CONCURRENT DESALINATION AND BORON REMOVAL (CDBR) PROCESS

Abstract

A concurrent desalination and boron removal (CDBR) process and a system thereof are provided. The system includes: a plurality of single-stage reverse osmosis (SSRO) stages connected in series, and a countercurrent membrane cascade with recycle (CMCR). The process includes the following steps: introducing a retentate from one SSRO stage or a series of SSRO stages optimally as a feed to a CMCR; countercurrent a retentate flow and a permeate flow in the CMCR; permeate recycling to a retentate side in the CMCR; retentate self-recycling in at least one of membrane stages in the CMCR; introducing a permeate from the SSRO stage(s) as a feed to an LPMS; and blending permeate streams from the CMCR and LPMS to achieve concentrations in a water product.

Claims

1. A system for concurrent desalination and boron removal (CDBR) process, comprising: a plurality of single-stage reverse osmosis (SSRO) stages connected in series, wherein each SSRO stage comprises one or more reverse osmosis (RO) modules connected in series; and a countercurrent membrane cascade with recycle (CMCR), wherein the CMCR comprises at least two stages including a low pressure membrane stage (LPMS), wherein a retentate from the SSRO stage is fed to the CMCR and a permeate from the SSRO stage is fed to the LPMS; permeate streams from the CMCR and LPMS are blended to achieve a predetermined boron concentration and/or a predetermined salt concentrations in a water product.

2. The system according to claim 1, wherein each stage in the SSRO, CMCR, and LPMS consists of one or more membrane modules connected in parallel.

3. The system according to claim 1, wherein the predetermined salt concentration is equal to or less than 350 ppm.

4. The system according to claim 1, wherein the predetermined boron concentration is equal to or less than 0.5 ppm.

5. The system according to claim 1, wherein the SSRO stage and the CMCR operate at a same osmotic pressure differential (OPD), neglecting small losses owing to a pressure drop required for a flow through lines and membrane modules or to cause permeation in the membrane modules.

6. The system according to claim 1, wherein the system supplies a boron removal at a higher water recovery at a lower osmotic pressure differential (OPD) and at a reduced specific energy consumption (SEC) relative to a conventional SSRO for saline water or an aqueous feed containing relatively low molecular weight solutes.

7. The system according to claim 1, wherein the system supplies a salt removal at a higher water recovery at a lower osmotic pressure differential (OPD) and at a reduced specific energy consumption (SEC), relative to a conventional SSRO for saline water or an aqueous feed containing relatively low molecular weight solutes.

8. The system according to claim 1, comprising one or more stages of the CMCR, wherein an osmotic pressure differential (OPD) is reduced in the one or more stages of the CMCR relative to an OPD in the SSRO stage.

9. system according to claim 1, comprising one or more stages of the CMCR, wherein an osmotic pressure differential (OPD) is increased in the one or more stages of the CMCR relative to an OPD in the SSRO stage.

10. A concurrent desalination and boron removal (CDBR) process for a production of potable and irrigation water, by comprising the below steps: introducing a retentate from one SSRO stage or a series of SSRO stages optimally as a feed to a CMCR; countercurrent a retentate flow and a permeate flow in the CMCR; permeate recycling to a retentate side in the CMCR; retentate self-recycling in at least one of membrane stages in the CMCR; introducing a permeate from the SSRO stage(s) as a feed to an LPMS; and blending permeate streams from the CMCR and LPMS to achieve concentrations in a water product.

11. The process according to claim 10, wherein the retentate from the SSRO stage is the feed to a stage in the CMCR, where a concentration of the CMCR is closest to concentrations of streams entering this stage.

12. The process according to claim 10, wherein a salt rejection of the membrane stages in the CMCR decreases in a direction of a retentate product to permit a permeation of a salt or other low molecular weight solutes from a high pressure side of membranes to a low pressure side of membranes in order to reduce an osmotic pressure differential (OPD).

13. The process according to claim 10, wherein an effective rejection in each stage of the CMCR is achieved by decreasing or increasing a pressure of the each stage.

14. The process according to claim 10, wherein a portion of the retentate from one or more stages is recycled back to a feed to a same stage in order to increase a recovery.

15. The process according to claim 10, wherein a safety factor in a stage is a ratio of the retentate to permeate flow in the stage, the ratio is less than one owing to a removal of sparingly soluble fouling agents in one or more stages preceding the stage in a direction of the retentate flow.

16. The process according to claim 10, wherein a water recovery in the LPMS is optimized to lower a specific energy consumption.

17. The process according to claim 10, wherein a boron concentration and/or a salt concentrations are reduced in seawater or brackish water to produce the potable and/or irrigation water using RO and NF membranes and high flux membranes.

18. A method of production of potable water or irrigation water, comprising: using the system of claim 1 to produce the potable water or the irrigation water.

