On-Off Control Strategy in a BWRO System under Variable Power and Feedwater Concentration Conditions

Abstract

Although reverse osmosis (RO) is the technology of choice for solving water shortage problems, it is a process that consumes large amounts of energy. Brackish water (BW) desalination is more efficient than seawater desalination due to the lower salinity of the feedwater source. This makes coupling renewable energy sources with BWRO systems attractive. The operation of this type of systems is complex and requires the design of control strategies to obtain optimal operation. The novelty of this work was to propose a simple on-off control strategy for operating a BWRO system that can work with one and two stages and with different configurations considering six spiral wound membrane elements per pressure vessel (PV). The feedwater quality variations of a real groundwater well were used together with a computational tool to simulate the response of the different configurations with the purpose of selecting the most appropriate depending on the input power to the BWRO system. The most suitable configurations were found to be 1:0, 2:1 and 3:2 (PV first stage:PV second stage). It was additionally found that increased feedwater concentrations resulted in shorter operating ranges to maximize permeate water production for the 1:0 and 2:1 configurations, and that the 3:2 configuration was the most suitable for most of the operating range.

1. Introduction

Reverse osmosis (RO) is the predominant technology in seawater and brackish water desalination [1]. However, this technology continues to be an intensive energy consumption process [2,3]. Various options can be pursued with the aim of reducing the specific energy consumption ($SEC$) of RO [4,5,6], including optimizing the operation of RO desalination plants. Advances in RO membrane technology [7,8] are a key element in the goal of improving desalination efficiency. With respect to spiral-wound membrane modules (SWMMs), studies have been made on the effect of the permeability coefficients on the performance of RO systems in terms of production and solute rejection [9,10,11]. Significant efforts are being made to try to inhibit the effect of fouling on permeability coefficients during operating time by improving pre-treatment processes [12] and the resistance to fouling [13]. The application of renewable energy sources (RES) to power RO systems has attracted much interest [14]. The operation of RES-driven RO systems is considerably complicated by the problem of variations in power availability and in the characteristics of the feedwater. Given the operational complexity of RO systems and the importance of taking full advantage of technological improvements, it is essential to ensure that desalination plants are working at all times under appropriate operating conditions through efficient and effective process control [15,16].

