Using a numerical Gibbs free-energy minimization technique, the activity coefficients of actinide and rare-earth chlorides in molten LiCl/KCl eutectic at 450 °C have been calculated. Laboratory tests of an electrochemical process for separating actinide metals from rare-earth metals in LiCl/ KCl solvent at 450 °C provided experimental concentration and cathode potential data. The generalized expansion by Wohl was used to express the concentration dependence of the excess Gibbs free energy. The activity coefficients were expressed in terms of the Wohl volume and interaction energy parameters. The Wohl parameters for the activity coefficient expansions were obtained by minimizing the total Gibbs free energy expressed in terms of the experimental mole fractions. This thermodynamic model will be valuable for process design and scale-up calculations.

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T here exist several well-established techniques for feedback control design for dynamic systems. The technique employed depends on the structure of the controller, i.e., conventional proportionalintegral-derivative (PID), linear or nonlinear state feedback, and so on.For the control of industrial chemical processes, PID control is widely used, accounting for some 95% of all control loops (Wang and Shao, 1999). Therefore, it is not surprising that much attention has been paid to tuning this type of controller. Luyben (2001) presents a comparison of PID tuning methods for processes possessing varying degrees of dead-time. One of these methods is the classic Ziegler-Nichols tuning method, which determines the controller gain, integral time, and derivative time by using either the system ultimate gain or process reaction curve (Ziegler and Nichols, 1942;Dutton et al., 1997).Other PID design methods include frequency response and root locus, classical approaches to tuning parameter determination (Franklin et al., 1991;Smith and Corripio, 1985). Autotuning algorithms (Wang and Shao, 1999;Friman and Waller, 1997;Luo and Chen, 1998) and trial-and-error tuning by plant personnel are also commonly employed methods for tuning PID controllers.The Ziegler-Nichols process reaction curve, autotuning, and trialand-error approaches, while useful in many circumstances, have the potential disadvantage of introducing transients to the process, risking process upsets and unstable response. Closed-loop autotuning algorithms help to circumvent these potential problems. However, an autotuning feature is not available on many industrial PID controllers, so it is not always a viable alternative.Approaches to feedback control design that are based on state-space methods have gained popularity for chemical process control (Ray, 1989). One class of linear optimal control problem is the linear regulator, in which optimal, time-varying gains are computed which minimize a quadratic performance index. Ray (1989), Sage et al. (1977), and Kirk (1970) discuss solutions to the linear regulator problem, including solution via backward integration of the Riccati equation and by direct numerical techniques that require fi rst-and sometimes second-derivative information. For infi nite time problems, such as the continuous control of a chemical process, the time-varying gains become constant, resulting in constant gain proportional controllers. Integral control may be implemented as well, in order to eliminate steady-state offset (Franklin et al., 1991). Ray (1989) discusses application of optimal control theory to nonlinear systems and associated numerical solution techniques. Non-optimal state-space methods (Franklin et al., 1991) utilize pole placement or comparison with prototype response models such as Bessel functions, Integral of Time Multiplied by Absolute Value of Error (ITAE), or Integral of the Square of the Error (ISE) criteria in order to select appropriate controller gains. * Author to whom correspondence may be addressed. E-mail address: ...

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A computational fluid dynamics (CFD) technique applied to the turbulent flow of wastewater sludge in horizontal, smooth-wall, circular pipes is presented. The technique uses the Crank2Nicolson finite difference method in conjunction with the variable secant method, an algorithm for determining the pressure gradient of the flow. A simple algebraic turbulence model is used. A Bingham-plastic rheological model is used to describe the shear stress/shear rate relationship for the wastewater sludge. The method computes velocity gradient and head loss, given a fixed volumetric flow, pipe size, and solids concentration. Solids concentrations ranging from 3 to 10% (by weight) and nominal pipe sizes from 0.15 m (6 in.) to 0.36 m (14 in.) are studied. Comparison of the CFD results for water to established values serves to validate the numerical method. The head loss results are presented in terms of a head loss ratio, R hl , which is the ratio of sludge head loss to water head loss. An empirical equation relating R hl to pipe velocity and solids concentration, derived from the results of the CFD calculations, is presented. The results are compared with published values of R hl for solids concentrations of 3 and 6%. A new expression for the Fanning friction factor for wastewater sludge flow is also presented. Water Environ. Res., 77, 417 (2005).