GAS CHROMATOGRAPHIC DETERMINATION AND CORRELATION OF WEIGHT-FRACTION HENRY'S CONSTANTS FOR HYDROCARBON GASES AND VAPORS IN MOLTEN POLYMERS

In the polymer industry, separation equipment is required to separate unreacted monomers and solvents from polymers. In order to design such equipments, solubilities of gases and vapors in molten polymers are needed as fundamental data. It is very helpful if the weight-fraction Henry's constant, which gives solubilities of a solute at concentrated regions of a polymer, can be estimated by a predictive method.

In the present study, a new expression for the free volume term has been derived and is coupled with the UNIFAC model. The present UNIFAC-FV model was applied to common polymer systems. The weight-fraction Henry's constants were calculated for several volatile hydrocarbons and the calculated results were compared with the experimental data determined by a gas chromatographic technique.

The present UNIFAC-FV model with a new free volume expression was found to be helpful in predicting the weight-fraction Henry's constants of hydrocarbon solutes in molten polystyrene, in polypropylene, and in low-density polyethylene. It is advantageous that our model is applicable both supercritical gases and subcritical vapors with no adjustable parameters.     

The Influence of Structure on Autohesion (Self-Tack) and other forms of Diffusion into Polymers

Autohesion is discussed emphasising in particular the influence of polymer chain structure on apparent rates of diffusion. The full range of autohesive levels which exists amongst rubbery polymers is rationalised by proposing a distinction between inter-chain free volume and “intra-chain” free volume, the latter being a collation of free volume regions “contained” in cavities associated with permanent polymer chain structural features which especially apply for certain polymer types. The coincidence of several such cavities plus the intervening inter-chain space causes the formation of holes which may attain sufficient size during normal chain thermal fluctuations to facilitate forward motion of an incoming chain.

The concept of free volume has been used to demonstrate the proposed model semi-quantitatively. Comparison with a simple model, involving inter-chain free volume only, is made throughout the calculation. The proposed model, in showing general agreement for several elastomers between free volume considerations and autohesive characteristics, provides an explanation for the large difference in tackiness which exists between natural rubber and ethylene propylene copolymers.

The relationship of the proposed model with chain co-operative motion is discussed, and its apparent correlation with the diffusion through polymers of a range of gases and solvents is discussed in some detail.     

CO2 SOLUBILITY IN WATER AND BRINE UNDER RESERVOIR CONDITIONS

The reference Henry's constant was determined from 110 solubility data found in the literature for the CO₂/H₂O system over a temperature range of 298 to 523 K and a pressure range of 3.40 to 72.41 MPa. Since the Krichevsfcy-llinskaya equation was used to model the system, a correlation for the A parameter was also developed.

In addition to the Krichevsky-Ilinskaya equation, another two-parameter correlation for the solubility of carbon dioxide in water was obtained by using the Krichevsky-Kasarnovsky equation. The reference Henry's constant and partial molar volume of carbon dioxide at infinite dilution were treated as adjustable parameters. The calculated values of the partial molar volume at infinite dilution did not correspond to experimentally determined values found in the literature. Therefore, a third correlation for the reference Henry's constant was obtained by using the Krichevsky-Kasarnovsky equation in conjunction with the correct values of the partial molar volume. This one parameter (Henry's constant) model did not fit the experimental data as well as the two-parameter models.

The decreased solubility of CO₂ in brine was accounted for empirically by a single factor correlated to the weight percent of dissolved solids. A literature data set of 167 solubilities, with a temperature range of 298 to 523 K and a pressure range of 3.0 to 85.0 MPa, was used to develop this correlation. A wide scatter of data characterizes this correlation, which relates the CO₂ solubility in brine to the CO₂ solubility in water at the same temperature and pressure. The correlation is designed for applications in which the determination of concentrations of individual ions is impractical and the implementation of only one additional parameter is desirable, such as the use of compositional simulators to model miscible displacement in the petroleum industry.

These correlations can be easily implemented into reservoir simulation calculations to account for the effects of CO₂ solubility in brine. These effects are often ignored even though they can have dramatic effects on the performance of the CO₂ enhanced oil recovery process. The correlations presented in this paper for the Henry's constant and the effect of dissolved solids can adequately account for these CO₂ solubility effects.     

Prediction of solubilities for volatile hydrocarbons in low-density polyethylene using UNIFAC-FV model

The UNIFAC-FV model has been applied to predict the weight-fraction Henry's constant of n-hexane, n-octane, benzene, and toluene in low-density polyethylene in the region 124 to 250°C. By adjusting the number of external degrees of freedom per hydrocarbon molecule, the weight-fraction Henry's constant was correlated with good agreement by the model. Namely, the solubilities of hydrocarbons in the polymer can be obtained correctly from the model at low pressures, less than 2 atm. Although the model is very useful, its applicability is limited to the subcritical temperature range of a volatile hydrocarbon.     

