Economic evaluation of reverse osmosis desalination system coupled with tidal energy

Abstract

A reverse osmosis (RO) desalination system coupled with tidal energy is proposed. The mechanical energy produced by the tidal energy through hydraulic turbine is directly used to drive the RO unit. The system performances and the water cost of the conventional and tidal energy RO systems are compared. It is found that the proposed tidal energy RO system can save water cost in the range of 31.0%-41.7% in comparison with the conventional RO system. There is an optimum feed pressure that leads to the lowest water cost. The tidal RO system can save more costs at a high feed pressure or a high water recovery rate. The optimum feed pressure of the tidal energy RO system is higher than that of the conventional RO system. The longer lifetime of the tidal energy RO system can save even more water cost. When the site development cost rate is lower than 40%, the water cost of the tidal energy RO system will be lower than that of the conventional RO system. The proposed technology will be an effective alternative desalination method in the future.

Keywords

reverse osmosis (RO) desalination / tidal energy / model / economic evaluation

Introduction

Water is abundant, which covers three quarters of the earth’s surface. However, only about 3% of water sources are potable and about 25% of world’s population does not have access to water with satisfactory quality. According to the World Watch Institute, more than two-thirds of the world’s population may experience water shortages by 2025. Desalination may represent the major solution when facing the future problem. Desalination methods can be classified as phase change processes (two-phase methods) and membrane processes (single-phase methods). In the last several years, the seawater reverse osmosis (SWRO) desalination has gained much popularity. The present paper focuses on the SWRO desalination method. The reverse osmosis (RO) seawater desalination method has had a remarkable development and the number and capacity of large RO plants have increased significantly. Systems with a permeate capacity of up to 300000 m³/dare currently being built [¹] and the unit water cost has decreased to a reasonable level.

To further decrease the unit water cost or improve the RO process, the methods adopted include enhancing the efficient of the equipment used in the RO process [²], improving the operating conditions [³], and using hybrid systems. To model the RO process, numerous analytical models have been developed to describe the transport phenomenon across the RO membrane [⁴,⁵], and process optimizations have also been conducted. For example, Marcovecchio et al. [⁶] have proposed an iterative resolution method for the optimization of the total annual cost of either one-stage or two-stage hollow fiber pressure vessel (PV) configurations. Lu et al. [⁷] have presented an optimization of spiral-wound PV process configurations. Vince et al. [³] have developed a process optimization method for the design of RO processes. Malek et al. [⁸] have presented a parametric analysis on the water cost. Oh et al. [⁹] have presented a model based on the solution-diffusion theory and multiple fouling mechanisms to analyze the performance of RO systems.

For hybrid systems, Bouhelal et al. [¹⁰] have presented a RO system coupled with a combined cycle power plant. Nisana and Benzartib [¹¹] have put forward an economic model to analyze the environmental, power and desalination costs for fossil fuel based seawater desalination system. Kosmadakis et al. [¹²] have proposed an economic evaluation of a two-stage solar organic Rankine cycle for using the mechanical energy to drive a RO system. Khalifa [¹³] has found that the renewable energy such as wind and solar as the only source for RO system would increase the water cost. Iaquaniello et al. [¹⁴] have developed an alternative scheme by a proper integration of CSP with multi-effect distillation (MED) and RO desalination processes. The MED is powered by the low temperature exhaust steam delivered from the back pressure steam turbine, while the RO is powered by the electricity produced by the same steam turbine in addition to that generated by the conventional gas turbine integrated as a thermal backup system. Loutatidou and Arafat [¹⁵] have found that geothermal RO could potentially be a more cost-effective option for seawater geothermal desalination. Caldera et al. [¹⁶] have demonstrated RO desalination plants powered solely through renewable energy.

This paper presents a new hybrid RO system that is coupled with tidal energy. The mechanical energy produced by the tidal energy through hydraulic turbine is directly used to drive the RO system. The optimization of the coupling system and the water cost analysis are performed.

RO process synthesis

The key feature of the developed RO system is that it is directly driven by the mechanical energy produced by the tidal energy through hydraulic turbine as shown in Fig. 1. External power and motors are not needed for driving the system, which is the main reason that the tidal energy RO system has a lower water product cost. The tidal output has varying effects on the operating pressure of the RO system. Hence, a pressure stabilizer is used to stable the pressure. The pressure stabilizer is set before the RO pressure vessels set, as shown in Fig.1.