19. (canceled)

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0025] FIG. 1. The schematic of the 4-stage embodiment of the CDBR invention whereby the high pressure retentate from stage 1, an RO stage, is the feed to a CMCR consisting of stage 2, an NF stage, and stage 3, an RO stage, and the permeate is the feed to stage 4, an LPMS. The CMCR employs permeate recycle from stage 2 to the high pressure side of stage 3 and retentate recycle from the high to the low pressure side of stage 2 via an NF membrane. The permeate streams from stage 3 and stage 4 are blended to achieve the desired salt and boron concentrations.

[0026] FIG. 2. (a) Osmotic pressure difference and (b) net specific energy consumption in the CDBR invention as a function of overall water recovery values ranging from 50% to 75%. These results are for a feed containing 35000 ppm of salt and 10 ppm of boron and a potable water product containing no more than 350 ppm of salt and 0.5 ppm of boron. Values are compared to those of the conventional SSRO for desalination that cannot reduce the boron concentration to 0.5 ppm.

[0027] FIG. 3a. The schematic of an alternative embodiment of the CDBR invention: CDBR-B, where the permeate stream out of Stage 1 is split in two fractions through a flow splitter, and one fraction is fed to the Stage 4, whereas the other fraction bypasses Stage 4 to be mixed with the permeate streams out of Stage 4 and Stage 3.

[0028] FIG. 3b. The schematic of an alternative embodiment of the CDBR-B invention: CDBR-BR, where the retentate from Stage 4 is totally or partially recycled as feed to Stage 1.

[0029] FIG. 4. The schematic of an alternative embodiment of CDBR invention with two SSRO stages wherein the salt water feed is introduced to the high pressure side of the first SSRO stage and the retentate of the first SSRO stage is introduced to the high pressure side of the second SSRO stage while the retentate of the second SSRO stage is introduced to the CMCR unit.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0030] The present invention involves an SSRO stage (stage 1) whose retentate stream serves as the feed to a two-stage CMCR (stages 2 and 3) and whose permeate stream serves as the feed to an LPMS (stage 4). FIG. 1 is a schematic showing the 4-stage embodiment of this CDBR invention. The SSRO stage involves one or more reverse osmosis modules connected in parallel. In another embodiment of the CDBR invention, stage 1 could consist of two or more RO modules or parallel trains of RO modules connected in series. Each stage in the CMCR could involve one or more membrane modules connected in parallel. The direction of the retentate flow in the CMCR is referred to as the upstream direction (to the right in FIG. 1) and the direction of the permeate flow in the CMCR is referred to as the downstream direction (to the left in FIG. 1). In FIG. 1 the retentate (high pressure) stream from stage 1 is introduced between stages 2 and 3 in the CMCR. In another embodiment of the CDBR invention the CMCR could involve more than two stages in which case the retentate stream from stage 1 would be introduced optimally between two stages in the CMCR. The optimal point is that at which the concentration of the retentate stream from stage 1 that serves as the feed to the CMCR is closest to that of the retentate from the stage immediately downstream and the permeate recycle stream immediately upstream from the point at which the feed is introduced. In the 4-stage embodiment of this invention shown in FIG. 1, the CMCR operates at the same pressure as the retentate stream from stage 1 implying that no booster pump is required for the feed to the CMCR. When more than two stages are employed in the CMCR, all the stages can be operated at the same pressure implying that no interstage pumping is required on the high pressure side of the CMCR. Alternatively the pressure can be reduced between successive stages in the direction of the retentate flow in the CMCR in order to reduce the OPD at the expense of a reduced water recovery. The permeate stream from stage 1 is introduced as the feed to an LPMS (stage 4) in order to reduce its boron concentration. Stage 4 can be run at a pressure only slightly above the ambient pressure since there is very little difference in the salt concentration between the feed and permeate sides of the membrane in this stage. The boron concentration in the permeate from stage 4 will be well below 0.5 ppm. Hence, in order to achieve the desired boron concentration in the product stream, the permeate from stage 4 is blended with the permeate from stage 3 in the CMCR whose boron concentration usually is higher than 0.5 ppm for a typical saline water feed containing 10 ppm of boron.

[0031] The manner in which this CDBR invention reduces the SEC while reducing the OPD, increasing the water recovery, and achieving the desired salt and boron concentrations first will be explained in qualitative terms, after which the embodiment of this invention shown in FIG. 1 will be analyzed quantitatively. Note that the analysis done here is for operation of stage 1 and the CMCR stages at the thermodynamic limit. However, the thermodynamic limit is not relevant for stage 4 for which the required pressure differential is determined from the permeate volumetric flux and the permeability coefficient for the membrane in this stage. Design at the thermodynamic limit implies that the pressure is just equal to that required to overcome the OPD owing to the concentration difference between the high and low pressure sides of the membrane. No allowance is made for the small pressure losses in the lines leading to and from the membrane stages or within the membrane modules on the high pressure side or to cause permeation through the membranes. This is standard practice in determining the efficiency of a membrane process and will be used to assess the performance of this CDBR invention for concurrent desalination and boron removal as well as determining the performance of conventional SSRO for desalination in the absence of any boron removal, which is used as the basis for comparison.

