The origin of the more than 100 km wide Lycksele ring structure in Sweden has puzzled geoscientists for years. In this short note we present results from field analysis, detailed sampling and laboratory analysis executed in search for evidence of an impact, e.g. shatter cones and shock features in minerals. Both approaches gave negative results and consequently an impact origin could neither be confirmed nor rejected. The circular structure of the Lycksele ring and its central uplift are, however, typical features of large, complex impact structures.

This contribution presents a modeling and optimization method for multi-column counter-current purification (MCSGP) processes. The model is based on conventional column models and by using the symmetric and cyclic steady state characteristics of the process a single column analog model was developed. The model have been used for dynamic optimization of the MCSGP process. The optimization was based on a simultaneous method where the control and state variables were discretized using a direct and local collocation method on finite elements in the temporal dimension and a finite volume weighted essentially non-oscillatory (WENO) scheme in the spatial dimension. The resulting nonlinear program (NLP) were solved using an interior point method. The case study presented shows that the zero-order hold elution trajectories, developed for single column batch operation, can be extended to semi-continuous multi-column chromatography with product recycling. The optimization results is composed of a set of operating conditions where the product was upgraded to 95% purity with 99% process yield.

Biomolecular and pharmaceutical downstream processing is dominated by chromatographic separation, which is associated with high product quality, low capacity and high costs. The separation can be optimized to minimize the costs while achieving a high purity. This paper presents an experimental validation of a discretized multi-level elution (DiME) trajectory, implemented on commercially available chromatography equipment. The tertiary protein separation of ribonuclease A, cytochrome C and lysozyme was used as a case study. A mechanistic model was calibrated using step and linear gradient experiments. The model was simulated together with the state sensitivities with respect to model parameters, which was used in the Levenberg-Marquardt algorithm to fit the model response to the experimental data. The model was used to solve the dynamic optimization problem of maximizing the yield of cytochrome C given a 95% purity requirement, 1000 s processing time and 50 salt concentration levels in the elution trajectory. The model was spatially discretized using finite volumes and temporally discretized using direct collocation. The corresponding non-linear programming problem was solved with IPOPT. Once the optimal salt trajectory was found it was experimentally implemented on an AKTA Pure using an OPC interface. The optimal trajectory was analyzed in-line by UV absorbance measurements and off-line by analysis of collected fractions. The results presented in this study show the successful experimental realization of DIME trajectories and how to use model calibration, optimization and control to realize DiME trajectories for any chromatography separation problem. (C) 2016 Elsevier B.V. All rights reserved.

This contribution presents a novel model-based methodology for open-loop optimal control of batch high-pressure liquid chromatographic (HPLC) separation processes. The framework allows for simultaneous optimization of target component recovery yield and production rate with respect to a parameterization of the input elution trajectory and fractionating interval endpoints. The proposed methodology implies formulating and solving a large-scale dynamic optimization problem (DOP) constrained by partial differential equations (PDEs) governing the multi-component system dynamics. It is based on a simultaneous method where both the control and state variables are fully discretized in the temporal domain, using direct local collocation on finite elements, and the state variables are discretized in the spatial domain, using an adaptive finite volume weighted essentially non-oscillatory (WENO) scheme. The direct transcription of the DOP described by Modelica, and its extension Optimica, code into a sparse nonlinear programming problem (NLP) is thoroughly presented. The NLP was subsequently solved using CasADi's (Computer algebra system with Automatic Differentiation) interface to the primal-dual interior point method IPOPT. The advantages of the open-loop optimal control strategy are highlighted through the solution of a challenging ternary complex mixture separation problem of human insulin analogs, with the intermediately eluting component as the target, for a hydrophobic interaction chromatography system. Moreover, the high intercorrelation between the shape of the optimal elution trajectories and the fractionation interval endpoints is thoroughly investigated. It is also demonstrated that the direct transcription methodology enabled accurate and efficient computation of optimal cyclic-steady-state solutions, which govern that state and control variables conform to periodicity constraints imposed on column regeneration and re-equilibration. By these means, the generic methods and tools developed here are applicable to continuous chromatographic separation technologies, including the continuous simulated moving bed (SMB) and the multicolumn counter-current solvent gradient purification (MCSGP) process. (C) 2016 Elsevier Ltd. All rights reserved.

This contribution presents a novel process analytical technology (PAT) software interface for online monitoring and control of commercial high-pressure liquid chromatography (HPLC) systems. The developed interface is an add-on to chromatography control software and uses industrystandard bidirectional communication protocols to link sensor technologies with the individual HPLC system components in an overall automation framework that facilitates data acquisition, central operation and control of all instruments. The interface is encoded in the Python (TM) scripting language and supports versatile data transfer to chromatography control software using either OPC (OLE for process control) or COM (component object model) technologies, which are both based on client/server architectures. By these means, the interface utilizes the flexibility of the high-level programming language for formulating optimal control strategies and enables (semantic) interoperability between the chromatography control software and user defined scripts as well as third-party scientific libraries and numerical packages. The advantages and applicability of the developed interface are highlighted through the implementation of a model-based iterative learning control strategy, in order to assure batch-to-batch repeatability, and open-loop optimal controlled elution trajectories on a commercial HPLC separation system. It is, however, noteworthy that the software interface is completely generic and constitutes a novel framework for implementing any PID control schemes as well as sequential optimal experimental design and model predictive control strategies.

