Abstract—To develop and design the supercritical fluid dyeing (SFD) process a lot of basic dye solubility data and modeling of these solubility data are necessary. The solubility of six blue dispersed dyes, C.I. Disperse Blue 134, CI. Disperse Blue 79, C.I. Disperse Blue 79:1, C.I. Disperse Blue 3, C.I. Disperse Blue 60 and C.I. Disperse Blue 14 in supercritical carbon dioxide have been correlated with two equation of state. All critical properties have been estimated with a group contribution method (GCM). Solubility data for these dyes has never been correlated using an equation of state (EOS). Therefore, it is worthwhile to model the solubility of these dyes with EOSs. In this work, the aim is correlating reported data with a new EOS and comparing obtained results with the results of Peng-Robinson EOS (PR-EOS) together with two adjustable parameter van der Waals mixing and combining rules. The calculated results showed that new EOS is more accurate than PR-EOS. It can be employed to speed up the process of SCF applications in industry. Index Terms—Dispersed Blue Dye, Solubility, Supercritical Fluid, Equation of State (EOS), Modeling. I. INTRODUCTION In the past decades, there has been an increasing interest in the use of supercritical fluids as an alternative to the use of organic solvents in many industrial applications, such as in chemical and biochemical reactions, extraction and purification processes, particle production, textile industry, etc[1-12]. Since the dyeing industry uses water as a dyeing medium and a lot of dispersing agents and surfactants to overcome the inherent hydrophobicity of the textile and the dye, it discharges a lot of hard-to-destroy (very little biodegradable) wastewater. To reduce the environmental pollution problem, supercritical carbon dioxide is considered as a potential alternative dyeing medium to water as it is inherently nontoxic and does not require any dispersing agents and surfactants in the dyeing process. Furthermore, a lot of energy (roughly 50%) can be saved in the supercritical fluid dying (SFD) process, as it requires neither the washing step nor the drying step, whereas the conventional wet-dyeing process requires both steps [13-19]. Manuscript received June 29, 2011; revised July 20, 2011. School of Chemical Engineering, College of Engineering, University of Tehran, P.O. Box 11365-4563, Tehran, Iran Caspian Faculty of Engineering, College of Engineering, University of Tehran, Iran Corresponding author: Shahryar Jafari Nejad, E-mail: shjafarinejad@ut.ac.ir Supercritical carbon dioxide is the most commonly used supercritical fluid. The critical temperature and pressure of carbon dioxide is relatively low (304 K and 73.7 bar, respectively) [20] and one of the most environmentally acceptable solvents in use today, and textile processes using this solvent have many advantage when compared to conventional aqueous processes [21]. Supercritical carbon dioxide gives an option avoiding water discharge, it is low in cost, nontoxic, and nonflammable, and the carbon dioxide can be recycled. Also, when dying from an aqueous medium, reduction clearing is carried out to stabilize the color intensity, producing further water waste. Reduction clearing is not carried out following supercritical dyeing. Supercritical carbon dioxide also has other advantages. The application of the dye to the fabric can be controlled and a better quality of application achieved [22, 23]. The dyes used in supercritical dyeing are the nonionic, so-called disperse dyes. To develop and design the supercritical fluid dyeing (SFD) process a lot of basic dye solubility data and modeling of these solubility data are necessary. Disperse Dyes for dyeing polyester textile is divided into two groups: Azo and anthraquinone derivatives [24-26]. In the mathematical modeling of solubility data in supercritical fluids, one should keep in mind that the solubility systems can be categorized in three groups, a single solute in a supercritical fluid, mixed solutes in a supercritical fluid and a single solute in mixed supercritical fluids or supercritical fluid plus an organic solvent. Different equations have been presented for mathematical modeling of solubility data in SC CO 2 . One can categorize these models into two groups, theoretical or semi-empirical equations (similar to models based on equations of state) and empirical equations (such as density based equations). Models derived from equations of state need complicated computational procedures that are not provided in commonly used commercial software. Also, these models employ the solute properties, such as critical properties, acentric factor, molar volumes and vapor pressure, which often cannot be easily determined experimentally. The numerical values of the solute properties can affect solubility predictions using models derived from equations of state [27]. To avoid some of these difficulties as well as more complicated computational routines, most authors opt to use empirical correlations such as density-based correlations (Chrastil, Bartle, M´endez-Santiago–Teja, Jafari Nejad et al. and etc. models), or the Ziger–Eckert semi-empirical correlation. These models are based on simple error minimization using least-squares methods, and for the majority of them, there is no need to estimate and use critical and thermophysical Modeling of Solubility of Disperse Blue Dyes in Supercritical carbon Dioxide Using Equation of States (EOSs) Shahryar Jafari Nejad, Milad Asgarpour Khansary, and Farshad Amiri International Journal of Chemical Engineering and Applications, Vol. 2 , No. 4 , August 2011 272