A free-piston batch reverse osmosis (RO) system for brackish water desalination

Batch RO is designed to achieve high energy efficiency and high recovery in desalination. However, so far relatively few experiments on batch RO have been reported. Here we present an extensive experimental study of a single-acting, free-piston batch RO system using an 8-inch spiral wound membrane. The system was tested in the laboratory with brackish feed water containing up to 5 g/L NaCl. The objective was to quantify system performance in terms of Specific Energy Consumption (SEC), recovery, rejection, and output. Sensitivity to permeate flux and recirculation flow rate was also investigated. Performance was compared against the predictions of a theoretical model that accounts for salt retention, concentration polarization, and longitudinal concentration gradient in the RO module. For the first time, osmotic backflow was measured and incorporated into the model. For feed concentrations ranging from 1 to 5 g/L and recovery of 0.8, hydraulic SEC was measured in the range 0.22 – 0.48 kWh/m 3 and electrical SEC in the range 0.48 – 0.83 kWh/m 3 . With improvements to the membrane permeability from 4.4 to 8 LMH/bar, selection of more efficient pumps, and reduction of valve friction losses, the model predicts that hydraulic SEC will be lowered to 0.14 – 0.39 kWh/m 3 .

Batch RO is designed to achieve high energy efficiency and high recovery in desalination.However, so far relatively few experiments on batch RO have been reported.Here we present an extensive experimental study of a single-acting, free-piston batch RO system using an 8-inch spiral wound membrane.The system was tested in the laboratory with brackish feed water containing up to 5 g/L NaCl.The objective was to quantify system performance in terms of Specific Energy Consumption (SEC), recovery, rejection, and output.Sensitivity to permeate flux and recirculation flow rate was also investigated.Performance was compared against the predictions of a theoretical model that accounts for salt retention, concentration polarization, and longitudinal concentration gradient in the RO module.For the first time, osmotic backflow was measured and incorporated into the model.For feed concentrations ranging from 1 to 5 g/L and recovery of 0.8, hydraulic SEC was measured in the range 0.22-0.48kWh/m 3 and electrical SEC in the range 0.48-0.83kWh/m 3 .With improvements to the membrane permeability from 4.4 to 8 LMH/bar, selection of more efficient pumps, and reduction of valve friction losses, the model predicts that hydraulic SEC will be lowered to 0.14-0.39kWh/m 3 .

Introduction
Water scarcity has become a serious problem in many world regions and is expected to worsen with population growth, water pollution, improved standards of living, and rising demand from the industrial and agricultural sectors.To help address this issue, individual countries and regions are increasingly using desalination technologies.The two main categories of desalination technology are thermal and membrane-based systems.Thermal desalination methods, however, have high capital and operational costs and are energy-intensive [1].Thanks to advances in membrane science, membrane-based processesparticularly reverse osmosis (RO) -are the more promising and viable option today, enabling potable water production from various sources [2][3][4].Compared to thermal desalination, these processes are energy efficient, offering excellent prospects to help tackle the growing water crisis [2].
In recent years, the energy consumption of RO systems has steadily decreased thanks to enhancements in the fabrication of membranes with higher permeability and selectivity [5], improved pump efficiency, better energy recovery devices [6], and new feed spacer designs [7,8].Despite these improvements, RO desalination remains energy intensive compared to conventional potable water treatments such as coagulation and filtration [9].There is still potential to lower the SEC of desalination systems, to get closer to the thermodynamic minimum as represented by the following expression for the ideal Specific Energy Consumption (SEC ideal ) needed to desalinate a dilute feed solution [10]: where π feed is the osmotic pressure of the feed solution and r is recovery (0 ≤ r ≤ 1).For seawater with salinity 35 g/L and recovery of 50%, SEC ideal is thus calculated to be about 1 kWh/m 3 , while the most efficient state-of-the-art RO desalination plants can achieve real SEC just under twice this value [11].For brackish water systems, however, the gap between real and ideal efficiency is much greater, such that typically a tenfold reduction in SEC is theoretically possible [12,13].
Another drawback associated with RO desalination is depletion of groundwater and rejection of a high-salinity by-product (i.e.brine) that must be disposed of carefully.This means that RO systems having both low energy consumption and high recovery are desirable to overcome these limitations.Nevertheless, these two requirements conflict.Eq. (1) illustrates that SEC tends to increase with recovery and at an increasing rate.
This conflict has prompted researchers to investigate alternative system configurations to minimize SEC.Conventional single-stage RO configuration cannot achieve the ideal minimum SEC, because the applied feed pressure must overcome the osmotic pressure of the brine, which at high recovery, is several times above π feed [11].This problem can be mitigated by spatial or temporal separation [14].In spatial separation, the system is divided into multiple stages, each working at progressively higher pressure.In temporal separation, only one stage is employedbut the pressure varies with time to overcome the changing osmotic pressure of the water being desalinated [10,14,15].Timevarying pressure makes it possible, in theory, to achieve the theoretical minimum SEC ideal ; whereas multi-stage systems require an infinite number of stages to attain such ideal performance [14].Batch RO is a prominent example of a time-varying desalination system [10,[15][16][17][18].Batch RO operates in a cyclic manner, consisting of a pressurization (or permeate production) phase, during which the pressure increases, followed by purge (or flush) and refill (or recharge) phases.
Over the last decade, there have been several studies about batch RO.Two main types of design have been built and experimentally tested: one using a free piston and the other a bladder.Davies et al. [10] proposed and implemented a free-piston design and reported a hydraulic SEC of 0.31 kWh/m 3 for feed concentration of 5 g/L NaCl and r = 0.69.However, this SEC did not include the recirculation pump energy and included only the pressurization phase.In a more detailed theoretical study, a single-acting free-piston batch RO for brackish water treatment was designed, modelled, and optimized by the same group.Non-ideal correction factors -including salt retention, concentration polarization, and longitudinal concentration gradient -were identified and used in the calculation of SEC [19].To reduce the downtime of the batch system during refill, double-acting free-piston designs have also been proposed [15,20].
The bladder type of batch RO design has been studied by Wei et al. [17].These authors experimented with a bench top system and used the results to validate a numerical model which achieved 2.7% accuracy.The experiments included measurements of hydraulic work by both supply and recirculation pumps.Salt retention was also quantified, to show that salt retention decreases energy savings previously expected by researchers.Their experiments were limited to brackish water with operating pressures below 10 bar and recovery < 0.55.For example, at 3.5 g/L feed concentration, recovery of 0.52, and flux of 15 L/m 2 /h (LMH), hydraulic SEC was 0.28 kWh/m 3 .Model projections showed that, at higher recoveries, batch RO could save more energy.It was also predicted that with a seawater feed of 35 g/L salinity and recovery of 0.5, batch RO could save 11% energy compared to a single-stage continuous RO plant [17].
Apart from the examples above, the potential advantages of batch RO over its conventional rivals have been investigated mainly by modelling and design studies [15,16,[21][22][23][24][25], with relatively few detailed experimental studies reported [10,17].Therefore, in-depth experimental studies are needed to achieve a rigorous understanding of the process, and to identify optimal operating conditions that are critical for the practical implementation of the system.In this new study, an automated free-piston batch RO system, designed based on our previous study [19], has been experimentally investigated.The aim of the study is to achieve, using this system, energy-efficient desalination of brackish water at pilot scale with recovery of around 0.8.By measuring the hydraulic work of the pumps, we have measured the total SEC and used it to validate an updated model.Moreover, for the first time in the study of batch RO systems, electrical SEC is precisely measured for various salinities, water fluxes, and recirculation flow ratesthus giving a complete picture of system energy consumption and losses.Further, salt retention, rejection, and osmotic backflow are accurately quantified.Table 1 compares the current study against the two earlier experimental studies, showing that it achieves higher output and recovery, and that it examines a wider range of phenomena, than covered previously.With output more than 10 times greater than in previous studies, this pilot-scale system brings batch RO closer to the size needed in many practical applications.
The paper is structured as follows: Section 2 describes the design concept, while Section 3 presents the modified model.Section 4 describes the experimental equipment and procedure.Section 5 presents and discusses the results, including osmotic backflow, salt retention, salt rejection, validation of model predictions and experimental measurements regarding hydraulic and electrical SEC, average and peak pressure, and concentration vs time inside the recirculation loop.In Section 6, the model is used to predict the system's performance with improved membranes and pump efficiencies.Finally, the overall findings of this study are summarised in Section 7.

