Abstract:
A vibrated bed of particles is created by vibrating a chamber. Particles are flowed to a ceiling of the chamber and cascade through a gas flowing though the chamber, exchanging heat with the gas. Particles spouted to the ceiling spread there and cascade. Larger particles, raissed above the ceiling by a lateral vibrated elevator, cascade from channels beneath openings in the ceiling. A plenum and tubes release protective gas through the vibrated bed. Tubes embendded the vibrated bed move fluid to exchange heat with the particles in the vibrated beds. Serialized chambers are reversed and particles flow from one chamber to another.

Description:
FIELDS OF THE INVENTION  
         [0001]    The invention relates to a heat exchange between a gas and falling pulverulent matter.  
         BACKGROUND OF THE INVENTION  
         [0002]    A common industrial operation entails recovery of heat from the combustion of a fuel or of “waste heat” from a chemical process. Such recovery often entails the cooling of a hot gas against water, the water being either heated or converted to steam. Conventional equipment for cooling a gas is often large in size, because coefficients of heat transfer from a gas to a metal surface, in general, are relatively small, e.g., only a few tens of watts/m 2 −C. Achieving a high coefficient of heat transfer entails acceptance of a high pressure drop in the gas to be cooled. In practice, a balance must be struck between the capital expense for providing a larger heat exchanger and the running cost of a smaller exchanger, requiring higher pressure drop necessary in smaller equipment for it to perform the desired heat exchange.  
           [0003]    Often, gas to be cooled is dirty, and in some instances, the dirt has properties causing it to foul heat-transfer surfaces with which the gas comes into contact. A notorious example is the off-gas from an electrometallurgical procedure for making ferrosilicon. This gas, as it enters a waste-heat boiler, contains an exceedingly fine fume of silicon dioxide, which fouls boiler surface so rapidly that a practice is to subject the surface to a shower of ball bearings every few minutes, cleaning it of adhering fume particles; yet even with this expedient, a larger boiler surface must be provided than would be necessary for cooling a clean gas. In some instances, a gas to be cooled contains a corrosive chemical species (such as hydrogen chloride), harmful to metal surfaces and over time reducing their effectiveness for transferring heat. Another notorious example arises in the manufacture of a fine titanium dioxide powder by burning titanium tetrachloride. It is difficult to maintain a reasonably continuous operation of the enormous “trombone” heat-exchanger now used for cooling products of this combustion.  
           [0004]    Heterogeneously catalyzed reactions, in general, are carried out either in fixed beds of a granular catalyst or in fluidized beds of a catalyst powder. In the latter, control of reaction temperature is relatively easy, since coefficients of heat transfer from a fluid bed to surfaces embedded therein are generally high, often in the hundreds of watts/m 2 −C. If, however, outcomes of a reaction are highly sensitive to axial gas dispersion (see Tshabalala and Squires,  AIChE Journal,  vol. 42, pp. 2941-2947, 1995), a fluid bed may not be a good choice. If a fixed bed must be specified, either a low coefficient of heat transfer from the reaction to surfaces within the bed must be accepted or a designer must adopt other expedients for controlling the bed temperature, such as employing a large gas recycle or injecting cold gas at intervals along the bed.  
           [0005]    Herein, by the term “vibrated bed,” I mean a bed of powder in a chamber with a floor, this floor being vibrated vertically at a vibrational intensity sufficient to cause the powder to display the “coherent-condensed vibrated-bed state” (see Thomas, Mason, Liu, and Squires,  Powder Technology,  vol. 57, pp. 267-280, 1989). In this “state,” the powder becomes highly fluid. For example, application of only a small force is needed to move a stirring rod introduced into a vibrated bed from side to side. In general, intense vibration of a powder bed deeper than ˜1 mm causes the powder to enter the coherent-condensed vibrated-bed state.  
           [0006]    I now provide a definition of “vibrational intensity.” I take the “null position” of the aforementioned floor to be its elevation when at rest. When it is subjected to a vertical sinusoidal vibration, its vertical displacement ζ from its null position is given by ζ=α 0 sinωt, where α 0 =the maximum displacement (called “amplitude” in the terminology of vibrated-bed engineering art); ω=2πƒ; t=time and ƒ=frequency. Vibrational intensity is the ratio of the floor&#39;s maximum acceleration to the acceleration of gravity, and is given by α 0 ω 2 /g. For coarse powders, the threshold vibrational intensity for creation of a vibrated bed is a little greater than 1.0; for fine powders, the theshold intensity can be considerably higher than 1.0. (See Thomas, Mason, Liu, and Squires, 1989.) In commercial practice, vibrational intensities greatly exceed these thresholds. Intensities as high as 15 are commonly used.  
