- Email: [email protected]
A thermodynamic benchmark for assessing an emergency drinking water device based on forward osmosis
Desalination 227 (2008) 34–45
A thermodynamic benchmark for assessing an emergency drinking water device based on forward osmosis M. Wallace, Z. Cui, N.P. Hankins Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK Tel. +44 (1865) 273027; email: [email protected] Received 26 March 2007; Accepted 24 April 2007
Abstract Following the creation of the first reverse osmosis (RO) membrane in the 1960s, the technique has been widely used for the purposes of both small scale and municipal seawater desalination. Forward osmosis (FO) is now also emerging as a possible contender, with the potential for much lower energy consumption. In this study, we have developed a thermodynamic benchmark for use in assessing the suitability of a potable water system for purifying small amounts of brackish water in emergency situations. The light, portable and re-usable purification system is driven by FO. A pouch is filled with draw solution and immersed in brackish water; the pouch incorporates a traditional RO membrane. The ‘draw solution’ contains digestible salts and/or sugars to provide an osmotic pressure difference across the membrane, thus drawing in purified water across the membrane. Three such draw solutions were produced and tested, allowing the osmotic potential of the solution to be determined over a succession of dilutions. The results could be fitted with a power law function. In order to take account of the solution non-ideality and the non-linearity of flux rates, a thermodynamic relationship was used in conjunction with a membrane transport model to develop a benchmark which describes the ideal behaviour of a FO water system. This benchmark, in conjunction with the power law function, showed that such a system could be used in an emergency to provide safe, potable water in a reasonable time interval and without the need for a power source. The study has also suggested the possibility of a continuous water purification system based upon this principle, and has drawn attention to the benefits of novel draw solutes in such a system. Keywords: Forward osmosis; Membrane-based potable water system; Desalination; Thermodynamic model
*Corresponding author. Presented at the First Oxford and Nottingham Water and Membranes Research Event, 2–4 July 2006, Oxford, UK. 0011-9164/08/$– See front matter © 2008 Published by Elsevier B.V. doi:10.1016/j.desal.2007.04.097
M. Wallace et al. / Desalination 227 (2008) 34–45
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1. Introduction “Access to safe water is a fundamental human need and, therefore, a basic human right. Contaminated water jeopardizes both the physical and social health of all people. It is an affront to human dignity” (Kofi Annan, United Nations Secretary-General). Many situations exist where a plentiful supply of water exists, but is unsafe for human consumption. This is a large problem in many areas of the world, particularly those which are prone to natural disaster. Whenever such a disaster occurs water is very often contaminated with both organic and inorganic pollutants. Damage to local infrastructure can lead to sanitation problems, which further pollutes the water with faecal pathogens. In these situations, there is a requirement for a clean and easily administrated source of water, which is able to sustain life until a more permanent solution can be installed. Another group of people who are reliant on surface water are wilderness travellers or the military. Since the safety of surface water cannot be reliably estimated on the basis of appearance, smell and taste [1], there is a requirement for a safe source of potable water for these groups to use in emergency situations. The solution should be robust and capable of use in most situations where surface water is contaminated. This paper will describe the development of a thermodynamic benchmark for use in assessing the suitability of a membrane based potable water system for purifying small amounts of brackish water in emergency situations. See the Symbols section for definitions used throughout the paper.
2. Design basis 2.1. Principle of osmotic pressure Osmotic pressure can be defined as a pressure acting to restore the chemical potential of a
Fig. 1. Physical representation of osmotic pressure.
system [2] and can be physically described by considering a pure solvent separated from a solution by a semi-permeable membrane (Fig. 1). If the membrane is permeable to the solvent molecules only, then the net effect will be a flow of solvent molecules from left to right. If a pressure is applied to the solution, the flow can be counteracted; the pressure required to restore equilibrium is known as the osmotic pressure of the solution [3] and is denoted as π; it can be calculated from the concentration of the solution using van’t Hoff’s formula (1) [4]:
π = c.R.T
(1)
It can be noted from this expression that osmotic pressure is a colligative property, dependent only on the number of solute molecules, rather than on their nature. Other colligative properties include boiling point elevation and freezing point depression; they are all related to the lowering of vapour pressure when a solution is formed. Expression (1) alone is not sufficient to describe the osmotic pressure of a solution for two reasons: C If the solute is a salt then its ions will dissociate when it dissolves into solution. This results in the total number of molecules increasing, and since osmotic pressure is colli-
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M. Wallace et al. / Desalination 227 (2008) 34–45
gative, this results in a higher osmotic pressure than would be expected. The ‘dissociation number’ (n) is therefore required to correct this. C The osmotic coefficient, analogous to the activity coefficient, must also be used to correct for non-ideal behaviour of the solution. Osmotic and activity coefficients can be related by the Gibbs–Duhem equation. [6]. Therefore it is necessary to define osmolality [Eq. (2)], which can be substituted into van’t Hoff’s formula [Eq. (1)] to give an accurate prediction of the true osmotic pressure of a solution:
M = C.φ.n
(2)
Π = M .R.T
(3)
A difference of osmotic pressure across a semipermeable membrane forms the basis of an understanding of both forward and reverse osmosis. 2.2. Forward osmosis Forward osmosis (FO) is essential for water transport across biological cell membranes in all living organisms [2] and is the process by which an osmotic pressure difference causes a solvent to be drawn through a membrane. This is useful for altering the concentration of dissolved solutes in a solution, or for separating a solvent from unwanted solutes. When this occurs, there is a trade-off between the solutes of the feed and draw solutions so it is not possible to produce a pure solvent using FO. 2.3. Reverse osmosis On the other hand, reverse osmosis (RO) is used to produce pure solvents, primarily in the desalination of seawater, by applying high pressure to a solution and causing it to pass
Table 1 Characteristics of different membrane processes Membrane process
Nominal pore size, Å
Average permeability, L.m!2.H!1.bar!1
Microfiltration (MF) 1000–100,000 500 Ultra Filtration (UF) 10–1000 150 Reverse osmosis (RO) 2–5 5–10
through a solvent-permeable membrane. This results in the retention of the solute on the solution side of the membrane. 2.4. Membranes “Membrane technology has come of age”, stated Lonsdale in 1981 [7]. Yet over the past 26 years since his paper, ‘The Growth of Membrane Technology’, there has been a massive increase in the use of semi-permeable membranes in municipal water treatment and medical applications. Three well developed membrane separation processes currently exist, each providing for a different range of molecular sieving [8] as detailed in Table 1. Microfiltration membranes are used in processes where suspended particles must be removed from a solvent [8] but dissolved solids are permitted in the permeate [7]. An example is the bacteriological testing of water. Ultrafiltration membranes are used where macromolecules and colloids must be removed from a solute [8]. Salts and heavy metals will permeate readily. Reverse osmosis membranes have been developed primarily for use on desalination plants to allow the transport of water (~2Å dia.) whilst rejecting up to 99% of salt ions at high operating pressures. In general, they will allow the transport of molecules between approx 2Å and 5Å in diameter [8].