Batch RO design concept and operating principle
The concept of free-piston batch RO evolved from an earlier design in which the force to move the piston was provided by a mechanical linkage driven by a Rankine cycle [26,27].In the current design, the force is provided by pressurized water supplied from a motorized pump.This results in the concept of the free piston.Though various free-piston designs have been described [28], some of these are quite complex requiring numerous pumps and valves.In this study, the single-acting 2phase design has been chosen as it minimizes this complexity in the sense that it requires just two pumps (recirculation and supply pump) The recirculation pump is an important feature of batch RO, needed to homogenize the solution in the pressurized loop and reduce concentration polarization, thus reducing supply pump energy consumption [22].Nevertheless, the recirculation pump itself adds to the energy consumption of the batch RO system, thus raising the real SEC above the theoretical minimum of Eq. ( 1).This study looks in detail at the energy consumption and savings associated with the recirculation pump.
Of the three typical phases of the typical batch RO cycle (i.e.pressurization, purge, and refill), only the pressurization phase produces output of permeate.To compensate for the lost output during the other two phases, a larger operating flux is needed to achieve the same daily output as a conventional continuous desalination system.This incurs a penalty in SEC [24].In the single-acting 2-phase design, purge and refill phases occur simultaneously as one phase, thus achieving higher output and reduced penalty as the non-productive time is minimized.
The resulting two phases of the free-piston batch RO cycle are shown in Fig. 1.In the pressurization phase, the recirculation valve is open while the bypass and brine valves are closed.Initially, the free piston is at the left-hand end of the work exchanger vessel.The supply pump generates high pressure, which is transferred to the feed water inside the work exchanger via the free piston.Once the pressure exceeds the osmotic pressure of feed water, permeate exits the system, while brine flows back to the work exchanger via the recirculation pump, thus completing the batch RO loop.As more permeate exits, concentration inside the loop gradually rises.Therefore, the supply pump must apply higher pressure to overcome the increased osmotic pressure and maintain constant permeate flow rate.Pressurization finishes when the piston reaches the right end of the work exchanger.
At the end of the pressurization phase, the RO module contains concentrated brine.The purge-and-refill phase is now required to flush the brine from the system and refill the right compartment of the work exchanger.In this phase, the bypass and brine valves are open while the recirculation valve is closed.The recirculation pump transfers feed solution from the left to the right end of the work exchanger, displacing the piston from right to left.Simultaneously, the supply pump supplies feed solution (without applying high pressure) to purge the remaining brine inside the RO module and pipes via the brine valve.The direction of flow inside the RO module is reversed with respect to the pressurization phase, with the inlet now on the left.Typically, purging continues until the volume collected at the brine outlet equals the volume of brine contained inside the RO module [29].Once the brine is purged from the system, and the piston has moved back to the left, the brine and bypass valves are closed automatically and the recirculation valve is reopened, thus starting the next cycle.

Theory
Our previous study modelled the main parameters of the free-piston batch RO system including recovery, energy consumption, average and peak pressures, and rejection [19].The modelling approach used here is similar but with certain differences.The main difference is that osmotic   backflow, neglected in previous studies [17,19], is now included.Osmotic backflow occurs at the end of the pressurization phase when the hydraulic pressure falls to zero, allowing the salinity gradient to draw permeate back across the membrane.The design intention of the free-piston batch RO was to set the recovery based on the system geometry.Therefore, recovery was calculated previously by Eq. (2) based on internal volumes i.e.
where V b0 is the swept volume of the work exchanger, and the V pg is the nominal volume needed to purge the system (comprising the internal volume of the membrane channel and associated connecting pipes and ports).However, pilot experiments showed that the permeate volume was less than V b0 because of osmotic backflow, resulting in a lower recovery.Thus, we modified Eq. ( 2) by subtracting the osmotic backflow volume (V backflow ) from V b0 to calculate the permeate output and thus recovery: The energy consumption model includes the energy used by the supply pump and recirculation pump.It neglects, however, auxiliary loads of valves and instrumentation, as these are considered circumstantial to the nature of the experimental set up, and not fundamental to the batch RO concept.Furthermore, the energy used by the valves is estimated at <0.5% of the total consumption and as such negligible [19].
Following the above assumptions, the SEC is calculated as the energy consumption (E) in each cycle divided by the permeate output (taking into account V backflow ).E is broken down by phase of operation, resulting in the energy of pressurization (E P ) and energy of purge-and-refill (E P&R ).SEC is broken down similarly as follows: For each respective phase, SEC can be further broken down between the supply pump (SP) and recirculation pump (RP) contributions.Using the corresponding subscripts, The hydraulic energy consumption of each pump is calculated by multiplying the differential pressure by the volume of water displaced by that pump, i.e.PΔV (or ∫ PdV when P varies with V).Pressure is needed to overcome osmotic pressure and to compensate frictional losses related to the membrane, pipework, and the piston seal.Because osmotic pressure changes through the pressurization phase, it is appropriate to use the average pressure P (such that PΔV = ∫ PdV) in calculating SEC P, SP .
Of the four SEC contributions in Eqs. ( 5) and ( 6), the largest is generally SEC P, SP ; therefore, this contribution is analysed in the greatest detail.The analysis uses a top-down approach in calculating P (and therefore SEC P, SP ), which starts from the ideal minimum SEC as presented in Eq. ( 1) and brings in terms to represent non-ideal behaviour and losses in the system.This approach enables us to quantify the causes of non-ideality and to pinpoint readily the scope for improving the system towards the ideal case.Accordingly, the average pressure is given by: where the pressurization recovery r p is given by: This refers to the gross volume of water recovered before osmotic backflow, as a fraction of the total initial internal volume including the volume of the unpurged pipe section (V pipe,R ) [19].Note that r p is the variant of the recovery relevant for calculating the pressure in the system.It differs slightly from the overall system recovery, r, which is relevant for comparing performance against other desalination systems.
The non-ideal correction factors, S p , S L , and S R represent respectively the concentration polarization factor, the longitudinal concentration gradient, and salt retentionfollowing the same calculation procedures as in [19].S L is a function of the ratio of recirculation flow to feed flow ratio (Q r /Q f ) as explained in the Supplementary Information (SI) section 4. The membrane pressure losses comprise two components: a major component of the hydrodynamic friction of flow through the membrane (second term in Eq. ( 7)) and a minor component of pressure drop ΔP m along the membrane channel caused by friction with the membrane surface and spacer element (third term in Eq. ( 7)).The correlation developed by Haidari et al. [30] has been used for ΔP m [kPa].
where v is the cross-flow velocity [m/s] and L is the module length [m].
Eq. ( 7) also includes, unlike in the previous work, terms representing the valve loss ΔP V2 in the supply path, and the piston seal friction, ΔP S , as explained next.
Pipework friction losses may in general include losses in pipes, fittings and valves.According to the construction of the rig used in this study, however, only the valves contribute a significant loss.The pipes and fittings are sized to ensure negligible losses in comparison.The pressure loss in the valves is calculated based on the Torricelli equation for flow through an orifice [31]: where ν is the velocity at the valve orifice, and C d is the coefficient of discharge.According to Massey [31], C d typically has values in the range of 0.6 to 0.7.The precise value has to be determined by experiment.All three valves used in this study are of the same type; therefore, only one value of C d is needed.The piston friction ΔP S arises because, although the piston in this design is theoretically a free piston, in practice it uses a seal that presents a small amount of friction.This results in a finite pressure drop which is approximately constant and opposing the direction of motion.
Besides SEC P, SP , the other three SEC contributions on the right-hand side of Eqs. ( 5) and ( 6) depend only on friction, such that the corresponding pressure drops remain constant throughout the respective phase.Analysis of these pressure drops requires consideration of the flow path, flow rates and displaced volume in each case, the details of which are included in SI section 1.The resulting SEC calculation is implemented in a spreadsheet appended as a supplementary file.The above equations provide the hydraulic SEC, which is divided by the pump efficiency (including the motor efficiency) to provide the electrical SEC.
Peak pressure ( P) is another important factor in the design of RO systems since materials and components must be selected to withstand this pressure.It is calculated by using Eq.(11).Maximum peak pressure occurs at the end of the pressurization cycle, at which time longitudinal concentration gradient becomes zero (see SI, section 4).Thus, the term S L is excluded from this equation.
Salt rejection in the batch RO system is calculated by using Eq. ( 12), where B is the salt permeability of the membrane calculated from the manufacturer's datasheet where R s is the salt rejection).
This equation uses the ratio of the salt flux J s through the membrane divided by the water flux J w .The salt flux is driven by the concentration difference across the membrane, averaged over time and over the duration of the pressurization phase.Thus, the driving concentration takes into account the increase of concentration during the phase, as well as concentration polarization, longitudinal gradient, and salt retention effectsgiving Eq. ( 12) a similar form to the first term in Eq. (7).As this study deals with high rejection systems (R s > 90%), salt concentration on the permeate side is approximated to zero in calculating the concentration difference.