           [0007]    Industry employs vibrated beds extensively for drying particulate material. The beds are sometimes large, e.g., several meters in width and ten or more meters in length. Heat of drying is sometimes provided by indirect heat transfer across heat-exchange surface positioned within the drying bed. A vibrated bed presents coefficients of heat transfer comparable to those afforded by fluid beds (see Thomas, Mason, Sprung, Liu, and Squires,  Powder Technology,  vol. 99, pp. 293-301, 1998). Accordingly, the quantity of heat-exchange surface required for indirect heat transfer in a vibrated bed drier can be small. In other vibrated-bed driers, heat of drying is provided by direct heat transfer from a hot gas introduced into the bed from below (thereby creating an “aerated vibrated bed”).  
           [0008]    Little power is required for vibrating a vibrated-bed drier if it is spring-mounted and vibrated at a natural frequency of its mount. An aerated vibrated bed for drying a relatively coarse pulverulent solid can often require far less power than a fluid bed for drying the same solid. The velocity of hot gas across the aerated vibrated bed can be small relative to the velocity necessary to fluidize the coarse solid, and so power required for gas compression can be far below that needed to supply hot fluidizing gas to a fluid-bed drier for the same solid. Power required for vibration can be as little as 10% of that which a fluid-bed drier requires for gas compression.  
           [0009]    The high heat-transfer coefficients generally afforded by vibrated beds make them, in principle, attractive candidate devices for heat-exchange applications other than for drying particulate materials. As a practical matter, how to use a vibrated bed for recovery of heat from a hot gas, for example, is not obvious. Contemplating use of a vibrated bed for this application, I hoped to develop a heat exchanger in which hot gas would flow horizontally across the surface of a bed in which heat-exchange surface is embedded (see Sprung, Thomas, Liu, and Squires, in  Fluidization V,  edited by V. K. Ostergaard, Engineering Foundation, New York, 1986, pp. 409-416). With proper choice of particle size and vibration parameters, the surface of the bed would be dilute (i.e., surface powder would display the diffuse “coherent-expanded vibrated-bed state” -see Thomas, Mason, Liu, and Squires, 1989). I hoped for an effective exchange of heat from the hot gas to the diffuse surface of the bed; or, failing that, I hoped that obliging the gas to flow through constrictions created by vertical baffles extending from the ceiling nearly to the bed&#39;s surface would cause a sufficient quantity of powder to become entrained in the gas, thereby cooling the gas. Unfortunately, the coefficient for transfer of heat from horizontally flowing gas to a vibrated-bed surface was disappointingly small; and, as well, providing the vertical baffles did not sufficiently improve the rate of heat transfer at an acceptable pressure drop in the gas.  
         SUMMARY OF THE INVENTION  
         [0010]    My invention overcomes the shortcomings of my aforementioned idea.  
           [0011]    In the invention, a duct of substantially rectangular cross-section houses a vibrated bed of a pulverulent material and a superjacent space. The invention employs the vibratory motion that creates the vibrated bed to lift pulverulent matter from the bed in a continuous flow to substantially the elevation of the ceiling of the duct. The invention also employs the vibratory motion to distribute the matter across the duct&#39;s ceiling, where the matter is allowed to fall into the aforementioned space. A gas is caused to flow horizontally along the space, the temperature of the gas being different from that of the pulverulent matter and, accordingly, exchanging heat therewith.  
           [0012]    Two methods are available for employing the vibratory motion that creates the vibrated bed to lift the pulverulent matter to the elevation of the duct&#39;s ceiling. One method is useful if the pulverulent matter, generally speaking, is a fine powder. A second method is useful if the pulverulent matter is coarse. Below, I will specify more closely what I mean by the terms “fine powder” and “coarse powder.” 
           [0013]    I now describe the two methods in turn.  
           [0014]    The fine powder method  
           [0015]    I have discovered that a spout of particles emerges spontaneously from a small-bore tube positioned vertically in a vibrated bed of a fine powder and extending from an elevation close to the floor of the chamber housing the bed to an elevation comparable to that of the surface of the bed (Thomas, Mason, and Squires,  Powder Technology,  vol. 111, pp. 34-49, September 2000).  
