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.

Technoeconomic modelling of coal conversion processes for liquid fuel production

Since the oil crisis of 1973 considerable interest has been shown in the production of liquid fuels from alternative sources. In particular processes utilizing coal as the feedstock have received considerable interest. These processes can be divided into direct and indirect liquefaction and pyrolysis. This thesis describes the modelling of indirect coal liquefaction processes for the purpose of performing technical and economic assessment of the production of liquid fuels from coal and lignite, using a variety of gasification and synthesis gas liquefaction technologies. The technologies were modeled on a 'step model' basis where a step is defined as a combination of individual unit operations which together perform a significant function on the process streams, such as a methanol synthesis step or a gasification and physical gas cleaning step. Sample results of the modelling, covering a wide range of gasifiers, liquid synthesis processes and products are presented in this thesis. Due to the large number of combinations of gasifier, liquid synthesis processes, products and economic sensitivity cases, a complete set of results is impractical to present in a single publication. The main results show that methanol is the cheapest fuel to produce from coal followed by fuel alcohol, diesel from the Shell Middle Distillate Synthesis process,gasoline from Mobil Methanol to Gasoline (MTG) process, diesel from the Mobil Methanol Olefins Gasoline Diesel (MOGD) process and finally gasoline from the same process. Some variation in production costs of all the products was shown depending on type of gasifier chosen and feedstock.

Modelling data and voice traffic over IP networks using continuous-time Markov models

Common approaches to IP-traffic modelling have featured the use of stochastic models, based on the Markov property, which can be classified into black box and white box models based on the approach used for modelling traffic. White box models, are simple to understand, transparent and have a physical meaning attributed to each of the associated parameters. To exploit this key advantage, this thesis explores the use of simple classic continuous-time Markov models based on a white box approach, to model, not only the network traffic statistics but also the source behaviour with respect to the network and application. The thesis is divided into two parts: The first part focuses on the use of simple Markov and Semi-Markov traffic models, starting from the simplest two-state model moving upwards to n-state models with Poisson and non-Poisson statistics. The thesis then introduces the convenient to use, mathematically derived, Gaussian Markov models which are used to model the measured network IP traffic statistics. As one of the most significant contributions, the thesis establishes the significance of the second-order density statistics as it reveals that, in contrast to first-order density, they carry much more unique information on traffic sources and behaviour. The thesis then exploits the use of Gaussian Markov models to model these unique features and finally shows how the use of simple classic Markov models coupled with use of second-order density statistics provides an excellent tool for capturing maximum traffic detail, which in itself is the essence of good traffic modelling. The second part of the thesis, studies the ON-OFF characteristics of VoIP traffic with reference to accurate measurements of the ON and OFF periods, made from a large multi-lingual database of over 100 hours worth of VoIP call recordings. The impact of the language, prosodic structure and speech rate of the speaker on the statistics of the ON-OFF periods is analysed and relevant conclusions are presented. Finally, an ON-OFF VoIP source model with log-normal transitions is contributed as an ideal candidate to model VoIP traffic and the results of this model are compared with those of previously published work.

Human performance modelling as an aid in the process of manufacturing system design

Manufacturing system design is an ongoing activity within industry. Modelling tools based on Discrete Event Simulation are often used by practitioners during this design cycle. However, such tools do not adequately model the behaviour of 'direct' workers in manufacturing environments. There is an important need to expand the capability of modelling to include the relationships between human centred factors (demography, attitudes, beliefs, etc), their working environment (physical and organizational), and their subsequent performance in terms of productive routines. Therefore, this paper describes research that has formed a pilot modelling methodology that is an important first step in providing such a capability.

Computationsl modelling of dimethyl ether separation and steam reforming in fluidized bed reactors