General description of system
The experimental free-piston batch RO system is shown in Figs. 2 and 3 and its main design parameters are listed in Table 2. Major components of this system are a work exchanger vessel housing the free piston, a RO module, a high-pressure pump, a recirculation pump, and three motorized ball valves.These components are connected by 1.25-inch diameter stainless steel pipework.The system control panel allows for both manual and automated operation.For automated operation, a Programmable Logic Controller (PLC) controls the pumps and valves in a cyclic sequence.The PLC receives feedback signals from pressure, conductivity, and flow sensors.A one-way valve installed on the permeate line prevents permeate from returning to the RO module when osmotic backflow occurs.An 8-inch spiral-wound RO module has been selected since most industries use this size for various applications [3].The system is designed to be used for pressures up to 20 bar nominally.If pressure exceeds 25 bar, the system automatically shuts down to avoid damage.SI section 2 contains a detailed list of the components and instruments employed.

Detailed description of equipment 4.2.1. Supply and recirculation pumps
During pressurization, the supply pump must provide steadily increasing pressure up to about 20 bar.During purge-and-refill, in contrast, it operates at pressures of less than 1 bar.To cover this range of pressure, a positive displacement pump is preferred (Lorentz Solar Submersible Pump PS2-1800 HR-05HL, helical rotor type pump).The high-pressure supply pump is powered by a DC power supply (Keysight N5770A) which enables measurement of electrical power consumption with error <2%.The pump is connected to the RO system by a hydraulic hose.To remove any suspended particles, a 5-micron cartridge pre-filter is used at the inlet of the RO system.
The recirculation pump is used to recirculate the batch during the pressurization phase and to restore the piston to its initial position during the refill phase.A centrifugal pump is a suitable choice since it works over a smaller range of differential pressures, contrary to the supply pump.A special pump was designed and made with a maximum flow of 60 L/min and system pressure rating up to 25 bar gauge.It uses a 24 V DC power supply and current is logged to monitor its power consumption.Both pumps allow for speed adjustment via manual or PLC control.

Membrane and work exchanger
The RO membrane element is an 8-inch spiral wound type (Eco Pro-440, manufactured by DuPont Filmtec™) with 41 m 2 active area.Two fibre-reinforced polymer pressure vessels are used, with pressure rating of 30 bar, and dimensions 8 in.× 1.5 m (for the RO module) and 9.45 in.× 2 m (for the work exchanger).The free-piston is machined from polyoxymethylene to provide a clearance fit inside the work exchanger vessel, and it is fitted with a two C-seals to ensure sealing in both directions.

Sensors
Nine sensors are used with continuous data logging.Two pressure transmitters (PT) measure supply and batch pressure on corresponding sides of the piston; five conductivity transmitters (CT) measure conductivity of supply, batch, brine, permeate, and RO outlet in the recirculation loop; and two flow transmitters (FT) measure supply and recirculation flow rate.Refer to SI for detailed specifications and accuracies.

Weighing platforms and tanks
For precise measurements of flow, weighing platforms are used with the accuracy of 0.2, 0.1, and 0.05 kg for feed, permeate, and brine tanks respectively, allowing automatic logging of mass change throughout the experiment.The capacities of the feed, permeate, and brine tanks are 1500, 1000, and 600 L, respectively.A mixing pump ensures and uniforms feed water solution inside the feed tank at the start of each experiment.A thermostatic immersion heater provides a constant temperature of 25 ± 0.5 • C in the feed tank.

Experimental procedure
Feed solution was prepared using tap water (salt concentration ~ 0.1 g/L) and analytical grade sodium chloride (Fisher Scientific, purity > 99.5%).Feed solutions were made up with concentrations of 1 to 5 g/ L, to represent brackish water salinity.To prevent membrane oxidation, 3 g sodium metabisulfite was added per m 3 of feed solution to counteract free chlorine.
The control sequence is as follows.Operation starts with an extra Fig. 2. High-recovery batch RO prototype installed in the laboratory.
purge-and-refill phase which is not part of the typical cycle.This clears any concentrated salts from the system and thus ensures a consistent starting condition.The first pressurization phase is then run, followed by the first purge-and-refill phase, thus completing the first cycle.Pilot experiments showed that stable repetitive cyclic conditions were reached after 3-4 cycles (see SI section 3).Therefore at least 3 cycles are performed before the test cycle (i.e. the cycle that is used for collecting and analysing results).All parameters, including time, weight of the tanks, conductivities, differential pressure of recirculation pump, power consumption of pumps, pressures, and flow rates are logged at a frequency of at least once per second, resulting in at least 470 sets of readings per cycle.

