Determination of Concentration of the Aqueous Lithium–Bromide Solution

data

Technical Note Determination of Concentration of the Aqueous Lithium–Bromide Solution in a Vapour Absorption Refrigeration System by Measurement of Electrical Conductivity and Temperature

Salem M. Osta-Omar * and Christopher Micallef

Mechanical Engineering Department, University of Malta, MSD 2080 Msida, Malta; [email protected] * Correspondence: [email protected]; Tel.: +35-699-357-005

Academic Editor: Jamal Jokar Arsanjani Received: 24 November 2016; Accepted: 11 January 2017; Published: 19 January 2017

Abstract: Lithium–bromide/water (LiBr/water) pairs are widely used as working medium in vapour absorption refrigeration systems where the maximum expected temperature and LiBr mass concentration in solution are usually 95 °C and 65%, respectively. Unfortunately, published data on the electrical conductivity of aqueous lithium–bromide solution are few and contradictory. The objective of this paper is to develop an empirical equation for the determination of the concentration of the aqueous lithium–bromide solution during the operation of the vapour absorption refrigeration system when the electrical conductivity and temperature of solution are known. The present study experimentally investigated the electrical conductivity of aqueous lithium–bromide solution at temperatures in the range from 25 °C to 95 °C and concentrations in the range from 45% to 65% by mass using a submersion toroidal conductivity sensor connected to a conductivity meter. The results of the tests have shown this method to be an accurate and efﬁcient way to determine the concentration of aqueous lithium–bromide solution in the vapour absorption refrigeration system.

Keywords: electrical conductivity measurements; LiBr/water solution; vapour absorption refrigeration system; regression analysis

1. Introduction The basic principle of the vapour absorption refrigeration technology is the phenomenon of sorption. This process occurs as a result of the chemical afﬁnity of one substance (sorbent) for holding another one (sorbate). In LiBr/water vapour absorption refrigeration systems, the sorbate is the water vapour and the sorbent is the aqueous lithium–bromide solution, which is responsible for the sorption and desorption of the sorbate. The desorption process, which consists of separating the sorbate from the sorbent, takes place in the generator by means of heat input. The sorption process, where the sorbate is absorbed again by the sorbent, takes place in the absorber via an exothermic reaction [1]. Aqueous lithium–bromide is a salt solution substance. The maximum amount of salt which can dissolve in water is highly dependent on the water temperature. The higher the water temperature, the more salt can be dissolved in water, and it is said that the solubility of the salt increases with temperature. When no more salt can be dissolved in water the solution is said to be saturated. If the temperature of a saturated solution drops, precipitation/crystallization of the salt takes place [2]. Thus, the sorption and desorption processes of the LiBr/water solution in the vapour absorption refrigeration system should be designed properly to avoid the precipitation and crystallization of the salt in the solution, which can lead to blockage of solution passage ways.

Data 2017, 2, 6; doi:10.3390/data2010006 www.mdpi.com/journal/data Data 2017, 2, 6 2 of 11

Data 2017, 2, 6 2 of 12 When the crystallization of the LiBr/water solution, which leads to the shutting down of the vapour absorptionWhen the crystallization refrigeration of system, the LiBr/water appears solu duringtion, which the operationleads to the of shutting the vapour down absorptionof the refrigerationvapour absorption system due refrigeration to a signiﬁcant system, temperature appears during drop orthe increase operation in LiBrof the mass vapour concentration absorption of the solution,refrigeration the ﬂow system of the due LiBr/water to a significant solution temperature in the system drop isor blocked.increase in To LiBr avoid mass this, concentration the concentration of of thethe solution solution, has the to flow be monitored of the LiBr/water at critical solution positions in the prone system tocrystallization, is blocked. To inavoid order this, to the heat up the LiBr/waterconcentration solution of the solution before has the to saturation be monitored limit at critical is reached. positions The prone crystallization to crystallization, problem in order tends to to heat up the LiBr/water solution before the saturation limit is reached. The crystallization problem occur in the weak LiBr/water solution between the throttling valve and the absorber as indicated in tends to occur in the weak LiBr/water solution between the throttling valve and the absorber as Figureindicated1, at which in Figure point 1, theat which temperature point the temperature of the LiBr/water of the LiBr/water solution solution is at its is relative at its relative lowest lowest and LiBr massand concentration LiBr mass concentration of the solution of the is solution at its highest is at its in highest the system in the [system3]. [3].

