In this part, we will present the different systems that can be used from heat recovery in production of sulfuric acid as in the diagrams (Fig. 6).
The steam produced by the boiler field runs a Rankine power cycle to produce electricity for the RO system and auxiliary components of the MED system after steam of acid sulfuric production (thermal energy) is used to power the other MED desalination system which shows the energy efficiency of our system. The Thermodynamic models of each of the two main system components (RO and MED) were constructed in Engineering Equation Solver (EES) and solved numerically. The effect of all parametric system is investigated in this study, especially the reverse osmosis system.
RO system model
In the RO process, the solution declined by the membrane, also called brine, is more concentrated than the power solution. Its pressure is slightly smaller than the working pressure, although it is still very important. The same capacity can be collected using a recovery unit to generate mechanical energy to drive pumps.
In this paper, we assume that (Cardona and Piacentino 2004):
Flow rate is steady;
Salt and saltwater are incompressible substances;
Salinity at the inlet is constant (point 5);
Kinetic and potential energies are negligible;
Terms of saltwater at the entrance match ambient conditions (reference conditions);
Performance of all pumps and turbines is set at the same value of 75%;
In the former case (system # 1), the RO subsystem embodying a hydraulic turbine is mechanically coupled with the Rankine cycle subsystem, as shown in Fig. 7.
Thermodynamic study in steady state
System # 1:
Boiler:
The first law of thermodynamics in steady state (Bouzayani et al. 2007; Cangel and Boles 2002) for the volume control of the boiler, not taking into account the heat loss to the outside, is expressed as:
$$h_{2} - h_{1} = \frac{{\dot{Q}_{1} }}{{\dot{M}}} = q_{1}$$
Steam turbine:
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The first law of thermodynamics in steady state for superheated steam control volume contained between sections 2 and 3 of the steam turbine, not taking into account heat exchanges with the outside, is expressed as:
$$w_{\text{TV}} = h_{2} - h_{3} = \eta_{\text{TV}} \cdot (h_{2} - h_{3s} )$$
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The reversible work of the steam turbine in steady state is expressed as:
$$w_{\text{r,TV}} = w_{\text{TV}} - T_{0} \cdot (S_{2} - S_{3} )$$
Condenser:
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The first law of thermodynamics in steady state for the vapor control volume contained between sections 3 and 4 of the condenser, by not taking into account the heat exchange with the outside, is expressed as:
$$q_{3} = \frac{{\dot{Q}_{3} }}{{\dot{M}}} = h_{4} - h_{3}$$
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The reversible work of the capacitor in steady state is given as:
$$w_{\text{r,cond}} = - T_{0} \cdot \left( {\frac{{q_{2} }}{{T_{0} }} + (S_{3} - S_{4} )} \right)$$
Pump 1:
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The first law of thermodynamics steady state for the volume control of pure liquid water contained between sections 1 and 4 of the pump Pm1, not taking into account the heat exchanges with the outside, is expressed as:
$$w_{\text{Pm1}} = \frac{{\dot{W}_{\text{Pm1}} }}{{\dot{M}}} = \frac{{P_{1} - P_{4} }}{{\rho_{\text{W}} \cdot \eta_{\text{Pm1}} }} = h_{1} - h_{4}$$
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Entropy in point 4 is expressed as:
$$h_{4} = h_{1} + \frac{{P_{4} - P_{1} }}{{\rho_{\text{W}} \cdot \eta_{\text{Pm1}} }}$$
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The reversible work of pump Pm1 in steady state is given as:
$$w_{\text{r,Pm1}} = h_{4} - h_{1} - T_{0} \cdot (S_{4} - S_{1} )$$
Pump 2:
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The first law of thermodynamics in steady state for seawater control volume contained between sections 5 and 6 of the pump Pm2, not taking into account the heat exchanges with the outside, is expressed as:
$$w_{\text{Pm2}} = \frac{{\dot{W}_{\text{Pm2}} }}{{\dot{m}}} = \frac{{P_{6} - P_{5} }}{{\rho_{\text{W}} \cdot \eta_{\text{Pm2}} }} = h_{6} - h_{5}$$
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Entropy in point 6 is expressed as:
$$h_{6} = h_{5} + \frac{{P_{6} - P_{5} }}{{\rho_{\text{W}} \cdot \eta_{\text{Pm2}} }}$$
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The work of reversible pump Pm2 in steady state is given as:
$$w_{\text{r,Pm2}} = (h_{5} - h_{6} ) - T_{0} \cdot (S_{5} - S_{6} )$$
Pump 3:
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The first law of thermodynamics steady volume for the water control of maple contained between sections 7 and 8 of the pump Pm3, not taking into account the heat exchanges with the outside, is expressed as:
$$w_{\text{Pm3}} = \frac{{\dot{W}_{\text{Pm3}} }}{{\dot{m}}} = \frac{{P_{8} - P_{7} }}{{\rho_{\text{W}} \cdot \eta_{\text{Pm3}} }} = h_{8} - h_{7}$$
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Entropy in point 8 is expressed as:
$$h_{8} = h_{7} + \frac{{P_{8} - P_{7} }}{{\rho_{\text{W}} \cdot \eta_{\text{Pm3}} }}$$
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The work of reversible pump Pm3 in steady state is given as:
$$w_{\text{r,Pm3}} = (h_{7} - h_{8} ) - T_{0} \cdot (S_{7} - S_{8} )$$
Hydraulic turbine:
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The first law of thermodynamics in steady state for the brine control volume contained between sections 10 and 11 of the hydraulic turbine is expressed as:
$$w_{\text{TH}} = \frac{{\dot{W}_{\text{TH}} }}{{\dot{m}_{10} }} = h_{10} - h_{11} = \frac{{P_{10} - P_{11} }}{{\rho_{{10_{\text{SW}} }} \cdot \eta_{\text{TH}} }}$$
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Entropy in point 11 is expressed as:
