Abstract:
Portions of a feed liquid are passed through respective condensers and liquid-liquid heat exchangers. The feed liquid is then heated and injected into a first feed-liquid containment chamber, where vapor from the feed is passed through a first gas-permeable membrane and directed into a first condenser, where the vapor is cooled by the feed liquid passing through the first condenser and condenses as it cools to produce a first liquid permeate. The first liquid permeate is passed through the first liquid-liquid heat exchanger where the first liquid permeate is cooled by the feed liquid passing therethrough. After the vapor is removed from the feed liquid in the first feed-liquid containment chamber, the remaining feed liquid from the first feed-liquid containment chamber is injected into a second feed-liquid containment chamber, where the process is repeated. The first liquid permeate from the first liquid liquid-liquid heat exchanger is combined with the second liquid permeate from the second condenser to form a combined liquid permeate; and the combined liquid permeate is passed through the second liquid-liquid heat exchanger where the combined liquid permeate is cooled by the feed liquid passing therethrough.

Description:
BACKGROUND 
       [0001]    In this century, the shortage of fresh water may surpass the shortage of energy as a global concern for humanity, and these two challenges are inexorably linked, as explained, e.g., in the “Special Report on Water” in the 20 May 2010 issue of  The Economist . Fresh water is one of the most fundamental needs of humans and other organisms; each human needs to consume a minimum of about two liters per day. The world also faces greater freshwater demands from farming and industrial processes. 
         [0002]    The hazards posed by insufficient water supplies are particularly acute. A shortage of fresh water may lead to a variety of crises, including famine, disease, death, forced mass migration, cross-region conflict/war, and collapsed ecosystems. Despite the criticality of the need for fresh water and the profound consequences of shortages, supplies of fresh water are particularly constrained. 97.5% of the water on Earth is salty, and about 70% of the remainder is locked up as ice (mostly in ice caps and glaciers), leaving only a fraction of all water on Earth as available fresh (non-saline) water. 
         [0003]    Moreover, the earth&#39;s water that is fresh and available is not evenly distributed. For example, heavily populated countries, such as India and China, have many regions that are subject to scarce supplies. Further still, the supply of fresh water is often seasonally inconsistent. Meanwhile, demands for fresh water are tightening across the globe. Reservoirs are drying up; aquifers are falling; rivers are dying; and glaciers and ice caps are retracting. Rising populations increase demand, as do shifts in farming and increased industrialization. Climate change poses even more threats in many regions. Consequently, the number of people facing water shortages is increasing. Naturally occurring fresh water, however, is typically confined to regional drainage basins; and transport of water is expensive and energy-intensive. 
         [0004]    One method for obtaining fresh water from sea water is membrane distillation, wherein water from a heated saline liquid stream is allowed to vaporize through a hydrophobic microporous membrane. Membrane distillation is thermally driven, where a temperature difference across the two sides of the membrane leads to a vapor-pressure difference that causes water to evaporate from the hot side of the membrane and pass through the pores as vapor to the cold side. Additionally, membrane distillation runs at relatively low pressure, can withstand high salinity feed streams, and is potentially more resistant to fouling than other distillation approaches. Consequently, membrane distillation can be used for desalination where reverse osmosis is not a practical option. The use of thermal energy, rather than electrical energy, and the fact that membranes for membrane distillation can withstand dryout make this technology attractive for renewable power applications, as well. However, most research on membrane distillation has focused on maximizing membrane flux as opposed to minimizing energy consumption and cost [see E. K. Summers, H. A. Arafat, J. H. Lienhard V, “Energy Efficiency Comparison of Single-Stage Membrane Distillation (MD) Desalination Cycles in Different Configurations,” Desalination, 290, pp. 54-66 (2011)]; and current membrane distillation systems suffer from poor energy efficiency compared to other desalination systems. 
         [0005]    Membrane-distillation systems can be used in many configurations, depending on how liquid is collected from the permeate (cold) side. In direct-contact membrane distillation (DCMD), the vapor is condensed on a pure water stream that contacts the other side of the membrane. In air-gap membrane distillation (AGMD), an air gap separates the membrane from a cold condensing plate which collects vapor that moves across the gap. In sweeping-gas membrane distillation (SGMD), a carrier gas is used to remove the vapor, which is condensed in a separate component. SGMD is typically used for removing volatile vapors and is typically not used in desalination. 
