Melt transport across the ductile mantle is essential for oceanic crust formation or intraplate volcanism. However, mechanisms of melt migration and associated chemical interaction between melt and solid mantle remain unclear. Here, we present a thermo-hydro-mechanical-chemical (THMC) model for melt migration coupled to chemical differentiation. We consider melt migration by porosity waves and a 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 MgO and SiO2 mass concentrations, are functions of pressure (P), temperature (T), and total silica mass fraction (urn:x-wiley:15252027:media:ggge22741:ggge22741-math-0001). These variables are pre-computed with Gibbs energy minimization and their variations with evolving P, T, and urn:x-wiley:15252027:media:ggge22741:ggge22741-math-0002 are implemented in the THMC model. We consider P and T conditions relevant around the lithosphere-asthenosphere boundary. Systematic 1D simulations quantify the impact of initial distributions of porosity and urn:x-wiley:15252027:media:ggge22741:ggge22741-math-0003 on the melt velocity. Larger perturbations of urn:x-wiley:15252027:media:ggge22741:ggge22741-math-0004 cause larger melt velocities. An adiabatic or conductive geotherm cause fundamentally different vertical variations of densities and concentrations, and an adiabatic geotherm generates higher melt velocities. We quantify differences between melt transport (considering incompatible tracers), major element transport and porosity evolution. Melt transport is significant in the models. We also quantify the relative importance of four porosity variation mechanisms: (a) mechanical compaction and decompaction, (b) density variation, (c) compositional variation, and (d) solid-melt mass exchange. In the models, (de)compaction dominates the porosity variation. We further discuss preliminary results of 2D THMC simulations showing blob-like and channel-like porosity waves.