Chapter 14: External Diffusion Effects on Heteregeneous Reactions

Example 11.1: Prediction of Binary Gas Diffusivities

Fuller, Schettler, and Giddings Correlation

One of the most common equations used in predicting binary gas diffusivities owing to its theoretical foundations, is the Hirschfelder-Bird-Spotz equation†. A more recent empirical correlation has been developed by Fuller‡. Fuller used 308 experimental values of the diffusivities of various gases to determine the coefficients a, b, c, d, g, and f equation

\( D_{AB} = \frac{c T^b \left( \frac{1}{M_A} + \frac{1}{M_B} \right)^{1/2}}{P \left[ \left( \sum V_A \right)^a + \left( \sum V_B \right)^g \right]^f} \)

Using a nonlinear least-squares analysis, the empirical equation that gives the smallest standard deviation is

\( D_{AB} = \frac{10^{-3} T^{1.75} \left( \frac{1}{M_A} + \frac{1}{M_B} \right)^{1/2}}{P \left[ \left( \sum V_A \right)^{1/3} + \left( \sum V_B \right)^{1/3} \right]^2} \)

where P = total pressure, atm
Mi = molecular weight
DAB = diffusivity, cm2/s
T = temperature, K
ΣVi = Sum of the diffusion volume for component i, as given in Table D-1

† See R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena (New York: Wiley, 1960), p. 511.

‡ E. N. Fuller, P. D. Schettler, and J. C. Giddings, Ind. Eng. Chem. 58(5), 19 (1966).
Several other equations for predicting diffusion coefficients can be found in R. C. Rcid, J. M. Prausnitz and T. K Sherwood, The Properties of Gases and Liquids 3rd ed. (New York: McGraw-Hill, 1977), Chap 11.

Table D-1 titled 'Special Atomic Diffusion Volumes.' It lists atomic and structural diffusion volume increments for elements like C (16.5), H (1.98), O (5.48), N (5.69), Cl (19.5), S (17.0), and aromatic rings (-20.2). It also lists diffusion volumes for simple molecules like H2 (7.07), O2 (16.6), Air (20.1), CO2 (26.9), and others. Source: Fuller, Schettler, and Giddings, Ind. Eng. Chem., 58(5), 19 (1966).

Example

Calculate the diffusivity of CS2 in air at 35°C at 1 atm

Solution

\( D_{CS_2\text{-}air} = \frac{10^{-3} T^{1.75} \left( \frac{1}{M_A} + \frac{1}{M_{CS_2}} \right)^{1/2}}{P \left[ \left( \sum V_{CS_2} \right)^{1/3} + \left( \sum V_A \right)^{1/3} \right]^2} \)

For air:

  1. VA = 20.1.
  2. 2. Molecular weight = 29.0.

For CS2, from Table D-1:

C = 16.5 C = 16.5
S = 17.0 S2 = 34.0
total 50.5

  1. VCS2 = 50.5
  2. Molecular weight = 76.

\( D_{CS_2\text{-}air} = \frac{10^{-3} (308)^{1.75} \left( \frac{1}{29} + \frac{1}{76} \right)^{1/2}}{1 \left[ (50.5)^{1/3} + (20.1)^{1/3} \right]^2} \)

\( = 0.12 \, \frac{\mathrm{cm}^2}{\mathrm{s}} \)

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