         [0006]    Vacuum membrane distillation (VMD) is another variation of membrane distillation in which the driving pressure difference is increased by lowering the pressure on the vapor (cold) side of the membrane. The heat of vaporization is then recovered in an external condenser. This process has been applied to the desalination of seawater. However, energy recovery is limited by the saturation temperature of the pressure in the condenser; and maximizing flux by increasing the pressure difference between the saline feed and the condenser results in poor energy recovery. 
         [0007]    In desalination systems, recovering the energy given off in condensation increases the thermal efficiency of the system, which is strongly correlated with low water cost. Some studies of VMD from an energy efficiency point of view have been conducted, but typically report low performance. Performance as measured by the Gained Output Ratio (GOR) is below 1 for these systems [A. Criscuoli, et al., “Evaluation of energy requirements in membrane distillation”, 47 Chemical Engineering and Processing: Process Intensification, Euromembrane 2006, 1098-1105 (2008); and X. Wang, et al., “Feasibility research of potable water production via solar-heated hollow fiber membrane distillation system, 247 Desalination 403-411 (2009)]. 
         [0008]    GOR is the ratio of the latent heat of evaporation of a unit mass of product water to the amount of energy used by a desalination system to produce that unit mass of product. The higher the GOR, the better the performance. For example, a solar still would have a GOR on the order of 1, whereas a good multi-effect distillation system may have a GOR of 12. 
         [0009]    A low GOR arises from the fact that energy recovery is limited by the saturation temperature of the pressure in the condenser. Maximizing flux by increasing the pressure difference between the saline feed and the condenser lowers the condensation temperature in the condenser, which requires high mass flow rates of colder water to condense the additional vapor, when compared to a system with a smaller pressure difference (higher saturation temperature) and lower flux. This trade-off, however, results in poor energy recovery. 
       SUMMARY 
       [0010]    A multi-stage membrane distillation apparatus and method for multi-stage membrane distillation are described herein. Various embodiments of the apparatus and methods may include some or all of the elements, features and steps described below. 
         [0011]    One embodiment of a multi-stage membrane distillation apparatus includes a source of liquid feed, a plurality of purification stages, a liquid-feed conduit extending from the source of liquid feed, a liquid-permeate extraction conduit, and at least one vacuum source. 
         [0012]    Each of the plurality of purification stages respectively includes a vacuum membrane distillation module, including a feed inlet in fluid communication with the source of liquid feed; a gas-permeable membrane contained in the vacuum membrane distillation module; a feed-liquid containment chamber for containing liquid feed from the feed inlet, wherein the feed-liquid containment chamber is positioned on one side of the gas-permeable membrane and is in fluid communication with the feed inlet; a vapor-permeate-containment chamber for containing vapor permeated from liquid feed through the gas-permeable membrane, wherein the vapor-permeate-containment chamber is positioned on an opposite side of the gas-permeable membrane from the feed-liquid containment chamber; and a vapor-permeate outlet in fluid communication with the vapor-permeate-containment chamber for extracting the vapor permeate from the vapor-permeate-containment chamber. 
         [0013]    The condenser is configured to condense the vapor permeate and includes (a) a vapor-permeate inlet in fluid communication with the vapor-permeate outlet of the vacuum membrane distillation module and (b) a condensed liquid-permeate outlet through which condensed liquid permeate can be removed from the condenser. 
         [0014]    The liquid-liquid heat exchanger is in fluid communication with the liquid-permeate outlet of the condenser and is configured for cooling condensed liquid permeate from the condenser. 
         [0015]    The liquid-feed conduit extends from the source of liquid feed and includes a bifurcation between (a) the liquid-feed source and (b) the condenser and the liquid-liquid heat exchanger in a flow path from the liquid-feed source through the liquid-feed conduit, where the bifurcation splits the liquid-feed conduit into respective conduits passing through the condenser and through the liquid-liquid heat exchanger, and a junction positioned to place the condenser and the liquid-liquid heat exchanger, where the junction is configured to rejoin the set of bifurcated conduits into a common conduit extending toward and in fluid communication with the liquid-feed-containment chamber of the vacuum membrane distillation module. 
         [0016]    The liquid-permeate extraction conduit including a plurality of liquid-permeate inlets in fluid, each respectively in communication with the liquid-permeate outlet of the condenser of a respective purification stage, wherein the liquid-permeate extraction conduit is configured to pass condensed liquid permeate from the liquid-permeate inlets through the liquid-liquid heat exchangers. 
