Mass Transfer

Mass transfer

Mass transfer is described by a linear driving force throughout, with the overall coefficient assembled from resistances in series (Glueckauf approximation):

$$\frac{1}{K}=\underbrace{\frac{R_p}{3k_f}\frac{q^{\ast}}{c}}_{\text{film}}+\underbrace{\frac{R_p^2}{15\varepsilon_p D_p}\frac{q^{\ast}}{c}}_{\text{macropore}}+\underbrace{\frac{r_c^2}{15D_c}}_{\text{micropore}}$$

Five modes are available:

Mode	Basis
Macropore	Macropore diffusion alone, with molecular diffusion or, optionally, molecular and Knudsen diffusion in series (Bosanquet equation) using the mean pore radius $r_{pore}$
Film	External film resistance alone, with $k_f$ from Wakao & Funazkri (1978)
Micropore	Intracrystalline diffusion alone, with $D_c$ specified per component
Combined	Any combination of film, macropore (with optional Knudsen) and micropore resistances, each selected individually
Constant k	A previously fitted LDF constant entered directly, bypassing all diffusivity estimates

The crystal radius $r_c$ is a property of the adsorbent rather than of the gas, so a single value applies to both components; only the micropore diffusivity $D_c$ is specified per component.

As in every packed-bed correlation in Ruthven Ch. 7, the Reynolds number in the Wakao & Funazkri correlation is based on the superficial velocity, $Re=\rho\,(\varepsilon v_0)\,d_p/\mu$. The correlation is stated for $3<Re<10^4$; outside that range the film coefficient is an extrapolation.

The molecular diffusivity is estimated for the selected gas pair with the Fuller–Schettler–Giddings correlation and previewed live in the Mass transfer step. A Reality Check panel compares your $h_{in}$, $h_{out}$ and $k_z$ with three published correlations (Leva & Grummer 1948; Yagi & Kunii 1957; Sieder & Tate 1936), providing an independent check on fitted heat-transfer coefficients.