Flow-through packed columns equation

If we cannot use the Ergun equation to scale a packed column unit operation, then we must devise a different method for scaling such a unit operation. Since scaling is based on dimensionless parameters, we should base our new scaling procedure for packed columns on dimensional analysis. We can perform a dimensional analysis of fluid flow through packed columns because the variables of the process are well known and have been studied for many decades [13,14]. The variables are fluid velocity v [LT ], column diameter D [L], characteristic length of the material mass Tchar that is dependent upon the size and shape of the material particles [L], pressure difference per physical height of the material column AP/Z [ML T ], fluid density p [ML ], and fluid viscosity p, [ML T ]. The Dimension Table for these variables is... 

Dalla Valle1 s Method—The author used an equation due to Burke and Plummer (1928) for determining the pressure-drop through packed columns. For streamline flow of air through packings of various sands in a 3 in. diameter column, the modified Burke-Plummer equation takes the form... 

The stationary phase is supported on the wall of the column, the carrier gas therefore has an uninterrupted flow through the column. The absence of column packing means that the unequal pathways term, A term, in the van Deemter equation (see section 2.5.1) is zero and band broadening is due to the effects of longitudinal diffusion, B term, and mass transfer, C term. The reduced equation is referred to as the Golay equation [15]. 

The column may be packed or it may be an open tube but in this example, a packed column will be specifically considered. The column is considered to have a length (L) and inlet and outlet pressures and inlet and outlet velocities of (Pi), (Po) (ui) and (uo), respectively. The pressure and velocity at a distance (x) from the front of the column is (Px) and (ux), respectively. According to D Arcy s equation for fluid flow through a packed bed, at any point in the column. 

Since the exact profile of the mobile phase flow through a packed bed is unknown, only an approximate description of the ] and broadening process can be attained. For packed column gas chronatography at low mobile phase velocities, equation (1.35) provides a reasonable description of the band broadening process [70,82,83]. 

The pattern of flow through a packed adsorbent bed can generally be described by the axial dispersed plug flow model. To predict the dynamic response of the column therefore requires the simultaneous solution, subject to the appropriate initial and boundary conditions, of the differential mass balance equations for an element of the column,... 

The flow of gas through the column and the diffusion of the solute in both gas and liquid all influence the solute band-width and, hence, efficiency and resolution. Early in the history of GC it was shown (by van Deemter and coworkers for packed columns, and by Golay for capillary columns) that H, height equivalent to a theoretical plate (HEPT) depends on the average linear gas velocity (u) through the column according to Equation 13.1 ... 

Finally, the concentration pulse chromatography will be shortly discussed. A pulse of a sample is injected into a carrier gas flow which is passed through an adsorbent-packed column. The response of the column is measured as concentration c(/) vs. time t. The mean retention time r of the sample is experimentally determined. With the superficial velocity w, the bed length L, and the adsorbent density, the modeling leads to the following equation for the Henry coefficient He ... 

For infinite dilution operation the carrier gas flows directly to the column which is inserted into a thermostated oil bath (to get a more precise temperature control than in a conventional GLC oven). The output of the column is measured with a flame ionization detector or alternately with a thermal conductivity detector. Helium is used today as carrier gas (nitrogen in earlier work). From the difference between the retention time of the injected solvent sample and the retention time of a non-interacting gas (marker gas), the thermodynamic equilibrium behavior can be obtained (equations see below). Most experiments were made up to now with packed columns, but capillary columns were used, too. The experimental conditions must be chosen so that real thermodynamic data can be obtained, i.e., equilibrium bulk absorption conditions. Errors caused by unsuitable gas flow rates, unsuitable polymer loading percentages on the solid support material and support surface effects as well as any interactions between the injected sample and the solid support in packed columns, unsuitable sample size of the injected probes, carrier gas effects, and imprecise knowledge of the real amount of polymer in the column, can be sources of problems, whether data are nominally measured under real thermodynamic equilibrium conditions or not, and have to be eliminated. The sizeable pressure drop through the column must be measured and accounted for. 

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