What Is the Affect of Salt on Boiling Water Peer Reviewed
Membranes (Basel). 2018 Sep; 8(3): 39.
Concentration and Temperature Furnishings on H2o and Salt Permeabilities in Osmosis and Implications in Pressure-Retarded Osmosis
Received 2018 Jun 12; Accepted 2018 Jul 3.
Abstract
Osmotic ability extracted from the mixing of freshwater with seawater is a renewable energy resource that has gained increasing attention during recent years. The estimated energy can significantly contribute to the production of ability worldwide. Yet, this power product will exist discipline to variation due to both local weather and seasonal variation. The present newspaper explores the effect of concentration and temperature on h2o and salt fluxes in osmosis at zip transmembrane pressure for five different membranes. Further, the measured fluxes have been utilized to model water and salt permeabilities (A and B), and the structure parameter (South). The observed flux variations at different combinations of concentration and temperature have been ascribed to skin properties, i.e., changes in A and B of each membrane, whereas S was assumed constant within the range of concentrations and temperatures that were tested. Simplified equations for the variation in A and B with temperature and concentration have been developed, which enable A and B to be calculated at any concentration and temperature based on permeabilities determined from osmotic experiments at standard test weather. The equations tin exist used to predict fluxes and specific power production with respect to geographical and seasonal variations in concentration and temperature for river water/seawater pressure-retarded osmosis. The obtained results are also useful for frontwards osmosis processes using seawater every bit draw solution.
Keywords: osmosis, osmotic ability, pressure-retarded osmosis, water permeability, salt permeability, temperature result, concentration effect
i. Introduction
During contempo years, osmotic power from mixing river water and seawater has gained increasing attending in the field of renewable energy research [1,2]. The latest estimate of worldwide power potential was reported to 1700 TWh per year [3].
The principle of osmotic power is to employ the mixing energy when two solutions with different salinities are mixed. Pressure-retarded osmosis is one of the technologies that may be used to harvest this energy [2,4]. For typical weather, the reversible mixing energy when 1 kg of freshwater is mixed with an excess of seawater is ii.7 kJ [4]. Since a pressure retarded osmosis (PRO) ability establish typically volition exist operated at half the osmotic pressure difference between the two solutions, the maximum mixing energy that can be extracted will exist express to 50% of the reversible mixing energy. However, frictional losses in, e.thousand., membrane modules, piping and pumps will reduce the exploitable internet free energy, and it will be realistic to exploit only approximately 40% of the reversible mixing energy [5].
Local atmospheric condition such as seawater concentration and h2o temperature will affect the power that tin be extracted per unit expanse of membrane, i.due east., the specific power. In addition, the seasonal variation of concentration and temperature volition affect power product and must be addressed when designing a PRO ability plant. In this respect, information technology will exist essential to gauge the water and salt fluxes through the membrane every bit functions of temperature and concentration in society to enable the prediction of ability production at relevant conditions.
Other processes exploiting osmotic free energy take recently been proposed, i.e., osmotic energy recovery to reduce energy consumption for the desalination of seawater by opposite osmosis [vi,7,8,ix,10,11,12,thirteen]. In add-on, several treatment processes exploiting the osmotic driving force have been proposed [xiv,xv,16,17]. All concepts volition depend on depict concentration and temperature.
Performance data published in the literature are typically measured using iii.v wt % NaCl and/or i M NaCl, e.grand., Han et al. [eighteen]. Still, data spanning concentrations in the range of 20–35 chiliad/Fifty that will exist relevant for conditions inside a membrane element for river h2o/seawater PRO and osmotic free energy recovery or treatment processes using forrad osmosis (FO) with seawater as draw solution are, to our cognition, missing. Further, most of the data presented in the literature are given at 20 °C, 25 °C, or at the less specific condition "room temperature".
A few papers accept addressed the outcome of temperature on osmotic functioning. Zhao and Zou [xix] studied the consequence of temperature on membrane performance in FO desalination and their findings confirmed that the flux increased with increasing temperature. A Cellulose Triacetate membrane (CTA) from Hydration Technology Innovations (HTI) operated in FO style was used in the experiments with a 1.5 Thousand Na2And theniv depict solution and brackish water as feed solution. The h2o flux was found to increase by 3.1% per degree Celsius when the temperature was increased from 25 °C to 35 °C, and past 1.2% per degree Celsius when the temperature was increased from 35 °C to 45 °C, indicating a non-linear result.
