Although the first law is an important tool in evaluating the overall performance of a desalination plant, such analysis does not take into account the quality of energy transferred. This is an issue of particular importance when both thermal and mechanical energy are employed, as they are in thermal desalination plants. First-law analysis cannot show where the maximum loss of available energy takes place and would lead to the conclusion that the energy loss to the surroundings and the blow-down are the only significant losses. Second-law (exergy) analysis is needed to place all energy interactions on the same basis and give relevant guidance for process improvement.
The use of exergy analysis in actual desalination processes from a thermo-dynamic point of view is of growing importance to identify the sites of greatest losses and improve the performance of the processes. In many engineering decisions, other facts, such as the impact on the environment and society, must be considered when analyzing the processes. In connection with the increased use of exergy analysis, second-law analysis has come into more common usage in recent years. This involves a comparison of exergy input and exergy destruction along various desalination processes. In this section, initially the thermodynamics of saline water, mixtures, and separation processes is presented, followed by the analysis of multi-stage thermal processes. The former applies also to the analysis of reverse osmosis, which is a non-thermal separation process.
Saline water is a mixture of pure water and salt. A desalination plant performs a separation process in which the input saline water is separated into two output streams, those of brine and product water. The water produced from the process contains a low concentration of dissolved salts, whereas the brine contains the remaining high concentration of dissolved salts. Therefore, when analyzing desalination processes, the properties of salt and pure water must be taken into account. One of the most important properties in such analysis is salinity, which is usually expressed in parts per million (ppm), which is defined as salinity = mass fraction (mfs) X 106. Therefore, a salinity of 2000 ppm corresponds to a salinity of 0.2%, or a salt mass fraction of mfs = 0.002. The mole fraction of salt, xs, is obtained from (Cengel et al., 1999):
NSMS
sw sw sw sw
where m = mass (kg). M = molar mass (kg/kmol). N = number of moles. x = mole fraction.
In Eqs. (8.1) and (8.2), the subscripts s, w, and sw stand for salt, water, and saline water, respectively. The apparent molar mass of the saline water is (Cerci, 2002):
NsMs + NwMw
The molar mass of NaCl is 58.5 kg/kmol and the molar mass of water is 18.0 kg/kmol. Salinity is usually given in terms of mass fractions, but mole fractions are often required. Therefore, combining Eqs. (8.1) to (8.3) and considering that xs + xw = 1 gives the following relations for converting mass fractions to mole fractions:
Solutions that have a concentration of less than 5% are considered to be dilute solutions, which closely approximate the behavior of an ideal solution, and thus the effect of dissimilar molecules on each other is negligible. Brackish underground water and even seawater are ideal solutions, since they have about a 4% salinity at most (Cerci, 2002).
Example 8.1
Seawater of the Mediterranean sea has a salinity of 35,000 ppm. Estimate the mole and mass fractions for salt and water.
Solution
From salinity, we get salinity (ppm) 35,000 mf = -— = -— = 0.03
0.035
As xs + xw = 1, we have xw = 1 - xs = 1 - 0.011 = 0.989. From Eq. (8.3),
M = xM + xwMw = 0.011 x 58.5 + 0.989 x 18 = 18.45 kg / kn sw ssww c
Finally, from Eq. (8.2), mf„, = x,,,^ = 0.989 —18— = 0.965
18.45
Extensive properties of a mixture are the sum of the extensive properties of its individual components. Thus, the enthalpy and entropy of a mixture are obtained from
Dividing by the total mass of the mixture gives the specific quantities (per unit mass of mixture) as h = £ mfihi = mfshs + mfwhw
The enthalpy of mixing of an ideal gas mixture is zero because no heat is released or absorbed during mixing. Therefore, the enthalpy of the mixture and the enthalpies of its individual components do not change during mixing. Thus, the enthalpy of an ideal mixture at a specified temperature and pressure is the sum of the enthalpies of its individual components at the same temperature and pressure (Klotz and Rosenberg, 1994). This also applies for the saline solution.
The brackish or seawater used for desalination is at a temperature of about 15°C (288.15 K), pressure of 1 atm (101.325 kPa), and a salinity of 35,000 ppm. These conditions can be taken to be the conditions of the environment (dead state in thermodynamics).
The properties of pure water are readily available in tabulated water and steam properties. Those of salt are calculated by using the thermodynamic relations for solids, which require the set of the reference state of salt to determine the values of properties at specified states. For this purpose, the reference state of salt is taken at 0°C, and the values of enthalpy and entropy of salt are assigned a value of 0 at that state. Then the enthalpy and entropy of salt at temperature T can be determined from and hs = hso + cps (T - To )
The specific heat of salt can be taken to be cps = 0.8368 kJ/kg-K. The enthalpy and entropy of salt at To = 288.15 K can be determined to be hso = 12.552kJ/kg and sso = 0.04473 kJ/kg-K, respectively. It should be noted that, for incompressible substances, enthalpy and entropy are independent of pressure (Cerci, 2002).
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