Results and discussion
This section discusses the experimental results for recovery, salt retention, hydraulic and electrical SEC, and compares them against the model results.In total, 53 tests have been conducted, each representing a different set of experimental conditions.The raw experimental data are included as electronic appendices and indexed in SI section 5.

Mass balance and recovery
The design intention of the batch RO system was that the recovery would be determined purely by the geometry of the machine (as in Eq. (2), giving a recovery of r = 0.807 with parameters from Table 2).The system would be fed at constant flow, such that the recovery would correspond to the duration of the pressurization phase (expected to provide output V b0 ) divided by the total cycle duration.Therefore, initial experiments were carried out to test the system with constant supply flow, using a flux of J w = 17.3 LMH and salinities of 0.1, 1, 2, 3, 4, and 5 g/L.Table 3 compares the observed recovery against expected recovery.The observed recovery is the permeate volume collected divided by the total feed volume supplied over the whole cycle; whereas the expected recovery is the feed supplied during the pressurization phase divided by the total feed volume supplied over the whole cycle.The observed recovery was substantially less than expected in all cases except at 0.1 g/L feed concentration.
This discrepancy was caused by osmotic backflow at the end of the pressurization phase when the system de-pressurized.Because of osmotic backflow, about 2.5-5 L of the batch volume failed to leave the system as permeate, instead remaining inside the system at the end of pressurization.This backflow volume corresponded to 0.07-0.12L per m 2 of membrane area, equivalent to 0.07-0.12mm of water distributed   over the membrane surface.This volume can be explained by water retained in the permeate side spacer, which has a thickness of about 0.3 mm.The mass balance of the batch RO system over pressurization and purge-and-refill phases at different feed salinities is further detailed in Fig. 4. The total input and output to the rig over each cycle was consistently 86.4 ± 0.2 L. During the pressurization phase, however, input exceeded output by the amount V backflow (see Table 3).Conversely, during purge-and-refill, output exceeded input by the same amount.
Observations of the weighing tanks with time gave further insight into the mass balance of the system over the cycle, as shown in Fig. 5.The feed tank mass decreased linearly with time over the whole cycle (R 2 = 0.999).The mass changes of the permeate and brine tanks, though mostly linear, showed non-linearity at the start and end of the pressurization and purge-and-refill phases respectively.The permeate output was delayed for the first 20 s of pressurization, during which time about 4.2 L of water was fed to the rig but no permeate came out.Afterwards, the permeate tank gained mass linearly up to the end of the pressurization phase.At the start of the purge-and-refill phase, there was a surge of brine leaving the rig for the first 20 s, before the brine outlet settled to a constant flow.
Fig. 5 also shows the total mass of the tanks against time, as a change from the initial total mass.A net loss of about 4 kg in total tank mass occurred during the pressurization phase, corresponding to a net gain in 4 kg of the RO rig itself.It was also observed that a vacuum formed in the permeate tube upstream of the one-way valve at the end of the pressurization cycle, as permeate was sucked back across the RO module and into the feed channel.This loss of permeate can explain the difference in the net weight of the rig.These observations confirm that, for feed salinities higher than 2 g/L, around 4-5 L of permeate were sucked back through the membrane, creating a vacuum on the permeate side upstream of the one-way valve, at the beginning of purge-and-refill phase.The vacuum had to be refilled at the start of pressurization phase before output recommences.For lower salinities, the backflow was smaller (e.g.only 2.6 L at 1 g/L).

Salt retention
Salt retention plays an important role in the performance of batch and semi-batch RO systems.When the pressurization phase ends, concentrated brine inside the RO module and pipes must be purged and a new feed solution is introduced to prepare the system for the next cycle.In an ideal case, during purge, the incoming feed would displace the brine with zero mixing.However, in practice, dispersion causes unwanted mixing of incoming feed with the concentrated brine.Moreover, a minor volume of our system (V pipe,R ) is not purged by the feed solution, causing additional salt retention.Thus, the initial concentration for the next cycle rises, increasing the required pressure and SEC of the system.
A series of experiments was carried out to measure directly salt retention in the free-piston batch RO.The experiments were conducted with 2 g/L feed solution and at flux J w = 17.9 LMH.In each experiment, a different volume of brine was purged, from 80% to 150% of the nominal purge volume (V pg = 16.5 L), corresponding to V = 13.4-25.4L of brine collected at the outlet.In each experiment, we ran the system for 4 cycles to reach the steady-state condition.At the end of the fourth cycle, after turning off the supply pump and opening the bypass valve, the whole solution inside the membrane and work exchanger was thoroughly mixed for 10 min by the recirculation pump.The solution inside the system was then sampled and its conductivity was compared to that of the feed tank.Fig. 6 demonstrates the effect of the purge volume V on salt retention and recovery.When the purge volume was equal to the volume of brine inside the membrane and piping (V/V pg = 1), the salt retention factor was 1.159 ± 0.023 and recovery was 0.8, which agrees with the theoretical value of 1.155 using the method of [19].
At larger purge volumes, salt retention decreased markedly.However, increased purge also lowered recovery as more feed was supplied for the same permeate output over the cycle.For example, on increasing the purge volume by 12, 30, and 54%, the salt retention factor was reduced to 1.10, 1.06, and 1.02 respectively; while recovery fell to 0.78, 0.75, and 0.72 respectively.Conversely, although recovery was higher with less purge, greater salt retention was observed.Salt retention rose sharply when purging with V < V pg whereas recovery rose less sharply (see Fig. 6A).
Though higher salt retention increased energy consumption by the supply working at increased pressure, this was largely compensated by the shorter purge time, and therefore, reduced energy consumption during purge and refill.Thus, overall SEC increased only marginally as purge volume decreased and recovery increased, as seen in Fig. 6(B).
Qiu and Davies [29] previously studied salt retention in a RO module by observing concentration vs. volume at the brine outlet during purge.They did not, however, conduct the experiment under the real conditions of a batch RO process in the sense that they did not apply pressure to the RO module.Therefore, we repeated their test but under real condition, with high pressure falling to low pressure at the beginning of purge.The results in Fig. 7 show the normalized concentration at the brine outlet as a function of normalized purge volume.These experiments were conducted at 2 g/L feed concentration and at various feed flow rates.Concentration curves were almost the same at different flow rates under the pressurized condition, indicating that salt retention is almost independent of the flow rate.However, there was a substantial difference between the cases of unpressurized and pressurized operation.Under zero pressure (Test 1 and 2 in Fig. 7) the concentration curve was very similar to that reported in [29].However, under pressurized conditions (initial high pressure, then falling to zero, as in the real batch RO process) the concentration curves initially fall more suddenly and then tail off more slowly.This is attributed to the osmotic backflow that enters the RO module, not just near the inlet, but over its whole length, allowing the low-concentration solution to break through sooner at the outlet.

