Membrane-based separation systems and related configurations

Abstract

Configurations for liquid solution separation (e.g., liquid concentration and / or desalination) methods and related systems involving membrane separators having at least one-semipermeable membrane are provided.

Description

MEMBRANE-BASED SEPARATION SYSTEMS AND RELATED CONFIGURATIONS RELATED APPLICATIONSThis application claims priority under 35 U.S.C. § 119(e) to U.S. Provisional Patent Application No. 63 / 621,793, filed January 17, 2024, and entitled “Membrane-Based Separation Systems and Related Configurations,” which is incorporated herein by reference in its entirety. TECHNICAL FIELDLiquid solution separation methods and related systems are generally described. SUMMARYConfigurations for liquid solution separation (e.g., liquid concentration and / or desalination) methods and related systems involving membrane separators having at least one-semipermeable membrane are provided. The subject matter of the present invention involves, in some cases, interrelated products, alternative solutions to a particular problem, and / or a plurality of different uses of one or more systems and / or articles.In one aspect, methods of treating feed streams comprising a liquid and a solute are provided. In some embodiments, the method comprises transporting a first membrane separator retentate inlet stream to a retentate side of a first membrane separator such that: a first membrane separator retentate outlet stream exits the retentate side of the first membrane separator, the first membrane separator retentate outlet stream having an osmotic pressure that is greater than an osmotic pressure of the first membrane separator retentate inlet stream, and at least a portion of liquid and solute from the first membrane separator retentate inlet stream is transported from the retentate side of the first membrane separator, through a semi-permeable membrane of the first membrane separator, to a permeate side of the first membrane separator; and transporting a second membrane separator retentate inlet stream to a retentate side of a second membrane separator and a second membrane separator permeate inlet stream to a permeate side of the second membrane separator such that: a second membrane separator retentate outlet stream exits the retentate side of the second membrane separator, the second membrane separator retentate outlet stream having an osmotic pressure that is greater than an osmotic pressure of the second membrane separator retentate inlet stream, and at least a portion of liquid from the second membrane separator retentate inlet stream is transported from the retentate side of the second membrane separator, through a semi-permeable membrane of the second membrane separator, to the permeate side of the second membrane separator where the portion of liquid is combined with the second membrane separator permeate inlet stream at the permeate side of the second membrane separator to form a second membrane separator permeate outlet stream; wherein: the first membrane separator retentate inlet stream comprises at least a portion of the feed stream; and the second membrane separator retentate inlet stream comprises at least a portion of the first membrane separator retentate outlet stream.In some embodiments, the method comprises transporting a first membrane separator retentate inlet stream to a retentate side of a first membrane separator and a first membrane separator permeate inlet stream to a permeate side of the first membrane separator such that: a first membrane separator retentate outlet stream exits the retentate side of the first membrane separator, the first membrane separator retentate outlet stream having an osmotic pressure that is greater than an osmotic pressure of the first membrane separator retentate inlet stream, and at least a portion of liquid from the first membrane separator retentate inlet stream is transported from the retentate side of the first membrane separator, through a semi-permeable membrane of the first membrane separator, to the permeate side of the first membrane separator where the portion of liquid is combined with the first membrane separator permeate inlet stream at the permeate side of the first membrane separator to form a first membrane separator permeate outlet stream; and transporting a second membrane separator retentate inlet stream to a retentate side of a second membrane separator such that: a second membrane separator retentate outlet stream exits the retentate side of the second membrane separator, the second membrane separator retentate outlet stream having an osmotic pressure that is greater than an osmotic pressure of the second membrane separator retentate inlet stream, and at least a portion of liquid and solute from the second membrane separator retentate inlet stream is transported from the retentate side of the second membrane separator, through a semi-permeable membrane of the second membrane separator, to a permeate side of the second membrane separator; wherein: the first membrane separator retentate inlet stream comprises at least a portion of the feed stream; and the second membrane separator retentate inlet stream comprises at least a portion of the first membrane separator retentate outlet stream.In some embodiments, the method comprises increasing the pressure of a first membrane separator retentate inlet stream to form a pressurized first membrane separator retentate inlet stream; transporting at least a portion of the pressurized first membrane separator retentate inlet stream to a retentate side of a first membrane separator such that: a first membrane separator retentate outlet stream exits the retentate side of the first membrane separator, the first membrane separator retentate outlet stream having an osmotic pressure that is greater than an osmotic pressure of the pressurized first membrane separator retentate inlet stream, and at least a portion of liquid and solute from the pressurized first membrane separator retentate inlet stream is transported from the retentate side of the first membrane separator, through a semi-permeable membrane of the first membrane separator, to a permeate side of the first membrane separator; and transporting a second membrane separator retentate inlet stream to a retentate side of a second membrane separator such that: a second membrane separator retentate outlet stream exits the retentate side of the second membrane separator, the second membrane separator retentate outlet stream having an osmotic pressure that is greater than an osmotic pressure of the second membrane separator retentate inlet stream, and at least a portion of liquid from the second membrane separator retentate inlet stream is transported from the retentate side of the second membrane separator, through a semi-permeable membrane of the second membrane separator, to a permeate side of the second membrane separator; wherein: the first membrane separator retentate inlet stream comprises at least a portion of the feed stream; the first membrane separator retentate inlet stream comprises at least a portion of the second membrane separator retentate outlet stream; the second membrane separator retentate inlet stream comprises at least a portion of the first membrane separator retentate outlet stream; and a pressure of the feed stream is reduced and / or a pressure of the at least a portion of the second membrane separator retentate outlet stream is increased such that a pressure of the first membrane separator retentate inlet stream is less than or equal to a pressure of the at least a portion of the second membrane separator retentate outlet stream.In some embodiments, the method comprises increasing the pressure of a first membrane separator retentate inlet stream to form a pressurized first membrane separator retentate inlet stream; transporting at least a portion of the pressurized first membrane separator retentate inlet stream to a retentate side of a first membrane separator such that: a first membrane separator retentate outlet stream exits the retentate side of the first membrane separator, the first membrane separator retentate outlet stream having an osmotic pressure that is greater than an osmotic pressure of the pressurized first membrane separator retentate inlet stream, and at least a portion of liquid and solute from the pressurized first membrane separator retentate inlet stream is transported from the retentate side of the first membrane separator, through a semi-permeable membrane of the first membrane separator, to a permeate side of the first membrane separator; wherein: the first membrane separator retentate inlet stream comprises at least a portion of the feed stream; the first membrane separator retentate inlet stream comprises at least a portion of the first membrane separator retentate outlet stream; and a pressure of the feed stream is reduced and / or a pressure of the at least a portion of the first membrane separator retentate outlet stream is increased such that a pressure of the first membrane separator retentate inlet stream is less than or equal to a pressure of the at least a portion of the first membrane separator retentate outlet stream.Other advantages and novel features of the present invention will become apparent from the following detailed description of various non-limiting embodiments of the invention when considered in conjunction with the accompanying figures. In cases where the present specification and a document incorporated by reference include conflicting and / or inconsistent disclosure, the present specification shall control. BRIEF DESCRIPTION OF THE DRAWINGSNon-limiting embodiments of the present invention will be described by way of example with reference to the accompanying figures, which are schematic and are not intended to be drawn to scale. In the figures, each identical or nearly identical component illustrated is typically represented by a single numeral. For purposes of clarity, not every component is labeled in every figure, nor is every component of each embodiment of the invention shown where illustration is not necessary to allow those of ordinary skill in the art to understand the invention. In the figures:FIG. 1A is a schematic diagram of a system comprising a first membrane separator and a second membrane separator that receives a permeate inlet stream, according to some embodiments;FIG. 1B is a schematic diagram of an example of a system comprising a first membrane separator and a second membrane separator that receives a permeate inlet stream comprising at least a portion of a retentate outlet stream, according to some embodiments;FIG. 2A is a schematic diagram of an example of a system comprising a first membrane separator and a second membrane separator that receives a permeate inlet stream, according to some embodiments;FIG. 2B is a schematic diagram of an example of a system comprising a first membrane separator and a second membrane separator that receives a permeate inlet stream comprising at least a portion of a retentate outlet stream, according to some embodiments;FIG. 3A is a schematic diagram of an example of a system comprising a first membrane separator, which receives a permeate inlet stream, and a second membrane separator, according to some embodiments;FIG. 3B is a schematic diagram of an example of a system comprising a first membrane separator, which receives a permeate inlet stream comprising at least a portion of a retentate outlet stream, and a second membrane separator, according to some embodiments;FIG. 4A is a schematic diagram of an example of a system comprising a first membrane separator, which receives a permeate inlet stream, and a second membrane separator, according to some embodiments;FIG. 4B is a schematic diagram of an example of a system comprising a first membrane separator, which receives a permeate inlet stream comprising at least a portion of a retentate outlet stream, and a second membrane separator, according to some embodiments;FIG. 5 is a schematic diagram of an example of a system comprising a membrane separator that receives a recirculated portion of a retentate outlet stream, according to some embodiments;FIG. 6 is a schematic diagram of an example of a system comprising a first membrane separator and a second membrane separator, with the first membrane separator receiving a recirculated portion of a retentate outlet stream from the second membrane separator, according to some embodiments;FIG. 7A is a schematic illustration of an example of a single-membrane membrane separator, according to some embodiments;FIG. 7B is a schematic illustration of an example of a membrane separator comprising multiple semi-permeable membranes fluidically connected in parallel, according to some embodiments;FIG. 7C is a schematic illustration of an example of a membrane separator comprising multiple semi-permeable membranes fluidically connected in series, according to some embodiments;FIG. 8A is a schematic illustration of an example of a single-membrane membrane separator, according to some embodiments;FIG. 8B is a schematic illustration of an example of a membrane separator comprising multiple semi-permeable membranes fluidically connected in parallel, according to some embodiments; andFIG. 8C is a schematic illustration of an example of a membrane separator comprising multiple semi-permeable membranes fluidically connected in series, according to some embodiments. DETAILED DESCRIPTIONLiquid solution separation (e.g., concentration and / or desalination) methods and related systems involving membrane separators having at least one-semipermeable membrane are provided. Separation at the membranes may occur via diffusion (e.g., as in osmotic separation), pore-based filtration (e.g., as in nanofiltration), or a combination of the two. In some instances, at least some of the membrane separators permit a portion of solute in a retentate side input stream to pass through the semi-permeable membrane. In some instances, multiple membrane separators are employed, with the membrane separators having different solute permeabilities (e.g., due to varying pore size, active layer morphologies, and / or molecular weight cutoffs).In some membrane-based separation processes, such as reverse osmosis and nanofiltration, hydraulic pressure is applied to promote passage of liquid through a semi-permeable membrane. In many such systems, the amount of hydraulic pressure required to cause passage of liquid through the membrane scales with the difference in solute concentration and / or osmotic pressure between the retentate side and the permeate side of the membrane. It can be desirable to configure systems and methods to reduce the required hydraulic pressure for a given solute concentration and / or osmotic pressure in order to promote energetic efficiency, an increase in concentration limits, and / or promote the durability of the system. It has been realized that one way to reduce required hydraulic pressure is to permit a greater portion of the influent solute to pass through the membrane compared to high-rejection (e.g., 99.9% rejection or 100% rejection) reverse osmosis (RO) membranes. Highly saline streams may be treated (e.g., desalinated) with such a membrane configuration because the higher solute permeability can reduce the required hydraulic pressure. In some instances, the membranes are configured such that a greater portion of the influent solute (e.g., solute ions) are rejected by the membrane as compared to nanofiltration (NF) membranes, reducing permeate salinity and increasing retentate outlet salinity. It is believed that highly concentrated streams can be produced using such membranes as compared to lower-rejection nanofiltration membranes because the lower ion permeability increases the degree of separation. But, it has also been realized in the context of this disclosure that performance of at least some membrane-based separation systems is based, at least in part, on the amount of permeate generated by the membranes and the extent of separation carried out by the membrane at a given operating condition. In the context of this disclosure, the amount of permeate generated (defined as a percentage calculated by dividing the value of the permeate outlet mass flow by the value of the retentate inlet mass flow and multiplying by 100) at a membrane separator is referred to as “recovery”. Also in the context of this disclosure, the extent of separation is described by the “rejection” of the membrane, as explained in more detail below. Generally, an increase in the feed salinity for a membrane results in a decrease in the recovery as well as rejection achieved by the membrane. Decreased recovery and rejection can result in poor membrane performance, and in such a case a substantially larger amount of membrane area may be required to separate certain liquids (e.g., to desalinate higher salinity waters).Some embodiments are directed to configurations in which at least some membrane separators receive a permeate inlet stream (e.g., a draw stream) while, in some instances, other membrane separators do not receive a permeate inlet stream. For example, an upstream membrane separator may permit a portion of solute to pass through a semi-permeable membrane along with liquid (e.g., during application of hydraulic pressure), while a downstream membrane separator may permit less or no solute to pass through its semi-permeable membrane. In some such instances, the downstream membrane separator permitting less or no solute to pass through may receive a draw stream to combine with its permeate. The draw stream may be derived from, for example, the downstream membrane separator’s retentate outlet stream (e.g., from a brine splitting configuration). Other embodiments may involve the upstream membrane separator receiving the permeate inlet stream (e.g., a draw stream) while the downstream membrane separator permits a greater amount of solute to pass through its semi-permeable membrane. It has been realized in the context of this disclosure that combining multiple membrane separators, at least one of which permits an amount of solute passage while at least another receives a permeate inlet stream, can facilitate the concentration of liquid streams (e.g., wastewater stream) to higher limits than would be practically achievable without such a combination.Other aspects of this disclosure are directed to processes for recirculating portions of membrane separator retentate outlet streams back to the retentate inlet stream of the same membrane separator and / or an upstream separator. It has been realized in the context of this disclosure that, in some instances, the pressure of the recirculated portion of the retentate outlet stream and / or the pressure of the feed stream can be modulated (e.g., with valving, pumps, and / or energy recovery devices) to reduce or prevent backflow.Methods (e.g., for concentrating liquids) and related systems are generally described. FIGS. 1-6 show schematic illustrations of systems 100, 200, and 300, respectively, which are examples of systems in which certain methods described herein may be carried out. The systems of this disclosure may comprise a single membrane separator or a plurality of membrane separators.Some embodiments comprise treating a feed stream comprising a liquid and a solute (e.g., for liquid concentration and / or desalination). Examples of types of feed streams that can be treated according to the methods and using the systems of this disclosure are described in more detail below. Referring again