Abstract:
A shell and tube heat exchanger particularly of enhanced diameter size of use, particularly, in the manufacture of sulfuric acid and having a plurality of an adjacent pair of longitudinal baffle plates located symmetrically and intermittently between and extending the length of the tube bundle. The exchanger is most advantageously made from segments which may be shipped to off-site locations for in situ manufacture of the heat exchanger, particularly when oversized heat exchangers are required when transportation of such large heat exchangers from an off-site manufacturing facility is not possible.

Description:
FIELD OF THE INVENTION  
       [0001]     This invention relates to shell and tube heat exchangers for exchanging heat between a gas and another fluid, particularly of use in the manufacture of sulfuric acid. It is of further particular value in the manufacture of large heat exchangers which may be assembled in-situ, on site from a plurality of segments, and to each of the segments per se.  
       BACKGROUND OF THE INVENTION  
       [0002]     Shell and tube heat exchangers are used extensively in the manufacture of sulfuric acid to exchange heat between a hot fluid and a colder fluid, such as a hot sulfur trioxide or sulfur dioxide-containing gas or sulfuric acid and cold air or a colder sulfur-dioxide containing gas.  
         [0003]     In some heat exchangers, a gas, generally sulfur dioxide/trioxide-containing gas or air is fed to a vestibule within a lower part of the shell and, subsequently, passed through the shell space containing the tube bundle and suitably arranged baffles to effect radial flow of the gas across the tube bundle, prior to exit. One such preferred heat exchanger having an advantageous tube layout is described generally in U.S. Pat. No. 4,357,991, issued Nov. 9, 1982 to C-I-L Inc., as assignee. Such heat exchangers, like other prior art heat exchangers, while being successful in commercial use over a long period of time, suffer from the disadvantage of being limited in size, particularly in diameter, since transportation from the engineering manufacturing facility to the in-situ site of operation is severely restricted by road width, weight, geography and other physical limitations.  
         [0004]     Aforesaid U.S. Pat. No. 4,357,991 describes a heat exchanger having a tube layout which produces more constant mass flow velocities in the area near the tubes and in which the heat transfer coefficient and pressure drop are more favorable than in other prior art exchanger arrangements. The heat exchanger has a plurality of tubes of circular cross-section, the tubes all having the same outer diameter and laid out according to a specific relationship wherein the tubes are arranged with their centers located on a plurality of concentric circular arcs, a plurality of tubes on each arc; the number of tubes in each arc differs from the number of tubes in each other arc by not more than one; the tubes in each arc are spaced uniformly apart along such arc; each tube in each arc, other than such end tubes as may be present in some of said arcs, is located circumferentially midway between the two adjacent tubes of each neighboring arc so that the centers of such three tubes form an isosceles triangle, each such tube in each arc being separated from each of the adjacent tubes in each adjacent arc by a ligament distance h being constant for all the tubes; and the distance between two adjacent tubes in any arc is at least as great as twice the ligament distance h.  
         [0005]     However, such heat exchangers suffer from the disadvantage of creating significant noise pollution problems caused by vibration of constituent parts of the heat exchanger when input gas is fed to the exchanger vestibule at relatively high flow rates.  
       SUMMARY OF THE INVENTION  
       [0006]     It is an object of the present invention to provide an improved shell and tube heat exchanger which reduces noise pollution caused by input gas flow into the exchanger.  
