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.

Variable impedance bearings for large rotating machinery

This thesis describes an investigation which was carried out under the Interdisciplinary Higher Degres (IHD) Scheme of The University of Aston in Birmingham. The investigation, which involved joint collaboration between the IHD scheme, the Department of Mechanical Engineering, and G.E.C. Turbine Generators Limited, was concerned with hydrostatic bearing characteristics and of how hydrostatic bearings could be used to enable turbine generator rotor support impedances to be controlled to give an improved rotor dynamic response. Turbine generator rotor critical speeds are determined not only by the mass and flexibility of the rotor itself, which are relatively easily predicted, but also by the dynamic characteristics of the bearing oil film, pedestal, and foundations. It is because of the difficulty in accurately predicting the rotor support characteristics that the designer has a problem in ensuring that a rotor's normal running speed is not close to one of its critical speeds. The consequence of this situation is that some rotors do have critical speeds close to their normal running speed and the resulting high levels of vibration cause noise, high rotor stresses, and a shortening of bearing life. A combined theoretical and experimental investigation of the effects of mounting the normal rotor journal bearing in a hydrostatic bearing was carried out. The purpose of the work was to show that by changing the oil flow resistance offered by capillaries connecting accumulators to the hydrostatic bearing, the overall rotor support characteristics could be tuned to enable rotor critical speeds to be moved at will. Testing of a combined journal and hydrostatic bearing has confirmed the theory of its operation and a theoretical study of a full size machine showed that its critical speed could be moved by over 350 rpm and that its rotor vibration at running speed could be reduced by 80%.

The controlled release of macromolecules from macroporous hydrophyllic polymer matrices

This work has used novel polymer design and fabrication technology to generate bead form polymer based systems, with variable, yet controlled release properties, specifically for the delivery of macromolecules, essentially peptides of therapeutic interest. The work involved investigation of the potential interaction between matrix ultrastructural morphology, in vitro release kinetics, bioactivity and immunoreactivity of selected macromolecules with limited hydrolytic stability, delivered from controlled release vehicles. The underlying principle involved photo-polymerisation of the monomer, hydroxyethyl methacrylate, around frozen ice crystals, leading to the production of a macroporous hydrophilic matrix. Bead form matrices were fabricated in controllable size ranges in the region of 100µm - 3mm in diameter. The initial stages of the project involved the study of how variables, delivery speed of the monomer and stirring speed of the non solvent, affectedthe formation of macroporous bead form matrices. From this an optimal bench system for bead production was developed. Careful selection of monomer, solvents, crosslinking agent and polymerisation conditions led to a variable but controllable distribution of pore sizes (0.5 - 4µm). Release of surrogate macromolecules, bovine serum albumin and FITC-linked dextrans, enabled factors relating to the size and solubility of the macromolecule on the rate of release to be studied. Incorporation of bioactive macromolecules allowed retained bioactivity to be determined (glucose oxidase and interleukin-2), whilst the release of insulin enabled determination of both bioactivity (using rat epididymal fat pad) and immunoreactivity (RIA). The work carried out has led to the generation of macroporous bead form matrices, fabricated from a tissue biocompatible hydrogel, capable of the sustained, controlled release of biologically active peptides, with potential use in the pharmaceutical and agrochemical industries.

Seasonal variations of EPG levels in gastro-intestinal parasitic infection in a southeast asian controlled locale:a statistical analysis

We present a data based statistical study on the effects of seasonal variations in the growth rates of the gastro-intestinal (GI) parasitic infection in livestock. The alluded growth rate is estimated through the variation in the number of eggs per gram (EPG) of faeces in animals. In accordance with earlier studies, our analysis too shows that rainfall is the dominant variable in determining EPG infection rates compared to other macro-parameters like temperature and humidity. Our statistical analysis clearly indicates an oscillatory dependence of EPG levels on rainfall fluctuations. Monsoon recorded the highest infection with a comparative increase of at least 2.5 times compared to the next most infected period (summer). A least square fit of the EPG versus rainfall data indicates an approach towards a super diffusive (i. e. root mean square displacement growing faster than the square root of the elapsed time as obtained for simple diffusion) infection growth pattern regime for low rainfall regimes (technically defined as zeroth level dependence) that gets remarkably augmented for large rainfall zones. Our analysis further indicates that for low fluctuations in temperature (true on the bulk data), EPG level saturates beyond a critical value of the rainfall, a threshold that is expected to indicate the onset of the nonlinear regime. The probability density functions (PDFs) of the EPG data show oscillatory behavior in the large rainfall regime (greater than 500 mm), the frequency of oscillation, once again, being determined by the ambient wetness (rainfall, and humidity). Data recorded over three pilot projects spanning three measures of rainfall and humidity bear testimony to the universality of this statistical argument. © 2013 Chattopadhyay and Bandyopadhyay.

Controlled synthesis of poly(neopentyl p-styrene sulfonate) via reversible addition-fragmentation chain transfer polymerisation

The controlled synthesis of poly(neopentyl p-styrene sulfonate) (PNSS) using RAFT polymerisation has been studied. Selected experimental conditions led to the production of PNSS with variable molecular weights and low dispersities (D{stroke}≤1.50). The controlled synthesis of poly(neopentyl p-styrene sulfonate) (PNSS) using reversible addition-fragmentation chain transfer polymerisation has been studied under a wide range of experimental conditions. PNSS can be used as an organic-soluble, thermally labile precursor for industrially valuable poly(p-styrene sulfonate), widely employed in technologies such as ionic exchange membranes and organic electronics. The suitability of two different chain transfer agents, three solvents, three different monomer concentrations and two different temperatures for the polymerisation of neopentyl p-styrene sulfonate is discussed in terms of the kinetics of the process and characteristics of the final polymer. Production of PNSS with systematically variable molecular weights and low dispersities (D{stroke} ≤1.50 in all cases) has been achieved using 2-azidoethyl 2-(dodecylthiocarbonothioylthio)-2-methylpropionate in anisole at 75°C, with an initial monomer concentration of 4.0molL-1. Finally, a poly(neopentyl p-styrene sulfonate)-b-polybutadiene-b-poly(neopentyl p-styrene sulfonate) (PNSS-b-PBD-b-PNSS) triblock copolymer has been synthesised via azide-alkyne click chemistry. Moreover, subsequent thermolysis of the PNSS moieties generated poly(p-styrene sulfonate) end blocks. This strategy allows the fabrication of amphiphilic copolymer films from single organic solvents without the need for post-deposition chemical treatment.