This work builds upon our previous two studies [Ramirez, W.F., Galvin, K.P., 2005. Dynamic model of multispecies segregation and dispersion in liquid fluidized beds. A.I.Ch.E. Journal 51, 2103–2108; Galvin, K.P., Swann, R., Ramirez, W.F., 2006. Segregation and dispersion of a binary system of particles in a fluidized bed. A.I.Ch.E. Journal 52, 3401–3410] in establishing a dynamic continuum description of the segregation and dispersion of multiple particle species in a liquid-fluidized bed. A correlation for the particle dispersion coefficient, based on the kinetic theory of gases, is investigated in this present paper. Our adjustable model parameter was found to vary inversely with a particle Froude number, in a manner similar to the variation of the particle drag coefficient with the particle Reynolds number. Hence a new relationship for the dispersion coefficient, based around the kinetic theory of gases, was proposed and validated. The validation applies to a nominal particle Reynolds number in the range of 20–1000. A new solution strategy to the dynamic segregation and dispersion model, a shell balance approach, was developed to overcome the potential for a singularity above the bed where exceedingly low particle concentrations arise. This approach guarantees mass conservation of the particles. The model was validated against steady-state experimental data of binary particle systems consisting notionally of one particle size and two different particle densities. When the particle densities of the two species are very similar, it becomes necessary to treat each particle species as having a range of particle sizes, given that the small size range was equally significant to the difference in particle density. In this case the model was applied to 10 particle species. Moreover, the model is capable of capturing the dynamics of the layer inversion problem, illustrating the power of the model to describe complex fluidization behaviour.

A new tool was developed to solve a wide range of optimal beer fermentation problems. Using a mathematical model of beer fermentation, the direct dynamic optimization technique of sequential quadratic programming was investigated for determining the optimal cooling policy to maximize ethanol production for a fixed final time, including effects that optimize flavor. The new tool is very efficient for determining optimal cooling strategies. New control strategies were found that increase ethanol production while decreasing the deleterious effects of fusel alcohols and keeping the acetaldehyde concentrations at moderate levels. Model parameter sensitivity was investigated and it was shown that the system could be regulated successfully around optimal temperature profiles.

An industrial pharmaceutical company has provided industrial pilot scale fed-batch data from a biological process used to produce a foreign protein from fed-batch fermentation. This process had proven difficult to control due to the complex behavior of the bacteria after induction. Because of the difficulty of modeling the process fundamentally, neural networks are an attractive alternative. To capture dynamic systems a gray box model approach of parameter function neural networks was used. The parameter function neural network approach has been able to capture well this pilot scale fed-batch fermentation process. In order to obtain accurate training data, the data sets were fit and smoothed using smoothing cubic spline functions. Neural networks were found for the five critical parameter functions of growth rate, glucose consumption rate, oxygen consumption rate, acetate production rate, and protein production rate. Relatively simple networks were used in order to capture process behavior and not the significant noise in the industrial scale pilot data. Simulations using the neural network parameters predicted dynamic response data well.

The steady-state segregation and dispersion of a binary system of particles in a liquid-fluidized bed was investigated. One of the species had a density of 1,600 kg/m3 and the other 1,900 kg/m3, and both exhibited a narrow size range of 1.00 to 1.18 mm. A generalized model for describing the dispersion coefficient, D, was proposed. That is, D = αdUf/ϕ, where d is the particle diameter, Uf the local interstitial fluid velocity, and ϕ the local volume fraction of solids. The model had one adjustable parameter α, which was fixed at 0.7 for both particle species and for the six different superficial fluidization velocities used. The particle segregation was described with reference to the monocomponent fluidization parameters of the two species, based on the Richardson and Zaki equation. Good descriptions of the concentration profiles of the two species were produced for all superficial velocities examined. Additional experiments involving other binary systems were also conducted in order to test the generality of the model. These systems involved particles of closer settling velocities, and, hence, displayed more mixing. Very small adjustments in the terminal velocities of the species, typically 2%, were needed to achieve satisfactory agreement between the theoretical and experimental concentration profiles, with the model parameter, α, equal to 0.7. This adjustment was justified because of apparent changes in the average particle sizes of the two species due to particle-size segregation. © 2006 American Institute of Chemical Engineers AIChE J, 2006

AIChE JournalVolume 51, Issue 7 p. 2103-2108 Particle Technology and Fluidization Dynamic model of multi-species segregation and dispersion in liquid fluidized beds W. Fred Ramirez, Corresponding Author W. Fred Ramirez [email protected] Dept. of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309Dept. of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309Search for more papers by this authorK. P. Galvin, K. P. Galvin School of Engineering, University of Newcastle, NSW 2308, AustraliaSearch for more papers by this author W. Fred Ramirez, Corresponding Author W. Fred Ramirez [email protected] Dept. of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309Dept. of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309Search for more papers by this authorK. P. Galvin, K. P. Galvin School of Engineering, University of Newcastle, NSW 2308, AustraliaSearch for more papers by this author First published: 10 May 2005 https://doi.org/10.1002/aic.10457Citations: 15Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Citing Literature Volume51, Issue7July 2005Pages 2103-2108 RelatedInformation

