# Multi-Component Separation

Multi-Component Separation is important in the chemical process industry.  For example, for the oil&gas application, the feed stock can be separated into many fuel products, such as methane, ethane, propane, n-butane and n-octane.  Effective separation is one that optimizes the \$-value given the pricing of each product.   For example, a single-stage gas-to-oil ratio (GOR) can be minimized by adjusting separation tank pressure and temperature. The solution is an iteration-to-convergence to conserve the mass of each component.  An example of this is the Rachford-Rice algorithm.  However the optimization is subject to uncertainty due to feed stock variations and local variations of separation conditions and measurements.

The Multi-Component Separation project was initiated to replace the Monte-Carlo method used in calculation of uncertainty.  The first step is to establish a baseline separation problem with specified feed.  Once a solution has been obtained, the input numbers are converted to duals by including uncertainty (as an error vector) and the numerical steps are converted to duals arithmetic.  Due to the multidimensional nature of the problem, an error budget is reported to identify the dominant contributions to uncertainty.

The solution is post-processed by applying the results-with-error to the economic calculation.  This provides the \$-value with error assessment of the separation process.  This allows the optimization, not just of the \$-value but also the uncertainty.  For example, it does not do much good if the profit is optimized to be relatively high but is then accompanied by a relatively large uncertainty.  Optimization, even in high dimensions, can be peaked and a slight variation about the peak can lead to a large drop-off in value.  The duals arithmetic provides the uncertainty and its vector components simultaneously so these vulnerabilities can be judged immediately for process adjustment.