives maximum mill capacity at U values in the range 0.4 to 0.6.     

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.     

A direct graphical analysis of polarographic kinetic currents

The linearity of logarithmic plots of i_k/(i_d ? i_k) vs C_j for polarographic kinetic currents allows direct graphical analysis of the kinetics of the prior chemical step with respect to species j without the need for reference to Koutecky's table. Results obtained in this way compare favorably with those secured using the conventional Koutecky analysis.     

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     

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.     

Onsager coefficients for binary mixture diffusion in nanopores

This paper presents a critical appraisal of current estimation methods for the Onsager coefficients L₁₁, L₂₂, and L₁₂ for binary mixture diffusion inside nanopores using pure component diffusivity data inputs. The appraisal is based on extensive sets of molecular dynamics (MD) simulation data on L_ij for a variety of mixtures in zeolites (MFI, AFI, TON, FAU, CHA, DDR, MOR, and LTA), carbon nanotubes (CNTs: armchair and zig-zag configurations), titanosilicates (ETS-4), and metal-organic frameworks (IRMOF-1, CuBTC). The success of the L_ij predictions is crucially dependent on the estimates of the degree of correlations in molecular jumps for different guest-host combinations; these correlations are captured in Maxwell-Stefan approach by the exchange coefficients ?_ij. Three limiting scenarios for correlation effects have been distinguished; for each of these scenarios appropriate expressions for the L_ij are presented. For CNTs, correlation effects are dominant and the interaction factor, defined by , is close to unity. For cage-type zeolites such as LTA, CHA, and DDR with narrow windows separating cages, correlation effects are often, but not always, negligibly small and the assumption of uncoupled diffusion, i.e., α₁₂=0, is a reasonable approximation provided the occupancies are not too high. In other cases such as zeolites with one-dimensional channel structures (AFI, TON), intersecting channels (MFI), cage-type zeolite with large windows (FAU), ETS-4, CuBTC, and in IRMOF-1, it is essential to have a reliable estimation of the ?_ij; MD simulations underline the wide variety of factors that influence the ?_ij.We also highlight two situations where estimations of the L_ij fail completely; in both cases the failure is caused due to segregated adsorption. In adsorption of CO₂-bearing mixtures in LTA and DDR zeolites, CO₂ is preferentially lodged at the narrow window regions and this hinders the diffusion of partner molecules between cages. The second situation arises in MOR zeolite that has one-dimensional channels connected to side pockets. Some molecules such as methane, get preferentially lodged in the side pockets and do not freely participate in the molecular thoroughfare. Current phenomenological models do not cater for segregation effects on mixture diffusion.     

Synthesis and structural characterizations of organolanthanide complexes with amino-tethered guanidinate ligand (C5H5)2Ln[H2N(CH2)3NC(NHiPr) NiPr)] (Ln = Yb,Y, Er,Dy)

Reaction of N,N′-diisopropylcarbodiimide (ⁱPrNCNⁱPr) with H₂N(CH₂)₃NH₂ and (C₅H₅)₃Ln, give (C₅H₅)₂Ln[H₂N(CH₂)₃NC(NHⁱPr) NⁱPr)] in high yields, indicating that the N–H bonds of one NH₂ group readily add to the CN double bonds of carbodiimide and one cyclopentadienyl group is eliminated to construct a novel amino-tethered guanidinate anionic ligand [H₂N(CH₂)₃N C(NHⁱPr)NⁱPr)]⁻.     

Analysis of the use of voltammetric results as a steady state approximation to evaluate kinetic parameters of the hydrogen evolution reaction

The use of the voltammetric response j^vol(η) of a potentiodynamic sweep at a slow scan rate vs in place of a steady state polarization curve j^ss(η) for the determination of the kinetic parameters of the hydrogen evolution reaction is analyzed. It is proposed to consider jvol(η,vs)≅jss(η) when the condition 0.99≤jvol(η,vs)/jss(η)≤1.01 is verified in the overpotentials range η ≤ −0.05 V. It has been also established a simple relationship between the maximum admissible scan rate and the equilibrium polarization resistance R_p. Finally, the application of this criterion on different electrodes is described and discussed.     

