Accurate knowledge of the solubility limits of impurities in LNG allows an optimized design of the purification units installed upstream of the liquefaction train and the prevention of solid formation in the main cryogenic heat exchanger that would reduce the performance of the heat exchanger, increase maintenance operations and cause potential safety problems. The solubility of p-xylene in methane and in methane + ethane (5 and 10% mole fraction of ethane) has been measured at p = 5 MPa from T = 183 down to T = 123 K. The experimental results have been obtained by a static-analytic method with analysis of the fluid phase samples by gas chromatography. Solubility of p-xylene in methane and methane + ethane mixtures has been measured for the first time in this temperature range. The obtained data have been modelled by the Soave-Redlich-Kwong (SRK) cubic Equations of State (EoS), tuning pure component parameters, alpha functions, and binary interaction parameters, considering thermodynamic constraints. A robust multi-phase flash algorithm was established for vapor-liquid-liquid-solid (VLLSE) equilibrium by applying phase stability analysis. The revamped thermodynamic methods and data allow accurate prediction of the multiple phase boundaries that can be present when cooling a typical natural gas mixture.