This paper discusses both fundamental mathematical modeling of dynamic biotechnology processes as well as the use of hybrid neural network modeling of these systems. In addition dynamic optimization techniques are discussed which are compatible with both modeling techniques. These modeling and optimization techniques are applied to a batch fermentation of foreign protein using inducible recombinant bacteria

A new software framework for modeling dynamic systems is introduced. Some of the main features of this software are speed, modularity, extensibility, ease of debugging, and a free software license. This software framework has been used to fit an empirical model to industrial pilot-scale data, and preliminary results are presented. The software is available at http://robust.colorado.edu/software.

The use of optimal parameter estimation for the online regulation of final etch depth in an ion milling process is described. A model-based control system utilizes a 3-D surface evolution model to predict dynamic surface profiles and etch depth. A heterodyne laser interferometer is used to measure trench height in situ for calculation of the difference in etch rates between the photoresist layer and the exposed portion of the underlying substrate layer. Adaptive material-specfic etch rate parameters and operating parameters such as ion beam strength and angle of incidence are estimated optimally with an extended Kalman filter. Optimal estimates of the in situ etch depth are calculated from the adaptive model, allowing the stopping time of the milling process to be varied from run to run to regulate final etch depth in the presence of disturbances. The system installed on an ion milling machine shows that the controller is capable of accurately regulating final etch depth in the presence of large process faults.

An important recent advance in the solution of the optimal regulator control problem for time-delayed systems is extended here to multivariable systems and to systems which exhibit multiple time delays. The state equations are partitioned into discrete and continuous portions through a state transformation such that the solution of the optimal regulator problem reduces to finding a steady-state controller gain based on both a discrete and continuous Riccati matrix. The discrete Ricatti matrix is found independently of the continuous solution due to the partitioning of the state equations, and it is not necessary to solve the system of partial differential Riccati equations which arise in the traditional solution of the linear quadratic regulator (LQR) problem for time-delayed systems. In addition, through this state transformation it becomes possible to extend the standard state controllability tests to time-delayed systems. It is shown that the controllability of the transformed state space is necessary for a feasible solution to the optimal regulator problem for time-delayed systems. This is an important test to determine the practicality of various time-delayed system realizations. Numerical examples illustrate the application of the technique to systems exhibiting multiple time delays, multivariable systems and time-series models. It is shown that the classic Wood-Berry distillation model realization does not possess state controllability properties which explains why this system has been historically difficult to control using feedback techniques.

We describe the design of a common-path heterodyne laser interferometer for the surface profiling of micron-sized photopatterned features during the microelectronic fabrication process. The common-path design of the interferometer’s reference and measurement arms effectively removes any path length difference in the measurement which can be attributed to the movement of the target surface. It is shown that repeated surface profiling during the ion milling process allows the difference in etch rates between the photoresist layer and the exposed portions of the underlying substrate layer to be monitored online. A prototype apparatus has been assembled and results demonstrating the usefulness of the device are reported. The surface profiles of both a photopatterned nickel–iron trench and an unmasked aluminum trench are measured and compared to those obtained using a stylus-based scanning profiler and an atomic force microscope.

The method of neural network parameter function modeling has been demonstrated to be very effective in modeling the complex dynamics of cell growth and protein production in biotechnology processes. The development of neural network models usually requires large amounts of experimental data. This work examines the ability to use interpolated parameter functions in conjunction with neural network parameter function models to reduce the number of experiments required to develop neural network-based models of dynamic systems. Simulation and experimental results confirming the efficiency of the proposed method are presented.

Ion milling applications in the micro-electronics industry are becoming more challenging due to decreasing feature sizes and increasing aspect ratios. A simulation of the milling problem which is capable of predicting surface evolution in the presence of high aspect ratios where local shadowing of the substrate surface becomes an important issue is described. A method of characteristics solution based on surface inclination angles is derived for a three-dimensional surface evolution model. An algorithm is developed to account for local shadowing effects, where raised areas of the substrate surface (i.e., the photomask) prevent the ion beam from reaching hidden or shadowed portions of the surface. The yield (sputtering) function is modified to account for beam voltage as well as the angle of beam incidence. Yield function parameters are determined experimentally for Al2O3, Ti, permalloy (83/17 wt % Ni–Fe) and postbaked AZ P4400 photoresist. Model predictions are in good agreement with experimental results for the surface evolution of a photopatterned Al2O3 substrate.

