Specifying Column Performance

It has been established on previous occasions (Sections 3.2.2 and 5.2.1) that a conventional two-product distillation column with a hxed feed and conhguration and operating at a given pressure has two degrees of freedom. The conhguration is dehned by the number of stages, type of condenser and reboiler, and the feed location. The feed is of hxed how rate, composition, and thermal conditions. 

The description rule introduced in Section 5.2.1 may be used to check the degrees 

The column may be operated to meet various performance specifications within certain ranges. The variables that can be specified in multi-component separation include all the component compositions, rates, or recoveries in the two products as well as the product rates, properties, and temperatures, the reflux and boilup ratios, the condenser and reboiler duties, and the tray temperatures and liquid and vapor rates. 

The two variables selected to define the column performance become the independent variables, and the others are calculated to satisfy the mass balances, energy balances, and equilibrium relations. Many of the parameters are interdependent to varying degrees, but the two selected as the independent variables must, at least, be independent of each other over certain ranges. In fact, the higher the degree of independence between the two specified variables, the wider the feasible ranges over which the column can operate and the easier for the specified values of the variables to be met. 

The extent of interdependence among the different variables may be investigated by observing the surface that represents each variable as a function of the two most independent variables, namely, the reflux ratio and one of the product rates. Stated mathematically, any variable may be expressed as 

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Each of the PLgel individual pore sizes is produced hy suspension polymerization, which yields a fairly diverse range of particle sizes. For optimum performance in a chromatographic column the particle size distribution of the beads should be narrow this is achieved by air classification after the cross-linked beads have been washed and dried thoroughly. Similarly, for consistent column performance, the particle size distribution is critical and is another quality control aspect where both the median particle size and the width of the distribution are specified. The efficiency of the packed column is extremely sensitive to the median particle size, as predicted by the van Deemter equation (4), whereas the width of the particle size distribution can affect column operating pressure and packed bed stability. 

Most manufacturers do not specify the asymmetry factor. Therefore this parameter can serve only for the observation of the column performance during its use. For interpretation, see the remarks about discarding a column. 

It is difficult to decide what should serve as adequate column quality parameters for describing the performance of a set of GPC columns. The two most common measures are plate count and resolution. While both of these can be useful for monitoring the performance of a column set over time, it is not generally possible to a priori specify the performance needed for a specific analysis. This will depend on the nature of the polymer itself, as well as the other matrix components. 

Table 5.21 shows the factors that were selected together with the levels tested. A range of factors was chosen such that each part of the method was examined. A common problem in HPLC methodology is the specification of columns. The column performance can be crucial to the separation and therefore must be adequately specified. 

The absorption column is sized according to two key parameters, these are to design for optimum mass transfer and optimum unit cost. A column internal diameter can be estimated according to the liquid and gas flowrates by utilizing graphs and nomographs such as those contained in Ref. A3. These recommendations have been refined using a computer-based mathematical model. The model predicts the required number of trays for a specified column internal diameter. These results enable a compromise to be achieved between tower cost and tower performance. 

It should be stressed that there is nothing wrong with these practices. In fact, column performance is best compared under ideal thermodynamic conditions CL). Hence, test systems should be chosen to produce the best column performance, since most workers like to see how well a column really can perform. However, it should be recognized that when considering the number of plates specified for a column, it is necessary to examine the test conditions used to generate that number. 

These column performance criteria should be specified by the manufacturer and users should measure them whenever a new column is received. These column specification measurements should be kept for future reference and re-checked whenever it is suspected that the column has deteriorated. 

Reduction in hatch time For a given fresh feed and a given separation, the column performance is measured in terms of minimum batch time required to achieve a desired separation (specified top product purity (x D]) and bottom product purity (x B2) for binary mixture). Then an optimal amount and composition of recycle, subject to physical bounds (maximum reboiler capacity, maximum allowable purity of the off-cut) are obtained in an overall minimum time to produce the same separation (identical top and bottom products as in the... 

If the laboratory employs a GC column that has a different elution order than those specified here, the laboratory must ensure that the isomers eluting closest to 2,3,7,8-TCDD are represented in the column performance solution. 