Models that estimate the behavior of RO systems are crucial when control strategies are applied to this kind of process. I.M. Alatiqi et al. [17] proposed the first multi-loop control system for a seawater RO (SWRO) process. The RO system had 4-inch hollow-fiber membranes (HFM) (B-10 Permasep from Dupont^®), which are not very common nowadays. Plant modeling was carried out using transfer functions, considering feed pressure ($p_{\mathrm{f}}$) and pH${}_{\mathrm{f}}$ as inputs and permeate flow ($Q_{\mathrm{p}}$) and permeate conductivity ($Con{d}_{\mathrm{p}}$) as outputs. M.W. Robertson et al. [18] presented an algorithm based on dynamic matrix control (DMC) for the control of an SWRO pilot plant. The process modeling of I.M. Alatiqi et al. [17] was used in this work. J.Z. Assef et al. [19] carried out a study on constrained model predictive control (CMPC) for a brackish water RO (BWRO) desalination unit. The process modeling was done considering four outputs ($Q_{\mathrm{p}}$, $Con{d}_{\mathrm{p}}$, trans-membrane pressure and pH${}_{\mathrm{f}}$) and two inputs (rejection flow ($Q_{\mathrm{b}}$) and inlet acid flow). The goal was to produce a specified $Q_{\mathrm{p}}$ with a desired $Con{d}_{\mathrm{p}}$, subject to the constraint that pH${}_{\mathrm{f}}$ and trans-membrane pressure were within specified bounds. A. Abbas [20] used a DMC algorithm with and without constraints for the control of a simulated SWRO desalination unit with HFM. The dynamic model used in their work was based on transfer functions and developed in a previous study by other authors [17]. A control system design for RO systems using advanced optimization techniques was proposed by A. Gambier et al. [21]. Trans-membrane pressure and pH${}_{\mathrm{f}}$ were considered as inputs, and $Q_{\mathrm{p}}$ and $Con{d}_{\mathrm{p}}$ as outputs in the transfer function-based model. A.R. Bartman et al. [22] designed and implemented a nonlinear model-based control system for a pilot-scale BWRO desalination plant. The model [23] used was based on a mass balance taken around the entire system and on an energy balance taken around the actuated concentrate valve. The model proposed by M.W. Robertson et al. [18] was implemented by G. Kim et al. [24] in an optimization algorithm with an immune-genetic approach to obtain the parameters of a proportional-integral-derivative (PID) controller. The previously mentioned mass/energy-based model proposed by C.W. McFall et al. [23] was used by A.R. Bartman et al. [25] in a simulated BWRO system with concentrate recirculation. In a later work, A.R. Bartman [26] minimized the $SEC$ of an SWRO system (18 pressure vessels (PVs) each with 6 SWMMs in series) through a non-linear optimization model. A robust model-based control for an RO desalination unit with tubular membranes was proposed by M. Al-haj Ali et al. [27]. The three-parameter nonlinear Spiegler–Kedem model was used in this work. The same model was used by A. Emad et al. [28] in a periodic control work in a tubular RO process. A. Gambier [29] designed a robust PID controller using a multi-objective normal boundary intersection algorithm. A pilot BWRO desalination plant for tap water purification was used. The model of the aforementioned plant was simplified to a single-input single-output (SISO) system, where input was the RO concentrate valve position and output the permeate flow. M.M. AlDhaifallah et al. [30] designed a PID controller for a simulated SWRO system with HFMs using the solution-diffusion model. D. Li et al. [31] proposed a cascade control system for a simulated RO system with SWMMs. The models (steady state and dynamic) used had previously been proposed by T. Zhao et al. [32], and were based on solution-diffusion, mass balance and momentum balance. S. Sobana and R.C. Panda [33] studied model-based controls in a simulated SWRO system taking into consideration servo and regulatory problems. The model was based on transfer functions and the outputs were $Q_{\mathrm{p}}$, permeate concentrate ($C_{\mathrm{p}}$) and pH${}_{\mathrm{f}}$ and the inputs $p_{\mathrm{f}}$ and flux recovery R. A modified PID control with H-infinity loop shaping synthesis for simulated RO systems was proposed by B.D.H. Phuc et al. [34]. A transfer function model was obtained for the RO system considering angular pump speed and RO concentrate valve position as inputs and $Q_{\mathrm{p}}$ and $C_{\mathrm{p}}$ as outputs. In a later work [35], the same authors carried out a dynamical analysis and control synthesis for RO systems against water hammering. In this case, a dynamical model based on a macroscopic kinetic energy balance and irreversible thermodynamics previously developed by A.R. Bartman et al. [25] was used. V. Feliu-Batlle et al. [36] used a transfer function-based model to propose a fractional order controller for a SWRO system. The dynamics of the system were experimentally identified. A control system comprised of two loops, the first using a loop-shaping design method and the second a super-twisting sliding mode control, was proposed by M. Zebbar et al. [37]. The RO system model was based on mass and energy balances. An implementation of an expert model predictive controller in a pilot BWRO and SWRO system was carried out by R. Rivas-Perez et al. [16]. The expert controller included an identification block with on-line calculation of the parameters of the prediction model. The model for the RO systems was based on transfer functions. W. Khiari et al. [38] proposed a power control strategy for a BWRO desalination plant powered by an isolated hybrid photovoltaic/wind source without battery. A solution-diffusion model was used for the RO process. Experimental work was done to determine performances under different operating conditions in the safe operating window (SOW). Different feedwater concentrations were considered (2, 4 and 6 g L${}^{-1}$) and R was limited to 20%. The proposed control system allowed operation of the BWRO desalination plant for a wide range of power variations. Most of the aforementioned works used process modeling based on transfer functions or more precise models without experimental validation.

