In this study divided in a series of three articles, the model for pure CO2 hydrate by Jager et al. [Fluid Phase Equilib. 338 (2013) 100-113] has been improved and extended to other gases relevant in Carbon Capture and Storage (CCS) applications. The new hydrate model is inspired by the model for natural gas hydrates by Ballard and Sloan [Fluid Phase Equilib. 194 (2002) 371-383], which belongs to the family of van der Waals and Platteeuw (vdWP) models [Adv. Chem. Phys. 2 (1959) 1]. The new model is combined with highly accurate equations of state (EoS) in form of the Helmholtz energy for fluid phases and with Gibbs energy models for pure solid phases. In part I, a critical analysis of the main parameters of the vdWP-based hydrate model was performed. A multi-property fitting algorithm developed for optimization of parameters of the new hydrate model is introduced in part II. Results of the model, including phase equilibria with hydrates, composition of hydrates, and enthalpy of formation of hydrates are provided in this article (part III). The model results are for most hydrate formers better or comparable to the results of the model of Ballard and Sloan. However, for ethane hydrates the overall results are worse which is discussed in the results section. The model has been implemented in the software package TREND 2.0 by Span et al. [Thermodynamic Reference and Engineering Data 2.0. (2015) Lehrstuhl fuer Thennodynamik, Ruhr-Universitaet Bochum]. Example calculations with the new hydrate model implemented in TREND 2.0 and applied to CCS-relevant problems are shown and discussed. (C) 2016 Elsevier B.V. All rights reserved.