$$h_{11} = h_{10} + \frac{{P_{10} - P_{11} }}{{\rho_{{10_{\text{SW}} }} \cdot \eta_{\text{TH}} }}$$
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The reversible work of hydraulic turbine in steady state is given as:
$$w_{\text{r,TH}} = w_{\text{TH}} - T_{0} \cdot (S_{10} - S_{11} )$$
Reverse osmosis unit:
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The first law of thermodynamics in steady state for the volume control of liquid water contained between sections 8, 9 and 10 of the unit reverse osmosis is expressed as
$$h_{8} = r_{1} \cdot h_{9} + r_{2} \cdot h_{10}$$
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The reversible work of the reverse osmosis unit in steady state is given as:
$$w_{\text{r,RO}} = - T_{0} \cdot (S_{8} - r_{1} \cdot S_{9} - r_{2} \cdot S_{10} )$$
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The global efficiency of the reverse osmosis system is:
$$\begin{aligned} \eta &= - \frac{{W_{\text{net}} }}{{q_{\text{in}} }} \cdot 100 \hfill \\ W_{\text{net}} &= W_{\text{TV,real}} + W_{\text{Pm1,real}} + \frac{1}{{r_{3} }} \cdot \left( {r_{2} \cdot W_{\text{TH,real}} + W_{\text{Pm2,real}} + W_{\text{Pm3,real}} } \right) \hfill \\ \end{aligned}$$
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The variation in efficiency versus flow mass rate (Fig. 8) has the same shape, by taking pressure for all, and the heat energy constant in each one, with a little growth in the beginning, and then it becomes constant, because of the limitation of the efficiency of system. The green, red and blue curves have maximum efficiencies of 44.76%, 30.18% and 8.308%, respectively.
Figure 9 describes the efficiency versus pressure by fixing the thermal heat of evaporator \(q_{\text{in}}\) in each curve and mass flow rate for all. They have a minimum and maximum extremity of variation. The green curve rises from 31.29 to 96.49%, red one from 20.39 to 92.26% and the blue one from 0.18 to 85.91%.
The efficiency \(\eta\) of system increases exponentially with thermal heat \(q_{\text{in}}\) of evaporator, see Fig. 10. The green curve increases from 1.87 to 89.58%, red one from 4.07 to 74.36% and the blue from 3.02 to 51.65%, as it is observed that the forms of all curves have the same shape, because of linearity of equation system.
In the latter case (system # 2), Fig. 11, the two subsystems are connected mechanically and thermally. Recovering the power unit is again a hydraulic turbine.
The heat exchanger (evaporator) effectiveness ε is a function of flow mass rate \(\dot{M}\) (kg/s) with four thermal heat constants \(q_{\text{in}}\) (kJ/kg) from 950 to 1250 kJ/kg. The four curves have the same exponential shape and distance between the them, because of linearity of the problem. The efficiency of red curve increases from 0 to 22%, the cyan from 11 to 31%, the brown from 21 to 40% and the green from 31 to 48% as shown in Fig. 12. The efficiency in Fig. 13 increases from 20 to 90% for the four curves, with different mass flow rates.
MED system model
We have worked in this paper just on the vacuum system, because it plays a key role in the regulation of the pressure in the evaporator; this improvement will be useful for the MED system (Fig. 14).
Using the results obtained from this case study, one can see that for a jet vacuum pump (Fig. 15), with liquid for creating a vacuum to a volume of 1.571 m3, a water pump is required along with a flow rate of 24 m3/h and a head of 52.23 m.
Change in the parameters has shown a lower vacuum pump (and therefore less than volume flow) will produce smaller heads and consequently you will certainly need lower vacuum pump. It means the size of required vacuum will play an essential role in selecting a vacuum pump. The selection of a vacuum pump for a certain vacuum size may be made from the datasheets provided from the manufacturer of the vacuum pump. One more observation which can be made is that the requisite head shall be smaller for the pump if the losses from domestic water are minimized.
The interface developed will give the ability of the control of all parameters required in the seizing of the vacuum system as shown in Fig. 15. The results which have been obtained from the EES program (Oulhazzan et al. 2016) can be used to choose correctly for water pump a specific liquid jet vacuum pump. It can be realized because the head (the height of the fluid to be pumped) and the volumetric flow to obtain the required vacuum have become known. Additional information for the jet vacuum pump liquid and the necessary time to achieve the required vacuum can be found in datasheet from the manufacturer of the liquid jet system of the vacuum pump. This information could then be combined together to develop a complete vacuum system for the evaporator of a desalination plant (Klein et al. 1992; Aroussy et al. 2016c, d).
Figure 16 presents the total height (H) that has to be pumped by the water system, in function of pressure entering the heater. The variations in curves are linear, just with a little curvature in the beginning; all calculus is made for different mechanical losses caused by valves and elbows in the auxiliary system. Also the volume of vacuum vessel increases significantly with the diameter for such values of lengths in Fig. 17.
By changing the input parameters, different comments may be made. For example, when the temperature of the steam is enhanced, it causes a greater overall coefficient of the heat transfer. It means that one smaller evaporator shall be required because a lower heat transfer area is necessary. A further observation which can be done is the mass flow of the saltwater is reduced; the overall coefficient of heat transfer also increases. This means that less of the product (freshwater) will be produced in a certain time (Fig. 18).