Publications

Authors: Rohit Ramachandran, Paul I.Barton

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Abstract: This study considers optimization problems with multi-dimensional population balance models embedded. The objective function is formulated as a least-squares problem, minimizing the difference between target data and simulated model output and the goal is to find model parameter values that best fit the data. Results show that derivative-free methods, such as the Nelder–Mead simplex method, fail to converge to an optimal solution. A similar result was obtained with gradient-based methods such as BFGS, quasi-Newton, Newton, Gauss–Newton, Levenberg–Marquardt and SQP, and with a stochastic genetic algorithm. It was hypothesized that three main issues could contribute to these convergence failures: (1) gradients were calculated based on finite differences, and as a result of improper step size determination, the numerical error could be prohibitive resulting in inaccurate derivative information, (2) the parameters may not be identifiable and (3) numerical instability could occur during the course of optimization. To circumvent these issues, this work addresses the calculation of derivative information based on automatic differentiation and sensitivity analysis to ensure increased accuracy. Issues such as parameter identifiability are also dealt with by analyzing an accurate Fisher information matrix. Given the computational burden in calculating accurate Jacobians and Hessians, compounded by the potential nonsmoothness introduced into the objective function as a result of granule nucleation, other optimization strategies may be warranted and this work addresses those accordingly. Overall, by systematically assessing the problem formulation and mechanisms, the results show that substantial improvements in convergence can be achieved by utilizing appropriate optimization techniques, thus leading to more successful and optimal parameter estimation.

Authors: Rohit Ramachandran, Charles D.Immanuel, Frantisek Stepanek, James D.Litster, Francis J.DoyleIII

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Abstract: In this study, a dynamic model is presented for the granulation process, employing a three-dimensional population balance framework. The major focus of this work is the theoretical development and experimental validation of a novel mechanistic breakage kernel that is incorporated within the population balance equation. Qualitative validation of breakage kernel/model was first performed and trends of lumped properties (i.e., total particles, average size, binder content and porosity) and distributed properties (i.e., granule size and fractional binder content) show good agreement with the expected phenomenological behaviour. Successful high-shear mixer granulation experiments using glass-ballotini as the primary powder and poly-vinyl alcohol in water (PVOH-H2O) as the liquid binder were then carried out to mimic predominantly breakage-only behaviour whereby the rate of breakage was greater than the rates of nucleation and aggregation. Good agreement between experimental and simulation results were obtained for the granule size distribution under different operating conditions. In addition, accurate model predictions were obtained for the evolution of the lumped properties.

Authors: Thomas Glaser, Constantijn F.W.Sanders, Fu.Y.Wang, Ian T.Cameron, James D.Litster, Jonathan M.-H.Poon, Rohit Ramachandran, Charles D.Immanuel, Francis J.DoyleIII

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Abstract: This paper details a methodology for the design of a model predictive controller for a continuous granulation plant. The work is based on a non-linear one-dimensional population balance model (1D-PBM), which was parameterized using experimental step test data generated at a continuous granulation pilot plant installed at the University of Queensland, Australia. The main objective was to operate the granulator under optimal conditions while off-specification material was fed back into the granulator to increase the economy of the process. The final algorithm design combines elements of model predictive control (MPC) with gain scheduling to cancel non-linearities in the recycle flow. A model directly identified from the step test data was the basis for testing a model predictive controller. Simulations show that the efficiency and robustness of this granulation process can be improved by applying the proposed control strategy. Ongoing work focuses on the implementation of the proposed control strategy on a full scale industrial plant.

Authors: F.Štěpánek, P.Rajniak, C.Mancinelli. R.T.Chern, R.Ramachandran

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Abstract: The effect of primary particle morphology on the spatial distribution of binder in wet granules was investigated by numerical simulations. The shape factors of four commonly used pharmaceutical excipients – mannitol, lactose, microcrystalline cellulose, and calcium phosphate – were evaluated by digital image analysis and used for three-dimensional computer reconstruction of virtual particle populations. The formation of wet agglomerates was simulated by close random packing of primary particles and then finding the equilibrium distribution of a liquid binder in the pore space within the close packed structures, using the Volume of Fluid (VOF) method. The spatial distribution of binder in the computer-generated wet agglomerates was then analysed and the dependence of the fractional surface coverage by liquid on the overall binder/solids ratio was systematically obtained for different values of primary particle surface roughness. The obtained dependence was used to explain experimentally observed differences in the granulation kinetics of the four pharmaceutical excipients under otherwise identical conditions.

