Optimal Design and Operation of Buffer Tanks Under Stochastic Conditions

Abstract Safety regulations demand the elimination of random mistakes and the reliable operation of production units. However, the control and maintenance of batch and semi-continuous processes haalways been difficult. In this paper, a way of preventing malfunctions in batch and semi-continuous processes is presented by using appropriately designed buffer tanks. A stochastic model was investigated in which batch and continuous subsystems were linked by an intermediate storage tank. The main concern was the reliability of the system. Reliable operation was defined as neither the exhaustion of raw materials nor the excessive accumulation of them. The counting processes that describe the random batch-input and random batch-output processes are supposed to be independent homogeneous Poisson processes with different rates. By introducing a function that describes the material in storage, reliable operation is defined as when this function satisfies two inequalities for a time interval of any duration. By applying probabilistic methods, an integral equation is set up for the the reliability. Nevertheless, its analytical solution cannot be determined, hence the values according to a Monte Carlo simulation are approximated. By applying this method, a link could be identified between the necessary initial buffer and tank capacities that belong to a reliability level. Economic investigations were conducted to help determine the optimal initial buffer and tank capacities that satisfy the appointed reliability level.