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M. Wallace et al. / Desalination 227 (2008) 34–45
2.5. A Membrane based device
3. Draw solution design
For the purpose of designing an emergency device, a ‘draw solution’ of salts and sugars can be used to provide the driving force to overcome membrane resistance and ‘drive’ brackish water through a RO membrane by the process of FO. The use of a RO membrane has the advantage that it will retain all of the ‘draw solution’ on the potable side of the membrane and produce a drinkable solution of clean water and solute. The disadvantage of using a RO membrane is that a much higher concentration of draw solution will be required than if a MF or UF membrane were used, due to its low permeability. The design objectives for the device are therefore that it should; be simple to operate, be temporary and portable (therefore light and small), be cheap and reusable, require no external power source, purify and clarify contaminated surface water (not seawater), produce potable water with adequate odour and taste improvement, and produce an adequate volume of potable water in a reasonable time interval.
In order to produce a FO membrane design, it was necessary to find a suitable mixture of non toxic salts and/or sugars for use as the draw solution. This must be safe for human consumption whilst generating a suitably large osmotic pressure difference across the membrane. Some preliminary investigations into the effectiveness of a variety of solutes used on their own showed that salts such as CaCl2, MgCl2 and NaCl can produce large differences in osmotic pressure whilst sucrose and glucose were not as effective. To ensure safety for consumption, both the World Health Organisation (WHO) 1993 Drinking Water Recommendation and the United Kingdom (UK) water regulations were consulted [9] to determine the maximum tolerable concentrations of salt ions in drinking water. The most conservative values are listed in Table 3. We therefore calculated that the maximum concentration of each salt would be (as determined from the data in Table 5): — 0.00355 M C CaCl2 — 0.00210 M C MgCl2 C NaCl — 0.00710 M
2.6. Contaminants In order to produce potable water from brackish water, it is necessary to remove a variety of contaminants. Table 2 details the classes and their molecular sizes. Table 2 Types of contaminant Contaminant type
Size, Å
Examples
Bacteria [1]
~5,000
Viruses [1] Protozoa [1]
~300 ~50,000
Parasites [1]
~200,000
Cholera, E. coli, Salmonella Polio, hepatitis Cryptosporidium, Giardia Intestinal worms
To determine a tolerable concentration of sugar, it was necessary to investigate the physiological effect of ingesting carbohydrate in solution. Blood has an osmolality of 280–330 mOsm. kg!1, which is generated by sodium, protein and glucose in the bloodstream. Isotonic drinks are those which have an osmolality in the same range as that of blood [10]. Isotonic drinks have Table 3 Maximum ion concentration in drinking water Cl! Na+ Mg2+ Ca2+ a
250 mg.l!1 200 mg.l!1 50 mg.l!1 250 mg.l!1
WHO recommended maximum. UK regulation maximum.
b
0.0071 Ma 0.0087 Ma 0.0021 Mb 0.0062 Mb
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M. Wallace et al. / Desalination 227 (2008) 34–45
Table 4 Solubility of sugars in water at 25EC
Sucrose Glucose
Solubility (g/100ml)
Maximum possible concentration, M
213.6 [11] 91 [12]
5.88 5.05
carbohydrate in the form of sugar at concentrations of 6–8%. This corresponds to 0.09 M of sucrose (C12H24O11) and 0.18 M of glucose (C6H12O6) at 8%. Another consideration is the solubility of both sugars in water at 25°C (Table 4). Using these data two mixtures were designed, which could maximise osmolality whilst minimising physiological effect. C Mixture one: 2 M sucrose + 0.1 M calcium chloride C Mixture two: 1 M sucrose + 1 M glucose + 0.1 M calcium chloride Due to non-linear behaviour, there is no method which can be used to calculate the osmolality of a solution which is composed of a mixture of solutes; therefore it was necessary to experimentally determine these values by making a high concentration solution from the mixture and measuring its osmolality. Repeated dilution and measurement provided sufficient results that a power law could be fitted which describes the variation of osmolality of the solution.