[0032] This CDBR invention combines SSRO with a CMCR by sending the retentate stream from the SSRO as the feed to the CMCR. In FIG. 1 the retentate stream from stage 1 is introduced as the feed between stages 2 and 3 of the CMCR. By introducing the retentate from stage 1 as the feed to the CMCR, more water can be recovered, which contributes to decreasing the SEC. This can be done without any increase in the OPD in order to minimize the pumping costs that contribute to the SEC. Hence, one embodiment of this CDBR invention involves operating the CMCR at the same pressure as the retentate stream from stage 1 and not employing any interstage pumping on the high pressure (retentate) side of the CMCR. Since the retentate from the SSRO has a higher salt concentration than that of the saline water feed to the SSRO, operating the CMCR without any interstage pumping requires reducing the OPD in the CMCR. This is done by permeate recycle from stage 2 to the high pressure side of stage 3 in the CMCR while at the same time using a membrane in stage 2 that passes more salt than the highly rejecting membrane used in stage 3. The combination of recycle of the permeate from stage 2 to the high pressure side of stage 3 and some salt permeation from the high pressure side to the permeate side of the membrane in stage 2 reduces the concentration difference across the membranes in both stages 2 and 3, thereby permitting a high recovery of potable water without the need to increase the pressure beyond that of the retentate stream from stage 1. Another embodiment of this CDBR invention would allow for a pressure decrease or increase from the point at which the feed is introduced in the direction of the retentate flow, which is to the right in FIG. 1. In particular, decreasing or increasing the pressure can be used to decrease or increase the recovery in stage 2 to compensate for not being able to obtain an NF membrane with the optimal salt rejection. The boron concentration in the permeate from the CMCR usually will be higher than 0.5 ppm since the CMCR is processing the retentate from stage 1 whose boron concentration will be much higher than that of the saline water feed to this stage. Hence, in order to achieve the desired boron concentration, the permeate from stage 1, whose boron concentration is already significantly reduced from that of the feed to this stage, serves as the feed to stage 4, an LPMS. The latter employs a membrane with a boron rejection similar to that of the membrane in stage 1 and hence reduces the boron concentration to well below 0.5 ppm. The permeate from stage 4 is blended in the proper proportion with that from stage 3 in the CMCR in order to achieve the desired boron concentration in the blended product stream. This configuration in the CDBR concurrently achieves desalination and boron removal while minimizing the amount of water that is sent to stage 4.

[0033] In order to demonstrate quantitatively that this CDBR invention can achieve a boron removal down to 0.5 ppm concurrently with desalinating seawater to produce a potable water product having a salt concentration less than 350 ppm at a high water recovery, reduced OPD, and competitive SEC, the mathematical equations describing the interrelationship between the volumetric fluxes denoted by Qi in FIG. 1, and the salt and boron concentrations expressed as mass per unit volume and denoted by C.sub.si and C.sub.bi, respectively, in FIG. 1, where the subscript i denotes the location of the particular stream or concentration, will be solved analytically. The solution to this system of algebraic equations will permit determining the recovery, OPD, SEC, and initially unspecified salt and boron rejections in each stage of the CDBR and LPMS.

[0034] The analysis of this 4-stage CDBR invention involves solving overall material and solute balances for each of the four stages and at the two mixing points. The balances over stage 1 constitute 3 equations involving 9 unknowns (Q.sub.f, C.sub.fs, C.sub.fb, Q.sub.0, C.sub.0s, C.sub.0b, Q.sub.1, C.sub.1s, C.sub.1b). The balances over stage 2 constitute 3 equations involving 9 unknowns (Q.sub.2, C.sub.2s, C.sub.2b, Q.sub.4, C.sub.4s, C.sub.4b, Q.sub.6, C.sub.6s, C.sub.6b). The balances over stage 3 constitute 3 equations involving 6 unknowns (Q.sub.3, C.sub.3s, C.sub.3b, Q.sub.5, C.sub.5s, C.sub.5b). The balances over stage 4 constitute 3 equations in 6 unknowns (Q.sub.7, C.sub.7s, C.sub.7b, Q.sub.8, C.sub.8s, C.sub.8b). The balances at the mixing point between stages 2 and 3 constitute 3 equations and 0 unknowns. The balances at the mixing point where the permeate streams from stages 3 and 4 are blended constitute 3 equations in 3 unknowns (Q.sub.9, C.sub.9s, C9b). This totals 18 equations that involve 33 unknowns. This implies 15 degrees of freedom in solving the equations for this 4-stage CDBR process.

