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Process of Lithium Recovery from Geothermal Brine

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Process of Lithium Recovery from Geothermal Brine ( process-lithium-recovery-from-geothermal-brine )

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Membranes 2021, 11, 175 6 of 20 Membranes 2021, 11, 175 As an example, Figure 3 shows Simulink code for the “membrane distillation mod- ule” subsystem, which calculated the amount of solvent (water) evaporated from the salt solution based on a number of parameters. Other subsystems are presented in the supplementary materials (Figures S1–S11). The amount of water m evaporated from saline solution in time [kg/min] can be described as follows: m = J􏰻T 􏰼·S·K·Z(t)·1/60 (1) f where J(Tf) is the polynomial equation that defines the flux of distilled water as a function of the feed temperature; Tf is the feed temperature [◦C]; S is the active surface area of one membrane module [m2]; K is the number of membrane modules, Z(t) is the parameter describing the deterioration of membrane performance in time due to scaling/fouling. During the modeling, the temperature of the solution was varied to about 60 ◦C, but the temperature of the coolant/permeate was kept constant and equal to 20 ◦C. The polynomial equation J(Tf) was determined from the experimental data and was taken for simulations as J(Tf) = 0.1071·Tf − 2.0757 (see Figure 5). The parameter Z(t) was determined from the experimental data as Z(t) = 5.2908·e−0.001·t (see Figure 4b) used to describe the flux decline within the single operation of the membrane module during 4.5, 10, or 20 h before the membrane washing step (0.5 h). The recovery ratio of membrane performance after washing was set as 99%; in addition, 95 and 97% were also considered in this work. Once the performance of the membrane module after washing reached 50, 40, or 30% from the initial one, the membrane module was replaced by the new one. The inner working of the system was modeled using a well-known principle of proportional-integral-derivative (PID) 7 of 21 control. Simulink performs calculations based on the input signals in every step, which avoids the need to pre-define the mathematical description for the long-term performance of the whole system. FiFgiugurere3.3R. eRperperseesenntatatitoionoofftthemembranemodulleiinSiimulilninkk::miissttheeamoouunnttooffwaatetrerevevapaoproartaedtedininMMDDmmodoudleule pepremr mininuutete[k[kgg/m/minin],],J(JT(Tf)f)isisththeeppoolylynnoomiiallequationthatdefifineesstthheeflfuluxxooffddisitsitlilleldedwwataetrearsaasafufnucnticotnioonfothfethfeefdeed 2◦22 TaTbablele22.[hk]g;/Tmf is·ht]h;eTffeisetdhetefmeepdetreamtupreera[t°uCre];[SCi]s;Sthiestahcetiavcetivsuersfuarcfeacaeraeraeaofofoonneemembranemoodduulele[m[m],]K,Kisitshethe nunmumbbeerrof membbrraanneemmodoudleusl,eZs(,t)Zi(st)thiesntohnelineoanrlfiunnecatriofnudnecstciorinbindgesthcreibdeintegriothraetidonetoefrimoermatbioranneofpemrfeomrmbarnacneedpuertfoor- msacnalciengd/ufeoutloinsgcaolvinergt/ifmoue.ling over time. 6 5 4 3 2 1 0 membrane washing 0 50 100 150 200 250 300 350 400 450 Permeate flux, kg/m2∙h Time, min a

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