In this section, the modification and definition o f fractionation diagram and purification factor for chromatographic operation will be discussed in detail in Sections 3.3.1 and 3.3.2. The contamination index developed in this work to deal with systems which aim to achieve contaminant removal in a separation will be discussed in Section 3.3.3.
3.3.1 Fractionation Diagram (FD)
The procedure to generate both fractionation diagram and maximum purification factor-yield diagram from a typical chromatogram is illustrated in Figure 3.4. The derivation is based on the simplification that in essence a chromatographic separation can be reduced to a problem o f resolution from nearest neighbours. Hence the derivation uses just 3 components to represent the feed. A fractionation diagram is constructed based upon the concentration profiles o f the different components being separated obtained either directly from the elution chromatogram, if a specific on line assay exists for the product and the total material, or from the corresponding off line data (Figure 3.4 (a)). This problem is first simplified into a three-component separation, the product and all the other contaminants being treated as two pseudo components: one which elutes before the product, the other after. This recognises that for the purposes o f processing the aim is to isolate the product peak from all the other species. The chromatogram is then fractionated into N steps (Figure 3.4(b)), such that the whole chromatographic profile is divided into N elements with equal width (time or volume intervals).
Hypothetically, if a system comprises three components (Figure 3.5), the product (P) and the two pseudo-impurities (A and B), the amount o f P, A and B, and the sum of them in each fraction can be estimated by using the Trapezoidal Rule to obtain the areas under the concentration curves (Figure 3.6).
C hapter 3: D evelopm ent o f Fractionation Diagram A pproach in C hrom atography
Such that the approximate area under the eoneentration eurve for interval between tj and t2 is evaluated as:
(3.3)
The amount o f each material, (mg), in a particular fraction is given by the product o f the area under the curve o f that component and volumetric mobile phase flow rate Q (ml/s):
Am ount o f material, Myyi = Area x Q
The amounts o f produet (M/>), impurity A {Ma) and impurity B {Mb) in each interval can be calculated. For the z-th interval they would be denoted as M p j ; Mji i and Mp^ i- Henee the total amount o f material in a particular fraction {Mp) is the sum o f all these all quantities:
M p i = Mp^ i + Ma, i + Mb, i (3-5)
For eaeh interval, we define an arithmetic mean time {tyf) as defined between the upper and lower limit o f the interval, for example, for the first interval:
L - - ( b +^2) (3.6)
2
The fraetionation diagram plots the changes in the cumulative fraetional mass of produet eluted with the eorresponding fractional total mass eluted. Hence the axes are defined as:
_ „ • , 1 1 Cumulative mass o f material eluted at time t
Fraetional mass of material eluted; X = --- Total mass eluted at t = 00
Cumulative mass o f product eluted at time t Fraetional mass o f product eluted; Y =
C h a p te rs : D evelopm ent o f Fractionation Diagram A pproach in C hrom atography
Mathematically, X and Y can be expressed as:
./=1_____
M ,
(3.7)
Y = . / = i (3.8)
M..
where N is the total number o f fractions, M g is the total load o f the sample and Mg is the total amount o f product component in the sample load. Since X and Y are fractions, the values fall in the range between 0 and 1. A theoretical fractionation diagram can then be generated as shown in Figure 3.4(c).
3.3.2 Purification Factor
Having defined the fractionation diagram it is now possible to calculate operating performance parameters such as the purification factor (PF), defined as the ratio between the final purity o f the product after purification to the starting purity o f a load sample: P F = Final Purity Initial Purity '
M y *
/
/
_ V v . (3.9)where Ms and Mq are the total amount o f product and impurity in the sample load and the amount o f product in the sample load respectively.
C hapter 3: Developm ent o f Fractionation Diagram A pproach in Chrom atography
Chromatogram
Analysis o f Fractions
Fractionation Diagram
Evaluation o f Yield and Purification factor
Max. Purification Factor vs. Yield Diagram (a) (b) (c) Yield = Y2- Y , PF = ^ X , X ,
(d)
max
PF
(e)Figure 3.4; Schematic illustration of the procedure to generate the fractionation diagram and the corresponding maximum purification factor-yield diagram from a elution chromatogram obtained either by experiment or simulation. X and Y, which are the x and y-axis of the fractionation diagram, represent the cumulative fraction o f total material and target product respectively eluted at any time. Subscripts 1 and 2 denote the start and end points of product collection on the fractionation curve. PF denotes the purification factor between any two points as defined by Equation (3.9).
Chapter 3: Development of Fractionation Diagram Approach In Chromatography
Fraction
Figure 3.5: Illustration on one fraction in a chrom atographic profile.
concentration (mg/ml)