Abstract:
A humidification-dehumidification system comprises a source of liquid; a humidifier including carrier-gas and liquid inlets and outlets and a chamber in which the liquid can contact a carrier gas containing a condensable fluid in vapor phase that is introduced from the carrier-gas inlet in a counterflow arrangement and in which a portion of the liquid can vaporize into the carrier gas; a bubble-column vapor mixture condenser including at least first and second stages, each stage including a carrier-gas inlet and outlet and a chamber configured to contain a liquid bath in fluid communication with the carrier-gas inlet and the carrier-gas outlet; a conduit passing from the source of the liquid through the chamber of each stage of the bubble-column condenser; and an intermediate exchange conduit coupled with (a) the bubble-column vapor mixture condenser and (b) the humidifier chamber at intermediate stages of each for transfer of the carrier gas therebetween.

Description:
RELATED APPLICATIONS 
     This application is a continuation of U.S. application Ser. No. 13/241,907, filed 23 Sep. 2011, the entire contents of which are incorporated herein by reference. 
    
    
     BACKGROUND 
     In this century, the shortage of fresh water will surpass the shortage of energy as a global concern for humanity, and these two challenges are inexorably linked, as explained 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. 
     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. 
     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. 
     On the other hand, many of the existing processes for producing fresh water from seawater (or to a lesser degree, from brackish water) require massive amounts of energy. Reverse osmosis (RO) is currently the leading desalination technology. In large-scale plants, the specific electricity required can be as low as 4 kWh/m 3  at 30% recovery, compared to the theoretical minimum of around 1 kWh/m 3 ; smaller-scale RO systems (e.g., aboard ships) are less efficient. 
     Other existing seawater desalination systems include thermal-energy-based multi-stage flash (MSF) distillation, and multi-effect distillation (MED), both of which are energy- and capital-intensive processes. In MSF and MED systems, however, the maximum brine temperature and the maximum temperature of the heat input are limited in order to avoid calcium sulphate precipitation, which leads to the formation of hard scale on the heat transfer equipment. 
     Humidification-dehumidification (HDH) desalination systems include a humidifier and a dehumidifier as their main components and use a carrier gas (e.g., air) to communicate energy between the heat source and the brine. In the humidifier, hot seawater comes in direct contact with dry air, and this air becomes heated and humidified. In the dehumidifier, the heated and humidified air is brought into (indirect) contact with cold seawater and gets dehumidified, producing pure water and dehumidified air. Some of the present inventors were also inventors on the following patent applications that include additional discussion relating to HDH processes for purifying water: U.S. application Ser. No. 12/554,726, filed 4 Sep. 2009; U.S. application Ser. No. 12/573,221, filed 5 Oct. 2009; and U.S. application Ser. No. 13/028,170, filed 15 Feb. 2011. 
     An approach from the University of Florida, which is described in U.S. Pat. No. 6,919,000 B2, reduced the thermal resistance associated with incondensable gases by using a direct-contact condenser instead of a standard, indirect contact dehumidifier. This method increases the heat transfer rates in the condenser at the expense of energy efficiency, as the energy from the humid air entering the dehumidifier is not directly recovered to preheat the seawater. Thus, although the cost of the dehumidification device is reduced, energy costs increase. 
     SUMMARY 
     Single-stage and multi-stage bubble-column vapor mixture condensers (referred to simply as a condenser elsewhere herein) and the operation thereof are described herein. 
     Various embodiments of the apparatus and methods may include some or all of the elements, features and steps described below. 
     In the multi-stage bubble-column condenser, a fluid source supplies a carrier-gas stream including a condensable fluid. The multi-stage condenser includes at least a first stage and a second stage, each of which includes an inlet, an outlet and a chamber in fluid communication with the inlet and the outlet. The inlet of the first stage of the bubble-column condenser is coupled with the fluid source, and the outlet of the first stage is in fluid communication with the inlet of the second stage to facilitate flow of the carrier-gas stream from the fluid source through the chamber of the first stage and then through the chamber of the second stage. The condensable fluid in liquid phase fills the chambers of the first stage and the second stage such that the carrier-gas stream passes through in direct contact with the liquid, which is stationary or in counterflow with the carrier-gas stream, when passing from the inlet to the outlet of each stage. The bubble-column condenser can be coupled with a humidifier in a humidification-dehumidification system, wherein an intermediate exchange conduit is provided for transferring the gas between intermediate stages of the bubble-column condenser and the humidifier. 