to FIGS. 1-6, feed stream 101 may be fed into system 100, 200, or 300 for treatment. In some embodiments, a hydraulic pressure of the feed stream is increased (e.g., via a pump to facilitate liquid separation). For example, in some embodiments, the feed stream is increased via a pump and / or energy recovery device (e.g., prior to the feed stream encountering a membrane separator).Some embodiments comprise transporting a first membrane separator retentate inlet stream to a retentate side of a first membrane separator. A membrane separator refers to a collection of components including one or more semi-permeable membranes configured to perform a membrane-based separation process (e.g., an osmotic process, a filtration process, or a combination thereof) on at least one input stream and produce at least one output stream. The first membrane separator may comprise at least one semi-permeable membrane defining a permeate side of the first membrane separator and a retentate side of the first membrane separator. Each membrane separator described herein may include further sub-units such as, for example, individual semi-permeable membrane modules (e.g., in the form of cartridges), valving, fluidic conduits, and the like. As described in more detail below, each membrane separator can include a single semi-permeable membrane or multiple semi-permeable membranes. In some embodiments, a single membrane separator can include multiple sub-units (e.g., multiple modules such as multiple cartridges) that may or may not share a common container.In some embodiments, a first membrane separator retentate inlet stream (which may comprise at least a portion (e.g., at least 5 wt%, at least 10 wt%, at least 20 wt%, at least 50 wt%, at least 80 wt%, at least 90 wt%, at least 95 wt%, at least 99 wt%, or more) of the feed stream, optionally with one or more other streams) is transported to a retentate side of a first membrane separator such that a first membrane separator retentate outlet stream exits the retentate side of the first membrane separator, the first membrane separator retentate outlet stream having an osmotic pressure that is greater (e.g., by a factor of at least 1.03, at least 1.035, at least 1.05, at least 1.10, at least 1.25, and / or up to 1.40, up to 1.50, up to 2, up to 3, up to 4, up to 5 or greater) than an osmotic pressure of the first membrane separator retentate inlet stream. For example, referring again to FIGS. 1-6, first membrane separator 102 may comprise at least one semi-permeable membrane defining retentate side 103 and permeate side 104, and first membrane separator retentate inlet stream 105 may be transported to retentate side 103 such that first membrane separator retentate outlet stream 106 exits retentate side 103. In some embodiments, such as those shown in FIGS. 1-6, first membrane separator retentate inlet stream 105 comprises at least a portion of feed stream 101. This step may be performed such that first membrane separator retentate outlet stream 106 has an osmotic pressure that is greater than an osmotic pressure of first membrane separator retentate inlet stream 105, according to some embodiments. For example, this step may be performed such that first membrane separator retentate outlet stream 106 has a concentration of the solute that is increased with respect to the concentration of first membrane separator retentate inlet stream 105 (e.g., by a factor of at least 1.03, at least 1.035, at least 1.05, at least 1.10, at least 1.25, and / or up to 1.40, up to 1.50, up to 2, up to 3, up to 4, up to 5 or greater). In some embodiments, a hydraulic pressure is applied (e.g., to facilitate transport of liquid and / or solute from the retentate side to the permeate side). In some embodiments, the system is operated such that the first membrane separator retentate inlet stream has a hydraulic pressure of at least 200 psi (at least 1.38 × 103 kPa), at least 500 psi (at least 3.45 × 103 kPa), at least 750 psi (at least 5.17 × 103 kPa), at least 1000 psi (at least 6.90 × 103 kPa), and / or up to 1500 psi (up to 1.03 × 104 kPa), up to 2000 psi (up to 1.38 × 104 kPa), or more.In some embodiments, at least a portion (e.g., at least 5 wt%, at least 10 wt%, at least 20 wt%, at least 50 wt%, at least 80 wt%, and / or up to 90 wt%, up to 95 wt%, up to 99 wt%, or more) of liquid from the first membrane separator retentate inlet stream is transported from the retentate side of the first membrane separator, through a semi-permeable membrane of the first membrane separator, to a permeate side of the first membrane separator. Referring again to FIGS. 1-6, for example, at least a portion of liquid from first membrane separator retentate inlet stream 105 may be transported from retentate side 103, through a semi-permeable membrane, to permeate side 104. Liquid transported from the retentate side to the permeate side of the first membrane separator may form some or all of a first membrane separator permeate outlet stream (e.g., first membrane separator permeate outlet stream 107 in FIGS. 1-6), which may be discharged from the system (e.g., as relatively pure liquid such as relatively pure water). In some embodiments, the first membrane separator retentate inlet stream comprises at least a portion (e.g., at least 5 wt%, at least 10 wt%, at least 20 wt%, at least 50 wt%, at least 80 wt%, and / or up to 90 wt%, up to 95 wt%, up to 99 wt%, or more) of the first membrane separator permeate outlet stream.In some, but not necessarily all embodiments, a portion (e.g., at least 5 wt%, at least 10 wt%, at least 20 wt%, at least 50 wt%, at least 80 wt%, and / or up to 85 wt%, up to 90 wt%, or more) of solute from the first membrane separator retentate inlet stream is transported from the retentate side of the first membrane separator, through a semi-permeable membrane of the first membrane separator, to a permeate side of the first membrane separator. However, in some embodiments, little or none (e.g., less than or equal to 10 wt%, less than or equal to 5 wt%, less than or equal to 2 wt%, less than or equal to 1 wt%, less than or equal to 0.1 wt%, or less) of the solute from the first membrane separator retentate inlet stream is transported from the retentate side of the first membrane separator, through a semi-permeable membrane of the first membrane separator, to a permeate side of the first membrane separator.In some embodiments, one or more membrane separators (e.g., the first membrane separator) is operated as an osmotic separator. For example, in some embodiments, the semi-permeable membrane is an osmotic membrane. Transport of solvent (e.g., water) through osmotic membrane(s) of membrane separators can be achieved via a transmembrane net driving force (i.e., a net driving force through the thickness of the membrane(s)), according to certain embodiments. Generally, the transmembrane net driving force (∆χ) is expressed as:[1]wherein P1 is the hydraulic pressure on the retentate side of the osmotic membrane, P2 is the hydraulic pressure on the permeate side of the osmotic membrane, Π1 is the osmotic pressure of the stream on the retentate side of the osmotic membrane, and Π2 is the osmotic pressure of the stream on the permeate side of the osmotic membrane. (P1 – P2) can be referred to as the transmembrane hydraulic pressure difference, and (Π1 - Π2) can be referred to as the transmembrane osmotic pressure difference.Those of ordinary skill in the art are familiar with the concept of osmotic pressure. The osmotic pressure of a particular liquid is an intrinsic property of the liquid. The osmotic pressure can be determined in a number of ways, with the most efficient method depending upon the type of liquid being analyzed. For certain solutions with relatively low molar concentrations of ions, osmotic pressure can be accurately measured using an osmometer. In other cases, the osmotic pressure can simply be determined by comparison with solutions with known osmotic pressures. For example, to determine the osmotic pressure of an uncharacterized solution, one could apply a known amount of the uncharacterized solution on one side of a non-porous, semi-permeable, osmotic membrane and iteratively apply different solutions with known osmotic pressures on the other side of the osmotic membrane until the differential pressure through the thickness of the membrane is zero.The osmotic pressure (Π) of a solution containing n solubilized species may be estimated as:[2]wherein ij is the van’t Hoff factor of the jth solubilized species, Mj is the molar concentration of the jth solubilized species in the solution, R is the ideal gas constant, and T is the absolute temperature of the solution. Equation [2] generally provides an accurate estimate of osmotic pressure for liquid with low concentrations of solubilized species (e.g., concentrations at or below between about 4 wt% and about 6 wt%). For many liquids comprising solubilized species, at species concentrations above around 46 wt%, the increase in osmotic pressure per increase in salt concentration is greater than linear (e.g., slightly exponential).As mentioned above, one type of osmotic separation technique that can be performed using the membrane separators of this disclosure, according to some embodiments, is reverse osmosis. Reverse osmosis generally occurs when the osmotic pressure on the retentate side of the osmotic membrane is greater than the osmotic pressure on the permeate side of the osmotic membrane, and a pressure is applied to the retentate side of the osmotic membrane such that the hydraulic pressure on the retentate side of the osmotic membrane is sufficiently greater than the hydraulic pressure on the permeate side of the osmotic membrane such that the osmotic pressure difference is overcome and liquid (e.g., a solvent such as water) is transported from the retentate side of the osmotic membrane to the permeate side of the osmotic membrane. Generally, such situations result when the transmembrane hydraulic pressure difference (P1-P2) is greater than the transmembrane osmotic pressure difference (Π1 - Π2) such that liquid (e.g., a solvent such as water) is transported from the retentate side of the osmotic membrane to the permeate side of the osmotic membrane (rather than having liquid be transported from the permeate side of the osmotic membrane to the retentate side of the osmotic membrane, which would be energetically favored in the absence of the pressure applied to the retentate side of the osmotic membrane). In some embodiments, the first membrane separator is operated to perform reverse osmosis.Some embodiments comprise transporting a second membrane separator retentate inlet stream to a retentate side of a second membrane separator. The second membrane separator may comprise at least one semi-permeable membrane defining a permeate side of the second membrane separator and a retentate side of the second membrane separator.In some embodiments, the second membrane separator retentate inlet stream (which may comprise at least a portion (e.g., at least 5 wt%, at least 10 wt%, at least 20 wt%, at least 50 wt%, at least 80 wt%, at least 90 wt%, at least 95 wt%, at least 99 wt%, or more) of the first membrane separator retentate outlet stream, optionally with one or more other streams) is transported to a retentate side of the second membrane separator such that a second membrane separator retentate outlet stream exits the retentate side of the second membrane separator, the second membrane separator retentate outlet stream having an osmotic pressure that is greater (e.g., by a factor of at least 1.03, at least 1.035, at least 1.05, at least 1.10, at least 1.25, and / or up to 1.40, up to 1.50, up to 2, up to 3, up to 4, up to 5 or greater) than an osmotic pressure of the second membrane separator retentate inlet stream. In some embodiments, the second membrane separator retentate inlet stream comprises at least a portion (e.g., at least 5 wt%, at least 10 wt%, at least 20 wt%, at least 50 wt%, at least 80 wt%, at least 90 wt%, at least 95 wt%, at least 99 wt%, or more) of the feed stream, optionally with one or more other streams. Having the retentate side of the second membrane separator receive at least a portion of the feed stream may facilitate the treatment of feed streams having a higher osmotic pressure than in some instances in which the feed stream is fed to the retentate side of the first membrane separator. The second membrane separator retentate inlet stream comprising at least a portion of the feed stream (and in some instances, at least a portion of the first membrane separator retentate outlet stream) may be transported to the retentate side of the second membrane separator such that the second membrane separator retentate outlet stream exits the retentate side of the second membrane separator, the second membrane separator retentate outlet stream having an osmotic pressure that is greater (e.g., by a factor of at least 1.03, at least 1.035, at least 1.05, at least 1.10, at least 1.25, and / or up to 1.40, up to 1.50, up to 2, up to 3, up to 4, up to 5, or greater) than an osmotic pressure of the second membrane separator retentate inlet stream. For example, referring again to FIGS. 1-4B and 6, second membrane separator 108 may comprise at least one semi-permeable membrane defining retentate side 109 and permeate side 110, and second membrane separator retentate inlet stream 111 may be transported to retentate side 109 such that second membrane separator retentate outlet stream 112 exits retentate side 109. In some embodiments, such as those shown in FIGS. 1-4B and 6, second membrane separator retentate inlet stream 111 comprises at least a portion of first membrane separator retentate outlet stream 106. This step may be performed such that second membrane separator retentate outlet stream 112 has an osmotic pressure that is greater than an osmotic pressure of second membrane separator retentate inlet stream 111, according to some embodiments. For example, this step may be performed such that second membrane separator retentate outlet stream 112 has a concentration of the solute that is increased with respect to the concentration of second membrane separator retentate inlet stream 111 (e.g., by a factor of at least 1.03, at least 1.035, at least 1.05, at least 1.10, at least 1.25, and / or up to 1.40, up to 1.50, up to 2, up to 3, up to 4, up to 5 or greater). In some embodiments, a hydraulic pressure is applied (e.g., to facilitate transport of liquid and / or solute from the retentate side to the permeate side). In some embodiments, the system is operated such that the second membrane separator retentate inlet stream has a hydraulic pressure that is at least 50%, at least 75%, at least 90%, at least 95%, or more of the pressure of the first membrane separator retentate inlet stream. In some embodiments, the system is operated such that the second membrane separator retentate inlet stream has a hydraulic pressure of at least 200 psi (at least 1.38 × 103 kPa), at least 500 psi (at least 3.45 × 103 kPa), at least 750 psi (at least 5.17 × 103 kPa), at least 1000 psi (at least 6.90 × 103 kPa), and / or up to 1500 psi (up to 1.03 × 104 kPa), up to 2000 psi (up to 1.38 × 104 kPa), or more.In some embodiments, at least a portion (e.g., at least 5 wt%, at least 10 wt%, at least 20 wt%, at least 50 wt%, at least 80 wt%, and / or up to 90 wt%, up to 95 wt%, up to 99 wt%, or more) of liquid from the second membrane separator retentate inlet stream is transported from the retentate side of the second membrane separator, through a semi-permeable membrane of the second membrane separator, to a permeate side of the second membrane separator. Referring again to FIGS. 1-4B and 6, for example, at least a portion of liquid from second membrane separator retentate inlet stream 111 may be transported from retentate side 109, through a semi-permeable membrane, to permeate side 110. Liquid transported from the retentate side to the permeate side of the second membrane separator may form some (e.g., at least 5 wt%, at least 10 wt%, at least 20 wt%, at least 50 wt%, at least 80 wt%, at least 90 wt%, at least 95 wt%, at least 99 wt%, or more) or all of the liquid of a second membrane separator permeate outlet stream (e.g., second membrane separator permeate outlet stream 113 in FIGS. 1-4B and 6).In some, but not necessarily all embodiments, at least a portion (e.g., at least 5 wt%, at least 10 wt%, at least 20 wt%, at least 50 wt%, at least 80 wt%, and / or up to 85%, up to 90%, or more) of solute from the second membrane separator retentate inlet stream is transported from the retentate side of the second membrane separator, through the semi-permeable membrane of the second membrane separator, to the permeate side of the second membrane separator. Referring again to FIGS. 1-4B and 6, for example, in some embodiments at least a portion of solute from second membrane separator retentate inlet stream 111 may be transported from retentate side 109, through a semi-permeable membrane, to permeate side 110. Solute transported from the retentate side to the permeate side of the second membrane separator may form some (e.g., at least 5 wt%, at least 10 wt%, at least 20 wt%, at least 50 wt%, at least 80 wt%, at least 90 wt%, at least 95 wt%, at least 99 wt%, or more) or all of any solute present in the second membrane separator permeate outlet stream (e.g., second membrane separator permeate outlet stream 113 in FIGS. 1-4B and 6). However, in some embodiments, little or none (e.g., less than or equal to 10 wt%, less than or equal to 5 wt%, less than or equal to 2 wt%, less than or equal to 1 wt%, less than or equal to 0.1 wt%, or less) of the solute from the second membrane separator retentate inlet stream is transported from the retentate side of the second membrane separator, through a semi-permeable membrane of the second membrane separator, to a permeate side of the second membrane separator.The amount of solute that may pass through the semi-permeable membrane of the second membrane separator may depend on any of a variety of parameters such as the solute concentration in the second membrane separator retentate inlet stream, the solute permeability of the membrane, the water permeability of the membrane, the temperature, and / or a magnitude of hydraulic pressure of the second membrane separator retentate inlet stream. In some embodiments, at least a portion of liquid and solute from the second membrane separator retentate inlet stream is transported from the retentate side of the second membrane separator, through the semi-permeable membrane of the second membrane separator, to the permeate side of the second membrane separator.While FIG. 1-6 show one or two membrane separators, it should be understood that a different number of membrane separators can be employed in the system and used in the methods of this disclosure. For example, a system comprising a plurality of membrane separators may have at least one, at least two, at least three, at least four, at least five, at least ten, and least twenty, or more membrane separators configured as described in this disclosure. For example, some embodiments comprise transporting a third membrane separator retentate inlet stream to a retentate side of a third membrane separator. The third membrane separator may comprise at least one semi-permeable membrane defining a permeate side of the third membrane separator and a retentate side of the third membrane separator. The third membrane separator retentate inlet stream may comprise at least a portion of the second