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.

The production of fructose from carbohydrate feedstocks

A review of the general chromatographic theory and of continuous chromatographic techniques has been carried out. Three methods of inversion of sucrose to glucose and fructose in beet molasses were explored. These methods were the inversion of sucrose using the enzyme invertase, by the use of hydrochloric acid and the use of the resin Amberlite IR118 in the H+ form. The preferred method on economic and purity considerations was by the use of the enzyme invertase. The continuous chromatographic separation of inverted beet molasses resulting in a fructose rich product and a product containing glucose and other non-sugars was carried out using a semi-continuous counter-current chromatographic refiner (SCCR6), consisting of ten 10.8cm x 75cm long stainless steel columns packed with a calcium charged 8% cross-linked polystyrene resin Zerolit SRC 14. Based on the literature this is the first time such a continuous separation has been attempted. It was found that the cations present in beet molasses displaced the calcium ions from the resin resulting in poor separation of the glucose and fructose. Three methods of maintaining the calcium form of the resin during the continuous operation of the equipment were established. Passing a solution of calcium nitrate through the purge column for half a switch period was found to be most effective as there was no contamination of the main fructose rich product and the product concentrations were increased by 50%. When a 53% total solids (53 Brix) molasses feedstock was used, the throughput was 34.13kg sugar solids per m3 of resin per hour. Product purities of 97% fructose in fructose rich (FRP) and 96% glucose in the glucose rich (GRP) products were obtained with product concentrations of 10.93 %w/w for the FRP and 10.07 %w/w for the GRP. The effects of flowrates, temperature and background sugar concentration on the distribution coefficients of fructose, glucose, betaine and an ionic component of beet molasses were evaluated and general relationships derived. The computer simulation of inverted beet molasses separations on an SCCR system has been carried out successfully.

Biosynthesis and separation of dextran fructose mixtures in a chromatographic reactor

A literature review of work carried out on batch and continuous chromatographic biochemical reactor-separators has been made. The major part of this work has involved the development of a batch chromatographic reactor-separator for the production of dextran and fructose by the enzymatic action of the enzyme dextransucrase on sucrose. In this reactor, simultaneous reaction and separation occurs thus reducing downstream processing and isolation of products as compared to the existing industrial process. The chromatographic reactor consisted of a glass column packed with a stationary phase consisting of cross linked polysytrene resin in the calcium form. The mobile phase consisted of diluted dextransucrase in deionised water. Initial experiments were carried out on a reactor separtor which had an internal diameter of 0.97cm and length of 1.5m. To study the effect of scale up the reactor diameter was doubled to 1.94cm and length increased to 1.75m. The results have shown that the chromatographic reactor uses more enzyme than a conventional batch reactor for a given conversion of sucrose and that an increase in void volume results in higher conversions of sucrose. A comparison of the molecular weight distribution of dextran produced by the chromatographic reactor was made with that from a conventional batch reactor. The results have shown that the chromatographic reactor produces 30% more dextran of molecular weight greater than 150,000 daltons at 20% w/v sucrose concentration than conventional reactors. This is because some of the fructose molecules are prevented as acting as acceptors in the chromatographic reactor due to their removal from the reaction zone. In the conventional reactor this is not possible and therefore a greater proportion of low molecular weight dextran is produced which does not have much clinical use. A theoretical model was developed to describe the behaviour of the reactor separator and this model was simulated using a computer. The simulation predictions showed good agreement with experimental results at high eluent flowrates and low conversions.

Lateral instability of slender reinforced concrete columns in a fire environment

The research concerns the development and application of an analytical computer program, SAFE-ROC, that models material behaviour and structural behaviour of a slender reinforced concrete column that is part of an overall structure and is subjected to elevated temperatures as a result of exposure to fire. The analysis approach used in SAFE-RCC is non-linear. Computer calculations are used that take account of restraint and continuity, and the interaction of the column with the surrounding structure during the fire. Within a given time step an iterative approach is used to find a deformed shape for the column which results in equilibrium between the forces associated with the external loads and internal stresses and degradation. Non-linear geometric effects are taken into account by updating the geometry of the structure during deformation. The structural response program SAFE-ROC includes a total strain model which takes account of the compatibility of strain due to temperature and loading. The total strain model represents a constitutive law that governs the material behaviour for concrete and steel. The material behaviour models employed for concrete and steel take account of the dimensional changes caused by the temperature differentials and changes in the material mechanical properties with changes in temperature. Non-linear stress-strain laws are used that take account of loading to a strain greater than that corresponding to the peak stress of the concrete stress-strain relation, and model the inelastic deformation associated with unloading of the steel stress-strain relation. The cross section temperatures caused by the fire environment are obtained by a preceding non-linear thermal analysis, a computer program FIRES-T.

Parametric study of the behaviour of reinforced concrete columns in fire

The research is concerned with the application of the computer simulation technique to study the performance of reinforced concrete columns in a fire environment. The effect of three different concrete constitutive models incorporated in the computer simulation on the structural response of reinforced concrete columns exposed to fire is investigated. The material models differed mainly in respect to the formulation of the mechanical properties of concrete. The results from the simulation have clearly illustrated that a more realistic response of a reinforced concrete column exposed to fire is given by a constitutive model with transient creep or appropriate strain effect The assessment of the relative effect of the three concrete material models is considered from the analysis by adopting the approach of a parametric study, carried out using the results from a series of analyses on columns heated on three sides which produce substantial thermal gradients. Three different loading conditions were used on the column; axial loading and eccentric loading both to induce moments in the same sense and opposite sense to those induced by the thermal gradient. An axially loaded column heated on four sides was also considered. The computer modelling technique adopted separated the thermal and structural responses into two distinct computer programs. A finite element heat transfer analysis was used to determine the thermal response of the reinforced concrete columns when exposed to the ISO 834 furnace environment. The temperature distribution histories obtained were then used in conjunction with a structural response program. The effect of the occurrence of spalling on the structural behaviour of reinforced concrete column is also investigated. There is general recognition of the potential problems of spalling but no real investigation into what effect spalling has on the fire resistance of reinforced concrete members. In an attempt to address the situation, a method has been developed to model concrete columns exposed to fire which incorporates the effect of spalling. A total of 224 computer simulations were undertaken by varying the amounts of concrete lost during a specified period of exposure to fire. An array of six percentages of spalling were chosen for one range of simulation while a two stage progressive spalling regime was used for a second range. The quantification of the reduction in fire resistance of the columns against the amount of spalling, heating and loading patterns, and the time at which the concrete spalls appears to indicate that it is the amount of spalling which is the most significant variable in the reduction of fire resistance.

The transference of axial load from reinforced concrete columns to bases

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The modelling of buoyancy driven flow in bubble columns

Using the analogy between lateral convection of heat and the two-phase flow in bubble columns, alternative turbulence modelling methods were analysed. The k-ε turbulence and Reynolds stress models were used to predict the buoyant motion of fluids where a density difference arises due to the introduction of heat or a discrete phase. A large height to width aspect ratio cavity was employed in the transport of heat and it was shown that the Reynolds stress model with the use of velocity profiles including the laminar flow solution resulted in turbulent vortices developing. The turbulence models were then applied to the simulation of gas-liquid flow for a 5:1 height to width aspect ratio bubble column. In the case of a gas superficial velocity of 0.02 m s-1 it was determined that employing the Reynolds stress model yielded the most realistic simulation results. © 2003 Elsevier B.V. All rights reserved.