[0035] The 15 degrees of freedom were satisfied by specifying the following quantities shown in figure above: [0036] 1. Q.sub.f, flow rate of saline water feed to stage 1 [0037] 2. C.sub.fs, salt concentration in the feed to stage 1 [0038] 3. C.sub.fb, boron concentration in the feed to stage 1 [0039] 4. C.sub.9b, boron concentration in blended permeate streams from stages 3 and 4 [0040] 5. C.sub.0s=C.sub.3s required to have OPD in CMCR equal to OPD in stage 1 [0041] 6. .sub.1, OPD in stage 1 [0042] 7. .sub.2=.sub.3, equal OPDs in stages 2 and 3 of the CMCR [0043] 8. Y.sub.2, recovery in stage 2 [0044] 9. Y.sub.3, recovery in stage 3 [0045] 10. Y.sub.4, recovery in stage 4 [0046] 11. .sub.1s, salt rejection in stage 1 [0047] 12. .sub.1b, boron rejection in stage 1 (scaled to salt rejection in stage 1) [0048] 13. .sub.2b, boron rejection in stage 2 (scaled to salt rejection in stage 2) [0049] 14. .sub.3b, boron rejection in stage 3 (scaled to salt rejection in stage 3) [0050] 15. .sub.4s, salt rejection in stage 4 (scaled to boron rejection in stage 4)

[0051] Specification of the 15 quantities is not unique. The values of other input parameters could be specified.

[0052] Overall and solute mass balances for stage 1 are given by the following:

Q.sub.f=Q.sub.0+Q.sub.1 (1)

Q.sub.fC.sub.fs=Q.sub.0C.sub.0s+Q.sub.iC.sub.1s (2)

Q.sub.fC.sub.fb=Q.sub.0C.sub.0b+Q.sub.1C.sub.1b (3)

[0053] Overall and solute mass balances for stage 2 are given by the following:

Q.sub.6=Q.sub.2+Q.sub.4 (4)

Q.sub.6C.sub.6s=Q.sub.2C.sub.2s+Q.sub.4C.sub.4s (5)

Q.sub.6C.sub.6b=Q.sub.2C.sub.2b+Q.sub.4C.sub.4b (6)

[0054] Overall and solute mass balances for stage 3 are given by the following:

Q.sub.4=Q.sub.3+Q.sub.5 (7)

Q.sub.4C.sub.4s=Q.sub.3C.sub.3s+Q.sub.5C.sub.5s (8)

Q.sub.4C.sub.4b=Q.sub.3C.sub.3b+Q.sub.5C.sub.5b (9)

[0055] Overall and solute mass balances for stage 4 are given by the following:

Q.sub.0=Q.sub.7+Q.sub.8 (10)

Q.sub.0C.sub.0s=Q.sub.7C.sub.7s+Q.sub.8C.sub.8s (11)

Q.sub.0C.sub.0b=Q.sub.7C.sub.7b+Q8C.sub.8b (12)

[0056] Overall and solute mass balances at the mixing point between stages 2 and 3 are given by the following:

Q.sub.6=Q.sub.1+Q.sub.5 (13)

Q.sub.6C.sub.6s=Q.sub.1C.sub.1s+Q.sub.5C.sub.5s (14)

Q.sub.6C.sub.6b=Q.sub.1C.sub.1b+Q.sub.5C.sub.5b (15)

[0057] Overall and solute mass balances at the mixing point where the permeate streams from stages 3 and 4 are blended are given by the following:

Q.sub.9=Q.sub.3+Q.sub.7 (16)

Q.sub.9C.sub.9s=Q.sub.3C.sub.3s+Q.sub.7C.sub.7s (17)

Q.sub.9C.sub.9b=Q.sub.3C.sub.3b+Q.sub.7C.sub.7b (18)

[0058] The additional equations that relate the volumetric fluxes and concentrations are given by the following:

.sub.1=K(C.sub.1sC.sub.0s) OPD is specified in stage 1 (19)

.sub.2=.sub.3.Math.C.sub.2sC.sub.4s=C.sub.5sC.sub.3s OPDs set equal in CMCR (20)

[00001]$\begin{array}{cc}{Y}_2=\frac{Q_4}{Q_6}& \left(21\right)\\ Y_3=\frac{Q_3}{Q_4}& \left(22\right)\\ Y_4=\frac{Q_7}{Q_0}& \left(23\right)\\ {}_{1.Math.s}=\frac{C_{\mathrm{fs}}-C_{0.Math.s}}{C_{\mathrm{fs}}}& \left(24\right)\\ {}_{1.Math.b}=\frac{C_{\mathrm{fb}}-C_{0.Math.b}}{C_{\mathrm{fb}}}=\frac{0.90}{0.97}.Math.{}_{1.Math.s}& \left(25\right)\\ {}_{2.Math.b}=\frac{C_{6.Math.b}-C_{4.Math.b}}{C_{6.Math.b}}=\frac{{}_{1.Math.b}}{{}_{1.Math.s}}.Math.{}_{2.Math.s}& \left(26\right)\\ {}_{3.Math.b}=\frac{C_{4.Math.b}-C_{3.Math.b}}{C_{4.Math.b}}=\frac{{}_{1.Math.b}}{{}_{1.Math.s}}.Math.{}_{3.Math.s}& \left(27\right)\\ {}_{4.Math.s}=\frac{C_{0.Math.s}-C_{7.Math.s}}{C_{0.Math.s}}=\frac{{}_{1.Math.s}}{{}_{1.Math.b}}.Math.{}_{4.Math.b}& \left(28\right)\end{array}$