This study presents a computational fluid dynamic (CFD) study of Dimethyl Ether (DME) gas adsorptive separation and steam reforming (DME-SR) in a large scale Circulating Fluidized Bed (CFB) reactor. The CFD model is based on Eulerian-Eulerian dispersed flow and solved using commercial software (ANSYS FLUENT). Hydrogen is currently receiving increasing interest as an alternative source of clean energy and has high potential applications, including the transportation sector and power generation. Computational fluid dynamic (CFD) modelling has attracted considerable recognition in the engineering sector consequently leading to using it as a tool for process design and optimisation in many industrial processes. In most cases, these processes are difficult or expensive to conduct in lab scale experiments. The CFD provides a cost effective methodology to gain detailed information up to the microscopic level. The main objectives in this project are to: (i) develop a predictive model using ANSYS FLUENT (CFD) commercial code to simulate the flow hydrodynamics, mass transfer, reactions and heat transfer in a large scale dual fluidized bed system for combined gas separation and steam reforming processes (ii) implement a suitable adsorption models in the CFD code, through a user defined function, to predict selective separation of a gas from a mixture (iii) develop a model for dimethyl ether steam reforming (DME-SR) to predict hydrogen production (iv) carry out detailed parametric analysis in order to establish ideal operating conditions for future industrial application. The project has originated from a real industrial case problem in collaboration with the industrial partner Dow Corning (UK) and jointly funded by the Engineering and Physical Research Council (UK) and Dow Corning. The research examined gas separation by adsorption in a bubbling bed, as part of a dual fluidized bed system. The adsorption process was simulated based on the kinetics derived from the experimental data produced as part of a separate PhD project completed under the same fund. The kinetic model was incorporated in FLUENT CFD tool as a pseudo-first order rate equation; some of the parameters for the pseudo-first order kinetics were obtained using MATLAB. The modelling of the DME adsorption in the designed bubbling bed was performed for the first time in this project and highlights the novelty in the investigations. The simulation results were analysed to provide understanding of the flow hydrodynamic, reactor design and optimum operating condition for efficient separation. Bubbling bed validation by estimation of bed expansion and the solid and gas distribution from simulation agreed well with trends seen in the literatures. Parametric analysis on the adsorption process demonstrated that increasing fluidizing velocity reduced adsorption of DME. This is as a result of reduction in the gas residence time which appears to have much effect compared to the solid residence time. The removal efficiency of DME from the bed was found to be more than 88%. Simulation of the DME-SR in FLUENT CFD was conducted using selected kinetics from literature and implemented in the model using an in-house developed user defined function. The validation of the kinetics was achieved by simulating a case to replicate an experimental study of a laboratory scale bubbling bed by Vicente et al [1]. Good agreement was achieved for the validation of the models, which was then applied in the DME-SR in the large scale riser section of the dual fluidized bed system. This is the first study to use the selected DME-SR kinetics in a circulating fluidized bed (CFB) system and for the geometry size proposed for the project. As a result, the simulation produced the first detailed data on the spatial variation and final gas product in such an industrial scale fluidized bed system. The simulation results provided insight in the flow hydrodynamic, reactor design and optimum operating condition. The solid and gas distribution in the CFB was observed to show good agreement with literatures. The parametric analysis showed that the increase in temperature and steam to DME molar ratio increased the production of hydrogen due to the increased DME conversions, whereas the increase in the space velocity has been found to have an adverse effect. Increasing temperature between 200 oC to 350 oC increased DME conversion from 47% to 99% while hydrogen yield increased substantially from 11% to 100%. The CO2 selectivity decreased from 100% to 91% due to the water gas shift reaction favouring CO at higher temperatures. The higher conversions observed as the temperature increased was reflected on the quantity of unreacted DME and methanol concentrations in the product gas, where both decreased to very low values of 0.27 mol% and 0.46 mol% respectively at 350 °C. Increasing the steam to DME molar ratio from 4 to 7.68 increased the DME conversion from 69% to 87%, while the hydrogen yield increased from 40% to 59%. The CO2 selectivity decreased from 100% to 97%. The decrease in the space velocity from 37104 ml/g/h to 15394 ml/g/h increased the DME conversion from 87% to 100% while increasing the hydrogen yield from 59% to 87%. The parametric analysis suggests an operating condition for maximum hydrogen yield is in the region of 300 oC temperatures and Steam/DME molar ratio of 5. The analysis of the industrial sponsor’s case for the given flow and composition of the gas to be treated suggests that 88% of DME can be adsorbed from the bubbling and consequently producing 224.4t/y of hydrogen in the riser section of the dual fluidized bed system. The process also produces 1458.4t/y of CO2 and 127.9t/y of CO as part of the product gas. The developed models and parametric analysis carried out in this study provided essential guideline for future design of DME-SR at industrial level and in particular this work has been of tremendous importance for the industrial collaborator in order to draw conclusions and plan for future potential implementation of the process at an industrial scale.

About Methods of Mathematical Modelling in the Development of Information Systems

This article describes the approach, which allows to develop information systems without taking into consideration details of physical storage of the relational model and type database management system. Described in terms of graph model, this approach allows to construct several algorithms, for example, for verification application domain. This theory was introduced into operation testing as a part of CASE-system METAS.

