Liquid-liquid extraction is an important separation process and a key step in recently emerging technologies such as hydrometallurgical production of non-ferrous metals, treatment of dilute waste streams for metal recovery and hazardous waste elimination, refining and reprocessing uranium and plutonium in the nuclear fuel cycle and nuclear waste management, and biochemical separations. It all plays a major role in traditional separation such as hydrodesulfurization in the petroleum industry. Industrial scale equipment for liquid-liquid extraction include column contactors and continuous flow stirred tanks. There is a lack of measuring techniques for column contactors which has been one of the reasons for the limited number of control studies for this process. The development of a noninvasive ultrasonic technique in the PI's laboratory provides the opportunity of a new initiative in the control of the extraction process. Also, in situ miniature phase-separation devices developed at Syracuse University can be used in combination with concentration measuring probes (e.g., fiber optic, conductivity, refraction probes, etc.) and introduce a new possibility for multivariable control and on-line optimization. This work is an attempt to utilize the above techniques for a safe, multivariable control of the extractors at optimal conditions. Further, these techniques are the impetus for the second objective, to develop a multivariable non-linear predictive control algorithm for optimal operation. An optimizing control strategy for liquid-liquid extraction columns is planned with the objectives of (i) controlling the dispersed phase holdup inside the extractor, (ii) ensuring safe operation with respect to flooding or phase inversion, and (iii) controlling the solute concentration to provide optimum extraction efficiency. The process will be modelled by (i) linear models of first order transfer functions with dead time, and (ii) nonlinear models of population balance equations which include droplet interactions of breakage and coalescence. Both models will be applied for the control of the process in the following sequence: - Adaptive gain-scheduling control of the dispersed phase holdup by using linear models, with the objective of showing the application of the ultrasonic technique in the control of the extraction process. - Nonlinear predictive control of the dispersed phase holdup without mass transfer by applying the population balance equations, to demonstrate the usefulness of physical models. - Nonlinear predictive control of the dispersed phase holdup during mass transfer. - Multivariable nonlinear predictive control of holdup and concentration using the population balance equations in an extended formulation to include mass transfer and concentrations.