Dead time chromatographic

Time-Delay Compensation Time delays are a common occurrence in the process industries because of the presence of recycle loops, fluid-flow distance lags, and dead time in composition measurements resulting from use of chromatographic analysis. The presence of a time delay in a process severely hmits the performance of a conventional PID control system, reducing the stability margin of the closed-loop control system. Consequently, the controller gain must be reduced below that which could be used for a process without delay. Thus, the response of the closed-loop system will be sluggish compared to that of the system with no time delay. 

Dead time. Probably the best example of a measurement device that exhibits pure dead time is the chromatograph, because the analysis is not available for some time after a sample is injected. Additional dead time results from the transportation lag within the sample... 

H is the plate height (cm) u is linear velocity (cm/s) dp is particle diameter, and >ni is the diffusion coefficient of analyte (cm /s). By combining the relationships between retention time, U, and retention factor, k tt = to(l + k), the definition of dead time, to, to = L u where L is the length of the column, and H = LIN where N is chromatographic efficiency with Equations 9.2 and 9.3, a relationship (Equation 9.4) for retention time, tt, in terms of diffusion coefficient, efficiency, particle size, and reduced variables (h and v) and retention factor results. Equation 9.4 illustrates that mobile phases with large diffusion coefficients are preferred if short retention times are desired. 

The stationary phase in SEC is a highly porous substrate whose pores are penetrated best by small solute molecules. Because larger solute molecules are unable to enter as deeply into the pores, they will travel further down the column in the same time. The largest molecules, which are totally excluded from the pores, are eluted first from the column. Because the solvent molecules are usually the smallest, they are normally the last to be eluted. The rest of the solute molecules are eluted between these two extremes, at a time dependent on their ability to penetrate into the pores. In SEC, therefore, unlike other chromatographic methods, the entire sample often is eluted before the solvent dead time peak, t0, as shown in Figure 2.13.53... 

In part (a) of Figure 2.85, the analyzer controller (ARC) uses the chromatographic measurement to manipulate the reflux flow by adjusting the set point to the reflux flow controller (FRC). Controllability of the process is degraded by the dead time between measurement updates. 

In this context, the capacity factor k = (/r — /o)//o is important to is the dead time of the chromatographic system, roughly the time the pure eluent needs to travel from the injector to the detector. It may be determined by injection of a methanoEwater mixture since H2O does not show any significant retention in a C18 column. For cyclic and acycUc organic polysulfanes, it has been found that the logarithm of the capacity factor is a linear function of the number of sulfur atoms (equation 118). 

An especially challenging task is maintaining the selectivity of the method for separation of compounds whose elution time is very short, close to the dead time. In such cases, it is necessary to perform a preliminary review of the planned chromatographic conditions, including the composition of the analyzed material. For example, a typical eluent employed in anion-exchange chromatography (with pH of 8.5) is intended to facilitate the dissociation of separated compounds. Neglecting the time necessary to achieve acid/base equilibrium of substances loaded into the column in a neutral solution can result in their elution in the dead volume. The phenomenon is observed, for example, for MMA(V), whose consecutive dissociation constants are p/sTi 3.6 and p/sT2 8.22 [164]. 

The column dead volume can be defined as the space in the column which is not working for the chromatographic separations (i.e., not occupied by the stationary phase and its support). Its value is generally determined by an elution time or elution volume of a nonretained solute in the chromatographic system. If the column dead volume is measured by a retention time of a nonretained solute, one can refer to this as a column dead time t. ... 

The dead time (void time) fw is the time it takes for an unretained species to pass through a chromatographic column. All components spend this amount of time in the mobile phase. Separations are based on the different times fs that components spend in the stationary phase. 

Retention factor, k A term used to describe the migration of a species through a chromatographic column. Its numerical value is given by k = (f — ty lt, where /r is the retention time for a peak and fjvi is the dead time also called the capacity factor. 

Section 6.2 presents various models for chromatographic columns. But it has to be kept in mind that these models only account for effects occurring within the packed bed. A HPLC-plant, however, consists of several additional equipment and fittings besides the column. Therefore, the effect of this extra column equipment has to be accounted for to obtain reasonable agreement between experimental results and process simulation. Peripheral equipment (for example pipes, injection system, pumps and detectors) causes dead times and mixing. Thus, it can contribute considerably to the band broadening measured by the detector. 

Two different components are separated in a chromatographic column only if they spend different times in or at the stationary phase, respectively. The time in which the components do not travel along the column, is called the solute retention time, f5. The column dead time, tm, is defined as the time necessary for a non-retained component to pass through the column. The gross retention time, solute retention time and the column dead time ... 

Since the capacity ratio is typically determined according to Eq. (80) from the chromatographic data, inversely, the column dead time may be calculated when k is known. 

The most convenient way to calculate k is from the retention time (/r) of a sample ion and from the dead time (r or tfyi), measured from a chromatogram. The value of to (also called Tm) is the time for a nonretained substance to pass through the chromatographic column and detector. The substance chosen can be either a detectable ion or molecule, but care must be taken to choose a substance that passes through the column with absolutely no retention. 

The adjusted retention time corresponds to the retention time of an alkane having n atoms of carbon, minus the dead time d b are numerical coefficients. The slope of the graph obtained depends on the overall performance of the column and the operating conditions of the chromatograph. 

The dominant dynamic feature of composition analyzers is the time delay (dead time) in their response, which can be quite large. Thus, for a chromatographic column, the time required by the sample to travel from the process stream to the column, plus the time required to travel through the column, plus the time needed by the detector at the end of the column to respond, can be quite large. Such long time delays result in ineffective control. 

Retention volume and retention time are measured from the time the sample is introduced into the chromatograph to when the component(s) are eluted from the column no allowance is made for the volume of mobile phase in the system nor the time the mobile phase takes to pass from the injector to the detector. A correction therefore has to be made to obtain a more accurate representation of the retention of a component by the stationary phase. Fr, the corrected retention volume, accounts for the volume of mobile phase in the system, and tR, the corrected retention time, takes into account the time the mobile phase takes to pass through the system. and are often referred to as the dead volume and dead time, respectively (Figure 2.2). 

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