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A statlc, volumetrlc method has been used to determine the adsorptlon equlllbrla of C2H4, C,H6, I-C4Hlo, and CO, and thelr blnary mlxtures on 13X molecular sleves at varlous temperatures between 273 and 373 K. Pressures for the puretomponent data extend up to 137.8 kPa, whlle all blnary data were obtalned at 137.8 kPa. The I-C4Hlo-C,H, system at 298 and 323 K and the C2H4-C02 system at 298 K were found to be highly nonldeal In their behavlor-they exhlblt adsorptlon azeotropes. Methods for predlctlng gas-mlxture adsorptlon data from the pure-component Isotherms were evaluated. Only the vacancy solutlon model was able to predlct the areotroplc behavlor even qualltatlvely. I ntroductlonGas adsorption on sdid surfaces is an important unit operation for the separation of gases. The technology of adsorption, however, is less advanced than that of other common separation processes such as distillation, extraction, and absorption. The complexity of adsorption phenomena and the lack of accurate and complete experimental adsorption data have been major factors in inhibiting developments in adsorption technology.Molecular sieves (zeolites) have been widely used as adsorbents because of their selectivity, adsorption capacity, and thermal and chemical stability. I n practice, adsorption processing involves the treatment of multicomponent mixtures. Very few experimental data are available for adsorption systems which exhibit highly nonideal behavior. The systems reported in this paper are quite nonideal-they have adsorption azeotropes. Thus, they should be quite useful for evaluating and developing adsorption equilibrium models. Three such models are evaluated herein. Experlmental SectionApparatus. The apparatus was of the volumetric type and used the difference technique for determining adsorbed-phase compositions. The total quantity of each gas admitted to the adsorbent and the amount of each gas remaining in the vapor phase after adsorption equilibrium had been established were determined by P -V -T measurements, and an analysis of the remaining vapor phase was determined by gas chromatography. The adsorbed-phase parameters were then determined by the difference between the quantities of admitted and remaining gases. Details of the equipment and the operating procedure are described in the paper by Dorfman and Danner (1).Maferlals. The adsorbent was molecular sieve type 13X in the form of '/i6-in. pellets manufactured by the Linde Division of Union Carbide (Lot No. 13945390174). This sieve contained 20% by weight of an inert clay as a binding material. The unit cells of 13X molecular sieve are cubic with a large cell dimension of nearly 25 A. The pore volume as determined by adsorption from n-pentane at 25 OC by Breck (2) is about 0.3 cm3/g. The surface area determined by the BET method using nitroqen at 77 K is 525 m2/g (2). For the pellets used in this 0021-9568/82/ 1727-0196$01.25/0 study, these values had to be decreased by 20% to account for the inert binder. A differential thermal analysis of the adsorbent indicated t...

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New equations for the physical adsorption of gases on solids have been developed based on the vacancy solution model of adsorption in conjunction with the Flory-Huggins activity coefficient equations. The isotherm equation contains three regression parameters: a Henry's law constant, the limiting amount of adsorption, and a gas-solid interaction term. Pure-gas data over a range of temperature can be correlated using only five parameters. Gas-mixture equilibria can be predicted using only the parameters obtained from the pure-gas data. Pure-component, binary, and ternary adsorption equilibrium data on activated carbons, silica, and zeolites over a wide range of conditions have been used to evaluate the model. The results show that, except for a few systems, this model predicts gas-mixture equilibria better than any other model. SCOPEIn order to exploit the physical adsorption of gases in separation processes, quantitative characterization of the multicomponent adsorption equilibria are needed as functions of temperature and pressure. Experimental multicomponent adsorption data are difficult and tinie-consuming to obtain; therefore, a reliable method of predicting multicomponent equilibria at various temperatures and pressures from purecomponent adsorption data, and if necessary binary mixture data, would be preferred. Suwanayuen and Danner (1980a, b) proposed a vacancy solution model using the Wilson model for the activity coefficients. Although this approach has been successful for the prediction of isothermal multicomponent equilibria from single-gas isotherms alone, it fails to explicitly include the effect of temperature. Also, the equations in the Suwanayuen and Danner (S&D) model are complex, and it is often difficult to obtain physically significant parameters from the regression of limited isothermal data sets.The objective of this work was to develop a new gas adsorption model based on vacancy solution theory which corrects the deficiencies inherent in the S&D model and surpasses it in accuracy. Any new model should account for nonideal behavior in the adsorbed phase including the adsorbate-adsorbate interactions and should predict the temperature dependency of the equilibria as well as the pressure and compositional dependencies. The model should be flexible enough to allow the use of binary data to characterize the adsorbate-adsorbate interactions if such data are available and if such binary parameters are needed. Preferably the model should include a method of estimating these adsorbate-adsorbate parameters, thus eliminating the need for the binary data which are seldom available and difficult to obtain experimentally. The model presented in this paper meets these criteria. CONCLUSIONS AND SIGNIFICANCEA new model for pure-and multicomponent gas adsorption is developed based on the vacancy solution theory as presented by Suwanayuen and Danner (1980a, b). Activity coefficients based on a Flory-Huggins type expression have been introduced to account for the nonideality in the adsorbed phase. By regress...