[0059] Solving these equations gives the following for the volumetric fluxes:

[00002]$\begin{array}{cc}{Q}_0=\frac{Q_f\left(C_{1.Math.s}-C_{\mathrm{fs}}\right)}{C_{1.Math.s}-C_{0.Math.s}}& \left(29\right)\\ Q_1=\frac{Q_f\left(C_{\mathrm{fs}}-C_{0.Math.s}\right)}{C_{1.Math.s}-C_{0.Math.s}}& \left(30\right)\\ Q_2=Q_6-Q_4& \left(31\right)\\ Q_3=Y_2.Math.Y_3.Math.Q_6& \left(32\right)\\ Q_4=Y_2.Math.Q_6& \left(33\right)\\ Q_5=\left(1-Y_3\right).Math.Y_2.Math.Q_6& \left(34\right)\\ Q_6=\frac{Q_1}{1-\left(1-Y_3\right).Math.Y_2}& \left(35\right)\\ Q_7=Y_4.Math.Q_0& \left(36\right)\\ Q_8=Q_0-Q_7& \left(37\right)\\ Q_9=Q_3+Q_7& \left(38\right)\end{array}$

[0060] Solving for the salt concentrations gives the following:

[00003]$\begin{array}{cc}{C}_{0.Math.s}=\left(1-{}_{1.Math.s}\right).Math.C_{\mathrm{fs}}& \left(39\right)\\ C_{1.Math.s}=\frac{{}_1}{K}+C_{0.Math.s}& \left(40\right)\\ C_{2.Math.s}=\frac{Q_1.Math.C_{1.Math.s}-Q_3.Math.C_{3.Math.s}}{Q_2}& \left(41\right)\\ C_{3.Math.s}=C_{0.Math.s}& \left(42\right)\\ C_{4.Math.s}=\frac{Q_1.Math.C_{1.Math.s}+Q_5.Math.C_{5.Math.s}-Q_2.Math.C_{2.Math.s}}{Q_4}& \left(43\right)\\ C_{5.Math.s}=\frac{\left(Q_4-Q_2\right).Math.Q_1.Math.C_{1.Math.s}+Q_2^2.Math.C_{2.Math.s}+\left(Q_2-Q_3\right).Math.Q_4.Math.C_{3.Math.s}}{Q_2\left(Q_4+Q_5\right)}& \left(44\right)\\ C_{6.Math.s}=\frac{Q_1.Math.C_{1.Math.s}+Q_5.Math.C_{5.Math.s}}{Q_6}& \left(45\right)\\ C_{7.Math.s}=\left(1-{}_{4.Math.s}\right).Math.C_{0.Math.s}& \left(46\right)\\ C_{8.Math.s}=\frac{Q_0.Math.C_{0.Math.s}-Q_7.Math.C_{7.Math.s}}{Q_8}& \left(47\right)\\ C_{9.Math.s}=\frac{Q_3.Math.C_{3.Math.s}+Q_7.Math.C_{7.Math.s}}{Q_9}& \left(48\right)\end{array}$

[0061] Solving for the boron concentrations gives the following:

[00004]$\begin{array}{cc}{C}_{0.Math.b}=\left(1-{}_{1.Math.b}\right).Math.C_{\mathrm{fb}}& \left(49\right)\\ C_{1.Math.b}=\frac{Q_f.Math.C_{\mathrm{fb}}-Q_0.Math.C_{0.Math.b}}{Q_1}& \left(50\right)\\ C_{2.Math.b}=\frac{Q_1.Math.C_{1.Math.b}-Q_3.Math.C_{3.Math.b}}{Q_2}& \left(51\right)\\ C_{3.Math.b}=\frac{\left(1-{}_{3.Math.b}\right).Math.\left(1-{}_{2.Math.b}\right).Math.Q_1.Math.C_{1.Math.b}}{Q_6-\left(1-{}_{3.Math.b}\right).Math.\left(1-{}_{2.Math.b}\right).Math.\left(\frac{Q_4}{1-{}_{3.Math.b}}-Q_3\right)}& \left(52\right)\\ C_{4.Math.b}=\left(1-{}_{2.Math.b}\right).Math.C_{6.Math.b}& \left(53\right)\\ C_{5.Math.b}=\frac{Q_4.Math.C_{4.Math.b}-Q_3.Math.C_{3.Math.b}}{Q_5}& \left(54\right)\\ C_{6.Math.b}=\frac{Q_1.Math.C_{1.Math.b}+\left(\frac{Q_4}{1-{}_{3.Math.b}}-Q_3\right).Math.C_{3.Math.b}}{Q_6}& \left(55\right)\\ C_{7.Math.b}=\frac{Q_9.Math.C_{9.Math.b}-Q_3.Math.C_{3.Math.b}}{Q_7}& \left(56\right)\\ C_{8.Math.b}=\frac{Q_0.Math.C_{0.Math.b}-Q_7.Math.C_{7.Math.b}}{Q_8}& \left(57\right)\end{array}$