membrane separator retentate outlet stream.In some embodiments, at least a portion of a stream exiting one or more membrane separator is recirculated and fed back into a membrane separator (e.g., an upstream membrane separator). Such recycle processes may allow for relatively high amounts of liquid to be removed by the system (in some instances using fewer system components) and / or for relatively high recovery rates and / or efficiencies compared to some embodiments in which no such recycle occurs.In some, but not necessarily all embodiments, the first membrane separator and / or the second membrane separator receives a permeate inlet stream at its permeate side (e.g., as a draw stream).As example, in some, but not necessarily all embodiments, a first membrane separator permeate inlet stream is transported to the permeate side of the first membrane separator. In some embodiments, liquid transported from the retentate side to the permeate side of the first membrane separator is combined with the first membrane separator permeate inlet stream to form the first membrane separator permeate outlet stream. The first membrane separator permeate outlet stream may be transported out of the permeate side, e.g., for further processing, recycling, discharge, or combinations thereof, as described in more detail below. As an example, in the embodiments shown in FIGS. 3A-4B, first membrane separator permeate inlet stream 115 is transported to permeate side 104 of first membrane separator 102, where it can be combined with liquid transported from first membrane separator retentate inlet stream 105 that has passed through a semi-permeable membrane, to form first membrane separator permeate outlet stream 107. In some embodiments, the first membrane separator permeate inlet stream serves as a draw stream comprising a draw solution, non-limiting examples of compositions of which are described in further detail below. A draw stream (e.g., from first membrane separator permeate inlet stream 115) may, in accordance with certain embodiments, reduce a hydraulic pressure necessary for a membrane-based separation process (e.g., an osmotic process) to be performed at the first membrane separator (e.g., when the draw stream has an osmotic pressure such that a lower hydraulic pressure is required to achieve a given transmembrane net driving force relative to operation without the draw stream). In some embodiments, the system is operated such that the first membrane separator permeate inlet stream has a hydraulic pressure of less than or equal to 250 psi (less than or equal to 1.72 × 103 kPa), less than or equal to 200 psi (less than or equal to 1.38 × 103 kPa), less than or equal to 100 psi (less than or equal to 6.90 × 102 kPa), and / or as low as 50 psi (as low as 3.45 × 102 kPa), or less.In some embodiments, the first membrane separator permeate inlet stream has a higher osmotic pressure than an osmotic pressure of the first membrane separator retentate inlet stream (e.g., by a factor of at least 1.03, at least 1.05, at least 1.1, at least 1.2, at least 1.5, at least 2, at least 5, and / or up to 10, or more). In some embodiments, the first membrane separator permeate inlet stream comprises at least a portion (e.g., at least 5 wt%, at least 10 wt%, at least 20 wt%, at least 50 wt%, at least 80 wt%, at least 90 wt%, and / or up to 95 wt%, up to 99 wt%, or more) of the first membrane separator retentate outlet stream. Such a configuration may, in some instances, contribute to beneficial performance of the system by providing a draw stream with dissolved solute, the presence of which may reduce a required hydraulic pressure at the retentate side for performing a membrane-based separation process (thereby saving energy and / or increasing system durability). In some embodiments, the retentate side of the first membrane separator is fluidically connected to the permeate side of the first membrane separator. In such a way, in FIGS. 3B and 4B, some (e.g., at least 5 wt%, at least 10 wt%, at least 20 wt%, at least 50 wt%, at least 80 wt%, at least 90 wt%, and / or up to 95 wt%, up to 99 wt%, or more) of first membrane separator retentate outlet stream 106 may be transported (e.g., via one or more fluidic conduits) to permeate side 104 of first membrane separator 102 by forming some or all of first membrane separator permeate inlet stream 115 (which can serve as a draw stream).In some, but not necessarily all embodiments, a second membrane separator permeate inlet stream is transported to the permeate side of the second membrane separator. In some embodiments, liquid transported from the retentate side through the membrane and to the permeate side of the second membrane separator is combined with the second membrane separator permeate inlet stream to form the second membrane separator permeate outlet stream. The second membrane separator permeate outlet stream may be transported out of the permeate side, e.g., for further processing, recycling, discharge, or combinations thereof, as described in more detail below. As an example, in the embodiments shown in FIGS. 1A-2B, second membrane separator permeate inlet stream 114 is transported to permeate side 110 of second membrane separator 108, where it can be combined with liquid transported from second membrane separator retentate inlet stream 111 that has passed through a semi-permeable membrane, to form second membrane separator permeate outlet stream 113. In some embodiments, the second membrane separator permeate inlet stream serves as a draw stream comprising a draw solution, non-limiting examples of compositions of which are described in further detail below. A draw stream (e.g., from second membrane separator permeate inlet stream 114) may, in accordance with certain embodiments, reduce a hydraulic pressure necessary for a membrane-based separation process (e.g., osmotic separation process) to be performed at the second membrane separator (e.g., when the draw stream has an osmotic pressure such that a lower hydraulic pressure is required to achieve a given transmembrane net driving force relative to operation without the draw stream). In some embodiments, the system is operated such that the second membrane separator permeate inlet stream has a hydraulic pressure of less than or equal to 250 psi (less than or equal to 1.72 × 103 kPa), less than or equal to 200 psi (less than or equal to 1.38 × 103 kPa), less than or equal to 100 psi (less than or equal to 6.90 × 102 kPa), and / or as low as 50 psi (as low as 3.45 × 102 kPa), or less.In some embodiments, the second membrane separator permeate inlet stream has a higher osmotic pressure than an osmotic pressure of the second membrane separator retentate inlet stream (e.g., by a factor of at least 1.03, at least 1.05, at least 1.1, at least 1.2, at least 1.5, at least 2, at least 5, and / or up to 10, or more). In some embodiments, the second membrane separator permeate inlet stream comprises at least a portion (e.g., at least 5 wt%, at least 10 wt%, at least 20 wt%, at least 50 wt%, at least 80 wt%, at least 90 wt%, and / or up to 95 wt%, up to 99 wt%, or more) of the second membrane separator retentate outlet stream. Such a configuration may, in some instances, contribute to beneficial performance of the system by providing a draw stream with dissolved solute, the presence of which may reduce a required hydraulic pressure at the retentate side for performing a membrane-based separation process (thereby saving energy and / or increasing system durability). In some embodiments, the retentate side of the second membrane separator is fluidically connected to the permeate side of the second membrane separator. In such a way, in FIGS. 1B and 2B, some (e.g., at least 5 wt%, at least 10 wt%, at least 20 wt%, at least 50 wt%, at least 80 wt%, at least 90 wt%, at least 95 wt%, at least 99 wt%, or more) or all of second membrane separator retentate outlet stream 112 may be transported (e.g., via one or more fluidic conduits) to permeate side 110 of second membrane separator 108 by forming some or all of second membrane separator permeate inlet stream 114 (which can serve as a draw stream).In some embodiments in which a first membrane separator permeate inlet stream is transported to the permeate side of the first membrane separator (e.g., as a draw stream), no second membrane separator permeate inlet stream is transported to the permeate side of the second membrane separator (or a second membrane separator permeate inlet stream is transported to the permeate side of the second membrane separator, but the second membrane permeate inlet stream has a mass flow rate that is lower than the mass flow rate of the first membrane separator permeate inlet stream (e.g., lower by at least 80%, at least 90%, at least 95%, at least 98%, at least 99%, or more)). As one example, the first membrane separator may be operated in a counter-flow configuration, while the second membrane separator may be operated in a cross-flow configuration. In some such embodiments, the second membrane separator has a lower rejection and / or a higher solute permeability, water permeability, and / or salt passage percentage at standard conditions than the first membrane separator, as described in more detail below. It has been realized in the context of this disclosure that combining multiple membrane separators, a downstream one of which (e.g., the second membrane separator) permits an amount of solute passage through its semi-permeable membrane while an upstream one of which (e.g., the first membrane separator) receives a permeate inlet stream, can reduce sensitivity of the system to certain liquid solution components such as divalent ions.In some embodiments in which a second membrane separator permeate inlet stream is transported to the permeate side of the second membrane separator (e.g., as a draw stream), no first membrane separator permeate inlet stream is transported to the permeate side of the first membrane separator (or a first membrane separator permeate inlet stream is transported to the permeate side of the first membrane separator, but the first membrane permeate inlet stream has a mass flow rate that is lower than the mass flow rate of the second membrane separator permeate inlet stream (e.g., lower by at least 80%, at least 90%, at least 95%, at least 98%, at least 99%, or more)). As one example, the second membrane separator may be operated in a counter-flow configuration, while the first membrane separator may be operated in a cross-flow configuration. In some such embodiments, the first membrane separator has a lower rejection and / or a higher solute permeability, water permeability, and / or salt passage percentage at standard conditions than the second membrane separator, as described in more detail below. Various of the combinations described herein may contribute to an ability to concentrate liquid streams (e.g., wastewater stream) to higher concentrations of solute than would be achievable without such a combination (e.g., in a system without at least some membrane separators having a permeate inlet stream and some other membrane separators not having a permeate inlet stream (but permitting a portion of solute to pass through their semi-permeable membranes)).In some embodiments, a pressure of the first membrane separator retentate inlet stream is increased, thereby forming a pressurized first membrane separator retentate inlet stream. For example, referring to FIGS. 5-6, in system 200 or system 300, the hydraulic pressure of first membrane separator retentate inlet stream 105 is increased (e.g., by a factor of at least 1.03, at least 1.05, at least 1.1, at least 1.2, at least 1.5, at least 2, at least 5, and / or up to 10 or more) by pump 116 to form pressurized first membrane separator retentate inlet stream 117, which is then transported to retentate side 103 of first membrane separator 102. In some embodiments, the pump (e.g., where a first membrane separator retentate inlet stream may be pressurized) is a high-pressure pump. Examples of pumps (e.g., high-pressure pumps) that may be suitable include, but are not limited to, multi-stage centrifugal pumps, piston pumps, and positive displacement pumps.While FIGS. 5-6 show pump 116 as the device that increases the pressure of first membrane separator retentate inlet stream 105, other devices may be used in addition to or instead of a pump. For example, an energy recovery device may be used. As an example, the energy recovery device may be in the form of a of a pressure exchanger configured to transfer pressure energy from a high pressure fluid stream to a low pressure fluid stream. Various forms of energy recovery devices that may be suitable include, but are not limited to, work exchangers, recuperators, double-acting cylinders, reverse-positive-displacement pumps, centrifugal energy recovery devices, and axial-piston motors.In some embodiments, the energy recovery device is a turbine energy recovery device. A turbine energy recovery device generally refers to one that transfers hydraulic energy from a higher pressure stream to mechanical energy (e.g., to an impeller via a turbine), and the mechanical energy is then transferred to a lower pressure stream (e.g., via the impeller spinning the lower pressure stream to increase the stream’s hydraulic pressure). Examples of potentially suitable turbine energy recovery devices include, but are not limited to, turbochargers, Pelton wheels, and Francis turbines.In some embodiments, the energy recovery device is an isobaric energy recovery device. An isobaric energy recovery device generally refers to one that directly transfers pressure from a higher pressure stream to a lower pressure stream via a pressure equalization mechanism (e.g., via positive displacement, piston, and / or rotary action). Examples of isobaric energy recovery devices are described in U.S. Patent No. 2,675,173 to Jendrassik, entitled “Apparatus Effecting Pressure Exchange” and issued on Apr. 13, 1954, and U.S. Patent No. 4,887,942 to Hauge, entitled “Pressure Exchanger for Liquids” and issued on Dec. 19, 1989, each of which is incorporated herein by reference in its entirety. Specific types of isobaric energy recovery devices include, but are not limited to, piston isobaric energy recovery devices, double-acting cylinder isobaric energy recovery devices, two-cylinder isobaric energy recovery devices, rotary energy recovery devices, and combinations, thereof. Energy may be recovered from one or more other streams described in this disclosure. Non-limiting examples of configurations of energy recovery devices are described in U.S. Patent No. 11,667,549, issued on June 6, 2023, and entitled “Osmotic Methods and Systems Involving Energy Recovery,” which is incorporated herein by reference in its entirety.In some embodiments, at least a portion of a membrane separator retentate outlet stream is recirculated (e.g., to be transported to the retentate side of an upstream membrane separator or the same membrane separator). As one example, at least a portion (e.g., at least 5 wt%, at least 10 wt%, at least 20 wt%, at least 50 wt%, at least 80 wt%, and / or up to 85 wt%, up to 90 wt%, up to 95 wt%, up to 99 wt%, or more) of the first membrane separator retentate outlet stream may be recirculated such that the first membrane separator retentate inlet stream comprises at least a portion of the first membrane separator retentate outlet stream. For example, in FIG. 5, a portion (e.g., at least 5 wt%, at least 10 wt%, at least 20 wt%, at least 50 wt%, at least 80 wt%, and / or up to 85 wt%, up to 90 wt%, up to 95 wt%, up to 99 wt%, or more) of first membrane separator retentate outlet stream 106 is recirculated back (via stream 119) such that first membrane separator retentate inlet stream 105 comprises a portion of first membrane separator retentate outlet stream 106.As another example, at least a portion (e.g., at least 5 wt%, at least 10 wt%, at least 20 wt%, at least 50 wt%, at least 80 wt%, and / or up to 85 wt%, up to 90 wt%, up to 95 wt%, up to 99 wt%, or more) of the second membrane separator retentate outlet stream may be recirculated such that the first membrane separator retentate inlet stream comprises at least a portion of the second membrane separator retentate outlet stream. For example, in FIG. 6, a portion (e.g., at least 5 wt%, at least 10 wt%, at least 20 wt%, at least 50 wt%, at least 80 wt%, and / or up to 85 wt%, up to 90 wt%, up to 95 wt%, up to 99 wt%, or more) of second membrane separator retentate outlet stream 112 is recirculated back (via stream 120) such that first membrane separator retentate inlet stream 105 comprises a portion of first membrane separator retentate outlet stream 112. As noted above, recirculation of a membrane separator retentate outlet stream (e.g., from a downstream membrane separator) back to a membrane separator retentate inlet stream (e.g., of an upstream membrane separator) can, in some embodiments, increase crossflow velocity (e.g., to reduce concentration polarization) and better utilize later-stage semi-permeable membranes for additional solute concentration (e.g., brine concentration).It has been realized in the context of this disclosure that in some instances, the hydraulic pressure of the recirculated retentate outlet stream (e.g., recirculated first membrane separator retentate outlet stream and / or second membrane separator retentate outlet stream) and / or the hydraulic pressure of the feed stream can be modulated to reduce or eliminate backflow (e.g., from the pump or energy recovery device used to increase a pressure of the first membrane separator retentate inlet stream). In some embodiments in which at least a portion of the first membrane separator retentate outlet stream is recirculated (e.g., in FIG. 5), the hydraulic pressures of one or both of the feed stream and the recirculated portion of the first membrane separator retentate outlet stream are modulated such that the pressure of the first membrane separator retentate inlet stream is less than or equal to a pressure of the at least a portion of the first membrane separator retentate outlet stream. In some embodiments in which at least a portion of the second membrane separator retentate outlet stream is recirculated (e.g., in FIG. 6), the hydraulic pressures of one or both of the feed stream and the recirculated portion of the second membrane separator retentate outlet stream are modulated such that the pressure of the first membrane separator retentate inlet stream is less than or equal to a pressure of the at least a portion of the first membrane separator retentate outlet stream.This pressure modulation to establish and / or maintain the pressure relationship discussed above (e.g., to reduce or prevent backflow) may be accomplished at least in part by reducing the at least a portion of the feed stream (e.g., feed stream 101) being fed to the first membrane retentate inlet stream (e.g., first membrane retentate inlet stream 105). For example, the hydraulic pressure of feed stream 101 in FIGS. 5-6 may be reduced using valve 118 (e.g., prior to being fed to pump 116 as part of first membrane separator retentate inlet stream 105). An energy recovery device (e.g., a pressure exchanger) may be used in addition or as an alternative to the valve (e.g., valve 118).Additionally or alternatively, this pressure modulation to establish and / or maintain the pressure relationship discussed above (e.g., to reduce or prevent backflow) may be accomplished at least in part by increasing hydraulic pressure of the portion of the