Salt passage and rejection
At the beginning of the pressurization phase, permeate quality was poor, but it improved after initially saline permeate left the system.Fig. 8 shows the permeate conductivity as a function of time at 1 g/L feed concentration, r = 0.8, and J w = 18.1 LMH.The results were taken from the fifth cycle such that the system was at the steady-state condition.Permeate conductivities were measured and logged 10 times per second for increased resolution.Over the first 30 s of the pressurization phase, permeate conductivity peaked sharply, dropped, and then increased again slowly.The initial peak may be attributed to the salt diffusion during the purge-and-refill phase.Because of the concentration gradient across the membrane, salt passed through it and reached the permeate spacer, even in the absence of permeate flux.The salt accumulated and exited the system shortly after the next pressurization phase commenced.Similarly, Wei et al. [17] reported that permeate was relatively poor at the start of each pressurization phase, but then improved quickly.Further, Davies et al. [10] observed that permeate concentration decreased 4 times from 0.4 to 0.1 g/L after 50 s of pressurization (at 2 g/L feed concentration).
Regarding salt rejection over the whole cycle, Fig. 9 compares model predictions (based on Eq. ( 12)), against experimental measurements at different water fluxes ranging from 11 to 22 LMH.Experiments were conducted at 3 g/L feed concentration and Q r /Q f = 2.1.Model predictions were 2 to 2.5% higher than the experimental results.This is because of the low quality permeate at the start of each pressurization phase, as discussed above.The difference between experimental and theoretical rejection decreased slightly as flux increased.

Hydraulic SEC
Though there have been several modelling studies on the energy consumption of batch RO systems [15,16,18,19,21,23,25,32,33], most studies did not consider all losses in such systems; and only Wei et al. [17] reported model validation by experiment.In the current study, the experimental hydraulic work of the batch RO system was calculated by integrating, at each measurement time step, the differential pressure of each pump by the amount of water displaced by that pump.Hydraulic SEC was thus measured and compared against model predictions.The model used two adjustable parameters: (1) the discharge coefficient of the valves, C d , which was adjusted to 0.62 (within the expected range of 0.6 to 0.7 [31]); and (2) the permeability of the membrane, which was adjusted to A w = 4.4 LMH/bar.This permeability value was consistent with readings taken in separate tests using tap water without salt added.In addition, piston friction was determined at ΔP s = 3.5 kPa from the difference in readings between the pressure sensors at either side of the piston.
The experiments in this section were conducted at recovery of 0.8 in accordance with the design intention of the system.Though the results of Section 5.1 showed that recovery was, at constant feed flow, less than 0.8, this shortfall was corrected by slowing the supply pump during the purge-and-refill phase so as to compensate for the secondary purge effect of the osmotic backflow.Thus, the target recovery of 0.8 was achieved.
Fig. 10 illustrates hydraulic SEC measured experimentally and predicted by our model at different salinities, recirculation flow ratios and water fluxes.Experimental hydraulic SEC at r = 0.8, J w = 17.3 LMH, and feed salinities of 2, 3, 4, and 5 g/L were 0.3, 0.37, 0.43, and 0.48 kWh/ m 3 respectively, giving a maximum error of 2% against model predictions (see Fig. 10(A)).Hydraulic work of the recirculation pump in both phases and supply pump in the purge-and-refill phase were approximately the same for all feed concentrations.Only in the case of the supply pump in the pressurization phase did the hydraulic work increase with concentration, because of the increased osmotic pressure.Fig. 7. concentration at RO brine outlet normalized purge volume.Tests 1-2 (11.5 L/min) were conducted without applying pressure, using a similar procedure to [29].The remaining tests used an initial high pressure condition, as in the real batch RO process.C 0 is the feed water concentration, and C max is the initial concentration of brine leaving the system at the start of the purge phase.

E. Hosseinipour et al.
The hydraulic SEC measured in this study was consisted with previous batch RO studies, although the recovery was higher than before.Wei et al. [17] reported hydraulic SEC of 0.25 kWh/m 3 at 2 g/L feed concentration, and J w = 20 LMH in their bladder system.In comparison, this study measured slightly higher hydraulic SEC of 0.31 kWh/m 3 at similar flux and concentration, which may be explained by the higher recovery of this study (r = 0.8 compared to r = 0.5 in [17]).Davies et al. [10] reported hydraulic SEC of 0.22, 0.24, and 0.27 kWh/m 3 at the recovery of 0.4, 0.57, and 0.7, respectively in a free-piston batch RO design using 4-inch membrane at similar flux and concentration.However, those results only included supply pump work during pressurization.Our corresponding result was slightly higher at SEC P,SP = 0.28 kWh/m 3 which again may be explained by the higher recovery of 0.8.Variations in membrane permeability and pipework details may also contribute to the observed differences.
Total hydraulic SEC increased from 0.42 to 0.47 kWh/m 3 on increasing recirculation flow ratio, Q r /Q f , from 1.55 to 3.92 at flux of J w = 17.3 LMH (Fig. 10B).As expected, higher recirculation flow increased recirculation pump SEC but decreased supply pump SEC.Experimental hydraulic SEC for Q r /Q f = 1.55, 2.13, and 2.73 was roughly constant at 0.43 kWh/m 3 .However, at Q r /Q f = 3.35 and 3.92, the drawback of using a larger recirculation flow rate outweighed the benefit.The largest error between model predictions and experimental measurements of SEC was 3.1% at Q r /Q f = 1.55.This may be because of inaccuracy of the longitudinal concentration gradient model at low recirculation flow.At higher recirculation flow, the error was less than 2.5%.
We also investigated the model accuracy at different water fluxes (see Fig. 10C).The biggest error of 2.8% occurred at the highest flux of 21.2 LMH, when the experimental value and model predictions were 0.477 and 0.463 kWh/m 3 , respectively.Overall, with osmotic backflow included, we obtained a good agreement (<3% error in SEC) between model and experiments at different salinities, recirculation flow rates, and water fluxes.Thus, our model can be used to predict the free-piston batch RO performance under various in the treatment of the brackish water.Further, since the model uses only explicit algebraic equations, it is readily implemented as a spreadsheet and made accessible here for general use.

Electrical SEC
For the first time in batch RO studies, we measured electrical SEC and compared it to hydraulic SEC.Whereas hydraulic SEC is of academic interest in understanding and improving the fundamental system, industries will be more interested in electrical SEC as it determines the cost of operation.

Comparison of electrical and hydraulic SEC
Electrical SEC was determined by integrating measured power over time for each pump, and dividing by water output.Fig. 11 compares the hydraulic and electrical SEC breakdown of the batch RO system at different salinities, recirculation flow ratios, and water fluxes.The total measured electrical SEC at salinities of 2, 3, 4, and 5 g/L were respectively 0.57, 0.67, 0.74, and 0.83 kWh/m 3 at flux J w = 17.3 LMH and Q r / Q f = 2.1 (Fig. 11A).The difference between electrical and hydraulic SEC becomes smaller when concentration increases; e.g. the electrical SEC was 1.9 and 1.7 times higher than the hydraulic SEC at 2 and 5 g/L respectively, showing an increase of the supply pump efficiency with pressure.
Regarding the effect of recirculation flow on SEC (Fig. 11B), at Q r /Q f = 1.55 and 2.13, both electrical SECs and hydraulic SECs were unchanged (0.43 kWh/m 3 for hydraulic SECs and 0.73 kWh/m 3 for electrical SECs); whereas electrical SEC increased at a higher rate than hydraulic SEC at larger recirculation flow rates.Thus, electrical SEC increased from 0.73 to 0.85 kWh/m 3 , whereas hydraulic SEC rose from 0.43 to 0.47 kWh/m 3 when Q r /Q f increased to 3.92.
Measurement of electrical and hydraulic SEC at different water fluxes (Fig. 11C) showed that, by increasing water flux from 11 to 21.2 LMH, both SECs increased, giving a 31% and 20% rise in hydraulic and electrical SEC, respectively.This was because of the greater membrane friction loss represented by the 2nd term in Eq. (7).On the other hand, the higher flux gave a 74% increase in system output (an increase from 9.6 to 16.7 m 3 /day).
The electrical SEC of the system is greatly affected by the supply and recirculation pump efficiencies.Table 4 shows measured pumps efficiencies (i.e.hydraulic SEC/electrical SEC).Supply pump efficiency acceptable (mostly >60%) during the pressurization phase, but poor during the purge-and-refill phase (<15%).This is because the supply pump was not optimized for low-pressure operation.