[0062] The pressure required in stage 4 is given by the following:

[00005]$\begin{array}{cc}.Math..Math.P_4=\frac{Q_0}{P_4}& \left(58\right)\end{array}$

[0063] where P.sub.4 is the permeability coefficient of the membrane in stage 4. The overall water recovery from this 4-stage CDBR process is given by the following:

Y=Q.sub.9 (59)

[0064] The net specific energy consumption (SEC.sub.net), which is the energy required per unit of water produced allowing for the recovery of the pressure energy in the retentate via an energy-recovery device (ERD), is given by the following:

[00006]$\begin{array}{cc}{\mathrm{SEC}}_{\mathrm{net}}=\frac{Q_f.Math.{}_1+Q_4.Math.{}_3+Q_0.Math.{}_4}{{}_p.Math.Q_9}-\frac{{}_{\mathrm{ERD}}.Math.Q_2.Math.{}_1}{Q_9}& \left(60\right)\end{array}$

[0065] where p is the efficiency of the pumps and ERD is the efficiency of the ERD.

[0066] The predictions of Equations (29)-(60) will be used to establish the proof-of-concept for this CDBR invention. The performance of the CDBR invention will be assessed in terms of the OPD and SEC.sub.net required to produce a potable water product containing 0.5 ppm of boron and no more than 350 ppm of salt from a saline water feed containing 35000 ppm of salt and 10 ppm of boron. The fractional water recovery values for stages 2 and 3 are input parameters in solving the model equations, which were chosen to be 0.3 and 0.7, respectively.

[0067] Running stage 2 at a lower recovery increases the safety factor (ratio of retentate to permeate flow) in this stage, thereby helping to mitigate concentration polarization and fouling in this stage that has a feed containing a high concentration of divalent salts. Running stage 3 at a higher recovery is possible since the feed to this stage has passed through both stage 1 and stage 2, thereby removing all the divalent salts that could cause scaling. The feed to stage 4 is nearly pure water since it has passed through stage 1, an RO stage; hence, the OPD in stage 4 is negligible. Moreover, the foulants have been removed in the feed to stage 4. Hence, stage 4 can be run at a very high water recovery or equivalently a very low safety factor. The only requirement is that there be sufficient retentate flow to remove the small amount of boron rejected by the membrane in stage 4. Hence, stage 4 is assumed to have a water recovery of 95%. Pump and ERD efficiencies of 85% and 90%, respectively, are assumed, which are consistent with commercially available devices. The performance of the CDBR invention will be assessed in terms of the OPD and SEC.sub.net required to achieve the specified boron and salt concentrations in the product water for a range of overall water recoveries. The implications on the CDBR invention of using membranes having a range of salt rejections and a range of boron rejections also will be assessed. Whereas the salt and boron rejections are specified input parameters for stage 1, the salt rejections are predicted quantities in stages 2 and 3, and the boron rejection is a predicted quantity in stage 4. For stages 2 and 3 the boron rejection is scaled to the predicted salt rejection, whereas in stage 4 the salt rejection is scaled to the predicted boron rejection; that is, the ratio of the boron rejection to the salt rejection is assumed to be the same as that attainable via currently available commercial membranes that can achieve rejections of 90.0% and 99.7% for boron and salt, respectively.

[0068] The OPD is a specified input parameter used in solving Equations (1) to (28) for the volumetric fluxes and concentrations in the CDBR invention. The overall water recovery is determined from Equation (59) using the volumetric fluxes determined from Equations (29) to (38). FIG. 2 shows a plot of the OPD and SEC.sub.net as a function of overall water recovery ranging from 50% to 75%; these predictions are for achieving a product water with a salt concentration equal to or less than 350 ppm and a boron concentration of 0.5 ppm, both of which meet WHO recommendations for potable and irrigation water. The salt and boron rejections of the membranes for stages 1 to 4 and the recovery at stage 2 are summarized in Table 1. FIG. 2 also shows the OPD and SEC.sub.net for SSRO which cannot achieve 0.5 ppm of product water boron concentration.

