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 intraparti cle diffusion of gas species. This approach involves the use of a general m odulus (MT) and using the first-order curve of eta vs MT. This method was o riginally referred to as the general asymptotic solution. It has been sugge sted that a simple Langmuir rate equation is more suitable for modeling the effects of pressure on char reactivity. Therefore, several methods of deve loping general moduli for the Langmuir rate expression are shown. The gener al 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), t he general asymptotic solution exhibits errors of up to -17% error in spher ical coordinates and -24% error in Cartesian coordinates. A correction func tion was constructed to improve the accuracy of predictions in the intermed iate range of general modulus for both the mth-order and the Langmuir rate equations, The general asymptotic solution, combined with this correction f unction, is able to predict the effectiveness factor for all mth-order (0 < = m <= 1) and Langmuir rate equations within +/-2%. The observed reaction o rder of char oxidation has been reported to change as a function of tempera ture, 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 ra te equation in conjunction with the effectiveness factor approach.