         [0017]    The vacuum source in fluid communication with and configured to establish a reduced pressure in the vacuum membrane distillation modules and in the condensers. 
         [0018]    In a method for distillation of a feed liquid, portions of the feed liquid are passed through a second condenser, through a first condenser, through a first liquid-liquid heat exchanger and through a second liquid-liquid heat exchanger. The feed liquid is then heated and injected into a first feed-liquid containment chamber. Vapor from the feed liquid in the first feed-liquid containment chamber is passed through a first gas-permeable membrane. Vapor that has passed through the first gas-permeable membrane into is directed into the first condenser, where the vapor is cooled by the feed liquid passing through the first condenser and condenses as it cools to produce a first liquid permeate. The first liquid permeate is passed through the first liquid-liquid heat exchanger where the first liquid permeate is cooled by the feed liquid passing therethrough. After the gas is removed from the feed liquid in the first feed-liquid containment chamber, the remaining feed liquid from the first feed-liquid containment chamber is injected into a second feed-liquid containment chamber. Vapor from the feed liquid in the second feed-liquid containment chamber is then passed through a second gas-permeable membrane. A reduced pressure is established for the vapors passed through the first and second membranes; and vapor that has passed through the second gas-permeable membrane is directed into the second condenser, where the vapor is cooled by the feed liquid passing through the second condenser and condenses as it cools to produce a second liquid permeate. The first liquid permeate from the first liquid liquid-liquid heat exchanger is combined with the second liquid permeate from the second condenser to form a combined liquid permeate; and the combined liquid permeate is passed through the second liquid-liquid heat exchanger where the combined liquid permeate is cooled by the feed liquid passing therethrough. 
         [0019]    The apparatus and methods, described herein can provide a simple cycle in which many membrane modules and condensers can be cascaded at successively lower pressure as more vapor is removed from the feed and as the feed temperature decreases. By reducing the pressure step-wise over many stages, the feed can be preheated to a higher temperature in the condenser. 
         [0020]    This type of cycle shares some similarities with multi-stage flash (MSF) desalination systems. MSF systems, however, generally require large-scale components and associated infrastructure, particularly for the flash chambers that produce vapor. By replacing the flash chambers with membrane-distillation modules, as described herein, a more-compact system can be built, lending itself to small-scale and off-grid desalination applications. Modeling has shown that these multi-stage vacuum-membrane-distillation systems can achieve performance comparable to MSF for the same operating conditions. Additionally, multi-stage vacuum-membrane-distillation can operate at lower temperatures without the need for a steam generator, allowing the use of low temperature heat sources, such as unconcentrated solar energy. 
         [0021]    Advantages that can be offered by these methods and apparatus over reverse osmosis may include the following: no requirement for a high-pressure feed, an ability to tolerate complete dryout of the membrane, and a capacity for processing very-high-salinity brines. Compared to other large thermal processes, these methods are easily scalable. Demonstrated pilot plants have been used at a small scale (e.g., 0.1 m 3 /day), including stand-alone systems disconnected from municipal power or water networks. 
         [0022]    Additional advantages of this apparatus may include the potential use of lower-strength and less-expensive materials to support the (lower) pressure differences in embodiments of the methods and apparatus of this invention. Further still, the ability to use lower temperatures in embodiments of the methods and apparatus also means that the membrane and heat exchanger surfaces may be less prone to fouling. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0023]      FIG. 1  is a schematic illustration of an embodiment of a multi-stage membrane distillation apparatus with a vapor condenser that is external to a vacuum membrane distillation module. 
           [0024]      FIG. 2  is a sectional view showing the inside of an embodiment of the vacuum membrane distillation module. 
           [0025]      FIG. 3  is a sectional view showing the inside of an embodiment of the vacuum membrane distillation module with a plurality of membranes mounted in parallel. 
           [0026]      FIG. 4  is a is a schematic illustration of an embodiment of a multi-stage membrane distillation apparatus with a vapor condenser that is external to a vacuum membrane distillation module in which the brine output from the second stage is passed through a heat exchanger where thermal energy from the brine is transferred to the initial feed liquid. 