           [0016]    I do not fully understand this new phenomenon, but I associate it with the variation in floor pressure, beneath a vibrated bed, that accompanies a vibration cycle. Early in a sinusoidal vibration cycle (that is to say, at a relatively low phase angle), the floor pressure falls below the ambient pressure at the bed&#39;s surface. Later (at a relatively high phase angle), the floor pressure exceeds the ambient. In general, the maximum positive deviation from floor pressure, late in the cycle, is much greater than the negative deviation, early in the cycle. More particularly, I associate the spouting phenomenon with the maximum positive pressure deviation occurring late in a vibration cycle. This deviation is a function of many variables, including vibrational intensity, density of the powder, depth of the powder bed, properties of the ambient gas, and (especially) the size of the powder. At the floor of a vibrated bed of a fine powder, the pressure deviation can be many times larger than it is for a coarse powder (see Thomas, Liu, Chan, and Squires,  Powder Technology,  vol. 52, pp. 77-92, 1987; Thomas and Squires,  Physical Review Letters,  vol. 81, pp. 574-577, 1998; and Thomas and Squires,  Powder Technology,  vol. 100, pp. 200-210, 1998). The discovery of spouting came about when a (conveniently at hand) small-bore tube was used to stir a vibrated bed of a fine powder, rather than a solid rod. The tube had a bore of 6 mm; its length was ˜15 cm. At a vibrational intensity of ˜6, the powder spouted to a distance amounting to a significant fraction of a meter. The powder was ˜70 micrometers in size and had bulk and intrinsic densities of 740 and 2,570 kilograms/m 3 , respectively. Spouts of this powder were seen at bed depths as small as ˜2 cm. Whether a bed of a given particulate will spout is a function of tube bore and length as well as the aforementioned variables that influence the maximum positive pressure deviation. I have not been able to explore a sufficiently wide range of the variables to provide a guide for predicting when a spout will form and when it will not. From equipment limitations, I have not been able to study vibrational intensities higher than ˜7 or beds deeper than ˜5 cm. Large-scale commercial vibration equipment is available for vibrational intensities as high as 15.0. If such a high intensity is employed and if a bed deeper than 5 cm is specified, it is probable that useful spouts can be created over a wide range of the remaining relevant parameters. In the practice of my invention, experimentation on a small scale can readily determine whether a spout will form under whatever set of conditions is of interest.  
           [0017]    Herein, by the term “fine powder,” I mean a powder from which a useful spout can be created. In general, this will be a Group A powder in the Geldart classification (see Squires, Kwauk, and Avidan,  Science,  vol. 230, pp. 1329-1337, 1985).  
           [0018]    The spouts of my discovery can be employed for lifting a fine powder from a vibrated bed of the invention to substantially the elevation of the ceiling of the duct. The vibration that created the vibrated bed is employed to create the spouts. This vibration is also employed to disperse powder transversely across the ceiling. For the latter objective, the vibrational intensity should be such that a spout colliding with the ceiling has a momentum sufficient to create a “cloud” of powder directly beneath the ceiling, within which powder moves laterally, and from which the powder is allowed to fall into the space.  
           [0019]    The surface of a vibrated bed of a fine powder often displays heaps and depressions. The term of engineering art for the phenomenon is “bunkering”; the bed is said to “bunker.” Desirably, however, a vibrated bed for practice of my invention should not bunker excessively. A downward flow of powder surrounds each spouting tube, and such flows mitigate against bunkering. In practice, providing a sufficient number of the tubes SHOULD avoid excessive bunkering.  
           [0020]    The coarse powder method  
           [0021]    Herein, by the term “coarse powder” I mean a powder that will not form a useful spout as described above. In general, this will be a Group B or D powder in the Geldart classification (see Squires, Kwauk, and Avidan,  op. cit. ).  
           [0022]    A fact well known to practitioners of vibrated bed art is that powder tends to move upward along a side wall if the wall diverges outward toward higher elevations. See, for example, H. Takahashi, A. Suzuki, and T. Tanaka,  Powder Technology,  vol. 2, pages 65-71 (1968/69). A vertical lift conveyor (U.S. Pat. No. 3,850,288, Nov. 26, 1975) employs the phenomenon. Herein, I use the term “vibratory lift” to signify a powder lifting device of this general nature. A vibratory lift can be used to elevate a relatively coarse powder to a height comparable to that of the ceiling of the substantially horizontal duct hereinbefore described. The vibration can also be employed in various ways to spread the powder across the ceiling of the duct, wherein openings allow the powder to fall into the space above the vibrated bed of the invention.  
           [0023]    Bunkering is less of a problem for a coarse powder than it is for a fine powder.  
           [0024]    Commercially available, nearly spherical particles of a crude alumina (designated “Master Beads” by the manufacturer, Norton-Alcoa) are advantageously employed as the coarse powder in some applications of the invention. They are highly resistant to breakage, reducing their size, or to attrition, producing a fine powder. They are available in several sizes.  