         [0007]     It is a further object to provide a process of heat exchange between a gas and another fluid, which process reduces noise pollution caused by input gas flow within the heat exchanger.  
         [0008]     It is a further object to provide shell and tube heat exchangers of enhanced diameters over typical prior art exchangers.  
         [0009]     It is a further object to provide an alternative method of construction of said enhanced diameter exchangers.  
         [0010]     It is a further object to provide said method application to in-situ, construction at on-site chemical plants.  
         [0011]     It is a further object to provide pre-assembled segments of aforesaid exchangers suitable for transportation to said on-site location.  
         [0012]     Accordingly, in one aspect, the invention provides a heat exchanger for exchanging heat between fluids and having a heat exchanger shell and a plurality of parallel tubes of circular cross-section, said tubes all having the same outer diameter, the improvement wherein said tubes are laid out according to the following relationship:  
         [0013]     (i) said tubes are arranged with their centers located on a set of concentric circular arcs, said set comprising at least first, second and third such arcs, a plurality of tubes on each arc,  
         [0014]     (ii) the number of tubes in each arc differs from the number of tubes in each other arc by not more than one,  
         [0015]     (iii) the tubes in each arc are spaced uniformly apart along such arc,  
         [0016]     (iv) each tube in each arc, other than such end tubes as may be present in some of said arcs, is located circumferentially midway between the two adjacent tubes of each neighboring arc so that the centers of each such three tubes form an isosceles triangle, each tube in each arc being separated from each of said adjacent tubes in each adjacent arc by a diagonal ligament distance h, said distance h being constant for all said tubes, and  
         [0017]     (v) the distance between each two adjacent tubes in any said arc is at least as great as twice said diagonal ligament distance h, so that the minimum cross-sectional area for radial fluid flow between adjacent arcs of said set is defined as to its circumferential dimension by the sum of said diagonal ligament distances h between the tubes of said adjacent arcs and is substantially constant independent of the radial position of said arcs,  
         [0018]     the improvement wherein said exchanger further comprises a plurality of an adjacent pair of longitudinal baffle plates located symmetrically and intermittently between transverse disc and donut baffles and extending the length of said plurality of tubes.  
         [0019]     Preferably, each of the arcs extends through 360° so that each arc is a closed circular ring without end tubes, each ring having the same number of tubes as each other ring and is coaxial with said heat exchanger shell.  
         [0020]     Alternatively, each said arc extends through 360° so that each arc is a closed circular ring without end tubes, each ring having the same number of tubes as each other ring and is non-coaxial with said heat exchanger shell.  
         [0021]     Alternatively, each said arc comprises a plurality of arc segments, each segment extending through 360° divided by said plurality, such that each arc is a part of a closed “petal” shaped ring with end tubes and wherein, each non-adjacent arc has the same number of tubes, and adjacent arcs have a number of tubes differing by not more then one, and each arc is off-centered with said heat exchanger shell.  
         [0022]     Preferably, the radius of one of the rings is R n  and the radius of the next ring radially within the ring is R n +1 and the radii are related by the relationship  
           R     n   +   1       +     b   n       =         R   n     ·   cos     ⁢           ⁢     α   2           
 
