simulation of chromatographic processes_sou_roy
TRANSCRIPT
Simulation of Chromatographic Processes: Uptake Kinetics and
Lumped Body KineticsSandeep Ramesh Hadpe
Vijay MaranholkarSouhardya Roy
Modelling of Uptake Kinetics using Pore Diffusion Model
• Equation to solve:
• Nature of equation: • System of Partial Differential Equation (PDE). • 2 variables: c q • Equations: 1.
• Thus, it can not be solved directly.
• Solution: • Elimination of one of the variables• Substitution
• Reduced Equation:• Substitution:
• Elimination: q gets eliminated. • Reduced Equation: Single Partial Differential Equation. • Solver used: ‘pdepe’ solver for PDE in MatLab.
• Boundary Conditions:
• Initial Conditions:
• Bulk Fluid Concentration:• Conservation Equation:
• Valid in general.
• Analytical Form:• Valid for external film mass transfer.
• Both the conservation equation and the analytical form can be separately modelled using MatLab.
• There will be some difference between the two plots due to the extra constraint introduced in the analytical form. However, the trend should be same in both.
• The plots obtained can also be used to find the value of the parameter Film Mass Transfer coefficient kf directly using Curve Fitting in MatLab.
• This further can be used to determine De, i.e. Effective Pore Diffusion coefficient.
Conservative Equation Analytical Form
Time
C (Bulk Conc.)
Parameter EstimationResin R x 104 kf x 104
(Estimated)De x 108 (Estimated)
Resin S 75 2 1.245Resin T 45 3.3 1.1Resin K 75 1.06 2.25Resin A 35 4.5 1Resin M 75 2 1.24
35 45 75 750
0.5
1
1.5
2
2.5
3
3.5
4
4.5
54.5
3.3
2
1.061 1.1 1.24
2.25
Kf and De variation with Re
kf x 10^4(Estimated) De x 10^8 (Estimated)
Rx10^4
Modelling of Lumped Body Kinetics using Breakthrough Model
• Equation to Solve:
• Nature of Equation: • System of two Partial Differential Equations. • 2 variables: c q• Varied w.r.t: t x • Equations: 2.
• Solution using: ‘pdepe’ solver in MatLab.
• Substitution:
• Initial Conditions:
• Boundary Conditions:
• BC w.r.t q have to be designed for validating the form of the ‘pdepe’ solver.