4. Experimental determination of osmolality 4.1. Materials The following materials were used: C Sucrose: Cane sugar, Sigma-Aldrich S-5016, M.W. 342.3. C Glucose: Sigma Ultra Anhydrous, 99.5% purity, Sigma-Aldrich G-7528, M.W. 180.2g/ mole
C Calcium chloride: Sigma Ultra Dihydrate, 99% min purity, Sigma-Aldrich C-5080 M.W. 147.01 C Deionised water (produced in a Millipore deionising unit) We used a Mettler Toledo AB54-5 balance to measure out the solutes and the osmolality of each solution was measured using an Osmomat 030 Freezing Point Osmometer (Gonotec GmbH). The osmometer determines the total osmolality of an aqueous solution by performing a comparative measurement of the freezing point of pure water and of that of the solution being tested: “Water has a freezing point of 0EC, a solution with a salt concentration of 1 Osmol/kg has a freezing point of !1.858E” [13]. This thermodynamic basis provides an accurate value for osmolality, since both freezing point depression and osmotic pressure are colligative properties [3], meaning that they can be calculated from one another without any regard for the nature of the solute. 4.2. Osmomat 030 measurement principle “The sample solution is cooled using a peltier element cooling system. At the same time the temperature of the sample is monitored electronically. When the sample reaches a defined temperature below the freezing point of pure water the crystallisation of the solution is automatically initiated. “A stainless steel needle is held well below 0EC such that water vapour in the air condensing on its tip freezes as tiny ice crystals; the needle tip, covered in tiny ice crystals, is stabbed into the super-cooled solution. Thus, initiation of crystallisation occurs by inoculation of the solution with ice crystals. Immediately after this, the temperature of the solution begins to rise spontaneously as heat of crystallisation is released during the freezing process. The rise in temperature is measured with an accuracy of 1.858×10E!3 EC” [13].
M. Wallace et al. / Desalination 227 (2008) 34–45
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Table 5 Determination of maximum salt concentration for draw solution Salt concentration
Ion concentrations
Ca2+ (Cl!)2 0.00620 M 0.00355 M Mg2+(Cl!)2 0.00210 M 0.00355 M Na+Cl! 0.00870 M 0.00710 M
Ca2+ 0.00620 M 0.00355 M Mg2+ 0.00210 M 0.00355 M Na+ 0.00870 M 0.00710 M
Cl! 0.01240 M 0.00710 M Cl! 0.00420 M 0.00710 M Cl! 0.00870 M 0.00710 M
4.3. Procedure For each mixture, the first step of the procedure was to make up three 20 ml samples of the draw solution. From one of the samples, 0.1 ml was decanted (using Finnpipette®) into ten separate containers. Each container was then diluted with de-ionised water (×2, ×5, ×10, ×15, ×20 … ×50) and mixed well. We then extracted and tested 0.1 ml of each in the osmometer. This procedure was repeated for each of the other two samples. The solutions used were composed of the following: C Mixture one: 14.4 g sucrose + 0.222 g calcium chloride (+20 ml de-ionised water) C Mixture two: 7.2 g sucrose + 3.604 g glucose + 0.222 g calcium chloride (+20 ml de-ionised water) It was also decided to test a commercially available salt/sugar mixture so a third mixture was made from a ‘dioralyte’ rehydration sachet (dioralyte is indicated for the replacement of essential body water and salts in the treatment of acute diarrhoea in infants, children and adults).dioralyte: 0.47 g NaCl + 0.30 g KCl + 3.56 g glucose + 0.53 g disodium hydrogen citrate + silicon dioxide + saccharin sodium + black currant flavour (+20 ml de-ionised water).
Comments Chlorine ion concentration is above limit Maximum allowable salt concentration Maximum allowable salt concentration Magnesium ion concentration is above limit Chlorine ion concentration is above limit Maximum allowable salt concentration
The results follow: 1. Mixture one: The osmometer was unable to obtain a value for the undiluted sample as the sample was too viscous, so an additional measurement at ×1.5 dilution was taken and used to approximate the value for ×1. This was necessary to allow a good fit of a power law function to the data. Fig. 2 shows the plotted results with a power law (y = 1.795×–1.0858) fitted to describe the change in osmolality of the solution as it is diluted. 2. Mixture two: In this case it was possible to obtain measurements for the ×1 dilution, but the data for one of the three original samples had to be discarded prior to further analysis due to significant difference between it and the other samples. Fig. 3 shows the plotted results, with a power law (y = 1.6298×!1.1177) fitted to the results. 3. Since this mixture was tested only for comparative purposes, only one sample was tested. Fig. 4 shows the plotted results with a power law (y = 2.467×!1.0292) fitted to the results.
5. Development of benchmark 5.1. Model assumptions To develop the benchmark it is helpful to consider the system being modelled as two
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M. Wallace et al. / Desalination 227 (2008) 34–45
Fig. 2. Mixture one: dilution vs. osmolality (and power law function).
Fig. 3. Mixture two: dilution vs osmolality (and power law function).
M. Wallace et al. / Desalination 227 (2008) 34–45
41
Fig. 4. Mixture three: dilution vs osmolality (and power law function).
5.2. Modelling The modelling of an RO ‘pouch’ is relatively straightforward, since (at low pressure) no salt ions will be lost through the membrane so a model can be developed based upon this principle. Therefore, a simple mass balance yields the membrane flux relationship (4): Fig. 5. Mechanical representation of system.
volumes of water separated by a membrane, as show in Fig. 5 [14]. The volume of water marked (1) is the brackish water and volume (2) is potable water. It can be assumed that the RO membrane is impermeable to all solute; therefore, js = 0. The device will be used in a large source of water; therefore V1 = 4 and Δp is only significant when the pouch is full.
