Gupta, ShreshthaYang, YiTalei, Mohsen2026-07-232026-07-230360-3199ORCID:/0000-0001-7956-4949/work/221318918https://hdl.handle.net/1885/733813574Injecting hydrogen into natural gas pipelines offers promising opportunities for storage, transportation, and decarbonisation. However, gas mixing does not occur instantaneously, which may pose challenges for pipeline safety, custody transfer, and end-use applications. This study performs numerical simulations to model the minimum pipeline length required to attain homogeneous gas mixing. The analysis considers direct injection within a straight pipeline across a variety of injection and flow conditions, including the diameter ratio between natural gas and hydrogen pipelines, the hydrogen blending ratio, the natural gas mass flow rate, injection orientation, and pipeline temperature and pressure. Mixing is quantified by the coefficient of variation of hydrogen molar concentration, plotted against flow distance for various dimensionless parameters, such as the momentum flux ratio (M), Reynolds number (Re), Froude number (Fr), and Grashof number (Gr). A simplified correlation incorporating these dimensionless parameters has been developed using linear regression, and is calibrated for the ranges 0.01 < M < 20, 1.1 × 104 < Re < 8.5 × 104, 0 < Fr < 0.84, and 3 × 108 < Gr < 1.6 × 109. These ranges correspond to fully turbulent, moderate-pressure flow conditions, which are highly relevant to practical hydrogen–natural gas distribution networks.14en2026-08-03105044113174