She et al. [20] as well used a CTA membrane from HTI and measured the h2o flux at 25 °C and 35 °C at various pressures, applying a 1 M NaCl describe solution and a 1 mM NaCl feed solution. At isobaric condition, the flux increased approximately 4.1% per temperature caste increase, whereas the specific power increased past 3.4% per degree when the temperature was increased from 25 °C to 35 °C. They related the temperature outcome to increased water and common salt permeabilities and noted that the ratio betwixt water and salt permeabilities was close to constant. They also ended that increased h2o permeability was the dominating factor to improved h2o flux. Further, the increment in diffusivity at elevated temperatures was claimed to reduce the internal concentration polarization in membrane support, which also contributed to the increased water flux.
Kim and Elimelech [21] studied the effect of temperature on the h2o flux past also using a CTA membrane from HTI. They measured the isobaric water flux at 20 °C and thirty °C with a 0.v M NaCl feed solution and 1 Yard, ane.5 One thousand, or 2 M NaCl draw solutions, respectively. The observed increment in h2o flux for the different draw concentrations was 7.1%, 3.9%, and 5.0% per degree increase in temperature, respectively. They related the increased h2o flux to increased water permeability and claimed that the simultaneous increase that was expected in salt permeability was not important for the efficiency in PRO. A comparison of the measured fluxes at different concentrations at abiding temperature resulted in an increase in the h2o flux of approximately 3% per g/L increment in concentration difference across the membrane.
Touati et al. [22,23] also studied the effect of temperature and concentration on the h2o flux using a CTA membrane from HTI and a membrane from the Fraunhofer IGB Institute. Both the water and salt permeabilities were fitted to Arrhenius equations, giving adept correlation to the observed temperature dependency. An increment of 0.33 W/g2 was reported for the CTA membrane when the temperature inverse from 25 °C to 60 °C, equal to approximately 1% increase in specific power per degree increase in temperature.
The work presented in the electric current paper has focused on the effects of concentration and temperature on water and salt fluxes in FO/PRO. The water and salt fluxes take been measured in both FO and PRO mode at isobaric atmospheric condition for five membranes at dissimilar combinations of concentration and temperature. The main objective was to quantify the impact of concentration and temperature on water and common salt fluxes, respectively, and to model these effects in terms of variation in water and common salt permeabilities. As a result, simplified equations that tin be used to predict the touch on of variations in concentration and temperature on water and salt permeabilities for a given membrane accept been developed. Utilization of these equations presupposes that the water and salt permeability of the membrane is obtained for one unmarried combination of concentration and temperature, e.g., nether standard examination conditions. Subsequently, water and table salt fluxes, besides as PRO performance, can exist calculated for whatsoever procedure condition using an appropriate membrane transport model.
2. Theory
2.ane. Ship Model
In PRO, h2o will be transported against a pressure gradient due to the difference in osmotic force per unit area between the 2 water sources flowing on each side of the membrane. The net volume increase on the loftier saline side, which is operated at elevated pressure, tin can be converted into power in a turbine. Effigy 1 illustrates the concentration profile over a Thin Film Composite (TFC) membrane in PRO [24], including concentration boundary layers on either side of the membrane, and indicates the management of salt and water fluxes.
Concentration profile over a Sparse Film Composite (TFC) membrane and the boundary layers in PRO, modified from [24].
The produced power, P, equals the amount of h2o transported through the membrane multiplied with the hydraulic pressure level departure, i.e.,
where Jwestward is the h2o flux and Δp is the pressure divergence across the membrane. Since the water flux in PRO will decrease as the pressure difference increases, the produced specific ability will have a theoretical optimum at half the osmotic pressure difference. Unlike model frameworks describing the transport of salt and water through the membrane have been adult by several authors [4,25,26,27,28,29]. For the piece of work presented in the electric current paper, a send model developed past Thorsen and Holt [4], which calculates the h2o and salt send in four transport zones, i.e., the boundary layer on both membrane surfaces, within the porous support structure, and across the membrane skin, was applied. The model will be briefly presented in the following section, whereas a more detailed deduction, including the solving of respective mass balances for the unlike transport zones is given in the Supplementary Materials.
