The Rawlings Research Group -- Daniel Patience

James B. Rawlings Research Group

Daniel Patience
B.S. Ch.E., University of Canterbury
Ph.D., University of Wisconsin-Madison, 2002
daniel[AT]bevo[DOT]che[DOT]wisc[DOT]edu

Current Work

Current practice of crystal engineering can be characterized as largely empirical. This state of development leads to large risk associated with scale-up and operation of crystallization processes. The resulting final product's crystal size and shape distribution cannot be reliably produced. Small, uncontrolled operational changes, such as feed impurity level and vessel mixing, can lead to large changes in the final product properties. As these types of processing problems arise, researchers and operators often have no recourse but to address them in a trial and error fashion without guidance from a systematic approach based on sound scientific principles and without exploiting the latest particle measurement technologies. The challenges faced by practitioners are especially pronounced when addressing manufacture of new products. Generating product and process understanding quickly is essential if manufacturers wish to capitalize on their large investment in new product discovery research.

This research develops and assembles tools to enable improved crystal engineering: reliable modeling frameworks, sound particle size and shape measurement technology, nucleation and growth kinetic determination from data, optimal operations policies given the identified models, and prediction of final product size, shape and purity.

This project is currently focused on the following four areas.

On-line particle size and shape measurement. Transmittance and video microscopy and imaging. With real-time digital imaging, we are able to detect habit transformations and use this information for monitoring, modeling and control.

Sodium chlorate (NaClO₃) shape manipulation

225ppm Na₂S₂O₆ No habit modifier

Modeling particle size and shape: deterministic and stochastic modeling frameworks. The deterministic model for mathematically describing the evolution of a population of crystals in crystallizer is given by

$\displaystyle \frac{\partial f(L,t)}{\partial t} = -G \frac{\partial f(L,t)}{\partial L} \qquad {\mbox{(PBE)}}$

The solution to this model requires different solution techniques depending on which crystal nucleation, growth and agglomeration mechanisms are occurring. Instead, the stochastic framework is a simple and flexible algorithm that can be used to model many phenomena with the same solution technique, and is becoming computationally feasible to solve. A stochastic model for describing the growth of a single crystal in a crystallizer is given by

$\displaystyle L_{k+1} = L_k + Gk + \sqrt{{\mathcal{D}}}w_k \qquad {\mbox{(SDE)}}$

Objective function contours and
95% inference region for an
experimental design that enables
good inference of model parameters
for para-xylene crystallization

Determining nucleation and growth kinetic models from data. Information rich and information poor examples such as an industrially relevant pharmaceutical and para-xylene, respectively.
Oftentimes in practice, we can be limited by the number of sensors and measurement types available making estimation of model parameters difficult. This part of the project investigates alternative experimental designs at different operating conditions. This figure shows the result of estimating nucleation rate parameters if data are collected over significantly different supersaturation profiles, instead of just one profile in which no unique parameters can be found.
Feedback control of particle size and shape using on-line measurements. In this work, we demonstrate successful closed-loop control of crystal shape using real-time measurements of shape.

Feedback control of particle shape of sodium
chlorate based on on-line measurements of cubes
in a semi-batch crystallizer

An impurity-free sodium chlorate solution stream is fed to the reactor and a solids-free solution is removed from the reactor at equal rates, of 80 mL/min. The impurity-free solution entering the reactor acts as a disturbance by flushing the habit modifier from the system and preventing the crystal from remaining in the tetrahedral shape.
To illustrate a simple control example, it is desired that the percentage of cubes remains below 40%. If more than 40% of the particles are cubes, then the controller adjusts the habit modifier level until the percentage is below 40%. The fresh feed reactant stream disturbance is fed to the crystallizer and a solids-free stream removed from the crystallizer at equal rates after 60 minutes. The exit stream is removing the added habit modifier so the controller is required to maintain the level of habit modifier over the course of crystallization. The figure below shows that without any prior knowledge of the nucleation and growth kinetics of the sodium chlorate system, the controller is able to determine a critical concentration of 140-150 ppm sodium dithionate required to maintain the percentage of cubes less than 40%.

Publications

1: Eric L. Haseltine, Daniel B. Patience, and James B. Rawlings.
On the stochastic simulation of particulate systems.
Chem. Eng. Sci., 60(10):2627-2641, 2005.
2: Daniel. B. Patience, Philip. C. Dell'Orco, and James B. Rawlings.
Optimal operation of a seeded pharmaceutical crystallization with growth-dependent dispersion.
Org. Process Res. Dev., 8(4):609-615, 2004.
3: James B. Rawlings, Daniel B. Patience, Eric L. Haseltine, and Philip Dell'Orco.
Stochastic population modeling and application to particle size control in pharmaceutical crystallization.
Annual AIChE Meeting, Indianapolis, IN, November 2002.
4: Daniel B. Patience, Eric L. Haseltine, Philip Dell'Orco, and James B. Rawlings.
Stochastic modeling and control of particle size in crystallization of a pharmaceutical.
World Congress On Particle Technology 4, Sydney, Australia, July 2002.
5: Daniel B. Patience.
Crystal Engineering Through Particle Size and Shape Monitoring, Modeling and Control.
PhD thesis, University of Wisconsin-Madison, June 2002.
6: Daniel B. Patience, Eric L. Haseltine, Phillip Dell'Orco, and James B. Rawlings.
Crystallization of a pharmaceutical. experimental data and stochastic modeling of particle size and shape.
Annual AIChE Meeting, Reno, Nevada, November 2001.
7: Daniel B. Patience, James B. Rawlings, and Hazim A. Mohameed.
Crystallization of para-xylene in scraped-surface crystallizers.
AIChE J., 47(11):2441-2451, November 2001.
8: Daniel B. Patience and James B. Rawlings.
Particle-shape monitoring and control in crystallization processes.
AIChE J., 47(9):2125-2130, September 2001.
9: Daniel B. Patience and James B. Rawlings.
On-line monitoring and modeling of crystal shape in crystallization processes.
Annual AIChE Meeting, Los Angeles, California, November 2000.
10: James B. Rawlings and Daniel B. Patience.
Measuring, modeling and controlling particle size and shape in crystallization processes.
First Symposium on Particulate Processes, Max-Planck-Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany, October 12-13, 2000.
11: James B. Rawlings and Daniel B. Patience.
On-line monitoring of crystal shape in crystallization processes.
Annual Meeting of the International Fine Particle Research Institute, Den Haag, The Netherlands, July 2000.
12: James B. Rawlings and Daniel B. Patience.
Authors' reply to letter to the editor.
AIChE J., 45(8):1842-1843, August 1999.
13: James B. Rawlings and Daniel B. Patience.
On-line monitoring and control of crystal size and shape.
Annual Meeting of the International Fine Particle Research Institute, Somerset, New Jersey, June 1999.
14: Daniel B. Patience, Hazim Mohameed, and James B. Rawlings.
The kinetics of para-xylene crystallization in scraped surface crystallizers.
Association for Crystallization Technology, ACT 9, Kingsport, Tennessee, April 19-21, 1999.
15: Daniel B. Patience and James B. Rawlings.
On-line monitoring and stochastic modelling of particle size distributions.
Annual Meeting of the International Fine Particle Research Institute, Brighton, England, July 1998.
16: Daniel B. Patience and James B. Rawlings.
On-line monitoring and stochastic modelling of particle size distributions.
Annual Meeting of the International Fine Particle Research Institute, Osaka, Japan, June 1997.

Personal Web Page: jbrwww.che.wisc.edu/~daniel

University of Wisconsin
Department of Chemical Engineering
Madison WI 53706