In this research, pollution transport in a 1-D domain with a source/sink and a retardation term is simulated using a series of completely mixed reactors. It is shown that as the volume of these reactors approaches zero, the governing equation of the system becomes identical to the advection diffusion partial differential equation. By application of mass balance to a finite number of completely mixed reactors, a set of ordinary differential equations which is equivalent to spatially discretized form of the equation is obtained in a completely natural and intuitive way. More importantly, the proposed innovative model can offer a conceptual insight into pollution transport phenomena and is flexible to any change for different problems. List of Symbolṡm in Mass flux in mass ∕ time ṁ out Mass flux out mass ∕ time dm dt Mass accumulation rate mass ∕ time Q D Diffusion flow rate volume ∕ time Q A Advection flow rate volume ∕ time C Concentration mass ∕ volume K Decay rate S −1 V Volume of reactor (volume) u Velocity distance ∕ time ±S Source/sink term (x) (t) Dirac delta function