           [0025]    Advantages of the invention  
           [0026]    In conventional boiler plant raising steam for generation of power, fans (induced-draft) consume a significant fraction of the power generated. The fraction often approaches 5% of the power. Responsible for this loss of power is the pressure drop through a convective heat-exchanger conventionally used (following a radiative heat-recovery section of a boiler) to recover heat from combustion off-gas. A significant advantage of my invention is the exceptionally small pressure drop that gas will experience when exchanging heat with the falling powder.  
           [0027]    Sometimes a need arises to recover heat from a hot gas containing a corrosive chemical species, such as hydrogen chloride. An embodiment invention can provide protection of metal heat-transfer surfaces from substantial exposure to this species. In general, there is an in-and-out traffic of gas across the surface of a vibrated bed. Early in each (sinusoidal) vibration cycle, ambient gas enters the bed and causes it to expand. In a relatively shallow bed (e.g., in general, shallower than ˜25 cm), the gas penetrates all the way to the vibrating floor. (In beds of a relatively coarse powder, in general, the flow of ambient gas into the bed supplies gas for the formation of a “gap” between the floor and a “bottom surface” of the powder.) Later in the cycle, this gas leaves the bed. (In the aforementioned beds of the relatively coarse powder, the gap closes late in the cycle.) This in-and-out flow of ambient gas, however, can be prevented by “aerating” the bed, i.e., by causing gas to flow into the bed at a sufficient rate from a plenum beneath the vibrating floor. In my alternative embodiment, I introduce a non-corrosive gas (such as air) into the vibrated bed of my invention via tubes extending from such a plenum to a mid-elevation within the bed. With these tubes so disposed, the lower levels of the vibrated bed act as a non-aerated bed, ensuring (in the fine-powder embodiment) the production of spouts from the small-bore, vertical tubes, while aeration of the bed&#39;s upper levels substantially prevents penetration of the bed by the corrosive species.  
         OBJECTS OF THE INVENTION  
         [0028]    An object of the invention is to provide a compact, non-fouling, long-lived, easily maintained heat exchanger for recovery of heat from a hot gas containing fume or dust or a corrosive chemical species.  
           [0029]    Another object is to recover heat from a hot gas while causing only a small loss of pressure in the gas.  
           [0030]    Another object is to provide a heat exchanger for control of temperature in a powdered catalyst promoting a chemical reaction.  
           [0031]    Another object is to heat a powder.  
           [0032]    Another object is to exchange heat between two gas streams.  
           [0033]    Yet another object is to exchange heat from gaseous products of a combustion step to the oxygen-containing gas to be provided to this step, thereby heating this gas.  
           [0034]    The invention relates to a heat exchange between a gas and falling pulverulent matter. The invention also relates to a double transfer of heat: a first exchange occurs between a gas and the falling pulverulent-matter; a second (transferring substantially the same quantity of heat) occurs between the matter and either a liquid or a second gas. The invention employs a coherent-condensed vibrated bed occupying the lower portion of a duct of generally rectangular cross-section. Gas flows in the horizontal direction through a space above the bed. Matter is conveyed from the bed to the elevation of the ceiling of the space, is distributed horizontally across the ceiling, and allowed to fall into the space. One object of the double heat exchange is to transfer heat from a hot gas to water. The gas may be a hot gas from combustion of a fuel. Alternatively, the gas may comprise chemical species capable of entering into a certain chemical reaction, the object of the exchange being to maintain a temperature favorable for this reaction in a space within which a catalyst is present with power to promote the reaction. In another alternative, a hot gas from combustion of a fuel may be cooled against a flow of air to be supplied to the combustion.  
           [0035]    My invention relates to an improved method for exchanging heat between a gas and a pulverulent matter. The matter is introduced into a chamber having a substantially horizontal floor, a ceiling, a front wall, a back wall, and two side walls. The volume of the matter within the chamber is maintained at a volume that is significantly smaller than the volume of the chamber. Substantially vertical vibration is imparted to the chamber at a vibrational intensity sufficient to cause the matter to enter the coherent-condensed vibrated-bed state, thereby creating a vibrated bed that occupies a lower part of the chamber and a space that extends from the surface of the bed to the ceiling of the chamber. Matter is withdrawn from the vibrated bed and, through employment of the vibration, is elevated to substantially the elevation of the ceiling. Also through employment of the vibration, the elevated matter is distributed transversely across the ceiling. The distributed matter is permitted to fall through the aforementioned space. A gas is caused to enter the space across the front wall, to flow horizontally through the space, and to exit the space across the back wall, the gas having a temperature different from the falling matter and exchanging heat therewith.  