Trends in research on the possible effects of climate change concerning aquatic ecosystems with special emphasis on the modelling approach

Knowledge on the expected effects of climate change on aquatic ecosystems is defined by three ways. On the one hand, long-term observation in the field serves as a basis for the possible changes; on the other hand, the experimental approach may bring valuable pieces of information to the research field. The expected effects of climate change cannot be studied by empirical approach; rather mathematical models are useful tools for this purpose. Within this study, the main findings of field observations and their implications for future were summarized; moreover, the modelling approaches were discussed in a more detailed way. Some models try to describe the variation of physical parameters in a given aquatic habitat, thus our knowledge on their biota is confined to the findings based on our present observations. Others are destined for answering special issues related to the given water body. Complex ecosystem models are the keys of our better understanding of the possible effects of climate change. Basically, these models were not created for testing the influence of global warming, rather focused on the description of a complex system (e. g. a lake) involving environmental variables, nutrients. However, such models are capable of studying climatic changes as well by taking into consideration a large set of environmental variables. Mostly, the outputs are consistent with the assumptions based on the findings in the field. Since synthetized models are rather difficult to handle and require quite large series of data, the authors proposed a more simple modelling approach, which is capable of examining the effects of global warming. This approach includes weather dependent simulation modelling of the seasonal dynamics of aquatic organisms within a simplified framework.

Modelling of Stress-Corrosion Cracking by Using Peridynamics

Acknowledgement The authors are grateful to Prof. Siegfried Schmauder and Prof. Erdogan Madenci for the useful discussions that occurred throughout the realization of this study and acknowledge the Defence Science and Technology Laboratory (DSTL) for the financial support. A special thanks go to the anonymous reviewers, whose time and contribution have been highly appreciated. Results were obtained using the EPSRC funded ARCHIE-WeSt High Performance Computer (www.archie-west.ac.uk). EPSRC grant no. EP/K000586/1.

Modelling of stiffness degradation due to cracking in laminates subjected to multi-axial loading

Funding Financial support of this research by the Engineering and Physical Sciences Research Council (EPSRC/GR/L51348) and the British Ministry of Defence is gratefully acknowledged.

Modelling Provenance of Sensor Data for Food Safety Compliance Checking

Postprint

Constraint-force-based approach of modelling compliant mechanisms: principle and application

Numerous works have been conducted on modelling basic compliant elements such as wire beams, and closed-form analytical models of most basic compliant elements have been well developed. However, the modelling of complex compliant mechanisms is still a challenging work. This paper proposes a constraint-force-based (CFB) modelling approach to model compliant mechanisms with a particular emphasis on modelling complex compliant mechanisms. The proposed CFB modelling approach can be regarded as an improved free-body- diagram (FBD) based modelling approach, and can be extended to a development of the screw-theory-based design approach. A compliant mechanism can be decomposed into rigid stages and compliant modules. A compliant module can offer elastic forces due to its deformation. Such elastic forces are regarded as variable constraint forces in the CFB modelling approach. Additionally, the CFB modelling approach defines external forces applied on a compliant mechanism as constant constraint forces. If a compliant mechanism is at static equilibrium, all the rigid stages are also at static equilibrium under the influence of the variable and constant constraint forces. Therefore, the constraint force equilibrium equations for all the rigid stages can be obtained, and the analytical model of the compliant mechanism can be derived based on the constraint force equilibrium equations. The CFB modelling approach can model a compliant mechanism linearly and nonlinearly, can obtain displacements of any points of the rigid stages, and allows external forces to be exerted on any positions of the rigid stages. Compared with the FBD based modelling approach, the CFB modelling approach does not need to identify the possible deformed configuration of a complex compliant mechanism to obtain the geometric compatibility conditions and the force equilibrium equations. Additionally, the mathematical expressions in the CFB approach have an easily understood physical meaning. Using the CFB modelling approach, the variable constraint forces of three compliant modules, a wire beam, a four-beam compliant module and an eight-beam compliant module, have been derived in this paper. Based on these variable constraint forces, the linear and non-linear models of a decoupled XYZ compliant parallel mechanism are derived, and verified by FEA simulations and experimental tests.