用活度系数模型和PCOR状态方程预测聚合物溶液中的亨利常数（英文）

In this paper, the polymer chain of rotator (PCOR) equation of state (EOS) was used together with an EOS/GE mixing rule (MHV1) and the Wilson's equation as an excess-Gibbs-energy model in the proposed approach to extend the capability and improve the accuracy of the PCOR EOS for predicting the Henry's constant of solutions containing polymers. The results of the proposed method compared with two equation of state (van der Waals and GC-Flory) and three activity coefficient models (UNIFAC, UNIFAC-FV and Entropic-FV) indicated that the PCOR EOS/Wilson's equation provided more accurate results. The interaction parameters of Wilson's equation were fitted with Henry's constant experimental data and the property parameters of PCOR, a and b, were fitted with experimental volume data (Tait equation). As a result, the present work provided a simple and useful model for prediction of Henry's constant for polymer solutions.     

A MODEL FOR THE DISTRIBUTION OF ACID GASES BETWEEN AN AQUEOUS ALKANOLAMINE SOLUTION AND LPG

The model of Deshmukh and Mather (1981) is a popular method for correlating and predicting the vapor-liquid equilibria in systems containing acid gases (hydrogen sulfide and carbon dioxide) and aqueous solutions of alkanolamines. The model includes phase equilibrium between an aqueous liquid and a gas as well as chemical equilibrium in the aqueous phase. A recent review by Weiland et al. (1993) demonstrated the accuracy of the correlation. Presented here is a model based on that of Deshmukh and Mather (1981) for calculating the distribution of acid gases between two liquid phases - an aqueous phase and a non-aqueous liquid (typically a propane- or butane-rich liquid)

In the new model the phase equilibrium is modeled using a modified Henry's law approach. Fugacities of the components in the non-aqueous phase are calculated using the Peng and Robinson (1976a) equation of state. All of the parameters in the model are taken from the literature. Thus the model represents a prediction of the behavior. It is demonstrated that the predictions are in good agreement with the available experimental data     

RHEOLOGICAL AND MIST IGNITION PROPERTIES OF DILUTE POLYMER SOLUTIONS

A spinning disc atomizer has been used to characterize the mist flammability of Jet A and diesel fuels that contain high molecular weight polymers. The critical disc velocity required to produce significant flame propagation was shown to depend on polymer concentration, molecular weight, solvent viscosity, and polymer degradation.

The viscoelastic properties of these same polymer solutions have been characterized by a maximum Darcy viscosity measured from flow in packed tubes. For the polymers discussed in this paper, the maximum Darcy viscosity was independent of the bead size or tube length; however, it was strongly affected by the same variables that affected mist flammability; i.e., polymer concentration, molecular weight, solvent viscosity, and polymer degradation.

The critical ignition velocity of dilute polymer solutions is shown to depend on the Darcy viscosity in a similar manner as observed for viscous oils. At low viscosities, the ignition velocity is only slightly affected, but the dependence grows stronger as the viscosity (both shear and Darcy) increases. A close correspondence was also shown to exist between the ignition velocity of a polymer solution with a high Darcy viscosity and the ignition velocity of a Newtonian oil with approximately the same high shear viscosity.

Numerous similarities are described between flow-induced birefringence of dilute polymer solutions with opposed capillary jets and viscoelastic resistance of dilute polymer solutions in packed tubes. These similarities suggest that the maximum Darcy viscosity is associated with a condition of almost complete extension and alignment of the polymer molecules.     

SOLID-LIQUID MASS TRANSFER AT THE WALLS OF A RECTANGULAR AGITATED VESSEL

Rates of mass transfer between the walls of a rectangular agitated vessel and solution were studied by measuring the limiting current of the cathodic reduction of ferricyanide ion at the vessel wall. Variables studied were rotation speed of 45° pitched blade turbine impeller, physical properties of the solution and the presence of drag reducing polymer in lhe solution (Polyox WSR-301). The data were correlated for polymer free solution by the equation:

Sh= 1.925 Sc^0.33 Re^0.5

Comparison of the present data with previous heat and mass transfer studies conducted in cylindrical vessels has shown that the mass transfer behaviour of agitated rectangular vessels lie between baffled and unbaffled agitated cylindrical vessels. Polyox addition was found to reduce the mass transfer coefficient by an amount ranging from 5.6 to 37% depending on polymer concentration. Practical implications of using drag reducing polymers in agitated vessels were discussed.     