Under normal conditions, BWRO is more efficient than SWRO desalination due to the difference in the osmotic pressure of the feedwater solutions. This makes the use of RES an attractive option to power BWRO desalination systems. The composition of groundwater, one of the main feedwater sources tends to fluctuate as the result of variations in different factors (temperature, rainfall, agricultural irrigation, etc.) [39,40]. Significant fluctuations in osmotic pressure may occur that can affect the performance of BWRO systems. Several authors have studied RES-powered BWRO systems. S.M. Hasnain and S.A. Alajlan [41] studied a BWRO system powered by photovoltaic energy using real groundwater. A pilot plant was used and the study focused on cost assessment without providing operating data. W. Gocht et al. [42] used a pilot BWRO desalination plant with a $Q_{\mathrm{p}}$ capacity of 40 m${}^3$ d${}^{-1}$. A. Schäfer et al. [43] carried out a performance analysis of a photovoltaic-powered hybrid BWRO membrane system considering variations in feedwater salinity. The RO system only had one membrane element and $SEC$ variations of between 5.5 kWh m${}^{-3}$ at a feed concentration of 1 g L${}^{-1}$ salt and 26 kWh m${}^{-3}$ at a feed concentration of 7.5 g L${}^{-1}$ salt were reported. The same research group [44,45] continued their study by evaluating the effect of energy fluctuations and feed salinity on the performance of a small single-stage BWRO system. The $SEC$ and permeate quality were evaluated for different membranes along 12 h of operation. M. Khayet et al. [46] carried out an interesting work based on the optimization of a solar-powered BWRO system with a $Q_{\mathrm{p}}$ capacity of 0.2 m${}^3$ d${}^{-1}$ for drinking water. A synthetic solution of 6 g L${}^{-1}$ NaCl was used as feedwater in the aforementioned small single-stage plant. Runs of 2 h were done providing operating data in terms of production, salt rejection and energy. The authors concluded that the optimized RO plant could guarantee potable water production with a $SEC$ from 1.2 to 1.3 kWh m${}^{-3}$. H. Quiblawey et al. [47] analyzed the performance of a small, single-stage photovoltaic-powered BWRO desalination plant to produce 0.5 m${}^3$ d${}^{-1}$. The variation of R and salt rejection with temperature and the increase of $SEC$ when R decreased were reported. H. Cherif and J. Belhadj [48] evaluated a hybrid photovoltaic-wind system to produce desalinated water from a BW source. The BWRO desalination plant design was based on software simulation (ROSA software from Dupont^®). The first stage had 4 PVs, each with 4 SWMMs, and the second stage 4 PVs, each with 2 SWMMs. G.L. Park et al. [49] studyied the effect of wind speed fluctuation on the performance of an RES-powered BWRO plant comprised of one 4-inch diameter SWMM element. They used synthetic solutions of NaCl (2.75 and 5.5 g L${}^{-1}$) as feedwater in a system with a $Q_{\mathrm{f}}$ capacity of 0.3 m${}^3$ h${}^{-1}$. Similarly, B.S. Richards et al. [50] considered the effect of real wind fluctuation and energy buffering on the performance of a BWRO pilot plant in terms of $Q_{\mathrm{p}}$, $C_{\mathrm{p}}$ and $SEC$. The same group continued this research line considering a small single-stage BWRO system unit, studying a safe operating window methodology using a new and old SWMM [51] and the influence of solar irradiance fluctuation on plant performance [52]. Most of the studies that have been undertaken have only considered small size (pilot-scale or lab-scale) single-stage BWRO system configurations which differ considerably from full-scale BWRO systems that commonly have at least two stages and 4 SWMMs per PV [5,53].

The aim of this work was to evaluate through an on-off control strategy the different SOWs of a simulated BWRO system using the real feedwater fluctuation characteristics of a groundwater well that has been under study for 10 years. The BWRO system has three PVs in the first stage and 2 PVs in the second stage. Depending on the power input and $C_{\mathrm{f}}$ in the BWRO system, the control system established a BWRO system configuration to maximize $Q_{\mathrm{p}}$. A computational tool validated in a previous work by the authors [53] was used to simulate the behavior of the BWRO systems under different operating conditions.

