In this proposal, the governing equations and boundary conditions of the plug flow reactor with surface chemistry are discussed (Details see Section 2). The coding part will start with the simple boundary condition (pressure constant, adiabatic, etc.). SUNDIALS IDA solver for differential-algebraic equations will be employed to solve the governing equations, further research will be done on the coding part. Timeline is also neatly showed in Section 3, and previous related projects and courses are listed in Section 4. The reasons for the project choosing are also listed in Section 5.