How Does Temperature Affect Osmosis
Membranes (Basel). 2018 Sep; 8(3): 39.
Concentration and Temperature Effects on Water and Salt Permeabilities in Osmosis and Implications in Force per unit area-Retarded Osmosis
Received 2018 Jun 12; Accepted 2018 Jul three.
Abstruse
Osmotic power extracted from the mixing of freshwater with seawater is a renewable energy resource that has gained increasing attention during recent years. The estimated free energy tin can significantly contribute to the product of power worldwide. Still, this power production will exist subject to variation due to both local conditions and seasonal variation. The nowadays newspaper explores the effect of concentration and temperature on water and salt fluxes in osmosis at zilch transmembrane pressure for v different membranes. Further, the measured fluxes have been utilized to model water and salt permeabilities (A and B), and the structure parameter (S). The observed flux variations at different combinations of concentration and temperature have been ascribed to skin properties, i.east., 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 whatsoever concentration and temperature based on permeabilities determined from osmotic experiments at standard test conditions. The equations can be used to predict fluxes and specific ability production with respect to geographical and seasonal variations in concentration and temperature for river h2o/seawater pressure-retarded osmosis. The obtained results are too useful for forward osmosis processes using seawater every bit depict solution.
Keywords: osmosis, osmotic power, pressure-retarded osmosis, water permeability, salt permeability, temperature effect, concentration effect
ane. Introduction
During recent years, osmotic power from mixing river water and seawater has gained increasing attention in the field of renewable energy enquiry [1,2]. The latest estimate of worldwide power potential was reported to 1700 TWh per year [3].
The principle of osmotic power is to apply the mixing energy when 2 solutions with different salinities are mixed. Pressure-retarded osmosis is one of the technologies that may exist used to harvest this energy [2,4]. For typical conditions, the reversible mixing free energy when 1 kg of freshwater is mixed with an excess of seawater is two.seven kJ [4]. Since a pressure retarded osmosis (PRO) ability establish typically volition be operated at half the osmotic force per unit area divergence between the ii solutions, the maximum mixing energy that tin can be extracted will be limited to 50% of the reversible mixing energy. Still, frictional losses in, e.1000., membrane modules, piping and pumps volition reduce the exploitable net free energy, and it will be realistic to exploit but approximately 40% of the reversible mixing energy [5].
Local conditions such as seawater concentration and water temperature volition affect the ability that tin exist extracted per unit of measurement area of membrane, i.e., the specific power. In add-on, the seasonal variation of concentration and temperature will affect power product and must be addressed when designing a PRO ability plant. In this respect, information technology will be essential to estimate the h2o and salt fluxes through the membrane as functions of temperature and concentration in club to enable the prediction of power production at relevant conditions.
Other processes exploiting osmotic energy have recently been proposed, i.e., osmotic energy recovery to reduce energy consumption for the desalination of seawater by reverse osmosis [half dozen,7,eight,9,10,11,12,thirteen]. In addition, several treatment processes exploiting the osmotic driving force have been proposed [14,15,16,17]. All concepts will depend on depict concentration and temperature.
Operation data published in the literature are typically measured using 3.v wt % NaCl and/or 1 M NaCl, e.chiliad., Han et al. [18]. Withal, data spanning concentrations in the range of 20–35 g/L that will be relevant for conditions inside a membrane element for river h2o/seawater PRO and osmotic energy recovery or treatment processes using forward osmosis (FO) with seawater as draw solution are, to our knowledge, missing. Further, most of the data presented in the literature are given at 20 °C, 25 °C, or at the less specific status "room temperature".
A few papers have addressed the consequence of temperature on osmotic functioning. Zhao and Zou [19] studied the result 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 mode was used in the experiments with a one.5 1000 Na2SOfour describe solution and brackish h2o as feed solution. The water flux was plant to increment by three.1% per caste Celsius when the temperature was increased from 25 °C to 35 °C, and by 1.2% per caste Celsius when the temperature was increased from 35 °C to 45 °C, indicating a non-linear effect.