           [0036]    My invention also relates to improved apparatus for the exchange of heat between a gas and a pulverulent matter. Means are provided for introducing matter into a chamber having a substantially horizontal floor, a ceiling, a front wall, a back wall, and two side walls. Means are provided for maintaining within the chamber a volume of the matter that is significantly smaller than the volume of the chamber. Means are provided for imparting substantially vertical vibration to the chamber at a vibrational intensity sufficient to cause the matter to enter the coherent-condensed vibrated-bed state, thereby creating a vibrated bed of the matter that occupies a lower part of the chamber and also creating a space that extends from the surface of the bed to the ceiling of the chamber. Means are provided for withdrawing the matter from the vibrated bed. Means are provided, through employment of the vibration creating the vibrated bed, for elevating the withdrawn matter to substantially the elevation of the ceiling. Means are also provided employing the vibration for distributing the elevated matter transversely across the ceiling. The distributed matter is permitted to fall through the aforementioned space. Means are provided for causing a gas to enter the space across the front wall, to flow horizontally through the space, and to exit the space across the back wall, the gas having a temperature different from the falling matter and exchanging heat therewith. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0037]    The invention will be more particularly described in conjunction with the following drawings wherein:  
         [0038]    [0038]FIG. 1 is a vertical, longitudinal section view of my invention. FIG. 2 is a vertical, transverse section view (through the cross-section A-A identified in  
         [0039]    [0039]FIG. 1). To help the reader appreciate the major features of the invention, the introductory drawings of FIGS. 1 &amp; 2 present these features in highly schematic fashion.  
         [0040]    [0040]FIGS. 3 and 4 are sectional views (longitudinal and transverse, respectively) of an embodiment of the invention for exchanging heat between a flow of a gas and a flow of a fine powder.  
         [0041]    [0041]FIG. 5 is a vertical, longitudinal partial section view of an alternative embodiment.  
         [0042]    [0042]FIG. 6 is a horizontal section view of this alternative (through the section C-C identified in FIG. 5).  
         [0043]    [0043]FIGS. 7, 8, &amp;  9  sketch an embodiment of the invention for exchanging heat between a gas and a liquid, with use of a fine powder as a heat-carrying intermediary in the exchange.  
         [0044]    [0044]FIGS. 10, 11,  12 , and  13  sketch an embodiment of the invention for exchanging heat between a gas and a liquid, with use of a coarse powder as a heat-carrying intermediary in the exchange.  
         [0045]    [0045]FIG. 14 illustrates how the invention may be used to exchange heat between two gases.  
         [0046]    [0046]FIG. 15 illustrates an alternative arrangement for exchanging heat between two gases, with use of a coarse powder as a heat-carrying intermediary in the exchange.  
         [0047]    [0047]FIG. 16 is a plan view of a floor appropriate for the chamber of the invention in the embodiments of FIGS. 7 and 10. 
     
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0048]    In the several figures, like reference numerals refer to like parts having like functions. FIG. 1 is a highly schematic sketch of heat-exchanger  1 , showing the exchanger in a longitudinal, vertical section. FIG. 2 is a similarly schematic sketch of  1  in a transverse, vertical section. Exchanger  1  comprises a chamber with floor  2 , ceiling  3 , front wall  4 , back wall  5 , and side-walls  6  and  7  (the latter two walls are to be seen in FIG. 2).  
         [0049]    If the temperature of gas in line  18  is significantly different from the temperature of gas in line  17 , it is advantageous for the width of space  15  to vary. For example, if the line  18  temperature is significantly below the line  17  temperature, the distance between wall  6  and wall  7  is advantageously greater at front wall  4  than at back wall  5 , so that the two side walls diverge from one another, the divergence being such that the velocity of gas flowing in space  15  does not vary significantly form front to back.  
         [0050]    Powder bed  10  occupies a lower part of the chamber. Space  15  extends from the surface  28  of bed  10  to ceiling  3 . Spring mounts  9 , resting upon a stable support  51 , carry heat-exchanger  1 . Vibration-producing machine  8  (suitably an electric motor driving eccentric flywheels) causes heat exchanger  1  to vibrate substantially vertically at a vibrational frequency in substantial resonance with a natural frequency of vibration of spring mounts  9 . The intensity of the vibration is sufficient to cause bed  10  to enter the coherent-condensed vibrated-bed state, the bed thereby becoming a “vibrated bed.” Vibration means  55  (employing the vibration of chamber  1 ) lifts powder (withdrawn from bed  10  as indicated schematically in FIG. 2) to substantially the elevation of ceiling  3 . Vibration means  54  (also employing the vibration of chamber  1 ) distributes the withdrawn powder transversely across ceiling  3 . The distributed powder is permitted to fall by gravity through space  15 . A gas (at a temperature different from that of the falling powder in space  15 ) enters space  15  from line  17  across front wall  4 . The gas flows in a substantially horizontal direction through space  15 , exchanging heat with the falling powder. The gas leaves the space across back wall  5  via line  18 . Flexible couplings  16  connect stationary lines  17  and  18  with the vibrating chamber.  
