Mathematical modelling and control of agitated extraction columns

Liquid-liquid extraction has long been known as a unit operation that plays an important role in industry. This process is well known for its complexity and sensitivity to operation conditions. This thesis presents an attempt to explore the dynamics and control of this process using a systematic approach and state of the art control system design techniques. The process was studied first experimentally under carefully selected. operation conditions, which resembles the ranges employed practically under stable and efficient conditions. Data were collected at steady state conditions using adequate sampling techniques for the dispersed and continuous phases as well as during the transients of the column with the aid of a computer-based online data logging system and online concentration analysis. A stagewise single stage backflow model was improved to mimic the dynamic operation of the column. The developed model accounts for the variation in hydrodynamics, mass transfer, and physical properties throughout the length of the column. End effects were treated by addition of stages at the column entrances. Two parameters were incorporated in the model namely; mass transfer weight factor to correct for the assumption of no mass transfer in the. settling zones at each stage and the backmixing coefficients to handle the axial dispersion phenomena encountered in the course of column operation. The parameters were estimated by minimizing the differences between the experimental and the model predicted concentration profiles at steady state conditions using non-linear optimisation technique. The estimated values were then correlated as functions of operating parameters and were incorporated in·the model equations. The model equations comprise a stiff differential~algebraic system. This system was solved using the GEAR ODE solver. The calculated concentration profiles were compared to those experimentally measured. A very good agreement of the two profiles was achieved within a percent relative error of ±2.S%. The developed rigorous dynamic model of the extraction column was used to derive linear time-invariant reduced-order models that relate the input variables (agitator speed, solvent feed flowrate and concentration, feed concentration and flowrate) to the output variables (raffinate concentration and extract concentration) using the asymptotic method of system identification. The reduced-order models were shown to be accurate in capturing the dynamic behaviour of the process with a maximum modelling prediction error of I %. The simplicity and accuracy of the derived reduced-order models allow for control system design and analysis of such complicated processes. The extraction column is a typical multivariable process with agitator speed and solvent feed flowrate considered as manipulative variables; raffinate concentration and extract concentration as controlled variables and the feeds concentration and feed flowrate as disturbance variables. The control system design of the extraction process was tackled as multi-loop decentralised SISO (Single Input Single Output) as well as centralised MIMO (Multi-Input Multi-Output) system using both conventional and model-based control techniques such as IMC (Internal Model Control) and MPC (Model Predictive Control). Control performance of each control scheme was. studied in terms of stability, speed of response, sensitivity to modelling errors (robustness), setpoint tracking capabilities and load rejection. For decentralised control, multiple loops were assigned to pair.each manipulated variable with each controlled variable according to the interaction analysis and other pairing criteria such as relative gain array (RGA), singular value analysis (SVD). Loops namely Rotor speed-Raffinate concentration and Solvent flowrate Extract concentration showed weak interaction. Multivariable MPC has shown more effective performance compared to other conventional techniques since it accounts for loops interaction, time delays, and input-output variables constraints.

Seismic Response Analysis of a Full-Scale Base-Isolated Structure via Measurements and Modeling

The full-scale base-isolated structure studied in this dissertation is the only base-isolated building in South Island of New Zealand. It sustained hundreds of earthquake ground motions from September 2010 and well into 2012. Several large earthquake responses were recorded in December 2011 by NEES@UCLA and by GeoNet recording station nearby Christchurch Women's Hospital. The primary focus of this dissertation is to advance the state-of-the art of the methods to evaluate performance of seismic-isolated structures and the effects of soil-structure interaction by developing new data processing methodologies to overcome current limitations and by implementing advanced numerical modeling in OpenSees for direct analysis of soil-structure interaction.