She et al. [20] also used a CTA membrane from HTI and measured the water flux at 25 °C and 35 °C at various pressures, applying a 1 K NaCl draw solution and a 1 mM NaCl feed solution. At isobaric condition, the flux increased approximately 4.1% per temperature degree increment, whereas the specific power increased by 3.four% per degree when the temperature was increased from 25 °C to 35 °C. They related the temperature effect to increased water and salt permeabilities and noted that the ratio between water and salt permeabilities was close to abiding. They also concluded that increased water permeability was the dominating factor to improved h2o flux. Farther, the increase in diffusivity at elevated temperatures was claimed to reduce the internal concentration polarization in membrane back up, which also contributed to the increased water flux.
Kim and Elimelech [21] studied the outcome of temperature on the water flux by too using a CTA membrane from HTI. They measured the isobaric water flux at 20 °C and 30 °C with a 0.v M NaCl feed solution and i M, one.5 M, or 2 M NaCl describe solutions, respectively. The observed increase in water flux for the different draw concentrations was 7.1%, 3.9%, and 5.0% per degree increase in temperature, respectively. They related the increased water flux to increased water permeability and claimed that the simultaneous increment that was expected in common salt permeability was non important for the efficiency in PRO. A comparison of the measured fluxes at different concentrations at constant temperature resulted in an increment in the water flux of approximately iii% per one thousand/L increase in concentration difference across the membrane.
Touati et al. [22,23] also studied the effect of temperature and concentration on the water flux using a CTA membrane from HTI and a membrane from the Fraunhofer IGB Found. Both the h2o and common salt permeabilities were fitted to Arrhenius equations, giving practiced correlation to the observed temperature dependency. An increment of 0.33 W/m2 was reported for the CTA membrane when the temperature changed from 25 °C to sixty °C, equal to approximately 1% increase in specific power per caste increment in temperature.
The work presented in the current paper has focused on the effects of concentration and temperature on h2o and salt fluxes in FO/PRO. The water and salt fluxes have been measured in both FO and PRO mode at isobaric weather for 5 membranes at different combinations of concentration and temperature. The main objective was to quantify the touch on of concentration and temperature on water and common salt fluxes, respectively, and to model these effects in terms of variation in water and salt permeabilities. Equally a upshot, simplified equations that can exist used to predict the impact of variations in concentration and temperature on water and salt permeabilities for a given membrane have been developed. Utilization of these equations presupposes that the water and table salt permeability of the membrane is obtained for one unmarried combination of concentration and temperature, east.chiliad., under standard examination conditions. Subsequently, water and salt fluxes, likewise as PRO performance, can exist calculated for any procedure condition using an appropriate membrane transport model.
two. Theory
2.ane. Transport Model
In PRO, water will be transported against a force per unit area slope due to the departure in osmotic pressure between the ii water sources flowing on each side of the membrane. The net volume increase on the high saline side, which is operated at elevated pressure, can exist converted into power in a turbine. Figure one illustrates the concentration contour 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 Thin Movie Composite (TFC) membrane and the purlieus layers in PRO, modified from [24].
The produced ability, P, equals the corporeality of water transported through the membrane multiplied with the hydraulic pressure difference, i.due east.,
where Jwest is the h2o flux and Δp is the pressure level deviation across the membrane. Since the water flux in PRO volition subtract as the pressure difference increases, the produced specific power will have a theoretical optimum at one-half the osmotic force per unit area difference. Different model frameworks describing the transport of table salt and water through the membrane have been developed by several authors [4,25,26,27,28,29]. For the work presented in the current newspaper, a transport model developed by Thorsen and Holt [4], which calculates the water and common salt transport in four transport zones, i.e., the purlieus layer on both membrane surfaces, inside the porous support structure, and across the membrane peel, was practical. The model will be briefly presented in the post-obit department, whereas a more detailed deduction, including the solving of respective mass balances for the dissimilar transport zones is given in the Supplementary Materials.
The mass transport through the membrane skin can be described by the flux equations
and
J s = −BΔc southward grand i north = −B(c due south thou −c p )
(iii)
where Js is the table salt flux, A is the water permeability, B is the table salt permeability, and Δπpare is the osmotic pressure that corresponds to the concentration difference of salt over the membrane peel. It can be shown that the concentration difference over the membrane skin can be expressed every bit
(iv)
where the construction parameter Due 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, as well as the feature membrane parameters. Hence, the model describing the osmotic mass send through a PRO membrane includes v parameters, where A, B and Southward depict the membrane characteristics, and dsouth and df , which describe the thickness of the respective boundary layers, represent the flow regimes on each side of the membrane.
ii.2. Affect of Temperature and Concentration on PRO Operation
It tin can exist seen from the Van't Hoff relationship in Equation (5) that both the temperature and concentration will determine the osmotic pressure, and thus the PRO performance.