Individual-based modelling of the development and transport of a Karenia mikimotoi bloom on the North-West European continental shelf

In 2006, a large and prolonged bloom of the dinoflagellate Karenia mikimotoi occurred in Scottish coastal waters, causing extensive mortalities of benthic organisms including annelids and molluscs and some species of fish ( Davidson et al., 2009). A coupled hydrodynamic-algal transport model was developed to track the progression of the bloom around the Scottish coast during June–September 2006 and hence investigate the processes controlling the bloom dynamics. Within this individual-based model, cells were capable of growth, mortality and phototaxis and were transported by physical processes of advection and turbulent diffusion, using current velocities extracted from operational simulations of the MRCS ocean circulation model of the North-west European continental shelf. Vertical and horizontal turbulent diffusion of cells are treated using a random walk approach. Comparison of model output with remotely sensed chlorophyll concentrations and cell counts from coastal monitoring stations indicated that it was necessary to include multiple spatially distinct seed populations of K. mikimotoi at separate locations on the shelf edge to capture the qualitative pattern of bloom transport and development. We interpret this as indicating that the source population was being transported northwards by the Hebridean slope current from where colonies of K. mikimotoi were injected onto the continental shelf by eddies or other transient exchange processes. The model was used to investigate the effects on simulated K. mikimotoi transport and dispersal of: (1) the distribution of the initial seed population; (2) algal growth and mortality; (3) water temperature; (4) the vertical movement of particles by diurnal migration and eddy diffusion; (5) the relative role of the shelf edge and coastal currents; (6) the role of wind forcing. The numerical experiments emphasized the requirement for a physiologically based biological model and indicated that improved modelling of future blooms will potentially benefit from better parameterisation of temperature dependence of both growth and mortality and finer spatial and temporal hydrodynamic resolution.

Individual-based modelling of the development and transport of a Karenia mikimotoi bloom on the North-West European continental shelf

In 2006, a large and prolonged bloom of the dinoflagellate Karenia mikimotoi occurred in Scottish coastal waters, causing extensive mortalities of benthic organisms including annelids and molluscs and some species of fish ( Davidson et al., 2009). A coupled hydrodynamic-algal transport model was developed to track the progression of the bloom around the Scottish coast during June–September 2006 and hence investigate the processes controlling the bloom dynamics. Within this individual-based model, cells were capable of growth, mortality and phototaxis and were transported by physical processes of advection and turbulent diffusion, using current velocities extracted from operational simulations of the MRCS ocean circulation model of the North-west European continental shelf. Vertical and horizontal turbulent diffusion of cells are treated using a random walk approach. Comparison of model output with remotely sensed chlorophyll concentrations and cell counts from coastal monitoring stations indicated that it was necessary to include multiple spatially distinct seed populations of K. mikimotoi at separate locations on the shelf edge to capture the qualitative pattern of bloom transport and development. We interpret this as indicating that the source population was being transported northwards by the Hebridean slope current from where colonies of K. mikimotoi were injected onto the continental shelf by eddies or other transient exchange processes. The model was used to investigate the effects on simulated K. mikimotoi transport and dispersal of: (1) the distribution of the initial seed population; (2) algal growth and mortality; (3) water temperature; (4) the vertical movement of particles by diurnal migration and eddy diffusion; (5) the relative role of the shelf edge and coastal currents; (6) the role of wind forcing. The numerical experiments emphasized the requirement for a physiologically based biological model and indicated that improved modelling of future blooms will potentially benefit from better parameterisation of temperature dependence of both growth and mortality and finer spatial and temporal hydrodynamic resolution.

Modelling the crush behaviour of thermoplastic composites

Thermoplastic composites are likely to emerge as the preferred solution for meeting the high-volume production demands of passenger road vehicles. Substantial effort is currently being directed towards the development of new modelling techniques to reduce the extent of costly and time consuming physical testing. Developing a high-fidelity numerical model to predict the crush behaviour of composite laminates is dependent on the accurate measurement of material properties as well as a thorough understanding of damage mechanisms associated with crush events. This paper details the manufacture, testing and modelling of self-supporting corrugated-shaped thermoplastic composite specimens for crashworthiness assessment. These specimens demonstrated a 57.3% higher specific energy absorption compared to identical specimen made from thermoset composites. The corresponding damage mechanisms were investigated in-situ using digital microscopy and post analysed using Scanning Electron Microscopy (SEM). Splaying and fragmentation modes were the 2 primary failure modes involving fibre breakage, matrix cracking and delamination. A mesoscale composite damage model, with new non-linear shear constitutive laws, which combines a range of novel techniques to accurately capture the material response under crushing, is presented. The force-displacement curves, damage parameter maps and dissipated energy, obtained from the numerical analysis, are shown to be in a good qualitative and quantitative agreement with experimental results. The proposed approach could significantly reduce the extent of physical testing required in the development of crashworthy structures.