This dissertation presents a novel method for recovering force-displacement relations within the isolators of building structures with unknown nonlinearities from sparse seismic-response measurements of floor accelerations. The method requires only direct matrix calculations (factorizations and multiplications); no iterative trial-and-error methods are required. The method requires a mass matrix, or at least an estimate of the floor masses. A stiffness matrix may be used, but is not necessary. Essentially, the method operates on a matrix of incomplete measurements of floor accelerations. In the special case of complete floor measurements of systems with linear dynamics, real modes, and equal floor masses, the principal components of this matrix are the modal responses. In the more general case of partial measurements and nonlinear dynamics, the method extracts a number of linearly-dependent components from Hankel matrices of measured horizontal response accelerations, assembles these components row-wise and extracts principal components from the singular value decomposition of this large matrix of linearly-dependent components. These principal components are then interpolated between floors in a way that minimizes the curvature energy of the interpolation. This interpolation step can make use of a reduced-order stiffness matrix, a backward difference matrix or a central difference matrix. The measured and interpolated floor acceleration components at all floors are then assembled and multiplied by a mass matrix. The recovered in-service force-displacement relations are then incorporated into the OpenSees soil structure interaction model.

Numerical simulations of soil-structure interaction involving non-uniform soil behavior are conducted following the development of the complete soil-structure interaction model of Christchurch Women's Hospital in OpenSees. In these 2D OpenSees models, the superstructure is modeled as two-dimensional frames in short span and long span respectively. The lead rubber bearings are modeled as elastomeric bearing (Bouc Wen) elements. The soil underlying the concrete raft foundation is modeled with linear elastic plane strain quadrilateral element. The non-uniformity of the soil profile is incorporated by extraction and interpolation of shear wave velocity profile from the Canterbury Geotechnical Database. The validity of the complete two-dimensional soil-structure interaction OpenSees model for the hospital is checked by comparing the results of peak floor responses and force-displacement relations within the isolation system achieved from OpenSees simulations to the recorded measurements. General explanations and implications, supported by displacement drifts, floor acceleration and displacement responses, force-displacement relations are described to address the effects of soil-structure interaction.

Extended nonlinear analytical models of compliant parallelogram mechanisms: third-order models

This paper proposes extended nonlinear analytical models, third-order models, of compliant parallelogram mechanisms. These models are capable of capturing the accurate effects from the very large axial force within the transverse motion range of 10% of the beam length through incorporating the terms associated with the high-order (up to third-order) axial force. Firstly, the free-body diagram method is employed to derive the nonlinear analytical model for a basic compliant parallelogram mechanism based on load-displacement relations of a single beam, geometry compatibility conditions, and load-equilibrium conditions. The procedures for the forward solutions and inverse solutions are described. Nonlinear analytical models for guided compliant multi-beam parallelogram mechanisms are then obtained. A case study of the compound compliant parallelogram mechanism, composed of two basic compliant parallelogram mechanisms in symmetry, is further implemented. This work intends to estimate the internal axial force change, the transverse force change, and the transverse stiffness change with the transverse motion using the proposed third-order model in comparison with the first-order model proposed in the prior art. In addition, FEA (finite element analysis) results validate the accuracy of the third-order model for a typical example. It is shown that in the case study the slenderness ratio affects the result discrepancy between the third-order model and the first-order model significantly, and the third-order model can illustrate a non-monotonic transverse stiffness curve if the beam is thin enough.

Dimensionality hyper-reduction and machine learning for dynamical systems with varying parameters

Thesis (Ph.D.)--University of Washington, 2016-08

Variational ensemble Kalman filtering applied to data assimilation problems in computational fluid dynamics