           [0027]      FIG. 5  is a is a schematic illustration of an embodiment of a multi-stage membrane distillation apparatus with a vapor condenser that is external to a vacuum membrane distillation module in which the brine output from the second stage is mixed with the initial feed liquid. 
           [0028]      FIG. 6  is a plot of the pressure at each stage in an embodiment of the multi-stage membrane distillation module with 20 stages. 
           [0029]      FIG. 7  is a plot of the temperature of feed liquid (saline water) streams at each stage of the 20-stage system. 
           [0030]      FIG. 8  is a plot of the temperature of purified (permeate) water streams at each stage of the 20-stage system. 
           [0031]      FIG. 9  is a schematic illustration of an embodiment of a multi-stage membrane distillation apparatus with a vapor condenser that is integrated in the vacuum membrane distillation module. 
           [0032]      FIG. 10  is a sectional view of an embodiment of a vapor-membrane-distillation/air-gap hybrid module. 
           [0033]      FIG. 11  is a sectional view of an embodiment of a vapor-membrane-distillation/air-gap hybrid module with a plurality of membranes mounted in parallel. 
       
    
    
       [0034]    In the accompanying drawings, like reference characters refer to the same or similar parts throughout the different views; and apostrophes are used to differentiate multiple instances of the same or similar items sharing the same reference numeral. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating particular principles, discussed below. 
       DETAILED DESCRIPTION 
       [0035]    The foregoing and other features and advantages of various aspects of the invention(s) will be apparent from the following, more-particular description of various concepts and specific embodiments within the broader bounds of the invention(s). Various aspects of the subject matter introduced above and discussed in greater detail below may be implemented in any of numerous ways, as the subject matter is not limited to any particular manner of implementation. Examples of specific implementations and applications are provided primarily for illustrative purposes. 
         [0036]    Unless otherwise defined, used or characterized herein, terms that are used herein (including technical and scientific terms) are to be interpreted as having a meaning that is consistent with their accepted meaning in the context of the relevant art and are not to be interpreted in an idealized or overly formal sense unless expressly so defined herein. For example, if a particular composition is referenced, the composition may be substantially, though not perfectly pure, as practical and imperfect realities may apply; e.g., the potential presence of at least trace impurities (e.g., at less than 1 or 2%, wherein percentages or concentrations expressed herein can be either by weight or by volume) can be understood as being within the scope of the description; likewise, if a particular shape is referenced, the shape is intended to include imperfect variations from ideal shapes, e.g., due to manufacturing tolerances. 
         [0037]    Although the terms, first, second, third, etc., may be used herein to describe various elements, these elements are not to be limited by these terms. These terms are simply used to distinguish one element from another. Thus, a first element, discussed below, could be termed a second element without departing from the teachings of the exemplary embodiments. 
         [0038]    Spatially relative terms, such as “above,” “below,” “left,” “right,” “in front,” “behind,” and the like, may be used herein for ease of description to describe the relationship of one element to another element, as illustrated in the figures. It will be understood that the spatially relative terms, as well as the illustrated configurations, are intended to encompass different orientations of the apparatus in use or operation in addition to the orientations described herein and depicted in the figures. For example, if the apparatus in the figures is turned over, elements described as “below” or “beneath” other elements or features would then be oriented “above” the other elements or features. Thus, the exemplary term, “above,” may encompass both an orientation of above and below. The apparatus may be otherwise oriented (e.g., rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly. 
         [0039]    Further still, in this disclosure, when an element is referred to as being “on,” “connected to” or “coupled to” another element, it may be directly on, connected or coupled to the other element or intervening elements may be present unless otherwise specified. 
         [0040]    The terminology used herein is for the purpose of describing particular embodiments and is not intended to be limiting of exemplary embodiments. As used herein, singular forms, such as “a” and “an,” are intended to include the plural forms as well, unless the context indicates otherwise. Additionally, the terms, “includes,” “including,” “comprises” and “comprising,” specify the presence of the stated elements or steps but do not preclude the presence or addition of one or more other elements or steps. 
         [0041]    As shown in the embodiment illustrated in  FIG. 1 , a multi-stage membrane-distillation cycle can be carried out in a plurality of vacuum membrane-distillation modules  22 ,  24 , each associated with a respective vapor condenser  12 / 16  and a liquid-liquid heat exchanger or “permeate cooler”  14 / 18 , all of which are in fluid communication. In the embodiment of  FIG. 1 , the vapor condenser  12 / 16  is external to the vacuum membrane-distillation module  22 / 24 . The condenser  12 / 16  can include corrugated metal tubing (e.g., from Felton Machine, Niagara Falls, N.Y.) through which the liquid feed can flow and on which the permeate vapor can condense. 