R is the ideal gas constant, T is the absolute temperature, and i reflects the departure from the ideal solution. The latter has been determined to 1.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 by the osmotic pressure term, membrane parameters A and B can besides be influenced by variation in temperature and concentration. The working hypothesis of this paper is based on the assumption that the temperature and concentration human relationship for the water and salt permeabilities will follow the same relationship as diffusion coefficients in liquids [31]. Following this analogy, the water and table salt permeabilities can be expressed by:
and
A 0 and B 0 represent to h2o and table 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 human 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.ane. Apparatus
Two cross-menstruation cells with effective membrane areas of 6.one cm2 (1.1 cm × 5.5 cm) and 9.v cmtwo (i.ane cm × 8.6 cm), respectively, accept been used in this study. Figure 2 shows a simplified menstruum diagram for the ii cross-flow apparatuses. H2o was fed to each side of the membrane past 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 menstruum diagram for the two cantankerous menstruation apparatuses used in the study.
The membrane cells and cooling/heating coils upstream of the membrane cells were immersed in a h2o bath to control the temperature during the experiments. The force per unit area on both sides of the membrane, the temperature in the h2o bath, and the readings of the balances were monitored and logged in a data file at regular intervals.
three.2. Standard Test Protocol
As prescribed by the manufacturer, three of the membranes were immersed in 50 vol % methanol for sixty s and afterward immersed in rinsed h2o for a minimum of 60 min prior to associates in the membrane cells. The membranes that were non preconditioned with methanol were immersed in distilled water prior to assembly in the membrane cells.
Two pieces of a permeate spacer of 0.5 mm thickness were applied in the freshwater aqueduct comprising a channel thickness of 1.0 mm, and a diamond spacer of 0.7 mm thickness was applied in the saltwater aqueduct.
After assembly, a hydraulic water 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 sixty min at 5–vii different pressures, ranging from i–x bar.
Later on the hydraulic water permeability test, two independent osmotic flow experiments were performed at 20 °C and isobaric weather condition, one in PRO mode, i.due east., draw solution against the membrane skin, and one in FO mode, i.e., draw solution against the membrane support. The saltwater was made from NaCl (p.a.) and degassed and rinsed water. Degassed and rinsed water was also used equally feed h2o on the low concentration side. Equal catamenia rates were used for both pumps (300 mL/h). The water flux was determined based on weight changes in both reservoirs. The reported water fluxes were estimated for the initial phase of the experiments, i.due east., the first two hours, earlier the dilution of saltwater and salt accumulation in the freshwater influenced the experiment. Common salt fluxes were determined by potentiometric analyses of Cl− ions in the freshwater reservoir at the end of the experiments.
iii.three. Membranes
Five various types of noncommercial proprietary FO/PRO membranes were used in the study. One of the tested membranes was an disproportionate CTA membrane, whereas the four remaining membranes were TFC membranes referred to as TFC1–TFC4. Water permeability was in the ii × 10−12–iii × ten−eleven thou/due south/Pa range, salt permeability was in the 9 × 10−viii–2 × 10−6 m/s range, whereas the structure parameter was in the 0.2–ii.ii mm range.
3.iv. Experimental Design
To systematically study the impact of concentration and temperature on osmotic flux, several experiments were performed at different temperatures and concentrations, varying around the standard test conditions, which are twenty °C and 28 g/L NaCl. Concentration and temperature have been varied according to two alternative designs, (i) a Central Composite Design (CCD); or (2) a face-centered Central Composite Design (face-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 ane in PRO mode. The ii osmotic menses experiments performed for each test status resulted in four fluxes, two salt fluxes and ii water fluxes. In total, 118 water fluxes with 118 corresponding table salt fluxes were measured.
4. Results and Word
4.1. Measured H2o and Table salt Fluxes
Figure 3 shows measured water and salt fluxes as a role 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 tin exist explained past college internal concentration polarization in membrane support when the describe solution faces the support side of the membrane. This is in accordance with observations by other researchers [four,32,33].

Water (a) and common salt (b) fluxes measured for the CTA membrane at unlike concentrations and temperatures co-ordinate to a CCD. The figures indicated for each data point (PRO way simply) correspond to the applied draw concentration (g/50 NaCl) in that experiment.