The mass transport through the membrane skin can be described past the flux equations
and
J s = −BΔc s k i n = −B(c s m −c p )
(3)
where Js is the salt flux, A is the h2o permeability, B is the table salt permeability, and Δπpeel is the osmotic pressure that corresponds to the concentration difference of salt over the membrane skin. It tin can exist shown that the concentration difference over the membrane pare tin can exist expressed as
(4)
where the structure parameter South, which represents the effective diffusion length through the support membrane, has been introduced (cf. Equation (S5)). This equation relates the salt concentration difference over the membrane skin to both the majority concentration and the boundary layer thickness on both sides of the membrane, also equally the characteristic membrane parameters. Hence, the model describing the osmotic mass transport through a PRO membrane includes five parameters, where A, B and S describe the membrane characteristics, and ds and df , which describe the thickness of the respective boundary layers, correspond the period regimes on each side of the membrane.
2.2. Impact of Temperature and Concentration on PRO Performance
It tin can exist seen from the Van't Hoff relationship in Equation (5) that both the temperature and concentration will determine the osmotic force per unit area, and thus the PRO performance.
R is the platonic gas constant, T is the accented temperature, and i reflects the deviation from the ideal solution. The latter has been determined to one.nine for NaCl by using linear regression and literature data for the osmotic pressure [30].
In add-on to the impact of temperature and concentration that is given past the osmotic pressure term, membrane parameters A and B can likewise exist influenced by variation in temperature and concentration. The working hypothesis of this paper is based on the assumption that the temperature and concentration relationship for the h2o and salt permeabilities volition follow the same relationship equally diffusion coefficients in liquids [31]. Following this illustration, the water and salt permeabilities tin can exist expressed past:
and
A 0 and B 0 correspond to water and salt permeabilities measured at reference conditions T 0 and c 0, respectively. The β coefficients reflect the temperature and concentration dependencies of the water and table salt permeabilities that are non related to the suggested temperature and water viscosity relationship. These coefficients must be determined experimentally. A more detailed discussion of the impact of temperature and concentration on the permeabilities are given in the Supplementary Materials.
iii. Materials and Methods
3.one. Apparatus
Two cross-flow cells with effective membrane areas of 6.1 cm2 (ane.1 cm × 5.v cm) and 9.5 cm2 (1.1 cm × 8.6 cm), respectively, have been used in this written report. Figure 2 shows a simplified period diagram for the two cross-menstruum apparatuses. Water was fed to each side of the membrane by using dual-piston pumps with displacement volumes of approximately 10 mL/stroke. The feed reservoirs were placed on balances, and the discharge from the membrane cell was recycled back to the reservoirs.
Simplified catamenia diagram for the two cantankerous period apparatuses used in the study.
The membrane cells and cooling/heating coils upstream of the membrane cells were immersed in a water bath to command the temperature during the experiments. The force per unit area on both sides of the membrane, the temperature in the water bath, and the readings of the balances were monitored and logged in a data file at regular intervals.
3.two. Standard Examination Protocol
Equally prescribed by the manufacturer, three of the membranes were immersed in 50 vol % methanol for 60 s and after immersed in rinsed water for a minimum of 60 min prior to assembly in the membrane cells. The membranes that were not preconditioned with methanol were immersed in distilled water prior to assembly in the membrane cells.
Two pieces of a permeate spacer of 0.v mm thickness were practical in the freshwater channel comprising a channel thickness of ane.0 mm, and a diamond spacer of 0.7 mm thickness was applied in the saltwater aqueduct.
Afterward assembly, a hydraulic h2o permeability test was performed using degassed, rinsed water at 20 °C, and equal flow rates on both sides of the membrane (threescore mL/h). The water flux was measured for minimum 60 min at 5–seven unlike pressures, ranging from 1–10 bar.