2. Methodology

2.1. Feedwater Characterization

The feedwater source (groundwater well) is located on the island of Gran Canaria (Canary Islands, Spain), with coordinates latitude 27${}^{\circ }$50${}^{\prime }$52.04${}^{″}$ N, longitude 15${}^{\circ }$29${}^{\prime }$00.20${}^{″}$ W, and an elevation of 160 m above mean sea level. The feedwater characteristics as well as how the samples were collected and analyzed have been published by the authors in a previous work [54]. The well was monitored for 10 years, taking two or three samples per year.

Table 1. Feed water inorganic composition in mg L${}^{-1}$.

Sample	pH	HCO3−	Cl−	SO42−	NO3−	Na${}^{+}$	K+	Ca2+	Mg2+	Fe2+	SiO2	$TDS$	T
1	7.05	175	2620	165	7.9	400	29	474	475	0.6	60.5	4407.00	25.20
2	6.94	155	2500	180	5.3	422	38	532	383	0.2	36	4251.50	25.60
3	7.37	175	2650	168	5.3	450	30	561	406	0.15	55.7	4501.15	25.00
4	7.48	100	2420	192	5.7	307	30	512	409	0.11	53.4	4029.21	25.10
5	7.24	122	1715	150	6.9	257	28	368	292	0.09	52.5	2991.49	24.90
6	7.27	216	2230	323	9.6	369	30	480	399	0.1	65	4121.70	25.50
7	7.05	190	3180	306	3	458	17	783	483	0.35	57	5477.35	25.30
8	7.05	167	2418	175	6	451	29	660	264	0.5	57	4227.50	25.00
9	7.03	92	2680	166	4.3	339	35	605	428	0.13	30	4379.43	24.80
10	7.46	287	2684	196	1	720	48	432	370	0.09	59	4797.09	25.40
11	7.10	304	3362	180	2.2	830	85	566	453	1	32	5815.20	25.70
12	7.10	305	3360	180	2	828	83	570	450	0.8	30	5808.80	25.00
13	7.40	184	2420	182	1.4	324	32	570	390	0.27	56.3	4159.97	25.20
14	7.10	185	2872	200	5	383	28.9	594	505	0.48	55.8	4829.18	25.10
15	7.80	155	2610	209	0.5	399	38.1	645	405	0.21	92.9	4554.71	25.00
16	7.40	152	2966	273	12.9	469	33.6	600	504	0.19	54.5	5065.19	24.80
17	6.90	260	3023	218	5	425	36.9	632	552	0.08	54.7	5206.68	24.60
18	7.70	173	2930	253	6.8	410	17	620	504	0.14	46	4959.94	25.70
19	7.00	170	2758	232	7.2	363	38.2	669	546	0.15	50.8	4834.35	25.50
20	7.60	215	484	85.6	13.6	208	11.7	76.8	78.1	0.094	45.9	1218.79	25.00
21	8.04	193	1831	150	8.36	468	22.5	395	323	0.17	52.1	3443.13	25.50
22	8.19	197	1715	148	8.1	622	28.6	423	308	0.11	34.2	3484.01	25.20
23	7.72	227	654	108	6.73	214	15.6	120	88.5	1.21	66.6	1501.64	25.10
24	7.58	196	2259	152	74.8	354	35.1	465	418	1.22	62.3	4017.42	25.00

shows the feedwater characteristics in terms of pH, T and inorganic composition. The total dissolved salts ($TDS$) content was considered as the sum of the analyzed ions and not the measurement of $TDS$ itself as not every single ion was analyzed. The highest $TDS$ were found in sample 11 (5815.20 mg L${}^{-1}$) and the lowest in sample 20 (1218.79 mg L${}^{-1}$). The silt density index ($SDI$) was assumed to be between 2 and 3, as is usual for this type of water after a 5 $\mathsf{\mu }$m microfiltration stage [55].

