In this work, we propose a new kinetic theory model (Enskog-2 sigma model) to analyze and predict the viscosity of simple fluids. The model is based on the Enskog formulation and makes use of two effective diameters to represent two aspects of molecular interactions in Enskog's treatment; namely, the effective diameter representing the excluded volume of a molecule and the effective diameter accounting for the increased probability of collision in comparison to the dilute gas. We have tested the model by analyzing the viscosity of five simple fluids (Ar, CH4, N-2, CO2 and SF6) of increasing complexity at supercritical temperatures. The new Enskog-2 sigma model outperforms previous approaches based on Enskog theory in terms of its correlative ability. We demonstrate that the effective diameter associated with the excluded volume exhibits a universal behaviour as a function of reduced temperature. The conformal behaviour can be achieved by means of a single fluid-dependent length scaling parameter. We make use of this finding to develop a general model that allows the prediction of the viscosity of one fluid from the knowledge of the viscosity of a reference fluid, which in this work was chosen to be Ar. The accuracy of the predicted viscosity depends on the way in which the length scaling parameter was estimated. If the length scaling parameter is obtained from the knowledge of viscosity along a single isotherm, the accuracy of the predicted viscosity is similar to the uncertainty of the original correlation over its entire supercritical range. If a single viscosity value is used to estimate the length scaling parameter, the viscosities of supercritical CH4, N-2, CO2 and SF6 are predicted with the maximum deviation of 3.3%, 4.2%, 9.9% and 10.5% respectively over the entire range of validity of the Enskog-2 sigma model. (C) 2012 Elsevier B.V. All rights reserved.