RO element model

Figure 2 is the schematic diagram of a membrane unit with the variables. The two-parameter membrane model [³] is adopted according to membrane constructor practices.

The spiral-wound membranes are considered in the present model. The mass of salts in seawater is considered to be negligible in comparison with that of the water and the seawater density r is considered to be a constant at 1000 kg/m³. The product water flow rate, Q_p (m³/h); the salt flow rate, Q_s (m³/h); and the concentration, C_p (kg/m³) are predicted as follows:

(1){{\displaystyle Q}}_p=\mathrm{3.6}\times {\mathrm{10}}^{\mathrm{6}}AS(\Delta p-\Delta \pi )=\mathrm{3.6}\times {\mathrm{10}}^{\mathrm{6}}AS\left({\displaystyle \frac{{{\displaystyle p}}_{\mathrm{f}}+{{\displaystyle p}}_{\mathrm{B}}}{\mathrm{2}}}-{{\displaystyle p}}_{\mathrm{P}}-{\displaystyle \frac{{{\displaystyle \pi }}_{\mathrm{f}}+{{\displaystyle \pi }}_{\mathrm{B}}}{\mathrm{2}}}+{{\displaystyle \pi }}_{\mathrm{P}}\right),

(2){{\displaystyle Q}}_{\mathrm{s}}=\mathrm{1.0}\times {\mathrm{10}}^{\mathrm{6}}BS\Delta {{\displaystyle C}}_{\mathrm{s}}=\mathrm{1.0}\times {\mathrm{10}}^{-\mathrm{6}}BS\left({\displaystyle \frac{{{\displaystyle C}}_{\mathrm{f}}+{{\displaystyle C}}_{\mathrm{B}}}{\mathrm{2}}}-{{\displaystyle C}}_{\mathrm{P}}\right),

(3){{\displaystyle C}}_{\mathrm{P}}={\displaystyle \frac{B\Delta {{\displaystyle C}}_{\mathrm{s}}}{A(\Delta p-\Delta \pi )}},

(4){{\displaystyle p}}_{\mathrm{B}}={{\displaystyle p}}_{\mathrm{f}}-\mathrm{\delta }p,

where A (kg/(N·s)) is the membrane permeability for pure water, B (kg/(m²·s)) is the membrane permeability for salt, S (m²) is the module surface area, Dp (MPa) is the difference between trans-membrane pressures, and Dp (MPa) is the difference between trans-membrane osmotic pressures, which is defined by

(5)\pi ={\displaystyle \frac{\mathrm{2}RTC\times {\mathrm{10}}^{-\mathrm{6}}}{{{\displaystyle M}}_{\mathrm{N}\mathrm{a}\mathrm{C}\mathrm{l}}}}\cdot e^{\mathrm{0.7}\varphi },

where R is the universal gas constant, equal to 8.314 J/(mol·K); T(K) is the water temperature; and M_NaCl is the molar mass of NaCl, equal to 0.0585 kg/mol⁻¹. dp(MPa) in Eq. (4) is the pressure drop along the membrane channel and defined by [³]

(6)\mathrm{\delta }p=\mathrm{950}{{\displaystyle \left({\displaystyle \frac{{{\displaystyle Q}}_{\mathrm{f}}+{{\displaystyle Q}}_{\mathrm{B}}}{\mathrm{2}\times \mathrm{3600}}}\right)}}^{\mathrm{1.7}}.

The mass balance relationships for the membrane unit are given by

(7){{\displaystyle Q}}_{\mathrm{f}}={{\displaystyle Q}}_{\mathrm{p}}+{{\displaystyle Q}}_{\mathrm{B}},

(8){{\displaystyle Q}}_{\mathrm{f}}\times {{\displaystyle C}}_{\mathrm{f}}={{\displaystyle Q}}_{\mathrm{p}}\times {{\displaystyle C}}_{\mathrm{p}}+{{\displaystyle Q}}_{\mathrm{B}}\times {{\displaystyle C}}_{\mathrm{B}}.

