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.

A study of the dynamic behaviour of a pulsed column solvent extraction plant

A study has been made of the dynamic behaviour of a nuclear fuel reprocessing plant utilising pulsed solvent extraction columns. A flowsheet is presented and the choice of an extraction device is discussed. The plant is described by a series of modules each module representing an item of equipment. Each module consists of a series of differential equations describing the dynamic behaviour of the equipment. The model is written in PMSP, a language developed for dynamic simulation models. The differential equations are solved to predict plant behaviour with time. The dynamic response of the plant to a range of disturbances has been assessed. The interactions between pulsed columns have been demonstrated and illustrated. The importance of auxillary items of equipment to plant performance is demonstrated. Control of the reprocessing plant is considered and the effect of control parameters on performance assessed.

A study of liquid-liquid extraction in a sieve plate column

The literature relating to sieve plate liquid extraction columns and relevant hydrodynamic phenomena have been surveyed. Mass transfer characteristics during drop formation, rise and coalescence, and related models were also reviewed. Important design parameters i.e. flooding, dispersed phase hold-up, drop size distribution, mean drop size, coalescence/flocculation zone height beneath a plate and jetting phenomena were investigated under non-mass transfer and mass transfer conditions in a 0.45m diameter, 2.3m high sieve plate column. This column had provision for four different plate designs, and variable plate spacing and downcomer heights, and the system used was Clairsol `350' (dispersed) - acetone - deionised water (continuous) with either direction of mass transfer. Drop size distributions were best described by the functions proposed by Gal-or, and then Mugele-Evans. Using data from this study and the literature, correlations were developed for dispersed phase hold-up, mean drop size in the preferred jetting regime and in the non-jetting regime, and coalescence zone height. A method to calculate the theoretical overall mass transfer coefficient allowing for the range of drop sizes encountered in the column gave the best fit to experimental data. This applied the drop size distribution diagram to estimate the volume percentage of stagnant, circulating and oscillating drops in the drop population. The overall coefficient Kcal was then calculated as the fractional sum of the predicted individual single drop coefficients and their proportion in the drop population. In a comparison between the experimental and calculated overall mass transfer coefficients for cases in which all the drops were in the oscillating regime (i.e. 6.35mm hole size plate), and for transfer from the dispersed(d) to continuous(c) phase, the film coefficient kd predicted from the Rose-Kintner correlation together with kc from that of Garner-Tayeban gave the best representation. Droplets from the 3.175mm hole size plate, were of a size to be mainly circulating and oscillating; a combination of kd from the Kronig-Brink (circulating) and Rose-Kintner (oscillating) correlations with the respective kc gave the best agreement. The optimum operating conditions for the SPC were identified and a procedure proposed for design from basic single drop data.

Drop formation in non-newtonian liquids under pulsed conditions

Drop formation from single nozzles under pulsed flow conditions in non-Newtonian fluids following the power law model has been studied. An existing model has been modified to explain the experimental data. The flow conditions employed correspond to the mixer—settler type of operation in pulsed sieve-plate extraction columns. The modified model predicts the drop sizes satisfactorily. It has been found that consideration of non-Newtonian behaviour is important at low pulse intensities and its significance decreases with increasing intensity of pulsation. Further, the proposed model for single orifices has been tested to predict the sizes of drops formed from a sieve-plate distributor having four holes, and has been found to predict the sizes fairly well in the absence of coalescence.

Synthesis and evaluation of a solid supported molecular tweezer type receptor for cholesterol

A new macroporous stationary phase bearing 'tweezer' receptors that exhibit specificity for cholesterol has been constructed from rigid multifunctional vinylic monomers derived from 3,5-dibromobenzoic acid, propargyl alcohol and cholesterol. The synthesis of the novel tweezer monomer that contains two cholesterol receptor arms using palladium mediated Sonogashira methodologies and carbonate couplings is reported. The subsequent co-polymerisation of this tweezer monomer with a range of cross-linking agents via a 'pseudo' molecular imprinting approach afforded a diverse set of macroporous materials. The selectivity and efficacy of these materials for cholesterol binding was assessed using a chromatographic screening process. The optimum macroporous stationary phase material composition was subsequently used to construct monolithic solid phase extraction columns for use in the selective extraction of cholesterol from multi-component mixtures of structurally related steroids.