2.2. Bwro Desalination System

The BWRO system considered for this study has 3 PVs in the first stage and 2 PVs in the second stage (3:2) and is shown in Figure 1. Six SWMMs per PV were considered along with a FILMTEC™ membrane module. The BW30-400 computational tool used was validated with experimental data of full-scale BWRO desalination plants with the aforementioned SWMMs installed [53]. In the cited study, the purpose of the computational tool had been to provide optimal BWRO designs. In the present study, this tool is used to simulate the operating windows of the different configurations under different $C_{\mathrm{f}}$. PVs of 6 SWMMs were considered as this is a typical PV size [53]. Valves 1 to 6 allowed the configuration of the BWRO system to be changed depending on the feedwater solute concentration and the input power ($P_{\mathrm{in}}$) to the system. Non-return valves have to be installed (not shown in Figure 1) to avoid reverse flow to PVs that are in off position. The $P_{\mathrm{in}}$, supplied by the high pressure pump (output power of the high pressure pump) is a manipulable variable that depends on $Q_{\mathrm{f}}$ and $p_{\mathrm{f}}$ set by the variable frequency drive of the high pressure pump. Another manipulable variable is R through the reject flow which depends on the on/off percentage of the RO concentrate valve. Specific high pressure pumps and their performances were not considered in this study. The different configurations that could be established were 1:0, 2:0, 3:0, 2:1, 3:1 and 3:2. For each $P_{\mathrm{in}}$ and system configuration, the operating point that provided maximum production was selected as the use of RES to power the BWRO system was assumed. Most BWRO desalination plants in Gran Canaria are used for agricultural irrigation purposes so no permeate quality restrictions were added.

2.3. Process Modeling

The solution-diffusion transport model [56,57], which presumes that the RO membrane does not have porous or imperfections, was utilized. This model is based on considering that each solvent and solute are dissolved in the membrane separately on the feed-brine side and then diffused in individual fluxes through the membrane under the effect of pressure and concentration gradients. This is the most extended model and provides results close to the real behavior of RO systems for both seawater and brackish water [58]. The mentioned transport model was implemented in the algorithm [53] as it usually provides results close to the real behavior of these systems. The transport equations used mean membrane element values, and permeate pressure drops as well as T changes along the RO system were disregarded. The calculation algorithm considers some simplifications that have been detailed in a previous work [53]. Figure 2 shows the inputs and outputs of the calculation algorithm considering the constraints established by the membrane manufacturer (maximum permeate flow ($Q_{\mathrm{p}\text{-}\max }$), minimum rejection flow ($Q_{\mathrm{r}\text{-}\min }$) and maximum feed flow ($Q_{\mathrm{f}\text{-}\max }$). One of the main limiting factors in BWRO desalination is the presence of poorly soluble compounds in the feedwater that can cause scaling. As a result, antiscalant products are commonly used in BWRO desalination plants to avoid the problems caused by scaling and increase the maximum flux recovery ($R_{\max }$). $R_{\max }$ depends, amongst other things, on the type of antiscalant that is used. The calculation algorithm has a specific function (R function) where $R_{\max }$ is calculated for various antiscalants [59]. The aforementioned algorithm provides the possible operating points in accordance with the considered constraints and BWRO system configurations. With the inputs, the algorithm calculates the outputs considering the mean operating parameter values per SWMM. The calculation algorithm assumes a negligible pressure decrease on the permeate side, constant pressure drop along the membrane elements on the feed-brine side, constant permeate flow per membrane element, constant feed-brine concentration ($C_{{\mathrm{fb}}_{\mathrm{i}}}$) on the membrane surface ($C_{{\mathrm{m}}_{\mathrm{i}}}$) and constant membrane element feed pressure ($p_{{\mathrm{f}}_{\mathrm{i}}}$). Equations (1) and (2) [60] were used to determine the outputs of the BWRO system.