The statutory requirements addressed by each option are identified in the seventh column of Table X titled Statutory program. The specified compliance dates for each statutory program are also shown in the table, as are the implementation times for each option. Since the maximum achievable control technology (MACT) requirements have not yet been specified by EPA, projects directed toward those requirements have not yet been undertaken. That being the case, the implementation times identified indicate that options 5, 8, and 9 may have difficulty achieving timely compliance with these regulatory requirements. To proceed with the analysis, requirements that might be imposed under MACT were hypothesized to specify the performance characteristics of the associated pollution prevention options. It should be noted that only those options related with compliance with the Benzene Waste NESHAP (National Emissions Standard for... 

Robustness tests examine the effect operational parameters have on the analysis results. For the determination of a method s robustness, a number of chromatographic parameters (e.g., flow rate, column temperature, injection volume, detection wavelength, or mobile phase composition) are varied within a realistic range and the quantitative influence of the variables is determined. If the influence of the parameter is within a previously specified tolerance, the parameter is said to be within the method s robustness range. Obtaining data on these effects will allow one to judge whether a method needs to be revalidated when one or more of parameters are changed, for example, to compensate for column performance over time. 

In addition to specified validation criteria, it is also useful during method development to assess column durability and column-to-column performance. Benchmarks have been established in a series of papers by Kele and Guiochon for short- and long-term repeatabilities and column-to-column... 

The g functions (Equation 4.3) that define the column performance may be general functions of the primary variables designed to meet special separation specifications, or they may directly specify the values of the primary variables. Combinations of different types of specifications are possible. 

By taking an inventory of equations and variables for the above column, it was determined that two or three variables (depending on whether or not the number of stages is fixed) must be specified in order to define the column performance. An alternative to this mathematical analysis is to apply the description rule (Hanson et al., 1962), which can be a less tedious method for determining the number of independent variables, based on a practical evaluation of the process. 

The variation in some of the other parameters with overhead rate at a constant reflux ratio is shown in Figure 7.2. The significance of these relationships is in determining the feasibility of specifying the column performance in terms of a given pair of variables. This question is explored further in the following section. 

Studying the interdependence between column variables is important when attempting to select parameter pairs for specifying the performance of a conventional column. The reflux ratio and product rate are generally considered the most independent pair. The other extreme may be illustrated by a situation where both product rates are specihed. These are two-column variables that are totally dependent since specifying one of them hxes the other by simple material balance. Once one product rate is known, no additional information about the column performance is acquired by providing the other product rate. This fact is indicated by the horizontal line for the bottoms rate shown in Figure 7.1. 

If one variable is specified, the lean oil rate and the column performance are... 

It is essential, however, for defining the column performance, not only for the specification to be feasible, but for a unique solution to exist. If, for instance, the propane recovery in the bottoms is specified at 100%, no unique solution exists since any lean oil rate over about 800 mol/h satisfies the specification. 

Within different lean oil rate regions, different specifications provide "more unique" definitions of the column performance. For instance, at a lean oil rate of around 700 kmol/h, the key component is ethane. Therefore in this region the column performance is better defined by specifying the ethane recovery or concentration than, say, the methane concentration in the overhead. This is because at about this lean oil rate, the dependence of the ethane recovery or concentration on the lean oil rate is stronger than that of the methane concentration in the overhead. At lower lean oil rates, propane becomes the key component hence, its concentration or recovery would be a better variable for defining the column performance. 

In equation set 12.17, F and/ are known quantities. The relative volatilities a, are assumed constant and known for each component. At a fixed pressure, K, is a function of temperature only. The bottoms total flow rate, B, may be replaced by the sum of bi, the component fiow rates in the bottoms. There are therefore C + 2 variables in Equation 12.17 Z , (/ = 1, 2,..., C), N, and (or an average column temperature). Equation 12.17 is a set of C independent equations for i = 1, 2, C. With C+2 variables and C equations, the column has two degrees of freedom, that is, two variables must be specified in order to define the column performance. The two specifications could be any two of the above variables or functions thereof. For instance, the specifications could be N and B, or fc, and fc, the light and heavy key component fiow rates in the bottoms, or YdIi and Xg the mole fractions of the heavy key component in the distillate and the light key component in the bottoms, and so on. In each case, with two variables specified, all the other variables can be calculated from equation set 12.17. 

Performance qualification (PQ) is the process of demonstrating that an instrument can consistently perform an intended application within some predefined acceptance criteria. In practice, PQ testing is synonymous with system suitability testing conducted with specified columns, mobile phases, and test compounds. PQ is performed during initial system qualification or after the system... 

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