The water recovery rate Φ is defined by

(9)\varphi ={\displaystyle \frac{{{\displaystyle Q}}_{\mathrm{p}}}{{{\displaystyle Q}}_{\mathrm{f}}}}.

The membrane salt rejection rate r is defined by

(10)r=\mathrm{1}-{\displaystyle \frac{{{\displaystyle C}}_{\mathrm{p}}}{{{\displaystyle C}}_{\mathrm{f}}}}.

Pressure vessels

A pressure vessel (PV) contains N_m membrane elements collected in series as depicted in Fig. 3. Each membrane element is defined by Eqs. (6)–(10). The PV recovery rate Φ_t is defined by

(11){{\displaystyle \varphi }}_t=\mathrm{1}-{\displaystyle \prod _{k=\mathrm{1}}^{{{\displaystyle N}}_{\mathrm{m}}}(\mathrm{1}-{{\displaystyle \varphi }}_k),}

where Φ_k is the water recovery rate for membrane k for k = 1, …, N_m. For k = 1, …, N_m– 1,the concentrate flow rate, salinity and pressure of membrane k are the feed water flow rate, salinity and pressure of membrane k+1:

(12){{\displaystyle Q}}_{\mathrm{f}}^{k+\mathrm{1}}={{\displaystyle Q}}_{\mathrm{f}}^k(\mathrm{1}-{{\displaystyle \varphi }}_k)\mathrm{f}\mathrm{o}\mathrm{r}k=\mathrm{1},\dots ,{{\displaystyle N}}_{\mathrm{m}}-\mathrm{1},

(13){{\displaystyle C}}_{\mathrm{f}}^{k+\mathrm{1}}={{\displaystyle C}}_{\mathrm{B}}^k\mathrm{f}\mathrm{o}\mathrm{r}k=\mathrm{1},\dots ,{{\displaystyle N}}_{\mathrm{m}}-\mathrm{1},

(14){{\displaystyle p}}_{\mathrm{f}}^{k+\mathrm{1}}={{\displaystyle p}}_{\mathrm{B}}^k\mathrm{f}\mathrm{o}\mathrm{r}k=\mathrm{1},\dots ,{{\displaystyle N}}_{\mathrm{m}}-\mathrm{1},

where {{\displaystyle Q}}_{\mathrm{f}}^{\mathrm{k}} is the feed water flow through membrane k, {{\displaystyle C}}_{\mathrm{f}}^{\mathrm{k}} and {{\displaystyle C}}_{\mathrm{B}}^{\mathrm{k}} are respectively the feed water and concentrate salts concentration of membrane k, and {{\displaystyle p}}_{\mathrm{f}}^{\mathrm{k}} and {{\displaystyle p}}_{\mathrm{B}}^{\mathrm{k}} are respectively the feed water and concentrate pressure of membrane k.

System model

In this paper, a single stage configuration with hydraulic turbine type energy recovery device is adopted as illustrated in Fig. 3. A RO plant contains N_p pressure vessels. The total feed flow rate (Q_f,t) and total product rate (Q_p,t) are

(15){{\displaystyle Q}}_{\mathrm{f},\mathrm{t}}={{\displaystyle N}}_{\mathrm{p}}{{\displaystyle Q}}_{\mathrm{f}}^{\mathrm{1}},

(16){{\displaystyle Q}}_{\mathrm{p},\mathrm{t}}={{\displaystyle N}}_{\mathrm{p}}{\displaystyle \sum _{k=\mathrm{1}}^{{{\displaystyle N}}_{\mathrm{m}}}{{\displaystyle Q}}_{\mathrm{p}}^k},

where {{\displaystyle Q}}_{\mathrm{p}}^k is the product water flow rate through membrane k.

Economic model

For a seawater plant, the working time of the tidal energy RO system lies in the tidal barrage design. The tidal energy RO system could work the whole day if double reservoir were designed. To increase the utilization of the system, it is assumed that the double reservoir is adopted. The cost evaluation method developed by Malek et al. [⁸] is adopted to analyze the conventional and tidal energy RO systems. The functions are listed as follows.

Total capital charge

The capital cost of the intake and pretreatment systems is a function of the total feed flow rate expressed as

(17){{\displaystyle CC}}_{\mathrm{i}\mathrm{n}}=\mathrm{600}\times {({{\displaystyle Q}}_{\mathrm{f},\mathrm{t}}\times \mathrm{24})}^{\mathrm{0.8}}.

