The dry additive desulfurization process (DAP) is an appropriate approach for SOX-reduction in power plants with small and medium capacity and for the retrofit of existing boilers with spatial limitations. In engineering practice, it can be optimized by means of numerical modeling. In the present work, a comprehensive model for simulating the DAP in pulverized coal furnaces is established. A "pore model (PM)" is suggested to describe the gas-solid reaction between the sorbent and SOX. The overall DAP model is implemented into a coal combustion simulation CFD program "AIOLOS", because of the feature of two-phase-flow of DAP, in both Eulerian and Lagrangian (particle tracking) schemes. DAP-desulfurization in engineering processes can be simulated. Numerical studies were performed through various calculations with both Eulerian and Lagrangian approaches for a small-scale furnace. The behaviors and results of the two approaches were compared. The present DAP model offers reasonable results. In addition, it was found: (a) For sorbent particles finer than 60-70 mum, quite similar desulfurization results can be obtained from the two modeling schemes. Above this size range the slip between phases shows significant influence. (b) The CPU-time of the Lagrangian approach increases rapidly with decreasing particle size below about 30 mum. In the present study with 400 tracing particles, the Lagrangian approach requires less computing time than Eulerian above particle size of 60-70 mum. (c) The Lagrangian approach is more suitable for handling two-phase flow with detailed particle size distributions. The Eulerian approach has advantages for treating flows with finer particle suspensions. (d) The Eulerian scheme has less convergence problems, whereas. the Lagrangian approach is more sensitive to the computation procedure and requires small relaxation factors.