Figure 1. Schematic diagram of a LiBr/water (lithium–bromide/water) absorption refrigeration system Figure 1. Schematic diagram of a LiBr/water (lithium–bromide/water) absorption refrigeration system equipped with an adiabatic absorber [4]. equipped with an adiabatic absorber [4]. A number of feasible methods for determining the concentration of aqueous lithium–bromide Asolution number are ofimperative feasible methodsto review forhere. determining The most two the common concentration and well-known of aqueous methods lithium–bromide are: the solutiondetermination are imperative of the LiBr/water to review concentration here. The by most measuring two common the specific and gravity well-known of the solution methods with are: the determinationa hydrometer of[5,6] the and LiBr/water by use of concentrationtitration with bysilver measuring nitrate [2]. the Both speciﬁc methods gravity give of accurate the solution measurements but are necessarily time-consuming, as they require the extraction and manipulation with a hydrometer [5,6] and by use of titration with silver nitrate [2]. Both methods give accurate of a sample from the system in a laboratory [2,5]. However, an alternative method which could be measurements but are necessarily time-consuming, as they require the extraction and manipulation of used to determine the concentration of LiBr/water solution is that of measuring the secondary a sampleproperties from thethat system are associated in a laboratory with and [2 ,5affected]. However, by the an change alternative in concentration. method which An couldexample be usedof to determinesecondary the concentrationproperties which of can LiBr/water be measured solution properly is thatby using of measuring a sensor inside the secondarythe vapour absorption properties that are associatedrefrigeration with system and affectedis the electrical by the changeconductivi inty concentration. through which An the example concentration of secondary of LiBr/water properties whichsolution can be can measured be determined properly easily by usingin the system a sensor duri insideng the the operation vapour without absorption extracting refrigeration a sample system [6]. is the electrical conductivity through which the concentration of LiBr/water solution can be determined easily in the system during the operation without extracting a sample [6]. Data 2017, 2, 6 3 of 11

The electrical conductivity is the ability of the solution to conduct an electric current. This depends on such factors as concentration and temperature. An increase in the temperature of solution increases the mobility and the number of the ions in solution due to ionisation of molecules, which in turn leads to an increase in the electrical conductivity of the solution. Moreover, an increase in the concentration of solution leads to increase its electrical conductivity due to an increase in the number of ions per unit volume [7,8]. It is therefore always important to associate the electrical conductivity measurement of a solution with a reference concentration and temperature. The electrical conductance of the aqueous lithium–bromide solution for concentrations in the range of 40.7% to 63.55% was studied by Fried and Segal [5]. Their data shows that the electrical conductance increased from 162 mmho at 15 ◦C to 419 mmho at 80 ◦C for a concentration of 45% and from 115 mmho at 15 ◦C to 333 mmho at 80 ◦C for a concentration of 50%. Unfortunately their study gave measurements of the electrical conductance rather than electrical conductivity. Since electrical conductance measurement is a function of both the distance between the electrodes and the effective area of the electrodes, their results depends on the equipment being used and thus cannot be considered as reference data. Sun et al. [9] investigated the electrical resistivity (ohm × cm) of aqueous lithium–bromide solution for concentration and temperature ranges of 35% to 70% and of 10 ◦C to 100 °C respectively. Their results can be used to establish the concentration of aqueous lithium–bromide solutions when the electrical resistivity and the temperature of the solutions are known. Nowadays the majority of equipment which are readily available on the market measures the electrical conductivity (mS/cm) of solutions. Thus, the existing literature is no longer useful since it gives data based on electrical conductance and electrical resistivity. The purpose of this study is to ﬁnd an alternative, practical, and modern way which can be used to determine the concentration of the aqueous lithium–bromide solution in the vapour absorption refrigeration system without extracting samples. Furthermore, the techniques used in this study mimic the working conditions of the LiBr/water solutions inside the vapour absorption refrigeration system; therefore, the results presented in this study are considered as data simulating the real-time of LiBr/water solution inside the vapour absorption refrigeration system. As a result, control of the performance of the vapour absorption refrigeration system can be achieved easily, which, in turn, leads to a signiﬁcant reduction in costs prohibiting the wide spread adoption of the vapour absorption refrigeration technology.