         [0042]    A flow of feed liquid (e.g., sea water at 27° C.) is fed from the source  10  and split into respective portions that pass through the second condenser  12  and the second liquid-liquid heat exchanger  14 . The two portions are then recombined and then again split into respective portions that pass through the first condenser  16  and the first liquid-liquid heat exchanger  18 . These portions are then recombined and heated by a heat input (Q in ) at the heater  20 , which can be, e.g., a solar heater, before being injected into a first feed-liquid containment chamber  19  in the first vacuum membrane distillation module  22 . In the first vacuum membrane distillation module  22 , water vapor from the feed liquid can permeate from the first feed-liquid containment chamber  19  through the membrane and into a first vapor-permeate containment chamber  21  in the first vacuum membrane distillation module  22  and then passed through the first condenser  16  where the vapor permeate can be condensed to form purified water. 
         [0043]    The condensed water from the first condenser  16  is then passed through the first liquid-liquid heat exchanger  18 , where heat from the condensed water is transferred to the feed liquid passing through the first liquid-liquid heat exchanger  18 . After passing through the first liquid-liquid heat exchanger  18 , the cooled water is passed through the second liquid-liquid heat exchanger  14 , where additional heat is extracted from the condensed water and transferred to the feed liquid passing through the second liquid-liquid heat exchanger  18 . 
         [0044]    A concentrated remainder  42 ′ of the feed liquid is extracted from the first feed-liquid containment chamber  19  after the water vapor is extracted and passed to a second feed-liquid containment chamber  23  in the second vacuum membrane distillation module  24 , where water vapor from the concentrated remainder  42 ′ of the feed liquid can permeate from the second feed-liquid containment chamber  23  through the membrane and into a second vapor-permeate containment chamber  25  in the second vacuum membrane distillation module  24  and then passed through the second condenser  12  where the vapor permeate can be condensed to form purified water. 
         [0045]    The condensed water from the second condenser  12  is then combined with condensed water from first condenser  16  and passed through the second liquid-liquid heat exchanger  14 , where heat from the condensed water is transferred to the feed liquid passing through the second liquid-liquid heat exchanger  14  before being ejected to a permeate outlet  34  (e.g., a reservoir of purified water). 
         [0046]    A reduced vapor pressure is maintained in the first condenser  16  and a first vapor-permeate containment chamber  21  via a first regulator  28  in a conduit in fluid communication with the vacuum source  26 . Likewise, a reduced vapor pressure is maintained in the second condenser  12  and a second vapor-permeate containment chamber  25  via a second regulator  30  in a conduit in fluid communication with the vacuum source  26 . 
         [0047]    As shown in  FIGS. 4 and 5 , thermal energy from the brine output  37  of the second vacuum membrane distillation module  24  can be transferred to the initial feed liquid  42  from source  10  before the feed liquid  42  is passed through the condensers  12  and  16  and liquid-liquid heat exchangers  14  and  18 . In the embodiment of  FIG. 4 , the feed liquid  42  and brine  37  are both passed through an additional heat exchanger  33 , in which heat from the brine  37  is transferred to the cooler feed liquid  42 . In the embodiment of  FIG. 5 , the brine  37  is injected into the conduit carrying the feed liquid  42  at a juncture  35  such that the brine  37  and feed liquid  42  physically mix (in which case, the brine  37  here as well provides initial heating to the feed liquid  42 ). 
         [0048]    Although two modules  22  and  24  are shown here, many more modules (with associated condensers and liquid-liquid heat exchangers) can be incorporated in series with the apparatus shown here to continue to extract additional purified water from the concentrated remainder of the feed liquid at each stage. After the final module, the remaining brine is ejected to a brine outlet  32 . The respective pressure in the vapor-permeate containment chamber in each of up to 20 stages (i.e., 20 modules in series) is shown in  FIG. 6 , where the pressure can be seen to range from up to about 75 kPa in the first module down to about 5 kPa in the twentieth module. Additionally, in  FIG. 7 , the respective temperature of the feed liquid stream in each of the 20 stages is plotted as enters the module  52 , as it exits the liquid-liquid heat exchanger  54 , as it exits the condenser  56 , and as it enters the condenser  58 . Further still,  FIG. 8  plots the temperature of the purified (permeate) water streams at each stage of the 20-stage system as the permeate stream exits the module (as vapor)  62 , as it exits the condenser (as liquid)  64 , as it enters the liquid-liquid heat exchanger (after mixing)  66 , and as it exits the liquid-liquid heat exchanger  68 . 
