In order to utilize energy fully a mathematical model of parallel-feed multi-effect evaporation system for conventional design was established.The model included two sequential system—multi-evaporation system and multi-level preheating system.In this model

the energy-saving measures

such as condensate flash

using extra steam and thick liquor of each effect to preheat raw liquid were adopted.Solid separation was also considered in the process of evaporation.Material balance and energy balance equations of complex parallel-feed multi-effect evaporation system were expressed in matrix equation.By holding or omitting correlated block-matrix

the matrix equation could be used to describe the difference of parallel-feed multi-effect evaporation system with and without solid separation

with and without condensate flash

with and without preheating raw liquid.The model could also be used in the calculation of different effects to realize the universality of the model.The solid-liquid equilibrium data in the multi-effect evaporation system with solid separation was fitted by the intelligent fitting method

which helped to solve this problem by computer.The model was solved by the iterative method and matrix method.The result showed that the model had universality.Using extra steam to preheat raw liquid and condensate flash were effective methods to save energy.The steam consumption of four-effect parallel-feed evaporation with former energy saving methods was decreased by about 30% for evaporation of NaOH solution containing NaCl.The algorithm increased the convergence speed and stability.