$$\begin{array}{c}{Q}_{\mathrm{p}}=\sum _i^n{Q}_{{\mathrm{p}}_i}=\sum _i^n\left(A·TCF·FF·S_{{\mathrm{m}}_{\mathrm{i}}}·\right(p_{{\mathrm{f}}_i}-\frac{\mathrm{a}·{\left(\frac{Q_{{\mathrm{f}}_i}+Q_{{\mathrm{r}}_i}}{2}\right)}^{\mathrm{b}}·0.07}{2}-p_{{\mathrm{p}}_i}-0.0787·(273+T)·\hfill \\ \hfill {\left(\Sigma m_{\mathrm{j}}\right)}_{\mathrm{f}}·\frac{\frac{C_{{\mathrm{f}}_i}+C_{{\mathrm{b}}_i}}{2}}{C_{{\mathrm{f}}_i}}·{\mathrm{e}}^{0.7·\frac{Q_{{\mathrm{p}}_i}}{\frac{Q_{{\mathrm{f}}_i}+Q_{{\mathrm{r}}_i}}{2}}}+0.787·(273+T)·{\left(\Sigma m_{\mathrm{j}}\right)}_{\mathrm{p}}\left)\right)\end{array}$$

(1)

$$C_{{\mathrm{p}}_{\mathrm{j}}}=B_{\mathrm{j}}·{\mathrm{e}}^{0.7·\left(\frac{Q_{{\mathrm{p}}_i}}{\frac{Q_{{\mathrm{f}}_i}+Q_{{\mathrm{r}}_i}}{2}}\right)}·TCF·\frac{S_{\mathrm{m}}}{Q_{{\mathrm{p}}_i}}·\frac{C_{{\mathrm{f}}_{\mathrm{j}}}·\left(1+\frac{1}{1-\frac{Q_{\mathrm{p}}}{Q_{\mathrm{f}}}}\right)}{2}$$

(2)

If $T⩾25$ ${}^{\circ }$C:

$$TCF=\exp \left[2640·\left(\frac{1}{298}-\frac{1}{273+T}\right)\right]$$

(3)

If $T⩽25$ ${}^{\circ }$C:

$$TCF=\exp \left[3020·\left(\frac{1}{298}-\frac{1}{273+T}\right)\right],$$

(4)

where $Q_{\mathrm{p}}$ is the permeate flow of the RO system, i is the membrane element (1...n), n is the number of membrane elements in series, $Q_{{\mathrm{p}}_{\mathrm{i}}}$ is the permeate flow of the membrane element i, A is the average water permeability coefficient of the membrane, $TCF$ is the temperature correction factor, $FF$ is the fouling factor (considered $=1$, new SWMMs), $S_{{\mathrm{m}}_{\mathrm{p}}}$ is the membrane area, a and b are two parameters obtained experimentally to calculate the pressure drop, $p_{{\mathrm{p}}_{\mathrm{i}}}$ is the permeate pressure (considered as 5 psi), T is the feed temperature, m is the molal concentration of each ion j, $C_{\mathrm{b}}$ is the concentration in the brine, B is the average ion permeability coefficient of the membrane. The $p_{\mathrm{f}}$ range considered was between 7 and 20 bar in steps of 0.5 bar, and the $Q_{\mathrm{f}}$ range between $Q_{\mathrm{r}\text{-}\min }$ and $Q_{\mathrm{f}\text{-}\max }$ in steps of 10 m${}^3$ d${}^{-1}$.

3. Results and Discussion

Figure 3 and Figure 4 show the different SOWs considering the different BWRO configurations (1:0, 2:0…) and two different $C_{\mathrm{f}}$ (1.2 and 5.8 g L${}^{-1}$, respectively). The irregularities in the contours of the surfaces are due to the $p_{\mathrm{f}}$ and $Q_{\mathrm{f}}$ steps. It can be observed that with lower $C_{\mathrm{f}}$ there is greater separation along the x-axis between the different SOWs. This is because low osmotic pressure of the feed solution allows water production with low $P_{\mathrm{in}}$, which can result in SWMMs operating outside their recommended range (in terms of $Q_{\mathrm{r}\text{-}\min }$) due to the very high permeate production of the first SWMMs. Figure 3 shows a possible operating range for the 1.0 configuration at very low $P_{\mathrm{in}}$. However, the 2:0, 3:0 and 3:1 configurations can be discarded, as higher permeate productions can be attained with the 2:1 and 3:2 configurations with the same $P_{\mathrm{in}}$. The same occurs when considering higher $C_{\mathrm{f}}$ (Figure 4), although in this case the operating range of configuration 1:0 is shorter. Having higher $C_{\mathrm{f}}$ means higher osmotic pressure and a lower number of operating points that are outside the recommended range. This is because the first SWMMs do not produce a high amount of permeate due to osmotic pressure, resulting in the subsequent SWMMs remaining within the recommended range since, as we move along the PV, the SWMMs produce less permeate flow. For the solution with higher $C_{\mathrm{f}}$, operating conditions with higher $P_{\mathrm{in}}$ were found to be suitable as higher osmotic pressure allows the BWRO system to remain within the SOW. However, the energy required is also higher and production is decreased compared to the case with lower $C_{\mathrm{f}}$. It can be appreciated how permeate production of more than 700 m${}^3$ d${}^{-1}$ can be obtained with sample 20 as feed solution (Figure 3), whereas, with sample 11 as feed solution, permeate production is below 600 m${}^3$ d${}^{-1}$ and more energy is required. The SOWs are affected by SWMM characteristics such as $S_{\mathrm{m}}$ or permeability coefficients. As a result of changes in these characteristics, there is a shift in the SOWS and, consequently, in the optimal operating points.