The hydrodynamic behaviour and mass transfer characteristics of single droplets in a pulsed sieve plate column

The literature relating to the performance of pulsed sieve plate liquid-liquid extraction columns and the relevant hydrodynamic phenomenon have been surveyed. Hydrodynamic behaviour and mass transfer characteristics of droplets in turbulent and non-turbulent conditions have also been reviewed. Hydrodynamic behaviour, i.e. terminal and characteristic velocity of droplets, droplet size and droplet breakup processes, and mass transfer characteristics of single droplets (d≤0.6 cm) were investigated under pulsed (mixer-settler & transitional regimes) and non-pulsed conditions in a 5.0 cm diameter, 100 cm high, pulsed sieve plate column with three different sieve plate types and variable plate spacing. The system used was toluene (displaced) - acetone - distilled water. Existing photographic techniques for following and recording the droplet behaviour, and for observing the parameters of the pulse and the pulse shape were further developed and improved. A unique illumination technique was developed by which a moving droplet could be photographed using cine or video photography with good contrast without using any dye. Droplet size from a given nozzle and droplet velocity for a given droplet diameter are reduced under pulsing condition, and it was noted that this effect is enhanced in the presence of sieve plate. The droplet breakup processes are well explained by reference to an impact-breakup mechanism. New correlations to predict droplet diameter based on this mechanism are given below.vskip 1.0cm or in dimensionless groups as follows:- (We)crit= 3.12 - 1.79 (Eo)crit A correlation based on the isotropic turbulence theory was developed to calculate droplet diameter in the emulsion regime.vskip 1.0cm Experimental results show that in the mixer-settler and transitional regimes, pulsing parameters had little effect on the overall dispersed phase mass transfer coefficient during the droplet formation and unhindered travel periods.

Comparison and evaluation of the specificity and binding capacity of commercial and in house affinity columns used in sample preparation for analysis of growth-promoting drugs

Immunoaffinity chromatography (IAC) and affinity chromatography (AC:) are widely used for extraction of drugs from biological samples. Fifteen column types were purchased from five different manufacturers and;their ability to bind specific drugs including beta-agonists and anabolic steroids over a range of analyte concentrations in fortified bovine urine samples was assessed. The performance data obtained from these columns were compared with columns produced in this laboratory (in house columns). The in house columns gave the highest recoveries, ranging from 92 to 100% at the 1 ng spiking concentration, for five of the seven analytes assessed. Forty percent (11 of 27) of all the commercial column assessments recorded recoveries of less than 50% even when the lowest spiking concentration was applied (1 ng). For one manufacturer, only one of seven different columns purchased delivered extraction efficiencies greater than 50%. The extraction efficiencies of the clenbuterol columns were the highest with all commercially prepared columns showing at least 50% binding of radiolabelled tracer. Recoveries of alpha-nortestosterone were the lowest. The variability of these products with respect to quality control requires constant monitoring.

QuEChERS: a sample preparation for extraction of carbaryl from rat feces

Carbamate compounds are an important group of cholinesterase inhibitors. There is a need for creating awareness regarding the risks of the inadequate carbamate use in the residential areas due to potential adverse human effects. Carbaryl is a commonly used pesticide worldwide. A simple, fast, and high throughput method was developed employing liquid chromatography with fluorescence detector to determine carbaryl residues in rat feces. The extraction was performed by using a rapid, easy, cheap, effective, reliable, and safe (QuEChERS) method, using acetonitrile as the extracting solvent. The parameters for the performance of the extraction method were optimized, such as ratio of mass of sample per volume of extraction solvent, QuEChERS content, and cleanup columns. Linear response was obtained for all calibration curves (solven and matrix-matched) over the established concentration range (5 500 mg/L) with a correlation coefficients higher than 0.999. The achieved recovery was 97.9% with relative standard deviation values of 1.1% (n D 4) at 167 mg/kg fortified concentration level and the limits of detection and quantification were 27.7 and 92.3 mg/kg respectively.