2. Experimental Equipment and Measurement Technique The aqueous lithium–bromide solutions were prepared in a mass percent concentration of 45%, 50%, 55%, 60%, and 65% by using distilled water and lithium bromide salt (with a purity of 99.0% according to the technical specification of the supplier). The solution preparation and the tests were performed in a dry laboratory room, and the amount of each LiBr/water concentrated solution was about 1.5 liters. During the experiments, the solution was placed in lab glassware over an electric hot plate at an input capacity of 225 W. At the center of the glassware, the submersion toroidal conductivity sensor (Omega Engineering, Model No. CDE-45T2) was mounted and connected to the toroidal conductivity meter (Omega Engineering, Model No. CDTX-45T), which was powered by 24 V DC supply as shown in Figure2. The temperature and electrical conductivity measurement ranges of the instrument are from −10 ◦C to 210 ◦C and from 0.0 mS/cm to 200.0 mS/cm with 0.5% accuracy for both measurements. For each of the five solutions listed above, six tests were performed; in tests 1, 3, and 5 the solution temperature was raised slowly from room temperature (25 ◦C) to 95 ◦C using an electric heater, while in tests 2, 4, and 6, the solution was allowed to cool naturally from 95 ◦C to room temperature. Following the six tests performed for the heating and cooling processes, another test was performed for each of the five solutions listed above in order to obtain the electrical conductivity when the solution was allowed to reach steady state conditions. In this test, the electrical conductivity Data 2017, 2, 6 4 of 11 was measured in temperature-controlled oil bath (Memmert, Model No. One 7–45) at temperatures fixedData to2017 within, 2, 6 a setting accuracy and temperature fluctuation of 0.1 ◦C and ±0.2 ◦C respectively.4 of 12 The procedure adapted was to heat the solution from room temperature (25 ◦C) to the maximum The procedure adapted was to heat the solution from room temperature (25 ℃) to the maximum temperature of 95 ◦C in steps of 5 ◦C. After making sure that the solution reached a steady state temperature of 95 ℃ in steps of 5 ℃. After making sure that the solution reached a steady state condition, it was maintained at the set temperature for ten minutes before the electrical conductivity condition, it was maintained at the set temperature for ten minutes before the electrical conductivity was recorded. It was noted that the solution took about forty minutes to reach equilibrium between was recorded. It was noted that the solution took about forty minutes to reach equilibrium between temperaturetemperature settings. settings. During During the the experiments, experiments, the the nozzle nozzle of the of labthe glasswarelab glassware used used to hold to thehold solution the andsolution the sensor and wasthe sensor sealed was with sealed aluminum with aluminum foil tape infoil order tape toin maintainorder to maintain the concentration the concentration of solutions of assolutions prepared as for prepared the tests. for the tests.

FigureFigure 2.2. SchematicSchematic of the the test test rig. rig.

3. Results and Discussion 3. Results and Discussion The experimental data presented in Figures 3–7 show that for a constant concentration, the The experimental data presented in Figures3–7 show that for a constant concentration, electrical conductivity of the aqueous lithium–bromide solution increases as the solution temperature theincreases. electrical However, conductivity for low of concentrations the aqueous of 45% lithium–bromide and 50%, the electrical solution conductivity increases of as the the aqueous solution temperaturelithium–bromide increases. solution However, shows for less low sensitivity concentrations to temperature of 45% and increases 50%, the when electrical compared conductivity to the of thehigher aqueous solution lithium–bromide concentrations. solution As can shows be seen less in sensitivity Figures 3 to and temperature 4, the average increases values when of electrical compared to theconductivity higher solution increase concentrations. from 170 mS/cm As to can 177.7 be seenmS/cm in Figuresand from3 and 146.44, themS/cm average to 157.4 values mS/cm of electrical for the conductivitysolution concentrations increase from of 17045% mS/cmand 50% to respec 177.7tively, mS/cm when and the from temperature 146.4 mS/cm increases to 157.4 from mS/cm 25 ℃ to for the95 solution ℃. concentrations of 45% and 50% respectively, when the temperature increases from 25 ◦C to 95 ◦C.

