THE MODIFIED PGR EQUATION OF STATE: ASYMMETRIC MIXTURE VLE REPRESENTATIONS AND PREDICTIONS

A set of mixing rules was proposed for the modified Park-Gasem-Robinson (PGR) equation of state (EOS) to extend its predictions to mixtures. The phase behavior predictive capability of this segment-segment interaction model was evaluated for selected binary asymmetric mixtures involving ethane, carbon dioxide, and hydrogen in normal paraffins. The predicted bubble point pressures for the ethane + n-paraffin and carbon dioxide + n-paraffin binaries were compared to those of the Peng-Robinson (PR), simplified perturbed hard-chain theory (SPHCT), and original PGR equations. The a priori predictive capability of the modified PGR EOS is significantly better than that of the PR, SPHCT, and original PGR equations of state for ethane binaries with absolute-average percent deviation (%AAD) of 5%. However, this EOS produces comparable representations for ethane binaries (%AAD of 1.9%) and carbon dioxide binaries (%AAD of 2.0). For hydrogen binaries, the modified PGR EOS showed much better representations (%AAD of 1.7) than the original PGR equation and was comparable to the PR equation.     

THE MODIFIED PGR EQUATION OF STATE: ASYMMETRIC MIXTURE VLE REPRESENTATIONS AND PREDICTIONS

A set of mixing rules was proposed for the modified Park-Gasem-Robinson (PGR) equation of state (EOS) to extend its predictions to mixtures. The phase behavior predictive capability of this segment-segment interaction model was evaluated for selected binary asymmetric mixtures involving ethane, carbon dioxide, and hydrogen in normal paraffins. The predicted bubble point pressures for the ethane + n-paraffin and carbon dioxide + n-paraffin binaries were compared to those of the Peng-Robinson (PR), simplified perturbed hard-chain theory (SPHCT), and original PGR equations. The a priori predictive capability of the modified PGR EOS is significantly better than that of the PR, SPHCT, and original PGR equations of state for ethane binaries with absolute-average percent deviation (%AAD) of 5%. However, this EOS produces comparable representations for ethane binaries (%AAD of 1.9%) and carbon dioxide binaries (%AAD of 2.0). For hydrogen binaries, the modified PGR EOS showed much better representations (%AAD of 1.7) than the original PGR equation and was comparable to the PR equation.     

A practical equation of state for non‐spherical and asymmetric systems for application at high pressures. Part 1: Development of the pure component model

A practical, mathematically and computationally simple, equation of state (EOS) has been developed to accurately describe pure component phase behaviour of spherical and chain‐like molecules. The EOS consists of a newly developed hard sphere model and a perturbation term based on the Barker and Henderson approach using the Chen and Kreglewski intermolecular potential model and a double constrained summation as a mathematical expression thereof. The perturbed hard chain theory (PHCT) approach is used to extend the EOS to non‐spherical molecules. The EOS compares well with other more complex models such as the simplified perturbed hard chain theory (SPHCT) and statistically associating fluid theory (SAFT) models and will be extended to describe mixtures in Part 2 of this series. © 2011 Canadian Society for Chemical Engineering     

MOLECULAR PRINCIPLE OF CORRESPONDING STATES FOR VISCOSITY AND THERMAL CONDUCTIVITY OF FLUID MIXTURES

Conformal solution theory is developed for the viscosity and thermal conductivity of fluid mixtures. The procedure involves expanding the transport coefficient for the mixture about the value for an ideal solution, using groupings of the potential parameters and molecular mass as expansion coefficients. The parameters for the ideal solution are chosen so as to annul the first-order term in this expansion, thus encouraging rapid convergence. This yields mixing rules (similar to those of the van der Waals 1 theory for thermodynamic properties) for the potential parameters and molecular mass of the reference fluid. Reference fluid properties are obtained from pure fluid corresponding states correlations

By making calculations for dilute gas mixtures and comparing with Chapman-Enskog theory, it is found that the first-order theory works well for mixtures of quite widely different energy parameters (ε) and molecular masses; it is more sensitive to the size difference of the molecular components, however. For cryogenic liquid mixtures composed of simple liquids good results are obtained using two-parameter corresponding states for the reference fluid. For polyatomic fluids it is necessary to use a three-parameter corresponding states approach for the pure fluids. A method of introducing a third parameter, while retaining the simplicity of having only two independent variables, is used for such fluids. Good results are obtained for a variety of binary mixtures. The method is of particular value for multicomponent fluids. Thus, without fitting any parameters from ternary data the theory predicts viscosities for the system carbon tetrachloride/n-hexane/benzene over the full composition range with a standard deviation of only 1.69%.     