     The apparatus and methods can be used to separate pure water from a liquid mixture (including but not limited to seawater, brackish water and waste water) in a cost-efficient manner, which can result in substantially reduced costs compared with previous approaches. Embodiments of the apparatus and methods can offer numerous advantages. First, based on data for bubble columns given in open literature, the heat-transfer coefficient in the multi-stage bubble-column condenser is estimated to be 7 kW/m 2 ·K (i.e., at least one order of magnitude higher than the current state-of-art). This heat-transfer coefficient is comparable to, if not higher than, film condensation of steam. Second, the high energy recovery can be maintained using a novel multi-staging technique. Third, multi-extraction can be employed in the apparatus and methods to further increase heat recovery. Fourth, the overall cost of the system is reduced as the energy cost and the equipment cost are both reduced. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a sectional illustration of a single-stage bubble-column condenser. 
         FIG. 2  is a schematic illustration of an embodiment of a humidification-dehumidification water-purification system including a multi-stage bubble-column condenser. 
         FIG. 3  plots the temperature profile across columns in a multi-stage bubble-column condenser from the top of the bubbling columns. 
         FIG. 4  plots the temperature profile in a single-stage bubble-column condenser from the top of the bubbling column. 
         FIG. 5  is a schematic illustration of an embodiment of a multi-extraction humidification-dehumidification water-purification system including a multi-stage bubble-column condenser. 
         FIG. 6  is a sectional illustration of a bubble-column condenser oriented an angle to the vertical. 
     
    
    
     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, with emphasis instead being placed upon illustrating particular principles, discussed below. 
     DETAILED DESCRIPTION 
     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. 
     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% by weight or 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 machining tolerances. 
     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. 
     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. 
     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. 
     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. 
     The presence of incondensable gases can drastically increase the thermal resistance associated with film condensation of steam on a cold surface. For the typical mole fraction (about 70%) of air (incondensable gas) present in a dehumidifier (condenser) of a humidification-dehumidification system, the heat-transfer coefficient can be as low as 1/100 of that for pure steam condensation (in multi-effect-distillation and multi-stage-flash systems). In absolute value, the heat-transfer coefficient can be as low as 10 W/m 2 ·K. Hence, it is advantageous to reduce the thermal resistance associated with the incondensable gas, while at the same time preserving the advantageous increase in energy efficiency brought about by the methods described in the inventors&#39; previous patent applications, noted in the Background. 
     A sectional view of an embodiment of a single-stage bubble-column condenser  12  is provided in  FIG. 1 . The bubble column  14  contains a bath of a liquid  15  (e.g., distilled water in this embodiment). The liquid  15  is supported on a bubble generator  44  inside the bubble-column chamber. Gas chambers  17  and  19  are respectively positioned below and above the liquid. Chamber  17  below the liquid allows a moist carrier gas to be pumped from conduit  32 ′ via a compressor/blower  34  through orifices in the bubble generator  44  into the liquid  15  in the form of bubbles  21 , though the lower chamber  17  can be omitted where the bubble generator  44  includes a network of perforated pipes through which the carrier gas is pumped. A tube coil  20  that is coupled with a fluid source (e.g., sea water) snakes through the water  15  in the condenser  12 , allowing for heat transfer from the water  15  in the chamber to the sea water being directed through the tube coil  20 . Accordingly, cool fluid enters the tube coil  20  at the lower left and exits as heated fluid at the upper right. After passing through the liquid  15 , the dry carrier gas collects in the gas chamber  19  at the top of the chamber and is extracted through gas conduit  32 ″. 
     The bubble generator  44  can have a diameter, e.g., of 1.25 m, and can have a plurality of orifices, each having a diameter, e.g., of 1 mm for generating bubbles of approximately the same diameter. The bubble generator  44  can be in the form of, for example, a sieve plate, wherein the carrier gas is pumped through the orifices in the sieve plate. Alternatively, the bubble generator  44  can be in the form of a sparger with perforated pipes for distributing the carrier gas, wherein the sparger distributes the bubbles through the perforated pipes, which can extend from a central conduit. The perforated pipes in the sparger can feature, e.g., a radial, multiple-concentric-ring, spider-web, or hub-and-spoke wheel-type configuration of the perforated pipes through which the carrier gas is pumped from an external source. 