         [0051]    The exchanger of FIGS. 1 and 2 can be used to exchange heat between a continuous flow of a gas and a continuous flow of a powder. In such a usage, lines  52  and  53  are provided whereby the powder enters and exits bed  10 . Attention must be paid to maintaining a relatively constant volume of powder in bed  10 . That is to say, the flow of powder into the bed via line  52  must be modulated in accordance with a rise or a fall in the level of powder in bed  10 .  
         [0052]    A relatively constant volume of powder in bed  10  should also be maintained in applications (to be described below) for which lines  52  and  53  are omitted. In such applications, an appropriate volume of powder in bed  10  can be established on the first addition of powder to the bed, accompanied by minor additions from time to time as the level of powder in the bed may rise or fall.  
         [0053]    The drawings of FIGS. 3 and 4 (longitudinal and transverse vertical sections, respectively) illustrate an embodiment of the invention that employs a fine powder in bed  10 . Small-bore, vertical tubes  12  extend upward from an elevation near floor  2 . The number of tubes  12  is such that bunkering (if any) is moderate. Spontaneously, powder erupts from each vertical tube  12  to form a spout  13 . The vibrational intensity imparted by vibrated machine  8  is sufficient to cause each spout  13  to collide with ceiling  3 , the powder possessing sufficient momentum that the collision with the ceiling distributes the powder laterally along the underside of the ceiling. Transverse, vertical baffles  56  extend a short distance from ceiling  3  into space  15 , tending to limit powder distribution in the longitudinal direction. FIG. 4 illustrates the transverse distribution of powder in a “cloud” of the powder,  57 , created by the collision of spouts with the ceiling. The powder tends to fall through space  15  in form of strands  14  (or in clumps or in “sheets” resembling the falling of water droplets in a heavy rainstorm).  
         [0054]    Notice that a temperature gradient may exist in the longitudinal direction along bed  10  (i.e., between wall  4  and wall  5 ). Although some longitudinal mixing of powder will occur in bed  10 , in general the degree of mixing will be insufficient to prevent the development of a gradient in the temperature. A large degree of mixing would limit the amount of heat that could be transferred between the gas and the powder. If in practice the degree of mixing were to be undesirably great, transverse baffle means could be provided to limit longitudinal mixing of powder in bed  10 .  
         [0055]    Gas (either heated or cooled by heat exchange with powder entering bed  10  via line  52  and leaving via line  53 ) leaves heat-exchanger  1  via pipe  18 , entering powder collector  19 , from which substantially powder-free gas exits via pipe  20 . Powder separated from the gas in  19  is returned to heat-exchanger  1  via line  21 .  
         [0056]    If the gas entering space  15  from line  17  is hot and contains a fine dust, the dust tends to collect upon surfaces of powder falling through space  15 . Optional lines  22  and  24  (fitted with valves  23  and  25 , respectively, for control of flows therein) may be provided for periodic withdrawal of powder contaminated with dust; and optional line  26  (fitted with valve  27  for control of flow therein) is provided for adding clean powder to make good the withdrawals via  22  and  24 .  
         [0057]    [0057]FIG. 5 is an upper, partial view (in a horizontal cross-section) of an alternative heat-exchanger  1  for use with a fine powder. In the alternative, vertical baffles  36  are provided, each baffle tending to cause powder to fall back promptly from space  15  and return to bed  10 . The object of the baffles is to minimize the conveying of the powder longitudinally by the gas. FIG. 6 shows horizontal section C-C as indicated in FIG. 5. Baffles  36  are V-shaped in horizontal cross-section, the point of the V heading away from the direction of flow of gas from front wall  4  toward back wall  5 . Each baffle tends to create a “quiet zone” in front of the point of the V, down which powder tends to fall.  
         [0058]    [0058]FIGS. 7, 8, and  9  sketch an embodiment useful for recovering heat from a hot gas, which enters space  15  from line  17 . Heat-transfer pipes  11  are positioned near the vertical tubes  12 . Water is introduced into the pipes  11  via line  31  and header  33 , the latter providing water to pipes  11 .  
