Driven by both environmental and industrial motives, there is a considerable interest, extending beyond researchers, in the incorporation of environmentally friendly fluids into secondary refrigeration systems. The goal is to optimize performance from the generation phase to the point of use. The primary focus is on the study of CO \(_2\) hydrate slurries due to their advantageous properties for high-performance secondary refrigeration. Notably, their latent heat of melting is considered the highest compared to other phase change material slurries, such as ice slurry or salt hydrate slurry. The purpose of this paper is to describe the modeling task of hydrate slurry generation through a population balance equation, which accounts for particle growth and nucleation rate. We employ a 2nd-order finite volume method to solve this equation. The paper concludes by providing a brief introduction to the coupling of the population balance with the mass/thermal model to predict hydrate formation kinetics.