J v = Lp . ( Δp − ΔΠ )
(4)
Combining this result with Eq. (3), it can be shown that it is possible to obtain the result [15]:
J v = − Lp . R.T . ( M 1 − M 2 )
(5)
However, flux Jv can also be expressed as
Jv =
d Vw A.d t
(6)
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M. Wallace et al. / Desalination 227 (2008) 34–45
Therefore,
d Vw = − Lp .R. A.T . ( M se − M si ) .d t
Table 6 Variables used for simulation
(7)
where
⎛V i ⎞ M se = M si ⎜ w ⎟ ⎝ Vw ⎠
(8)
i.e., a function of the dilution, and M = C.φ.n as previously in Eq. (2). 5.3. Simulation The simulation was then based upon a pouch, constructed of an RO membrane with an assumed hydraulic permeability of 5 L.m!2.hour!1.atm!1, of dimensions 20×10×2 cm and a maximum volume of 400 ml. A Microsoft Excel spreadsheet was then set up using expressions (6), (7) and each of the experimentally determined power laws. Table 6 details the variables that were required.
Fig. 6. Mixture one simulation: pouch volume vs time.
Variables Surface area of pouch (A), m2 Maximum pouch volume (Vmax), l Hydraulic permeability (Lp), L.m2h.l.atm!1 Initial external molarity (Mes0), Osmols.kg H2O-l Initial pouch volume (Vw0), l Time increment (dt), s Calculated values Hydraulic permeability (Lp), L.m2h.l.atm!1 Initial internal molarity (Mis0) Osmols.kg H2O-l
0.052 0.4 5 0 0.01 30 0.001389 1.795000
The spreadsheet calculates the dilution within the pouch at each increment of time (= t + dt), and uses this value to determine the molality within the pouch from the power law. Expression (7) is then used to calculate the change in volume over that time increment, which is added to a running total volume.
M. Wallace et al. / Desalination 227 (2008) 34–45
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Fig. 7. Mixture two simulation: pouch volume vs time.
Fig. 8. Mixture three simulation: pouch volume vs time.
Plots of volume vs time allow for easy comparison of the effectiveness of a variety of solutes used as the draw solution. Fig. 6 shows that Mixture 1 could fill the pouch in 55 mins. Fig. 7
shows that Mixture 2 could fill the pouch in 64.5 mins. Fig. 8 shows that dioralyte could fill the pouch in 67.5 mins.
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M. Wallace et al. / Desalination 227 (2008) 34–45
6. Conclusions and future work This benchmark has shown, from a thermodynamic basis, that it would be possible to construct a potable water system capable of purifying small amounts of brackish water in emergency situations. Such a system could operate without access to any power supply at the point of use. Use of a RO membrane would significantly reduce harmful contaminants with the exception of some heavy metals. It would be effective in clarifying brackish water and would provide significant taste and odour improvement. The benchmark has also shown that such a device could be fast acting, providing a reasonable quantity of potable water in under 1 h. The benchmark could be used to provide an ‘early stage’ assessment of the suitability of variations on this design of device. Further work must include experimental work with brackish water and a membrane pouch to correlate actual performance to the benchmark. Testing is required to determine the effect of the hydrophilic nature of the membrane to check whether the pouch can be shipped dry, or whether a small volume of water is required within the pouch to form the initial draw solution. Testing is
required on the membranes used for the device to examine the way in which they foul and ways in which they could be cleaned for re-use. Nanoparticles can be created to produce an osmotic pressure [16] that could be used in the draw solution and then filtered out, or removed by a magnetic field, therefore producing pure potable water. Further research is required into novel draw solutes for this problem. Although no work has been carried out to model such a system, there is a possibility that the system described could be developed into a continuous potable water system. Fig. 9 shows such a system in diagrammatic form.
7. Symbols A c Jv, js Lp
— — — — —
Ms
—
n p R
— — —
T t Vw
— — —
Pouch surface area, m2 Concentration, mol.m!3 Water flux, m3.m!2.s!1 Solute flux, mol.m!2.s!1 Hydraulic conductivity, m3.m!2. s!1. Pa!1 Osmolality of solution, Osmoles. kg!1 Dissociation number Hydrostatic pressure, Pa Universal gas constant, m3.Pa. mol!1.K!1 Temperature, K Time, s Pouch water volume, m3
— —
Osmotic pressure, Pa Osmotic coefficient
Greek Π φ
Superscripts Fig. 9. Continuous system design based upon forward osmosis.
e i
— —
External Internal
M. Wallace et al. / Desalination 227 (2008) 34–45
References [1] H. Backer, Water disinfection for international and wilderness travellers, Travel Med., 34 (2002) 355– 364. [2] F. Kiil, Kinetic model of osmosis through semipermeable and solute-permeable membranes, Acta Physiol. Scand., 177 (2003) 107–117. [3] E. Brian Smith, Basic Chemical Thermodynamics, 4th ed., Oxford University Press, Oxford, 1990. [4] K. Janacek and K. Sigler, Osmosis membrane: impermeable and permeable for solutes, mechanism of osmosis across porous membrane, Physiol. Res., 49 (2000) 191–195. [5] W.J. Moore, Physical Chemistry, 5th ed., Longman, London, 1986. [6] J. Bevan Ott and J. Boerio-Goates, Chemical Thermodynamics; Principles and Applications, Elsevier Academic Press, London, 2000. [7] H.K. Lonsdale, The growth of membrane technology, J. Membr. Sci., 10 (1981) 81–181. [8] R.W. Baker, Membrane Technology and Applications, 2nd ed., Wiley, UK, 2004.
