Column, inlet and outlet

Methane is commonly used as a marker for measuring the gas holdup time (tm), which was done on a capillary column 25 m long by 0.25 mm ID by 0.25 pm film thickness. A retention time for methane of 1.76 min was obtained. Determine the average linear gas velocity (v) and the average volumetric flow rate (Fc). Explain how these values differ from the actual velocity and flows at the column inlet and outlet. 

Bj2 - vi )/RT, v = the partial molar volume of the sample at infinite dilution in the stationary (liquid) phase, (1) refers to the sample, (2) to the carrier gas, (3) to the stationary liquid, and is a function of the column inlet and outlet pressures, and pQ. 

The second possibility for influencing the fluid distribution is the design of the column inlet and outlet geometry. Geometry optimisation aims to equalize all fluid streams regardless of their radial position. A conical shape was first proposed by Stahl (1967) for the zone focusing in thin-layer chromatography (Fig. 3.6). 

The result of such column inlet and outlet design is shown in Fig. 3.9. The concentration profile is plotted against dimensionless eluted volume for the cylindrical and exponential funnel. As can be seen, the exponential funnel having the same volume exhibits a much steeper peak. 

Whether the open space in the column inlet or outlet has to be filled (by packing or frit material) is not yet decided, but it seems to be much easier to operate the column with an open funnel-type column inlet and outlet. However, today s machining possibilities allow the manufacturing of the stainless steel parts with high precision at nearly all diameters. 

An alternative approach to the conical form of column inlet and outlet is the conical column. Here the whole diameter of the column is narrowed in the axial direction (Jiping et al., 2003). 

As mentioned in Section 6.2.2, with general rate models, boundary conditions for the adsorbent phase are necessary in addition to the conditions at the column inlet and outlet (Section 6.2.7). The choice of appropriate boundary conditions is mathematically subtle and often a cause for discussion in the literature. The following is restricted to the form of the boundary condition derived by Ma et al. (1996) for a complete general rate model. 

In general, the overall balance for the mass transport streams (Eqs. 6.23 and 6.24) at the column inlet and outlet has to be fulfilled. In Eq. 6.92 the closed boundary condition is obtained by setting the dispersion coefficient outside the column equal to zero. In open systems, the column stretches to infinity and in these limits concentration changes are zero. 

The boundary condition expresses the continuity of the mass flux of solutes at the column inlet and outlet. The Danckwerts [1] conditions are written... 

Boundary condition Mathematical term for the conditions which the solution of a differential or partial differential equation must satisfy at its boimdary. In chromatography, translation into mathematical terms of the conditions imposed by the experiment to the composition of the mobile phase at the column inlet and outlet (e.g., pulse injection). 

In pressure-driven systems a pressure gradient exists between the column inlet and outlet resulting in a change in volume-dependent terms over the length of the column... 

Figure 8.14. Schematic diagram of a pneumatic system retrofitted to a capillary electrophoresis instrument for capillary electrochromatography with simultaneous pressurization of the column inlet and outlet reservoirs.

Packed colunms with sintered frits (section 8.4.2) are generally operated at an elevated pressure to minimize bubble formation by applying an equal pressure to the column inlet and outlet electrolyte solution reservoirs. Pressures less than 500 p.s.i. are adequate for this purpose. A suitable setup to adapt a capillary electrophoresis instrument for use in capillary electrochromatography with pressure-equalized column operation is shown in Figure 8.14 [262]. 

Third, the conditions for scale-up from lab to process plant are constant figures for the dimensionless parameters. But in practice it is not certain that the packing of the columns is always identical. Slight variations of the void fraction and HETP may occur. Additionally, differences in the fluid dynamics, especially at the column inlet and outlet, have to be taken into account. The theoretical scale-up strategy ignores these deviations. But in order to make sure that real numbers of plates of both plants are really the same, it is recommended to determine the Van Deemter plot, void fraction, and friction number for the new packing and to correct the interstitial velocity, the flow rate, and the injection volume. 

In this experiment the same type of column was used as in Experiment 1. Experiment 2 was run for 109 days. The mean flow rate was reduced to 290 mL d for the initial 22 days and was further reduced to 150 mL d for the remaining 87 days. Concentrations were only recorded at the column inlet and outlet. As in Experiment 1 the inflow concentrations for o-xylene and toluene varied with time, with maximum concentrations of 374 pM of toluene and 478 pM of o-xylene. o-Xylene was added more or less constantly throughout the experiment, while four periods of elevated toluene concentrations were applied. Period 1 lasted from the beginning of the experiment until day 11 with a mean toluene concentration of approximately 120 pM, and periods 2 and 3 lasted from day 53 until day 74 and from day 82 until day 101, respectively, with mean toluene input concentrations of approximately 50 pM. Period 4 from day 101 until the end of the experiment (day 109) was characterized by distinctly increased input concentrations for toluene of about 300 pM. Between these periods inflow concentration for toluene were less than 10 pM. The intemiittent supply of toluene should promote the observation of the effects of toluene on o-xylene degradation. 

These net retention volumes are reduced to specific retention volmnes, V, by division of equation (1) with the mass of the hquid (here the hquid is the molten copolymer). They are corrected for the pressure difference between column inlet and outlet pressure, and reduced to a temperature Tq = 273.15 K. 

Here ns is the amount of substance of stationary liquid, pi is the saturated vapour pressure of the solute at temperature r. Bag is the mixture virial coefficient for solute 4- carrier gas interaction, Bcc is the virial coefficient of the carrier gas, Fjj is the partial molar volume of the solute at infinite dilution in the solvent, is the molar volume of pure liquid A, and pi and po are the column inlet and outlet pressures. The chemical potential at infinite dilution can be calculated by measuring the retention volume of an infinitely small sample for various inlet and outlet pressures and extrapolation to zero pressure drop across the column. Everett and Stoddart proposed using equation (33) to determine the mixture second virial coefficients. The precision in Bag from this method is nearly equivalent to the best static methods. The assumptions required to derive the above equation have been examined by a number of authors. - ... 

The normal gas chromatography apparatus is used for inverse gas chromatography however it requires more precise measurements of column inlet and outlet pressure, better thermostatting, to within 0.01°C and a more accurate control of carrier gas flow rate. 

The "rate" theory predicts the nature of the dependence of column efficiency (i. e., the "height of an equivalent theoretical, plate" ) on various factors such as eluent flow rate, adsorbent particle size, column inlet and outlet pr.essure, nature of the eluent gas, etc. Although the development of the theory becomes mathematically fairly complicated, application of the results to practice is often relatively simple. The radiochemist who plans to make much use of gas chromatography will certainly find study of the theory interesting and profitable. 

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