Data 2017, 2, 6 5 of 12 Data 2017, 2, 6 5 of 11 Data 2017, 2, 6 5 of 12 200

195200

190195

185190

180185

175180

170175

165170

160165 Electrical conductivity (mS/cm) 155160 Electrical conductivity (mS/cm) 150155 20 30 40 50 60 70 80 90 100 150 20 30 40 50Temperature 60 (℃) 70 80 90 100 Temperature (℃) Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Average values

Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Average values Figure 3. Electrical conductivity of aqueous lithium–bromide solution concentration of 45% by mass. FigureFigure 3. Electrical 3. Electrical conductivity conductivity ofaqueous of aqueous lithium–bromide lithium–bromide solution solution concentration concentration of of45% 45% byby mass. mass. 180

180 170

170 160

160 150

150 140

140

Electrical conductivity (mS/cm) 130

Electrical conductivity (mS/cm) 130 120 20 30 40 50 60 70 80 90 100 120 20 30 40 50Temperature 60 (℃) 70 80 90 100 Temperature (℃) Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Average values

Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Average values Figure 4. Electrical conductivity of aqueous lithium–bromide solution concentration of 50% by mass. Figure 4. Electrical conductivity of aqueous lithium–bromide solution concentration of 50% by mass. Figure 4. Electrical conductivity of aqueous lithium–bromide solution concentration of 50% by In contrast, the average values of electrical conductivity increase from 119 mS/cm to 143.4 mS/cm mass. and fromIn contrast, 97.8 mS/cm the average to 126.3 values mS/cm of electrical for the conductivity solution concentrations increase from of 119 55% mS/cm and 60%to 143.4 respectively, mS/cm and from 97.8 mS/cm to 126.3 mS/cm for◦ the soluti◦ on concentrations of 55% and 60% respectively, when theIn contrast, temperature the average increases values from of 25 electricalC to 95 conductivityC, as shown increase in Figures from5 119 and mS/cm6. As a to result, 143.4 mS/cm it can be when the temperature increases from 25 ℃ to 95 ℃, as shown in Figures 5 and 6. As a result, it can concludedand from that97.8 whenmS/cm the to concentration126.3 mS/cm for of the soluti solutionon concentrations is increased, the of electrical55% and 60% conductivity respectively, of the be concluded that when the concentration of the solution is increased, the electrical conductivity of solutionwhen the becomes temperature more sensitiveincreases tofrom the 25 change ℃ to 95 in ℃ temperatures, as shown in of Figures the solution. 5 and 6. As a result, it can the solution becomes more sensitive to the change in temperatures of the solution. be concluded that when the concentration of the solution is increased, the electrical conductivity of the solution becomes more sensitive to the change in temperatures of the solution.

Data 2017, 2, 6 6 of 12 Data 2017, 2, 6 6 of 11 Data 2017160, 2, 6 6 of 12

160 150

150 140

140 130

130 120

120

Electrical conductivity (mS/cm) 110

Electrical conductivity (mS/cm) 110 100 20 30 40 50 60 70 80 90 100 100 ℃ 20 30 40 50Temperature 60 ( ) 70 80 90 100 Test 1 Test 2 Test 3 TemperatureTest 4 (Test℃) 5 Test 6 Average values

Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Average values Figure 5. Electrical conductivity of aqueous lithium–bromide solution concentration of 55% by Figure 5. mass. FigureElectrical 5. Electrical conductivity conductivity ofaqueous of aqueous lithium–bromide lithium–bromide solution solution concentration concentration of of55% 55% byby mass. mass. 150

150 140

140 130

130 120

120 110

110 100

100 Electrical conductivity (mS/cm) 90

Electrical conductivity (mS/cm) 90 80 20 30 40 50 60 70 80 90 100 80 ℃ 20 30 40 50Temperature 60 ( ) 70 80 90 100 Temperature (℃) Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Average values