 substantially within the limit that the radius of the innermost ring  
         R   min     ≥       Do   +     2   ⁢   h           2   ·   sin     ⁢           ⁢       180   ⁢   °     Ntr             
 
 where b n  is the height of a said isosceles triangle between two adjacent tubes in said one ring and one tube in said next ring,  
         α   2     =         180   ⁢   °       N   tr       .         
 
 N tr  is the number of tubes per ring, 
 
 D o  is the outer diameter of said tubes. 
 
 Preferably, the tubes are arranged subject to the restriction that
 
 R   n   −R   n+2   ≧D   o   +h 
 
 so that for the outermost ring R n ,  
         θ   n     ≥       30   ⁢   °     -       180   ⁢   °       N   tr             
 
 where θ n  is the angle between the base and one side of said isosceles triangle between two adjacent tubes in said outermost ring and one tube in the next ring. 
 
         [0023]     Preferably, the heat exchanger includes a wall defining a shell extending parallel to and encircling said tubes, and first and second baffles each extending at right angles to said wall and intersecting at least some of said tubes, said first baffle extending to said wall and having an inner opening within the innermost of said rings, and hence being of donut configuration, said second baffle being of disc shape and extending from the centre of said innermost ring outwardly past said tubes and having an annular gap between its periphery and said wall, said first and second baffles alternating with each other to form a disc and donut baffle configuration. Preferably, each of the baffles intersects all of the tubes.  
         [0024]     Preferably, a heat exchanger according to the invention includes two sets of said rings, each set containing a plurality of rings, the number of tubes in each ring of one set being different from the number of tubes in each ring of the other set.  
         [0025]     Preferably, the heat exchanger has said diagonal ligament distance h in said one set is different from said diagonal ligament distance in said other set.  
         [0026]     Preferably, the number of tubes in each ring of said one set multiplied by said diagonal ligament distance of said one set is equal to the number of tubes in each ring of said other set multiplied by said diagonal ligament distance of said other set, so that said minimum cross-sectional area for said one set is equal to said minimum cross-sectional area for said other set.  
         [0027]     Preferably, the heat exchanger includes two sets of said arcs, each said set containing a plurality of arcs, the number of tubes in each arc of one set being different from the number of tubes in each arc of the other set.  
         [0028]     Preferably, said diagonal ligament distance h in said one set is different from said diagonal ligament size distance in said other set.  
         [0029]     Preferably, a heat exchanger as hereinabove defined comprises an odd integer selected from 3 to 15 of said plurality of said longitudinal baffle plates. More preferably, an integer selected from 5, 7 and 9.  
         [0030]     Preferably, the plurality of tubes extend between tube sheet end plates; and said plurality of longitudinal baffle plates extend between said tube sheet end plates.  
         [0031]     Preferably, a heat exchanger as hereinabove defined has a diameter selected from 3 m to 8 m, and more preferably a diameter selected from 4 m and 5 m.  
         [0032]     In a further aspect, the invention provides a method of manufacturing a heat exchanger having the tube layout as hereinabove defined which method comprises  
         [0000]     (A) providing a plurality of exchanger segments, wherein each of said segments  
         [0033]     (a) define a segment of an annulus having a longitudinal baffle plate along the radial sides of and extending the length of said segment;  
         [0034]     (b) comprise a plurality of tubes of circular cross-section within said segment, said tubes all having the same outer diameter wherein said tubes are laid out according to the following relationship:  
         [0035]     (i) said tubes are arranged with their centers located on a set of concentric circular arcs, said set comprising at least first, second and third such arcs, a plurality of tubes on each arc,  
         [0036]     (ii) the number of tubes in each arc differs from the number of tubes in each other arc by not more than one,  