Breakdown of electrical SEC
The electrical SEC breakdowns of each pump during the pressurization and purge-and-refill are shown in Fig. 12.In general, the main contribution to SEC came from the supply pump during the pressurization phase, contributing 75 to 85% of total SEC.At increased feed salinity, the supply pump contributed a greater fraction.For example, supply pump pressurization SEC at 1, 2, 3, 4, and 5 g/L salinity contributed 75, 79, 82, 84, and 85% respectively.In contrast, SEC in the purge-and-refill phase for both pumps, and during the pressurization phase for the recirculation pump, are independent of feed salinity.Therefore, as salinity increases, the supply pump must apply higher pressure and its energy consumption increases, while other SEC components remain constant.About 6% of SEC came from the supply pump in the purge-and-refill phase, as needed to flush the brine out of the system.This significant fraction is not favourable since it reduces the system's potential to minimize SEC.The main cause is the low efficiency of the supply pump  (<15%) in the purge-and-refill phase.
The recirculation pump contributed 10 to 20% to the total SEC, with lower percentage contribution at higher salinities.Thus, this contribution dropped from 19 to 11% when feed salinity increased from 1 to 5 g/ L. The lower the recirculation SEC, the closer the system comes to achieving the theoretical minimum SEC.

Sensitivity of electrical SEC to recirculation flow rate
Table 5 presents the effect of increasing recirculation flow rate on the electrical SEC breakdown.On increasing the ratio Q r /Q f while keeping other parameters constant, the recirculation pump provided higher flow during pressurization and consequently the SEC of this pump rose (Table 5).On the other hand, at low recirculation flow, concentration polarization (S p ) and longitudinal concentration gradient (S L ) inside the RO module increase and the supply pump must apply a slightly higher pressure to compensate.For example, when Q r /Q f increased from 1.55 to 3.92, SEC P,RP increased by 0.146 kWh/m 3 while SEC P,SP decreased by 0.026 kWh/m 3 .At the higher values, as recirculation increased, recirculation pump SEC rose faster than the fall in supply pump SEC.Meanwhile, SEC of pumps in the purge-and-refill phase was approximately constant and insignificant.Therefore, it is better to operate with Q r /Q f between 1.5 and 2.2, as concluded in our previous theoretical study [19].Fig. 13 also shows the effect of recirculation rate on the total electrical SEC at various feed salinities.

Sensitivity of electrical SEC to permeate flux
Another factor having an important effect on the performance of RO systems is permeate flux.We measured the effect of permeate water flux on the main factors of the system including electrical SEC (see Table 6).Electrical SEC increased with flux as expected from Eq. (7).However, at higher fluxes, the system output was higher in direct proportion to the flux.Thus, there was a trade-off between SEC and output.For example, when flux was doubled, electrical SEC increased by 28% while output rose by 74%.Additionally, at lower fluxes, permeate quality worsened, and by increasing the system flux, rejection of batch RO system slightly improved.System flux is always lower than the permeate flux because of the reset time in the purge-and-refill phase when permeate is not produced.
The effect of feed salinity on the total electrical SEC at various water   fluxes is also illustrated in Fig. 14.Higher feed salinity resulted in higher electrical SEC.

Concentration in the recirculation loop
Concentration difference from the inlet to outlet of a RO module tends to increase system pressure and energy consumption.We have measured how the concentration at both inlet and outlet vary against time, how these concentrations were affected by the recirculation flow rate, and how they compared to model predictions (see SI Section 4 for details of the Ordinary Differential Equation model used).The concentration difference becomes zero at recirculation flow, which represents the ideal case as regards minimizing the work done by the supply pump, but overall SEC minimisation requires a finite optimum recirculation rate as seen in Section 5.4.
Fig. 15 shows experimental and theoretical results for concentration vs. time with recirculation flow of Q r /Q f = 2.1.The experimental results are for two cases: A) constant feed flow over both phases of operation (such that the total purge volume equalled the nominal purge volume V pg plus the osmotic backflow, as in Section 5.1, giving recovery r < 0.8); and B) reduced feed flow and volume (such that the purge volume equalled just V pg and recovery of r = 0.8 was achieved).The time axis is normalized to the duration of the pressurization phase.In case A, there was good agreement between the theoretical and experimental values during the first half of the phase, except for the initial peak in the experimental outlet concentration.This peak reflected salt retention inside the RO module at the end of the purge-and-refill phase.As the flow reversed to start the pressurization phase, a portion of concentrated brine inside the RO module flowed back towards the outlet (which was the inlet during purge-and-refill) causing this initial peak to be detected.Subsequently, this portion of brine entered the work exchanger to become mixed with the bulk of recirculating solution.In the second half of the pressurization phase, experimental inlet and outlet concentrations were slightly lower than the theoretical predictions.
In case B, the initial peak was larger due to the higher salt retention associated with less purging.The experimental outlet concentration was slightly above the theoretical prediction mostly, except over the last 20% of the pressurization phase where there was a good agreement.The outlet concentration was higher than the ideal concentration in both cases.Furthermore, the difference between the experimental outlet concentration and ideal concentration varied through the phase, being higher at the beginning and lower at the end.Thus, a varying recirculation (faster in the first half of the pressurization phase) may be helpful to reduce this gap.

Pressure
Experimental and theoretical supply pump pressures over a pressurization phase of the free-piston batch RO system are shown in Fig. 16.The calculation of theoretical pressure considers all the inefficiencies and losses including concentration polarization, salt retention, longitudinal concentration gradient, net driving pressure to overcome the hydrodynamic resistance in the pores of the RO membrane, pressure drop in the RO module, pressure drop caused by piston seal, and frictional pressure drop over the recirculation valve (see SI section 4).Therefore, a good agreement between model predictions and experimental measurements was achieved (Fig. 16).However, there are still some minor differences.First, at the beginning of the pressurization phase, the model predicted instantaneous pressure rise and permeate production; whereas in reality, it took 15-20 s for the pressure to rise to the predicted value and for production to begin.This corresponded to about 5% of the total duration of the pressurization phase and to a supplied volume of 3-4 L. Second, corresponding to the initial concentration peak discussed above, we observed a small peak in the pressure at the start of the pressurization phase.This peak increased with feed solution salinity, as shown in Fig. 16 at 4 g/L feed concentration.Furthermore, the theoretical peak pressure at the end of the pressurization phase was about 1 bar higher than the experimental measurement.This may be because the internal volume of the RO channel expanded under pressure, resulting in a slightly lower final concentration and lower peak osmotic pressure than predicted.Such expansion could also explain the slow initial rise in pressure, as incoming feed pressure gets cushioned by deformation of the membrane.
Deformation of RO membranes under pressure (i.e.compaction) has been observed in several studies [34,35], especially under high pressure Fig. 13.Recirculation flow rate effect on the total electrical SEC of the batch RO system over a cycle at various salinities, and J w = 17.3 LMH.

