In this paper, we present a steady-state analysis of a double-effect evaporator with thermal vapor compression (MED-TVC) installed in the Tunisian Chemical Group (GCT) factory. A thermodynamic model including mass and energy balances of the system is developed and integrated in a Matlab program. The model resolution yields to the determination of the operating parameters of the plant and the Gain Output Rate (GOR) was found to be roughly equal to 5. In a second step, the simulation results served to conduct a second law analysis of the unit. The performance criterion used in this analysis is the second law efficiency, i.e., the ratio of the least theoretical work of separation to the actual work input to the plant. The second law efficiency was found to be 2.4%. The distribution of the irreversibility between the different components of the plant was, in addition, assessed. As a conclusion, it was established that the most irreversibility occurs in the thermo-compressor which contributes with more than 50% to the global imperfection and which presents an exergy efficiency of less than 77%. The remaining irreversibility comes from the three exchangers (the two evaporators and the condenser) with an average contribution of 16%. As it is very difficult to introduce modifications into an existing unit, we assume that the importance of the results is not limited to the studied unit. They serve, rather, as an aid to the future design of a MED-TVC plant.