Page 115 - Separation process principles 2

80 Chapter 3 Mass Transfer and Diffusion

Defi was 1.0 x cm2/s. As might be expected from the Table 3.10 Diffusivities of Solutes in Crystalline Metals
effects of porosity and tortuosity, the effective value is about and Salts
one order of magnitude less than the expected ordinary mol-
MetaVSalt Solute T, "C D, cm2/s
ecular diffusivity, D, of oil in the solvent.
Ag Au 760 3.6 x lo-''
Crvstalline Solids Sb 20 3.5 x
Sb
Diffusion through nonporous crystalline solids depends
A1 Fe
markedly on the crystal lattice structure and the diffusing
Zn
entity. As discussed in Chapter 17 on crystallization, only
Ag
seven different lattice structures are possible. For the cubic
lattice (simple, body-centered, and face-centered), the dif- Cu A1
fusivity is the same in all directions (isotropic). In the six A1
other lattice structures (including hexagonal and tetragonal), Au
the diffusivity can be different in different directions Fe H2
(anisotropic). Many metals, including Ag, Al, Au, Cu, Ni, Hz
Pb, and Pt, crystallize into the face-centered cubic lattice C
structure. Others, including Be, Mg, Ti, and Zn, form Ni H2
anisotropic, hexagonal structures. The mechanisms of diffu- Hz
sion in crystalline solids include: CO
1. Direct exchange of lattice position by two atoms or W u
ions, probably by a ring rotation involving three or AgCl Agf
more atoms or ions Ag+
2. Migration by small solutes through interlattice spaces c1-
called interstitial sites KBr H2
3. Migration to a vacant site in the lattice Br2
4. Migration along lattice imperfections (dislocations),
or gain boundaries (crystal interfaces)

Diffusion coefficients associated with the first three
mechanisms can vary widely and are almost always at least
one order of magnitude smaller than diffusion coefficients in Gaseous hydrogen at 200 psia and 300°C is stored in a small,
low-viscosity liquids. As might be expected, diffusion by the 10-cm-diameter, steel pressure vessel having a wall thickness of
0.125 in. The solubility of hydrogen in steel, which is proportional
fourth mechanism can be faster than by the other three
to the square root of the hydrogen partial pressure in the gas, is
mechanisms. Typical experimental diffusivity values, taken
equal to 3.8 x moVcm3 at 14.7 psia and 300°C. The diffusiv-
mainly from Barrer [14], are given in Table 3.10. The diffu-
ity of hydrogen in steel at 300°C is 5 x lop6 cm2/s. If the inner sur-
sivities cover gaseous, ionic, and metallic solutes. The val-
face of the vessel wall remains saturated at the existing hydrogen
ues cover an enormous 26-fold range. Temperature effects partial pressure and the hydrogen partial pressure at the outer sur-
can be extremely large. face is zero, estimate the time, in hours, for the pressure in the ves-
sel to decrease to 100 psia because of hydrogen loss by dissolving
Metals in and diffusing through the metal wall.
Important practical applications exist for diffusion of light
gases through metals. To diffuse through a metal, a gas must SOLUTION
first dissolve in the metal. As discussed by Barrer [14], all Integrating Fick's first law, (3-3), where A is H2 and B is the metal,
light gases do not dissolve in all metals. For example, assuming a linear concentration gradient, and equating the flux to
hydrogen dissolves in such metals as Cu, Al, Ti, Ta, Cr, W, Fe, the loss of hydrogen in the vessel,
Ni, Pt, and Pd, but not in Au, Zn, Sb, and Rh. Nitrogen dis-
solves in Zr, but not in Cu, Ag, or Au. The noble gases do not.
dissolve in any of the common metals. When Hz, N2, and O2
dissolve in metals, they dissociate and may react to form hy- Because PA = 0 outside the vessel, ACA = CA = solubility of A at
drides, nitrides, and oxides, respectively. More complex mol- the inside wall surface in moVcm3 and CA = 3.8 x 10-~(fi)~'~,
where p~ is the pressure of A in psia inside the vessel. Let p~~
ecules such as ammonia, carbon dioxide, carbon monoxide,
be
and n~, the initial pressure and moles of A, respectively, in the
and sulfur dioxide also dissociate. The following example
vessel. Assuming the ideal-gas law and isothermal conditions,
illustrates how pressurized hydrogen gas can slowly leak
through the wall of a small, thin pressure vessel.