         [0037]     (iii) the tubes in each arc are spaced uniformly apart along such arc,  
         [0038]     (iv) each tube in each arc, other than such end tubes as may be present in some of said arcs, is located circumferentially midway between the two adjacent tubes of each neighboring arc so that the centers of each such three tubes form an isosceles triangle, each tube in each arc being separated from each of said adjacent tubes in each adjacent arc by a diagonal ligament distance h, said distance h being constant for all said tubes, and  
         [0039]     (v) the distance between each two adjacent tubes in any said arc is at least as great as twice said diagonal ligament distance h, so that the minimum cross-sectional area for radial fluid flow between adjacent arcs of said set is defined as to its circumferential dimension by the sum of said diagonal ligament distances h between the tubes of said adjacent arcs and is substantially constant independent of the radial position of said arcs; and  
         [0040]     (B) welding the requisite number of said segments one to another adjacent said longitudinal baffle plates to produce said heat exchanger having said tube layout and a plurality of an adjacent pair of longitudinal baffle plates located symmetrically and intermittently between and extending the length of said plurality of tubes.  
         [0041]     The segment of an annulus as termed herein may be also considered to be a double arc sector of a right circular cylinder.  
         [0042]     Preferably, the requisite number of segments is an odd number selected from 3 to 15, more preferably, 5, 7 or 9.  
         [0043]     The tube layouts in each of the double arc sectors is as hereinabove defined.  
         [0044]     Accordingly, in a further aspect the invention provides a heat exchanger segment as hereinabove defined of use in the method as hereinabove defined.  
         [0045]     Preferably, the segment has longitudinal baffle plates which subtend an angle therebetween, selected from the group consisting of about 120°; 72°; 51.5°; 40°; 33°; 28° and 24°.  
         [0046]     In a yet further aspect, the invention provides a plant for the manufacture of sulfuric acid by the oxidation of sulfur dioxide to sulfur trioxide in a catalytic converter and subsequent absorption of the sulfur trioxide in sulfuric acid, the plant comprising an absorption tower, a heat exchanger and a catalytic converter, the improvement comprising a heat exchanger as hereinabove defined.  
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0047]     In order that the invention may be better understood, preferred embodiments will now be described, by way of example only, with reference to the accompanying drawings wherein  
         [0048]      FIG. 1  is a diagrammatic view of a typical prior art heat exchanger, illustrating a disc and donut baffle configuration;  
         [0049]      FIG. 2  is a view of a portion of a tubesheet of a prior art heat exchanger showing the layout of the tubes;  
         [0050]      FIG. 3  is a view of a more complete portion of a tubesheet showing the layout of tubes therein according to the prior art;  
         [0051]      FIG. 4  is a view showing the layout of five tubes according to the prior art and illustrating the mathematical design by which the tubes are laid out;  
         [0052]      FIG. 5  is a view showing the layout of six tubes according to the prior art for calculation of certain limits;  
         [0053]      FIG. 6  is a view showing a heat exchanger according to the prior art and having the form of a section of an annulus;  
         [0054]      FIG. 7  is a diagrammatic isometric view of a heat exchanger segment, according to the invention;  
         [0055]      FIG. 8  is an end view of a tube array in a heat exchanger according to the invention;  
         [0056]      FIG. 9  is a diagrammatic, partly-exploded, isometric view of a plurality of segments of  FIG. 7  suitably arranged according to the invention;  
         [0057]      FIG. 10  is a radical sectional view along the line  10 - 10 ′ of  FIG. 9 ;  
         [0058]      FIG. 11  is a diagrammatic end view of the tube array showing the arc layouts of use in the heat exchanger and segments according to the invention;  
         [0000]     and wherein the same numerals denote like parts. 
     