Figure 5 and Figure 6 show the R for the most relevant BWRO system configurations (1:0, 2:1 and 3:2), considering the $C_{\mathrm{f}}$ of samples 20 and 11, respectively. A wider operating range can be observed for configuration 3:2. This is due to the higher number of SWMMs allowing more possible operating points without exceeding the membrane manufacturer constraints. Higher R values were obtained for the configurations with two stages as more SWMMS are arranged in series in this sort of configuration. While the highest R can be attained with both the 2:1 and 3:2 configurations, the 2:1 configuration requires less input power but has a lower production than the 3:2 configuration (Figure 3). The highest R value attained with a single-stage configuration was around 60%. Considering as $C_{\mathrm{f}}$ a feed solution with higher $TD{S}_{\mathrm{f}}$ (5.82 g L${}^{-1}$), the surfaces of the three configurations considered are closer together, as observed previously (Figure 4). The change in feedwater inorganic composition results in a decrease in $R_{\max }$. With higher $TD{S}_{\mathrm{f}}$, the difference in terms of R between the single- and two-stage configurations is lower. It should be mentioned that, in terms of production, the 2-stage configurations outperform the others as more SWMMs are arranged in series and so more elements are producing permeate. The influence of $TD{S}_{\mathrm{f}}$ (and therefore of $\pi$) can be observed by comparing Figure 5 and Figure 6. With the 3:2 configuration and a $P_{\mathrm{in}}$ of 8 kW, an R of about 77% can be observed in Figure 5 compared to a value of about 64% in Figure 6. Naturally, this also affects the production of the system and its efficiency.

Figure 7 and Figure 8 show the operating points that maximize $Q_{\mathrm{p}}$ for the BWRO configurations 1:0, 2:1 and 3:2, considering the $C_{\mathrm{f}}$ of samples 20 and 11, respectively. It can be observed that with higher $C_{\mathrm{f}}$ the curves are closer together and even intersect. Another factor affected by $C_{\mathrm{f}}$ is the appropriate $P_{\mathrm{in}}$ (for maximizing $Q_{\mathrm{p}}$) range using each configuration. This range is notably lower for configurations 1:0 and 2:1. The operating curves of the 2:1 and 3:2 configurations are so close that a jump from 1:0 to 3:2 can be made directly depending on the trend of $P_{\mathrm{in}}$. It can be observed that the curves are longer for the feedwater with higher $C_{\mathrm{f}}$ than for sample 20 (lower $C_{\mathrm{f}}$). This is because at lower $C_{\mathrm{f}}$, SWMMs produce more $Q_{\mathrm{p}}$ and are more likely to not meet the $Q_{\mathrm{r}\text{-}\min }$ constraint or exceed the $Q_{\mathrm{p}\text{-}\max }$ per SWMM. The BWRO system operation with higher $C_{\mathrm{f}}$ allows a wider operating range without exceeding the imposed constraints but producing a lower $Q_{\mathrm{p}}$ with the same $P_{\mathrm{in}}$.