The overall observed tendency indicates that both water and salt fluxes increment with temperature. This was expected and in accordance with other results reported in the literature [20,21]. The outcome of the concentration is implicitly given in Effigy 3, e.1000., past studying the h2o fluxes measured in PRO mode at twenty °C the water flux increases as the concentration increases from 15 yard/L via 28 1000/50 to 42 g/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.
iv.2. Analysis 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). It was found that the main furnishings of both temperature and concentration were significant for both water and salt fluxes (Table S2). This observation applied to all membranes. The interaction effect between temperature and concentration was observed to have minimal impact and was found to be significant for just three salt fluxes. In full general, the high values of the adjusted coefficient of determination, R2(adj) (Tabular array S2), betoken that the resulting regression models for h2o and salt flux give an excellent representation of experimental data sets that were obtained from the osmotic experiments performed with each membrane. In Figure four, the modelled values for water and salt flux are plotted as function of experimental data, i.eastward., measured fluxes. Virtually data points appear on a line with a slope of unity, indicating a good fit betwixt modelled values and measured data.

Linear regression modelled versus measured h2o and salt fluxes for (a) CTA; (b) TFC1; (c) TFC2; (d) TFC3 and (due east) TFC4.
iv.three. Determination of A, B and S as Function of Concentration and Temperature
Assuming abiding thickness of boundary layers on membrane surfaces, Equation (4) will incorporate three unknown parameters, i.e., water permeability, salt permeability, and structure parameter. Since water 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 condition. The supposition of constant boundary layer thickness is farther discussed in the Supplementary Materials.
The determination of characteristic membrane parameters followed a two-step process. Firstly, A, B and S were determined freely for each temperature and concentration combination, and secondly, A and B were remodeled by presuming constant structure parameter equal to the average values determined for the diverse conditions in the first step. The resulting water and table salt permeabilities for the 5 membranes when presuming constant structure parameter are shown in Figure 5 and Figure vi, respectively. The permeabilities are shown relative to the values determined for the center signal condition (28 yard/L and 20 °C). Both water and salt permeabilities were observed to increase with increasing temperature.

Relative changes in h2o permeability equally part of temperature for (a) CTA; (b) TFC1; (c) TFC2; (d) TFC3 and (east) TFC4. Concentration dependency is implicitly shown for each temperature past multiple data points representing different concentrations. Solid lines represent the regression models following Equation (half-dozen).

Relative changes in salt permeability equally part of temperature for (a) CTA; (b) TFC1; (c) TFC2; (d) TFC3 and (e) TFC4. Concentration dependency is implicitly shown for each temperature past multiple data points representing unlike concentrations. Solid lines represent the regression models following Equation (7).
iv.4. Modelling of A and B
The experiments were also modelled by applying Equations (six) and (7) and subsequently analyzed by ANOVA (Table S4). The predicted values obtained by using the mentioned regression models are shown in Figure 5 and Figure 6 as solid lines for varying temperature and abiding concentration (28 thousand/L). Evaluation of the calculated Rii(adj) (cf. Supplementary Materials) indicates a proficient fit to the water permeability model for four of the membranes, CTA, TFC1, TFC3 and TFC4, whereas TFC2 deviates somewhat from the model. Further, the models for table salt permeability for TFC1 and, to some degree, TFC2, were observed to take relatively depression R2(adj), indicating a less good fit between experimental data and modelled values. The latter was partly ascribed to the uncertainty in the salt fluxes.
An interesting finding from the data assay was that the regression coefficients plant for the h2o and salt permeability when using Equations (6) and (vii), respectively, were close to unity. Presuming regression coefficients equal to unity, the water and table salt permeabilities can be estimated at any concentration and temperature if the three characteristic membrane parameters are determined experimentally for one combination of concentration and temperature, e.g., at the status corresponding to the centre bespeak (28 1000/Fifty and 20 °C). This presumption implies that the water and common salt permeabilities can be calculated from the following simplified equations
and
respectively.
To exam this supposition, the water and salt fluxes were calculated for the dissimilar test conditions by applying Equations (eight) and (ix) and compared with respective experimental data. A 0 and B 0 refer to the standard test condition (28 one thousand/L and xx °C). Figure 7 shows modelled versus measured fluxes for the 5 different membranes. Information technology tin can exist observed that the correlation between measured and modelled fluxes was generally high, with some divergence for the TFC1 membrane.