         [0049]    The membrane distillation module  22 / 24  is typically made from some polymer material (e.g., polypropylene or acetyl). As shown in  FIG. 2 , attached to the housing  36  of the module  22 / 24  is a membrane  38  that is very hydrophobic [e.g., formed of polytetrafluoroethylene (PTFE), aka Teflon, or polyvinylidene fluoride (PVDF)]. The membrane  38  may or may not have a support layer manufactured onto the active layer of the membrane  38 . The support is typically made from polypropylene, and provides additional mechanical strength to the membrane  38  and adds tearing resistance to tearing. Membranes  38  typically have a pore size of 0.2-0.5 micrometers and a thickness of 50-200 micrometers. The pore channels can be selected to balance the heat-transfer coefficient (to minimize temperature polarization) and pressure drop. 
         [0050]    On one side of the membrane  38 , a heated saline/contaminated water stream flows, coming from a heating step, as in the case with the first stage, or the reject from a previous membrane-distillation module  22 / 24 , as with subsequent stages. A meniscus forms on the small pores and prevents liquid breakthrough. The water-vapor pressure of the water on the feed side of the membrane  38  increases with increasing temperature of the feed  42  (the feed  42  provides the latent heat of evaporation) and with higher molar fractions of water in the feed  42  at the membrane  38 . 
         [0051]    Driven by the pressure differential across the feed and condensate sides of the membrane, a vapor stream  44  from the heated liquid-feed stream evaporates from the surface of the meniscus, through the pores of the membrane  38 , and enters a channel (to the right of the membrane  28 , as shown) kept at reduced pressure by a mechanical pump or vapor compressor  26 . Pressure is regulated at each stage (i.e., with a differential height water column, or other mechanical regulator). The reduced-pressure channel may also contain a woven screen/mesh  40  acting as a mechanical support against the pressure difference between the contaminated water stream  42  and the reduced-pressure vapor channel leading to the fresh water condensate flow  46 . 
         [0052]    As shown in  FIG. 3 , the membranes  38  can be laid out in parallel (e.g., 300 membrane sheets in parallel) with alternating feed  42  and vapor  46  channels, separated by spacers. The length in the flow direction is typically shorter than other membrane-distillation systems, and a typical aspect ratio may be 5:1. The membranes  38  can be sealed to the polymer housing  36  by adhesive, heat sealing or something similar. The housing  36  can also contain channels guiding liquid and vapor from piping connections to the channels. 
         [0053]    The vapor then passes to a condenser  12 / 16 , the interior of which is at the same reduced pressure of the attached membrane module  22 / 24 . This is typically a standard steam condenser  12 / 16 , made primarily of copper. The vacuum source  26 , which is powered by an energy input  27 , is connected through the condenser  12 / 16  to eliminate non-condensable vapors, such as air or carbon dioxide, and to maintain reduced pressure. The vacuum source  26  can establish a vacuum pressure sufficient to maintain the terminal temperature difference in the condenser at 3° C. The coolant comes from the inlet saline/contaminated stream flowing from the feed source  10 , allowing the latent heat of condensation to pre-heat the stream. 
         [0054]    Pure water from the condensers  12 ,  16  is sent to the liquid-liquid heat exchangers  14 ,  18 . In stage 2 onward, the permeate joins the cooled permeate from the previous stage, which has been cooled to a temperature close to that of the permeate exiting the current stage. An amount of inlet water is bled off from the condenser  12 / 16  at that stage to act as cooling water for the liquid-liquid heat exchanger  14 / 18 . This amount is determined by balancing the heat capacity rates (mass flow times specific heat capacity). In the last stage the permeate exits at the temperature close to the inlet fluid. 
         [0055]    Pressure from each stage is determined by the difference of saturation temperature of water vapor in each stage. The set point pressure is the saturation pressure corresponding to that temperature. The difference in saturation temperature from stage to stage may be in the range of 1.5-3 degrees Celsius. The following figures show the temperature and pressure at each stage. 