The effect of increasing MgO content in dendromass on ash fusibility and corrosion of corundum refractory castable

Low melting temperatures of the biomass ash at the intensive combustion can generate the slag with a portion of unburned fuel. The portion of imperfectly burned fuel reduces the efficiency of its use. An alternative route to solve the problem without changing the combustion condition is a modification of the chemical composition of the ash with the addition of an agent increasing the melting temperature of the ash/slag. In this paper, we report on the impact of adding the magnesite waste sludge to ash on their melting. Three types of ashes with different SiO₂ and K₂O content were selected for the tests. The melting temperatures of ash and ash mixtures with magnesite sludge (mass ratio 0.5–2:1) have been determined. The addition of magnesite sludge to ash increased the temperature of fusibility index of the mixtures by 50–100 °C. The ash fusibility temperature rose with a decrease of the SiO₂ content in the ash. Subsequently, the interaction of the ash/ash mixtures with the refractory corundum castable was monitored at a temperature of 1450 °C using a static crucible corrosion test. The addition of magnesite sludge to ash reduced the aggression of the slags to the refractory corundum materials. The Al₂O₃ concentration in the post mortem slags of the ash mixtures with the magnesite sludge (2:1) was about 20–23 wt% lower in comparison to the slag without magnesite. The evaluation of the effect of magnesite sludge addition to ash and the elements (K, Ca, Mg, Fe, Si) penetration on the extent of corrosion is the subject of further work aimed at analyses of the corrosion interface of the slag – corundum refractory material.     

MOLECULAR PRINCIPLE OF CORRESPONDING STATES FOR VISCOSITY AND THERMAL CONDUCTIVITY OF FLUID MIXTURES

Conformal solution theory is developed for the viscosity and thermal conductivity of fluid mixtures. The procedure involves expanding the transport coefficient for the mixture about the value for an ideal solution, using groupings of the potential parameters and molecular mass as expansion coefficients. The parameters for the ideal solution are chosen so as to annul the first-order term in this expansion, thus encouraging rapid convergence. This yields mixing rules (similar to those of the van der Waals 1 theory for thermodynamic properties) for the potential parameters and molecular mass of the reference fluid. Reference fluid properties are obtained from pure fluid corresponding states correlations

By making calculations for dilute gas mixtures and comparing with Chapman-Enskog theory, it is found that the first-order theory works well for mixtures of quite widely different energy parameters (ε) and molecular masses; it is more sensitive to the size difference of the molecular components, however. For cryogenic liquid mixtures composed of simple liquids good results are obtained using two-parameter corresponding states for the reference fluid. For polyatomic fluids it is necessary to use a three-parameter corresponding states approach for the pure fluids. A method of introducing a third parameter, while retaining the simplicity of having only two independent variables, is used for such fluids. Good results are obtained for a variety of binary mixtures. The method is of particular value for multicomponent fluids. Thus, without fitting any parameters from ternary data the theory predicts viscosities for the system carbon tetrachloride/n-hexane/benzene over the full composition range with a standard deviation of only 1.69%.     

THE MODIFIED PGR EQUATION OF STATE: PURE-FLUID PREDICTIONS

The Park-Gasem-Robinson (PGR) equation of state (EOS) has been modified to improve its volumetric and equilibrium predictions. Specifically, the attractive term of the PGR equation was modified to enhance the flexibility of the model, and a new expression was developed for the temperature dependence of the attractive term in this segment-segment interaction model.

The predictive capability of the modified PGR EOS for vapor pressure and saturated liquid and vapor densities was evaluated for selected normal paraffins, normal alkenes, cyclo-paraffins, light aromatics, argon, carbon dioxide, and water. The generalized EOS constants and substance-specific characteristic parameters in the modified PGR EOS were obtained from pure component vapor pressures and saturated liquid and vapor molar volumes. The calculated phase properties were compared with those of the Peng-Robinson (PR), the simplified-perturbed-hard-chain theory (SPHCT), and the original PGR equations. Generally, the performance of the proposed EOS (%AAD of 1.3, 2.8, and 3.7 for vapor pressure, saturated liquid, and vapor densities, respectively) was better than the SPHCT and original PGR equations in predicting the pure fluid properties.     