A LINEAR CORRELATION FOR SOLID SOLUBILITIES IN SUPERCRITICAL GASES

A previously derived equation (Jonah, 1986) for solid solubilities in supercritical gases is tested in empirically abbreviated form against experimental data on six solutes in supercritical ethylene and carbon dioxide. The solids considered are benzoic acid, 2,3- and 2,6-dimethylnaphthalene, naphthalene, phenanthrene and anthracene.

Our equation correlates these solid solubilities linearly with certain functions of pure solvent thermodynamic properties, thereby making possible the interpolation and extrapolation of sparse experimental data.     

STUDY OF THE PARAMETERS CONTROLLING THE ALTERNATING COPOLYMERIZATION OF METHYL METHACRYLATE AND STYRENE

The copolymerization of methyl methacrylate and styrene, in the presence of zinc chloride, was conducted in the aqueous phase. The zinc chloride acting as a complexing agent

Among the factors affecting the polymerization yield, we have; the level of complexing agents, the monomer ratio and the temperature

The polymers were characterized for their molecular weight (G.P.C.) and analyzed by N.MR, and D.T.A

A model taking into account the various parameters is proposed.     

MEASUREMENT OF INTERFACIAL AREA AND MASS TRANSFER COEFFICIENTS BY CHEMICAL METHOD OF C02 ABSORPTION INTO AQUEOUS SOLUTIONS OF NaOH IN A MODEL COLUMN WITH EXPANDED METAL SHEET PACKING

The theory of gas absorption accompanied by fast pseudo-fast order reaction which considered dependences of diffusivity, kinetic constant and Henry's law constant on absolute temperature and ionic strength was used to obtain values of effective interfacial areas and mass transfer coefficients in gas and liquid phase.

Experimental measurement of carbon dioxide absorption from mixture with air was performed in a pilot-plant column with expanded metal sheet packing irrigated with sodium hydroxide solution.

Resulting liquid and gas-side mass transfer coefficients are compared with values obtained from physical Absorption measurement of carbon dioxide into water and with measurement of gas-side mass transfer coefficient for sulphur dioxide in the same column.

The differences between determined values are discussed.     

High gas permeability in open-structure membranes

For most polymeric membranes, the gas permeability coefficient (P) is often interpreted as the product of diffusivity (D) and solubility (S) of a penetrant gas in the polymer (P=D S). The basic assumption is that molecular diffusion is primarily responsible for mass transport in the membrane permeation process. However, for some open structure membranes, such as poly(1-trimethylsilyl-1-propyne) [PTMSP] or poly(dimethylsiloxane) [PDMS], the high permeabilities of some gases yield much higher diffusivities when calculated from the above relationship (P=D S) than when calculated by using the direct kinetic measurement of diffusivity. It is hypothesized that this discrepancy is due to the convective transport of gas molecules through such open structured polymers. In most cases, the convective contribution to mass transport through membranes is negligible. However, for polymer membranes with high free volume, such as PTMSP, whose free volume fraction is 20 to 25%, the convective term may dominate the permeation flux. In this study, a non-equilibrium thermodynamic formalism is employed to properly treat the diffusion term and convective term that constitute the Nernst-Planck equation. The current analysis indicates that the total permeation flux, which consists of a diffusion term and a convective term, agrees well with the experimental data for several permeation systems: pure components propane and n-butane/PTMSP, pure gas hydrogen/PTMSP, and mixed gas hydrogen/PTMSP. Also, the permeation systems of a nonporous rubbery membrane, PDMS, and eight organophosphorus compounds were included in the study. It is recommended that the proposed model be validated by using other polymers with high free volumes and high permeabilities of gases and vapors, such as poly(1-trimethylgermyl-1-propyne) [PTMGeP] and poly(4-methyl-2-pentyne) [PMP]. This paper is dedicated to Professor Hyun-Ku Rhee on the occasion of his retirement from Seoul National University.     

SELECTIVITY STUDIES IN THE PHOTOCHLORINATION OF METHANE I: REACTOR MODEL AND KINETIC STUDIES IN A NON-ISOTHERMAL, POLYCHROMATIC ENVIRONMENT

The photochlorination of methane employing nitrogen as an inert diluent is studied in a continuous flow, tubular, non-isothermal, bench-scale, polychromatically irradiated photoreactor with particular emphasis on selectivities.

Using a mechanistic sequence of 22 steps, predictions from the mathematical model are compared with experimental results obtained for three different nominal temperatures (297.9 K, 312.8 K and 322.2 K) and three different radiation sources (40, 360 and 1200 W ) that also differ in their output emission characteristics.

