The criteria of fluid phase equilibrium can be expressed in terms of derivatives of the Helmholtz energy density, which takes component densities (concentrations) as its natural variables. The resulting formulation is very symmetric, avoids shortcomings of other approaches, and leads to a very efficient computer algorithm for the calculation of phase envelopes of multicomponent mixtures. The new algorithm does without inverting the equation of state (calculate the density from pressure and temperature) at each iteration step, and thus achieves a significant acceleration of phase diagram computations with noncubic equations of state. The estimation of initial values for the iteration is reduced to a 1-dimensional search problem even for multicomponent mixtures. (C) 2012 Elsevier B.V. All rights reserved.