This paper describes a novel approach to obtain desired release profiles from diffusion-controlled matrix devices by employing nonuniform initial concentration profiles theoretically and experimentally. Theoretically, a model was developed to examine the effect of nonuniform initial concentration profiles on matrix release behavior, and an optimization technique was investigated to determine suitable nonuniform initial concentration profiles which provide desired release patterns. Experimentally, release rates of an organic dye from photopolymerized matrix devices were measured to test the application of these mathematical techniques and the efficacy of photolaminated matrices in approximating the optimized release behavior. All system parameters were measured by independent experiments, and the experimental release data agree very well with the computed results.

We propose an Extended Implicit Kalman Filter for fault diagnosis of air contaminants in three-dimensional environments. In order to accurately detect and diagnose air contamination faults in environments such as a space station, we combine the use of an Extended Implicit Kalman Filter with the use of sensitivity matrices that provide the filter with an initial guess of the capacity and location of the contamination source. We show that this hybrid system works well in simulations for obtaining an optimal solution to the ill-posed inverse problem of determining the location and strength of an unknown source emission in a space station cabin.

The enzyme cellulase, a multienzyme complex made up of several proteins, catalyzes the conversion of cellulose to glucose in an enzymatic hydrolysis-based biomass-to-ethanol process. Production of cellulase enzyme proteins in large quantities using the fungus Trichoderma reesei requires understanding the dynamics of growth and enzyme production. The method of neural network parameter function modeling, which combines the approximation capabilities of neural networks with fundamental process knowledge, is utilized to develop a mathematical model of this dynamic system. In addition, kinetic models are also developed. Laboratory data from bench-scale fermentations involving growth and protein production by T. reesei on lactose and xylose are used to estimate the parameters in these models. The relative performances of the various models and the results of optimizing these models on two different performance measures are presented. An approximately 33% lower root-mean-squared error (RMSE) in protein predictions and about 40% lower total RMSE is obtained with the neural network-based model as opposed to kinetic models. Using the neural network-based model, the RMSE in predicting optimal conditions for two performance indices, is about 67% and 40% lower, respectively, when compared with the kinetic models. Thus, both model predictions and optimization results from the neural network-based model are found to be closer to the experimental data than the kinetic models developed in this work. It is shown that the neural network parameter function modeling method can be useful as a "macromodeling" technique to rapidly develop dynamic models of a process.

An experimental verification and validation of the neural network parameter function approach to modeling dynamic systems is provided. The neural-network parameter-function modeling scheme utilizes some a priori process knowledge (usually material balances) and experimental data to develop a dynamic neural-network model. Other models based on fundamental principles are also developed. The experimental system under consideration is the host-vector system Escherichia coli D1210 and plasmid pSD8, which produces the foreign protein beta-galactosidase under the effect of the inducer IPTG. Optimal operational conditions are derived and the neural-network-based model is shown to better predict the dynamics and optimum for protein production than the proposed fundamental kinetic models.

Two-phase theory is applied to solid-liquid fluidization in die Stokes flow regime. Because inertial terms can be neglected in the Stokes flow regime, the momentum balances are simplified to all algebraic relation between drag, buoyant, and diffusive forces. The resulting convection-dispersion model is then applied to all experimental expanded-bed adsorption system. Two flows are investigated, namely: step changes in the fluidization velocity and step changes in the fluid properties. Experimental data and model simulations are in excellent agreement for both flow configurations. Furthermore, the two-phase model provides an accurate prediction of the observed time delay in bed expansion for step changes in fluid properties, as well as a mechanistic explanation for its observation.

Expanded-bed adsorption (EBA) is a technique for the purification of proteins from cellular debris in downstream processing. An expanded bed presents the possibility of protein recovery in a single step, eliminating the often costly clarification processing steps such as ultrafiltration, centrifugation, and precipitation. An obstacle to the successful commercialization of this technology is the inability to accurately monitor and control the bed height in these systems.In this paper, we present an overview of work in our laboratory addressing monitoring, modeling, and control strategies as applied to EBA. First, we present the development of a level measurement technique based upon ultrasonics. It is shown that this technique has great promise for bed-height measurement in EBA systems. Second, we present modeling strategies for bed-height dynamics due to flow rate and fluid property changes, and lastly, we show how monitoring and modeling information can be used for the control and regulation of bed expansion.

The design and modeling of drug delivery devices using laminated layers to produce spatially nonuniform matrix devices leading to desired release rates were investigated with the focus on their optimal laminated hydrogel matrices for the diffusion-controlled release of dissolved drugs. The model consists of polymer layers laminated together through a photopolymerization process to form matrices with a spatially nonuniform initial drug distribution and/or nonuniform drug diffusivities. The model solution establishes that the drug diffusion behavior especially the early time release behavior, can be manipulated by altering spatially nonuniform initial drug distributions and drug diffusivities ities in the assembly. Furthermore, optimal control theory and calculus of variation were used to determine a set of initial drug concentrations in the layers to attain a system that exhibits a drug release profile as close to required profile as possible for all time.