Energy efficiency of RO and FO–RO system for high-salinity seawater treatment

Abstract

Forward osmosis (FO) has been proposed as an alternative method for seawater desalination, wherein reverse osmosis (RO) membrane technology is used for regeneration of the draw solution. Previous studies have indicated that a standalone RO unit is more energy efficient than an FO–RO system, and as such it was recommended that an FO–RO system is best employed only for the desalination of high-salinity seawaters. This study examined FO–RO applicability in more detail by examining the impact of seawater salinity, impact of an energy recovery device (ERD), and the effect of membrane fouling. For comparison purposes, the performance of the FO process was improved to minimize the impact of concentration polarization and optimize the concentration of draw solution. Model calculations revealed that FO–RO is more energy efficient than RO when no ERD was employed. However, results showed that there was no significant difference in the power consumption between the FO–RO system and the RO unit at high seawater salinities particularly when a high-efficiency ERD was installed. Moreover, the FO–RO system required more membrane area than a conventional RO unit which may further compromise the FO–RO desalination cost.

Appendices

Appendix 1: Optimization of FO performance

FO optimization was performed to reduce the energy requirements of the FO–RO system. Calculation was carried out at 35 g/L seawater salinity and 46 % recovery rate using NaCl draw solution. We assumed that Q _p was equal in both the FO and RO membranes and Q _Di was 1000 L/h (Table 3); permeate flow rate of the RO step in the FO–RO system was given as

$$\% \text{Re} = 0.46 = \frac{{Q_{\text{p}} }}{{Q_{\text{Di}} + Q_{\text{p}} }} = \frac{{Q_{p} }}{{1000\,{\text{L}}/{\text{h}} + Q_{\text{p}} }}\quad Q_{\text{p}} = 851\,{\text{L/h}}.$$

Membrane flux, J _w, was calculated from the following equation assuming that FO membrane area was 250 m² (Table 3):

$$J_{\text{w}} = \frac{{851\,{\text{L/h}}}}{{250\,{\text{m}}^{2} }} = 3.4\,{\text{L}}/{\text{m}}^{2} \,{\text{h}}.$$

The permeate TDS was calculated from Eq. 22 and using B value from Table 1 as follows:

$$C_{\text{p}} = \frac{{0.12\,{\text{kg}}/{\text{m}}^{2} \,{\text{h}} \times 35000\,{\text{mg}}/{\text{kg}}}}{{0.34\,{\text{L}}/{\text{m}}^{2} \,{\text{h}} + 0.12\,{\text{kg}}/{\text{m}}^{2} \,{\text{h}}}} = 1208\,{\text{mg/kg}}.$$

The outlet concentration of Na, C _Nao, was calculated from Eq. 18; $\pi_{\text{Do}} (\pi_{\text{Do}} = \pi_{\text{Fi}} + 2)$ was 28.2 bar (Table 3) and C _Clo = 1.54 × C _Nao:

$$\begin{aligned} & \pi_{\text{Do}} = \frac{{C_{\text{Nao}} \times 1.12 \times T}}{{M_{\text{Na}} \times 14.5}} + \frac{{\left({\frac{{M_{\text{Cl}} }}{{M_{\text{Na}} }}} \right) \times C_{\text{Nao}} \times 1.12 \times T}}{{M_{\text{Cl}} \times 14.5}} \\ & 28.2\,{\text{bar}} = \frac{{C_{\text{Nao}} \times 1.12 \times (273 + 30)}}{{23 \times 10^{3} \times 14.5}} \\&\quad\quad\qquad + \frac{{1.54 \times C_{\text{Nao}} \times 1.12 \times (273 + 30)}}{{35.45 \times 10^{3} \times 14.5}} \\ & C_{\text{Nao}} = 13864\,{\text{mg/L}}. \\ \end{aligned}$$