         [0059]    The falling powder acts as an intermediary promoting a transfer of heat to the water from a hot gas flowing horizontally along space  15 . Heat is transferred from gas to falling powder strands  14 , raising their temperature. Returning to bed  10 , the strands give up their heat to the bed. In turn, this heat is transferred across outer and inner surfaces of pipes  11  and enters water flowing through these pipes. Header  34  receives heated water (or steam) from the pipes  11 , and water (or steam) leaves header  34  via line  35 . Pump  32  is provided to cause water to flow through the pipes  11 .  
         [0060]    If an ultra-fine dust is present in the hot gas from line  17  (e.g., the silica fume in gas from ferrosilicon production), there is little or no tendency for the dust to foul the external surfaces of pipes  11 . A large part of such ultra-fine dust adheres to larger particles of the powder; and there is a scrubbing action of powder in vibrated-bed  10  against these external surfaces, tending to remove any dust that might temporarily adhere thereto.  
         [0061]    Heat-exchanger  1  of FIGS. 7, 8, and  9  may also serve as a reactor for conducting a heterogeneously catalyzed reaction. A powder having catalytic virtue for the reaction is provided to constitute bed  10 , and the heat exchange can serve to maintain a temperature suitable for the reaction in space  15 . Gas flowing from wall  4  to wall  5  experiences small axial dispersion (i.e., dispersion in the horizontal direction) relative to that experienced by gas traversing a large fluid bed.  
         [0062]    If the hot gas entering space  15  from pipe  17  contains a corrosive chemical species, such as hydrogen chloride, it will be advantageous to supply a non-corrosive gas from optional line  41  into optional plenum  42  situated beneath floor  2 . Optional tubes  43  (see in FIG. 9) carry this gas from plenum  42  into a mid-elevation of bed  12  The effect of the introduction of the non-corrosive gas into bed  12  is to reduce the exposure of heat-exchange pipes  11  to corrosive species in the hot gas reaching space  15  from pipe  17 . In absence of plenum  42  and tubes  43 , corrosive species from space  15  would enter bed  10  via a cyclic flow of gas, into bed  10  from space  15  and back out again, this cyclic flow occurring during each vibration cycle. Desirably, a tube  43  is fitted at its top end with an inverted cup or “hat”  44 , which prevents powder from entering the tube from bed  10 .  
         [0063]    The embodiment of FIGS. 7, 8, and  9  should also be useful as a reactor for a heterogeneously catalyzed reaction where it would be advantageous to subject a powdered catalyst periodically to a “regenerative” treatment. For example, in conducting Fischer-Tropsch synthesis over an iron catalyst, it should be feasible to employ a synthesis gas at a lower ratio of hydrogen content to carbon monoxide content (yet avoiding problems arising from formation of carbon and catalyst decrepitation) if the iron catalyst were exposed to synthesis gas (entering heat-exchanger  1  in FIG. 7 from pipe  17 ) for only the relatively short time interval during which the catalyst is present in space  15 , while exposing the catalyst for a much longer time in bed  10  to a gas rich in hydrogen, supplied via pipe  41 . Notice that a flow of the hydrogen rich gas from pipe  41  may advantageously be much smaller than the flow of low H 2 :CO synthesis gas from pipe  17 , yet hydrogen treatment during a catalyst particle&#39;s relatively long residence time in bed  10  may “scavenge” nascent carbon formed upon the catalyst during its brief exposure to synthesis gas (and, as well, may reduce yields of heavy oils and waxes in favor of products in the gasoline range). Methane oxidation and oxychlorination provide other examples where an intermittent “regenerative” catalyst treatment should be useful.  
         [0064]    It should be pointed out that the embodiment of FIGS. 3 and 4 may also be used for conducting a catalytic reaction, if the fine catalyst powder is circulated through bed  10  via lines  52  and  53 , the temperature of bed  10  and powder falling in space  15  being controlled by maintaining an appropriate temperature in line  52 . Such maintenance may be accomplished, of course, through a variety of means for exchanging heat with powder in line  53  (including a heat-exchanger of the instant invention).  