After the hydraulic water permeability test, ii independent osmotic flow experiments were performed at twenty °C and isobaric conditions, 1 in PRO way, i.e., depict solution confronting the membrane pare, and ane in FO fashion, i.e., draw solution against the membrane back up. The saltwater was made from NaCl (p.a.) and degassed and rinsed water. Degassed and rinsed h2o was besides used every bit feed water on the low concentration side. Equal catamenia rates were used for both pumps (300 mL/h). The water flux was adamant based on weight changes in both reservoirs. The reported water fluxes were estimated for the initial phase of the experiments, i.eastward., the beginning ii hours, before the dilution of saltwater and common salt aggregating in the freshwater influenced the experiment. Common salt fluxes were determined by potentiometric analyses of Cl− ions in the freshwater reservoir at the stop of the experiments.
iii.3. Membranes
Five diverse types of noncommercial proprietary FO/PRO membranes were used in the report. Ane of the tested membranes was an asymmetric CTA membrane, whereas the four remaining membranes were TFC membranes referred to every bit TFC1–TFC4. H2o permeability was in the 2 × 10−12–three × ten−eleven m/s/Pa range, salt permeability was in the ix × 10−eight–2 × 10−6 yard/s range, whereas the construction parameter was in the 0.two–2.2 mm range.
3.4. Experimental Blueprint
To systematically study the impact of concentration and temperature on osmotic flux, several experiments were performed at unlike temperatures and concentrations, varying effectually the standard examination conditions, which are 20 °C and 28 g/L NaCl. Concentration and temperature accept been varied according to ii alternative designs, (1) a Key Composite Blueprint (CCD); or (two) a face-centered Central Composite Design (confront-centered CCD) which are described in more detail in the Supplementary Materials. Two osmotic flow experiments were performed for each combination of temperature and concentration, one in FO mode and one in PRO mode. The two osmotic flow experiments performed for each exam status resulted in four fluxes, two salt fluxes and two water fluxes. In total, 118 water fluxes with 118 respective common salt fluxes were measured.
4. Results and Word
iv.1. Measured Water and Salt Fluxes
Figure 3 shows measured water and salt fluxes as a function of temperature for the CTA membrane. As can be observed, the water and table salt fluxes measured in FO mode are lower compared to the fluxes measured in PRO mode at the same conditions, which can exist explained by college internal concentration polarization in membrane support when the draw solution faces the back up side of the membrane. This is in accordance with observations by other researchers [4,32,33].
H2o (a) and salt (b) fluxes measured for the CTA membrane at different concentrations and temperatures according to a CCD. The figures indicated for each data point (PRO mode only) stand for to the applied describe concentration (g/L NaCl) in that experiment.
The overall observed trend indicates that both water and salt fluxes increase with temperature. This was expected and in accordance with other results reported in the literature [twenty,21]. The effect of the concentration is implicitly given in Figure 3, due east.1000., past studying the h2o fluxes measured in PRO mode at xx °C the h2o flux increases every bit the concentration increases from 15 g/L via 28 g/L to 42 chiliad/L common salt. Evaluation of all flux data confirmed a similar relationship, indicating that both common salt flux and water flux were increasing with increasing concentration for all temperatures tested.
4.2. Assay of Variance of Flux Data
To obtain an objective mensurate of the observed effects of temperature and concentration on measured fluxes, the experimental data have been analyzed by using Analysis of Variance (ANOVA). Information technology was found that the main effects of both temperature and concentration were meaning for both water and table salt fluxes (Table S2). This observation applied to all membranes. The interaction effect between temperature and concentration was observed to have minimal affect and was institute to exist significant for merely iii common salt fluxes. In general, the high values of the adapted coefficient of determination, R2(adj) (Table S2), indicate that the resulting regression models for h2o and salt flux give an excellent representation of experimental information sets that were obtained from the osmotic experiments performed with each membrane. In Effigy four, the modelled values for water and salt flux are plotted as function of experimental data, i.due east., measured fluxes. Most data points appear on a line with a gradient of unity, indicating a practiced fit betwixt modelled values and measured information.
Linear regression modelled versus measured water and salt fluxes for (a) CTA; (b) TFC1; (c) TFC2; (d) TFC3 and (due east) TFC4.