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[9] O.W. Lau and S.F. Luk, A survey on the composition of mineral water and identification of natural mineral water, Int. J. Food Sci. Tech., 37 (2002) 309–317. [10] J. Decombaz, B. Gmunder, N. Daget, R. Munoz-Box and H. Howald, Acceptance of isotonic and hypotonic rehydrating beverages by athletes during training, Int. J. Sports Med., 13 (1992) 40–46. [11] R. Hartel, Crystallization in Foods, Aspen, USA, 1951. [12] Temperature and solubility of solids, http://www. mpcfaculty.net/mark_bishop/supersaturated.htm, accessed 3rd Jan 2007. [13] Gonotec GmbH, Instruction Manual, Osmomat 030 Freezing Point Osmometer, 1996, p. 2. [14] M. Kargol and A. Kargol, Mechanistic formalism for membrane transport generated by osmotic and mechanical pressure, Gen. Physiol. Biophys., 22 (2003) 51–68. [15] S. Chuenkhum and Z. Cui, The parameter conversion from the Kedem-Katchalsky model into the twoparameter model, CryoLetters, 27 (2006) 185–199. [16] M. Chaudhury, Complex fluids: Spread the word about nanofluids, Nature, 423 (2003) 131–132.
A thermodynamic benchmark for assessing an emergency drinking water device based on forward osmosis M. Wallace, Z. Cui, N.P. Hankins Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK Tel. +44 (1865) 273027; email: [email protected] Received 26 March 2007; Accepted 24 April 2007
Abstract Following the creation of the first reverse osmosis (RO) membrane in the 1960s, the technique has been widely used for the purposes of both small scale and municipal seawater desalination. Forward osmosis (FO) is now also emerging as a possible contender, with the potential for much lower energy consumption. In this study, we have developed a thermodynamic benchmark for use in assessing the suitability of a potable water system for purifying small amounts of brackish water in emergency situations. The light, portable and re-usable purification system is driven by FO. A pouch is filled with draw solution and immersed in brackish water; the pouch incorporates a traditional RO membrane. The ‘draw solution’ contains digestible salts and/or sugars to provide an osmotic pressure difference across the membrane, thus drawing in purified water across the membrane. Three such draw solutions were produced and tested, allowing the osmotic potential of the solution to be determined over a succession of dilutions. The results could be fitted with a power law function. In order to take account of the solution non-ideality and the non-linearity of flux rates, a thermodynamic relationship was used in conjunction with a membrane transport model to develop a benchmark which describes the ideal behaviour of a FO water system. This benchmark, in conjunction with the power law function, showed that such a system could be used in an emergency to provide safe, potable water in a reasonable time interval and without the need for a power source. The study has also suggested the possibility of a continuous water purification system based upon this principle, and has drawn attention to the benefits of novel draw solutes in such a system. Keywords: Forward osmosis; Membrane-based potable water system; Desalination; Thermodynamic model
*Corresponding author. Presented at the First Oxford and Nottingham Water and Membranes Research Event, 2–4 July 2006, Oxford, UK. 0011-9164/08/$– See front matter © 2008 Published by Elsevier B.V. doi:10.1016/j.desal.2007.04.097
M. Wallace et al. / Desalination 227 (2008) 34–45
35
1. Introduction “Access to safe water is a fundamental human need and, therefore, a basic human right. Contaminated water jeopardizes both the physical and social health of all people. It is an affront to human dignity” (Kofi Annan, United Nations Secretary-General). Many situations exist where a plentiful supply of water exists, but is unsafe for human consumption. This is a large problem in many areas of the world, particularly those which are prone to natural disaster. Whenever such a disaster occurs water is very often contaminated with both organic and inorganic pollutants. Damage to local infrastructure can lead to sanitation problems, which further pollutes the water with faecal pathogens. In these situations, there is a requirement for a clean and easily administrated source of water, which is able to sustain life until a more permanent solution can be installed. Another group of people who are reliant on surface water are wilderness travellers or the military. Since the safety of surface water cannot be reliably estimated on the basis of appearance, smell and taste [1], there is a requirement for a safe source of potable water for these groups to use in emergency situations. The solution should be robust and capable of use in most situations where surface water is contaminated. This paper will describe the development of a thermodynamic benchmark for use in assessing the suitability of a membrane based potable water system for purifying small amounts of brackish water in emergency situations. See the Symbols section for definitions used throughout the paper.
2. Design basis 2.1. Principle of osmotic pressure Osmotic pressure can be defined as a pressure acting to restore the chemical potential of a
Fig. 1. Physical representation of osmotic pressure.
system [2] and can be physically described by considering a pure solvent separated from a solution by a semi-permeable membrane (Fig. 1). If the membrane is permeable to the solvent molecules only, then the net effect will be a flow of solvent molecules from left to right. If a pressure is applied to the solution, the flow can be counteracted; the pressure required to restore equilibrium is known as the osmotic pressure of the solution [3] and is denoted as π; it can be calculated from the concentration of the solution using van’t Hoff’s formula (1) [4]:
π = c.R.T
(1)
It can be noted from this expression that osmotic pressure is a colligative property, dependent only on the number of solute molecules, rather than on their nature. Other colligative properties include boiling point elevation and freezing point depression; they are all related to the lowering of vapour pressure when a solution is formed. Expression (1) alone is not sufficient to describe the osmotic pressure of a solution for two reasons: C If the solute is a salt then its ions will dissociate when it dissolves into solution. This results in the total number of molecules increasing, and since osmotic pressure is colli-
36
M. Wallace et al. / Desalination 227 (2008) 34–45
gative, this results in a higher osmotic pressure than would be expected. The ‘dissociation number’ (n) is therefore required to correct this. C The osmotic coefficient, analogous to the activity coefficient, must also be used to correct for non-ideal behaviour of the solution. Osmotic and activity coefficients can be related by the Gibbs–Duhem equation. [6]. Therefore it is necessary to define osmolality [Eq. (2)], which can be substituted into van’t Hoff’s formula [Eq. (1)] to give an accurate prediction of the true osmotic pressure of a solution:
M = C.φ.n
(2)
Π = M .R.T
(3)
A difference of osmotic pressure across a semipermeable membrane forms the basis of an understanding of both forward and reverse osmosis. 2.2. Forward osmosis Forward osmosis (FO) is essential for water transport across biological cell membranes in all living organisms [2] and is the process by which an osmotic pressure difference causes a solvent to be drawn through a membrane. This is useful for altering the concentration of dissolved solutes in a solution, or for separating a solvent from unwanted solutes. When this occurs, there is a trade-off between the solutes of the feed and draw solutions so it is not possible to produce a pure solvent using FO. 2.3. Reverse osmosis On the other hand, reverse osmosis (RO) is used to produce pure solvents, primarily in the desalination of seawater, by applying high pressure to a solution and causing it to pass
Table 1 Characteristics of different membrane processes Membrane process
Nominal pore size, Å
Average permeability, L.m!2.H!1.bar!1
Microfiltration (MF) 1000–100,000 500 Ultra Filtration (UF) 10–1000 150 Reverse osmosis (RO) 2–5 5–10
through a solvent-permeable membrane. This results in the retention of the solute on the solution side of the membrane. 2.4. Membranes “Membrane technology has come of age”, stated Lonsdale in 1981 [7]. Yet over the past 26 years since his paper, ‘The Growth of Membrane Technology’, there has been a massive increase in the use of semi-permeable membranes in municipal water treatment and medical applications. Three well developed membrane separation processes currently exist, each providing for a different range of molecular sieving [8] as detailed in Table 1. Microfiltration membranes are used in processes where suspended particles must be removed from a solvent [8] but dissolved solids are permitted in the permeate [7]. An example is the bacteriological testing of water. Ultrafiltration membranes are used where macromolecules and colloids must be removed from a solute [8]. Salts and heavy metals will permeate readily. Reverse osmosis membranes have been developed primarily for use on desalination plants to allow the transport of water (~2Å dia.) whilst rejecting up to 99% of salt ions at high operating pressures. In general, they will allow the transport of molecules between approx 2Å and 5Å in diameter [8].
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2.5. A Membrane based device
3. Draw solution design
For the purpose of designing an emergency device, a ‘draw solution’ of salts and sugars can be used to provide the driving force to overcome membrane resistance and ‘drive’ brackish water through a RO membrane by the process of FO. The use of a RO membrane has the advantage that it will retain all of the ‘draw solution’ on the potable side of the membrane and produce a drinkable solution of clean water and solute. The disadvantage of using a RO membrane is that a much higher concentration of draw solution will be required than if a MF or UF membrane were used, due to its low permeability. The design objectives for the device are therefore that it should; be simple to operate, be temporary and portable (therefore light and small), be cheap and reusable, require no external power source, purify and clarify contaminated surface water (not seawater), produce potable water with adequate odour and taste improvement, and produce an adequate volume of potable water in a reasonable time interval.
In order to produce a FO membrane design, it was necessary to find a suitable mixture of non toxic salts and/or sugars for use as the draw solution. This must be safe for human consumption whilst generating a suitably large osmotic pressure difference across the membrane. Some preliminary investigations into the effectiveness of a variety of solutes used on their own showed that salts such as CaCl2, MgCl2 and NaCl can produce large differences in osmotic pressure whilst sucrose and glucose were not as effective. To ensure safety for consumption, both the World Health Organisation (WHO) 1993 Drinking Water Recommendation and the United Kingdom (UK) water regulations were consulted [9] to determine the maximum tolerable concentrations of salt ions in drinking water. The most conservative values are listed in Table 3. We therefore calculated that the maximum concentration of each salt would be (as determined from the data in Table 5): — 0.00355 M C CaCl2 — 0.00210 M C MgCl2 C NaCl — 0.00710 M
2.6. Contaminants In order to produce potable water from brackish water, it is necessary to remove a variety of contaminants. Table 2 details the classes and their molecular sizes. Table 2 Types of contaminant Contaminant type
Size, Å
Examples
Bacteria [1]
~5,000
Viruses [1] Protozoa [1]
~300 ~50,000
Parasites [1]
~200,000
Cholera, E. coli, Salmonella Polio, hepatitis Cryptosporidium, Giardia Intestinal worms
To determine a tolerable concentration of sugar, it was necessary to investigate the physiological effect of ingesting carbohydrate in solution. Blood has an osmolality of 280–330 mOsm. kg!1, which is generated by sodium, protein and glucose in the bloodstream. Isotonic drinks are those which have an osmolality in the same range as that of blood [10]. Isotonic drinks have Table 3 Maximum ion concentration in drinking water Cl! Na+ Mg2+ Ca2+ a
250 mg.l!1 200 mg.l!1 50 mg.l!1 250 mg.l!1
WHO recommended maximum. UK regulation maximum.
b
0.0071 Ma 0.0087 Ma 0.0021 Mb 0.0062 Mb
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Table 4 Solubility of sugars in water at 25EC
Sucrose Glucose
Solubility (g/100ml)
Maximum possible concentration, M
213.6 [11] 91 [12]
5.88 5.05
carbohydrate in the form of sugar at concentrations of 6–8%. This corresponds to 0.09 M of sucrose (C12H24O11) and 0.18 M of glucose (C6H12O6) at 8%. Another consideration is the solubility of both sugars in water at 25°C (Table 4). Using these data two mixtures were designed, which could maximise osmolality whilst minimising physiological effect. C Mixture one: 2 M sucrose + 0.1 M calcium chloride C Mixture two: 1 M sucrose + 1 M glucose + 0.1 M calcium chloride Due to non-linear behaviour, there is no method which can be used to calculate the osmolality of a solution which is composed of a mixture of solutes; therefore it was necessary to experimentally determine these values by making a high concentration solution from the mixture and measuring its osmolality. Repeated dilution and measurement provided sufficient results that a power law could be fitted which describes the variation of osmolality of the solution.