Modelled h2o and common salt fluxes using h2o and salt permeabilities from Equations (8) and (9), respectively, as function of measured fluxes for (a) CTA; (b) TFC1; (c) TFC2; (d) TFC3 and (east) TFC4.
five. Implications in River H2o/Seawater PRO
The changes in water and common salt permeabilities related to variation in operating conditions volition directly influence the water flux and hence the power production. Local atmospheric condition at dissimilar sites and seasonal variations volition determine the PRO potential and must be addressed in the planning stage of a PRO ability plant. Using the CTA membrane as an example, the membrane parameters adamant for each combination of concentration and temperature can be used to simulate the optimal power production, by optimizing the operating pressure for each condition. The faux values of specific power at each combination of concentration and temperature accept been used to construct a contour plot for specific ability shown in Figure 8. The CTA membrane was determined to have an optimum operation of approximately 2 W/thoutwo at the heart point, i.due east., 28 grand/L, twenty °C, and a significant dependency to both concentration and temperature was observed.

Contour plot of the specific ability (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 volition typically have seasonal variations in temperature betwixt 5 °C to 15 °C, whereas the temperature in the sea, which volition additionally depend on intake depth, tin be causeless to vary, in the range of 5 °C to 10 °C. Considering a seawater concentration of 3.five%, which is equivalent to 32 yard/Fifty NaCl (with respect to osmotic pressure), the expected variation in produced power volition approximately exist 30% within indicated temperature range. This corresponds to a 5% increase per degree Celsius. The ability production of TFC membranes will vary in a comparable style with respect to changes in temperature. The modelled touch on on ability due to variation in temperature corresponds well with values reported in the literature. Kim and Elimelech [21] take modelled the upshot in PRO and estimated a 4.half-dozen% increase per °C, whereas She et al. [20] have measured the increase in specific power to three.4% per °C.
vi. Conclusions
The effect of concentration and temperature on h2o and salt fluxes in PRO has been investigated for five different membranes. The fluxes were measured at different combinations of concentration and temperature, and the effect of each variable was quantified. Further, the measured fluxes were used to model the membrane parameters A, B and S by fitting the PRO transport model to the measurements. Information technology has been substantiated that the structure parameter can be considered independent of variations in concentration and temperature, and consequently that all experimental variation in the conducted FO/PRO experiments tin can exist ascribed to changes in h2o and salt permeabilities.
The subsequent information assay showed that the variation in the water and common salt permeabilities could be modelled with reasonable accuracy by only applying the dependency between accented temperature and water viscosity. Therefore, the water and common salt permeabilities tin be estimated at any concentration and temperature by using two simplified equations that require water and table salt permeabilities obtained for one single combination of concentration and temperature every bit input. In practice, it will be sufficient to perform two osmotic experiments, one in FO manner and i in PRO mode. The calculated fluxes that were institute past using the simplified equations give a satisfactory correlation to experimental information. Thus, these equations can be considered a valuable tool for prediction of the impact of changes in concentration and temperature on the salt and water fluxes, and hence, the process efficiency.
The simplified equations are valid for saltwater concentrations corresponding 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 equally a describe solution.
Acknowledgments
We thank Statkraft Every bit 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/three/39/s1, Details virtually the transport model development, assumptions and hypothesis of the impact of temperature and concentration on the film thicknesses and membrane parameters, presentation of the pattern of experiments used in the study, supplementary comments to the analysis of variance of the results, visualization of examination conditions (Figure S1), measured water and salt fluxes (Figures S2–S5), relative changes in film thickness as part of temperature (Figure S6), relative changes in the structure parameter every bit office of temperature and concentration (Effigy S7), summary of type of design and number of experiments for each membrane (Table S1), pregnant regression coefficients and coefficient of decision of the water and salt fluxes (Tabular array S2), ANOVA of the construction parameter (Table S3), regression coefficients and coefficient of determination of the h2o and salt permeabilities (Table S4).
Writer Contributions
Conceptualization, T.H., W.R.T. and E.S.; Methodology, T.H., Westward.R.T. and E.S.; Formal Assay, E.S. and T.H.; Data Curation, E.S.; Writing-Original Draft 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 conflict of interest.
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How Does Temperature Affect Osmosis,
Source: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6161017/
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