membrane separator retentate outlet stream (e.g., portion 119 of first membrane separator retentate outlet stream 106 and / or portion 120 of second membrane separator retentate outlet stream 112) being fed to the first membrane retentate inlet stream (e.g., first membrane retentate inlet stream 105). This increasing of the pressure of the recirculated portion of the first membrane separator retentate outlet stream and / or the second membrane separator retentate outlet stream may be accomplished using a pump (e.g., a booster pump) and / or an energy recovery device. For example, the hydraulic pressure of portion 119 in FIG. 5 and / or portion 120 in FIG. 6 may be increased using pump 121 (e.g., prior to being fed to pump 116 as part of first membrane separator retentate inlet stream 105). An energy recovery device may be used in addition to or as an alternative to the pump (e.g., pump 121).In some embodiments, a pressure of any of the streams described herein can be increased via one or more additional components, such as one or more booster pumps. In some embodiments, a pressure of any of the streams described herein can be decreased via one or more additional components, such as one or more additional valves and / or energy recovery devices. In some embodiments, a membrane separator described herein further comprises one or more heating, cooling, or other concentration or dilution mechanisms or devices.The membrane separators described herein (e.g., the first membrane separator, the second membrane separator, the third membrane separator) can each include a single semi-permeable membrane or a plurality of semi-permeable membranes.FIG. 7A is a schematic illustration of membrane separator 400A, in which a single semi-permeable membrane is used to separate permeate side 204 from retentate side 206. Membrane separator 400A can be operated by transporting retentate inlet stream 210 across retentate side 206. At least a portion of a liquid (e.g., a solvent) and, in some instances, solute within retentate inlet stream 210 can be transported across semi-permeable membrane 202 to permeate side 204. This can result in the formation of retentate outlet stream 212, which can include a higher concentration of solute than is contained within retentate inlet stream 210, as well as permeate outlet stream 214. Permeate outlet stream 214 can correspond to the liquid (e.g., solvent) and, in some instances, solute, of retentate inlet stream 210 that was transported from retentate side 206 to permeate side 204.In some embodiments, a membrane separator (e.g., the first membrane separator, the second membrane separator, the third membrane separator) comprises a plurality of semi-permeable membranes connected in parallel. One example of such an arrangement is shown in FIG. 7B. In FIG. 7B, membrane separator 400B comprises three semi-permeable membranes 202A, 202B, and 202C arranged in parallel. Retentate inlet stream 210 is split into three sub-streams, with one sub-stream fed to retentate side 206A of semi-permeable membrane 202A, another sub-stream fed to retentate side 206B of semi-permeable membrane 202B, and yet another sub-stream fed to retentate side 206C of semi-permeable membrane 202C. Membrane separator 400B can be operated by transporting the retentate inlet sub-streams across the retentate sides of the semi-permeable membranes. At least a portion of a liquid (e.g., a solvent), and, in some instances, solute, within retentate inlet stream 210 can be transported across each of semi-permeable membranes 202A, 202B, and 202C to permeate sides 204A, 204B, and 204C, respectively. This can result in the formation of three retentate outlet sub-streams, which can be combined to form retentate outlet stream 212. Retentate outlet stream 212 can include a higher concentration of solute than is contained within retentate inlet stream 210. Permeate outlet stream 214 can also be formed (from three permeate outlet sub-streams). Permeate outlet stream 214 can correspond to the liquid (e.g., solvent), and, in some instances, solute of retentate inlet stream 210 that was transported from retentate sides 206A-206C to permeate sides 204A-204C.While FIG. 7B shows three semi-permeable membranes connected in parallel, other embodiments could include 2, 4, 5, or more semi-permeable membranes connected in parallel.In some embodiments, a membrane separator (e.g., the first membrane separator, the second membrane separator) comprises a plurality of semi-permeable membranes connected in series. One example of such an arrangement is shown in FIG. 7C. In FIG. 7C, membrane separator 400C comprises three semi-permeable membranes 202A, 202B, and 202C arranged in series. In FIG. 7C, retentate inlet stream 210 is first transported to retentate side 206A of semi-permeable membrane 202A. At least a portion of a liquid (e.g., a solvent), and, in some instances, solute, within retentate inlet stream 210 can be transported across semi-permeable membrane 202A to permeate side 204A of semi-permeable membrane 202A. This can result in the formation of permeate outlet stream 214 and first intermediate retentate stream 240 that is transported to retentate side 206B of semi-permeable membrane 202B. At least a portion of a liquid (e.g., a solvent), and, in some instances, solute, within first intermediate retentate stream 240 can be transported across semi-permeable membrane 202B to permeate side 204B of semi-permeable membrane 202B. This can result in the formation of permeate outlet stream 250 and second intermediate retentate stream 241 that is transported to retentate side 206C of semi-permeable membrane 202C. At least a portion of a liquid (e.g., a solvent), and, in some instances, solute within second intermediate retentate stream 241 can be transported across semi-permeable membrane 202C to permeate side 204C of semi-permeable membrane 202C. This can result in the formation of permeate outlet stream 251 and retentate outlet stream 212.While FIG. 7C shows three semi-permeable membranes connected in series, other embodiments could include 2, 4, 5, or more semi-permeable membranes connected in series.For membrane separators comprising a plurality of semi-permeable membranes, parameters such as rejection percentage, recovery, and salt passage percentage at standard conditions for the membrane separators are calculated by performing a mass balance on the entire membrane separator. This means that all initial retentate streams for the membrane separator would be added and considered together, all final permeate outlet streams for the membrane separator would be added and considered together, and all final retentate outlet streams for the membrane separator would be added and considered together. For example, as mentioned above, in FIG. 7B, membrane separator 400B comprises three semi-permeable membranes 202A, 202B, and 202C arranged in parallel. Accordingly, calculation of the composition of the retentate inlet stream of membrane separator 400B for the purpose of calculating parameters such as the rejection percentage, recovery, and salt passage percentage at standard conditions for membrane separator 400B would involve taking measurements of retentate inlet stream 210 prior to it being split into the three inlet sub-streams fed to retentate sides 206A, 206B, and 206C of semi-permeable membranes 202A, 202B, and 202C, respectively. Similarly, calculation of the composition of the retentate outlet stream of membrane separator 400B for the purpose of calculating parameters such as the rejection percentage, recovery, and salt passage percentage at standard conditions for membrane separator 400B would involve taking measurements of retentate outlet stream 212, which is a combination of the three outlet sub-streams from retentate sides 206A, 206B, and 206C from semi-permeable membranes 202A, 202B, and 202C, respectively. Also similarly, calculation of the composition of the permeate outlet stream of membrane separator 400B for the purpose of calculating parameters such as the rejection percentage, recovery, and salt passage percentage at standard conditions would involve taking measurements of permeate outlet stream 214, which is a combination of the three outlet sub-streams from permeate sides 204A, 204B, and 204C from semi-permeable membranes 202A, 202B, and 202C, respectively.As another example of the calculation of parameters corresponding to a membrane separator comprising a plurality of semi-permeable membranes, reference is made to membrane separator 400C in FIG. 7C. Membrane separator 400C comprises three semi-permeable membranes 202A, 202B, and 202C arranged in series. Accordingly, calculation of the composition of the retentate inlet stream of membrane separator 400C for the purpose of calculating parameters such as the rejection percentage, recovery, and salt passage percentage at standard conditions for membrane separator 400C would involve taking measurements of retentate inlet stream 210 prior to it entering semi-permeable membrane 202A because semi-permeable membrane 202A is the initial semi-permeable membrane in the series. Similarly, calculation of the composition of the retentate outlet stream of membrane separator 400C for the purpose of calculating parameters such as the rejection percentage, recovery, and salt passage percentage at standard conditions for membrane separator 400C would involve taking measurements of retentate outlet stream 212 exiting semi-permeable membrane 202C because semi-permeable membrane 202C is the final semi-permeable membrane in the series with respect to the retentate outlet streams, thereby making retentate outlet stream 212 the final retentate outlet stream of membrane separator 200C. Calculation of the composition of the permeate outlet stream of membrane separator 400C for the purpose of calculating parameters such as the rejection percentage, recovery, and salt passage percentage at standard conditions would involve taking measurements of a combination of permeate outlet streams 214, 250, and 251 exiting semi-permeable membranes 202A, 202B, and 202C respectively. In addition, in some embodiments, a given membrane separator could include multiple semi-permeable membranes connected in parallel as well as multiple semi-permeable membranes connected in series.As noted above, in some instances a membrane separator receives a membrane separator permeate inlet stream. Second membrane separator 108 in one such membrane separator in the embodiments shown in FIGS. 1A-2B. Such a membrane separator may include a single semi-permeable membrane or multiple semi-permeable membranes (connected in series and / or parallel), as illustrated in FIGS. 8A8C. FIG. 8A is a schematic illustration of membrane separator 500A, in which a single semi-permeable membrane is used to separate permeate side 204 from retentate side 206. Membrane separator 500A can be operated by transporting retentate inlet stream 210 across retentate side 206. At least a portion of a liquid (e.g., a solvent) within retentate inlet stream 210 can be transported across semi-permeable membrane 202 to permeate side 204. This can result in the formation of retentate outlet stream 212, which can include a higher concentration of solute than is contained within retentate inlet stream 210, as well as permeate outlet stream 214. Permeate inlet stream 208 may also present. When permeate inlet stream 208 is present, it can be combined with the liquid (e.g., solvent) that has been transported to permeate side 204 from retentate side 206 to form permeate outlet stream 214.In some embodiments, a membrane separator (e.g., the first membrane separator, the second membrane separator) that receives a permeate inlet stream comprises a plurality of semi-permeable membranes connected in parallel. One example of such an arrangement is shown in FIG. 8B. In FIG. 8B, membrane separator 500B comprises three semi-permeable membranes 202A, 202B, and 202C arranged in parallel. Retentate inlet stream 210 is split into three sub-streams, with one sub-stream fed to retentate side 206A of semi-permeable membrane 202A, another sub-stream fed to retentate side 206B of semi-permeable membrane 202B, and yet another sub-stream fed to retentate side 206C of semi-permeable membrane 202C. Membrane separator 500B can be operated by transporting the retentate inlet sub-streams across the retentate sides of the semi-permeable membranes. At least a portion of a liquid (e.g., a solvent) within retentate inlet stream 210 can be transported across each of semi-permeable membranes 202A, 202B, and 202C to permeate sides 204A, 204B, and 204C, respectively. This can result in the formation of three retentate outlet sub-streams, which can be combined to form retentate outlet stream 212. Retentate outlet stream 212 can include a higher concentration of solute than is contained within retentate inlet stream 210. Permeate outlet stream 214 can also be formed (from three permeate outlet sub-streams). Permeate inlet stream 208 may also be present. When permeate inlet stream 208 is present, it can be divided into three sub-streams and transported to the permeate sides (204A, 204B, and 204C) of the three semi-permeable membranes (202A, 202B, and 202C) and combined with the liquid (e.g., solvent) that has been transported from the retentate sides (206A-206C) to the permeate sides (204A-204C) of the semi-permeable membranes (202A-202C) to form permeate outlet stream 214.While FIG. 8B shows three semi-permeable membranes connected in parallel, other embodiments could include 2, 4, 5, or more semi-permeable membranes connected in parallel.In some embodiments, a membrane separator (e.g., the first membrane separator, the second membrane separator) comprises a plurality of semi-permeable membranes connected in series. One example of such an arrangement is shown in FIG. 8C. In FIG. 8C, membrane separator 800C comprises three semi-permeable membranes 202A, 202B, and 202C arranged in series. In FIG. 8C, retentate inlet stream 210 is first transported to retentate side 206A of semi-permeable membrane 202A. At least a portion of a liquid (e.g., a solvent) within retentate inlet stream 210 can be transported across semi-permeable membrane 202A to permeate side 204A of semi-permeable membrane 202A. This can result in the formation of permeate outlet stream 214 and first intermediate retentate stream 240 that is transported to retentate side 206B of semi-permeable membrane 202B. At least a portion of a liquid (e.g., a solvent) within first intermediate retentate stream 240 can be transported across semi-permeable membrane 202B to permeate side 204B of semi-permeable membrane 202B. This can result in the formation of intermediate permeate outlet stream 250 and second intermediate retentate stream 241 that is transported to retentate side 206C of semi-permeable membrane 202C. At least a portion of a liquid (e.g., a solvent) within second intermediate retentate stream 241 can be transported across semi-permeable membrane 202C to permeate side 204C of semi-permeable membrane 202C. This can result in the formation of intermediate permeate outlet stream 251 and retentate outlet stream 212. When permeate inlet stream 208 is present, it can be transported to permeate side 204C of semi-permeable membrane 202C and combined with the liquid (e.g., solvent) that has been transported from retentate side 206C of semi-permeable membrane 202C to form intermediate permeate outlet stream 251. In some embodiments, as shown in FIG. 8C, intermediate permeate outlet stream 251 can be fed to permeate side 204B of semi-permeable membrane 202B and used as a sweep stream (i.e., combined with liquid that is transported through semi-permeable membrane 202B to form intermediate permeate outlet stream 250). In other embodiments, intermediate permeate outlet stream 251 is used directly as part (or all) of permeate outlet stream 214 (with another stream serving as the sweep stream across permeate side 204B of semi-permeable membrane 202B, or with semi-permeable membrane 202B being operated in cross-flow mode). In some embodiments, as shown in FIG. 8C, intermediate permeate outlet stream 250 can be fed to permeate side 204A of semi-permeable membrane 202A and used as a sweep stream (i.e., combined with liquid that is transported through semi-permeable membrane 202A to form permeate outlet stream 214). In other embodiments, intermediate permeate outlet stream 250 is used directly as part (or all) of permeate outlet stream 214 (with another stream serving as the sweep stream across permeate side 204A of semi-permeable membrane 202A, or with semi-permeable membrane 202A being operated in cross-flow mode).While FIG. 8C shows three semi-permeable membranes connected in series, other embodiments could include 2, 4, 5, or more semi-permeable membranes connected in series.In some embodiments, the first membrane separator comprises a plurality of semi-permeable membranes. In some such embodiments, the plurality of semi-permeable membranes within the first membrane separator are connected in series. In some such embodiments, the plurality of semi-permeable membranes within the first membrane separator are connected in parallel. In certain embodiments, the first membrane separator comprises a plurality of membranes a first portion of which are connected in series and another portion of which are connected in parallel.In some embodiments, the second membrane separator comprises a plurality of semi-permeable membranes. In some such embodiments, the plurality of semi-permeable membranes within the second membrane separator are connected in series. In some such embodiments, the plurality of semi-permeable membranes within the second membrane separator are connected in parallel. In certain embodiments, the second membrane separator comprises a plurality of membranes a first portion of which are connected in series and another portion of which are connected in parallel.As mentioned above, each membrane separator of the system may comprise at least one semi-permeable membrane. In general, a semi-permeable membrane is a barrier that allows some components of a mixture to pass through while blocking at least some of other components (e.g., blocking all of another component, or reducing the relative rate of permeation of another component). For example, a semi-permeable membrane may block some molecules in a liquid solution from passing through while allowing others to pass through. In some instances, a semi-permeable membrane blocks some molecules and permits other molecules to pass through based on their molecular weight and / or charge. As noted above, a semi-permeable membrane can be used for osmotic processes. For example, the semi-permeable membrane may be an osmotic membrane. An osmotic membrane may be capable of producing an osmotic pressure difference between solutions on either side of the membrane upon application of a hydraulic pressure difference across the two sides of the membrane. For example, if an osmotic membrane is placed between two solutions of identical composition such that there is initially no osmotic pressure difference across the membrane, application of a hydraulic pressure difference across the osmotic membrane may allow for transport of components from one side of the membrane to the other such that an osmotic pressure difference across the two sides of the membrane is established. Semi-permeable membranes may also be used for nanofiltration processes. Semi-permeable membranes may be configured for osmotic processes, nanofiltration processes, and / or processes in which separation is achieved