This paper studies the dynamic mass transfer effects of solute through fluid-solid interactions in a heterogeneous system. It is found that the convective velocity in internal pores of the membrane can be used to accelerate the speed of the solute by convective velocity at the fluid phase. The theoretical model for the membrane transport is studied in this paper by using the operator theoretic method. A typical example of this dynamic interaction problem is applied in a multi-layered composite membrane. Danckwerts Boundary conditions are analyzed in the inner and outer regions of membrane process. A spectral evaluation of the transport operator is performed by the operator properties in the system. The findings of this paper are useful in guiding the design of membrane separation devices as well as in proving useful to the synthetic performance of composite membrane.