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS  
       [0059]     Reference is first made to  FIG. 1 , which shows diagrammatically a typical cylindrical heat exchanger  2 . The heat exchanger  2  has a cylindrical shell  4  having an inlet conduit  6  and an outlet conduit  8  for fluid which is to be heated or cooled. Located within the shell  4  are a number of annular or donut shaped baffles  10  which extend to and are adjacent to the wall of the shell  4  and which have central apertures  12 . Located between each pair of donut baffles  10  is a disc-shaped baffle  14 , of smaller diameter than that of the shell  4  and therefore leaving an annular gap  16  extending there around. Both sets of baffles  10 ,  14 , are intersected by all the tubes  18  of the heat exchanger. The tubes  18  extend parallel to the shell  4  and at right angles to the baffles  10 ,  14 . Heating or cooling fluid (liquid or gas) from a source not shown, is directed into the tubes  18  of the heat exchanger from outside one tube sheet  20  and leaves the tubes  18  at the outside of the other tube sheet  22 . Fluid (liquid or gas) from the conduit  6  passes through the heat exchanger in the path indicated by arrows  24  and is warmed or cooled by the fluid in the tubes  18 . In some cases the central aperture  12  and the annular gap  16  are made sufficiently large that the baffles  10 ,  14  intersect only some of the tubes  18 .  
         [0060]     Reference is now made to  FIG. 2 , which shows a set of tubes  18  according to the prior art shown as being located in rings identified by their radii, namely rings R 1 , R 2 , R 3 , R 4  and R 5 .  
         [0061]     The design parameters used to lay out the tubes  18  include the following. Firstly, the diagonal distance between each tube in any ring and its adjacent tubes in the neighboring ring is a constant distance h (referred to as the ligament size or ligament width). Secondly, the shortest distance between two adjacent tubes in the same ring (such distances are identified by reference characters d 1 , d 2 , etc.) is a constant in each ring but varies from ring to ring and is always greater than or equal to 2h. Thirdly the number of tubes in each ring is always the same. However, the radial distance between rings is varied so that the ligament size h between a tube in one ring and its adjacent tubes in each neighboring ring is as mentioned always the same. A mathematical design procedure for calculating the various radii will be set forth shortly.  
         [0062]     It will be seen from  FIG. 2  that so long as the ligament gaps h adjacent to a tube  18  are no more than half as large as the gaps d 1 , d 2 , etc., the ligament gaps and not the gaps d 1 , d 2 , etc. will determine the maximum fluid velocity near that tube. This is the opposite of the conventional concentric ring arrangement in which the tube count is varied for constant distance between the tubes of a ring. It will also be seen from  FIG. 2  that the total minimum flow area through which fluid must pass as it travels radially inwardly through rings R 1 , R 2 , R 3 , etc. is the distance 2h multiplied by the number of tubes per ring (the product is termed the area factor constant or AFC) multiplied by the distance between baffles. As indicated, since the AFC is never greater than the sum of the distances between the tubes of any one ring, the maximum velocity through the rings is determined by the AFC, which is constant between each pair of adjacent rings in the set.  
         [0063]     A more complete tube sheet drawing is shown in  FIG. 3 .  FIG. 3  illustrates portions of two sets of circular rings, indicated at  26  and  28 . In set  26  the ligament size h 1  between each tube  18  and its adjacent tubes  18  in each neighboring ring is always the same constant distance, and the number of tubes  18  in each ring R 1  to R 7  is the same. In tube set  28 , the ligament size h 2  between each tube  18  and its adjacent tubes in each neighboring ring is also a constant, but ligament size distance h 2  is greater than ligament size h 1 . The number of tubes in each ring R 8  to R 11  is constant, but this number is less than the number of tubes in each ring R 1  to R 7 . However the controlling flow distance or AFC between the tubes of any two adjacent rings of set  26  is the same as the controlling flow distance or AFC between the tubes of any two adjacent rings of set  28 . In other words distance h 1  multiplied by the number of tubes in any ring of set  26  is equal to distance h 2  multiplied by the number of tubes in any ring of set  28 . Therefore fluid flowing through tube sets  26 ,  28  will always be subject to the same controlling AFC and the flow velocities through both sets of rings  26 ,  28  will be nearly constant. The AFC between the adjacent rings of sets  26 ,  28  will of course normally be greater than the AFC of each of the two sets.  
         [0064]     A mathematical procedure for laying out the tubes according to the prior art as given hereinbelow, with reference to  FIG. 4 .  
         [0065]     As shown in  FIG. 4 , the following quantities have the following meanings:  
         [0066]     h is the diagonal distance between each tube and the adjacent tubes in each neighboring ring, or in other words is the ligament width,  
         [0067]     n is the ring number,  
         [0068]     R 1 , R 2 , R 3 -R n  are the ring radii,  
         [0069]     α is the angle between radii directed through the centers of adjacent tubes in a ring,  
         [0070]     a n  is a chord of the circle having radius R n  extending between the centers of two adjacent tubes on the circle of radius R n ,  
         [0071]     D o  is the outer diameter of each tube, assumed to be the same for all tubes,  
         [0072]     N tr  is the number of tubes per ring, assumed to be the same for all rings in each set of rings,  
         [0073]     P is the pitch, i.e. the distance between the centers of adjacent tubes in adjacent rings, and is to be constant.  
         [0074]     Then with reference to  FIG. 4 :  
             h   =     P   -     D   o               (   1   )                 α   2     =       180   ⁢   °       N   tr               (   2   )                   a   n     2     =       P   ·   cos   ·     Θ   n       =         R   n     ·   sin     ⁢           ⁢     α   2                 (   3   )             
 