AN EXPLICIT APPROXIMATE SOLUTION OF THE GENERALIZED MAXWELL-STEFAN EQUATIONS FOR THE MULTICOMPONENT FILM MODEL

A solution of the generalized system of Maxwell-Stefan equations is proposed. As a result an explicit method of calculating mass transport in multicomponent mixtures of real fluids has been developed, this method constituting an extension of Taylor and Smith (1982) method for the case of real fluids.

The numerical example has shown that the method presented yields results being very close to those obtained by implicit methods of Krishna (1977) and Stewart and Prober (1964).     

Behaviour of activated carbons obtained from mixtures of oil-fired fly ash and oil refining pitch

Chars were obtained by the pyrolysis of mixtures of oil refining pitch and carbon-fired fly ash. These materials, after activation with CO₂ at 900 °C, produced activated carbons with high surface area, high content of oxygen, and surface sites with prevalent basic characteristics. The amount of SO₂ adsorbed by the carbons produced increases with an increase in the amount of added ash. Subsequent leaching with water allows the distinction of three forms of SO₂: (a) a portion that desorbs as SO₂; (b) a portion that desorbs as SO₃; and (c) a portion that cannot be recovered by leaching with water. The addition of ash favours the process by which SO₂ can be desorbable as SO₃ or cannot be desorbable. This behaviour is enhanced by the presence of NO_x in the gaseous adsorption mixture.     

借助变阱宽方阱链流体状态方程模拟非电解质体系表面张力和粘度(英文)

The equation of state(EOS)for square-well chain fluid with variable range(SWCF-VR) developed in our previous work based on statistical mechanical theory for chemical association is employed for the correlations of surface tension and viscosity of common fluids and ionic liquids(ILs).A model of surface tension for multi-component mixtures is presented by combining the SWCF-VR EOS and the scaled particle theory and used to produce the surface tension of binary and ternary mixtures.The predicted surface tensions are in excellent agreement with the experimental data with an overall average absolute relative deviation(AAD)of 0.36%.A method for the calculation of dynamic viscosity of common fluids and ILs at high pressure is presented by combining Eyring’s rate theory of viscosity and the SWCF-VR EOS.The calculated viscosities are in good agreement with the experimental data with the overall AAD of 1.44% for 14 fluids in 84 cases.The salient feature is that the molecular parameters used in these models are self-consistent and can be applied to calculate different thermodynamic properties such as pVT,vapor-liquid equilibrium,caloric properties,surface tension,and viscosity.     

Viscosity of crude oils

A series of experimental viscosity data for seven different North Sea oils is presented. A new corresponding states method for prediction of the viscosity of both gaseous and liquid hydrocarbon fluids has been developed. The required input is critical constants and the molecular weight of each component. Very accurate results were obtained for the crude oils using the C₇₊-characterization procedure of Pedersen et al.[1]. The viscosity correlation is also shown to give satisfactory results for pure hydrocarbons and binary mixtures.     

High-pressure phase equilibrium for the hydroformylation of 1-octene to nonanal in compressed CO2

The hydroformylation reaction in supercritical carbon dioxide or CO₂-expanded liquids (CXLs) has many advantageous properties. However, accurate phase behavior and equilibrium must be known to properly understand and engineer these systems. In this investigation, the vapor-liquid equilibrium and mixture critical points of CO₂ systems with 1-octene, nonanal, 1-octene and nonanal mixtures, and mixtures of 1-octene, nonanal and syngas (CO/H₂) were measured at 60 °C up to 120 bar of pressure. The Peng-Robinson equation of state with van der Waals two-parameter mixing rule was employed successfully to correlate the binary mixture data and predict the ternary mixture data. The presence of CO/H₂ pressure increased the mixture critical points and decreased the volume expansion at any given pressure. In an actual reaction, the mixture critical point would increase throughout the reaction, while the volume of the liquid phase would decrease. These data will aid the understanding and reaction engineering for the hydroformylation reaction in CO₂-expanded liquids and supercritical fluids.     

CRITICAL POINT PREDICTION USING A MULTI-FLUID GENERALIZED CORRESPONDING STATES PRINCIPLE

The Generalized Corresponding States Principle (GCSP), based on the properties of two non-spherical reference fluids, offers flexibility and ease of computation for the prediction of thermodynamic and transport properties of pure fluids and fluid mixtures. In this work, the multi-fluid GCSP is used for the calculation of the critical properties of mixtures. Classes of mixtures studied include those containing: (1) simple spherical molecules; (2) large quasi-spherical molecules such as the cyclosiloxanes; (3) both spherical and large nonspherical molecules such as those important in supercritical extraction and hydrocarbon processing; and (4) molecules exhibiting strong dipole moments. The advantages of the GCSP method are outlined, particularly for fluids not usually amenable to conventional corresponding states treatments.     