This contribution concerns the development of generic methods and tools for robust optimal control of high-pressure liquid chromatographic separation processes. The proposed methodology exploits a deterministic robust formulation, that employs a linearization of the uncertainty set, based on Lyapunov differential equations to generate optimal elution trajectories in the presence of uncertainty. Computational tractability is obtained by casting the robust counterpart problem in the framework of bilevel optimal control where the upper level concerns forward simulation of the Lyapunov differential equation, and the nominal open-loop optimal control problem augmented with the robustified target component purity inequality constraint margin is considered in the lower level. The lower-level open-loop optimal control problem, constrained by spatially discretized partial differential equations, is transcribed into a finite dimensional nonlinear program using direct collocation, which is then solved by a primal-dual interior point method. The advantages of the robustification strategy are highlighted through the solution of a challenging ternary complex mixture separation problem for a hydrophobic interaction chromatography system. The study shows that penalizing the changes in the zero-order hold control gives optimal solutions with low sensitivity to uncertainty. A key result is that the robustified general elution trajectories outperformed the conventional linear trajectories both in terms of recovery yield and robustness.

This contribution presents a novel offline dynamic multi-objective optimization framework for high-pressure liquid chromatographic (HPLC) processes in batch elution mode. The framework allows for optimization of general elution trajectories parametrized with piecewise constant control signals. It is based on a simultaneous method where both the control and state variables are fully discretized in the temporal domain, using orthogonal collocations on finite elements, and the state variables are discretized in the spatial domain, using a finite volume weighted essentially non-oscillatory (WENO) scheme. The resulting finite dimensional nonlinear program (NLP) is solved using a primal-dual interior point method and automatic differentiation techniques. The advantages of this open-loop optimal control methodology are highlighted through the solution of a challenging ternary complex mixture separation problem for a hydrophobic interaction chromatography (HIC) system. For a bi-objective optimization of the target component productivity and yield, subject to a purity constraint, the set of Pareto solutions generated with general elution trajectories showed considerable improvement in the productivity objective when compared to the Pareto set obtained using conventional linear elution trajectories.

The importance of rare earth elements in modern technological industry grows, and as a result the interest for developing separation processes increases. This work is a part of developing chromatography as a rare earth element processing method. Process optimization is an important step in process development, and there are several competing objectives that need to be considered in a chromatographic separation process. Most studies are limited to evaluating the two competing objectives productivity and yield, and studies of scenarios with tri-objective optimizations are scarce. Tri-objective optimizations are much needed when evaluating the chromatographic separation of rare earth elements due to the importance of product pool concentration along with productivity and yield as process objectives. In this work, a multi-objective optimization strategy considering productivity, yield and pool concentration is proposed. This was carried out in the frame of a model based optimization study on a batch chromatography separation of the rare earth elements samarium, europium and gadolinium. The findings from the multi-objective optimization were used to provide with a general strategy for achieving desirable operation points, resulting in a productivity ranging between 0.61 and 0.75 kgEu/mcolumn(3), h(-1) and a pool concentration between 0.52 and 0.79 kgEu/m(3), while maintaining a purity above 99% and never falling below an 80% yield for the main target component europium.

This paper presents the elaboration of an experimentally validated model of a continuous cross-flow atomic layer deposition (ALD) reactor with temporally separated precursor pulsing encoded in the Modelica language. For the experimental validation of the model, in situ quartz crystal microbalance (QCM) diagnostics was used to yield submonolayer resolution of mass deposition resulting from thin film growth of ZnO from Zn(C2H5)2 and H2O precursors. The ZnO ALD reaction intrinsic kinetic mechanism that was developed accounted for the temporal evolution of the equilibrium fractional surface concentrations of precursor adducts and their transition states for each half-reaction. This mechanism was incorporated into a rigorous model of reactor transport, which comprises isothermal compressible equations for the conservation of mass, momentum and gas-phase species. The physically based model in this way relates the local partial pressures of precursors to the dynamic composition of the growth surface, and ultimately governs the accumulated mass trajectory at the QCM sensor. Quantitative rate information can then be extracted by means of dynamic parameter estimation. The continuous operation of the reactor is described by limit-cycle dynamic solutions and numerically computed using Radau collocation schemes and solved using CasADi׳s interface to IPOPT. Model predictions of the transient mass gain per unit area of exposed surface QCM sensor, resolved at a single pulse sequence, were in good agreement with experimental data under a wide range of operating conditions. An important property of the limit-cycle solution procedure is that it enables the systematic approach to analyze the dynamic nature of the growth surface composition as a function of process operating parameters. Especially, the dependency of the film growth rate per limit-cycle on the half-cycle precursor exposure dose and the process temperature was thoroughly assessed and the difference between ALD in saturating and in non-saturating film growth conditions distinguished.