Table 2. $P_{\mathrm{in}}$ (kW) range for different BWRO configurations and five $C_{\mathrm{f}}$ (samples 20, 5, 22, 3 and 11 (Table 1)).

	${\mathit{C}}_{\mathbf{f}}$ (g L−1)
Configuration	1.2	2.99	3.48	4.5	5.82
$1:0$	1.37–2.89	1.13–2.4	1.13–2.4	0.89–1.93	0.81–2.07
$2:1$	2.73–4.57	2.26–3.71	2.26–3.71	1.78–2.90	1.91–3.39
$3:2$	4.34–12.34	3.39–15.36	3.39–17.26	2.67–17	3.05–19.22

shows the range of $P_{\mathrm{in}}$ in which each BWRO configuration should be applied considering five samples (20, 5, 22, 3 and 11 (Table 1)) representing different $C_{\mathrm{f}}$ of the studied groundwater well. Some overlap was considered in $P_{\mathrm{in}}$ to avoid excessive configuration changes, depending on the $P_{\mathrm{in}}$ trend (increasing or decreasing). It should be mentioned that some operating points that were very close to the constraints established by the membrane manufacturer were removed to avoid instabilities in the operation of the BWRO system. This is the main reason why higher $P_{\mathrm{in}}$ was required for lower $C_{\mathrm{f}}$ in addition to the selected $p_{\mathrm{f}}$ and $Q_{\mathrm{f}}$ steps that eliminate some possible operating points. The $P_{\mathrm{in}}$ required depends, among other things, on the osmotic pressure of the feed solution, which in turn not only depends on the amount of $TDS$ but on its inorganic composition.

Table 3. R (%) range for different BWRO configurations and five $C_{\mathrm{f}}$ (samples 20, 5, 22, 3 and 11 (Table 1)).

	${\mathit{C}}_{\mathbf{f}}$ (g L−1)
Configuration	1.2	2.99	3.48	4.5	5.82
$1:0$	53.32–61.02	43.13–59.88	43.34–60.17	35.66–50.60	25.64–50.71
$2:1$	69.92–80.91	52.28–66.78	52.45–66.96	41.58–52.85	32.27–50.76
$3:2$	71.22–79.77	55.68–66.82	55.82–58.11	43.99–61.13	39.22–56.44

shows the R range for each configuration. These values are important as the reference for the on/off percentages of the RO concentrate valve (Figure 1). The data of the operating points for maximizing $Q_{\mathrm{p}}$ using configurations 1:0, 2:1 and 3:2 for the five samples shown in Table 2 and Table 3 can be found in Appendix A.

4. Conclusions

Operating a BWRO system is far from simple and acquires greater complexity under variable conditions of $C_{\mathrm{f}}$ (usual for groundwater sources) and $P_{\mathrm{in}}$ (for example when the BWRO is powered by renewable energy sources). An on-off control strategy based on simulations is presented in this work considering a BWRO system with a 3:2 configuration that is able to operate with other configurations (1:0, 2:0, 3:0, 2:1 and 3:1) depending on the $P_{\mathrm{in}}$ available. The operating points of each configuration that maximize $Q_{\mathrm{p}}$ for each $P_{\mathrm{in}}$ were considered. The simulations showed that only the 1:0, 2:1 and 3:2 configurations were of interest in the studied case. Depending on the variation of $C_{\mathrm{f}}$ and the $Q_{\mathrm{f}}$ available from the source, larger BWRO systems are possible with a wider range of possible configurations. It was found that with higher $C_{\mathrm{f}}$ there was closer concordance between the SOWs for the different configurations considered. Lower $C_{\mathrm{f}}$ values allowed the BWRO system to produce more permeate water with a wider operating range for the 1:0, 2:1 and 3:2 configurations. In future works, high pressure pump performances and the modelling and control of variable frequency drives and RO concentrate valves should be considered to obtain more accurate results in the operation of this type of system under variable operating conditions. Permeate quality constraints were not considered in this study as the water product was assumed to be for agricultural irrigation. Consideration of a maximum $C_{\mathrm{p}}$ would also be of interest in terms of its impact on SOWs and suitable operating ranges.