A new Isotherm equation for pure gas adsorption is developed and tseted. In the new method, the adsorption equilibrium is treated as an osmotic equilibrium between two “vacancy” slutions having different compsoitions. One solutions represents the gas phase and the other the adsorbed phase. The vacancy solution is composed fo adsorbates and vacancies. the latter is an imaginary entity defined as the vacuum space which acts as the solvent for the system. Thermodynamic equations governignt he euilibrium of this system are used to derive the equation of state for the adsorbed phase. The non‐ideality of the adsorbed solution is accounted for in terms of an activity coefficent whose compsotion dependence is decribed by the Wilson equation. The equation of state, together the Gibbs adsorption equation, is then used in the derivaion of the adsorption isotherm equation. The developed correlation has been evalued with the adsorption isotherm data of O2, N2, and CO on zeolite 10X at 144.3 K, 172.0 K, 227.6 K and 273.2 K, and that of CH4, C2H2, C2H4, C2H6, C3H8, nC4H10, and CO2 on Nuxit‐AL activated carbon at 293.2 K, 313.2K, 333.2 K and 363.2 K. For both adsorbents, the correlations are better than those obtained by any other adsorption model which has been extended to gas mixtures. The parametes obtained from the pure component data can be use to predict a priori, gas‐mixture equilibria.

A new correlation that improves predictions of gas mixtrue adsorption equilibria from single‐component adsorption isotherm data is eveloped, based on the vacancy solution theory. In this theory, the adsorbed phase and the gas phase are treated as two cavancy solutions. The vacancy is an imaginary solvent occupying spaces that will be filled by adsorbates. The composition relationship between the two phases is derived from thermodynamic equilibrium criteria. The non‐ideality of the absorbed solution is accounted for by an acitivity coefficient, whose composition dependence is described by the Wilson equation. For an adsorption system, the binary parameters, adsorbate and vacancy, can be obtained from regression of the pure gas adsorptio data with the cavancy solution isotherm equation. These parameters are then used to predict multicomponent adsorption equilibirum, assuming hat the adsorbate‐adsorbate interactions are negligible. The new correlation has been tested on two different kinds of binary adsorption systems. The new method is more geneeral, simpler to apply, and more accurate than other available models. The predictions can be further improved by taking into account the assorbate‐adsorbate interactions.

Pure gas adsorption isotherms of ethane and ethylene on 13X molecular sieves were determined at 25 and 50 °C. Data for the binary adsorption equilibria of these two gases were collected at the same temperatures and a pressure of 1033.9 mmHg (20 psia). With these data, models based on the following types of approaches have been evaluated: assuming the adsorbed phase is a thermodynamically ideal solution, assuming the adsorbed phase has a quasicrystalline structure (lattice solution model), treating the adsorbed phase as a two-dimensional gas, and applying simplified statistical thermodynamics to the adsorption process. For these systems the thermodynamically ideal adsorbed solution model gave the best results overall, while the two-dimensional gas model and the statistical thermodynamic approach also gave reasonably good predictions.

Theories based on free-volume concepts have been developed to characterize the self and mutual-diffusion coefficients of low molecular weight penetrants in rubbery and glassy polymer-solvent systems. These theories are applicable over wide ranges of temperature and concentration. The capability of free-volume theory to describe solvent diffusion in glassy polymers is reviewed in this article. Two alternative free-volume based approaches used to evaluate solvent self-diffusion coefficients in glassy polymer-solvent systems are compared in terms of their differences and applicability. The models can correlate/predict temperature and concentration dependencies of the solvent diffusion coefficient. With the appropriate accompanying thermodynamic factors they can be used to model concentration profiles in mutual diffusion processes that are Fickian such as drying of coatings. The free-volume methodology has been found to be consistent with molecular dynamics simulations. INTRODUCTIONThe diffusion of small molecules in polymers is of considerable practical importance and has been studied extensively. Diffusion theories based on the free-volume concept have been used extensively to correlate and predict solvent self-diffusion coefficients in rubbery polymersolvent systems.1-6 These methods provide accurate predictions over a wide range of temperatures and concentrations above the glass transition temperature of the pure polymer. As polymer solutions are cooled over practical time scales, the rate of cooling exceeds the rate of relaxation of the polymer, and a nonequilibrium state referred to as the glassy state results. This phenomenon causes volume to be trapped in the polymer in excess of that expected at equilibrium. Free-volume theory presumes that this extra volume is available to facilitate mass transport in the glassy state. Based on this concept, the original free-volume theory was adapted to describe the diffusion of a trace amount of a solvent in a glassy polymer, 7,8 and it was further extended to describe self-diffusion below the mixture glass transition temperature at finite concentrations of the solvent.