         [0075]     The radius R n+1  is related to radius R n  by  
                 R     n   +   1       +     b   n       =         R   n     ·   cos     ⁢           ⁢     α   2               (   4   )             
 
         [0076]     In practice, the design may be started by selecting the required area for flow, i.e. the AFC, which is 2h.N tr . If a ligament width h is chosen, this determines the number of tubes for the first ring of radius R 1 , which is laid out adjacent the shell  4  of the heat exchanger.  
         [0077]     Once N tr  is chosen, this yields a value for α/2 and for chord a 1 , which with the value of h sets a value for θ 1 . Since b 1 =P sin θ 1 , this yields a value for b 1 , so that R 2  can be calculated.  
         [0078]     There are certain limits applicable to the values that may be chosen. Firstly, as discussed, the minimum flow area between adjacent rings is to be limited by the ligaments h and not by the gaps d 1 , d 2 , etc. Therefore
 
 a   n   ≧D   o +2 h   (5) 
 
         [0079]     As will be explained, equation (5) results in the limit  
               R   min     ≥       Do   +     2   ⁢   h           2   ·   sin     ⁢           ⁢       180   ⁢   °       N   tr                   (   6   )             
 
 Equation (6) gives the minimum ring radius which may be used in order to satisfy equation (5). 
 
         [0080]     The derivation of equation (6) is as follows with reference to  FIG. 5 .  
         [0081]     Assuming that a n ≧D o +2h  
                     Therefore   ⁢             ⁢             ⁢       a   n     2       =         R   n     ·   sin     ⁢           ⁢     α   2                       Hence   ⁢           ⁢   2   ⁢           ⁢       R   n     ·   sin     ⁢           ⁢     α   2       ≥       D   o     +     2   ⁢   h   ⁢           ⁢   or         ⁢     
     ⁢       R   min     ≥       Do   +     2   ⁢   h           2   ·   sin     ⁢           ⁢       180   ⁢   °       N   tr                           (   6   )             
 
         [0082]     If the minimum ring radius is less than R min, the chord distance between two adjacent tubes in the same ring will be less than twice the ligament width, so that the minimum flow area will no longer be governed by the ligaments, which is undesirable. It will however be appreciated that when a number of rings of tubes are to be packed into a heat exchanger, and if space considerations so demand, one or more of the inner rings can be more tightly packed, so that the chord distance between two adjacent tubes in ring is in fact less than 2h. This of course has the disadvantage that the flow through these rings will not behave as ideally as the flow through the rings laid out as described. Such rings, where the chord distance is less than 2h, would not be considered as being members of the set of rings laid out according to the invention. Similarly an outer ring or rings can be provided near the shell with tube spacing other than those described, to provide higher or lower heat transfer near the shell wall.  
         [0083]     The second limit for tubes laid out as described is as follows. It is normally necessary to ensure that the radial distance between any two rings which are separated by one ring is greater than the pitch, i.e. that R n −R n−2 ≧.P. This results in the limit (7)  
         θ   n     ≥       30   ⁢   °     -     180     N   tr             
 
 degrees for the largest radius ring, i.e. ring R 1 . 
 
         [0084]     The derivation of equation (7) is as follows. Since it has been postulated, with reference to  FIG. 5 , that  
                     c   1     +     b   2       ≥   P     ⁢     
     ⁢     and   ⁢           ⁢   since     ⁢     
     ⁢       c   1     =     P   ⁢           ⁢   cos   ⁢           ⁢   ϕ       ⁢     
     ⁢   where   ⁢     
     ⁢     ϕ   =       90   ⁢   °     -     (       θ   1     +     α   2       )         ⁢     
     ⁢   Hence   ⁢     
     ⁢       c   1     =       P   ⁢           ⁢     cos   ⁡     [       90   ⁢   °     -     (       θ   1     +     α   2       )       ]         =     P   ⁢           ⁢     sin   ⁡     (       θ   1     +     α   2       )             ⁢     
     ⁢   and   ⁢     
     ⁢     b   2     =         P   2     -       (       a   2     2     )     2           ⁢     
     ⁢   Where   ⁢     
     ⁢         a   2     2     =         P   ·   sin     ⁢           ⁢   Φ     =     P   ·     cos   ⁡     (       Θ   1     +     α   2       )             ⁢     
     ⁢   Hence   ⁢     
     ⁢         P   ⁢           ⁢     sin   ⁡     (       θ   1     +     α   2       )         +       P   ⁡     [     1   -       cos   2     ⁡     (       θ   1     +     α   2       )         ]         1   /   2         ≥   P     ⁢     
     ⁢   For   ⁢     
     ⁢           θ   1     +     α   2       ≤     90   ⁢   °       ,     
     ⁢     we   ⁢           ⁢   have       ⁢     
     ⁢       2   ⁢     sin   ⁡     (       θ   1     +     α   2       )         ≥   1     ⁢     
     ⁢   or   ⁢     
     ⁢       sin   ⁡     (       θ   1     +     α   2       )       ≥     1   /   2       ⁢     
     ⁢   or   ⁢     
     ⁢         θ   1     +     α   2       ≥     30   ⁢   °       ⁢     
     ⁢   Since   ⁢     
     ⁢       α   2     =     180     N   tr         ⁢     
     ⁢   Therefore   ⁢     
     ⁢       θ   1     ≥       30   ⁢   °     -     180     N   tr                   (   7   )             
 
