Diffusion-absorption refrigeration (DAR) is a cooling technology that uses a three-component working fluid and a thermally-activated bubble-pump for fluid circulation. DAR cooling modules can be manufactured at low cost and entirely driven by thermal energy, making this a promising technology for cold-chain services in off-grid regions. In this work, we investigate the performance potential of an ammonia-water-hydrogen solar-DAR system for application in rural India. In Part I of the investigation, a semi-empirical system model is developed that considers both the steady-state operation of the DAR system and dynamic behaviour during start-up with a solar-thermal heat source. The model is calibrated using experimental data from a laboratory DAR system where heat input rate and system charge pressure are variables that can be adjusted. Under steady-state conditions, the system achieves a maximum coefficient of performance (COP) of 0.25 with a system pressure of 14 bar. However, at the minimum heat input rate of 100 W the system can take up to 2 h or longer for bubble pump activation, prior to which no cooling is produced. In the accompanying paper (Part II), the model is used to investigate the influence of various parameters on system performance and to identify promising areas for improvement.