A set of equations used for calculating the material, energy, and thermodynamic profiles within a distillation column. They combine material balances, equilibrium conditions, summation conditions, and heat balances, which are required to (p. 236) be solved simultaneously. Due to the complexity of the computations, computer simulation software uses algorithms based on Newton-Raphson methods to converge onto solutions. Once the calculations have been solved rigorously for one stage, the next stage is computed. When the traverse of the entire column is completed, a comparison is made of the computed and assumed overall material balance. Another trial is used where there is an unacceptable difference.