         [0056]    In another embodiment, illustrated in  FIG. 9 , the vapor condenser  12 / 16  is integrated with the membrane-distillation module  22 / 24 . This embodiment is similar to the apparatus of  FIG. 1  in layout, except the external condenser  12 / 16  of  FIG. 1  is eliminated in favor of condensing the vapor that permeates (as shown with arrows  44 ) through the membrane  38  to form, e.g., liquid water  76  on a condensation surface  84  directly in the vapor-permeate containment chamber  21 / 25 , wherein the purified water flows  46  out of the base of the chamber  21 / 25 , as shown in  FIG. 10 . This can be considered a hybrid of a vacuum membrane distillation module  22 / 24  and an air-gap membrane-distillation module  70 / 72 , as the vapor stream  44  diffuses across and is condensed inside an air gap  74  (e.g., having a thickness on the order of 1 mm), which provides thermal insulation between the hot liquid water stream  46  and the cold condensate  46 . 
         [0057]    The membrane  38  and module materials are similar to the system with an external condenser  12 / 16 , except a copper or other highly thermally conductive material plate  84  is used to collect condensate  46 . The surface of plate  84  may be enhanced to aid the removal of condensate droplets  76 . The condensate film  76  thickness can be, e.g., one-tenth the width of the air gap  74 . The membrane  38  and condenser surface  84  are separated with a spacer, and pressure is reduced in this space in the same way it would be for an external condenser system. The copper condenser plate  84  separates the initial contaminated/saline feed liquid stream  78  as it collects the energy of condensation from the condensed water  76 , such that the initial feed liquid  78  acts as a coolant. The coolant  78  gains temperature and is passed to the next stage to again be used as a coolant  78 . It continues being used as a coolant until it reaches the first stage, where it is then passed through a heater  20  and sent to the first feed-liquid containment chamber  19 , where it is treated. 
         [0058]    An embodiment of a vapor-membrane-distillation/air-gap hybrid module  70 / 72  with a plurality of membranes  38  mounted in parallel is shown in  FIG. 11 . In this embodiment, alternating and cross-flowing channels of vaporizing feed liquid  42  and coolant  78  are separated by the parallel membrane  38  and condenser assemblies. 
         [0059]    In describing embodiments of the invention, specific terminology is used for the sake of clarity. For the purpose of description, specific terms are intended to at least include technical and functional equivalents that operate in a similar manner to accomplish a similar result. Additionally, in some instances where a particular embodiment of the invention includes a plurality of system elements or method steps, those elements or steps may be replaced with a single element or step; likewise, a single element or step may be replaced with a plurality of elements or steps that serve the same purpose. Further, where parameters for various properties or other values are specified herein for embodiments of the invention, those parameters or values can be adjusted up or down by 1/100 th , 1/50 th , 1/20 th , 1/10 th , ⅕ th , ⅓ rd , ½, ⅔ rd , ¾ th , ⅘ th , 9/10 th , 19/20 th , 49/50 th , 99/100 th , etc. (or up by a factor of 1, 2, 3, 4, 5, 6, 8, 10, 20, 50, 100, etc.), or by rounded-off approximations thereof, unless otherwise specified. Moreover, while this invention has been shown and described with references to particular embodiments thereof, those skilled in the art will understand that various substitutions and alterations in form and details may be made therein without departing from the scope of the invention. Further still, other aspects, functions and advantages are also within the scope of the invention; and all embodiments of the invention need not necessarily achieve all of the advantages or possess all of the characteristics described above. Additionally, steps, elements and features discussed herein in connection with one embodiment can likewise be used in conjunction with other embodiments. The contents of references, including reference texts, journal articles, patents, patent applications, etc., cited throughout the text are hereby incorporated by reference in their entirety; and appropriate components, steps, and characterizations from these references may or may not be included in embodiments of this invention. Still further, the components and steps identified in the Background section are integral to this disclosure and can be used in conjunction with or substituted for components and steps described elsewhere in the disclosure within the scope of the invention. In method claims, where stages are recited in a particular order—with or without sequenced prefacing characters added for ease of reference—the stages are not to be interpreted as being temporally limited to the order in which they are recited unless otherwise specified or implied by the terms and phrasing.