TABLE-US-00001 TABLE 1 Required salt and boron rejections and recovery in stage 2 in the CDBR invention for both desalination and boron removal producing a water product with a salt concentration equal to 350 ppm and a boron concentration of 0.5 ppm. Recovery .sub.1s .sub.2s .sub.3s .sub.4s .sub.1b .sub.2b .sub.3b .sub.4b Y2 50% 0.997 0.833 0.990 0.545 0.900 0.752 0.894 0.492 0.165 65% 0.997 0.660 0.996 0.645 0.900 0.596 0.899 0.582 0.339 75% 0.996 0.543 0.997 0.731 0.899 0.490 0.900 0.660 0.456

[0069] It is of interest to determine the minimum value of the boron rejection required for the CDBR invention to produce product water that contains no more than 350 ppm of salt and a specified boron concentration of 0.5 ppm and to determine the implications for the CDBR invention if membranes with boron rejections higher than 90% could be obtained. FIG. 3 shows a plot of the boron rejection of the membrane in stage 4 as a function of the specified boron rejection of the membrane in Stage 1 required to achieve a product water containing no more than 350 ppm of salt and a specified boron concentration of 0.5 ppm for overall water recovery values of 50%, 65%, and 75%. Table 2 indicates that the specified water product concentrations can be achieved even with a membrane having a boron rejection as low as 0.804, 0.834, and 0.851 for an overall water recovery values of 50%, 65%, and 75%, respectively. These boron rejections are well below the 0.90 boron rejection attainable via currently available commercial RO membranes.

TABLE-US-00002 TABLE 2 Minimum boron rejections in the CDBR invention for overall water recovery values of 50%, 65%, and 75% required to produce a water product having a salt concentration equal to or less than 350 ppm and a specified boron concentration of 0.5 ppm. Recovery .sub.1b .sub.2b .sub.3b .sub.4b 50% 0.804 0.672 0.798 0.803 65% 0.834 0.552 0.833 0.833 75% 0.850 0.464 0.851 0.851

[0070] Table 3 compares the OPD and SEC.sub.net for conventional SSRO for just desalination and the novel CDBR invention for achieving a water product having a salt concentration of 350 ppm and a boron concentration of 0.5 ppm for overall water recoveries of 50%, 65% and 75%. Note that conventional SSRO cannot reduce the boron concentration to 0.5 ppm for a typical saline water feed containing 10 ppm of boron using commercially available RO membranes. The CDBR invention can achieve the same overall water recovery as conventional SSRO at a substantially reduced OPD. The CDBR invention reduces the OPD required for just desalination via SSRO by 10%, 18%, and 20% at overall water recovery values of 50%, 65%, and 75%, respectively. The CDBR invention results in an increase in the SEC.sub.net of 8%, 4%, and 2% for overall water recovery values of 50%, 65%, and 75%, respectively, relative to using conventional SSRO for just desalination. Since the CDBR invention can desalinate and reduce the boron concentration to 0.5 ppm at a substantially reduced OPD, it will translate to a significant reduction in the fixed costs for the pumps, piping, and pressure vessels relative to using SSRO for just desalination. Moreover, operation at lower pressure via the CDBR invention will reduce the maintenance costs for desalination and boron removal.

TABLE-US-00003 TABLE 3 Comparison of the OPD and SEC.sub.net for desalination using SSRO and the CDBR invention for both desalination and boron removal producing a water product with a salt concentration equal to or less than 350 ppm and a boron concentration of 0.5 ppm. 50% Recovery 65% Recovery 75% Recovery OPD SEC.sub.net OPD SEC.sub.net OPD SEC.sub.net Process (bar) (kWh/m.sup.3) (bar) (kWh/m.sup.3) (bar) (kWh/m.sup.3) SSRO 55.5 2.242 79.3 2.922 111 3.915 CDBR 50.2 2.420 64.9 3.033 88.9 3.990

[0071] The proof-of-concept for the CDBR invention has been shown in detail for the four-stage embodiment involving sending the retentate from an SSRO stage to a 2-stage CMCR and sending the permeate from the SSRO stage to an LPMS after which the permeate streams from the CMCR and LPMS are blended to achieve the desired salt and boron concentrations. The CDBR invention has been shown to capable of producing a water product having a salt concentration equal to or less than 350 ppm and a specified boron concentration of 0.5 ppm, which meets WHO recommendations for potable and irrigation water. The CDBR invention has been shown to achieve the specified water product concentrations at substantially lower pressures than required for just desalination via conventional SSRO for the same overall water recovery. Moreover, the CDBR invention can achieve the specified water product concentrations at a SEC.sub.net only slightly higher than for just desalination via conventional SSRO at moderate recoveries of 50% and at nearly the same values as conventional SSRO for recoveries of 65% and 75%. Since the CDBR invention substantially reduces the pressure required for desalination and concurrent boron removal, it will reduce the fixed costs of construction associated with the pumps, piping, and pressure vessels and will reduce the maintenance costs associated with continuous operation at high pressure. These additional cost reductions are not included in the proof-of-concept analysis.

