Mathematical modeling and simulation of countercurrent multiple effect evaporation for fruit juice concentration

• A mathematical model of countercurrent multiple effect evaporation is established.
• Various energy conservation measures are introduced in the MEE system.
• Iteration method combining with matrix method is used to solve the model.
• The model has the advantage of strong generality by expressing as matrix equation.
• The specific heat and heat transfer coefficient are regarded as variables.

In order to greatly reduce the energy consumption of fruit juice concentration process, a general mathematical model of countercurrent multiple effect evaporation (MEE) system contains various energy saving measures simultaneously (such as steam jet heat pump technology, solution flash and condensed water flash) is established in this paper. The systematic material balance equations and heat balance equations are described as the form of matrix equation to realize the generality of this model. The general model can be simplified to a countercurrent multi-effect evaporation model contains several or none energy saving measures and it can achieve the function of pumping steam at any effect. The model is solved by matrix method combining with iteration method, which has advantages of less sensitive to initial values, high convergence speed and stability. The developed model is used to simulate the fruit juice concentration process under different operating strategies. The simulation results indicate that heat pump is an effective energy saving measure in countercurrent MEE system. The larger values of ejection coefficient and effect for pumping, the more fresh steam consumption saves and heat transfer area increases when some constraint conditions are satisfied. After combining condensed water flash and solution flash, it achieves a more pronounced effect.