         [0085]     Equation (7) represents a normal limit on how closely the rings can be spaced without unduly weakening the tube sheets  20 ,  22  and the baffles  10 ,  14 . In some special cases it may be possible to achieve slightly closer spacing. 
 
The minimum flow area in the space between adjacent baffles  10  and  14  is 
 
min. flow area=AFC× D   bc  
 
where
 
AFC=area factor constant=2( P−D   o ) N   tr 
 
and
 
D bc =distance between baffles
 
         [0086]     Where two sets of rings are used, each with its own ligament size, as shown in  FIG. 3 , then the AFC of each set is as discussed normally held the same as that of the other set. If ring n is the last ring in one set and ring n−1 is the first ring in the second set, this is accomplished by maintaining  
               N       tr   ⁢           ⁢   n     -   1       =       N   trn     ⁡     (         P   n     -     D   o           P     n   -   1       -     D   o         )               (   8   )             
 
 where P n  is the pitch for ring n and P n−1  is the pitch for ring n−1. This ensures that the mass flow velocity is nearly constant throughout the tube bundle. 
 
         [0087]     If in special cases it is desired to have a different AFC in each set of tube rings, for example more rapid flow through the outer set than through the inner set, then the AFC can be made larger in the outer set than the inner set.  
         [0088]     It will be seen from  FIGS. 4, 5  that the tubes  18  are laid so that each tube is located circumferentially midway between the two adjacent tubes in each neighboring arc, so that the centers of such three tubes form an isosceles triangle. As shown in  FIG. 3 , this results in the tubes of each set of rings  26 ,  28  being laid out in a spiral configuration. This facilitates cleaning, which may be accomplished by inserting a corresponding shaped tool through the tubes between the spirals. When two sets of rings are used, as shown in  FIG. 3 , then since each set of tubes has a different spiral configuration, it is necessary to clean the outer set of rings by a tool inserted from the outside, and the inner set of rings by a tool inserted from the inside.  
         [0089]     In the typical embodiment shown in  FIG. 3 , each ring R 1  to R 7  contains 68 tubes (total 476), and the radii are  
         [0090]     R 1 =35.90 inches  
         [0091]     R 2 =34.745 inches  
         [0092]     R 3 =33.51 inches  
         [0093]     R 4 =32.21 inches  
         [0094]     R 5 =30.84 inches  
         [0095]     R 6 =29.40 inches  
         [0096]     R 7 =27.90 inches  
         [0097]     The tube outer diameter is 1.5 inches and the pitch is 2.0 inches. In addition each ring R 8  to R 11  contains 43 tubes, and the radii are  
         [0098]     R 8 =25.90 inches  
         [0099]     R 9 =24.54 inches  
         [0100]     R 10 =23.05 inches  
         [0101]     R 11 =21.43 inches  
         [0102]     The tube outer diameter remains 1.5 inches and the pitch is 2.29 inches. The values given for  FIG. 3  are exemplary only and will of course vary depending on the application.  
         [0103]     In  FIG. 3  it is assumed that each set of rings  26 ,  28  extends through a full circle of 360 degrees, i.e. that each ring R 1  to R 11  is a closed circle. However if desired the sets of rings  26 ,  28  may be arranged not as closed rings but as sections of annuli. This arrangement is shown in  FIG. 6 , where the heat exchanger  2  is shown in section as a section of an annulus and the tubes  18  are arranged along concentric arcs where the arcs do not extend through a full 360 degrees. The  FIG. 6  arrangement of tubes is in fact simply a portion of the  FIG. 3  set  26 , and the same radii R 1  to R 7  are shown in the drawings. The shell of the heat exchanger is shown at  40 .  
