Reconciliation of size–density bivariate distributions over a separating node

Data reconciliation considers the restoration of mass balance among the noise prone measured data by way of component adjustments for the various particle size or particle density classes or assays over the separating node. In this paper, the method of Lagrange multipliers has been extended to balance bivariate feed and product size–density distributions of coal particles split from a settling column. The settling suspension in the column was split into two product fractions at 40% height from the bottom after a minute settling of homogenized suspension at start. Reconciliation of data assists to estimate solid flow split of particles to the settled stream as well as helps to calculate the profiles of partition curves of the marginal particle size or particle density distributions. In general, Lagrange multiplier method with uniform weighting of its components may not guarantee a smooth partition surface and thus the reconciled data needs further refinement to establish the nature of the surface. In order to overcome this difficulty, a simple alternative method of reconciling bivariate size–density data using partition surface concept is explored in this paper.