How to Get the Software?
Chromulator-IEX has been used by top biotech companies such as Amgen and
Genentech. Both academic and commercial buyers need to pay a license fee ($3k for
commercial buyers). Academic discount is available. Buyer pays our invoice with a check payable to "Ohio
University Foundation." Please e-mail Prof. Tingyue Gu (email@example.com
Chromulator-IEX solves the general rate model for ion-exchange
chromatography, and provides several methods of visualizing the
solution. The solution data can be exported to a Matlab®
m-file or a text file. It can be used to model a variety of IE
applications including water treatment
and protein separations. The data can be visualized as effluent
histories (chromatograms), position-time plots, and animations
displaying the changing column profiles with time.
The flow through the column is assumed to be axial, with perfect radial
mixing in the column. Axial dispersion is described by the
Peclet number (Pe). Mass transfer from the bulk mobile
to the particle surfaces is described by the Biot number (Bi).
Diffusion within the particle pores is accounted for by the eta
number (lower-case eta).
The mass-action isotherm is used to describe the ion-exchange
equilibrium. An equilibrium constant is specified for each
component except the first,
with the first component being the reference species. The
equilibrium constant can also be specified so that its logarithm is a
polynomial function of the pH. In addition, the absolute charge
(lower-case nu) for each component is specified. This can be a
constant or a polynomial function of the pH. The steric factor
(lower-case sigma) allows for the Steric Mass-Action (SMA) isotherm to
be used. When all of the steric factors are zero, the isotherm
reduces to the mass-action equations. The equations for the
In the above equations, Qi, is the adsorbed
concentration of species 1, Ci is the its
fluid-phase concentration, nui
is the characteristic charge of species i, Lambda is the ion
capacity in equivalents per unit particle skeleton, and sigmai
is the steric factor for species i. Q1 with an
is the concentration of species 1 available for exchange (i.e., not
by a large adsorbed molecule).
The equations are solved numerically using a combination of finite
elements, orthogonal collocation, and a stiff ordinary equation solver.
A Galerkin formulation with uniform quadratic finite elements is
used to discretize the
bulk mobile phase equations. Orthogonal collocation is used to
the particle phase equations. This results in a set of
Ns(2Ne+1)(2Nc+1) ordinary differential equations, where Ns is the
number of species, Ne is
the number of finite elements, and Nc is the number of interior
points. The VODE solver provided by Lawrence Livermore National
is used to solve this set of equations. The local error tolerance
the ODE solver can be specified. In practice, accurate solutions
usually be obtained with 15-30 elements and 1-3 internal collocation
and an ODE error tolerance of 10-5.
The user interface allows the system parameters, the parameters for
each of the components, and the parameters for the numerical solution
procedure to be entered.
The main window provides a graphical
which all of the simulation parameters can be specified.
The column feed can be specified by
using one of the built-in modes of
operation (isocratic elution, step displacement, or gradient elution),
a values interpolated from a text file, or using the feed editor window
specify a sum of step, pulse, and ramp functions.
|A plot of the effluent history
for a ternary separation is shown with
the displacer salt displayed in blue.
Two ternary separations are displayed,
one data solution plotted with dotted lines. The displacing salt
is not shown.
Above left is the effluent history of a binary separation. To the
right is the position-time plot for this same separation.
The animation window allows the column
profiles to be examined at
specific times. The changing column profiles can be viewed like a