Understanding the thermophysical properties and phase behaviour of gas hydrates is essential for industrial applications ranging from energy transport and storage, CO2 capture and sequestration, to gas production from hydrates found on the seabed. Current tools for predicting hydrate equilibrium boundaries typically use van der Waals-Platteeuw-type models which are over-parameterised containing terms with limited physical basis. Here we present a new model for hydrate equilibrium calculations with 40% fewer parameters than existing tools but with equivalent accuracy, including for multicomponent gas mixtures and/or systems with thermodynamic inhibitors. By eliminating multi-layered shells from the model's conceptual basis and focusing on Kihara potential parameters for guest-water interactions specific to each hydrate cavity type, this new model provides insight into the physical chemistry governing hydrate thermodynamics. The model retains the improved description of the empty lattice developed recently by Hielscher et al. but couples the hydrate model with a Cubic-Plus-Association Equation of State (CPA-EOS) to describe fluid mixtures with many more components including inhibitors such as methanol and mono-ethylene glycol used by industry. An extensive database of over 4000 data points was used to train and evaluate the new model and compare its performance against existing tools. The absolute average deviation in temperature (AADT) achieved with the new model is 0.92 K for multicomponent gas mixtures, compared with 1.00 K for the widely-known model of Ballard and Sloan, and 0.86 K for the CPA-hydrates model implemented in the MultiFlash 7.0 software package. With fewer, more physically justified parameters, this new cage-specific model provides a robust basis for improved hydrate equilibrium predictions particularly for industrially-important, multi-component mixtures containing thermodynamic inhibitors.