     As shown in  FIG. 6 , all components of the bubble column (e.g., all walls and the bubble generator) can be oriented at an angle to the vertical, a, between 0° and 60° with respect to vertical (e.g., with respect to an axis along a radian passing through the center of the earth). As the bubble column  14  is oriented at an angle, the hydrostatic head reduces from ρgH to ρgH·(cos α), where ρ is density (kg/m 3 ), g is gravitational acceleration (9.81 m/s 2 ), and h is the height of the liquid in the column. This reduction in hydrostatic head comes with a reduction in fluid pressure drop of up to 50%. This pressure drop, however, will come with a reduction in the fluid-side heat transfer coefficient at higher angles (α&gt;45°). This is because, at higher angles, the liquid circulation will not be set up in a regular manner. However, for optimized design, the angled configuration with lesser pressure drop may provide significant savings in energy cost. 
     An embodiment of a multi-stage bubble-column condenser in a humidification-dehumidification (HDH) water purifier system  10  is shown in  FIG. 2 , wherein the dehumidifier is a multi-stage, bubble-column, vapor mixture condenser (also referred to as a “bubbler”)  12  instead of using an indirect-contact heat exchanger (as is common with conventional HDH systems) to dehumidify moist carrier gas (e.g., moist air) and produce fresh liquid water efficiently. The carrier gas is humidified with vaporized water from a liquid composition (e.g., sea water or waste water) in the humidifier  24 ; and the water vapor entrained in the carrier gas is then transported via conduit  32 ′ to the bubble-column condenser  12 , where the water in the moist air is condensed to produce fresh (i.e., substantially pure) water. 
     The liquid composition (e.g., sea water) is provided from a source  16  (e.g., a tank) and circulated through the system by a pump  36 , which can mounted in the conduit  18  between the source  16  and the bubble-column condenser  12 . The liquid composition is passed through each stage  14  of the condenser  12  via internal conduits  20  mounted in each stage  14 , wherein the design of each of the stages  14  can substantially match that of the single-stage bubble column of  FIG. 1 . In this embodiment, the liquid composition is passed between stages  14  via adjoining external conduits  18  to preheat the liquid composition. The internal conduits  20  can have thermally conductive surfaces (e.g., fins)  23  extending from the conduits  20  (as shown in  FIG. 2 ) to increase the heat transfer from the liquid in the stages  14  to the liquid composition passing through the tube coil  20 . After exiting the internal tube coil  20  in the bottom (first) stage  14 ′ of the bubble-column condenser  12 , the liquid composition passes through an additional conduit  18  to a heater  22  (e.g., a solar water heater or a waste-heat source) that further heats the liquid composition (e.g., to 80° C.) before the liquid composition is passed into the humidifier  24  and atomized and dispersed via a nozzle  26 . 
     Inside the humidifier, packing material  28  is provided in the form, e.g., of polyvinyl chloride (PVC) packing to facilitate the gas flow and to increase the liquid surface area that is in contact with the carrier gas to increase the portion of the vaporizable liquid that is vaporized into the carrier gas. The body of the humidifier  24  (and the dehumidifier  12  as well as the conduits  18  and  32 ) can be formed, e.g., of stainless steel and is substantially vapor impermeable. In one embodiment, the humidifier  24  is substantially cylindrical with a height of about 2.5 m and a radius of about 0.5 m. 
     The humidifier  24  and dehumidifier  12  are both of a modular construction (i.e., each in the form of a separate and discrete device) and are substantially thermally separated from one another. The characterization of the humidifier  24  and dehumidifier  12  as being “substantially thermally separated” is to be understood as being structured for little or no direct conductive thermal energy transfer through the apparatus between the humidifier  24  and the dehumidifier  12 , though this characterization does not preclude a mass flow carrying thermal energy (via gas and/or liquid flow) between the chambers. This “substantial thermal separation” characterization thereby distinguishes the apparatus from, e.g., a dew vaporation apparatus, which includes a shared heat-transfer wall between the humidifier and dehumidifier. In the apparatus of this disclosure, the humidifier  24  and dehumidifier  12  need not share any common walls that would facilitate conductive heat transfer there between. 
