We present a new compressive scheme to simulate species transfer across fluid interfaces using the Volume-Of-Fluid method. We show that at high Peclet numbers, the standard Continuous Species Transfer (CST) generates large numerical diffusion in the phase concentration that can lead to inaccurate simulation of interface exchanges in a two-phase system. To solve this issue, the derivation of the concentration advection flux is revisited. We obtain an additional compressive term in the species concentration equation. This novel approach is labelled Compressive CST approach (C-CST). The method and the input of the compressive term are validated by comparison with analytical solutions of two-phase flow and species transport in a 1D tube. The C-CST approach reduces significantly the numerical errors. Then, the approach is used to investigate and upscale species transfer during drainage in 2D porous media. (C) 2018 Elsevier Ltd. All rights reserved.