The outlet concentration of Cl, C _Clo, was calculated from the following equation:

$$C_{\text{Clo}} = 1.54 \times 13864 = 21369\,{\text{mg/L}}.$$

The outlet concentration of NaCl draw solution is 35,233 mg/L. Inlet concentration of the draw solution was calculated from mass balance (Fig. 3) using Eq. 21:

$$\begin{aligned} C_{\text{Di}} & = \frac{{(C_{\text{Do}} \times Q_{\text{Do}} ) - (Q_{\text{p}} \times C_{\text{p}} )}}{{Q_{\text{Di}} }} \\ & = \frac{(1851 \times 35234) - (851 \times 1208)}{1000} = 64190\,{\text{mg/L}}. \\ \end{aligned}$$

The inlet concentrations of Na⁺ and Cl⁻, C _Nai and C _Cli, respectively, were

$$\begin{aligned} & C_{\text{Nai}} = 64190 \times \frac{23}{58.45} = 25259\,{\text{mg/L}} \\ & C_{\text{Cli}} = 64190 \times \frac{35.45}{58.45} = 38931\,{\text{mg/L}}. \\ \end{aligned}$$

The inlet osmotic pressure of draw solution, $\pi_{\text{Di}} ,$ was calculated from C _Nai and C _Cli as follows:

$$\begin{aligned} \pi_{\text{Di}} & = \frac{25663 \times 1.12 \times (273 + 30)}{{23 \times 10^{3} \times 14.5}} + \frac{38931 \times 1.12 \times (273 + 30)}{{35.45 \times 10^{3} \times 14.5}} \\ & = 51.4\,{\text{bar}}. \\ \end{aligned}$$

The bulk osmotic pressure of draw solution, $\pi_{\text{Db}} ,$ was (51.4 + 28.2)/2 = 39.8 bar. The bulk osmotic pressure of the feed solution, $\pi_{\text{Fb}} ,$ was calculated from Eq. 23 as follows:

$$\begin{aligned} & \pi_{\text{Fb}} = \frac{{\pi_{\text{Db}} \times {\text{e}}^{{\frac{{ - J_{\text{w}} }}{k}}} - \left[ {\left( {1 + \frac{B}{{J_{\text{w}} }}\left( {{\text{e}}^{{J_{\text{w}} K}} - {\text{e}}^{{\frac{{ - J_{\text{w}} }}{k}}} } \right)} \right) \times \frac{{J_{\text{w}} }}{{A_{\text{w}} }}} \right]}}{{e^{{J_{w} K}} }} \\ & \pi_{\text{Fb}} = \frac{{39.8 \times 0.989 - \left[ {\left( {1 + \left( {\frac{0.12}{3.4}} \right) \times (1.08 - 0.989)} \right) \times \frac{3.4}{0.79}} \right]}}{1.08}\\&\quad = 32.4\,{\text{bar}}. \\ \end{aligned}$$

The outlet osmotic pressure of feed solution, $\pi_{\text{Fo}} ,$ was calculated from Eq. 24:

$$\pi_{\text{Fo}} = \pi_{\text{Fb}} \times 2 - \pi_{\text{Fi}} = (32.4 \times 2) - 26.2 = 38.6\,{\text{bar}}.$$

FO recovery rate was calculated from Eq. 27 as follows:

$$\text{Re} = 1 - \frac{{\pi_{\text{Fi}} }}{{\pi_{\text{Fo}} }} = 1 - \frac{26.2}{38.6} = 0.32\,\%.$$

The feed flow rate was calculated from Eq. 28:

$$Q_{\text{Fi}} = \frac{{Q_{\text{p}} }}{\text{Re}} = \frac{851}{0.32} = 2656\,{\text{L/h}}.$$

Appendix 2: Water flux decline in RO

Annual decline in membrane flux was calculated from Eq. 2, assuming 8 and 3 % annual flux decline in the conventional RO and the RO step in the FO–RO system, respectively. For the FO–RO system operating at 46 % recovery rate and 3 % annual flux decline, the initial water flux was 6.19 L/m² h. Water flux in year 1 was calculated as follows (Fig. 8):

$$J_{\text{n}} = J_{\text{o}} - (Y_{n} \cdot J_{0} ) = 6.19 - (6.19 \times 0.3) = 6\,{\text{L}}/{\text{m}}^{2} {\text{h}}.$$

Fig. 8

Membrane flux in the RO step in the FO–RO system at 35 g/L feed salinity