The operating cost of the seawater intake system of the conventional RO system is taken as the operating cost of the intake pumps. The cost function is given by

(18){{\displaystyle OC}}_{\mathrm{i}\mathrm{n}}=(\Delta {{\displaystyle p}}_{\mathrm{i}\mathrm{n}}\times {{\displaystyle Q}}_{\mathrm{f},\mathrm{t}}\times {{\displaystyle C}}_{\mathrm{e}}\times \mathrm{24}\times \mathrm{365}\times F)/(\mathrm{3.6}\times {{\displaystyle \eta }}_{\mathrm{i}\mathrm{n}}),

where F is the plant load factor, C_e is the electricity cost, and \mathrm{\Delta }{p}_{\mathrm{i}\mathrm{n}} is the difference between the intake pumps. The outlet pressure is assumed to be 0.5 MPa.

For the high pressure pumps of the conventional RO system, the power law cost model is adopted. For the tidal energy RO system, it is very difficult to characterize the capital cost of the pressure device. It is assumed that the capital cost of the pressure device is equal to that of high pressure pumps of the conventional RO system. Hence, the cost function is defined by

(19){{\displaystyle CC}}_{\mathrm{H}\mathrm{p}\mathrm{p}}={{\displaystyle CC}}_{\mathrm{p}\mathrm{d}}=\mathrm{81}\times {(\Delta {{\displaystyle p}}_{\mathrm{f}}\times {{\displaystyle Q}}_{\mathrm{f},\mathrm{t}})}^{\mathrm{0.96}},

where \mathrm{\Delta }{p}_{\mathrm{f}} is the difference between feed water pressures.

A hydraulic turbine is used to output shaft work and drive the pressure device of the tidal energy RO system. The capital cost is calculated by

(20){{\displaystyle CC}}_{\mathrm{T}\mathrm{B},\mathrm{i}\mathrm{n}}=\mathrm{52}\times (\Delta {{\displaystyle p}}_{\mathrm{f}}\times {{\displaystyle Q}}_{\mathrm{f},\mathrm{t}}\times \mathrm{10}/{{\displaystyle \eta }}_{\mathrm{T}\mathrm{b}}).

The operating costs of the high pressure pump and high pressure device are related to the energy requirement. For the high pressure device, the operating energy is the shaft work supplied by the hydraulic turbine, which is driven by tidal energy. Hence, there is no power consumption. For the high pressure pump of the conventional RO system, the required power is given by

(21){{\displaystyle OC}}_{\mathrm{H}\mathrm{p}\mathrm{p}}=(\Delta {{\displaystyle p}}_{\mathrm{H}\mathrm{p}\mathrm{p}}\times {{\displaystyle Q}}_{\mathrm{f},\mathrm{t}}\times {{\displaystyle C}}_{\mathrm{e}}\times \mathrm{24}\times \mathrm{365}\times F)/(\mathrm{3.6}\times {{\displaystyle \eta }}_{\mathrm{H}\mathrm{p}\mathrm{p}}).

Another hydraulic turbine is used for energy recovery. The capital cost and the operating cost are given by

(22){{\displaystyle CC}}_{\mathrm{T}\mathrm{b},\mathrm{e}\mathrm{n}\mathrm{r}}=\mathrm{52}\times (\Delta {{\displaystyle p}}_{\mathrm{T}\mathrm{b}}\times {{\displaystyle Q}}_{\mathrm{T}\mathrm{b}}\times \mathrm{10}),

(23){{\displaystyle OC}}_{\mathrm{T}\mathrm{b},\mathrm{e}\mathrm{n}\mathrm{r}}=(\Delta {{\displaystyle p}}_{\mathrm{T}\mathrm{b},\mathrm{e}\mathrm{n}\mathrm{r}}\times {{\displaystyle Q}}_{\mathrm{T}\mathrm{b},\mathrm{e}\mathrm{n}\mathrm{r}}\times {{\displaystyle C}}_{\mathrm{e}}\times \mathrm{24}\times \mathrm{365}\times F\times {{\displaystyle \eta }}_{\mathrm{T}\mathrm{b}})/\mathrm{3.6.}

The capital cost of the membrane modules is defined by

(24){{\displaystyle CC}}_{\mathrm{m}}={{\displaystyle C}}_{\mathrm{m}}\times S\times {{\displaystyle N}}_{\mathrm{p}}\times {{\displaystyle N}}_{\mathrm{m}},

where C_m is the base price of the membrane.

