An Optimal Control Model of the Adsorption Process of a Metallurgical Plant: A Case Study of Gold

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The model developed is an optimal control model of the adsorption process of a hydrometallurgical process called Carbon-In-Pulp. The model took into consideration the fact that the metallurgical process encounters several losses chief among them being gold solution losses. Several assumptions were made and among them was the assumption that the amount of gold in solution that goes to waste is equal to the amount of gold solution in the adsorption unit less the amount of gold adsorbed unto the activated carbon phase. With the rate of adsorption proportional to the capacity of activated carbon and the concentration of gold on the carbon phase, the model has a state variable x(t) which is the concentration of gold in the solution phase at any given time and a control variable u(t) which is the concentration of gold on the activated carbon phase at any given time. The optimal control model developed gives complete overview of the process of adsorption process of dissolved gold solution unto activated carbon. The model reveals that the process is fast and spontaneous initially and slows down with time until it reaches the carrying capacity of the activated carbon where the reverse process is observed. Activated carbons with high capacities (i.e. activated carbon that is believed to be fresh and therefore has not been fouled) have the ability to absorb gold faster. The model reveals that the rate at which gold is lost from the solution phase is the same but a reverse process to the rate at which it is adsorbed unto the activated carbon phase and this rate, as mentioned earlier, is dependent on the maximum capacity of the activated carbon. It has also been observed that the choice of concentration of activated carbon affects greatly the nature of adsorption. The rate at which gold is adsorbed unto activated carbon reduces with time but the process is quicker and very spontaneous with increased amount of activated carbon in the adsorption circuit.
A Thesis submitted to the Institute of Distance Learning, Kwame Nkrumah University of Science and Technology, Kumasi in partial fulfillment of the requirements for the degree of Masters of Science in Industrial Mathematics, November-2012