The study used the advection – diffusion equation to simulate the concentration of crude oil spilled on surface water as it disperses in the oil rich Niger Delta area of Nigeria. An assumed amount of crude oil spilled was considered which is the Idoho oil spill of 1998 of about 40,000 barrels (5440000 kg). Also varying values of distances, time, diffusion coefficient and the speed of the river were considered which is peculiar to the Niger Delta environment. The effect of distance, time, diffusion coefficient and the speed of the flowing were also discussed. These parameters have distinct effect on the concentration of oil spilled as it disperses. For a given diffusion coefficient and at a given distance, the concentration of the spill increases with time up to a certain maximum value and then begins to decrease very slowly. Also, on the effect of speed at a given diffusion coefficient and at a given distance, the concentration of the spill increases swiftly and then decreases with time.