[0072] The proof-of-concept for this CDBR invention has been shown based on maintaining the same OPD in stages 1, 2, and 3. This embodiment of the EERO invention is advantageous since it avoids any interstage pumping on the high pressure side of the CMCR. However, another embodiment of this CDBR invention is to allow for a reduced OPD in one or more of the stages in the CMCR while at the same time avoiding any interstage pumping on the high pressure side of the CMCR membrane cascade. This will reduce the pumping costs at the expense of a reduced potable water recovery. For some applications this embodiment of the CDBR invention could be desirable. The CDBR invention may be also implemented in two additional embodiments that are illustrated in FIG. 3: [0073] a) The permeate stream out of Stage 1 may be split in two fractions through a flow splitter, where one fraction is fed to the Stage 4 as in the case of the original invention, whereas the other fraction bypasses Stage 4 to be mixed with the permeate streams out of Stage 4 and Stage 3. This embodiment is called CDBR-B and introduces a new input parameter, the split ratio (S) which is defined as the ratio of the flowrate of the stream bypassing Stage 4 to the flow rate of the permeate stream out of Stage 1. When S=0, the original CDBR invention is recovered. Having a flow splitter that affects the concentrations in the final product could be also an advantage since it provides a simple way to compensate for any changes in the system elsewhere such as changes in the permeability due to fouling or concentration polarization, membrane aging, etc. [0074] b) The retentate from Stage 4 may be totally or partially recycled as feed to Stage 1. This embodiment is called CDBR-BR. Since the salt concentration of the retentate from Stage 4 is less than that of the seawater feed to Stage 1, which it might well be, it will dilute the feed and thereby should lower the required OPD in Stages 1, 2, and 3. Increasing the feed flow to Stage 1 by recycling the retentate from Stage 4 would also increase the safety factor (i.e., ratio of retentate flow rate to permeate flow rate) and permit running Stage 1 at a higher recovery.

[0075] The process conditions for the CDBR-B invention to produce a product water that contains no more than 350 ppm of salt and a specified boron concentration of 0.5 ppm are summarized in Table 4. It yields the OPD and SEC.sub.net lower than SSRO at all recoveries.

TABLE-US-00004 TABLE 4 Comparison of the OPD and SEC.sub.net for desalination using SSRO and the CDBR-B invention for both desalination and boron removal producing a water product with a salt concentration equal to or less than 350 ppm and a boron concentration of 0.5 ppm. OPD SEC.sub.net Recovery Y2 S .sub.1s .sub.4s .sub.1b .sub.4b (bar) (kWh/m.sup.3) 75% 0.392 0.30 0.996 0.997 0.899 0.900 88.7 3.81 65% 0.295 0.37 0.997 0.997 0.900 0.900 65.0 2.92 50% 0.150 0.44 0.997 0.997 0.900 0.900 49.8 2.35

[0076] It is also of interest to determine the performance of the proposed invention for desalination only. It would be possible to obtain a water product with 0.350 ppm salt concentration at lower OPD and SEC.sub.net values than SSRO when the CDBR-BR invention is used. In Table 5, the performance of the CDBR-BR invention with a split ratio of 0.95 and a complete recycle of the retentate from Stage 4 is compared to that of SSRO for desalination for 65% and 75% water recoveries.

TABLE-US-00005 TABLE 5 Comparison of the OPD and SEC.sub.net for desalination using SSRO and the CDBR-BR invention producing a water product with a salt concentration equal to 350 ppm. 65% Recovery 75% Recovery OPD SEC.sub.net OPD SEC.sub.net Process (bar) (kWh/m.sup.3) (bar) (kWh/m.sup.3) SSRO 79.3 2.922 111 3.915 CDBR-BR 61.0 2.718 79.3 3.387

[0077] Furthermore, instead of the SSRO stage in the embodiments described in FIGS. 1, 3a and 3b, two or more SSRO stages can be used, wherein the salt water feed is introduced to the high pressure side of the first SSRO stage and the retentate of each SSRO stage is introduced to the high pressure side of the subsequent SSRO stage while the retentate of the last SSRO stage is introduced to the CMCR unit. The permeate of all SSRO stages are introduced to LMPS. In this embodiment, the OPD may be increased gradually between the first and last SSRO stages, and last SSRO stage operates at the same OPD as the CMCR unit, which results in a lower SEC.sub.net compared to the original embodiment. As an example, in an embodiment of the CDBR invention with two SSRO stages, described in FIG. 4; for 75% water recovery, the first SSRO stage can operate at an OPD of 52.8 bar while the second SSRO stage and the rest of the CDBR unit operate at an OPD of 100 bar, resulting in a SEC.sub.net of 3.117 kWh/m.sup.3, whereas for 65% water recovery, the first SSRO stage can operate at an OPD of 43.1 bar while the second SSRO stage and the rest of the CDBR unit operate at an OPD of 66.8 bar, resulting in a SEC.sub.net of 2.606 kWh/m.sup.3 for producing a water product with a salt concentration equal to or less than 350 ppm and a boron concentration of 0.5 ppm.