A Study of Thermodynamic (Cylinder-Piston) Model Energy Production By Pressure Retarded Osmosis (PRO) (Case Study of Lake Orumiyeh)

The renewable energies are infinite sources of energy that, unlike fossil fuels, have no environmental problems; therefore, interest in such sources is increasingly growing in recent years. In this study, we have studied the thermodynamic model for production of osmotic energy through the Pressure Retarded Osmosis (PRO) and its dominant equations. The thermodynamic cylinder-piston model was utilized for calculation of the produced work. Through this model we have investigated the possibility of producing osmotic energy from waters of Lake Orumiyeh and the rivers entering it, in order to decide about establishment of an osmotic power plant in Iran. The results indicated that the amount of osmotic energy attained from mixture of Lake Orumiyeh water with that of its rivers, respectively with different concentrations of 320 gram/lit (5641.042 mol/m3) and 1 gram/lit (17.1 mol/m3), is -15.5487 mega-Joules per one cubic meter of mixed water. Therefore, the Pressure Retarded Osmosis confirmed that economically it is a method comparable with other methods of energy production. water with that of its rivers, respectively with


Introduction
As renewable energies are sustainable unending sources of energy without the environmental problems of fossil fuels, interest in these sources of energy has increased (Brogioli 2009). One type of renewable energy is salinity gradient energy or osmotic power which, based on thermodynamic principles, can be extracted from mixture of freshwater and saltwater entropy (Skilhagen.et al. 2008;Seppak and Lampinen 1999) . When we mix seawater and river water, salt concentration difference between the two solutions with different concentrations produces entropy (Loeb 1988). The achieved work results from cooling of the mixture for less than 0.08°c for an optimized process. This kind of energy has many advantages; here we mention some of these advantages: Salinity gradient is a special renewable, frequent and environment-friendly source of energy. It is a source of energy with permanent yield, that is, its energy production does not depend on climate conditions, and it can produce power constantly for 24 hours. Osmosis is a natural process that releases no carbon dioxide. This type of energy is harvested with no interference in environmental parameters.
In places like estuaries where the saltwater mixes with freshwater a large amount of potential energy is water with that of its rivers, respectively with water with that of its rivers, respectively with water with that of its rivers, respectively with water with that of its rivers, respectively with water with that of its rivers, respectively with water with that of its rivers, respectively with water with that of its rivers, respectively with

Osmotic Pressure
To obtain osmotic energy from the process of mixing cylinder-piston, we consider Fig (1), the piston is a permeable membrane which only allows for water molecules to cross and holds salt molecules (the cylinder is isolate and has no heat dissipation). It is assumed that river water and seawater just contain NaCl, so we filled two sides of the cylinder with seawater and river water with specific initial concentrations and specific primary volumes (these solutions are not refreshable).

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Water molecules cross the membrane from river water side and entering the seawater make the solution dilute; consequently volume of water in seawater side gradually increases. This action continues until that salt concentration in both sides of the cylinder equals. Fig (2a) and (2b) show the primary and final condition of the process.
Regarding mass balance the final volumes of the sides for seawater and river water can reach to the following measures:    [ + ] ( (4)

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As in comparison with water, salt amount is insignificant, Ψ almost equals mole fraction.
According to Vant Hoff rule difference of osmotic pressure can be expressed by the following equation : In which, ΔV is volume of the water that crossed the membrane, and according to equation (6) it has a linear proportion with concentration difference.
The process is generally toward decreasing hydraulic pressure, this processing continues with short paces towards reduction of ΔP to reach to ΔP=Δπ on a point throughout the process.

Calculation of Ideal Work
It is expected that in the thermodynamic reversible process of PRO the achieved work be ideal. While the volume of seawater is increasing, through integrating ΔP, we can write: By placing equation (5) in equation (7) considering

Calculation of Real Work
In the real process of PRO the saltwater side experiences a hydraulic pressure, and then permeation of water through the membrane starts; it continues till pressure reaches to Δπ, therefore, we can write: that ΔV f is the volume of the final permeation.
]. ∆ The permeation volume is function of ΔV and P , therefore maximum ΔV and maximum ΔP obtains

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So, maximum work that obtain of the PRO proceeding as flow ( Lee et al., 1981) :

Frictional Dissipation
As the process of constant pressure PRO is not a totally reversible, the real work is less than the attainable ideal work. While water crosses the membrane, friction force among molecules of water and membrane resist to reach to hydraulic pressure (overcoming the resistance formed by hydraulic pressure). In order to get to a nonzero amount the water flow crossing the membrane spends a part of osmotic force to overcome resistances. Equation (18) shows friction losses.

Unusable Energy
In a constant pressure PRO the real volume of permeation is a bit less than the volume of the water needed for pressurizing saltwater, which, is due to permeation limits. When difference of osmotic pressur equals the hydraulic pressure (ΔV f -ΔV*) volume is not applied for production of useful work, called unusable energy. The following equation indicates this fact (Loeb 1976;Loeb et al.1990).

Energy of Mixture
Ψ A and Ψ B are total mole fraction ratios in solutions A and B, which are related to each other as follows:

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As the system volume remains constant during mixing process (V A +V B =V M ) and the salt volume fraction is ignorable compared with water volume. Therefore, the mole fraction is almost equals volume fraction, and Gibbs free energy of the mixture per volume unit of mixture ΔG Mix , VM is defined as follows: For production of power from salinity gradient, seawater is often unlimited and river waters that enter it are limited. In the diluted solution energy of mixing is accessible and measureable per volume unit. Since: Gibbs free energy of mixing process (in the diluted solution) is given by equation (26). For mixing G Mix is a function of seawater, river water and mole fracture of river water.

Thermodynamic Cylinder-Piston Model for Theoretical Energy Production in PRO
The processes of solving and permeation can be similar through a cylinder-piston in which the piston is a permeable membrane. Water permeates from river water-side to the sea water-side and seawater-side increase and produces energy Using the relation = we can write: So the thermodynamic work of the expansion process is defined as: The amount of the work produced (expansion process) by the volume increase that resulting permeation river water into the seawater side in PRO model, is obtained as follows:

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Therefore, The work produced by condensation process (the energy consume for contraction of river water) can be computed as well. Considering condensation work can be expressed as follows: entering similar relations and integration leads to the following relation:

The potential of Lake Orumiyeh for production of energy through PRO model
Lake

Orumiyeh water and interring rivers water with use thermodynamic model processing (cylinderpiston)
Table (2) shows the experimental concentration and volume of Lake Orumyeh water and its rivers'. As the data of the table indicate Lake Orumiyeh has a high potential for a good electrolyte with high RESEARCH PAPER entropy degree. Lake's salt is mostly NaCl, for which in an ideal diluted solution Vant Hoff's Coefficient (i) is 2 (i=2) and its osmotic coefficient is (Φ= 0.9). The value of the released energy via the above thermodynamic model is computed as follows:      .This concentration decrease and pressure increase in dense water side leads to production of osmotic pressure in saltwater.
Because of high amount of salts in salty lakes their water density is much higher than normal water.
The most frequent cations are sodium and magnesium respectively; and the most frequent anions are chlorors and sulfates respectively. The results obtained from this study indicate that the amount of osmotic energy attained from mixture of Lake Orumiyeh water with that of its rivers, respectively with different concentrations of 320 gram/lit (5641.042 mol/m 3 ) and 1 gram/lit (17.1 mol/m 3 ), is -15.5487 mega-Joules per one cubic meter of mixed water. Therefore, the Pressure Retarded Osmosis showed that economically it is a method comparable with other methods of energy production.