applied sciences  
Modeling and Parametric Analysis of a Brine Treatment Unit Using a High-Temperature Heat Pump and a Vacuum Evaporator  
**[PERSON] 1,*(r)**, **[PERSON] 1,** [PERSON] 2,** [PERSON] 2(r) and [PERSON] 2(r)  
Footnote 1: The term “\  
degradation. From these technologies, MSF is widely used for brine treatment towards a MLD/ZLD approach, even if it was first developed for seawater desalination treatment. This technology incorporates the heating of brine and its instantaneous pressure drop, forcing it to almost flash into steam [1]. The rest of the brine stream moves on to the next stage to become steam in even lower pressures and the cycle goes on. Freshwater is produced by steam condensation with the use of the cool brine stream. An MSF assembly can usually include up to 30 stages depending on the brine load and salinity, while the maximum capacity of freshwater production can reach 75,000 m\({}^{3}\)/d. MSF requires minimum pretreatment and shows low fouling potential [2]; however, it exhibits high electricity consumption (3.5-5 kWh\({}_{\text{e}}\)/m\({}^{3}\)) and high thermal energy consumption (up to 83.3 kW\({}_{\text{th}}\)/m\({}^{3}\) for stand-alone systems and up to 47.2 kW\({}_{\text{th}}\)/m\({}^{3}\) considering co-generation) [3]. On the other side, a variant of the MSF called vacuum membrane distillation (VMD) is one of the most favorable MD configurations [4]. In VMD, the vapor is isolated with the exercise of a vacuum pressure to the permeate flow side of the membrane, which is maintained at just lower than the saturation pressure of volatile components in the hot feed flow. The membrane is kept between the hot feed flow stream and a vacuum space, while vapor is selected in an external condenser, outside of the membrane module [5]. The vacuum on the permeate flow stream permits a higher partial pressure gradient, leading to an additional driving force for the process, and thus a higher permeate production rate compared to other membrane distillation (MD) configurations [6; 7]. Another benefit of the use of VMD is the fact that a vacuum leads to negligible heat loss by conduction. However, it should be highlighted that additional electrical power is needed due to the vacuum pump use [8]. In industrial applications, a simplified configuration of VMD is usually used for oil or other substance refinery [9; 10]. It is simply called vacuum distillation and it is a preferred solution when elements that decompose when heated in atmospheric pressure, or have high boiling points that would increase the heating system requirements, are involved. The process is similar to VMD; the pressure is lowered in a column above the solvent to less than the vapor pressure of the mixture in discussion, creating a vacuum and evaporating the substances with lower vapor pressures. With the decrease in the pressure below atmospheric, the temperature demand for the evaporation of the distillate decreases as well, resulting in an overall heating requirement decrease for the system. Vacuum distillation is also used in large industrial plants for seawater desalination. The seawater is put under vacuum pressure in a column to lower its boiling point and with the application of heat, the permeate is distilled and condensed in an external condenser. Thus, the process runs continuously without the loss of vacuum pressure. The condensation heat removal is realized in a sink using the feed seawater to cool it down and preheat the seawater stream. In some cases, instead of condensers, pumps are used to mechanically compress vapor, acting as heat pumps, concentrating the heat from the vapor and allowing it to be returned and reused by the feed seawater [11; 12]. Extended research has been conducted in the field of MSF and MEE systems simulation for brine treatment and ZLD technologies. [PERSON] et al. [13] have developed a steady-state simulation model for a multiple-effect evaporator for application in the caustic soda industry.