4.3. Determination of A, B and South as Function of Concentration and Temperature
Assuming abiding thickness of purlieus layers on membrane surfaces, Equation (iv) will incorporate three unknown parameters, i.e., water permeability, table salt permeability, and construction parameter. Since h2o and common salt fluxes have been measured in both FO and PRO mode, the degrees of freedom are sufficient to enable determination of the three parameters in each test status. The assumption of constant boundary layer thickness is farther discussed in the Supplementary Materials.
The conclusion of characteristic membrane parameters followed a two-stride procedure. Firstly, A, B and S were determined freely for each temperature and concentration combination, and secondly, A and B were remodeled past presuming constant structure parameter equal to the average values determined for the various weather condition in the first step. The resulting water and salt permeabilities for the five membranes when presuming abiding structure parameter are shown in Effigy v and Figure 6, respectively. The permeabilities are shown relative to the values adamant for the center point condition (28 g/50 and 20 °C). Both water and common salt permeabilities were observed to increment with increasing temperature.
Relative changes in water permeability equally function of temperature for (a) CTA; (b) TFC1; (c) TFC2; (d) TFC3 and (due east) TFC4. Concentration dependency is implicitly shown for each temperature past multiple data points representing dissimilar concentrations. Solid lines represent the regression models following Equation (6).
Relative changes in salt permeability as office of temperature for (a) CTA; (b) TFC1; (c) TFC2; (d) TFC3 and (e) TFC4. Concentration dependency is implicitly shown for each temperature by multiple data points representing different concentrations. Solid lines represent the regression models following Equation (7).
iv.iv. Modelling of A and B
The experiments were also modelled by applying Equations (6) and (seven) and subsequently analyzed by ANOVA (Table S4). The predicted values obtained by using the mentioned regression models are shown in Effigy 5 and Figure six every bit solid lines for varying temperature and constant concentration (28 m/Fifty). Evaluation of the calculated R2(adj) (cf. Supplementary Materials) indicates a good fit to the h2o permeability model for four of the membranes, CTA, TFC1, TFC3 and TFC4, whereas TFC2 deviates somewhat from the model. Further, the models for salt permeability for TFC1 and, to some caste, TFC2, were observed to have relatively low Rtwo(adj), indicating a less practiced fit betwixt experimental data and modelled values. The latter was partly ascribed to the incertitude in the salt fluxes.
An interesting finding from the data assay was that the regression coefficients found for the water and salt permeability when using Equations (half-dozen) and (vii), respectively, were shut to unity. Presuming regression coefficients equal to unity, the h2o and common salt permeabilities can exist estimated at whatever concentration and temperature if the three characteristic membrane parameters are determined experimentally for one combination of concentration and temperature, due east.1000., at the condition corresponding to the center point (28 one thousand/L and xx °C). This presumption implies that the water and salt permeabilities can be calculated from the following simplified equations
and
respectively.
To test this assumption, the h2o and salt fluxes were calculated for the different test conditions past applying Equations (viii) and (9) and compared with corresponding experimental data. A 0 and B 0 refer to the standard exam condition (28 grand/Fifty and xx °C). Effigy 7 shows modelled versus measured fluxes for the five different membranes. It tin can be observed that the correlation between measured and modelled fluxes was mostly high, with some departure for the TFC1 membrane.
Modelled water and salt fluxes using water and salt permeabilities from Equations (8) and (9), respectively, every bit part of measured fluxes for (a) CTA; (b) TFC1; (c) TFC2; (d) TFC3 and (e) TFC4.
5. Implications in River Water/Seawater PRO
The changes in water and table salt permeabilities related to variation in operating weather will straight influence the water flux and hence the power product. Local weather condition at different sites and seasonal variations will decide the PRO potential and must be addressed in the planning phase of a PRO power plant. Using the CTA membrane as an case, the membrane parameters determined for each combination of concentration and temperature can be used to simulate the optimal ability production, by optimizing the operating pressure for each condition. The false values of specific power at each combination of concentration and temperature have been used to construct a contour plot for specific power shown in Figure 8. The CTA membrane was determined to have an optimum performance of approximately 2 West/thoutwo at the centre indicate, i.east., 28 1000/Fifty, twenty °C, and a significant dependency to both concentration and temperature was observed.