This paper presents the development of a non-dimensional model of a continuous cross-flow atomic layer deposition (ALD) reactor with temporally separated precursor pulsing and a structured model-based methodology for scaling up the substrate dimensions. The model incorporates an ALD gas-surface reaction kinetic mechanism for the deposition of thin ZnO films from Zn(C2H5)(2) and H2O precursors that was experimentally validated in our previous work (HoInacivist et al., 2012, 2013a). In order to maintain dynamic similarity, a scaling analysis was applied based on the dimensionless numbers, appearing in non-dimensionalized momentum and species mass conservation equations, that describe the convective laminar flow, mass transfer and heterogeneous reaction. The impact on these dimensionless numbers and, more importantly, the impact on the limit-cycle deposition rate and its relative uniformity was thoroughly investigated when linearly scaling up the substrate dimensions. In the scale-up procedure, the limit-cycle precursor utilization was maximized by means of dynamic optimization, while ensuring that identical deposition profiles were obtained in the scaled-up system. The results presented here demonstrated that the maximum precursor yields were promoted at higher substrate dimensions. Limit-cycle dynamic solutions to the non-climensionalized model, computed with a collocation discretization in time, revealed that it is a combination of the degree of precursor depletion in the flow direction and the magnitude of the pressure drop across the reactor chamber that governs the extent of the deposition profile non-uniformity. A key finding of this study is the identification of optimal scaling rules for maximizing precursor utilization in the scaled-up system while maintaining fixed absolute growth rate and its relative uniformity. (C) 2014 Elsevier Ltd. All rights reserved.

This paper presents a structured methodology for the constrained multi-objective optimization (MO) of a continuous cross-flow atomic layer deposition (ALD) reactor model with temporal precursor pulsing. The process model has been elaborated and experimentally validated in the first two papers of this series (Holmqvist et al., 2012, Holmqvist et al., 2013). A general constrained MO problem (MOP) was formulated to simultaneously optimize quasi-steady-state reactor throughput and overall precursor conversion for the controlled deposition of ZnO films from Zn(C2H5)2 and H2O, subject to a set of operational constraints. These constraints included lower bounds for the cross-substrate film thickness uniformity and post-precursor purge duration. The non-dominated Pareto optimal solutions obtained successfully revealed the relation between the incommensurable process objectives and reduced the design space of the ALD process into a feasible set of design alternatives. The results presented here show that post-precursor purge duration is essential when optimizing throughput in temporally separated ALD processes, and that this is a major drawback when considering operation at atmospheric pressure. Finally, the robustness of the process along the Pareto optimal front, i.e. the ability of the process to accommodate variations in the associated set of optimal decision variables (DVs), was assessed by Monte Carlo simulations, in which the values of the parametric uncertainties were randomly generated from a multivariate normal distribution. The uncertainty and sensitivity analysis showed that the inherent robustness of the process is progressively lost with the precursor conversion, and revealed the mechanistic dependence of all DVs on the proposed optimization specifications.

This paper demonstrates the experimental validation and mechanistic analysis of the continuous cross-flow atomic layer deposition (ALD) reactor model developed in the first article of this series (Holmqvist et al., in press). A general nonlinear parameter estimation problem was formulated to identify the kinetic parameters involved in the developed ALD gas–surface reaction mechanism, governing ZnO film growth, from ex situ film thickness measurements. The presented methodology for comprehensive model assessment considers the statistical uncertainty of least-squares estimates and its ultimate impact on the model predicted response. Joint inference regions were determined to assess the significance of parameter estimates and results indicate that all estimates involved in the precursor half-reactions were adequately determined. The reparameterization of the Arrhenius equation effectively decreased the characteristically high correlations between Arrhenius parameters, leading to improvement in precision of individual parameter estimates. Model predictions of the spatially dependent film thickness profile with narrow confidence band were in good agreement with both calibration and validation experimental data, respectively, under a wide range of operating conditions. The subsequent extensive theoretical analysis exhibits that the experimentally validated model successfully reproduces the detailed process dynamics revealed by in situ quartz crystal microbalance and quadrupole mass spectroscopy diagnostics, and thereby provides a supplementary analysis tool. Finally, the univariate sensitivity analysis revealed the mechanistic dependence of all the measured process operating parameters on the spatially dependent film thickness profile, resolved at the level of a single pulse sequence. Hence, the presented model-based framework serves as a means to guide future research efforts in the field of ALD process optimization.