Figure 6. TestElectrical 1 conductivityTest 2 ofTest aqueous 3 lithium–bromideTest 4 Test solution 5 concentrationTest 6 Average of 60% values by mass. Figure 6. Electrical conductivity of aqueous lithium–bromide solution concentration of 60% by mass. Figure 6. Electrical conductivity of aqueous lithium–bromide solution concentration of 60% by Additionally, Figure7 shows a rapid decrease in conductivity when the temperature of the solution mass. havingAdditionally, a concentration Figure of 65%7 shows approaches a rapid 40decrease◦C. This in coincidesconductivity with when the onsetthe temperature of crystallization of the of solution having a concentration of 65% approaches 40 ℃ . This coincides with the onset of the lithium–bromideAdditionally, Figure from solution.7 shows Asa rapid a result, decrease the average in conductivity values of when electrical the conductivitytemperature of decrease the crystallization of the lithium–bromide from solution. As a result, the average values◦ of electrical◦ rapidlysolution from having 78 mS/cm a concentration to 51 mS/cm of 65% when approaches the temperature 40 ℃ . decreasesThis coincides from 40withC the to 25onsetC. Inof all conductivity decrease rapidly from 78 mS/cm to 51 mS/cm when the temperature decreases from charts,crystallization for each solutionof the lithium–bromide concentration, averagefrom solution values. As of thea result, six tests the and average error values bar corresponding of electrical to 40 ℃ to 25 ℃. In all charts, for each solution concentration, average values of the six tests and error twoconductivity sample standard decrease deviations rapidly from (95% 78 confidence mS/cm to 51 interval) mS/cm werewhen plotted. the temperature In practice, decreases the confidence from bar corresponding to two sample standard deviations (95% confidence interval) were plotted. In intervals40 ℃ to are25 ℃ typically. In all charts, stated for at each the 95%solution confidence concentratio leveln, so average that the values result of hasthe onlysix tests a 5% and chance error of practice, the confidence intervals are typically stated at the 95% confidence level so that the result has beingbar corresponding false [10]. to two sample standard deviations (95% confidence interval) were plotted. In only a 5% chance of being false [10]. practice, the confidence intervals are typically stated at the 95% confidence level so that the result has only a 5% chance of being false [10].

Data 2017, 2, 6 7 of 11 Data 2017, 2, 6 7 of 12

140 130 120 110 100 90 80 70 60 Electrical conductivity (mS/cm) 50 40 20 30 40 50 60 70 80 90 100 Temperature (℃)

Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Average values

FigureFigure 7. Electrical 7. Electrical conductivity conductivity ofaqueous of aqueous lithium–bromide lithium–bromide solution solution concentration concentration of of 65% 65% byby mass. mass. Another interesting point which can be seen in Figures3–7 is that almost all the test results (tests 1, 3, and 5)Another which interesting had been recorded point which when can the be solution seen in Figures temperature 3–7 is wasthat increasingalmost all the are test above results the (tests average values.1, 3, and On 5) the which other had hand, been the recorded test results when (test the2, solution 4, and 6)temperature recorded whenwas increasing the solution are temperatureabove the wasaverage decreasing values. are On below the theother average hand, values.the test Thisresults discrepancy (test 2, 4, canandbe 6) attributedrecorded when to the the rate solution of heating temperature was decreasing are below the average values. This discrepancy can be attributed to the being much higher than the rate of cooling during the tests. rate of heating being much higher than the rate of cooling during the tests. Table1 lists the average values of the electrical conductivity of the aqueous lithium–bromide Table 1 lists the average values of the electrical conductivity of the aqueous lithium–bromide solution for concentrations of 45%, 50%, 55%, 60%, and 65% at various temperatures, and Figure8 solution for concentrations of 45%, 50%, 55%, 60%, and 65% at various temperatures, and Figure 8 shows this data in graphical form. shows this data in graphical form.

Table 1. Electrical conductivity of aqueous lithium–bromide solution. Table 1. Electrical conductivity of aqueous lithium–bromide solution.

