J. of Supercritical Fluids 55 (2010) 455–461 Contents lists available at ScienceDirect The Journal of Supercritical Fluids journal homepage: www.elsevier.com/locate/supflu Critical behavior of pure confined fluids from an extension of the van der Waals equation of state Leonardo Travalloni a , Marcelo Castier b,∗ , Frederico W. Tavares a , Stanley I. Sandler c a Escola de Química, Universidade Federal do Rio de Janeiro, C.P. 68542, CEP 21949-900, Rio de Janeiro, RJ, Brazil b Department of Chemical and Petroleum Engineering, United Arab Emirates University, P.O. Box 17555, Al Ain, United Arab Emirates c Department of Chemical Engineering, University of Delaware, 19716-3110, Newark, DE, USA article info Article history: Received 13 April 2010 Received in revised form 12 September 2010 Accepted 15 September 2010 Keywords: Confined fluid State equation Critical point Adsorption abstract The critical behavior of pure fluids confined in porous solids is investigated using an extension of the van der Waals equation of state. The effects of pore size and of the interaction between fluid molecules and pore walls are evaluated. Fluid molecules were assumed spherical, interacting with each other and with the walls of cylindrical pores through distinct square-well potentials. It was found that our model may predict either one or two mechanically stable critical points for the confined fluid, depending on its specifications. When two critical points are predicted, one is attributed to a major contribution of molecule–molecule interactions and the other to a major contribution of molecule–wall interactions. The confined fluid critical point(s) presented a complex dependence on the pore size, due to the interplay of molecule–molecule and molecule–wall interactions. It is shown that the prediction of two critical points for confined fluids is useful to describe adsorption isotherms with two phase transitions. © 2010 Elsevier B.V. All rights reserved. 1. Introduction The thermodynamic behavior of fluids confined in porous media is a subject of fundamental importance to many indus- trial applications, such as oil extraction, separation processes, and heterogeneous catalysis. In particular, the knowledge of the equi- librium phase behavior and the critical properties of confined fluids is required for the design and optimization of such processes. Confinement changes the fluid behavior due to the geometric con- straint of the fluid molecules and the interaction of these molecules with the pore walls (the molecule–wall interaction). Experimental results suggest that a confined fluid has a depressed critical tem- perature and an increased critical density compared to its bulk properties [1–4]. Moreover, some results indicate that the crit- ical temperature shift increases linearly with inverse pore size [5,6]. The effect of confinement on the fluid critical properties has also been investigated by theory and molecular simulation, giving rise to several interesting predicted behaviors. The linear rela- tion between the critical temperature shift and the inverse pore size was corroborated by both lattice gas modeling and molecu- lar simulation [7], but nonlinear relations have also been observed ∗ Corresponding author. Currently at: Texas A&M University at Qatar, on leave from the Federal University of Rio de Janeiro, Brazil. Tel.: +974 44230534; fax: +974 44230065. E-mail address: marcelo.castier@qatar.tamu.edu (M. Castier). in recent simulations [8–10]. Theoretical and simulation results for the confined fluid critical density suggest that it increases under confinement in attractive pores, but the inverse occurs in purely repulsive pores [11–14]. However, nonmonotonic relations between the critical density and the pore size have been found for both pore types [7,9,10]. The dependence of the confined fluid crit- ical point on the strength of the molecule–wall interaction has also been studied. There are recent reports of a nonmonotonic behavior for the critical temperature, with a maximum at an intermediate value of the molecule–wall interaction strength, while the crit- ical density seems to increase monotonically with this strength [15–17]. Some authors have focused on developing analytical equation of state models in the attempt to describe the thermodynamic behavior of confined fluids with low computational effort [18–23]. Extensions of the van der Waals equation of state to confined fluids have been shown to predict the critical temperature reduction with pore size reduction either qualitatively [18,22] or quantitatively [20], and a positive shift in the critical density could be predicted with this approach [22]. In our previous work [23], the van der Waals equation of state was extended to confined fluids based on the generalized van der Waals theory [24,25]. It has been found that the proposed model is able to describe different types of adsorp- tion isotherms and to correlate experimental data of pure fluid adsorption quite well. In this work, the critical behavior of pure con- fined fluids as predicted by this model is investigated. The effects of pore size and of the intensity of the molecule–wall interaction are evaluated. 0896-8446/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.supflu.2010.09.008