Inverse problems in population balances: Growth and nucleation from dynamic data

Particulate process modeling is critical for system design and control used widely in the chemical industly. Previous methods have focused on the assumption of appropriate models that can capture system behavior. A new technique presented is based on viewing the population balance from an inverse problem perspective that allows to determine appropriate models directly from experimental data. Under suitable assumptions (deterministic growth rate, no aggregation), the population balance equation may be solved by the method of characteristics, which associates the number density for any size at any time with a single point from the initial or boundary condition. The key to using this is the recognition that these characteristics correspond to the size history of individual particles and can be associated with constant cumulative number densities (quantiles) of the population. These quantiles are easily identifiable from experimental data. The variation of size and number density along these characteristics provides decoupled equations used to determine the growth rate. Validity of the determined growth law is checked by the collapse of the experimental data onto initial and boundary conditions.     

On the effect of crystallinity on the elastic properties of semicrystalline polyethylene

The small strain elastic response of a semicrystalline polyethylene has been simulated with a simple finite element model comprising a composite microstructure of alternating amorphous and crystalline layers arranged in a multi‐layered spherical shell structure. The crystalline lamella is modeled as an isotropic solid having the experimentally determined modulus properties of bulk linear polyethylene and extrapolated to 100% crystallinity. The amorphous layer is modeled as an elastomeric solid with the modulus that of molten linear polyethylene extrapolated to room temperature. Assuming constancy of these phase properties, the finite element calculations of elastic modulus versus crystallinity fit quite well the experimental data of Crist for linear polyethylene above 55% crystallinity. At lower crystallinity the experimental modulus data, which are for copolymers, fall below the model calculations. Two possible causes are discussed: the loss of deformation constraint in lamellae of finite and decreasing width as crystallinity declines, and an expansion of the crystal lattice as a result of the crowding of the comonomer units excluded from the crystal lamella. Either effect would reduce both the modulus and the yield stress as is observed.     

Identification of models for control of wet granulation

The modeling work in this paper provides insight on improved control and design (including measurement selection) of a granulation process. Two different control strategies (MPC and PID) are evaluated on an experimentally validated granulation model. This model is based on earlier work done at The University of Sheffield, UK and Organon, The Netherlands [C.F.W. Sanders, W. Oostra, A.D. Salman, M.J. Hounslow, Development of a predictive high-shear granulation model; experimental and modeling results, 7th World Congress of Chemical Engineering, Glasgow (2005), C11-002]. The granulation kinetics were measured in a 10 liter batch granulator with an experimental design that included four process variables. The aggregation rates were extracted with a Discretized Population Balance (DPB) model. Knowledge of the process kinetics was used to model a continuous (well mixed) granulator. The controller model for the Model Predictive Controller is a linearized state space model, derived from the nonlinear DPB model. It has the four process variables from the experimental design and a feed ratio as input variables. Since the DPB model describes the whole Granule Size Distribution (GSD), candidate sets of lumped output variables were evaluated. When measuring controller performance based on the full granule size distribution, it is shown that a PID controller can actually produce results that fluctuate more than the open-loop response. An MPC controller improves stability on both process outputs and the full granule size distribution. The work shows that measuring and controlling specific number based lumped outputs result in a more stable process than when mass based lumped outputs are used. The paper describes a general strategy of using lab scale batch experiments to design and control (small or large scale) continuous granulators. The continuous experiments in this paper are based on simulation, therefore future experimental validation will elucidate further the link between batch and continuous granulation.     