TemperatureTemperature ElectricalElectrical Conductivity (mS/cm) (mS/cm) (°C)(℃) 45%45% by by Mass Mass 50% 50% by by Mass Mass 55% byby MassMass 60% 60% by Mass 65% 65% by by Mass Mass 25 170.0 146.4 119.0 97.8 51.1 * 25 170.0 146.4 119.0 97.8 51.1 * 3030 170.5170.5 147.5147.5 122.5122.5 100.6 100.6 54.0 54.0 * * 3535 171.2171.2 148.9148.9 124.8124.8 102.6 102.6 63.7 63.7 * * 4040 171.8171.8 150.3150.3 126.7126.7 105.3 105.3 78.0 78.0 * * 4545 172.5172.5 151.3151.3 128.6128.6 108.5 108.5 83.8 83.8 5050 172.9172.9 152.1152.1 130.1130.1 110.6 110.6 87.5 87.5 5555 173.7173.7 152.7152.7 131.3131.3 112.6 112.6 91.6 91.6 60 174.2 153.7 132.9 113.9 95.7 6560 174.8174.2 154.4153.7 134.4132.9 113.9 115.2 95.7 98.1 7065 175.4174.8 154.9154.4 135.5134.4 115.2 116.6 98.1 100.3 7570 176.0 175.4 155.3154.9 136.4135.5 116.6 118.0 100.3 101.9 8075 176.4 176.0 155.9155.3 137.4136.4 118.0 119.2 101.9 102.9 8580 177.0 176.4 156.3155.9 138.9137.4 119.2 120.7 102.9 105.0 9085 177.3 177.0 156.9156.3 141.3138.9 120.7 122.6 105.0 107.5 95 177.7 157.4 143.4 126.3 109.9 90 177.3 156.9 141.3 122.6 107.5 95 177.7 * Crystallization157.4 was detected.143.4 126.3 109.9 * Crystallization was detected.

Data 2017, 2, 6 8 of 11 Data 2017, 2, 6 8 of 12

200

180

160

140

120

100

80 Electrical conductivity (mS/cm) 60

40 20 30 40 50 60 70 80 90 100 Temperature (℃)

65% 60% 55% 50% 45%

FigureFigure 8. Electrical 8. Electrical conductivity conductivity of aqueous aqueous lithium–bro lithium–bromidemide solution solution for different for different concentrations concentrations (% (% byby mass). mass).

RegressionRegression analysis analysis using using all all data data except except the the 65% 65% concentrationconcentration set set was was done done in inorder order to toarrive arrive at the empiricalat the empirical correlation correlation shown shown in Equation in Equation (1). (1). 0.236 × T − EC + 343.93 C =0.236 × T − EC + 343.93 (1) C = 4.09 (l) where C is the LiBr mass concentration of solution4.09 (% by mass), T is the temperature of LiBr/water wheresolution C is the (℃ LiBr), and mass EC isconcentration the electric conductivity of solution of the (% LiBr/water by mass), Tsolution is the temperature(mS/cm). This ofempirical LiBr/water solutionequation (◦C), is and only EC valid is the for electrica LiBr mass conductivity concentration of the range LiBr/water of 45 ≤ C solution ≤ 60% and (mS/cm). for a temperature This empirical range of 25 ℃ ≤ T ≤ 95 ℃. equation is only valid for a LiBr mass concentration range of 45 ≤ C ≤ 60% and for a temperature Equation (1) can be used to estimate the concentration of aqueous lithium–bromide solution in range of 25 ≤ T ≤ 95 . any vapour absorption refrigeration system that uses a similar measurement technique to that which wasEquation used in (1) this can experimental be used to estimatework for the elec concentrationtrical conductivity of aqueous and temperature lithium–bromide of aqueous solution in anylithium–bromide vapour absorption solution. refrigeration This empirical system correlation that has uses been a similardetermined measurement with predictive technique values (p to- that whichvalues) was usedof 3.85 in ×this 10 experimental and 7.89 × work 10 forfor thethe electricaltemperature conductivity and the concentration, and temperature respectively. of aqueous lithium–bromideBoth p-values solution.are lower Thisthan the empirical common correlation alpha level has of been0.05, which determined indicates with that predictive both of the values (p-values)independent of 3.85 variables× 10−22 (temperatureand 7.89 × and10− 57concentrfor theation) temperature are statistically and thesignificant concentration, [11]. respectively. Both p-valuesTable 2 are lists lower the values than of the electrical common conducti alphavity level of the of aqueous 0.05, which lithium–bromide indicates that solution both for of the independentconcentrations variables of 45%, (temperature 50%, 55%, and and 60% concentration) with temperatures are statistically ranging from signiﬁcant 25 ℃ and [11 95]. ℃. These values have been estimated by using Equation (1). The maximum error in the concentration when Table2 lists the values of the electrical conductivity of the aqueous lithium–bromide solution using Equation (1) was calculated to be 5.8%. for concentrations of 45%, 50%, 55%, and 60% with temperatures ranging from 25 ◦C and 95 ◦C. These valuesTable have2. Electrical been conductivity estimated of by aqueous using lithium–br Equationomide (1). solution The maximum for different error concentrations in the concentration (% when usingby mass) Equation estimated (1) wasby the calculated empirical correlation. to be 5.8%. Electrical Conductivity (mS/cm) Table 2. ElectricalTemperature conductivity of aqueous lithium–bromide solution for different concentrations (% by (℃) 45% by Mass 50% by Mass 55% by Mass 60% by Mass mass) estimated by the empirical correlation. 25 165.4 144.9 124.4 103.9 30 166.6 Electrical146.1 Conductivity125.6 (mS/cm) 105.1 Temperature35 (°C) 167.8 147.3 126.8 106.3 45% by Mass 50% by Mass 55% by Mass 60% by Mass 40 168.9 148.4 128.0 107.5 25 165.4 144.9 124.4 103.9 30 166.6 146.1 125.6 105.1 35 167.8 147.3 126.8 106.3 40 168.9 148.4 128.0 107.5 45 170.1 149.6 129.1 108.7 50 171.3 150.8 130.3 109.8 Data 2017, 2, 6 9 of 11

