We developed a method for the solution of the compressible flow with mass transfer of semi-continuous mixtures and it is based on the quadrature method of moments (QMoM) for continuous thermodynamics. The method extends the adaptive characterization of the continuous mixture to field problems and solves the mass transport equation for the continuous component. The method is referred as direct QMoM, or DQMoM, for continuous thermodynamics. It was implemented in the Open FOAM (R) as a compressible ideal gas flow solver. The DQMoM was applied to the mixing flow of two gas streams with different compositions of a mixture with 57 hydrocarbons diluted in nitrogen. We showed that 4 adaptive components reproduced the mixture properties within 3% accuracy. Furthermore, the DQMoM CFD solution was approximately two times faster than the solution using 58 discrete components. (C) 2014 Elsevier Ltd. All rights reserved.