<p> Rate of adsorption data for gases on molecular sieve·s and coals
have been interpreted using equations for unsteady state diffusion derived
from Fick's law for spheres usually, ignoring the amount adsorbed and the
shape of the adsorption isotherm. These inappropriate equations result
in calculated diffusivities that are too low and activation energies that
are too large. </p> <p> Numerical. solutions of Fick's law were made for diffusion and
adsorption in a porous sphere of radius R by finite difference methods
for the following conditions:
a. Diffusion is the rate-controlling step, and the diffusivity, D,
is constant.
b. Within an increment of the particle the total amount of adsorbate
per unit volume, T is related to the "effective" concentration, c,
by a Langmuir-like isotherm T = abC/(1 + bC).
c. At zero tine the particle containing no adsomate is surrounded by
adsozbate of concentration, Co, which remains constant throughout the rate process, and d. Equilibrium is established immediately at the periphery of the
sphere. </p> <p> The solutions are obtained in terms of Z = Q/Q and T=(DCo/QR^2) t = kt, where t is time, k is a constant equal to the term
within the brackets, and Q and Q are the amounts adsorbed per unit
volume at time t and at equilibrium. The quantity within brackets is
also a valid expression for linear and Freundlich-like adsorption
isotherms and probably holds for other isotherms. Plots of z as a function
of T shift systematically as the parameter B = bCo increased from 0,
corresponding to a linear adsorption isotherm, to large values; the
value of Z at a given T increasing with increasing values of B. For
B = 0 the numerical solution is identical with analytical solution for
the linear adsorption isotherm which for values of z <0.87 is given by
kt = (2/π) { (-1 - πZ/6) - (1 ~πZ/3) ^1/2 }
where k = DCo/R^2Q. For large values of B the numerical solutions
approach as a limit the parabolic law kt = (1/2) {(1- 2Z/3) - (1- Z) }
The value of (1/k~) o.zidt~ at short times increases fran 3.385 for
B = 0 to 4 .. 243 for very large values of B.. From experimental data the value
of k derived using the equation for B = 0 is 1.56 larger than for the
parabolic equation. Hence the values of D obtained from the initial linear
portions of t.he rate curve change by only a factor of 1.56 when the type
of isotherm is changed from linear to rectangular. </p> <p> Rates of adsorption and the adsorption isotherm were determined for N2 , CH4, co2 , and C2H6 on samples of Linde 4A molecular sieve at
several temperatures from -78° to +50°C in a manostatic volumetric aborption apparatus. The Langmuir equation satisfactorily approximatedthe isotherms and the values of B were moderately large at the lower temperatures of each series of experiments, eg., for N2 at -78°C,
10.6; for CH4 at -78°C, 7.3; for co2 at 0°C, 64; for Ci!6 at 0° and 30°C,
37 and 10.3. </p> <p> The rate data plotted as Z against t^1/2 were not linear at short
times but curved upward initially before becoming linear. The initial
(, nonlinear portion persisted significantly longer than the brief uncertain
period at the beginning of the experiment. This phenomena could result
from the equilibration at the periphecy of the particles requiring a finite
time rather than being instantaneous. </p> <p> An equation based on the parabolic law model and a first order equilibration process was derived, which fits. the experimental data for
0.05 < Z < 0.95. This equation is appropriate only to data with a
large value of B, but is probably a reasonable approximation for other
rate data. </p> <p> The rates of adsorption for different molecules were co2 > N2
> CH4 > c2H6 · The activation energies for the diffusivity were
found to be 4.1 and 6.0 kcal./nole for methane and ethane. The _heats
of adsorption were found to be 7.2 and 8.3 kcal/mole for methane
and ethane. </p> / Thesis / Master of Engineering (MEngr)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/20240 |
| Date | 10 1900 |
| Creators | Stifel, George |
| Contributors | Anderson, Robert, Chemical Engineering |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
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