This work has developed a simple, reliable and fast algorithm for the simulation of multicomponent distillation columns, where any equilibrium stage can accept a feed-stream and/or a vapor-side-stream and/or liquid-side-stream. The new scheme considers internal molar overflows and constant relative volatilities to avoid the need of heat balances and vapor-liquid equilibrium calculations. The solution scheme is founded on a Newton-based formulation in block algebra, which relies in a simple, reliable and fast algorithm. Although the proposed calculation scheme can be classified as an approximate method, it is very useful when accurate phase equilibrium and enthalpy data are lacking. Numerical experimentations show good agreement with the results obtained with well-known rigorous simulation approaches. (C) 2012 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.