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.

Mechanical properties and the evolution of matrix molecules in PTFE upon irradiation with MeV alpha particles

The morphology, chemical composition, and mechanical properties in the surface region of α-irradiated polytetrafluoroethylene (PTFE) have been examined and compared to unirradiated specimens. Samples were irradiated with 5.5 MeV 4He2+ ions from a tandem accelerator to doses between 1 × 106 and 5 × 1010 Rad. Static time-of-flight secondary ion mass spectrometry (ToF-SIMS), using a 20 keV C60+ source, was employed to probe chemical changes as a function of a dose. Chemical images and high resolution spectra were collected and analyzed to reveal the effects of a particle radiation on the chemical structure. Residual gas analysis (RGA) was utilized to monitor the evolution of volatile species during vacuum irradiation of the samples. Scanning electron microscopy (SEM) was used to observe the morphological variation of samples with increasing a particle dose, and nanoindentation was engaged to determine the hardness and elastic modulus as a function of a dose. The data show that PTFE nominally retains its innate chemical structure and morphology at a doses <109 Rad. At α doses ≥109 Rad the polymer matrix experiences increased chemical degradation and morphological roughening which are accompanied by increased hardness and declining elasticity. At  α doses >1010 Rad the polymer matrix suffers severe chemical degradation and material loss. Chemical degradation is observed in ToF-SIMS by detection of ions that are indicative of fragmentation, unsaturation, and functionalization of molecules in the PTFE matrix. The mass spectra also expose the subtle trends of crosslinking within the α-irradiated polymer matrix. ToF-SIMS images support the assertion that chemical degradation is the result of a particle irradiation and show morphological roughening of the sample with increased a dose. High resolution SEM images more clearly illustrate the morphological roughening and the mass loss that accompanies high doses of a particles. RGA confirms the supposition that the outcome of chemical degradation in the PTFE matrix with continuing irradiation is evolution of volatile species resulting in morphological roughening and mass loss. Finally, we reveal and discuss relationships between chemical structure and mechanical properties such as hardness and elastic modulus.

Heavy ion irradiation effects in zirconium nitride

Polycrystalline zirconium nitride (ZrN) samples were irradiated with He +, Kr ++, and Xe ++ ions to high (>1·10 16 ions/cm 2) fluences at ∼100 K. Following ion irradiation, transmission electron microscopy (TEM) and grazing incidence X-ray diffraction (GIXRD) were used to analyze the microstructure and crystal structure of the post-irradiated material. For ion doses equivalent to approximately 200 displacements per atom (dpa), ZrN was found to resist any amorphization transformation, based on TEM observations. At very high displacement damage doses, GIXRD measurements revealed tetragonal splitting of some of the diffraction maxima (maxima which are associated with cubic ZrN prior to irradiation). In addition to TEM and GIXRD, mechanical property changes were characterized using nanoindentation. Nanoindentation revealed no change in elastic modulus of ZrN with increasing ion dose, while the hardness of the irradiated ZrN was found to increase significantly with ion dose. Finally, He + ion implanted ZrN samples were annealed to examine He gas retention properties of ZrN as a function of annealing temperature. He gas release was measured using a residual gas analysis (RGA) spectrometer. RGA measurements were performed on He-implanted ZrN samples and on ZrN samples that had also been irradiated with Xe ++ ions, in order to introduce high levels of displacive radiation damage into the matrix. He evolution studies revealed that ZrN samples with high levels of displacement damage due to Xe implantation, show a lower temperature threshold for He release than do pristine ZrN samples.