4. Experimental determination of osmolality 4.1. Materials The following materials were used: C Sucrose: Cane sugar, Sigma-Aldrich S-5016, M.W. 342.3. C Glucose: Sigma Ultra Anhydrous, 99.5% purity, Sigma-Aldrich G-7528, M.W. 180.2g/ mole
C Calcium chloride: Sigma Ultra Dihydrate, 99% min purity, Sigma-Aldrich C-5080 M.W. 147.01 C Deionised water (produced in a Millipore deionising unit) We used a Mettler Toledo AB54-5 balance to measure out the solutes and the osmolality of each solution was measured using an Osmomat 030 Freezing Point Osmometer (Gonotec GmbH). The osmometer determines the total osmolality of an aqueous solution by performing a comparative measurement of the freezing point of pure water and of that of the solution being tested: “Water has a freezing point of 0EC, a solution with a salt concentration of 1 Osmol/kg has a freezing point of !1.858E” [13]. This thermodynamic basis provides an accurate value for osmolality, since both freezing point depression and osmotic pressure are colligative properties [3], meaning that they can be calculated from one another without any regard for the nature of the solute. 4.2. Osmomat 030 measurement principle “The sample solution is cooled using a peltier element cooling system. At the same time the temperature of the sample is monitored electronically. When the sample reaches a defined temperature below the freezing point of pure water the crystallisation of the solution is automatically initiated. “A stainless steel needle is held well below 0EC such that water vapour in the air condensing on its tip freezes as tiny ice crystals; the needle tip, covered in tiny ice crystals, is stabbed into the super-cooled solution. Thus, initiation of crystallisation occurs by inoculation of the solution with ice crystals. Immediately after this, the temperature of the solution begins to rise spontaneously as heat of crystallisation is released during the freezing process. The rise in temperature is measured with an accuracy of 1.858×10E!3 EC” [13].
M. Wallace et al. / Desalination 227 (2008) 34–45
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Table 5 Determination of maximum salt concentration for draw solution Salt concentration
Ion concentrations
Ca2+ (Cl!)2 0.00620 M 0.00355 M Mg2+(Cl!)2 0.00210 M 0.00355 M Na+Cl! 0.00870 M 0.00710 M
Ca2+ 0.00620 M 0.00355 M Mg2+ 0.00210 M 0.00355 M Na+ 0.00870 M 0.00710 M
Cl! 0.01240 M 0.00710 M Cl! 0.00420 M 0.00710 M Cl! 0.00870 M 0.00710 M
4.3. Procedure For each mixture, the first step of the procedure was to make up three 20 ml samples of the draw solution. From one of the samples, 0.1 ml was decanted (using Finnpipette®) into ten separate containers. Each container was then diluted with de-ionised water (×2, ×5, ×10, ×15, ×20 … ×50) and mixed well. We then extracted and tested 0.1 ml of each in the osmometer. This procedure was repeated for each of the other two samples. The solutions used were composed of the following: C Mixture one: 14.4 g sucrose + 0.222 g calcium chloride (+20 ml de-ionised water) C Mixture two: 7.2 g sucrose + 3.604 g glucose + 0.222 g calcium chloride (+20 ml de-ionised water) It was also decided to test a commercially available salt/sugar mixture so a third mixture was made from a ‘dioralyte’ rehydration sachet (dioralyte is indicated for the replacement of essential body water and salts in the treatment of acute diarrhoea in infants, children and adults).dioralyte: 0.47 g NaCl + 0.30 g KCl + 3.56 g glucose + 0.53 g disodium hydrogen citrate + silicon dioxide + saccharin sodium + black currant flavour (+20 ml de-ionised water).
Comments Chlorine ion concentration is above limit Maximum allowable salt concentration Maximum allowable salt concentration Magnesium ion concentration is above limit Chlorine ion concentration is above limit Maximum allowable salt concentration
The results follow: 1. Mixture one: The osmometer was unable to obtain a value for the undiluted sample as the sample was too viscous, so an additional measurement at ×1.5 dilution was taken and used to approximate the value for ×1. This was necessary to allow a good fit of a power law function to the data. Fig. 2 shows the plotted results with a power law (y = 1.795×–1.0858) fitted to describe the change in osmolality of the solution as it is diluted. 2. Mixture two: In this case it was possible to obtain measurements for the ×1 dilution, but the data for one of the three original samples had to be discarded prior to further analysis due to significant difference between it and the other samples. Fig. 3 shows the plotted results, with a power law (y = 1.6298×!1.1177) fitted to the results. 3. Since this mixture was tested only for comparative purposes, only one sample was tested. Fig. 4 shows the plotted results with a power law (y = 2.467×!1.0292) fitted to the results.
5. Development of benchmark 5.1. Model assumptions To develop the benchmark it is helpful to consider the system being modelled as two
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M. Wallace et al. / Desalination 227 (2008) 34–45
Fig. 2. Mixture one: dilution vs. osmolality (and power law function).
Fig. 3. Mixture two: dilution vs osmolality (and power law function).
M. Wallace et al. / Desalination 227 (2008) 34–45
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Fig. 4. Mixture three: dilution vs osmolality (and power law function).
5.2. Modelling The modelling of an RO ‘pouch’ is relatively straightforward, since (at low pressure) no salt ions will be lost through the membrane so a model can be developed based upon this principle. Therefore, a simple mass balance yields the membrane flux relationship (4): Fig. 5. Mechanical representation of system.
volumes of water separated by a membrane, as show in Fig. 5 [14]. The volume of water marked (1) is the brackish water and volume (2) is potable water. It can be assumed that the RO membrane is impermeable to all solute; therefore, js = 0. The device will be used in a large source of water; therefore V1 = 4 and Δp is only significant when the pouch is full.
