A Reconciliation of Packed Column Permeability Data: Column Permeability as a Function of Particle Porosity

Table 2

Cross-reference for terms.

														𝐾𝐹
Particle/column description	𝜀𝑡	Φ	𝜀0	𝜀𝑖	𝜀𝑝	Δ𝑃	𝜙	𝜙0	Ψ	Ψ0	𝑘0	𝑃0	𝑃𝑡	𝑘	𝐿	𝐷	Ω𝑝	𝑑𝑝𝑚	𝑑𝑝	𝜂	𝑄	𝜇𝑠	𝜇𝑖	𝜇𝑡
			𝜀𝑡Φ	(𝜀𝑡−𝜀0)	𝜀𝑖		Δ𝑃𝑑𝑝^2	Δ𝑃𝑑𝑝^2	(1−𝜀𝑡Φ)^2𝜀𝑡	(1−𝜀0)^2	1	𝜙	𝑃0𝜀𝑡	𝑑𝑝^2𝜀𝑡					(𝑑𝑝𝑚Ω𝑝)
					(1−𝜀0)		𝜇𝑡𝜂𝐿	𝜇𝑠𝜂𝐿	(𝜀𝑡Φ)^3	(𝜀0)^3	𝜙	Ψ		𝜙						poise
Units	None	None	None	None	None	psi	None	None	None	None	None	None	None	cm^2	cm	cm	None	cm	cm	gcm^−1 sec^−1	cm^3 min^−1	cm sec^−1	cm sec^−1	cm sec^−1
Nonporous particles
Giddings' traditional nonporous column	0.400	1.000	0.400	0.000	0.000	135	601	1,502	2.250	5.63	1.66𝐸−03	267	107	6.66𝐸−10	15	0.46	1.0	0.0010	0.0010	0.010	0.399	0.040	0.100	0.100
Guiochon's traditional spherical particle (apparent)	0.362	1.000	0.362	0.000	0.000	187	830	2,293	3.106	8.58	1.20𝐸−03	267	97	4.36𝐸−10	15	0.46	1.0	0.0010	0.0010	0.010	0.361	0.036	0.100	0.100
Gidding's table 5.3-1
50/60 mesh glass beads	0.422	1.000	0.422	0.000	0.000	113	500	1,184	1.873	4.44	2.00𝐸−03	267	113	8.44𝐸−10	15	0.46	1.0	0.0010	0.0010	0.010	0.421	0.042	0.100	0.100
50/60 mesh glass beads	0.409	1.000	0.409	0.000	0.000	126	560	1,371	2.097	5.13	1.79𝐸−03	267	109	7.29𝐸−10	15	0.46	1.0	0.0010	0.0010	0.010	0.407	0.041	0.100	0.100
Guiochon's teaching
Ex. A irregular particle (apparent)	0.400	1.000	0.400	0.000	0.000	225	1,000	2,500	2.250	5.63	1.00𝐸−03	444	178	4.00𝐸−10	15	0.46	1.00	0.0010	0.0010	0.010	0.399	0.040	0.100	0.100
Ex. A corrected for particle irregularity	0.400	1.000	0.400	0.000	0.000	225	601	1,502	2.250	5.63	1.66𝐸−03	267	107	4.00𝐸−10	15	0.46	0.78	0.0010	0.0008	0.010	0.399	0.040	0.100	0.100
Ex. B spherical particle (apparent)	0.400	1.000	0.400	0.000	0.000	187	830	2,075	2.250	5.63	1.20𝐸−03	369	148	4.82𝐸−10	15	0.46	1.00	0.0010	0.0010	0.010	0.399	0.040	0.100	0.100
Ex. B corrected	0.400	1.000	0.400	0.000	0.000	135	601	1,502	2.250	5.63	1.66𝐸−03	267	107	6.66𝐸−10	15	0.46	1.00	0.0010	0.0010	0.010	0.399	0.040	0.100	0.100
Porous particles
Giddings' traditional porous column	0.600	0.667	0.400	0.200	0.333	203	900	1,500	3.375	5.63	1.11𝐸−03	267	160	6.67𝐸−10	15	0.46	1.00	0.0010	0.0010	0.010	0.599	0.060	0.150	0.100
Gidding's table 5.3-1
30/40 mesh alumina	0.803	0.498	0.400	0.403	0.672	271	1,204	1,499	4.510	5.62	8.30𝐸−04	267	214	6.67𝐸−10	15	0.46	1.00	0.0010	0.0010	0.010	0.801	0.080	0.201	0.100
50/60 mesh alumina	0.837	0.499	0.417	0.420	0.721	235	1,043	1,246	3.906	4.67	9.59𝐸−04	267	224	8.03𝐸−10	15	0.46	1.00	0.0010	0.0010	0.010	0.835	0.084	0.201	0.100
60/80 mesh chromosorb W (5% DNP)	0.766	0.498	0.382	0.384	0.621	316	1,404	1,833	5.259	6.87	7.12𝐸−04	267	204	5.45𝐸−10	15	0.46	1.00	0.0010	0.0010	0.010	0.764	0.077	0.201	0.100
60/80 mesh chromosorb W (20% DNP)	0.785	0.495	0.389	0.396	0.648	300	1,333	1,698	4.991	6.36	7.50𝐸−04	267	210	5.89𝐸−10	15	0.46	1.00	0.0010	0.0010	0.010	0.783	0.079	0.202	0.100