Improving the accuracy of predicting effectiveness factors for mth order and Langmuir rate equations in spherical coordinates

Char oxidation is often modeled using an mth order intrinsic reaction rate in conjunction with an effectiveness factor (eta) to account for intraparticle diffusion of gas species. This approach involves the use of a general modulus (MT) and using the first-order curve of eta vs MT. This method was originally referred to as the general asymptotic solution. It has been suggested that a simple Langmuir rate equation is more suitable for modeling the effects of pressure on char reactivity. Therefore, several methods of developing general moduli for the Langmuir rate expression are shown. The general asymptotic solution is most accurate as MT approaches the limits of zero and infinity. However, in the intermediate range of M-T (0.2 < M-T < 5), the general asymptotic solution exhibits errors of up to -17% error in spherical coordinates and -24% error in Cartesian coordinates. A correction function was constructed to improve the accuracy of predictions in the intermediate range of general modulus for both the mth-order and the Langmuir rate equations, The general asymptotic solution, combined with this correction function, is able to predict the effectiveness factor for all mth-order (0 <= m <= 1) and Langmuir rate equations within +/-2%. The observed reaction order of char oxidation has been reported to change as a function of temperature, with limits of 0 and 1. A theory has been developed to quantitatively explain and predict this change of reaction order based on the Langmuir rate equation in conjunction with the effectiveness factor approach.