J v = Lp . ( Δp − ΔΠ )
(4)
Combining this result with Eq. (3), it can be shown that it is possible to obtain the result [15]:
J v = − Lp . R.T . ( M 1 − M 2 )
(5)
However, flux Jv can also be expressed as
Jv =
d Vw A.d t
(6)
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M. Wallace et al. / Desalination 227 (2008) 34–45
Therefore,
d Vw = − Lp .R. A.T . ( M se − M si ) .d t
Table 6 Variables used for simulation
(7)
where
⎛V i ⎞ M se = M si ⎜ w ⎟ ⎝ Vw ⎠
(8)
i.e., a function of the dilution, and M = C.φ.n as previously in Eq. (2). 5.3. Simulation The simulation was then based upon a pouch, constructed of an RO membrane with an assumed hydraulic permeability of 5 L.m!2.hour!1.atm!1, of dimensions 20×10×2 cm and a maximum volume of 400 ml. A Microsoft Excel spreadsheet was then set up using expressions (6), (7) and each of the experimentally determined power laws. Table 6 details the variables that were required.
Fig. 6. Mixture one simulation: pouch volume vs time.
Variables Surface area of pouch (A), m2 Maximum pouch volume (Vmax), l Hydraulic permeability (Lp), L.m2h.l.atm!1 Initial external molarity (Mes0), Osmols.kg H2O-l Initial pouch volume (Vw0), l Time increment (dt), s Calculated values Hydraulic permeability (Lp), L.m2h.l.atm!1 Initial internal molarity (Mis0) Osmols.kg H2O-l
0.052 0.4 5 0 0.01 30 0.001389 1.795000
The spreadsheet calculates the dilution within the pouch at each increment of time (= t + dt), and uses this value to determine the molality within the pouch from the power law. Expression (7) is then used to calculate the change in volume over that time increment, which is added to a running total volume.
M. Wallace et al. / Desalination 227 (2008) 34–45
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Fig. 7. Mixture two simulation: pouch volume vs time.
Fig. 8. Mixture three simulation: pouch volume vs time.
Plots of volume vs time allow for easy comparison of the effectiveness of a variety of solutes used as the draw solution. Fig. 6 shows that Mixture 1 could fill the pouch in 55 mins. Fig. 7
shows that Mixture 2 could fill the pouch in 64.5 mins. Fig. 8 shows that dioralyte could fill the pouch in 67.5 mins.
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M. Wallace et al. / Desalination 227 (2008) 34–45
6. Conclusions and future work This benchmark has shown, from a thermodynamic basis, that it would be possible to construct a potable water system capable of purifying small amounts of brackish water in emergency situations. Such a system could operate without access to any power supply at the point of use. Use of a RO membrane would significantly reduce harmful contaminants with the exception of some heavy metals. It would be effective in clarifying brackish water and would provide significant taste and odour improvement. The benchmark has also shown that such a device could be fast acting, providing a reasonable quantity of potable water in under 1 h. The benchmark could be used to provide an ‘early stage’ assessment of the suitability of variations on this design of device. Further work must include experimental work with brackish water and a membrane pouch to correlate actual performance to the benchmark. Testing is required to determine the effect of the hydrophilic nature of the membrane to check whether the pouch can be shipped dry, or whether a small volume of water is required within the pouch to form the initial draw solution. Testing is
required on the membranes used for the device to examine the way in which they foul and ways in which they could be cleaned for re-use. Nanoparticles can be created to produce an osmotic pressure [16] that could be used in the draw solution and then filtered out, or removed by a magnetic field, therefore producing pure potable water. Further research is required into novel draw solutes for this problem. Although no work has been carried out to model such a system, there is a possibility that the system described could be developed into a continuous potable water system. Fig. 9 shows such a system in diagrammatic form.
7. Symbols A c Jv, js Lp
— — — — —
Ms
—
n p R
— — —
T t Vw
— — —
Pouch surface area, m2 Concentration, mol.m!3 Water flux, m3.m!2.s!1 Solute flux, mol.m!2.s!1 Hydraulic conductivity, m3.m!2. s!1. Pa!1 Osmolality of solution, Osmoles. kg!1 Dissociation number Hydrostatic pressure, Pa Universal gas constant, m3.Pa. mol!1.K!1 Temperature, K Time, s Pouch water volume, m3
— —
Osmotic pressure, Pa Osmotic coefficient
Greek Π φ
Superscripts Fig. 9. Continuous system design based upon forward osmosis.
e i
— —
External Internal
M. Wallace et al. / Desalination 227 (2008) 34–45
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[9] O.W. Lau and S.F. Luk, A survey on the composition of mineral water and identification of natural mineral water, Int. J. Food Sci. Tech., 37 (2002) 309–317. [10] J. Decombaz, B. Gmunder, N. Daget, R. Munoz-Box and H. Howald, Acceptance of isotonic and hypotonic rehydrating beverages by athletes during training, Int. J. Sports Med., 13 (1992) 40–46. [11] R. Hartel, Crystallization in Foods, Aspen, USA, 1951. [12] Temperature and solubility of solids, http://www. mpcfaculty.net/mark_bishop/supersaturated.htm, accessed 3rd Jan 2007. [13] Gonotec GmbH, Instruction Manual, Osmomat 030 Freezing Point Osmometer, 1996, p. 2. [14] M. Kargol and A. Kargol, Mechanistic formalism for membrane transport generated by osmotic and mechanical pressure, Gen. Physiol. Biophys., 22 (2003) 51–68. [15] S. Chuenkhum and Z. Cui, The parameter conversion from the Kedem-Katchalsky model into the twoparameter model, CryoLetters, 27 (2006) 185–199. [16] M. Chaudhury, Complex fluids: Spread the word about nanofluids, Nature, 423 (2003) 131–132.