Prediction of biological response for large combinatorial libraries of biodegradable polymers: Polymethacrylates as a test case

A large virtual combinatorial library of polymethacrylates was, for the first time, designed for computer-aided prediction of biorelevant and material properties and focused polymer synthesis. The distinguishing features of this virtual library include its size (about 40 000 compounds), its explicit representation of relatively long polymer chains, and its accounting for different compositions in the case of copolymers and terpolymers. A subset of 79 polymers taken from a representative sub-library of 2000 polymethacrylates was employed to build initial QSPR-based polynomial neural network models, which were then deployed to predict cell attachment, cell growth, and fibrinogen adsorption on polymer surfaces for these 2000 polymethacrylates. The agreement between predicted and experimentally measured property values for the 50 polymethacrylate copolymers within this virtual polymer space encourages further pursuit of polymethacrylate-based biomaterials, and justifies more extensive deployment of computational models derived from larger experimental data sets for the rational design of biorelevant polymers endowed with targeted performance properties.     

Managing rivers under changing environmental and societal boundary conditions,Part 1: National trends and U.S. Army Corps of Engineers reservoirs

Most major rivers in the United States are managed by a system of reservoirs; many of which were built more than a half century ago. These reservoirs were designed based on environmental, societal, and regulatory assumptions at the time of construction. Since then, we have learned that climate is not stationary, population growth is being decoupled from energy needs and water demand, and new regulations (such as the Clean Water Act and Endangered Species Act) affect how river systems are managed. This study explores changing environmental, societal, and regulatory conditions relevant to the design and operation of U.S. Army Corps of Engineers reservoirs across the conterminous United States. Results demonstrate large geographic variability in how these conditions have changed over time. In the south‐western United States, there is an amplified trend towards drier conditions and less reservoir flexibility with warmer temperatures, less precipitation, high sedimentation rates, and large population growth. In the north‐eastern United States, the impacts of increased temperature on reservoirs may be masked by greater precipitation and lower water demand. Environmental, societal, and regulatory changes can reduce the flexibility of reservoir operations and, in some instances, make it challenging for the reservoir to meet its intended purpose as designed decades ago. This study is the first step towards formalizing a process for monitoring broad trends relevant to water resources management for the purpose of moving towards adaptation of infrastructure. An interactive tool was developed for each condition: https://nicholasinstitute.duke.edu/reservoir‐national‐trends/ .     

Fate of Escherichia coli O157:H7 during composting of bovine manure in a laboratory-scale bioreactor

Inactivation profiles of Escherichia coli O157:H7 in inoculated bovine manure-based compost ingredients were determined by composting these ingredients in a bioreactor under controlled conditions. A 15-liter bioreactor was constructed to determine the fate of E. coli O157:H7 and changes in pH, moisture content, temperature, and aerobic mesophilic and thermophilic bacterial counts during composting. Fresh cow manure, wheat straw, cottonseed meal, and ammonium sulfate were combined to obtain a moisture content of ca. 60% and a carbon/nitrogen ratio of 29:1. The compost ingredients were held in the bioreactor at a constant external temperature of 21 or 50 degrees C. Self-heating of the ingredients due to microbial activity occurred during composting, with stratified temperatures occurring within the bioreactor. At an external temperature of 21 degrees C, self-heating occurred for 0 to 3 days, depending on the location within the bioreactor. E. coli O157:H7 populations increased by 1 to 2 log10 CFU/g during the initial 24 h of composting and decreased by ca. 3.5 log10 CFU/g near the bottom of the bioreactor and by ca. 2 log10 CFU/g near the middle and at the top during 36 days of composting. At an external temperature of 50 degrees C. E. coli O157:H7 was inactivated rapidly (by ca. 4.9 log10 CFU/g at the top of the bioreactor, by 4.0 log10 CFU/g near the middle, and by 5.9 log10 CFU/g near the bottom) within 24 h of composting. When inoculated at an initial level of ca. 10(7) CFU/g. E. coli O157:H7 survived for 7 days but not for 14 days at all three sampling locations, as indicated by either direct plating or enrichment culture. At the top of the bioreactor a relatively constant moisture content of 60% was maintained, whereas the moisture content near the bottom decreased steadily to 37 to 45% over 14 days of composting. The pH of the composting mixture decreased to ca. 6 within 1 to 3 days and subsequently increased to 8 to 9. Results obtained in this study indicate that large populations (10(4) to 10(7) CFU/g) of E coli O157:H7 survived for 36 days during composting in a bioreactor at an external temperature of 21 degrees C but were inactivated to undetectable levels after 7 to 14 days when the external temperature of the bioreactor was 50 degrees C. Hence, manure contaminated with large populations (e.g., 10(7) CFU/g) of E. coli O157:H7 should be composted for more than 1 week, and preferably for 2 weeks, when held at a minimum temperature of 50 degrees C.     

