OCR Text |
Show in internal surface area which occur during devolatilization and char combustion. Thus the reaction rate can change with heat-up conditions or during the course of a burn. Analytical treatment of such situations can be extremely complex, and it is frequently advantageous to deal with this empirically. Combining Mass-Transfer and Chemical-Reaction Rates In many cases, the rates of external mass transfer and intrinsic chemical reaction are of approximately the same order of magnitude. This results in a condition in which the surface concentration of oxygen is intermediate between 0 (pure mass transfer control) and C, (pure chemical control). In order to calculate the combustion rate, it is necessary to use the steady-state approximation (i.e., set the rates of mass transfer and chemical reaction equal) and algebraically eliminate the surface concentration. Young and Smith (10) show that in the general case, this can be done to obtain the following expression: R = Rc [l-CR/R^,)]11, (7) where R is evaluated at the bulk oxygen concentration and R^ is calculated from Eq. (4). Thus Eq. (7) can be solved iteratively for R. Another form of Eq. (7) which is sometimes useful is R = R^ [l-(R/Rc)1/n]. (8) The effects of uncertainties in estimating R and R can be minimized by using Eq. (7) when R/Rwrp <0.5 and Eq. (8) when R/R*^ > 0.5. Estimation of Char Burnout Time The combustion rate is sometimes difficult to measure directly, and many investigators have used char burnout time instead. Burnout time can be a useful design parameter since it directly indicates the 3 |