Column modular method

Two approaches exist for solving problems involving systems of columns, the column modular method and the system modular method proposed by Hess.15 In the column modular approach, the equations for each column of a system are solved in succession, and in the system modular approach, the complete set of equations for the system are solved simultaneously. While the system... 

Solution of Systems of Columns by Use of the Column Modular Method... 

To demonstrate the application of the column modular method and system modular method (the Almost Band Algorithm for Systems), Examples 6-1 and 6-2 are presented. The statements of Examples 6-1 and 6-2 are presented in Table 6-3, and the solutions are given in Tables 6-4 through 6-6. Example 6-1 is a relatively easy problem to solve while Example 6-2 is more difficult. A flow diagram of the system involved in Examples 6-1 and 6-2 is shown in Fig. 6-11. 

The following procedure was used in the solution of Example 6-1 by the column modular method. After one complete trial had been made on column 1 by use of the Almost Band Algorithm, the component flow rates bit J so obtained were used as the feecLto the second column. Then one trial on column 2 was made by use of the Almgst Band Algorithm. Next the capital 0 method was applied to the most recentfets of terminal flow rates di%l, bitl 9 dit 2, and bu 2, and corrected sets were obtained which satisfied the component-material balances enclosing each column and the specified values of Bj and B2. To... 

Column modular method Almost Band Algorithm ... 

Example 6-1 was also solved by the Almost Band Algorithm for Systems (the system modular method) as well as the column modular method. Results obtained by each of these methods are presented in Tables 6-3 through 6-6. 

Example 6-2 differs from Example 6-1 by the specification of more plates, the temperature of the feed F2, and the flow rate Bx. With the additional stages specified, this problem becomes very sensitive to the value specified for Bt. For Bl = 277 instead of the specified value Bx = 275, Example 6-2 is relatively easy to solve by use of the combination of the column modular method. When Bt was taken equal to 275, Example 6-2 could not be solved by either the column modular or the system modular method. However, Example 6-2 could be solved... 

A column modular method which makes use of the capital 0 method of convergence is presented for solving problems involving systems containing both mass and energy recycle streams. On the basis of an assumed set of values of the variables for the recycle streams, one complete trial is made on each column or unit of the system by use of the most appropriate calculational procedure for the column or unit. Then the capital 0 method is used to place all terminal streams in material and energy balance. The values of the variables so obtained for the recycle streams are used to make the next trial on each column or unit of the system.6, 7... 

The modular shortcut column section method can also be applied to extractors, as described in Chapter 12. 

The modular method as described above cannot directly calculate the column section to satisfy performance specifications such as product composition or quality. Performance specifications could be handled by superimposing an external iterative loop tliat would vary a fixed model parameter such as the feed rate or temperature to meet the specification. 

Using the modular column section method, calculate the absorber product rates anrJ compositions. The relative volatilities and column pressure may be assumerJ constant for the entire computational cycle. 

A liquid stream of hydrocarbons with a flow rate of 500 kmol/h is sent to the top of a reboiled stripper column. The column has the equivalent of seven equilibrium stages and a reboiler in a configuration similar to Figure 12.6. The column and reboiler pressure may be assumed uniform at 1000 kPa. The feed temperature to the column is controlled such that the average column temperature is 95°C. The heat duty to the reboiler is controlled such as to maintain the reboiler temperature at 120°C. The feed stream is given below, along with average component K-values in the column and reboiler, evaluated at the pressure and temperatures provided. Determine by the modular column section method the rates and compositions of the stripper column products. 

A hydrocarbon gas stream contains some heavy components which must be removed by absorption. The absorber has six theoretical stages and operates at 2750 kPa. The overhead product should contain 0.01 kmol/h nCg. Using the modular column section method, calculate the required absorbent flow rate and the product streams flow rates and compositions. The feed streams are deflned below, along with the component relative volatilities which are referred to pentane and assumed constant. The A -valuc of pentane at the column pressure of 2750 kPa is given by... 

In the absorber column of Example 12.5, it is required to determine the absorbent rate necessary to bring the mole fraction of n-butane in the overhead stream down to 0.001. Use data from Example 12.5, and solve the problem by the modular column section method to close all the model equations. 

Absorbent rates of 200, 250, or 300 kmol/h are possible. It is required to determine the lowest among these that would meet the butane speci-hcation, and to calculate the product rates and compositions when the column is operated with the selected absorbent rate. Use the modular column section method with stripping factors based on inlet liquid and vapor flow rates. The gas and absorbent streams are defined below. 