CRITICAL POINT PREDICTION USING A MULTI-FLUID GENERALIZED CORRESPONDING STATES PRINCIPLE

The Generalized Corresponding States Principle (GCSP), based on the properties of two non-spherical reference fluids, offers flexibility and ease of computation for the prediction of thermodynamic and transport properties of pure fluids and fluid mixtures. In this work, the multi-fluid GCSP is used for the calculation of the critical properties of mixtures. Classes of mixtures studied include those containing: (1) simple spherical molecules; (2) large quasi-spherical molecules such as the cyclosiloxanes; (3) both spherical and large nonspherical molecules such as those important in supercritical extraction and hydrocarbon processing; and (4) molecules exhibiting strong dipole moments. The advantages of the GCSP method are outlined, particularly for fluids not usually amenable to conventional corresponding states treatments.     

Effects of syngas composition on combustion induced vortex breakdown (CIVB) flashback in a swirl stabilized combustor

Flame flashback attributed to combustion induced vortex breakdown (CIVB) is a major design challenge for swirl stabilized burner combustors. This paper presents an experimental investigation of combustion induced vortex breakdown (CIVB) flashback propensity for flames yielded from Hydrogen (H₂)–Carbon Monoxide (CO) fuel blends and actual synthesized gas (syngas) mixtures. A two-fold experimental approach, consisting of a high definition digital imaging system and a high speed PIV system, was employed. The main emphasis was on the effect of concentration of different constituents in fuel mixtures on flashback limit. In addition, the effect of Swirl Number on flashback propensity was discussed. The percentage of H₂ in fuel mixtures played the dominant role when CIVB flashback occurred. For a given air mass flow rate, the mixture containing a higher percentage of H₂ underwent flashback at much leaner conditions. Flashback maps for actual syngas fuel compositions showed a distinct behavior when various concentrations of diluents were introduced in the mixture. For the two major diluents tested, carbon dioxide (CO₂) and nitrogen dioxide (NO₂), CO₂ was more dominant. The effect of Swirl Number on the flashback propensity was also tested and showed a decrease with an increase in Swirl Number. The final portion of this paper also provides an analysis of flow field of reacting flames which revealed complex vortex–chemistry interactions leading to vortex breakdown and flashback. Based on the experimental results a parametric model similar to Peclet Number approach was developed employing a flame quenching concept. A value of the quench parameter, C_quench was obtained from the correlation of flow Peclet Number and flame Peclet Number, which was observed to be dominated by the fuel composition rather than Swirl Number.     

Corresponding-states and parachor models for the calculation of interfacial tensions

A generalized corresponding-states model based on two reference fluids and a parachor correlation were developed for the prediction of interfacial tensions for non-polar and weakly polar pure fluids and mixtures. Pure methane and n-octane were chosen as reference fluids of the corresponding-states model. The two models were tested on 86 pure substances, more than 30 binary and multicomponent mixtures, 11 naphtha reformate cuts, 6 petroleum cuts and 2 North Sea oil mixtures. The calculated results were found to be in good agreement with experimental data.     

Analysis of tensile modulus of PP/nanoclay/CaCO3 ternary nanocomposite using composite theories

The tensile modulus of PP/nanoclay/CaCO₃ hybrid ternary nanocomposite was analyzed using composite models. Rule of mixtures, inverse rule of mixtures, modified rule of mixtures (MROM), Guth, Paul, Counto, Hirsch, Halpin–Tsai, Takayanagi, and Kerner–Nielsen models were developed for three‐phase system containing two nanofillers. Among the studied models, inverse rule of mixtures, Hirsch, Halpin–Tsai, and Kerner–Nielsen models calculated the tensile modulus of PP/nanoclay/CaCO₃ ternary nanocomposite successfully compared with others. Furthermore, the Kerner–Nielsen model was simplified to predict the tensile modulus by volume fractions of nanofillers. Also, Takayanagi model was modified for the current ternary system. The developed Takayanagi model can predict the tensile modulus using Young's modulus and volume fractions of matrix and nanofillers. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012