     The carrier gas flows upward through the chamber defined by the humidifier  24  from the port for conduit  32 ′″ to the port for conduit  32 ′, where it exits with a higher content of vaporized liquid. Humidification of the carrier gas is achieved by spraying the liquid composition from one or more nozzles  26  at the top of the humidifier  24  down through a zone including packing material  28 , where some of the water in the liquid composition will evaporate, while a non-evaporated remnant of the liquid composition (e.g., brine) flows down through a rain zone to the base of the chamber defined by the humidifier  24 , where the brine is drained via a conduit  18  into a brine-collection tank  30 . Meanwhile, the carrier gas moves up through the humidifier  24  and is brought into contact with the liquid composition, particularly in the bed of packing material  28 , to humidify the carrier gas with water vapor evaporated from the liquid composition. The carrier gas can consequently be saturated with water vapor before being withdrawn from the humidifier  24  via conduit  32 ′ and pumped via a compressor/blower  34  through the inlet of a first stage  14 ′ of the multi-stage bubble column condenser  12 . In particular embodiments, an air heater and/or an air compressor or thermal vapor compressor can be mounted in conduit  32 ′ to heat and/or compress the carrier gas before it is pumped into the dehumidifier  12 . Where an air compressor or thermal vapor compressor is mounted in conduit  32 ′, a complimentary air expander can be mounted in conduit  32 ″″ to expand the carrier gas, as it is circulated back to the humidifier  24 . In other embodiments, the compressor/blower  34  can be positioned in the conduit  32 ″″ leading to the humidifier  24  because of operational considerations. 
     The flow of seawater through the tube coil  20  inside the dehumidifier  12  can ensure that the heat is directly recovered to preheat the liquid composition (e.g., sea water in this embodiment) during the condensation process. The bubble-column condenser  12  includes a plurality of stages  14 , each filled with a bath of liquid (e.g., distilled water) through which moist, hot carrier gas is passed using a compressor/blower  34  and a bubble generator  44  that injects gas bubbles (or through which bubbles are injected) into the bath. 
     The hot water-vapor-laden carrier gas emitted from the humidifier (evaporator)  24  passes (e.g., at a temperature of 70° C.) through the conduit  32 ′ extending from the top of the humidifier  24  and is bubbled through each of the stages  14  in the dehumidifier  12 , where the carrier gas is cooled and dehumidified. The carrier gas collects at the top of each stage  14  and is passed from an outlet atop each stage  14  via a conduit  32  into and through an inlet of the next stage  14  and through the bubble generator  44 , which generates bubbles of the carrier gas that then pass through the distilled water in the stage  14 , and the carrier gas is then again collected at the top of the column. This process is sequentially repeated in each subsequent column. 
     A low pressure drop in the present dehumidifier  12  can keep pumping power low, thereby enabling an economically feasible system. This focus on maintaining low pumping power is in contrast to many bubble columns in the chemical industry, where the primary concern is heat and mass transfer, and where pressure drop may not be a significant design constraint. Pressure drop in the bubble chamber in each stage  14  occurs largely due to the following three factors: (1) head loss at the bubble generator  44 , where bubbles are generated, (2) friction between the carrier gas and the distilled water as the bubbles rise through the liquid, and (3) the hydrostatic head. As the hydrostatic head is the largest contributor to total pressure drop across a given stage  14 , the height of each stage  14  (measured vertically in the orientation shown in the Figures) is advantageously kept low. To obtain a pressure drop lower than 1 kPa, for example, the total height of all the stages  14  sum to less than about 1 m. Typically, this height constraint manifests itself in the form of a low-aspect-ratio bubble column, where the ratio of column height to diameter (measured horizontally in the orientation shown) is less than 1. In particular embodiments, the diameter of the column is 0.5 to 1 m, while the height of the column is 0.0.5 to 0.1 m (for an aspect ratio of the column is about 0.1). 
     The temperature of the carrier gas can drop at least 5° C. from each stage to  14  the next in the humidifier  12 , as it is cooled by the liquid bath in each stage  14 . For example, in the conduit  32 ″ from the outlet of the first stage  14 ′ to the inlet second stage  14 ″, the carrier gas can have a temperature, e.g., of about 60° C., while the carrier gas in the conduit  32 ′″ from the outlet of the second stage  14 ″ to the inlet of the third stage  14 ′″ can have a reduced temperature, e.g., of about 50° C. When the carrier gas exits the bubble-column condenser  12  through the top conduit  32 ″″, the carrier gas circles back to the bottom of the humidifier  24  (with a reduced content of the vaporizable liquid), its temperature can be further reduced to, e.g., about 30° C. In the initial transient period during process startup, water vapor in the hot-humid carrier gas transmits the latent heat to the water in each stage  14  (in which a natural circulation loop is established); and a mixed average temperature of the water stage  14  is eventually achieved at steady state. Once steady state is achieved, the heat of condensation is directly extracted by seawater that is sent through the coiled tube  20 . Thus, direct heat recovery is achieved. 