         [0065]    [0065]FIGS. 10, 11,  12 , and  13  depict an embodiment for use with a coarse powder. Asymmetrical serrations, running longitudinally in respect to space  15 , are provided on this space&#39;s side wall  107 , each serration having a longer surface  61  facing upward and a shorter surface  62  facing downward, the two surfaces articulated with one another at substantially a right angle. The serrations, as shown in FIG. 11, are present on the side of  107  facing away from space  15 . Side wall  107  has a slot opening  60  near the bottom of vibrated bed  10  and running longitudinally in respect to space  15  and bed  10 . The upper edge of opening  60  is the lower edge of baffle  59  articulating with side wall  107  and inclined at an angle substantially parallel with upper surfaces  61  of the aforesaid asymmetrical serrations. Inclined outwardly in respect to wall  107 , and opposite the asymmetrical serrations of  107 , is wall  63 . Vibrated bed  113  generally occupies the space between the asymmetrically serrated side of wall  107  and wall  63 . The latter two elements cooperate with slot-opening  60  and baffle  59  in an implementation of the vibration of exchanger  1  that lifts powder from bed  10  to substantially the elevation of ceiling  103 . In other words, elements  107 ,  59 ,  60 ,  61 ,  62 , and  63  constitute a vibratory lift conveying powder upwardly in bed  113  and delivering the powder to vibrated bed  157  resting upon the upper side of ceiling  103  of space  15 . Ceiling  103  is sloped downwardly from its articulation with side wall  107  toward its articulation with side wall  6 . Through this downward slope, the vibration of exchanger  1  is implemented to cause powder in bed  157  to distribute transversely across ceiling  103 . Slot-perforations  58  in ceiling  103  permit the distributed powder to fall into space  15 . Perforations  58  extend transversely across the ceiling, as illustrated generally in FIG. 11 and more particularly in FIG. 12. Baffles  67  extend downward from the edges of slot-perforation  58 , and lean away from these edges. Channel  69  is situated beneath the lower edges of baffles  67 . Notches  70  comprise the upper edge of each side wall  68  of channel  69 , as seen in FIG. 13. Powder moves downward from bed  157  through slot  58  and spills into space  15  via the notches  70 .  
         [0066]    If it is preferred that the ceiling  103  be level, an alternative can be suggested for causing powder to move across the ceiling&#39;s upper surface. In this alternative, the surface would carry asymmetrical serrations running longitudinally, the orientation of a serration being such as to cause powder to move transversely across the ceiling. In general, this alternative is more complicated mechanically and will usually be more costly to provide than the preferred alternative sketched in the figures.  
         [0067]    Optionally, a mid-portion  64  of wall  63  is perforated, as seen in FIG. 11. Space  71  behind wall  63  communicates with a gas source  66  via line  65 . Valve  72  controls the pressure in space  71  at a level substantially equal to the pressure in space  15  by allowing gas to flow, as necessary, either into or from space  71 . If the mid-portion  64  is perforated, the vibratory lift of FIG. 11 can be employed using powders at sizes smaller than the sizes that otherwise can be specified.  
         [0068]    [0068]FIG. 14 illustrates how two side-by-side heat exchangers of the invention,  1  and  101 , can be used to exchange heat between two gases, for example by heating air to be supplied to a combustion step by heat exchange between the air and hot gaseous products from this step. A first gas enters exchanger  1  from line  17 . Powder at a lower temperature enters exchanger  1  via line  52 . Heat is exchanged in exchanger  1  between the first gas and the solid. The first gas leaves exchanger  1  via line  18 . Powder leaves exchanger  1  via line  53 , which delivers the powder to exchanger  101 . A second gas enters exchanger  101  from line  117  and leaves via line  118 . Powder leaves exchanger  101  via line  52 , which delivers the powder to exchanger  1 .  
         [0069]    [0069]FIG. 15 is a transverse cross-section of an alternative arrangement, useful in an application of the invention using a coarse powder, for exchanging heat between two gases. Exchangers  201  and  301  are mounteq side-by-side. By means of a vibratory lift, powder from vibrated bed  210  of is lifted via bed  213  to bed  257 , which rests upon ceiling  303  of exchanger  301 ; and powder falls from ceiling  303  onto bed  310 . Similarly, powder from bed  310  is lifted via bed  313  onto inclined surface  204 , which articulates with ceiling  203  of exchanger  201 .  
         [0070]    I do not wish my invention to be limited to the preferred embodiments illustrated by the figures. Although for practice of my invention, vibration of heat-exchanger  1  should be substantially vertical, I do not rule out use of complex-mode vibrational patterns that create swirl within bed  10  (see Fraas,  Mechanical Engineering,  vol. 120, No. 1, pp. 76-79, 1998). Complex-mode vibration can significantly increase the coefficient for transfer of heat between bed  10  and pipes  11  or tubes  65  (see Thomas, Mason, Sprung, Liu, and Squires, 1998). FIG. 16 generally illustrates another method for creating swirl. The drawing in FIG. 16 is a schematic plan view of a floor  2  in which asymmetrical serrations  262  are disposed in a checker-board fashion, the asymmetries being oriented in the several squares to cause a swirl flow of the powder in directions indicated by arrows in the square located centrally in the drawing.