filter porosity can be envisioned as being made up of a series of capillary tubes under such conditions u2207 p q can be determined or calculated according to equation 1 u2207 p q u03bc u2062 2 u2062 u2062 l u2062 u2062 u025b ar h 2 equation u2062 u2062 1 u2207 p soot filter differential pressure q volumetric flow u03bc absolute viscosity a cross sectional area of filter u03b5 void fraction or porosity r h hydraulic radius of passage l length of passage the geometric parameters void fraction passage radius and length can be combined with viscosity if it is assumed constant into a single value that is a function of the soot load as described by equation 2 u2207 p q k s u2032 equation u2062 u2062 2 where k s u2032 is a value that correlates to the soot load using u2207 p q as a soot loading metric assumes that pressure loss between pressure taps is entirely from laminar wall friction viscosity is constant flow is adiabatic no heat transfer or heat source and density is constant preferred embodiments include methods systems and software which include an improved soot loading metric in a preferred embodiment the improved metric can include the effects of the turbulent pressure loss mechanism and fluid viscosity the relationship between the soot filter pressure loss coefficient c l to reynolds.