     Where the condensed vapor is water, the dehumidification of the carrier gas in each stage  14  releases water from the carrier gas to the distilled water through which carrier gas is bubbled. The water is drained from each stage  14  (equivalent to the water increase provided by the dehumidification of the carrier gas) through conduits  38  to a pure-water collection tank  40 . Alternatively, the liquid (e.g., water) can be extracted via a conduit from the bath in the third stage  14 ′″ and passed to the lower-temperature second stage  14 ″ and extracted via another conduit from the second-stage  14 ″ and passed to the still-lower-temperature first stage  14 ′, from which it is finally extracted from the multi-stage, bubble-column condenser  12  as product. 
     Though a single stage/column  14  can be used, the use of multiple stages in the bubble-column condenser  12  pushes the temperature to which the seawater is preheated toward the maximum possible (which is the temperature of the carrier gas inlet). The effects of this staging can be clearly understood via the temperature profiles in a multi-stage bubble-column condenser (shown in  FIG. 3 ) and in a single-stage bubble-column condenser (shown in  FIG. 4 ), where the seawater exit temperature can be seen to be much higher in the plots for the multi-stage bubble-column condenser, as shown in  FIG. 3 . Each of the plotted horizontal segments  46  ( ˜ 308 K), 48 ( ˜ 318 K), 50 ( ˜ 327 K), 52 ( ˜ 335 K), 54 ( ˜ 342 K), 56 ( ˜ 348 K) in  FIG. 3  represents the temperature in a respective column/stage  14  in a six-stage bubble-column condenser, where the horizontal axis of the chart represents non-dimensional distance from the top to the bottom of the bubble-column condenser  12  (i.e., reference line  46  represents the temperature of the top-most stage  14 ). The diagonal line  58  represents the temperature of the seawater as it flows through the bubble-column condenser  12  as a function of distance from the top of the bubble-column condenser  12 . Meanwhile, the temperature  60  in the single-stage, bubble-column condenser (shown in  FIG. 4 ) is seen to be substantially constant (at 323 K) throughout the bubble-column condenser and approximately equal to the average of the inlet and the outlet carrier gas temperatures. 
     The multi-stage bubble-column condenser  12 , additionally, presents a direct advantage of enabling extraction/injections of seawater from in-between the bubble-column stages via intermediate exchange conduits  42 , as shown in  FIG. 5 , where the intermediate exchange conduits  42  are coupled with the bubble-column condenser  12  between the first and second stages  14 ′ and  14 ″ and between the second and third stages  14 ″ and  14 ′″ of a three-stage bubble-column condenser system. Saline water is collected in intermediate trays  43 ′ and  43 ″ at respective intermediate stages in the chamber of the humidifier  24  and injected into the external conduits  18  through which the sea water flows between stages  14 ′ and  14 ″ and between stages  14 ″ and  14 ′″, respectively. In other embodiments, the direction of injection/extraction can be reversed (e.g., saline water can be extracted from the condenser  12  and injected into the humidifier  24 ), depending on the conditions of operation. Such extraction flows can enable construction of systems that are thermodynamically balanced. In additional embodiments, the moist carrier gas can be extracted/injected instead of extracting/injecting saline water. Owing to the higher heat-transfer coefficients in a bubble-column condenser and a lower terminal temperature difference, the apparatus described herein (such as the one shown in  FIG. 5 ) can provide superior performance in terms of dehumidification and the efficiency thereof. 
     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 are specified herein for embodiments of the invention, those parameters can be adjusted up or down by 1/100, 1/50, 1/20, 1/10, ⅕, ⅓, ½, ⅔, ¾, ⅘, 9/10, 19/20, 49/50, 99/100, 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 (for example, the condensed liquid can be a composition other than water; more or fewer stages can be used in the bubble-column condenser; and the configuration of those stages can be readily altered). 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 optionally 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.