Kinetics of Sedimentation of a Coagulating Suspension

The coagulation–sedimentation kinetics in a spatially heterogeneous disperse system is theoretically analyzed. The expression for the suspension concentration c as a function of time t and depth h is obtained in the form c ～ t ^?ε h ^εν. The concentration of the dispersed phase formed in coagulant hydrolysis depends on the coagulant concentration c ₀ as c ～ c ₀ ^{? γ} . It is determined how the exponents in the expressions derived are related to the characteristics of the coagulation kinetics and the aggregate size distribution. The results obtained are compared with published experimental data.     

Prediction of Henry's law constants by matrix completion

Methods for predicting Henry's law constants H_ij are important as experimental data are scarce. We introduce a new machine learning approach for such predictions: matrix completion methods (MCMs) and demonstrate its applicability using a data base that contains experimental H_ij values for 101 solutes i and 247 solvents j at 298 K. Data on H_ij are only available for 2661 systems i + j. These H_ij are stored in a 101 × 247 matrix; the task of the MCM is to predict the missing entries. First, an entirely data-driven MCM is presented. Its predictive performance, evaluated using leave-one-out analysis, is similar to that of the Predictive Soave-Redlich-Kwong equation-of-state (PSRK-EoS), which, however, cannot be applied to all studied systems. Furthermore, a hybrid of MCM and PSRK-EoS is developed in a Bayesian framework, which yields an unprecedented performance for the prediction of H_ij of the studied data set.     

A mass transfer model for the autocatalytic dissolution of a rotating copper disc in oxygen saturated ammonia solutions

A mathematical model of mass transfer processes during autocatalytic dissolution of metallic copper in oxygen-containing ammonia solutions using the rotating disc technique is presented. The model is based on the equations of steady state convective diffusion with volumetric mass generation terms and boundary conditions of the third kind, in more generalized form, at the disc surface and of the first kind in the bulk solution. The boundary value problem was solved numerically using the finite difference method with variable mesh spacing. Comparison of calculated and experimental results indicates that the model quantitatively represents the measurements. The rate of the reaction Cu(II)+Cu2Cu(I) determines the overall rate of the process.Nomenclature A rotating disc surface area, (cm²) - B dimensionless constant,B=k ₃ c ₁ ^{0 –1} - c _i concentration of speciesi, c _i=c _i(y) (mol cm^–3) - c _i ⁰ concentration of species i in the bulk of solution,c _i ⁰ =c _i ⁰ (t) (mol cm^–3) - c _{i, 0} concentration of species i at the disc surface,c _i,0=c _i (y=0) (mol cm^–3) - C _i concentration ratio,C _i=c _i/c _i ⁰ ,C _i=C _i() - C _i ⁰ concentration ratio (in the bulk of solution),C _i=c _i ⁰ /c _i ⁰ - C _i,0 concentration ratio (at the disc surface),C _i,0=c _i,0/c _i ⁰ - D _i molecular diffusivity of species i (cm² s^–1) - h space increment,h==(/v)^1/2y, dimensionless - j _i mass flux of species i (mol cm^–2 s^–1) - k _i first-order reaction rate constant (cm s^–1 or cm³ mol^–1 s^–1) - K _i,j diffusivity ratio,K _i,j=D _i/D _j, dimensionless - M number of space increments - n _i total number of moles of Cu(II) entering the bulk of solution referred to the unit disc surface area (mol cm^–2) - rate of production of species i by the chemical reaction (mol cm^–3 s^–1) - Sc _i Schmidt number,Sc _i=v _i/D _i - t time, (s) - t time increment (s) - v fluid velocity vectorv=(u, v, w) (cm s^–1) - V volume of solution (cm³) - W ₁,W ₂ dimensionless group,W ₁=(K _3,2/D ₁) (v/)^1/2,W ₂ = (K _1,2/D ₂(v/)^1/2 - x ₁ coordinates,l=1, 2, 3 - y axial coordinate (perpendicular to the disc surface) - y space increment (cm) Greek letters nabla operator - kinematic viscosity of solution (cm² s^–1) - _i stoichiometric coefficients - disc angular velocity (s^–1) - dimensionless axial coordinate, =(/v)^1/2 y - dimensionless space increment, =(/v)^1/2y     

