The nature of nonlinear flow in porous media is analyzed by means of the volumetric averaging approach for a medium modeled by diverging/converging capillaries. To clarify the mechanism responsible for the nonlinearity, a physical explanation is deduced for the dispersion term in the averaged momentum equation. With the present periodical model, the numerically obtained microscopic flow fields, in association with the macroscopic coefficients calculated by the average momentum balance, indicated quantitatively that the microscopic inertial phenomena, which lead to distorted pore velocity and pressure fields, is the fundamental reason for the onset of nonlinear effects as filtration velocity increases.