based on a combination of nanofiltration and osmotic mechanisms (e.g., based on, for example, the molecular weight cutoff of the membranes, pore sizes of the membranes, the nature of the mixtures to which they are exposed, and a magnitude of applied hydraulic pressure).The semi-permeable membrane medium can comprise, for example, a metal, a ceramic, a polymer (e.g., polyamides, polyethylenes, polyesters, poly(tetrafluoroethylene), polysulfones, polycarbonates, polypropylenes, poly(acrylates)), and / or composites or other combinations of these. The semi-permeable membranes generally allow for the selective transport of solvent (e.g., water) through the membrane, where solvent is capable of being transmitted through the membrane while solute (e.g., solubilized species such as solubilized ions) are inhibited from being transported through the membrane. Examples of commercially available semi-permeable membranes that can be used in association with certain of the embodiments described herein include, but are not limited to, those commercially available from Dow Water and Process Solutions (e.g., FilmTecTM membranes), Hydranautics, GE Osmonics, Suez, LG, Toyobo, Microdyn, and Toray Membrane, among others known to those of ordinary skill in the art.In some embodiments, the semi-permeable membrane(s) of the first membrane separator and / or the second membrane separator has an average pore size of greater than or equal to 0.0001 microns, greater than or equal to 0.001 microns, greater than or equal to 0.002 microns or greater. In some embodiments, the semi-permeable membrane of the first membrane separator and / or the second membrane separator has an average pore size of less than or equal to 0.01 microns, less than or equal to 0.005 microns, or less. Combinations of these ranges (e.g., greater than or equal to 0.0001 microns and less than or equal to 0.01 microns) are possible.In some embodiments (such as some embodiments in which the first membrane separator receives a permeate inlet stream), the semi-permeable membrane(s) of the second membrane separator has an average pore size that is greater than that of the semi-permeable membrane(s) of the first membrane separator (e.g., by a factor of at least 1.05, at least 1.1, at least 1.2, at least 1.5, at least 2, at least 3, at least 5, or more). In some embodiments (such as some embodiments in which the second membrane separator receives a permeate inlet stream), the semi-permeable membrane(s) of the second membrane separator has an average pore size that is less than that of the semi-permeable membrane(s) of the first membrane separator (e.g., by a factor of at least 1.05, at least 1.1, at least 1.2, at least 1.5, at least 2, at least 3, at least 5, or more). The average pore size of the semi-permeable membrane may affect any of a variety of the parameters discussed below, such as solute permeability, water permeability, salt passage, rejection, and / or recovery. Average pore size can be determined, for example, using mercury intrusion porosimetry.In some embodiments, the semi-permeable membrane of a membrane separator of this disclosure has an average molecular weight cutoff (MWCO) that is sufficiently high such that a desired amount of liquid and / or solute (and / or type of solute) can pass through during operation of the system. In some embodiments, the semi-permeable membrane(s) of the first membrane separator and / or the second membrane separator, has an average MWCO of greater than or equal to 50 Daltons, greater than or equal to 75 Daltons, greater than or equal to 100 Daltons, greater than or equal to 150 Daltons, or greater. In some embodiments, the semi-permeable membrane of a membrane separator of this disclosure has an average molecular weight cutoff (MWCO) that is sufficiently low such that a desired amount of solute (and / or type of solute) is rejected such that an effective separation is performed. In some embodiments, the semi-permeable membrane(s) of the first membrane separator and / or the second membrane separator has an average MWCO of less than or equal to 400 Daltons, less than or equal to 300 Daltons, less than or equal to 250 Daltons, less than or equal to 200 Daltons, or less. Combinations of these ranges (e.g., greater than or equal to 50 Daltons and less than or equal to 400 Daltons, greater than or equal to 50 Daltons and less than or equal to 250 Daltons) are possible. The average MWCO of a membrane refers to the lowest molecular weight solute in which 90% of the solute is retained by the membrane.In some embodiments (such as some embodiments in which the first membrane separator receives a permeate inlet stream), the semi-permeable membrane(s) of the second membrane separator has an average MWCO that is greater than that of the semi-permeable membrane(s) of the first membrane separator (e.g., by a factor of at least 1.05, at least 1.1, at least 1.2, at least 1.5, at least 2, at least 3, at least 5, and / or up to 10, up to 20, or more). In some embodiments (such as some embodiments in which the second membrane separator receives a permeate inlet stream), the semi-permeable membrane(s) of the second membrane separator has an average MWCO that is less than that of the semi-permeable membrane(s) of the first membrane separator (e.g., by a factor of at least 1.05, at least 1.1, at least 1.2, at least 1.5, at least 2, at least 3, at least 5, and / or up to 10, up to 20, or more). The average MWCO of the semi-permeable membrane may affect any of a variety of the parameters discussed below, such as solute permeability, salt passage, rejection, and / or recovery.The solute permeability of each membrane separator may be chosen based on any of a variety of design criteria such as desired purity of permeate, desired hydraulic pressure to be used, and nature of incoming influent (e.g., solute concentration of incoming influent). The solute permeability of a membrane separator can be calculated from the solute flux through the membrane and the respective concentrations of solute on either side using equation [3] below:JS = B(CR – CP) [3]In the above equation, Js represents the ion flux, CR represents the concentration of solute on the retentate side of the membrane, CP represents the concentration of solute on the permeate side of the membrane, and B represents the solute permeability. Solute permeability is dependent on the species of solute in the retentate inlet stream and the concentrations on either side of the membrane.In some embodiments, the solute permeabilities of the first membrane separator and the second membrane separator (and, if present a third membrane separator, a fourth membrane separator, or more) during operation of the method are chosen to afford good, consistent performance across all membrane separators by accounting for differences in concentrations of their respective retentate inlet streams. In some embodiments, the solute permeability of the first membrane separator during the step of transporting the first membrane separator retentate inlet stream to the retentate side of the first membrane separator is different than the solute permeability of the second membrane separator during the step of transporting the second membrane separator retentate inlet stream to the retentate side of the second membrane separator. The difference in solute permeabilities between the first membrane separator and the second membrane separator may be due, at least in part, to use of different semi-permeable membranes in the first and second membrane separators (e.g., having different pore sizes, MWCOs, and / or surface chemistries). In some embodiments, the solute permeability of the first membrane separator during the step of transporting the first membrane separator retentate inlet stream to the retentate side of the first membrane separator and the solute permeability of the second membrane separator during the step of transporting the second membrane separator retentate inlet stream to the retentate side of the second membrane separator are at least 5% different, at least 10% different, at least 20% different, at least 50% different, and / or up to 100% different or more different from each other.In some embodiments (such as some embodiments in which the first membrane separator receives a permeate inlet stream), the solute permeability of the second membrane separator during the step of transporting the second membrane separator retentate inlet stream to the retentate side of the second membrane separator is greater than the solute permeability of the first membrane separator during the step of transporting the first membrane separator retentate inlet stream to the retentate side of the first membrane separator (e.g., by a factor of at least 1.05, at least 1.1, at least 1.2, at least 1.5, at least, 2, at least, 3, at least 5, or more). In some embodiments (such as some embodiments in which the first membrane separator receives a permeate inlet stream), the first membrane separator has a solute permeability of 0 during operation of the first membrane separator. In some embodiments (such as some embodiments in which the second membrane separator receives a permeate inlet stream), the solute permeability of the second membrane separator during the step of transporting the second membrane separator retentate inlet stream to the retentate side of the second membrane separator is less than the solute permeability of the first membrane separator during the step of transporting the first membrane separator retentate inlet stream to the retentate side of the first membrane separator (e.g., by a factor of at least 1.05, at least 1.1, at least 1.2, at least 1.5, at least, 2, at least, 3, at least 5, or more). In some embodiments (such as some embodiments in which the second membrane separator receives a permeate inlet stream), the second membrane separator has a solute permeability of 0 during operation of the first membrane separator. In this context, the solute permeability refers to the permeability of all total solute in the streams. However, in some embodiments, the relationships between permeabilities of the first and second membrane separators hold for one or more specific solute species described in this disclosure, such as solubilized NaCl and / or solubilized lithium cations.When calculating the percentage difference between two values (unless specified otherwise herein), the percentage calculation is made using the value that is larger in magnitude as the basis. To illustrate, if a first value is V1, and a second value is V2 (which is larger than V1), the percentage difference (V%Diff) between V1 and V2 would be calculated as:[4]and the first and second values would be said to be within X% of each other if V%Diff is X% or less, and the first and second values would be said to be at least X% different than each other if V%Diff is X% or more.Water permeability can be calculated from the water flux, pressure differential and osmotic differential, as shown below in equation [5]:JW = A(ΔP - Δπ) [5]In the above equation [5], Jw represents the flux of water through the membrane, ΔP represents the hydraulic pressure differential across the membrane, Δπ represents the osmotic pressure differential across the membrane, and A represents the water permeability.The salt passage percentage at standard conditions of each membrane separator may be chosen based on any of a variety of design criteria such as desired purity of permeate, desired hydraulic pressure to be used, and nature of incoming influent (e.g., solute type and / or concentration of incoming influent). The salt passage percentage at standard conditions of a membrane separator is an intrinsic property of the separator based on the quantity of salt, as a percentage, which passes through the semi-permeable membrane(s) from the retentate side to the permeate side of the membrane separator under defined reference conditions. The salt passage percentage at standard conditions of a membrane separator can be determined using the standardized test described in ASTM D4516-19a.In some embodiments, the salt passages at standard conditions of the first membrane separator and the second membrane separator (and, if present a third membrane separator, a fourth membrane separator, or more) used in in the operation of the method are chosen to afford good, consistent performance across all membrane separators by accounting for differences in concentrations of their respective retentate inlet streams. In some embodiments, the salt passage percentage at standard conditions of the first membrane separator is different than the salt passage percentage at standard conditions of the second membrane separator. The difference in salt passages at standard conditions between the first membrane separator and the second membrane separator may be due, at least in part, to use of different semi-permeable membranes in the first and second membrane separators (e.g., having different pore sizes, MWCOs, and / or surface chemistries). In some embodiments, the salt passage percentage at standard conditions of the first membrane separator and the salt passage percentage at standard conditions of the second membrane separator are at least 5% different, at least 10% different, at least 20% different, at least 50% different, and / or up to 100% different or more different from each other. In some embodiments (such as some embodiments in which the first membrane separator receives a permeate inlet stream), the salt passage percentage at standard conditions of the second membrane separator is greater than the salt passage percentage at standard conditions of the first membrane separator (e.g., by a factor of at least 1.05, at least 1.1, at least 1.2, at least 1.5, at least, 2, at least, 3, at least 5, and / or up to 10, up to 20, or more). In some embodiments (such as some embodiments in which the second membrane separator receives a permeate inlet stream), the salt passage percentage at standard conditions of the second membrane separator is less than the salt passage percentage at standard conditions of the first membrane separator (e.g., by a factor of at least 1.05, at least 1.1, at least 1.2, at least 1.5, at least, 2, at least, 3, at least 5, and / or up to 10, up to 20, or more).In some embodiments, the salt passage percentage at standard conditions of the first membrane separator and / or the second membrane separator membrane separator are independently greater than or equal to 0%, greater than or equal to 1%, greater than or equal to 2%, greater than or equal to 5%, greater than or equal to 10%, greater than or equal to 15%, greater than or equal to 20%, greater than or equal to 50%, greater than or equal to 75%, and / or up to 80%, up to 85%, up to 90%, or greater. In some embodiments, the first membrane separator has a relatively low salt passage percentage at standard conditions. Such a low salt passage percentage at standard conditions may be useful in embodiments in which the first membrane separator is operated as a high-rejection reverse osmosis separator. In some embodiments, the first membrane separator has a salt passage percentage at standard conditions of less than or equal to 10%, less than or equal to 5%, less than or equal to 2%, less than or equal to 1%, less than or equal to 0.1%, or less. In some embodiments, the second membrane separator has a relatively low salt passage percentage at standard conditions. Such a low salt passage percentage at standard conditions may be useful in embodiments in which the second membrane separator is operated as a high-rejection reverse osmosis separator. In some embodiments, the second membrane separator has a salt passage percentage at standard conditions of less than or equal to 10%, less than or equal to 5%, less than or equal to 2%, less than or equal to 1%, less than or equal to 0.1%, or less.Intrinsic properties of a semi-permeable membrane such as salt passage percentage at standard conditions, pore size, and / or MWCO can be selected based on supplier specifications for commercially-obtained membranes, by controlling the synthesis of membranes, and / or by physically and / or chemically modifying existing membranes (e.g., commercially obtained membranes). As an example of the latter, in some embodiments, a set of identical membranes may be obtained commercially (or prepared synthetically). A first subset of the membranes may be used without further modification. A second subset may be subjected to a first type of modification procedure (e.g., chemical treatment) that enlarges the pores of the membranes and / or modifies the surface chemistry of the membranes in such a way that the intrinsic salt passage (salt passage percentage at standard conditions), average pore size, and / or MWCO is increased. In such a way, the first subset of membranes could be incorporated into the first membrane separator and the second subset of membranes into the second membrane separator. Each of the first membrane separator and the second membrane separator may then have a differing salt passage percentage at standard conditions and, in use, differing permeabilities, rejections, and recoveries.In some embodiments, the semi-permeable membrane comprises cross-links. For example, the membrane may be a cross-linked polyamide membrane. In some embodiments, the semi-permeable membrane comprises an active layer which comprises the cross-links (e.g., a cross-linked polyamide active layer). One way in which a semi-permeable membrane of can be modified (e.g., such that the intrinsic salt passage, average pore size, and / or MWCO is increased) is via disruption of at least some (e.g., at least 0.01 mole percent (mol%), at least 0.1 mol%, at least 0.2 mol%, at least 0.5 mol%, at least 1 mol%, at least 2 mol%, at least 5 mol%, and / or up to 10 mol%, up to 20 mol%, or more) of the cross-links of the membrane. For example, cross-links (e.g., of polyamide chains) of the membrane may be disrupted via physical treatment (e.g., thermal treatment and / or mechanical disruption) and / or chemical treatment (e.g., via treatment with a chemical reagent and / or ultraviolet or visible light). Chemical treatment may result in chemical disruption (e.g., via breaking of chemical bonds due to a chemical reaction, breaking of noncovalent interactions such as hydrogen bonding) of at least some (e.g., at least 0.1 mole percent (mol%), at least 0.2 mol%, at least 0.5 mol%, at least 1 mol%, at least 2 mol%, at least 5 mol%, and / or up to 10 mol%, up to 20 mol%, or more) of the cross-links. In some embodiments in which the semi-permeable membrane comprises cross-links (e.g., as part of an active layer), the semi-permeable membrane comprises a cross-linked polymeric material derived from monomers. In some such embodiments, fewer than or equal to 99.9 mol% (e.g., fewer than or equal to 99 mol%, fewer than or equal to 98 mol%, fewer than or equal to 95 mol%, and / or as few as 90 mol%, as few as 80 mol%, or fewer) of the monomers participate in at least one cross-link (e.g., due at least in part to disruption such as chemical disruption).One example of a way in which at least some cross-links may be disrupted is by treating at least a portion of the membrane with a chemical reagent tending to break covalent and / or noncovalent bonds within the cross-links of the membrane. In some embodiments, the chemical reagent comprises an oxidant. One example of a potential oxidant for use with at least some membranes (e.g., polyamide membranes) is hypochlorite (ClO-). The hypochlorite may be provided as a solution comprising sodium hypochlorite (NaClO). The cross-links of the membrane may be disrupted by exposing at least a portion of the membrane to the chemical reagent (e.g., an oxidant such as hypochlorite). The duration of the exposure and / or the amount of chemical reagent (e.g., concentration of reagent in a solution contacting the membrane) may be selected based on a desired extent of disruption of the cross-links of the membrane. The desired extent of disruption of the cross-links of the membrane may in turn be based at least on a desired permeability of the semi-permeable membrane under certain conditions, a desired average pore size, and / or a desired MWCO.The presence and extent of disrupted cross-links may be determined by examination of the semi-permeable membrane. For example, the loss of cross-links due to chemical disruption may be detected and quantified by observing the presence and / or number of certain atoms or moieties (e.g., terminal functional groups) associated with the chemical dissociation of the cross-links being considered. The presence and / or number of such certain atoms or moieties may be observed using, for example spectroscopic techniques such as infrared (IR) spectroscopy (e.g., Fourier-Transform Infrared (FTIR) spectroscopy) or X-ray photoelectron spectroscopy (XPS). For example, XPS can be used to determine deviations from atomic ratios of certain atoms compared to ratios that would be expected in the absence of disruption of cross-linking. As an illustrative example, a partially oxidized polyamide membrane can be measured by determining the atomic ratio of oxygen to nitrogen using XPS. When polyamide is fully crosslinked, all oxygen atoms and nitrogen atoms in the polyamide polymer form amide groups, resulting in a 1:1 atomic ratio of oxygen to nitrogen. In a fully linear polyamide (thereby lacking cross-links), a free carboxyl group is present for every two amide groups, so the atomic ratio of oxygen to nitrogen is 2:1. Measurements of atomic ratio values between 1:1 and 2:1 can be used to determine extent of disruption of partially-oxidized polyamide accordingly. For example, an atomic ratio of oxygen to nitrogen of 1.5:1 in a polyamide membrane would indicate that 50 mol% of the crosslink are disrupted.The rejection of each membrane separator may be chosen based on any of a variety of design criteria such as desired purity of permeate, desired hydraulic pressure to be used, and nature of incoming influent (e.g., solute concentration of incoming influent). The rejection, R, of a membrane separator can be calculated from CR (the concentration of solute on the retentate side of the membrane) and CP (the concentration of solute on the permeate side of the membrane) and expressed as a percentage using Equation [6] below:R = [1 – (CP / CR)] * 100 [6]In some embodiments, the rejections (R) of the first membrane separator and the second membrane separator (and, if present the third membrane separator, the fourth membrane separator, or more) during operation of the method are chosen to afford good, consistent performance across all membrane separators by accounting for differences in concentrations of their respective retentate inlet streams. In some embodiments, the rejection of the first membrane separator for at least one solute (or all solutes) (e.g., the solute during the step of transporting the first membrane separator retentate inlet stream to the retentate side of the first membrane separator) is different than a rejection of the second membrane separator for the for at least one solute (or all solutes) (e.g., the solute during the step of transporting the second membrane separator retentate inlet stream to the retentate side of the second membrane separator). The difference in rejections between the first membrane separator and the second membrane separator may be due, at least in part, to use of different semi-permeable membranes in the first and second membrane separators (e.g., having different pore sizes, MWCOs, and / or surface chemistries).In some embodiments, the rejection of the first membrane separator for at least one solute (or all solute) (e.g., the solute during the step of transporting the first membrane separator retentate inlet stream to the retentate side of the first membrane separator) and the rejection of the second membrane separator for at least one solute (or all solute) (e.g., the solute during the step of transporting the second membrane separator retentate inlet stream to the retentate side of the second membrane separator) are at least 5% different, at least 10% different, at least 20% different, at least 50% different, and / or up to 100% different, or more different from each other. In some embodiments (such as some embodiments in which the first membrane separator receives a permeate inlet stream), the rejection of the second membrane separator for at least one solute (or all solutes) (e.g., the solute during the step of transporting the second membrane separator retentate inlet stream to the retentate side of the second membrane separator) is less than that of the first membrane separator for the at least one solute (or all solutes) (e.g., the solute during the step of transporting the first membrane separator retentate inlet stream to the retentate side of the second membrane separator) (e.g., by at least 5%, at least 10%, at least 20%, at least 50%, at least 75%, at least 90%, or more). In some embodiments (such as some embodiments in which the second membrane separator receives a permeate inlet stream), the rejection of the second membrane separator for at least one solute (or all solutes) (e.g., the solute during the step of transporting the second membrane separator retentate inlet stream to the retentate side of the second membrane separator) is greater than that of the first membrane separator for the at least one solute (or all solutes) (e.g., the solute during the step of transporting the first membrane separator retentate inlet stream to the retentate side of the second membrane separator) (e.g., by a factor of at least 1.05, at least 1.1, at least 1.2, at least 1.5, at least, 2, at least, 3, at least 5, and / or up to 10, up to 20, or more).In some embodiments, the rejection for at least one solute (or all solutes) (e.g., the solute during the step of transporting the first membrane separator retentate inlet stream to the retentate side of the first membrane separator) of the first membrane separator is greater than or equal to 10%, greater than or equal to 15%, greater than or equal to 20%, greater than or equal to 50%, greater than or equal to 75%, greater than or equal to 80%, greater than or equal to 85%, greater than or equal to 90%, greater than or equal to 95%, greater than or equal to 98%, greater than or equal to 99%, greater than or equal to 99.9%, or greater. In some embodiments, the rejection for at least one solute (or all solutes) (e.g., the solute during the step of transporting the first membrane separator retentate inlet stream to the retentate side of the first membrane separator) of the first membrane separator is less than or equal to 100%, less than or equal to 99%, less than or equal to 95%, less than or equal to 90%, less than or equal to 85%, less than or equal to 80%, less than or equal to 75%, less than or equal to 60%, less than or equal to 50%, or less. Combinations of these ranges (e.g., greater than or equal to 10% and less than or equal to 100%) are possible.In some embodiments, the rejection for at least one solute (or all solutes) (e.g., the solute during the step of transporting the first membrane separator retentate inlet stream to the retentate side of the first membrane separator) of the first membrane separator and / or the second membrane separator are, independently, greater than or equal to 10%, greater than or equal to 15%, greater than or equal to 20%, greater than or equal to 50%, greater than or equal to 75%, greater than or equal to 90%, greater than or equal to 95%, or greater. In some embodiments, the rejection for at least one solute (or all solutes) (e.g., the solute during the step of transporting the first membrane separator retentate inlet stream to the retentate side of the first membrane separator) of the second membrane separator is less than or equal to greater than or equal to 95%, less than or equal to 90%, less than or equal to 85%, less than or equal to 80%, less than or equal to 75%, less than or equal to 60%, less than or equal to 50%, or less. Combinations of these ranges (e.g., greater than or equal to 10% and less than or equal to 95%) are possible.The systems and methods described herein can be used to process a variety of feed streams. Generally, the feed stream comprises at least one liquid and at least one solute (also referred to herein as a solubilized species). According to certain embodiments, the feed stream comprises solubilized ions as a solute. The solubilized ion(s) may originate, for example, from a salt that has been dissolved in the liquid (e.g., solvent(s)) of the feed stream. A solubilized ion is generally an ion that has been solubilized to such an extent that the ion is no longer ionically bonded to a counter-ion. The feed stream can comprise any of a variety of solutes (e.g., solubilized ions) including, but not limited to, Na+, Mg2+, Ca2+, Sr2+, Ba2+, Cl-, ammonia cations, carbonate anions, bicarbonate anions, sulfate anions, bisulfate anions, and / or silica. In some embodiments, a feed stream (e.g., an aqueous feed stream) comprises at least one solubilized monovalent cation (i.e., a cation with a redox state of +1 when solubilized). For example, in some embodiments, a feed stream (e.g., an aqueous feed stream) comprises Na+ and / or K+. In certain embodiments, a feed stream (e.g., an aqueous feed stream) comprises at least one monovalent anion (i.e., an anion having redox state of -1 when solubilized). For example, in some embodiments, a feed stream (e.g., an aqueous feed stream) comprises Cl– and / or Br–. In some embodiments, a feed stream (e.g., an aqueous feed stream) comprises at least one monovalent cation and at least one monovalent anion. In some embodiments, a feed stream (e.g., an aqueous feed stream) comprises one or more divalent cations (i.e., a cation with a redox state of +2 when solubilized) and / or one or more divalent anions (i.e., an anion with a redox state of –2 when solubilized). Cations and / or anions having other valencies may also be present in feed streams (e.g., an aqueous feed stream), in some embodiments.The feed stream that may be incorporated into the first membrane separator retentate inlet stream may comprise streams or portions thereof previously subjected to one or more upstream treatment processes (e.g., by a membrane separator or other process such as solids removal, pH adjusted, divalent ion removal). For example, in some embodiments, the feed stream comprises at least a portion of an upstream membrane separator retentate outlet stream and / or at least a portion of an upstream membrane separator permeate outlet stream. Put another way, while first membrane separator 102 is called the “first” membrane separator in FIGS. 1-6, there may be additional upstream membrane separators not shown in the figures that produce some or all of feed stream 101.In some embodiments, the total concentration of solubilized ions in the feed stream can be relatively high. One advantage associated with certain embodiments is that initial feed streams (e.g., aqueous feed streams) with relatively high solubilized ion concentrations can be desalinated without the use of energy intensive desalination methods. In certain embodiments, the total concentration of solubilized ions in the feed stream transported into the system is at least 60,000 ppm, at least 80,000 ppm, or at least 100,000 ppm (and / or, in some embodiments, up to 200,000, up to 500,000 ppm, or more). Feed streams with solubilized ion concentrations outside these ranges could also be used.According to certain embodiments, the feed stream that is transported to the system comprises a suspended and / or emulsified immiscible phase. Generally, a suspended and / or emulsified immiscible phase is a material that is not soluble in in the liquid of the feed stream (e.g., solvent such as water) to a level of more than 10% by weight at the temperature and other conditions at which the stream is operated. In some embodiments, the suspended and / or emulsified immiscible phase comprises oil and / or grease. The term “oil” generally refers to a fluid that is more hydrophobic than water and is not miscible or soluble in water, as is known in the art. Thus, the oil may be a hydrocarbon in some embodiments, but in other embodiments, the oil may comprise other hydrophobic fluids. In some embodiments, at least 0.1 wt%, at least 1 wt%, at least 2 wt%, at least 5 wt%, or at least 10 wt% (and / or, in some embodiments, up to 20 wt%, up to 30wt%, up to 40 wt%, up to 50 wt%, or more) of a feed stream (e.g., an aqueous feed stream) is made up of a suspended and / or emulsified immiscible phase.While one or more of the membrane separators (e.g., the first membrane separator, the second membrane separator) can be used to separate a suspended and / or emulsified immiscible phase from an incoming feed stream, such separation is optional. For example, in some embodiments, the feed stream transported to the system is substantially free of a suspended and / or emulsified immiscible phase. In certain embodiments, one or more separation units upstream of the system can be used to at least partially remove a suspended and / or emulsified immiscible phase from a feed stream (e.g., an aqueous feed stream) before the feed stream is transported to a membrane separator. Non-limiting examples of such systems are described, for example, in International Patent Publication No. WO 2015 / 021062, published on February 12, 2015, which is incorporated herein by reference in its entirety for all purposes.In some embodiments, the feed stream is derived from any of a variety of types of wastewater. In some embodiments, the feed stream is derived from seawater. In some embodiments, the feed stream can be derived from seawater, ground water, brackish water, water used in or wastewater resulting from mining processes, wastewater from semiconductor manufacturing, wastewater from textile manufacturing, salar brines, wastewater from pharmaceutical manufacturing, and / or the effluent of a chemical process. In the oil and gas industry, for example, one type of aqueous feed stream that may be encountered is produced water (e.g., water that emerges from oil or gas wells along with the oil or gas). Due to the length of time produced water has spent in the ground, and due to high subterranean pressures and temperatures that may increase the solubility of certain salts and minerals, produced water often comprises relatively high concentrations of dissolved salts and minerals. For example, some produced water streams may comprise a supersaturated solution of dissolved strontium sulfate (SrSO4). In contrast, another type of aqueous feed stream that may be encountered in the oil and gas industry is flowback water (e.g., water that is injected as a fracking fluid during hydraulic fracturing operations and subsequently recovered). Flowback water often comprises a variety of constituents used in fracking, including surfactants, proppants, and viscosity reducing agents, but often has a lower salinity than produced water. In some cases, the systems and methods described herein can be used to at least partially desalinate aqueous feed streams derived from such process streams.A variety of types of liquids could also be used in the feed stream. In some embodiments, the liquid of the feed stream comprises water. For example, in some embodiments, at least 10 wt%, at least 25 wt%, at least 50 wt%, at least 75 wt%, at least 90 wt%, at least 95 wt%, at least 98 wt%, at least 99 wt%, at least 99.9 wt%, or more (e.g., all) of the liquid is water. Other examples of potential liquids for the feed steam include, but are not limited to alcohols and / or hydrocarbons. The liquid of the feed stream may be a mixture of different liquid-phase species. For example, the liquid may be a mixture of water and a water-miscible organic liquid, such as an alcohol.It should be understood that, in the present disclosure, the word “purified” (and, similarly, “pure” and “purify”) is used to describe any liquid that contains the component of interest in a higher percentage than is contained within a reference stream, and does not necessarily require that the liquid be 100% pure. That is to say, a “purified” stream can be partially or completely purified. As a non-limiting example, a water stream may be made up of 80 wt% water but could still be considered “purified” relative to a feed stream that is made up of 50 wt% water. Of course, it should also be understood that, in some embodiments, the “purified” stream could be made up of only (or substantially only) the component of interest. For example, a “purified” water stream could be made up of substantially only water (e.g., water in an amount of at least 98 wt%, at least 99 wt%, or more, or at least 99.9 wt%) and / or could be made up of only water (i.e., 100 wt% water).The draw solutions described herein (e.g., the first membrane separator permeate inlet stream, the second membrane separator permeate inlet stream) can include any of a variety of solutes and liquids (e.g., solvents). The solute(s) in the draw streams can be the same as or different from the solute(s) in the feed stream. The solvent(s) in the draw streams are generally the same as the solvent(s) in the feed stream, although variations in solvent compositions can be present at various points in the system.The draw solutions described herein can generally include any component(s) suitable for imparting an appropriate osmotic pressure to perform the functions described herein. In some embodiments, the draw stream(s) are aqueous solution(s) comprising one or more solubilized species, such as one or more dissolved ions and / or one or more dissociated molecules in water. For example, in some embodiments, the draw solution(s) (e.g., the second membrane separator permeate inlet stream in some embodiments) comprise Na+, Mg2+, Ca2+, Sr2+, Ba2+, and / or Cl-. In some embodiments, the draw solution(s) (e.g., the second membrane separator permeate inlet stream in some embodiments) comprises at least one solubilized monovalent cation, such as Na+ and / or K+. In certain embodiments, the draw solution(s) (e.g., the second membrane separator permeate inlet stream in some embodiments) comprises at least one monovalent anion, such as Cl– and / or Br–. Cations and / or anions having other valencies may also be present in the draw solution(s) (e.g., the second membrane separator permeate inlet stream in some embodiments). Other species could also be used in the draw solutions. For example, in some embodiments, the draw solution(s) (e.g., the second membrane separator permeate inlet stream in some embodiments) can be an aqueous stream comprising a solubilized non-ionic species, such as ammonia (NH3).Those of ordinary skill in the art, given the insight provided by the present disclosure, would be capable of selecting appropriate components for use in the various draw streams described herein.The draw streams may be prepared, according to certain embodiments, by suspending and / or dissolving one or more species in a solvent (such as an aqueous solvent) to solubilize the species in the solvent. For example, in some embodiments, one