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在Thiele模数很大和很小的情况下,运用摄动法可求等温下一维催化剂颗粒有效因子的渐近解.利用这两个渐近解的信息,得到一新的有效因子近似计算式:n=a_1(thφ/φ)+a_2(thφ/φ)~2+…+a_a(thφ/φ)~a该式在整个Thiele模数范围内有效,与一级反应精确解相比较,其精度十分令人满意.该式的假设考虑了系统的物理本质,因而克服了以往文献中近似式的种种不足,使之能可靠又方便地应用于实际计算.
Using the perturbation method, we can get the asymptotic solution of one-dimensional catalyst particle effective factor under the condition of large and small Thiele modulus. By using the information of these two asymptotic solutions, we get a new approximate formula of effective factor (thφ / φ) ~ 2 + ... + a_a (thφ / φ) ~ a This equation is valid over the entire Thiele modulus range, compared to the exact solutions of the first order reaction The accuracy is very satisfactory.The assumptions of this formula take into account the physical nature of the system, thus overcoming the shortcomings of the approximation in the previous literature, so that it can be reliably and easily applied to the actual calculation.