Authors: Jonathan M.-H.Poon, Rohit Ramachandran, Constantijn F.W.Sanders, Thomas Glaser, Charles D.Immanuel, Francis J.Doyle III, James D.Litster, FrantisekStepanek, Fu-YangWang, Ian T.Cameron

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Abstract: In this study, a dynamic model is presented for the granulation process, employing a three-dimensional population balance framework. As a first attempt to account for the multi-scale character of the process, the nucleation and aggregation kernels used in the population balance model are derived using mechanistic representations of the underlying particle physics such as wetting kinetics and energy dissipation effects. Thus, the fundamental properties of the powder and the liquid were used as parameters in the model to predict the granulator dynamics and granule properties. The population balance model is validated against experimental data from a  recipe obtained using a lab-scale drum granulator for granule size, fractional binder content and porosity. A reasonably good agreement between experimental and simulation results were obtained for the granule size distribution under different experimental conditions. In addition, accurate model predictions were made for the evolution of the average properties (i.e., size, fractional binder content and porosity) for various operating conditions.

Authors: Rohit Ramachandran, Jonathan M.-H.Poon, Constantijn F.W.Sanders, Thomas Glaser, Charles D.Immanuel, Francis J.DoyleIII, James D.Litster, Frantisek Stepanek, Fu-Yang Wang, Ian T.Cameron

Paper Link: Link

Abstract: Batch granulation experiments on a lab-scale drum granulator for a Calcite/Polyvinyl alcohol in water (Calcite/PVOH–H2O) system are presented in this study. Experimental studies were carried out to study the aggregation kinetics and mechanism for this granulation recipe, whilst investigating the effects of binder-to-solids ratio and drum load on the granule size, binder content and porosity distributions. In particular, the effect of formulation properties and the granulation operating conditions on the batch process dynamics and the end-granule properties are studied. The formulation properties considered include liquid surface tension, powder-liquid contact angle, dynamic yield stress, powder shape and liquid viscosity. The operating variables include the binder-to-solids ratio, binder addition duration and the binder addition mode. The sensitivity in the process and the non-homogeneity of key particle attributes (size, binder content, and porosity) is evident. The important process manipulations for feedback control and potential disturbances are identified, formulating a comprehensive control configuration for batch and continuous granulation, with the latter case being exemplified in Glaser et al. [T., Glaser, C.F.W., Sanders, F.Y., Wang, I.T., Cameron, R., Ramachandran, J.D., Litster, J.M.-H., Poon, C.D., Immanuel, F.J. Doyle, III, 2007. Model predictive control of drum granulation. Manuscript in preparation.]. The importance of multi-scale process models that link fundamental material properties with the granulation mechanisms and end-granule properties is also evident from the experiments.

Authors: Rohit Ramachandran, G.P.Rangaiah S.Lakshminarayanan

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Abstract: Considerable fluctuations were observed in the riser temperature of one of the fluid catalytic cracking (FCC) unit of a Southeast Asian refinery. This undesired occurrence has an adverse effect on the performance of the process unit. In the present study, several statistical tools are developed and then used, for the first time, for analyzing routine operating data in order to characterize the dynamics of the riser temperature and other critical variables that may be affecting the riser temperature. Subsequently, a first-principles-based dynamic model of the FCC unit is implemented to closely simulate the FCC unit under investigation. The model is validated by predicting the measured operating data of the FCC unit. This facilitated an in-depth study of the FCC unit, leading to the identification of several strategies for improving the control loop performance of the riser temperature.

Authors: Rohit Ramachandran, S. Lakshminarayanan and G.P Rangaiah

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Abstract: This paper is concerned with process identification by curve fitting step responses. Both open-loop and closed-loop identification are studied using simulated data for typical examples as well as experimental data from a laboratory plate heat exchanger. Timedomain curve fitting utilizing efficient local optimization techniques is employed to find the parameters of the process model. Process models are assumed to be first order plus dead time (FOPDT) and/or second order plus dead time with zero (SOPDTZ). Results show that closed-loop identification recovered model parameters that better represented the actual process compared to open-loop identification. Lastly, it was seen that, for experimental data, accurate recovery of model parameters was impeded by the presence of colored noise and/or unmeasured disturbances. Such impediments were absent in the simulated data enabling accurate estimation of model parameters.