The operating cost of the membrane modules containing cleaning and replacing scheduling is given by

(25){{\displaystyle OC}}_{\mathrm{m}}={{\displaystyle p}}_{\mathrm{m}}\times {{\displaystyle \mathrm{C}\mathrm{C}}}_{\mathrm{m}},

where p_m is the membrane replacement rate.

The unit product water cost of the tidal energy RO system is compared with that of the conventional RO system. The unit product water cost is calculated as follows.

The capital cost for plant equipment of the conventional RO system (CC_equip,cr) and of the tidal energy RO system (CC_equip,tr) are

(26){{\displaystyle \mathrm{C}\mathrm{C}}}_{\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{p}\mathrm{,}\mathrm{c}\mathrm{r}}={{\displaystyle \mathrm{C}\mathrm{C}}}_{\mathrm{i}\mathrm{n}}+{{\displaystyle \mathrm{C}\mathrm{C}}}_{\mathrm{H}\mathrm{p}\mathrm{p}}+{{\displaystyle CC}}_{\mathrm{T}\mathrm{b},\mathrm{e}\mathrm{n}\mathrm{r}}+{{\displaystyle \mathrm{C}\mathrm{C}}}_{\mathrm{m}},

(27){{\displaystyle \mathrm{C}\mathrm{C}}}_{\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{p},\mathrm{t}\mathrm{r}}={{\displaystyle \mathrm{C}\mathrm{C}}}_{\mathrm{i}\mathrm{n}}+{{\displaystyle \mathrm{C}\mathrm{C}}}_{\mathrm{p}\mathrm{d}}+{{\displaystyle \mathrm{C}\mathrm{C}}}_{\mathrm{T}\mathrm{b},\mathrm{i}\mathrm{n}}+{{\displaystyle \mathrm{C}\mathrm{C}}}_{\mathrm{T}\mathrm{b},\mathrm{e}\mathrm{n}\mathrm{r}}+{{\displaystyle \mathrm{C}\mathrm{C}}}_{\mathrm{m}}.

It can be seen that one more hydraulic turbine is needed for the tidal energy RO system in comparison with the conventional RO system.

The total capital cost (TCC) is composed of the direct capital cost (DCC) and the indirect capital cost (ICC). The direct capital cost is the sum of the cost for plant equipment (CC_equip) and the cost for site development (CC_site), which is set to be 10% of DCC for the conventional RO system. The cost of the site development for the tidal energy RO system is very different from that of the conventional RO system. For comparison, a variable cost rate of the site development is denoted by x of DCC and will be investigated in the cost studies conducted. The indirect capital cost (ICC) is set at 27% of the direct capital cost (DCC). Hence, the total capital cost for the conventional RO systems is given by

(28){{\displaystyle \mathrm{T}\mathrm{C}\mathrm{C}}}_{\mathrm{c}\mathrm{r}}=\mathrm{1.411}{{\displaystyle \mathrm{C}\mathrm{C}}}_{\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{p},\mathrm{o}\mathrm{r}}.

For comparison, the total capital cost for the tidal energy RO systems is given by

(29){{\displaystyle \mathrm{T}\mathrm{C}\mathrm{C}}}_{\mathrm{t}\mathrm{r}}={\displaystyle \frac{\mathrm{1.27}}{\mathrm{0.9}-x}}{{\displaystyle \mathrm{C}\mathrm{C}}}_{\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{p},\mathrm{t}\mathrm{r}}.

Annual operating cost and unit product water cost

The annual operating cost (AOC) is composed of the annual capital charge (ACC), the annual energy cost (AEC) and the labor, O&M, chemicals, filters, and miscellaneous (LOMC).

