Estimation of efficiency for aged catalysts

A method for estimating an efficiency of a catalyst in an exhaust of an engine, comprising:

• ageing the catalyst consecutively at different temperatures for definite time periods;
• measuring the catalyst conversion efficiency after each ageing step;
• calculating an ageing factor for each step of an ageing procedure and an accumulative value of the ageing factors for all steps of the ageing procedure based on a formulation AF=Σi(e(−E/RTi)dti) whereby E/R=activation energy of a sintering process, Ti=catalyst temperature over an i-th time interval over a catalyst lifetime and dti=length of the i-th time interval over the catalyst lifetime;
• estimating an activation energy of an ageing process (Ea/R) for the catalyst;
• estimating catalyst efficiency correlation factors related to the measured catalyst conversion efficiency for each temperature point and for all ageing conditions;
• determining a correlation between the catalyst efficiency correlation factors and the accumulative value of the ageing factors;
• calculating the conversion efficiency of the aged catalyst based on a predetermined correlation between the accumulative ageing factor and the catalyst efficiency correlation factor, obtaining the catalyst efficiency correlation factors for the catalyst aged at a lowest temperature;
• and
• estimating the activation energy of the ageing process (Ea/R) and a modified reaction rate coefficient (k0′) based on the obtained catalyst efficiency correlation factors;
• and
• calculating the conversion efficiency of the aged catalyst based on the activation energy of the ageing process (Ea/R) and the modified reaction rate coefficient (k0′) together with a predetermined correlation between the accumulative ageing factor and the catalyst efficiency correlation factor, wherein a reaction rate coefficient (k0) and/or a reaction rate constant (k) and/or a relative reaction rate constant (k′) and the activation energy of the ageing process (Ea/R) are based on a formulation where the reaction rate constant is a product of the modified reaction rate coefficient and an exponential of a negative of the activation energy divided by a temperature.