One challenge on data assimilation (DA) methods is how the error covariance for the model state is computed. Ensemble methods have been proposed for producing error covariance estimates, as error is propagated in time using the non-linear model. Variational methods, on the other hand, use the concepts of control theory, whereby the state estimate is optimized from both the background and the measurements. Numerical optimization schemes are applied which solve the problem of memory storage and huge matrix inversion needed by classical Kalman filter methods. Variational Ensemble Kalman filter (VEnKF), as a method inspired the Variational Kalman Filter (VKF), enjoys the benefits from both ensemble methods and variational methods. It avoids filter inbreeding problems which emerge when the ensemble spread underestimates the true error covariance. In VEnKF this is tackled by resampling the ensemble every time measurements are available. One advantage of VEnKF over VKF is that it needs neither tangent linear code nor adjoint code. In this thesis, VEnKF has been applied to a two-dimensional shallow water model simulating a dam-break experiment. The model is a public code with water height measurements recorded in seven stations along the 21:2 m long 1:4 m wide flume’s mid-line. Because the data were too sparse to assimilate the 30 171 model state vector, we chose to interpolate the data both in time and in space. The results of the assimilation were compared with that of a pure simulation. We have found that the results revealed by the VEnKF were more realistic, without numerical artifacts present in the pure simulation. Creating a wrapper code for a model and DA scheme might be challenging, especially when the two were designed independently or are poorly documented. In this thesis we have presented a non-intrusive approach of coupling the model and a DA scheme. An external program is used to send and receive information between the model and DA procedure using files. The advantage of this method is that the model code changes needed are minimal, only a few lines which facilitate input and output. Apart from being simple to coupling, the approach can be employed even if the two were written in different programming languages, because the communication is not through code. The non-intrusive approach is made to accommodate parallel computing by just telling the control program to wait until all the processes have ended before the DA procedure is invoked. It is worth mentioning the overhead increase caused by the approach, as at every assimilation cycle both the model and the DA procedure have to be initialized. Nonetheless, the method can be an ideal approach for a benchmark platform in testing DA methods. The non-intrusive VEnKF has been applied to a multi-purpose hydrodynamic model COHERENS to assimilate Total Suspended Matter (TSM) in lake Säkylän Pyhäjärvi. The lake has an area of 154 km2 with an average depth of 5:4 m. Turbidity and chlorophyll-a concentrations from MERIS satellite images for 7 days between May 16 and July 6 2009 were available. The effect of the organic matter has been computationally eliminated to obtain TSM data. Because of computational demands from both COHERENS and VEnKF, we have chosen to use 1 km grid resolution. The results of the VEnKF have been compared with the measurements recorded at an automatic station located at the North-Western part of the lake. However, due to TSM data sparsity in both time and space, it could not be well matched. The use of multiple automatic stations with real time data is important to elude the time sparsity problem. With DA, this will help in better understanding the environmental hazard variables for instance. We have found that using a very high ensemble size does not necessarily improve the results, because there is a limit whereby additional ensemble members add very little to the performance. Successful implementation of the non-intrusive VEnKF and the ensemble size limit for performance leads to an emerging area of Reduced Order Modeling (ROM). To save computational resources, running full-blown model in ROM is avoided. When the ROM is applied with the non-intrusive DA approach, it might result in a cheaper algorithm that will relax computation challenges existing in the field of modelling and DA.

Decoding complex flow phenomena via Dynamic Mode Decomposition

In this thesis, the viability of the Dynamic Mode Decomposition (DMD) as a technique to analyze and model complex dynamic real-world systems is presented. This method derives, directly from data, computationally efficient reduced-order models (ROMs) which can replace too onerous or unavailable high-fidelity physics-based models. Optimizations and extensions to the standard implementation of the methodology are proposed, investigating diverse case studies related to the decoding of complex flow phenomena. The flexibility of this data-driven technique allows its application to high-fidelity fluid dynamics simulations, as well as time series of real systems observations. The resulting ROMs are tested against two tasks: (i) reduction of the storage requirements of high-fidelity simulations or observations; (ii) interpolation and extrapolation of missing data. The capabilities of DMD can also be exploited to alleviate the cost of onerous studies that require many simulations, such as uncertainty quantification analysis, especially when dealing with complex high-dimensional systems. In this context, a novel approach to address parameter variability issues when modeling systems with space and time-variant response is proposed. Specifically, DMD is merged with another model-reduction technique, namely the Polynomial Chaos Expansion, for uncertainty quantification purposes. Useful guidelines for DMD deployment result from the study, together with the demonstration of its potential to ease diagnosis and scenario analysis when complex flow processes are involved.

Improved Selective Cholesterol Adsorption By Molecularly Imprinted Poly(methacrylic Acid)/silica (pmaa-sio₂) Hybrid Material Synthesized With Different Molar Ratios.

