Two important items must be considered in the early stages of design of a processing plant which contains a cyclic element such as a scaling crystallizer, a filter, a fixed bed adsorber, etc. They are the influence of cycle length on the size of all equipment elements in the process, and the effect of available storage capacity of feed to the cyclic element on process economics. These considerations are particularly important in the development of equipment sizes for industrial minerals processing plants, many of which contain scaling crystallizers.
The problem of determining cycle time for an item of equipment of fixed capacity to either maximize total production, or to minimize operating costs has been discussed previously. The present work examines a constrained version of this classical problem. It addresses the problem of determining the cycle time that minimizes annual operating costs after the annual plant production rate has been fixed. First, a generalized material balance is developed for a model processing plant which contains scaling and non-scaling elements. Second, a generalized equation which represents rate of scale formation is used in conjunction with the material balance equation to relate equipment design capacity and the required amount of storage capacity with cycle time. Third, a generalized cost equation is developed which can be used to determine optimum cycle time, optimum equipment sizes and required storage capacity. An example is given.
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