Table 6
The effect of varying flux on the important factors of batch RO system at 2 g/L feed salinity and Q r /Q f = 2.1.System flux is the flux averaged over the whole cycle.operation.For example, Davenport et al. reported 60% compressive strain in a seawater RO membrane at 150 bar.In our study, to accommodate 4 L of supplied fluid, the membrane would need to compress by 0.1 mm, approximately equivalent to the thickness of the membrane itselfand the operating pressure is lower (<25 bar).This shows that compressive strain is not the only cause of the slow pressure rise.Additional causes may include compression of the permeate-side spacer, and wavy deformation of the membrane within the spacer-membranespacer sandwich.Dilation of other components like the pressure vessels, and the hose connecting the supply pump to the rig, may also contributethough these contributions are to be individually small.If, as is likely, the membrane springs back upon release of pressure, this could contribute to the apparent backflow described in Section 5.1 above.The phenomena of membrane deformation and osmotic backflow may be interlinked in batch RO.At the end of the pressurization phase, pressure peaks again at a maximum value.Fig. 17 compares experimental final peak pressure against the value predicted by Eq. (11), at different water fluxes.At all water fluxes, experimental measurements were lower than model predictions, most likely because of membrane compliance as noted above.Nonetheless, error was less than 6%.In addition, the error was bigger at the lowest tested flux of 11 LMH and decreased by increasing the flux; the smallest difference was 3% at J w = 22 LMH.

Potential future improvements
The experiments have shown promising electrical SEC values of 0.40-0.84kWh/m 3 at 1-5 g/L feed salinities.These values compare well with many brackish water desalination systems available today, but are above the predictions of our earlier theoretical study [19].For example, we predicted 0.39 kWh/m 3 for high-flux membrane (DuPont XLE-440) at 3 g/L feed concentration (with J w = 22.06 LMH, and Q r /Q f = 2.03) [19].The main reasons for discrepancy are that: (1) the theoretical study assumed efficiencies of 70% for the supply pump and 50% for the recirculation pump, whereas actual efficiencies are in the range of only 10-65% (Table 4); (2) it assumed membrane permeability of A w = 8.32 LMH/bar compared to only 4.4 LMH/bar determined experimentally.
By using our modified model for such a high-permeability membrane, and assuming pump efficiencies of 70% and 50%, we now predict SEC of 0.48 kWh/m 3 at the same feed concentration and flux.The remaining discrepancy with the earlier value of 0.39 kWh/m 3 is due mainly to osmotic backflow and also to differences in friction losses associated detailed pipework and valve design.

Effect of membrane permeability on SEC
Membrane permeability has a significant effect on the energy consumption and performance of RO systems.Several studies have shown that SEC decreases with increasing permeability [23,37,38].We used our validated model to study further the potential of using highpermeability membranes in the current batch RO system (Fig. 18).The Eco Pro-440 element used in the experiments had a permeability of 4.4 LMH/bar.On increasing membrane permeability to 6, 8, and 10 LMH/bar, hydraulic SEC will decrease by 8.0, 13.5, and 16.8%, respectively (at 4 g/L feed concentration, r = 0.8, J w = 17.3 LMH, and Q r /Q f = 2.1).

Effect of pump efficiency
More efficient pumps will improve system performance considerably.In these experiments, pump efficiencies were mostly below 65% (Table 4).Table 7 shows how electrical SEC of the free-piston batch RO will improve using pumps with higher efficiencies, assuming that both pumps have the same efficiency over both phases of operation.If the pump efficiency were 80%, SEC would decrease to 0.37, 0.45, 0.54, and 0.6 kWh/m 3 at 2, 3, 4, and 5 g/L feed concentration, respectively.Therefore, pumps that are better matched to the system will significantly improve energy performance.

Effect of valve size
We also investigated the effect of valve orifice diameter on SEC (Fig. 19).By increasing the orifice diameter from 15 to 20 or 25 mm, we predict energy savings of 6 or 7.5% respectively.This results from the reduction of velocity in Eq. ( 10) and consequent reduction in friction losses.

Overall scope for improvement and comparison with existing systems
The above improvements may be implemented together to reduce further SEC.Table 8 shows predicted SEC after making improvements in membrane permeability (i.e.A w = 8 LMH/bar), pump efficiencies (i.e.70% for both supply and recirculation pumps) and in valve orifice diameter (i.e. 25 mm) at different feed concentrations.On implementing all these changes, electrical SEC should substantially decrease from the range of 0.48-0.83 to that of 0.2-0.56kWh/m 3 for feed concentration of 1-5 g/L.However, there is still a gap between predicted SEC of the improved system and the ideal minimum SEC ideal , indicating further theoretical scope for improvement (see Table 8).
The batch RO system has low energy consumption compared to conventional RO systems reported in the literature, as shown in Fig. 20 which compares its SEC against the results collated by Zhao et al. [39].Even before applying any improvement, the current system has lower SEC than the earlier studies at all feed salinities.Nonetheless, care must  be taken when making such comparisons, as SEC can be affected by several parameters, especially by recovery which is not always reported in the literature.To correct for both feed water salinity and recovery, 2nd law efficiency is a good criterion to use.Though not many studies provide 2nd law efficiency directly, Ahdab and Lienhard [40] have found that the 2nd law efficiency of conventional brackish water desalination is in the range 4-20%.This also suggests that batch RO compares favourably, as the 2nd law efficiency achieved here is 9.1-26.5% and predicted to increase to 21.6-39.1% with the improvements proposed above (see Table 8).One of the reasons for the typically low efficiency of brackish water RO is the absence of any Energy Recovery Device (ERD) in many existing systems.Greater use of ERDs would improve the 2nd law efficiency of conventional systems, perhaps making them compare more favourably against batch RO.Nonetheless, the typical ERDs (i.e.isobaric pressure exchangers and Pelton wheels) are mostly designed for larger systems (>100 m 3 /day capacity) compared to this study where the capacity is only 10-20 m 3 /day [41].This suggests that batch RO is particularly promising for high recovery brackish water desalination at small to medium scale.
There are further considerations about the practical and comparative performance of brackish water RO.Real systems usually contain several treatment steps, such as pre-and post-treatment besides the ROwhich have to be considered in overall SEC and running costs.These may or may not be included in reported values.In addition, the long-term performance is likely to deteriorate compared to short term tests.For example, after 80,000 h of operation, the SEC of a system installed in Gran Canaria rose from 0.8 to 2 kWh/m 3 [42].This deterioration was attributed to fouling and aging of the membranes.Laboratory and modelling studies suggest that batch RO has advantages regarding resistance to fouling in seawater and brackish water applications [43].Long term testing and fouling in pilot batch RO systems is certainly an important topic for future research.