The present paper describes the synthesis of molecularly imprinted polymer - poly(methacrylic acid)/silica and reports its performance feasibility with desired adsorption capacity and selectivity for cholesterol extraction. Two imprinted hybrid materials were synthesized at different methacrylic acid (MAA)/tetraethoxysilane (TEOS) molar ratios (6:1 and 1:5) and characterized by FT-IR, TGA, SEM and textural data. Cholesterol adsorption on hybrid materials took place preferably in apolar solvent medium, especially in chloroform. From the kinetic data, the equilibrium time was reached quickly, being 12 and 20 min for the polymers synthesized at MAA/TEOS molar ratio of 6:1 and 1:5, respectively. The pseudo-second-order model provided the best fit for cholesterol adsorption on polymers, confirming the chemical nature of the adsorption process, while the dual-site Langmuir-Freundlich equation presented the best fit to the experimental data, suggesting the existence of two kinds of adsorption sites on both polymers. The maximum adsorption capacities obtained for the polymers synthesized at MAA/TEOS molar ratios of 6:1 and 1:5 were found to be 214.8 and 166.4 mg g(-1), respectively. The results from isotherm data also indicated higher adsorption capacity for both imprinted polymers regarding to corresponding non-imprinted polymers. Nevertheless, taking into account the retention parameters and selectivity of cholesterol in the presence of structurally analogue compounds (5-α-cholestane and 7-dehydrocholesterol), it was observed that the polymer synthesized at the MAA/TEOS molar ratio of 6:1 was much more selective for cholesterol than the one prepared at the ratio of 1:5, thus suggesting that selective binding sites ascribed to the carboxyl group from MAA play a central role in the imprinting effect created on MIP.

Removal Of Glyphosate Herbicide From Water Using Biopolymer Membranes.

Enormous amounts of pesticides are manufactured and used worldwide, some of which reach soils and aquatic systems. Glyphosate is a non-selective herbicide that is effective against all types of weeds and has been used for many years. It can therefore be found as a contaminant in water, and procedures are required for its removal. This work investigates the use of biopolymeric membranes prepared with chitosan (CS), alginate (AG), and a chitosan/alginate combination (CS/AG) for the adsorption of glyphosate present in water samples. The adsorption of glyphosate by the different membranes was investigated using the pseudo-first order and pseudo-second order kinetic models, as well as the Langmuir and Freundlich isotherm models. The membranes were characterized regarding membrane solubility, swelling, mechanical, chemical and morphological properties. The results of kinetics experiments showed that adsorption equilibrium was reached within 4 h and that the CS membrane presented the best adsorption (10.88 mg of glyphosate/g of membrane), followed by the CS/AG bilayer (8.70 mg of glyphosate/g of membrane). The AG membrane did not show any adsorption capacity for this herbicide. The pseudo-second order model provided good fits to the glyphosate adsorption data on CS and CS/AG membranes, with high correlation coefficient values. Glyphosate adsorption by the membranes could be fitted by the Freundlich isotherm model. There was a high affinity between glyphosate and the CS membrane and moderate affinity in the case of the CS/AG membrane. Physico-chemical characterization of the membranes showed low values of solubility in water, indicating that the membranes are stable and not soluble in water. The SEM and AFM analysis showed evidence of the presence of glyphosate on CS membranes and on chitosan face on CS/AG membranes. The results showed that the glyphosate herbicide can be adsorbed by chitosan membranes and the proposed membrane-based methodology was successfully used to treat a water sample contaminated with glyphosate. Biopolymer membranes therefore potentially offer a versatile method to eliminate agricultural chemicals from water supplies.