From a least action principle to mass action law and extended affinity

Basic nonlinear laws that govern nonlinear chemical kinetics and diffusion in a far-from-equilibrium nonstationary regime are derived from an action functional of Hamilton's type. The functional operates with the difference between the kinetic and static free energies F^kin and F^stat and contains an exponential dissipative term that takes into account thermodynamic irreversibility. Unsteady-state generalization of Guldberg and Waage's kinetic law and Fick's law of diffusion is found which goes over into the classical laws at the steady state when local nonequilibrium effects are ignored.Nonlinear irreversible thermodynamics of chemically reacting systems are investigated. An extended chemical affinity Ã_j is obtained which depends not only on the usual equilibrium quantities T and C but also on nonequilibrium variables such as diffusive fluxes J_i and reaction rates r_j. It is shown that for a far-from-equilibrium and highly nonstationary regime the thermodynamic force for the j-th chemical reaction, X_j^ch, is the sum of Ã_j and the time derivative of the so-called “reaction momentum” ∂F^kin/∂r_j, and hence the reaction rate r_j depends not only on the current state but also on the past history of the reaction.     

Numerical models for reactions catalysed by homogeneous mediators: the case of Fenton's reagent

A numerical model has been developed to describe the behaviour of a batch reactor in which Fenton's reagent is used for hydroxylating aromatic hydrocarbons under conditions of electrochemical regeneration. The test reaction considered is the conversion of benzene into phenol. Comparison is made with previously published experimental results.Nomenclature A electrode area, m² - a ₁ parameter defined by Equation 21 - C _i concentration of species, i, in the bulk solution, mol m^–3 - c _i local concentration of species, i, in the diffusion layer, mol m^–3 - K _i effective mass-transfer coefficient, m s^–1 - k _j rate constant of reaction j - R _j rate of reaction j, mol m^–3 s^–1 - r _i rate of change of concentration of species i due to chemical reaction, mol m^–3 s^–1 - t time, s - V reactor volume, m³ - x distance from the cathode surface, m - x ^* maximum thickness of the diffusion layer, m - period of diffusion layer renewal, s Subscrpts 1 oxygen - 2 Fe³⁺ - 3 hydrogen peroxide - 4 Fe²⁺ - 5 benzene - 6 phenol - 7 biphenyl This paper was presented at the meeting on Electroorganic Process Engineering held in Perpignan, France, 19–20 September 1985.     

Potential distribution and electrode stability in a bipolar electrolysis cell

A computational model is presented, which enables the identification of those zones endangered by corrosion in a bipolar electrolysis cell stack. The method consists of two steps: first the potential profile in the electrolyser is computed by numerical solution of the Laplace equation using the finite difference method; then, making use of the Criss-Cobble correspondence principle, this profile is related to the potential-dependent thermodynamic stabilities of the respective metals. This may be a useful tool in the design of intermittently operating electrolysers (for example those powered by solar energy).Nomenclature A metal phase - A _i single A-phase point - B electrolyte phase - B _i single B-phase point - F Faraday constant - h mesh interval (m) - i local current density (A m^–2) - i ₀ exchange current density (A m^–2) - j local current across the double layer (A) - j _iA,j _iB tangential or normal component of the double layer current (A) - K A, B phase conductivity ratio - m molality mol kg^–1 - R gas constant - T absolute temperature (K) - U potential (V) - U ₀ water decomposition voltage (V) - U _tot end plate potential (V) - x, y cartesian coordinates - overrelaxation factor - _a, _c anodic or cathodic overpotential (V) - _A, _B electrical conductivity (^–1 m^–1) - potential (V) - _m local double layer potential, electrode end (V) - _s local double layer potential, electrolyte end (V)     

Particle entrainment model for industrial flotation cells

A simple empirical dimensionless model to calculate the mineral gangue recovered per size class (R_G,i) by entrainment, in terms of the water recovery (R_W), in an industrial flotation cell is presented. For modeling purposes, a dimensionless entrainment factor EF_i, corresponding to the ratio (R_G,i/R_W), was defined for each particle size class. From experimental data measured in an industrial 130 m³ flotation cell, it was found that EF_i was well correlated with the dimensionless ratio (d_P,i/δ) by