The annual capital charge (ACC) is calculated by [⁶]

(30)\mathrm{A}\mathrm{C}\mathrm{C}=\mathrm{T}\mathrm{C}\mathrm{C}\cdot {\displaystyle \frac{i\cdot {(\mathrm{1}+i)}^n}{{(\mathrm{1}+i)}^n-\mathrm{1}}},

where i is interest rate, and n is plant life.

The annual energy cost (AEC) is given by

(31){{\displaystyle \mathrm{A}\mathrm{E}\mathrm{C}}}_{\mathrm{c}\mathrm{r}}={{\displaystyle \mathrm{O}\mathrm{C}}}_{\mathrm{i}\mathrm{n}}+{{\displaystyle \mathrm{O}\mathrm{C}}}_{\mathrm{H}\mathrm{p}\mathrm{p}}+{{\displaystyle \mathrm{O}\mathrm{C}}}_{\mathrm{m}}-{{\displaystyle \mathrm{O}\mathrm{C}}}_{\mathrm{T}\mathrm{b},\mathrm{e}\mathrm{n}\mathrm{r},}

(32){{\displaystyle \mathrm{A}\mathrm{E}\mathrm{C}}}_{\mathrm{t}\mathrm{r}}={{\displaystyle \mathrm{O}\mathrm{C}}}_{\mathrm{m}}-{{\displaystyle \mathrm{O}\mathrm{C}}}_{\mathrm{T}\mathrm{b},\mathrm{e}\mathrm{n}\mathrm{r}}.

For the conventional RO system, LOMC_cr = 12% of AOC. The annual operating costs of the conventional RO system and the tidal energy system are respectively given by

(33){{\displaystyle \mathrm{A}\mathrm{O}\mathrm{C}}}_{\mathrm{c}\mathrm{r}}=\mathrm{1.136}({{\displaystyle \mathrm{A}\mathrm{C}\mathrm{C}}}_{\mathrm{c}\mathrm{r}}+{{\displaystyle \mathrm{A}\mathrm{E}\mathrm{C}}}_{\mathrm{c}\mathrm{r}}),

(34){{\displaystyle \mathrm{A}\mathrm{O}\mathrm{C}}}_{\mathrm{t}\mathrm{r}}=\mathrm{1.136}({{\displaystyle \mathrm{A}\mathrm{C}\mathrm{C}}}_{\mathrm{t}\mathrm{r}}+{{\displaystyle \mathrm{A}\mathrm{E}\mathrm{C}}}_{\mathrm{t}\mathrm{r}}).

The unit product water cost is calculated by

(35){{\displaystyle C}}_{\mathrm{p}\mathrm{w}}={\displaystyle \frac{\mathrm{A}\mathrm{O}\mathrm{C}}{{{\displaystyle Q}}_{\mathrm{p},\mathrm{t}}\cdot \mathrm{365}\cdot F}}.

Economic and plant data

In the present work, the following economic parameters are used:

The total product water rate, Q_f,t = 125 m³/h; the plant life, n = 15 year; the interest rate, i = 8% per year; the plant load factor, F = 0.85; the electricity cost, C_e = US $0.1·kWh; and the membrane replacement rate, P_m = 0.1 a⁻¹.

The large area and high rejection FilmTec SW30HR-380 membrane element is adopted. The performance and operating parameters of the membrane element are listed in Table 1. The other parameters for calculation are listed in Table 2.

The feed pressure, p_f; the recovery rate, {{\displaystyle \varphi }}_t; and the site development cost rate of the tidal energy RO system, x are varied to determine their effects on the unit product water cost.

Results and discussion

Figure 4 shows the unit product water costs for the two RO systems with different recovery rates at p_f = 7.2MPa and x = 10%. It can be seen that the product water costs for the two RO systems decrease with increasing water recovery rate. The most important fact is that the unit product water costs for the tidal energy RO system is significantly lower than those for the conventional RO system. The unit product cost for the tidal energy RO system is saved in the order of 36.8%–40.5% in comparison with the conventional RO system, and the tidal RO system can save more costs at high water recovery rate.