or more draw inlet streams can be made by dissolving one or more solid salts in an aqueous solvent. Non-limiting examples of salts that may be dissolved in water include NaCl, LiCl, CaCl2, MgCl2, NaOH, other inorganic salts, and the like. In some embodiments, the draw stream can be prepared by mixing ammonia with water. In certain embodiments, the draw stream can be prepared by dissolving one or more ammonia salts (e.g., ammonium bicarbonate, ammonium carbonate, and / or ammonium carbamate) in water. In some embodiments, the draw stream can be prepared by dissolving ammonia and carbon dioxide gasses in water.In some embodiments, the systems described herein can be used to achieve a relatively high level of purification. In some embodiments, the solute concentration in the first membrane separator and / or the second membrane separator retentate outlet streams is at least at least 1%, at least 2%, at least 5%, at least 10%, at least 25%, at least 50%, at least 100%, at least 200% higher, on a mass basis, than the concentration of the solute in the feed stream. As would be understood by one of ordinary skill in the art, an increase in concentration is measured relative to the lower concentration. For example, if the solute concentration in the first membrane separator retentate inlet stream is 35 grams / L, and the solute concentration in the first membrane separator retentate outlet stream is 38.5 grams / L, then the solute concentration in the first membrane separator retentate outlet stream is 10% higher, on a mass basis, than the solute concentration in first membrane separator retentate inlet stream (because the difference, 3.5 grams / L, is 10% of the lower value (i.e., 10% of 35 grams / L)).According to certain embodiments, the streams on either side of a semi-permeable membrane(s) within the membrane separator(s) can be operated in counter-current configuration. Operation of the system in this manner can, according to certain but not necessarily all embodiments, allow one to more easily ensure that the transmembrane net driving force is spatially uniform across the facial area of the semi-permeable membrane (e.g., osmotic membrane), for example, as described in International Patent Publication No. WO 2017 / 019944, filed July 29, 2016 as International Patent Application No. PCT / US2016 / 044663, and entitled “Osmotic Desalination Methods and Associated Systems,” which is incorporated herein by reference in its entirety. It should be understood that two streams do not have to be transported in perfectly parallel and opposite directions to be considered to be in counter-current configuration, and in some embodiments, the primary flow directions of two streams that are in a counter-current flow configuration can form an angle of up to 10° (or, in some cases, up to 5°, up to 2°, or up to 1°). In some, but not necessarily all embodiments, the first membrane separator is operated in a counter-current configuration. In some, but not necessarily all embodiments, the second membrane separator is operated in a counter-current configuration.As used herein, two elements are in fluidic communication with each other (or, equivalently, in fluid communication with each other) when fluid may be transported from one of the elements to the other of the elements without otherwise altering the configurations of the elements or a configuration of an element between them (such as a valve). Two conduits connected by an open valve (thus allowing for the flow of fluid between the two conduits) are considered to be in fluidic communication with each other. In contrast, two conduits separated by a closed valve (thus preventing the flow of fluid between the conduits) are not considered to be in fluidic communication with each other.As used herein, two elements are fluidically connected to each other when they are connected such that, under at least one configuration of the elements and any intervening elements, the two elements are in fluidic communication with each other. Two membrane separators connected by a valve and conduits that permit flow between the membrane separators in at least one configuration of the valve would be said to be fluidically connected to each other. To further illustrate, two membrane separators that are connected by a valve and conduits that permit flow between the membrane separators in a first valve configuration but not a second valve configuration are considered to be fluidically connected to each other both when the valve is in the first configuration and when the valve is in the second configuration. In contrast, two membrane separators that are not connected to each other (e.g., by a valve, another conduit, or another component) in a way that would permit fluid to be transported between them under any configuration would not be said to be fluidically connected to each other. Elements that are in fluidic communication with each other are always fluidically connected to each other, but not all elements that are fluidically connected to each other are necessarily in fluidic communication with each other.Various components are described herein as being fluidically connected. Fluidic connections may be either direct fluidic connections or indirect fluidic connections. Generally, a direct fluidic connection exists between a first region and a second region (and the two regions are said to be directly fluidically connected to each other) when they are fluidically connected to each other and when the composition of the fluid at the second region of the fluidic connection has not substantially changed relative to the composition of the fluid at the first region of the fluidic connection (i.e., no fluid component that was present in the first region of the fluidic connection is present in a weight percentage in the second region of the fluidic connection that is more than 5% different from the weight percentage of that component in the first region of the fluidic connection). As an illustrative example, a stream that connects first and second unit operations, and in which the pressure and temperature of the fluid is adjusted but the composition of the fluid is not altered, would be said to directly fluidically connect the first and second unit operations. If, on the other hand, a separation step is performed and / or a chemical reaction is performed that substantially alters the composition of the stream contents during passage from the first component to the second component, the stream would not be said to directly fluidically connect the first and second unit operations. In some embodiments, a direct fluidic connection between a first region and a second region can be configured such that the fluid does not undergo a phase change from the first region to the second region. In some embodiments, the direct fluidic connection can be configured such that at least 50 wt% (or at least 75 wt%, at least 90 wt%, at least 95 wt%, or at least 98 wt%) of the fluid (e.g., liquid) in the first region is transported to the second region via the direct fluidic connection. Any of the fluidic connections described herein may be, in some embodiments, direct fluidic connections. In other cases, the fluidic connections may be indirect fluidic connections.In some embodiments, the retentate side of the first membrane separator is fluidically connected to the retentate side of the second membrane separator. Such a fluidic connection may facilitate transport of at least a portion of the first membrane separator retentate side outlet stream from the retentate side of the first membrane separator (e.g., from a retentate side outlet of the first membrane separator) to the retentate side of the second membrane separator (e.g., by forming some or all of a second membrane separator retentate inlet stream that enters a retentate side inlet of the second membrane separator). In some embodiments, the retentate side of the first membrane separator is directly fluidically connected to the retentate side of the second membrane separator.In some embodiments, the permeate side of the second membrane separator is fluidically connected to the retentate side of the first membrane separator. Such a fluidic connection may establish a recycle stream. For example, in FIGS. 2A-2B permeate side 110 of second membrane separator 108 may be fluidically connected to retentate side 103 of first membrane separator 102 via stream 113. Such a fluidic connection may facilitate transport of at least a portion of the second membrane separator permeate outlet stream from the permeate side of the second membrane separator (e.g., from a permeate side outlet of the second membrane separator) to the retentate side of the first membrane separator (e.g., by forming a portion of the first membrane separator retentate inlet stream that enters the retentate side inlet of the first membrane separator). In some embodiments, the permeate side of the second membrane separator is directly fluidically connected to the retentate side of the first membrane separator. For example, in FIGS. 2A and 2B, permeate side 110 of second membrane separator 108 may be directly fluidically connected to retentate side 103 of first membrane separator 102 via stream 113. Some embodiments may comprise increasing a pressure (e.g., by a factor of at least 1.03, at least 1.05, at least 1.1, at least 1.2, at least 1.5, at least 2, at least 5, and / or up to 10 or more) of at least a portion (e.g., at least 5 wt%, at least 10 wt%, at least 20 wt%, at least 50 wt%, at least 80 wt%, at least 90 wt%, at least 95 wt%, at least 99 wt%, or more) of the second membrane separator permeate outlet stream to form a pressurized second membrane separator permeate outlet stream. In some such embodiments, at least a portion (or all) of the second membrane separator permeate outlet stream that is pressurized is recirculated back to the retentate side of the first membrane separator such that the first membrane separator retentate inlet stream comprises at least a portion (e.g., at least 5 wt%, at least 10 wt%, at least 20 wt%, at least 50 wt%, at least 80 wt%, at least 90 wt%, at least 95 wt%, at least 99 wt%, or more) of the pressurized second membrane separator permeate outlet stream. FIGS. 2A-2B show examples of some such embodiments. Such an increase in pressure may be performed using, for example, a booster pump and / or an energy recovery device (e.g., a pressure exchanger).Recirculating a pressurized portion (or all) of the second membrane separator permeate outlet stream back to the retentate side of first membrane separator may improve system efficiency. In some embodiments, the pressurized second membrane separator permeate outlet stream has a salinity that relatively close to the salinity of the first membrane separator retentate inlet stream. In some embodiments, the pressurized second membrane separator permeate outlet stream has a salinity that is within 20%, within 10%, within 5%, within 2%, within 1%, or within 0.5% of the salinity of the first membrane separator retentate inlet stream.As used herein, the salinity of a liquid stream refers to the weight percent (wt%) of all dissolved salts in the liquid stream. Salinity may be measured according to any method known in the art. For example, a non-limiting example of a suitable method for measuring salinity is the SM 2540C method. According to the SM 2540C method, a sample comprising an amount of liquid comprising one or more dissolved solids is filtered (e.g., through a glass fiber filter), and the filtrate is evaporated to dryness in a weighed dish at 180 °C. The increase in dish weight represents the mass of the total dissolved solids in the sample. The salinity of the sample may be obtained by dividing the mass of the total dissolved solids by the mass of the original sample and multiplying the resultant number by 100.U.S. Patent Application Publication No. 2023-0001355, published on January 5, 2023, filed as U.S. Patent Application No. 17 / 305,289, on July 2, 2021, and entitled “Membranes with Controlled Porosity for Serial Filtration,” is incorporated herein by reference in its entirety for all purposes. U.S. Patent Application Publication No. 2024-0109037, published on April 4, 2024, filed as U.S. Patent Application No. 18 / 315,130, on May 10, 2023, and entitled “Liquid Separation Using Solute-Permeable Membranes and Related Systems,” is incorporated herein by reference in its entirety for all purposes.U.S. Provisional Patent Application No. 63 / 621,793, filed January 17, 2024, and entitled “Membrane-Based Separation Systems and Related Configurations,” is incorporated herein by reference in its entirety. While several embodiments of the present invention have been described and illustrated herein, those of ordinary skill in the art will readily envision a variety of other means and / or structures for performing the functions and / or obtaining the results and / or one or more of the advantages described herein, and each of such variations and / or modifications is deemed to be within the scope of the present invention. More generally, those skilled in the art will readily appreciate that all parameters, dimensions, materials, and configurations described herein are meant to be exemplary and that the actual parameters, dimensions, materials, and / or configurations will depend upon the specific application or applications for which the teachings of the present invention is / are used. Those skilled in the art will recognize, or be able to ascertain using no more than routine experimentation, many equivalents to the specific embodiments of the invention described herein. It is, therefore, to be understood that the foregoing embodiments are presented by way of example only and that, within the scope of the appended claims and equivalents thereto, the invention may be practiced otherwise than as specifically described and claimed. The present invention is directed to each individual feature, system, article, material, and / or method described herein. In addition, any combination of two or more such features, systems, articles, materials, and / or methods, if such features, systems, articles, materials, and / or methods are not mutually inconsistent, is included within the scope of the present invention.As used herein in the specification and in the claims, the phrase “at least a portion” means some or all. “At least a portion” may mean, in accordance with certain embodiments, at least 1 wt%, at least 2 wt%, at least 5 wt%, at least 10 wt%, at least 25 wt%, at least 50 wt%, at least 75 wt%, at least 90 wt%, at least 95 wt%, or at least 99 wt%, and / or, in certain embodiments, up to 100 wt%.The indefinite articles “a” and “an,” as used herein in the specification and in the claims, unless clearly indicated to the contrary, should be understood to mean “at least one.”The phrase “and / or,” as used herein in the specification and in the claims, should be understood to mean “either or both” of the elements so conjoined, i.e., elements that are conjunctively present in some cases and disjunctively present in other cases. Other elements may optionally be present other than the elements specifically identified by the “and / or” clause, whether related or unrelated to those elements specifically identified unless clearly indicated to the contrary. Thus, as a non-limiting example, a reference to “A and / or B,” when used in conjunction with open-ended language such as “comprising” can refer, in one embodiment, to A without B (optionally including elements other than B); in another embodiment, to B without A (optionally including elements other than A); in yet another embodiment, to both A and B (optionally including other elements); etc.As used herein in the specification and in the claims, “or” should be understood to have the same meaning as “and / or” as defined above. For example, when separating items in a list, “or” or “and / or” shall be interpreted as being inclusive, i.e., the inclusion of at least one, but also including more than one, of a number or list of elements, and, optionally, additional unlisted items. Only terms clearly indicated to the contrary, such as “only one of” or “exactly one of,” or, when used in the claims, “consisting of,” will refer to the inclusion of exactly one element of a number or list of elements. In general, the term “or” as used herein shall only be interpreted as indicating exclusive alternatives (i.e. “one or the other but not both”) when preceded by terms of exclusivity, such as “either,” “one of,” “only one of,” or “exactly one of.” “Consisting essentially of,” when used in the claims, shall have its ordinary meaning as used in the field of patent law. As used herein in the specification and in the claims, the phrase “at least one,” in reference to a list of one or more elements, should be understood to mean at least one element selected from any one or more of the elements in the list of elements, but not necessarily including at least one of each and every element specifically listed within the list of elements and not excluding any combinations of elements in the list of elements. This definition also allows that elements may optionally be present other than the elements specifically identified within the list of elements to which the phrase “at least one” refers, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, “at least one of A and B” (or, equivalently, “at least one of A or B,” or, equivalently “at least one of A and / or B”) can refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including elements other than B); in another embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including elements other than A); in yet another embodiment, to at least one, optionally including more than one, A, and at least one, optionally including more than one, B (and optionally including other elements); etc.Unless clearly indicated to the contrary, concentrations and percentages described herein are on a mass basis.As used herein, “wt%” is an abbreviation of weight percentage. As used herein, “at%” is an abbreviation of atomic percentage.Some embodiments may be embodied as a method, of which various examples have been described. The acts performed as part of the methods may be ordered in any suitable way. Accordingly, embodiments may be constructed in which acts are performed in an order different than illustrated, which may include different (e.g., more or less) acts than those that are described, and / or that may involve performing some acts simultaneously, even though the acts are shown as being performed sequentially in the embodiments specifically described above.Use of ordinal terms such as “first,” “second,” “third,” etc., in the claims to modify a claim element does not by itself connote any priority, precedence, or order of one claim element over another or the temporal order in which acts of a method are performed, but are used merely as labels to distinguish one claim element having a certain name from another element having a same name (but for use of the ordinal term) to distinguish the claim elements.In the claims, as well as in the specification above, all transitional phrases such as “comprising,” “including,” “carrying,” “having,” “containing,” “involving,” “holding,” and the like are to be understood to be open-ended, i.e., to mean including but not limited to. Only the transitional phrases “consisting of” and “consisting essentially of” shall be closed or semi-closed transitional phrases, respectively, as set forth in the United States Patent Office Manual of Patent Examining Procedures, Section 2111.03.

