J. of Supercritical Fluids 32 (2004) 161–166 Modeling of adsorption equilibria in supercritical fluids Sujit Kumar Jha, Giridhar Madras ∗ Department of Chemical Engineering, Indian Institute of Science, Bangalore 560012, India Received in revised form 18 December 2003; accepted 25 December 2003 Abstract The adsorption equilibrium of various solutes on different solid matrices in supercritical carbon dioxide was modeled. The solutes were naphthalene, hexachlorobenzene, pentachlorophenol, salicylic acid, DDT, biphenyl, anthracene and 2,6-dimethyl naphthalene. The solid matrices were soil, activated carbon, ODS, ODS-2 and NaY-Type zeolite. The model is based on numerical integration of the differential equations that express the isothermal and isobaric dependence of the adsorption equilibrium constant. The residual infinite dilution partial molar enthalpy of the solutes in supercritical fluids was determined by the Peng–Robinson equation of state with quadratic mixing rules. Based on the observation that the heat of adsorption was independent of the solute, it was shown that the adsorption equilibrium constant at various temperatures and pressures could be predicted based on a single experimental adsorption isotherm. © 2004 Elsevier B.V. All rights reserved. Keywords: Adsorption; Capacity factor; Supercritical fluids; Solubility; Binary interaction parameter 1. Introduction Supercritical fluids (ScFs) are used in the food [1], phar- maceutical [2], petroleum [3] industries and in polymeriza- tions [4], biocatalysis [5] and supercritical water oxidation for the destruction of organic hazardous wastes [6]. ScFs are widely used as solvents for extraction in several applications because they are environmentally friendly, easy to separate from the extracted solute and leave no residue on the treated medium. The solid–solute interaction plays a crucial role in the extraction. Thus, the adsorption–desorption equilibria of the solute on the solid matrix is more critical than the solu- bility in the supercritical fluid [7] in the determination of the extraction efficiency. The adsorption isotherm is normally dependent on the interactions between the adsorbent and the adsorbate. However, in ScFs, the adsorption characteristics are highly influenced by the interactions between the solute and the solvent because the partial molar volumes and partial molar enthalpies of solutes in ScFs are large and negative. The knowledge of adsorption equilibria is crucial be- cause it determines the thermodynamic extent of extraction [7]. The initial study was on determining the adsorption equilibria of liquids in ScFs. The adsorption isotherms of ∗ Corresponding author. Tel.: +91-80-293-2321; fax: +91-80-360-0683. E-mail address: giridhar@chemeng.iisc.ernet.in (G. Madras). toluene-supercritical carbon dioxide (ScCO 2 )-activated car- bon (AcC) were determined [8]. The adsorption equilibrium constant decreased with increasing density, indicating that the interactions between toluene and ScCO 2 were more dom- inant compared to the interactions between the toluene and the activated carbon. The next studies were on the adsorp- tion equilibria of various solutes like naphthalene, phenan- threne, hexachlorobenzene and pentachlorophenol on soil [9] and AcC [10]. Because these studies were conducted in the retrograde region (wherein the solubility of the so- lute decreases with increase in temperature), the adsorption equilibrium constant increased with increase in temperature. Detailed studies on the adsorption equilibria of solute–solid matrix–ScCO 2 have been reported by other investigators [11–23]. Since the experimental determination of adsorption equi- libria at various temperature and pressure is difficult ow- ing to handling of equipment at high pressures, modeling and prediction of the adsorption equilibria becomes impor- tant. Wu et al. [24] modeled the adsorption equilibria of toluene-activated carbon–ScCO 2 system using real adsorp- tion solution theory (RAST) with a two suffix Margules equation to calculate the activity coefficients of the adsorbed phase. The estimation of six parameters for the model re- quires many experiments. The common technique, however, is to obtain the adsorption equilibrium constant using the van’t Hoff plot based on the adsorption isotherms at differ- 0896-8446/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.supflu.2003.12.010