Melt transport across the ductile mantle is essential for oceanic crust formation or intraplate volcanism. Metasomatic enrichment of the lithospheric mantle demonstrates that melts chemically interact with the lithosphere. However, mechanisms of melt migration and the coupling of physical and chemical processes remain unclear. Here, we present a new thermo-hydro-mechanical-chemical (THMC) model for melt migration coupled to chemical differentiation. We study melt migration by porosity waves and consider a simple chemical system of forsterite-fayalite-silica. We solve the one-dimensional (1D) THMC model numerically using the finite difference method. Variables, such as solid and melt densities or and mass concentrations, are fully variable and functions of pressure (P), temperature (T) and total silica mass fraction (C_T^SiO₂). These variables are pre-computed with thermodynamic Gibbs energy minimisation, which shows that dependencies of these variables to variations in P, T and C_T^SiO₂ are considerably different. These P-T-C_T^SiO₂ dependencies are implemented in the THMC model via parameterized equations. We consider P and T conditions relevant around the lithosphere-asthenosphere boundary and employ adiabatic and conductive geotherms. Variation of C_T^SiO₂ changes the densities of solid and melt and has a strong impact on melt migration. We perform systematic 1D simulations to quantify the impact of initial distributions of porosity and C_T^SiO₂ on the melt velocity. An adiabatic gradient generates higher melt velocities. Reasonable values for porosity, permeability, melt and compaction viscosities provide melt velocities between 10 [cm·yr^-1] and 100 [m·yr^-1]. We further discuss preliminary results of two 2D simulations showing blob-like and channel-like porosity waves.