An extremely high sensitivity to some of the values of the employed specific rate constants is found, particularly when an accurate prediction of selectivities is being sought. However, within the reported or attributable errors in the published values of the kinetic constants( ± 5%), the experiments show very good agreement with the computed predictions obtained from the mathematical model of the photoreactor.

Using these experimental results that show excellent reproducibility a complete and reliable set of process independent reaction kinetic constants, and a verified reactor model are obtained which can be used for photoreactor design purposes, including selectivity optimization.     

A NONDESTRUCTIVE METHOD TO MEASURE RESIDUAL ADSORPTION CAPACITY OF CHARCOAL FILTERS

High surface area charcoal bed filters have been used for over a half a century to adsorb undesirable vapors from gas streams. One problem encountered when using these niter beds is that there is presently no simple, reliable, nondestructive method to measure their Residual Adsorption Capacity, RAC. This is particularly critical in situations where harmful vapors are being adsorbed.

An investigation has been underway to use pulses of weakly adsorbed gases such as ethane and/or methane to measure RAC. The hypothesis being that these weakly adsorbed gases will “count” unoccupied adsorption sites. In the present study, dimethyl methylphosphonate (DMMP) was used to “irreversibly” occupy available siles to various extents on different niters. The Reduced Retention Time. θ, (the ratio of the adjusted retention time to the space time) and the Resolution (R) between peaks of methane and ethane were found to correlate to RAC under dry and wet (humid) conditions.     

Fluid phase behavior modeling of CO2 + molten polymer systems using cubic and theoretically based equations of state

Phase equilibrium data of CO₂ + molten polymer systems are of great relevance for chemical engineers because these are necessary for the optimal design of polymer final‐treatment processes. This kind of processes needs information about gas solubilities in polymers at several temperatures and pressures. In this work, CO₂ solubilities in molten polymers were modeled by the perturbed chain‐statistical associating fluid theory (PC‐SAFT) equation of state (EoS). For comparison, the solubilities were also calculated by the lattice gas theory (LGT) EoS, and by the well‐known Peng‐Robinson (PR) cubic EoS. To adjust the interactions between segments of mixtures, there were used classical mixing rules, with one adjustable temperature‐dependent binary parameter for the PC‐SAFT and PR EoS, and two adjustable binary parameters for the LGT EoS. The results were compared with experimental data obtained from literature. The results in terms of solubility pressure deviations indicate that the vapor–liquid behavior for CO₂ + polymer systems is better predicted by the PC‐SAFT model than by LGT and PR models. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers.     

INTERPOLATION BETWEEN TWO EXCESS GIBBS FREE ENERGY-COMPOSITION ISOTHERMS

It is shown in this paper how to interpolate a required excess Gibbs free energy-composition isotherm between two such given isotherms.

Efectively, our procedure employs semi-empirical equations for the excess Gibbs free energy, whose adjustable parameters can be identified with infinite dilution properties, and still be made to give close fits, to experimental data. Prediction of these infinite dilution properties is achieved through the use of a linear correlation between them and certain pure component properties. Thus in addition to the two given isotherms, the input into our theory consists of the Antoine vapor pressure constants, critical constants and acentric factors for the pure components.

Our theory has been tested against experimental data for four binary systems ranging from moderately non-ideal to highly non-ideal; the agreement is very good.

The successful execution of the present program highlights the possibility of predicting (g^E-x) isotherms, given limiting activity coefficients (determined chromatographically or otherwise), and a single data point for the equi-molar mixture.     

COMPARATIVE LIMITING FLUX ANALYSIS OF BLACK LIQUOR AND POLYETHYLENE GLYCOL IN ULTRAFILTRATION

Ultrafiltration of black liquor was carried out using an asymmetric membrane and the results were compared with that of polyethylene glycol, a standard macromolecule, in a stirred batch cell. The effects of system parameters, e.g., pressure, concentration and stirrer speed on permeate flux and solute rejection were studied extensively for both the solutes.

An osmotic pressure model was used to analyze experimental results. To take into account the phenomena of concentration polarization, an extra resistance term, called the polarization layer resistance (R_p), was incorporated into the model. The polarization layer resistance was found to be a function of flow regime and concentration at the membrane. To correlate these, the following two types of relationship were examined and tested with the experimental results,

and

where a, b, c, a₁, b₁, are constants.     

Physical Solubility of Gases in Fused Silica

Experimental data on the physical solubility of gases in fused silica are presented. A "free" volume for fused silica was calculated from these solubilities and was compared to the free volume calculated by other methods. The relation of this free volume to the molecular structure of fused silica is also discussed.