The objective of this report is to develop a model and an algorithm to design a multiple effect e evaporator system. Also, it is required to make to evaluate the amount of steam saved by the use of vapour compression. The use of vapour compression allows us to use the energy in the vapour leaving the last effect. Since evaporators are energy intensive system, use of vapour compression can considerably reduce steam consumption, but at the cost of electrical energy needed to run the compressor. To achieve above targets a model based on nonlinaer equations is developed to design the multiple effect evaporator system of seven effects to concentrate black liquor. For this system, first the live steam requirement will be evaluated for the evaporator without any vapour compression. Then vapour compression will be used and the live steam requirement will be calculated. Also the cost for compression of the steam should been taken into account. This gives us a thermo- economic solution wherein both energy and money is being saved. To select the best solution total 17 combinations of placing the compressor in the multiple effect system are identified. The best combination in terms of thermo- economic criterion is vapour from the sixth effect being compressed and sent into the second effect. The cost for running the equipment without any vapour compression is found out to be 4009 $/hr. however, for best combination cost is reduced to 3886 $/hr and the savings made are 23 $.hr.