Avaliação da biodegradabilidade anaeróbia de resíduos da bovinocultura e da suinocultura

The biodegradability of animal wastes production was evaluated through a simplified methodology that allowed the verification of the applicability of anaerobic processes. The experiments were performed in bath reactors, with granular sludge of three origins: UASB reactor treating dairy effluent, UASB reactor treating swine effluent and UASB reactor treating effluent of slaughterhouse of poultry. The experiments (1) - dairy effluent and poultry slaughterhouse non-adapted sludge; (2) -swine effluent and poultry slaughterhouse non-adapted sludge; (3) - dairy effluent and poultry slaughterhouse adapted sludge; (4) - swine effluent and poultry slaughterhouse adapted sludge; (5) - dairy effluent and dairy sludge, and (6) - swine effluent and swine sludge were performed in Incubator Shaker, at a temperature of 35 °C, under agitation at a 150 rpm, for 5 minutes, every 1 hour. A substrat:biomass relationship of 0.5 was used. Kinetic models of Monod, Zero Order, First and Second Order were tested and it was verified that the First Order model provided the best adjustment. The apparent First Order kinetic parameter (k1) was estimated for the experiments 1; 2; 3; 4; 5, and 6, as 2.51 x 10-2; 2.49 x 10-2; 1.90 x 10-2; 3.09 x 10-2; 2.54 x 10-2; 4.09 x 10-2 h-1, respectively.

Eddy Formation in the Tropical Atlantic Induced by Abrupt Changes in the Meridional Overturning Circulation

The variability of the meridional overturning circulation (MOC) in the upper tropical Atlantic basin is investigated using a reduced-gravity model in a simplified domain. Four sets of idealized numerical experiments are performed: (i) switch-on of the MOC until a fixed value when a constant northward flow is applied along the western boundary; (ii) MOC with a variable flow; (iii) MOC in a quasi-steady flow; and (iv) shutdown of the MOC in the Northern Hemisphere. Results from experiments (i) show that eddies are generated at the equatorial region by shear instability and detached northward; eddies are responsible for an enhancement of the mean flow and the variability of the MOC. Results from experiments (ii) show a transitional behavior of the MOC related to the eddy generation in interannual-decadal time scales as the Reynolds number varies due to the variations in the MOC. In experiments (iii), a critical Reynolds number Re(c) around 30 is found, above which eddies are generated. Experiments (iv) demonstrate that even after the collapse of MOC in the Northern Hemisphere, eddies can still be generated and carry energy across the equator into the Northern Hemisphere; these eddies act to attenuate the impact of the MOC shutdown on short time scales. The results described here may be particularly pertinent to ocean general circulation models in which the Reynolds number lies close to the bifurcation point separating the laminar and turbulent regimes.

Anaerobic sequencing batch biofilm reactor applied to automobile industry wastewater treatment: Volumetric loading rate and feed strategy effects

This paper presents a technological viability study of wastewater treatment in an automobile industry by an anaerobic sequencing batch biofilm reactor containing immobilized biomass (AnSBBR) with a draft tube. The reactor was operated in 8-h cycles, with agitation of 400 rpm, at 30 degrees C and treating 2.0 L wastewater per cycle. Initially the efficiency and stability of the reactor were studied when supplied with nutrients and alkalinity. Removal efficiency of 88% was obtained at volumetric loading rate (VLR) of 3.09 mg COD/L day. When VLR was increased to 6.19 mg COD/L day the system presented stable operation with reduction in efficiency of 71%. In a second stage the AnSBBR was operated treating wastewater in natura, i.e., without nutrients supplementation, only with alkalinity, thereby changing feed strategy. The first strategy consisted in feeding 2.0 L batch wise (10 min), the second in feeding 1.0 L of influent batch wise (10 min) and an additional 1.0 L fed-batch wise (4 h), both dewatering 2.0 L of the effluent in 10 min. The third one maintained 1.0 L of treated effluent in the reactor, without discharging, and 1.0 L of influent was fed fed-batch wise (4 h) with dewatering 1.0 L of the effluent in 10 min. For all implemented strategies (VLR of 1.40, 2.57 and 2.61 mg COD/L day) the system presented stability and removal efficiency of approximately 80%. These results show that the AnSBBR presents operational flexibility, as the influent can be fed according to industry availability. In industrial processes this is a considerable advantage, as the influent may be prone to variations. Moreover, for all the investigated conditions the kinetic parameters were obtained from fitting a first-order model to the profiles of organic matter, total volatile acids and methane concentrations. Analysis of the kinetic parameters showed that the best strategy is feeding 1.0 L of influent batchwise (10 min) and 1.0 L fed-batch wise (4 h) in 8-h cycle. (c) 2007 Elsevier B.V. All rights reserved.