Figure 5 shows the unit product water costs for the two RO systems with different feed pressures at {{\displaystyle \varphi }}_t= 0.4 and x = 10%. It can be seen that the tidal energy RO system has much lower cost than the conventional RO system, which is the same as the above result. The unit product cost for the tidal energy RO system is saved in the range of 31.0%–41.7% in comparison with the conventional RO system, and the tidal RO system can save more costs at high feed pressure. Furthermore, the water cost shows an optimum value as a function of feed pressure. The optimum feed pressures are 5.6 MPa and 5.3 MPa for the tidal energy RO system and the conventional RO system, respectively. Obviously, the optimum feed pressure is different at different recovery rates. For example, when {{\displaystyle \varphi }}_t=0.35, 0.4 and 0.45, the optimum feed pressure of the tidal energy RO system is 5.3 MPa, 5.6 MPa and 5.9 MPa, respectively while the optimum feed pressure of the conventional RO system is 5.0 MPa, 5.3 MPa and 5.6 MPa, respectively (see Fig. 6). From the above results, it can be observed that the optimum feed pressure of the tidal energy RO system is somewhat higher than that of the conventional RO system.

The above discussions indicate that the tidal energy RO system has a lower unit water cost in comparison with the conventional RO system, which is different from the other renewable energy using in the RO system [¹³]. The main reason is that the tidal energy RO system does not consume power energy. However, the tidal energy RO system contains a hydraulic turbine, which is not needed in the conventional RO system. Hence, it can be concluded that the longer plant lifetime maybe benefit to save the unit water cost since the utilization rate of the equipment increases. Figure 7 demonstrates the cost saving rate, s, for different plant lifetimes. It can be seen that the tidal energy RO system can save more water cost with a longer lifetime, which validates the above result. Furthermore, as the feed pressure increases, more water product cost can be saved. The cost saving rate, s, is defined by

(36)s={\displaystyle \frac{{{\displaystyle C}}_{\mathrm{p}\mathrm{w},\mathrm{c}\mathrm{r}}-{{\displaystyle C}}_{\mathrm{p}\mathrm{w},\mathrm{t}\mathrm{r}}}{{{\displaystyle C}}_{\mathrm{p}\mathrm{w},\mathrm{c}\mathrm{r}}}}.

Figure 8 depicts the water cost with recovery rate and the site development cost rate of the tidal energy RO system. It can be seen that the water cost increases with increasing site development cost rate. When the site development cost rate is about 40%, the water cost of the tidal energy RO system is almost the same as that of the conventional RO system. Hence, the site development cost rate needs to be controlled to less than 40%, so that the water cost of the tidal energy RO system will be less than that of the conventional RO system. And as the site development cost rate decreases, the cost saving increases. There are three methods to control the cost: choose an appropriate bay as a reservoir so that the barrage is easier to be built, the reservoir can be used for seafood farm, and the barrage can be used for transportation.

It should be noted that some seafood farms can be used as tidal reservoirs or the tidal barrage can be used for seafood. Furthermore, if there are some needs for comprehensive utilization, the tidal energy RO system can be made as a secondary system of an originaltidal power plant. Meanwhile, the site development cost will be very low. Hence, the water cost can further decrease. In addition, the utilization rate of the tidal energy RO system will decrease if the system cannot be used the whole day, and the unit water product cost will increase. To enhance the utilization rate of the tidal energy RO system, commercial power can be used for driving the RO system when the tidal energy is not available. Hence, the above cost analyses still validate the lower water product cost of the tidal energy RO system.

Conclusions

A RO desalination system coupled with tidal energy was proposed. The mechanical energy produced by the tidal through hydraulic turbine was directly used to drive the RO system. The parameters that affect the performance and the water costs of the conventional and tidal energy RO systems were analyzed. The main conclusions are summarized as follows.

In comparison with the conventional RO system, the tidal energy RO system can save water cost in the range of 31.0%–41.7%.

There is an optimum feed pressure that leads to the lowest water cost. The tidal RO system can save more cost at a high feed pressure or a high water recovery rate. The optimum feed pressure of the tidal energy RO system is higher than that of the conventional RO system.

The longer lifetime of the tidal energy RO system can save more water cost.

The water cost increases with increasing site development cost rate. When the site development cost rate is larger than 40%, the water cost of the tidal energy RO system is higher than that of the conventional RO system.

Considering the fact that the tidal energy RO system can be combined with other industries, such as seafood, the water cost can further decrease. Hence, the hybrid system of tidal energy RO desalination is promising for seawater desalination in the future.

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