Table 2. Cont.

Electrical Conductivity (mS/cm) Temperature (°C) 45% by Mass 50% by Mass 55% by Mass 60% by Mass 55 172.5 152.0 131.5 111.0 60 173.7 153.2 132.7 112.2 65 174.9 154.4 133.9 113.4 70 176.0 155.5 135.1 114.6 75 177.2 156.7 136.2 115.8 80 178.4 157.9 137.4 116.9 85 179.6 159.1 138.6 118.1 90 180.8 160.3 139.8 119.3 95 182.0 161.5 141.0 120.5

Also, Table3 lists the values of the electrical conductivity of the aqueous lithium–bromide solution for a concentration of 65% with temperatures ranging from 45 ◦C and 95 ◦C. These values have been estimated by using Equation 1 (extrapolation outside applicable range). The maximum error in the concentration when using Equation 1 was calculated to be 8.5%.

Table 3. Electrical conductivity of the aqueous lithium–bromide solution for concentration of 65% (by mass) estimated by the empirical correlation.

Electrical Conductivity Temperature (°C) (mS/cm) 45 50 55 60 65 70 75 80 85 90 95 65% by mass 88.7 89.8 91.1 92.2 93.4 94.6 95.8 96.9 98.1 99.3 100.5

Table4 lists the values of the electrical conductivity of the aqueous lithium–bromide solution for concentrations of 45%, 50%, 55%, 60%, and 65% at various temperatures when the solution was at steady state conditions, and Figure9 shows this data in graphical form. Furthermore, Figure 10 compares the results of average values of the electrical conductivity of the aqueous lithium–bromide solution for concentrations of 45%, 50%, 55%, 60%, and 65% obtained from the heating and cooling processes with that obtained from the steady state process in which the solution was allowed to reach thermal equilibrium. The comparison shows that both of the results were very close even though the techniques used to collect the data were different. As a result of the validation of the data obtained for concentrations of 45%, 50%, 55%, and 60% from both experiments, the empirical correlation presented in Equation (1) can always be used whether the solution is at steady state or transient phase.

Table 4. Electrical conductivity of aqueous lithium–bromide solution when the solution was in a steady state condition.

Electrical Conductivity (mS/cm) Temperature (°C) 45% by Mass 50% by Mass 55% by Mass 60% by Mass 65% by Mass 25 174.2 148.6 124.7 102.2 49.1 * 30 174.4 148.9 125.8 103.9 50.8 * 35 174.5 149.4 126.9 106.3 58.8 * 40 175.2 150.2 128.5 107.9 66.5 * 45 175.3 151.4 130 111.1 85.1 50 175.7 152.1 131.1 112.1 93.9 55 175.8 152.9 133.5 113.9 96.2 60 176.1 153.6 134.3 116.1 98.7 65 176.5 154.3 135.7 118 101.1 70 176.9 154.9 137.3 120.3 104 75 177 155.6 138.7 122.2 105.7 80 177.2 156.6 140.5 124 107.9 85 177.3 157 141.2 126.1 110.6 90 177.4 157.2 142.3 127.3 112.2 95 177.6 158 143.2 129.3 113.7 * Crystallization was detected. Data 2017, 2, 6 10 of 12

80 177.2 156.6 140.5 124 107.9 Data 2017, 2, 6 10 of 12 85 177.3 157 141.2 126.1 110.6 90 80 177.4177.2 157.2156.6 142.3140.5 127.3124 107.9112.2 95 85 177.6 177.3 158 157 143.2 141.2 129.3126.1 110.6113.7 90 177.4 * Crystallization157.2 was detected.142.3 127.3 112.2 95 177.6 158 143.2 129.3 113.7 Data 2017, 2, 6 10 of 11 200 * Crystallization was detected.