Claims

1. A method of treating a feed stream comprising a liquid and a solute, comprising: increasing the pressure of a first membrane separator retentate inlet stream to form a pressurized first membrane separator retentate inlet stream;transporting at least a portion of the pressurized first membrane separator retentate inlet stream to a retentate side of a first membrane separator such that: a first membrane separator retentate outlet stream exits the retentate side of the first membrane separator, the first membrane separator retentate outlet stream having an osmotic pressure that is greater than an osmotic pressure of the pressurized first membrane separator retentate inlet stream, and at least a portion of liquid and solute from the pressurized first membrane separator retentate inlet stream is transported from the retentate side of the first membrane separator, through a semi-permeable membrane of the first membrane separator, to a permeate side of the first membrane separator; andtransporting a second membrane separator retentate inlet stream to a retentate side of a second membrane separator such that: a second membrane separator retentate outlet stream exits the retentate side of the second membrane separator, the second membrane separator retentate outlet stream having an osmotic pressure that is greater than an osmotic pressure of the second membrane separator retentate inlet stream, and at least a portion of liquid from the second membrane separator retentate inlet stream is transported from the retentate side of the second membrane separator, through a semi-permeable membrane of the second membrane separator, to a permeate side of the second membrane separator;wherein: the first membrane separator retentate inlet stream comprises at least a portion of the feed stream;the first membrane separator retentate inlet stream comprises at least a portion of the second membrane separator retentate outlet stream; the second membrane separator retentate inlet stream comprises at least a portion of the first membrane separator retentate outlet stream; anda pressure of the feed stream is reduced and / or a pressure of the at least a portion of the second membrane separator retentate outlet stream is increased such that a pressure of the first membrane separator retentate inlet stream is less than or equal to a pressure of the at least a portion of the second membrane separator retentate outlet stream.

2. A method of treating a feed stream comprising a liquid and a solute, comprising: increasing the pressure of a first membrane separator retentate inlet stream to form a pressurized first membrane separator retentate inlet stream;transporting at least a portion of the pressurized first membrane separator retentate inlet stream to a retentate side of a first membrane separator such that: a first membrane separator retentate outlet stream exits the retentate side of the first membrane separator, the first membrane separator retentate outlet stream having an osmotic pressure that is greater than an osmotic pressure of the pressurized first membrane separator retentate inlet stream, and at least a portion of liquid and solute from the pressurized first membrane separator retentate inlet stream is transported from the retentate side of the first membrane separator, through a semi-permeable membrane of the first membrane separator, to a permeate side of the first membrane separator;wherein: the first membrane separator retentate inlet stream comprises at least a portion of the feed stream;the first membrane separator retentate inlet stream comprises at least a portion of the first membrane separator retentate outlet stream; anda pressure of the feed stream is reduced and / or a pressure of the at least a portion of the first membrane separator retentate outlet stream is increased such that a pressure of the first membrane separator retentate inlet stream is less than or equal to a pressure of the at least a portion of the first membrane separator retentate outlet stream. 3. The method of claim 1, wherein a pressure of the feed stream is reduced such that a pressure of the first membrane separator retentate inlet stream is less than or equal to a pressure of the at least a portion of second membrane separator retentate outlet stream.

4. The method of any one of claims 1 and 3, wherein a pressure of the at least portion of the second membrane separator retentate outlet stream is increased such that a pressure of the first membrane separator retentate inlet stream is less than or equal to a pressure of the at least a portion of the second membrane separator retentate outlet stream.

5. The method of any one of claims 1-4, the pressure of the feed stream is reduced via a valve and / or an energy recovery device.

6. The method of any one of claims 1 and 3-5, wherein the pressure of the at least portion of the second membrane separator retentate outlet stream is increased via a pump and / or an energy recovery device.

7. The method of any one of claims 1-6, wherein the increasing the pressure of the first membrane separator retentate inlet stream is performed using a pump and / or an energy recovery device.

8. The method of any one of claims 1-7, wherein the feed stream comprises at least a portion of an upstream membrane separator retentate outlet stream and / or at least a portion of an upstream membrane separator permeate outlet stream.

9. The method of any one of claims 1 and 3-8, wherein at least a portion of solute from the second membrane separator retentate inlet stream is transported from the retentate side of the second membrane separator, through the semi-permeable membrane of the second membrane separator, to the permeate side of the second membrane separator.

10. The method of any one of claims 1 and 3-9, wherein a salt passage percentage at standard conditions of the first membrane separator is different than a salt passage percentage at standard conditions of the second membrane separator, wherein the salt passage percentage at standard conditions is determined using ASTM D4516-19a.

11. The method of any one of claims 1 and 3-10, wherein the second membrane separator has a salt passage percentage at standard conditions that is greater than that of the first membrane separator.

12. The method of any one of claims 1 and 3-11, wherein a solute permeability of the first membrane separator during the step of transporting the at least a portion of the pressurized first membrane separator retentate inlet stream to the retentate side of the first membrane separator is different than a solute permeability of the second membrane separator during the step of transporting the second membrane separator retentate inlet stream to the retentate side of the second membrane separator.

13. The method of any one of claims 1 and 3-12, wherein the second membrane separator has a rejection for the solute on the retentate side that is less than that of the first membrane separator.

14. The method of any one of claims 1 and 3-13, wherein the first membrane separator and / or the second membrane separator has a rejection for the solute of less than or equal to 95%.

15. The method of any one of claims 1 and 3-14, wherein the first membrane separator and / or the second membrane separator has a rejection for the solute of greater than or equal to 10%.

16. A method of treating a feed stream comprising a liquid and a solute, comprising: transporting a first membrane separator retentate inlet stream to a retentate side of a first membrane separator such that: a first membrane separator retentate outlet stream exits the retentate side of the first membrane separator, the first membrane separator retentate outlet stream having an osmotic pressure that is greater than an osmotic pressure of the first membrane separator retentate inlet stream, and at least a portion of liquid and solute from the first membrane separator retentate inlet stream is transported from the retentate side of the first membrane separator, through a semi-permeable membrane of the first membrane separator, to a permeate side of the first membrane separator; andtransporting a second membrane separator retentate inlet stream to a retentate side of a second membrane separator and a second membrane separator permeate inlet stream to a permeate side of the second membrane separator such that: a second membrane separator retentate outlet stream exits the retentate side of the second membrane separator, the second membrane separator retentate outlet stream having an osmotic pressure that is greater than an osmotic pressure of the second membrane separator retentate inlet stream, and at least a portion of liquid from the second membrane separator retentate inlet stream is transported from the retentate side of the second membrane separator, through a semi-permeable membrane of the second membrane separator, to the permeate side of the second membrane separator where the portion of liquid is combined with the second membrane separator permeate inlet stream at the permeate side of the second membrane separator to form a second membrane separator permeate outlet stream;wherein: the first membrane separator retentate inlet stream comprises at least a portion of the feed stream; andthe second membrane separator retentate inlet stream comprises at least a portion of the first membrane separator retentate outlet stream.

17. A method of treating a feed stream comprising a liquid and a solute, comprising:transporting a first membrane separator retentate inlet stream to a retentate side of a first membrane separator and a first membrane separator permeate inlet stream to a permeate side of the first membrane separator such that: a first membrane separator retentate outlet stream exits the retentate side of the first membrane separator, the first membrane separator retentate outlet stream having an osmotic pressure that is greater than an osmotic pressure of the first membrane separator retentate inlet stream, and at least a portion of liquid from the first membrane separator retentate inlet stream is transported from the retentate side of the first membrane separator, through a semi-permeable membrane of the first membrane separator, to the permeate side of the first membrane separator where the portion of liquid is combined with the first membrane separator permeate inlet stream at the permeate side of the first membrane separator to form a first membrane separator permeate outlet stream; andtransporting a second membrane separator retentate inlet stream to a retentate side of a second membrane separator such that: a second membrane separator retentate outlet stream exits the retentate side of the second membrane separator, the second membrane separator retentate outlet stream having an osmotic pressure that is greater than an osmotic pressure of the second membrane separator retentate inlet stream, and at least a portion of liquid and solute from the second membrane separator retentate inlet stream is transported from the retentate side of the second membrane separator, through a semi-permeable membrane of the second membrane separator, to a permeate side of the second membrane separator;wherein: the first membrane separator retentate inlet stream comprises at least a portion of the feed stream; andthe second membrane separator retentate inlet stream comprises at least a portion of the first membrane separator retentate outlet stream.

18. The method of claim 16, wherein the second membrane separator permeate inlet stream has a higher osmotic pressure than an osmotic pressure of the second membrane separator retentate inlet stream.

19. The method of any one of claims 16 and 18, wherein the second membrane separator permeate inlet stream comprises at least a portion of the second membrane separator retentate outlet stream.

20. The method of claim 17, wherein the first membrane separator permeate inlet stream has a higher osmotic pressure than an osmotic pressure of the first membrane separator retentate inlet stream.

21. The method of any one of claims 17 and 20, wherein the first membrane separator permeate inlet stream comprises at least a portion of the first membrane separator retentate outlet stream.

22. The method of any one of claims 16-21, wherein a salt passage percentage at standard conditions of the first membrane separator is different than a salt passage percentage at standard conditions of the second membrane separator, wherein the salt passage percentage at standard conditions is determined using ASTM D4516-19a.

23. The method of claim 22, wherein the second membrane separator has a salt passage percentage at standard conditions that is less than that of the first membrane separator.

24. The method of claim 22, wherein the second membrane separator has a salt passage percentage at standard conditions that is greater than that of the first membrane separator.

25. The method of any one of claims 16-24, wherein a solute permeability of the first membrane separator during the step of transporting the first membrane separator retentate inlet stream to the retentate side of the first membrane separator is different than a solute permeability of the second membrane separator during the step of transporting the second membrane separator retentate inlet stream to the retentate side of the second membrane separator.

26. The method of any one of claims 16-25, wherein the second membrane separator has a rejection for the solute on the retentate side that is greater than that of the first membrane separator.

27. The method of any one of claims 16-25, wherein the second membrane separator has a rejection for the solute on the retentate side that is less than that of the first membrane separator.

28. The method of any one of claims 16-27, wherein the first membrane separator and / or the second membrane separator has a rejection for the solute of less than or equal to 95%.

29. The method of any one of claims 16-28, wherein the first membrane separator and / or the second membrane separator has a rejection for the solute of greater than or equal to 10%.

30. The method of any one of claims 16-29, wherein the first membrane separator and / or the second membrane separator has a rejection for the solute of greater than or equal to 90%.

31. The method of any one of claims 16-30, further comprising increasing a pressure of at least a portion of the second membrane separator permeate outlet stream to form a pressurized second membrane separator permeate outlet stream, wherein the first membrane separator retentate inlet stream comprises at least a portion of the pressurized second membrane separator permeate outlet stream.

32. The method of claim 31, wherein the pressurized second membrane separator permeate outlet stream has a salinity that is within 20% of a salinity of the first membrane separator retentate inlet stream.

Images