Fate of Campylobacter jejuni in butter

An outbreak of Campylobacter enteritis was associated with a restaurant in Louisiana during the summer of 1995. Thirty cases were identified, and four required hospitalization. Campylobacter jejuni was isolated from the patients, and epidemiologic studies revealed illness associated with eating garlic butter served at the restaurant. Three batches of garlic butter prepared by the restaurant associated with the outbreak and a C. jejuni isolate obtained from a patient involved in the outbreak were used for studies to determine the fate of C. jejuni in garlic butter. Studies also were done to determine the efficacy of the heat treatment used by the restaurant to prepare garlic bread to kill C. jejuni. Garlic butter was inoculated with approximately 10(4) and 10(6) CFU/g of C. jejuni and held at 5 or 21 degrees C. Results revealed that the survival of C. jejuni differed greatly, depending on the presence or absence of garlic. At 5 degrees C, C. jejuni populations decreased to an undetectable level (<10 CFU/g) within 3 h for two batches and within 24 h for another batch. In contrast, C. jejuni could survive at 5 degrees C for 13 days in butter with no garlic. At 21 degrees C, C. jejuni populations decreased to an undetectable level within 5 h for two batches and to 50 CFU/g in 5 h for another batch. In contrast, C. jejuni was detected at 500 CFU/g at 28 h after inoculation but was undetectable at 3 days in butter with no garlic held at 21 degrees C. The heating procedure (135 degrees C, 4 min) used to make garlic bread by the implicated restaurant was determined not to be sufficient for killing C. jejuni, with the internal temperature of the buttered bread after heating ranging from 19 to 22 degrees C. This study revealed that C. jejuni can survive for many days in refrigerated butter, but large populations (10(3) to 10(5) CFU/g) are killed within a few hours in butter that contains garlic. Furthermore, the heat treatment used by the restaurant to melt garlic butter in making garlic bread was not adequate to kill C. jejuni.     

Effects of diet on rumen proliferation and fecal shedding of Escherichia coil O157:H7 in calves

Calves inoculated with Escherichia coli O157:H7 and fed either a high-roughage or high-concentrate diet were evaluated for rumen proliferation and fecal shedding of E. coli O157:H7. Calves fed the high-roughage diet had lower mean rumen volatile fatty acid concentrations and higher rumen pH values than did calves fed the high-concentrate diet. Despite these differences in rumen conditions, the calves fed the high-roughage diet did not have greater rumen populations of E. coli O157: H7 and did not exhibit increased or longer fecal shedding compared with the calves fed the high-concentrate diet. Two calves shedding the highest mean concentrations of E. coli O157:H7 were both fed the high-concentrate diet. There was a significant (P < 0.05) positive correlation between fecal shedding and rumen volatile fatty acid concentration in calves fed a high-concentrate diet. The effects of diet on E. coli O157:H7 proliferation and acid resistance were investigated using an in vitro rumen fermentation system. Rumen fluid collected from steers fed a high-roughage diet, but not from steers fed a high-concentrate diet, supported the proliferation of E. coli O157:H7. Rumen fluid from steers fed a high-concentrate diet rapidly induced acid resistance in E. coli O157:H7. The impact of diet on fecal shedding of E. coli O157:H7 is still unclear and may depend on dietary effects on fermentation in the colon and on diet-induced changes in the resident microflora. However, rapid development of acid tolerance by E. coli O157:H7 in the rumens of calves fed high-concentrate diets, allowing larger populations to survive passage through the acidic abomasum to proliferate in the colon, may be one factor that influences fecal shedding in cattle on feed.