Conclusions
In this study, the performance of a high-recovery batch RO system using a free-piston has been experimentally investigated and modelled.The system has been designed for treating brackish water up to 5 g/L feed salinity and at recovery of 0.8, which is the highest recovery reported in practical batch RO studies so far.Using an 8-inch RO, an output of 10-17.3m 3 /day, and rejection > 94% was achieved.In total, 53 experimental runs have been conducted over a wide range of operating parameters, making this the most thorough and detailed experimental study of a high-recovery batch RO system reported in the literature.Key conclusions are: • Batch RO is subject to osmotic backflow when depressurization occurs during each cycle.Backflow volume increases with feed salinity and amounts to 2.5-5 L for the 8-inch spiral wound membrane element.• Osmotic backflow tends to reduce system recovery, but this can be offset by limiting the amount of purge, thus maintaining a high recovery of 0.8.• Batch RO reaches steady-state cyclic operation after 3-4 cycles.
• Once a steady state is reached, salt retained between cycles tends to increase the salinity at the beginning of each cycle by 16%, thus increasing system pressure and energy consumption.• Salt retention causes a minor peak in concentration at the outlet of the RO module shortly after the start of pressurization.• Both supply and recirculation pumps consume energy over both phases of operation.The greatest consumption is that of the supply pump during the pressurization phase, which contributes 75-85% to total SEC, while the recirculation pump contributes only 10-20% over the whole cycle.• SEC depends weakly on recirculation flow, such that any recirculation flow (as a ratio to feed flow) from 1.5 to 3 allows almost minimal SEC.At higher recirculation flows, SEC increases significantly.
• At a flux of 17.3 LMH, depending on feed salinity over the range 1-5 g/L, hydraulic SEC is 0.22-0.48kWh/m 3 and electrical SEC is 0.48-0.83kWh/m 3 .The flux of 17.3 LMH gives an output of 13.9 m 3 /day.Higher water fluxes give higher outputs up to 17.3 m 3 /day but at the expense of slightly higher SEC.• A simple spreadsheet model using explicit algebraic equations predicts hydraulic SEC with accuracy better than 3%.• During the pressurization phase, there is an initial delay in pressure rise, and the final pressure is slightly below the model prediction.This may be because of compliance of the membrane channel increasing its internal volume in response to the supply pressure.
The batch RO system performs competitively against conventional systems, especially for small-scale industrial applications.It can achieve electrical SEC < 0.8 kWh/m 3 at 4 g/L feed concentration with an output of 16.4 m 3 /day, which would normally require a much larger, multistage system.The batch RO system also has great potential for SEC minimization through future improvements.For example, though the pump efficiencies measured here were only 10-65%, if this were uniformly improved to 70% for both pumps and phases of operation, electrical SEC would reduce to 0.60 kWh/m 3 at 4 g/L.With membrane permeability increased from 4.4 to 8 LMH/bar and improvements to the valves used in this system, we expect hydraulic SEC of 0.14-0.39kWh/ m 3 and electrical SEC of 0.20-0.56kWh/m 3 for feed concentrations of

Table 8
Comparison of theoretical minimum SEC (based on Eq. ( 1)) with the measured results, and with predicted electrical SEC following improvements in membrane water permeability (A w = 8 LMH/bar), pump efficiencies (70% for both supply and recirculation pumps) and valve orifice diameter (25 mm) at various feed salinities (water flux J w = 17.3 LMH).The corresponding 2nd law efficiency (SEC ideal /SEC) is also shown.1-5 g/L.Therefore, future work should focus on: testing with innovative high-permeability membranes, developing or sourcing high-efficiency pumps, and refining the valves and pipework to optimize the trade-off between friction and salt retention.In addition to these modifications, hybrid batch/semi-batch RO designs [44] can be the next step towards improving energy efficiency at recoveries higher than 0.9 which will be advantageous especially for minimum liquid discharge applications.At such high recoveries, testing and research into fouling will become especially important.

•
A batch RO system operating over only two phases to reduce downtime • In-depth experimental study validates model with 3% accuracy in hydraulic SEC.• Osmotic backflow of 2.5-5 L measured and included in modelling.• Electrical SEC in the range 0.48-0.83kWh/m 3 measured at recovery of 0.8.• Model predicts electrical SEC of 0.14-0.39kWh/m 3 through improvements to membrane, valves and pumps.A R T I C L E I N F O

E
. Hosseinipour et al. and three 2-port valves.This is the first in-depth experimental study of the single-acting 2-phase batch RO design.

Fig. 1 .
Fig. 1. (A) Pressurization and (B) purge-and-refill phases of the free-piston batch RO cycle (single-acting, 2-phase design).Phases are changed by opening and closing the three on-off valves.During the pressurization phase, bypass and brine valves are closed while the recirculation valve is open.During the purge-and-refill phase, bypass and brine valves are open and the recirculation valve is closed.(Black shading and white shading indicate respectively closed and open valves.Solid and dashed lines represent flow and no flow respectively).

Fig. 3 .
Fig. 3. Schematic diagram of high-recovery batch RO system (PT, CT and FT are pressure, conductivity and flow transmitters, respectively.W1, W2, and W3 are weighing platforms for feed, permeate and brine tanks.M indicates motorized valves).

Fig. 4 .
Fig.4.Mass balance: total input and output to the batch RO system over pressurization and purge-and-refill phases at different feed salinities when supply pump was operating at a constant flow rate (J w = 17.3 LMH, Q r /Q f = 2.1).

Fig. 5 .
Fig. 5. Mass changes of feed, permeate, and brine tanks over a cycle.Red line shows total of mass changes of feed, permeate and brine tank.The experiment was conducted at 2 g/L feed concentration, and constant feed flow rate (water flux J w = 17.3 LMH).(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 11 .
Fig. 11.Hydraulic and electrical free-piston batch RO system over a cycle at various: (A) salinities, (B) recirculation flow ratios, and (C) water fluxes.

Fig. 14 .
Fig. 14.Effect of the permeate flux on the total electrical SEC at various salinities (Q r /Q f = 2.1).

Fig. 15 .
Fig. 15.Comparison of model predictions (MOD) and experimental (EXP) salt concentration vs. time (normalized to duration of pressurization phase) at the inlet and outlet of the RO module.(A) Constant feed flow, purging the nominal purge volume V pg plus the osmotic backflow (r = 0.74), and (B) purging V pg exactly (r = 0.8).Experiments were conducted at 4 g/L feed concentration, Q r /Q f = 2.1 and J w = 17.3 LMH.The ideal concentration corresponds to that expected at infinite recirculation flow and therefore homogeneous concentration.

Fig.
Fig. Predicted hydraulic SEC as a function of valves diameter in the freepiston batch RO at 4 g/L feed solution, J w = 17.3 LMH, r = 0.8, and Q r /Q f = 2.1.The orange point is the valve diameter used in the current prototype.(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Table 1
Comparison of experimental studies conducted on batch RO performance.

Table 2
General parameters of the experimental system and model.

Table 3
Observed and expected recoveries obtained at different salinitiesconstant flow operation (J w = 17.3,Q r /Q f = 2.1).

Table 4
Feed and recirculation pump efficiencies over a cycle for pressurization and purge-and-refill phases at various water fluxes, 4 g/L feed concentration and Q r / Q f = 2.1.

Table 5
Effect of varying recirculation flow rate ratio (Q r /Q f ) on the SEC breakdown and total SEC over a cycle at 4 g/L feed salinity and J w = 17.3 LMH.

Table 7
Predicted electrical SEC according to pump efficiencies at various feed salinities (J w = 17.3 LMH, and Q r /Q f = 2.1).In these experiments, the efficiencies are those in Table4.
Work exchanger swept volume V backflow m 3 , Backflow volume V pipe,pg m 3 , Pipe volume (purged section) τ -, Dimensionless time