Profile plot of the specific power (W/m2) as function of concentration and temperature for the CTA membrane. Note that the operating pressure has been optimized for each combination of concentration and temperature.
Norwegian rivers will typically have seasonal variations in temperature between 5 °C to fifteen °C, whereas the temperature in the ocean, which will additionally depend on intake depth, can be assumed to vary, in the range of 5 °C to x °C. Considering a seawater concentration of 3.5%, which is equivalent to 32 g/L NaCl (with respect to osmotic pressure), the expected variation in produced power volition approximately be thirty% within indicated temperature range. This corresponds to a 5% increase per caste Celsius. The ability production of TFC membranes volition vary in a comparable manner with respect to changes in temperature. The modelled impact on ability due to variation in temperature corresponds well with values reported in the literature. Kim and Elimelech [21] have modelled the issue in PRO and estimated a 4.half-dozen% increment per °C, whereas She et al. [20] have measured the increase in specific ability to 3.4% per °C.
6. Conclusions
The effect of concentration and temperature on water and salt fluxes in PRO has been investigated for v dissimilar membranes. The fluxes were measured at unlike combinations of concentration and temperature, and the issue of each variable was quantified. Further, the measured fluxes were used to model the membrane parameters A, B and Southward past fitting the PRO transport model to the measurements. It has been substantiated that the structure parameter tin can be considered independent of variations in concentration and temperature, and consequently that all experimental variation in the conducted FO/PRO experiments can exist ascribed to changes in water and salt permeabilities.
The subsequent data analysis showed that the variation in the water and common salt permeabilities could be modelled with reasonable accuracy by merely applying the dependency betwixt absolute temperature and h2o viscosity. Therefore, the water and salt permeabilities can be estimated at whatsoever concentration and temperature past using two simplified equations that require water and salt permeabilities obtained for one single combination of concentration and temperature as input. In exercise, it will be sufficient to perform two osmotic experiments, one in FO mode and one in PRO manner. The calculated fluxes that were institute by using the simplified equations give a satisfactory correlation to experimental data. Thus, these equations can exist considered a valuable tool for prediction of the touch on of changes in concentration and temperature on the salt and h2o fluxes, and hence, the procedure efficiency.
The simplified equations are valid for saltwater concentrations respective to the 16–46 g/L NaCl range, and temperatures in the range of 6–36 °C, which covers most of the concentration and temperature ranges of involvement utilizing seawater as a describe solution.
Acknowledgments
Nosotros give thanks Statkraft AS for funding the work and for permission to publish the results.
Supplementary Materials
The following are available online at http://www.mdpi.com/2077-0375/8/3/39/s1, Details about the send model development, assumptions and hypothesis of the impact of temperature and concentration on the film thicknesses and membrane parameters, presentation of the design of experiments used in the written report, supplementary comments to the analysis of variance of the results, visualization of examination conditions (Effigy S1), measured h2o and salt fluxes (Figures S2–S5), relative changes in flick thickness as function of temperature (Figure S6), relative changes in the construction parameter as function of temperature and concentration (Figure S7), summary of type of design and number of experiments for each membrane (Tabular array S1), significant regression coefficients and coefficient of determination of the water and salt fluxes (Table S2), ANOVA of the structure parameter (Table S3), regression coefficients and coefficient of determination of the water and common salt permeabilities (Tabular array S4).
Author Contributions
Conceptualization, T.H., Due west.R.T. and Due east.S.; Methodology, T.H., W.R.T. and E.Southward.; Formal Analysis, E.S. and T.H.; Data Curation, Due east.Due south.; Writing-Original Typhoon Grooming, E.S.; Writing-Review & Editing, T.H. and W.R.T.
Funding
This enquiry was funded by Statkraft AS, Grant No. 45001 03299.
Conflicts of Involvement
The authors declare no disharmonize of interest.
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Articles from Membranes are provided here courtesy of Multidisciplinary Digital Publishing Institute (MDPI)
Source: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6161017/
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