Analysis of a Chromatographic Model with (Part 5)

Analysis of a Chromatographic Model with Irreversible and Reversible Reactions

Numerical Test Problem

12D2L=u5. (3.71)

The analytical conclusions of the preceding sections are verified using a variety of numerical test problems. There have already been several numerical methods for modeling nonlinear and linear liquid chromatographic models. Comparison of LKM and EDM’s numerical and analytical solutions

Part 1: Analysis of a Chromatographic Model with Irreversible

Case I

In this case we used Danckwerts boundary conditions to analyse accurate and numerically calculated elution profiles for both LKM and EDM. HR-FVS and numerical Laplace transformation accurate or not, confirmed by the fair contract between solution profiles. Due to the limitations of analytical Laplace transforms, we’ve found numerical LT techniques to be highly effective in addressing these challenges. We plan to continue using this approach in future research.

Fig.3.2 shows the profiles created using LKM. Analytical inverse transformation solution not possible for LKM. As a conclusion, the numerical Laplace transformation solutions and high-resolution finite volume method are compared with one another. Whenever an exact solution isn’t possible, numerical Laplace inversion generally accepted as reliable method for solving the linear models. The reasonable contract between such solution profiles demonstrates high precision of the both processes.

Table 3.1 shows the values of the required fundamental parameters.

Read Part 2: Analysis of a Chromatographic Model with Irreversible and

Case II

In this section the numerical and analytical EDM solution for Dankwerts and Dirichlet BCs are compared. In Fig3.4 numerical solution b using Dirichlet BCs compared with EDM analytical solution for te breakthrough curves. The accuracy of the recommended numerical method confirmed by the good agreement of solution profile’s.

Fig.3.5 compares the numerical result for LKM calculated and numerical Laplace inversion

Sr. No.	Parameters	Values
1	Porosity	s = 0.4
2	Peclet no. for EDM	P ea = 500
3	Peclet no. for LKM	P e = 5000
4	Injection time	tinj	=	3 min
5	Column length	L=1 cm
6	EDM’s dispersion coefficient	Da = 0.002				cm 2 min
7	LKM’s dispersion coefficient	D = 0		.0002		cm2 min
8	Interstitial velocity	u =	1	cm min
9	Initial concentration	cinit	= 0		g l
10	Adsorption equilibrium constant	a = 1
11	Concentration at inlet	cinj	=	1	g l
12	Adsorption rate	k =	100		1 min

Table 3.1: Parameters that can be utilized for test problems.

for the continuous pulse injections as Dirichlet boundary conditions. These graphs shows that suggest numerical Laplace inversions HR-FVS are correct.

Part 3: Analysis of a Chromatographic Model with Irreversible and

For three different injection timings, the chromatograms for discontinuous profiles are presented differently in Fig.3.6. In this graph, same desorption and adsorption fronts are shown, but they are moved as per injection length. Fig.3.8 shows three different velocity values for the same injection, i.e. tinj=1min. Both elution profiles have the potential to be close to a normal distribution as they approach zero, shown in Fig.3.9. Because EDM’s values is higher than LKM’s, EDM’s elution profile has a higher peak than LKM’s.

Analysis of a Chromatographic Model with Irreversible (Part 4)

Table 3.2 shows the values of the required fundamental parameters.

Sr. No.	Parameters	Values
1	Porosity	s = 0.4
2	Injection time	tinj	=	2 sec
3	Column length	L=1 cm
4	Dispersion coefficient of EDM	Da = 0.002				cm 2 min
5	Interstitial velocity	u =	1	cm min
6	Initial concentration	cinit	= 0		g l
7	Henry’s constant	a = 1
8	Concentration at inlet	cinj	=	1	g l
9	Simulation time	tmax = 10 min