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 gas hydrate model is inspired by the currently most accurate model available 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. Part I describes a critical analysis of the main parameters of the vdWP-based hydrate model. The influences of the specific hydrate volume, of the Langmuir constant, and of the EoSs used for other phases than hydrate on the predicted hydrate composition and on phase equilibria with gas hydrates were investigated. A new correlation for the pressure dependency of the volume of gas hydrates forming structures sl and sll has been developed. The correlation based on the Murnaghan EoS [Proc. Natl. Acad. Sci. U. S. A. 30 (1944) 244] has good extrapolating behavior and behaves in a physically reasonable manner. It is shown that all experimental data for hydrate formers including mixed hydrates can be represented reasonably well by a universal bulk modulus around 10 GPa. Furthermore, it was found that the bulk modulus affects phase equilibria at high pressures while its impact on phase equilibria at moderate and low pressures below about 30 MPa is negligible. A strong influence of the Langmuir constant on the hydrate composition was observed, especially in case of small cavities of both SI and sll hydrate structures. Additionally, the influence of EoSs used for other phases than hydrate on the accuracy of quadruple point predictions is discussed. 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 part III. 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 Thermodynamik, Ruhr-Universitaet Bochum]. (C) 2016 Elsevier B.V. All rights reserved.