In the column modular approach, the equations for each column are solved by use of the most efficient procedure for each column. After one trial has been made on each column, the terminal flow rates are placed in component-material balance and in agreement with the specified values of the terminal flow rates by use of the capital 0 method for systems. The entire calculational process is repeated until convergence has been achieved. 

Alternatively, a column modular approach may be used wherein the Almost Band Algorithm is applied successively to each column of the system. After one or more trials have been made on each column of the system, the capital 0 method of convergence is applied in a manner similar to that described for systems of interconnected columns. 

Both multi-residue methods are presented in several parts, which separate general considerations from procedures for extraction, cleanup and determination/ confirmation. Whereas in EN 12393 several extraction and cleanup steps cannot be combined arbitrarily, the modular concept is utilized to a greater extent in EN 1528. In the latter standard, there is no limitation to the combination of several extraction procedures, mostly designed for different commodities, e.g., milk, butter, cheese, meat or fish, with different cleanup steps. Both standards, EN 1528 and EN 12393, do not specify fixed GC conditions for the determination and confirmation. All types of GC instruments and columns, temperature programs and detectors can be used, if suitable. 

In spite of the simplifications, these methods are still quite computation-intensive and in most cases must be solved using computer programs. However, due to the much shorter computing time, these methods are useful in situations where computing time is crucial, such as in online, real-time applications. Especially suited for these applications are the modular shortcut methods based on column sections— another topic discussed in this chapter. 

An alternative method for the design of an absorption or stripping column is based on the modular group method (Kremser equation, 12.33), primarily for dilute mixtures. The required number of stages for a specified separation is first determined. Once this is known, the packing height can be estimated from the relation... 

Shortcut computation methods, including modular techniques for online real-time applications, are discussed, followed by a discourse on the major rigorous algorithms in use for solving multi-component separations. The application of these methods is detailed for the various types of multistage separation processes discussed earlier. The models are also expanded to cover column dynamics. 

The optimum use of SPE procedures requires investigation of different stationary phases, their masses, the volume of conditioning, sample load, wash, elution solvents, and the sample size. These variables are readily studied in column format. But it is costly or inconvenierit to use only a fraction of the 96 wells to perform all the studies. Hence, modular well plates have been developed that have small removable plastic SPE cartridges that fit tightly in the 96-hole base plate, and only a portion needs to be used to develop a method. 

First, we define the objective function (see Figure 8.22b) such as energy consumption, the number of trays of a column, and the conversion of a reactor. We have up to three optimization algorithms for this case SQR, general reduced gradient, and simultaneous modular SQP. The particularities of the methods can be found elsewhere [44,45]. We define the independent variables and the constraints over variables from the streams or the equipment just by selecting the unit or the stream and the variable and the range of values of operation and an initial value. 

Recently we developed and validated a nice reverse phase PHLC method to analyze the lignans in Schisandra fruits. Analytical HPLC analyses were performed on a Hewlett-Pachard 1100 modular system equipped with an autosampler, a quaternary pump system, a photodiode array detector and a HP Chemstation data system. A pre-packed 250 x 4.6 mm (5 pM particle size) Luna Cl8 (2) column (Phenomenex, Torrance, CA) were selected for HPLC analysis. The absorption spectra were recorded from 200 to 400 nm for all peaks quantification was carried out at a single wavelength of255 nm. 

System volume is one of the parameters that instrument manufacturers have striven to reduce when the engineering of UHPLC systems began. Some reductions were simple. In others, for instance, in autosamplers, the volume reduction was more complicated. For this reason, total system volumes are not uniform across all available instrumentation. Some manufacturers strictly define their system volume, and the qualification of the instruments for use in regulated environments hinges on this volume being fixed. Other manufacturers offer more flexible options. Virtually all UHPLC systems are modular and can have different components (column switcher vs. single column, binary pump vs. quaternary pump, multiple detectors), and for some manufacturers, two systems may have the same components but be plumbed differently. All of these configurations have an effect on the system volume. Because some of the benefits of UHPLC are the speed of analysis, sharpness of the peaks, and retention of resolution, extra dead volume is undesirable, as it reduces these benefits. To ease method transfer problems, one must account for these types of differences. 

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