Considerations on the kinetics of froth flotation of ultrafine coal contained in tailings

This article presents a kinetic evaluation of froth flotation of ultrafine coal contained in the tailings from a Colombian coal preparation plant. The plant utilizes a dense-medium cyclones and spirals circuit. The tailings contained material that was 63% finer than 14 mu m. Flotation tests were performed with and without coal ""promoters"" (diesel oil or kerosene) to evaluate the kinetics of flotation of coal. It was found that flotation rates were higher when no promoter was added. Different kinetic models were evaluated for the flotation of the coal from the tailings, and it was found that the best fitted model was the classical first-order model.

Thermal inactivation of polyphenoloxidase and peroxidase in green coconut (Cocos nucifera) water

P>Coconut water is an isotonic beverage naturally obtained from the green coconut. After extracted and exposed to air, it is rapidly degraded by enzymes peroxidase (POD) and polyphenoloxidase (PPO). To study the effect of thermal processing on coconut water enzymatic activity, batch process was conducted at three different temperatures, and at eight holding times. The residual activity values suggest the presence of two isoenzymes with different thermal resistances, at least, and a two-component first-order model was considered to model the enzymatic inactivation parameters. The decimal reduction time at 86.9 degrees C (D(86.9 degrees C)) determined were 6.0 s and 11.3 min for PPO heat labile and heat resistant fractions, respectively, with average z-value = 5.6 degrees C (temperature difference required for tenfold change in D). For POD, D(86.9 degrees C) = 8.6 s (z = 3.4 degrees C) for the heat labile fraction was obtained and D(86.9 degrees C) = 26.3 min (z = 6.7 degrees C) for the heat resistant one.

Assessing flow in physical activity: The Flow State Scale-2 and Dispositional Flow Scale-2

The Flow State Scale-2 (FSS-2) and Dispositional Flow Scale-2 (DFS-2) are presented as two self-report instruments designed to assess flow experiences in physical activity. Item modifications were made to the original versions of these scales in order to improve the measurement of some of the flow dimensions. Confirmatory factor analyses of an item identification and a cross-validation sample demonstrated a good fit of the new scales. There was support for both a 9-first-order factor model and a higher order model with a global flow factor. The item identification sample yielded mean item loadings on the first-order factor of .78 for the FSS-2 and .77 for the DFS-2. Reliability estimates ranged from .80 to .90 for the FSS-2, and .81 to .90 for the DFS-2. In the cross-validation sample, mean item loadings on the first-order factor were .80 for the FSS-2, and .73 for the DFS-2. Reliability estimates ranged between .80 to .92 for the FSS-2 and .78 to .86 for the DFS-2. The scales are presented as ways of assessing flow experienced within a particular event (FSS-2) or the frequency of flow experiences in chosen physical activity in general (DFS-2).

A framework for extreme-event control in wastewater treatment

In this paper an approach to extreme event control in wastewater treatment plant operation by use of automatic supervisory control is discussed. The framework presented is based on the fact that different operational conditions manifest themselves as clusters in a multivariate measurement space. These clusters are identified and linked to specific and corresponding events by use of principal component analysis and fuzzy c-means clustering. A reduced system model is assigned to each type of extreme event and used to calculate appropriate local controller set points. In earlier work we have shown that this approach is applicable to wastewater treatment control using look-up tables to determine current set points. In this work we focus on the automatic determination of appropriate set points by use of steady state and dynamic predictions. The performance of a relatively simple steady-state supervisory controller is compared with that of a model predictive supervisory controller. Also, a look-up table approach is included in the comparison, as it provides a simple and robust alternative to the steady-state and model predictive controllers, The methodology is illustrated in a simulation study.