180 200

160 180

140 160

120 140

100 120

80 100 Electrical conductivivty (mS/cm) Electrical conductivivty 80 60 Electrical conductivivty (mS/cm) Electrical conductivivty 60 40 20 30 40 50 60 70 80 90 100 40 20 30 40 50Temperature 60 (℃) 70 80 90 100 Temperature (℃) 65% 60% 55% 50% 45% 65% 60% 55% 50% 45%

Figure 9. ElectricalElectrical conductivity conductivity of of aqu aqueouseous lithium–bromide lithium–bromide solution solution for for different different concentrations concentrations (% (%by bymass)Figure mass) when 9. whenElectrical the thesolution solutionconductivity was was in ofsteady in aqu steadyeous state statelithium–bromide condition. condition. solution for different concentrations (% by mass) when the solution was in steady state condition. 45% (Heating and Cooling Processes) 45% (Equilibrium Process) 50%45% (Heating (Heating and and Cooling Cooling Processes) Processes) 50%45% (Equilibrium (Equilibrium Process) 55%50% (Heating (Heating and and Cooling Cooling Processes) Processes) 55%50% (Equilibrium (Equilibrium Process) 60%55% (Heating (Heating and and Cooling Cooling Processes) Processes) 60%55% (Equilibrium (Equilibrium Process) 65%60% (Heating (Heating and and Cooling Cooling Processes) Processes) 65%60% (Equilibrium (Equilibrium Process) 190 65% (Heating and Cooling Processes) 65% (Equilibrium Process) 190 175 175 160 160 145 145 130 130 115 115 100 100 85 85 70 70 Electrical conductivivty (mS/cm) Electrical conductivivty Electrical conductivivty (mS/cm) Electrical conductivivty 55 55 40 40 2020 30 30 40 40 50 50 60 60 70 70 80 80 90 100 100 TemperatureTemperature (℃ (℃) )

Figure 10. Comparison of the results of the electrical conductivity of aqueous lithium–bromide solution forFigure differentFigure 10. 10.Comparison concentrations Comparison of (%ofthe bythe results mass)results of of of boththe the electrical experiments. electrical conductivity conductivity ofof aqueousaqueous lithium–bromide solution for different concentrations (% by mass) of both experiments. solution for different concentrations (% by mass) of both experiments. 4. Conclusions

An empirical equation to determine the concentration of the aqueous lithium–bromide solution has been presented with ranges of validity and estimated error. For intermediate values, a linear interpolation between the data in Table1 can be used to estimate the concentration of the LiBr/water solution within the range of study. This work has been performed due to the need for such an empirical equation to be used easily to determine the LiBr mass concentration of solution in the Data 2017, 2, 6 11 of 11 vapour absorption refrigeration system when the temperature and electrical conductivity are known. Moreover, this method has been tested in an experimental vapour absorption refrigeration facility under study at the University of Malta, and the results showed a good indication for determining the LiBr/water solution concentration. Therefore, the method used in this work has taken into consideration the working conditions of LiBr/water solutions inside a vapour absorption refrigeration system. Since the LiBr/water solution moves from one component to another inside the vapour absorption refrigeration system, and each component has a different operation temperature than any other one, the temperature of the LiBr/water solution is made to change drastically and frequently up and down during the operation of the vapour absorption refrigeration system. Consequently, similar working conditions were exposed to the LiBr/water solutions during this work by increasing and reducing the solution temperatures during the tests. Finally, given that the toroidal conductivity sensor used in this experimental work was designed to be used in submersion or pipe ﬂow applications, this conductivity measurement system can be used in any vapour absorption refrigeration system without disturbing the solution ﬂow or the system function.

Acknowledgments: The authors gratefully acknowledge the support from University of Malta. Author Contributions: Salem M. Osta-Omar performed the experiments and analyzed the data presented in this work. Christopher Micallef supervised this work. Both of the authors contributed equally to interpreting the results and to writing this article. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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