Method for calculating material balance of complex process flowcharts

When developing, analyzing, and optimizing chemical production technologies, one should first calculate the material and heat balances in order to quantify the products and wastes produced, the reagents and energy consumed, as well as to determine characteristics of equipment required. Thus, balance calculation helps to perform primary analysis of technology feasibility and to obtain initial data for estimation of capital and operational costs. Calculating material balance for the series-connected apparatus working in a steady-state mode is a trivial problem. For the process flowcharts with branching and recycled flows, however, calculations get more complicated. Iterative method of calculation with termination of iterations when convergence condition is met is frequently used to calculate the material balance of flowcharts with recycled flows. This method has several limitations, namely the increase in computational time, iterative accumulation of errors, possible oscillations of solution, etc. In complex flowcharts, branching and recycled flows often lead to internal cycles. For this reason, the more complex is the flowchart, the stronger is the influence of iterative method limitations that are mentioned above. This work is aimed to validate and improve material balance calculation for complex chemical process flowcharts with branching and recycled flows. We introduce the analytical solution instead of iterative algorithm used to perform such calculations and propose methods for convolution of straight, branched, and cycled segments of these flowcharts.