         [0104]     In the annulus arrangement shown in  FIG. 6 , all of the relationships previously described remain applicable, except that the arcs may not all have the same number of tubes  18 . In  FIG. 6  the odd numbered arcs have ten tubes each and the even numbered arcs have nine tubes each. This is because the end walls  42 ,  44  of the shell are straight and because of the location of such end walls. If end wall  44  were moved to the location shown in dotted lines at  46 , then each arc would have the same number of tubes (nine tubes in the  FIG. 6  embodiment). Thus, when the tube layout has the form of a section of an annulus, the number of tubes in each arc will be either the same as the number in each other arc or may differ from the number of tubes in each other arc by not more than one. In addition the end tubes in the odd numbered arcs do not of course form an isosceles triangle with the two adjacent tubes of each neighboring arc, because of the end walls  42 ,  44 , but these walls are sufficiently close to the end tubes of the odd numbered arcs to prevent “punch-through”.  
         [0105]     In the appended claims, reference is made to the distance between tubes. Such distance refers to the distance between the outer diameters of the tubes.  
         [0106]     With reference to  FIG. 7 , this shows generally as  50  a diagrammatic isometric view of a segment, in the form of part of an annulus for use in the construction of a heat exchanger to comprise seven such segments. The segment has a radial tube layout of tubes  52  between tube sheet end plates  54  and a pair of longitudinal baffle plates  56 ,  58  (with only  56  being seen), extending the length between end plates  54 . Radial edges  60 ,  62  of each of end plates  54  subtend on angle β of about 51.4° in the embodiment shown.  
         [0107]     In field assembly, the longitudinal baffle plate  56 A adjacent to end plate  54  is not present. A pair of segments  50  is positioned longitudinally adjacent one to the other with a radial edge  60  abutting radial edge  62  of adjacent segment  50 . The segments are welded together adjacent the edges. Thereafter, baffle plate  56 A is welded in place adjacent edge  62 . The method is repeated with the other segments  50  until the cylindrical exchanger having a diameter of over 5 m is constructed. The maximum width of each segment is about 2.4 m and is suitable for transportation in standard containers for truck, rail and cargo shipment.  
         [0108]      FIG. 8  shows generally as  60 , a end view of a heat exchanger having a plurality of segment tube arrays  50  welded together and having a pair of adjacent longitudinal baffle plates  56  between adjacent arrays according to the invention.  
         [0109]      FIG. 9  shows generally as  70  a plurality of seven segments  60  in the process of construction of the complete tube  52  layout with longitudinal baffle plates  56 ,  58  and end plates  54 .  
         [0110]      FIG. 10  shows the resultant connection between two adjacent segments  50 , welded in situ in the field to provide a “double plate” arrangement of a pair of parallel plates intermittently welded, one to the other, at at least one end thereof. The plates are so spaced apart as to provide a gap “g” between a plate  56 ,  56 A,  58 ,  58 A and its adjacent row of tubes, as to allow gas flow between each of the tubes and the plates, while preventing gas bypass between the adjacent row of tubes of adjacent bundles.  
         [0111]      FIG. 11  shows generally in end view  80 , the angles α for both the segments and the offset arcs. Dimension “f” is the offset distance between the center of shell  82  and the center of the “petal” arcs  84 . Dimension “m” denotes a maximum deviation between centered arc  86  and petal arc  84 . This figure also shows adjacent arcs  88  and non-adjacent arcs  90 .  
         [0112]     Although this disclosure has described and illustrated certain preferred embodiments of the invention, it is to be understood that the invention is not restricted to those particular embodiments. Rather, the invention includes all embodiments which are functional or mechanical equivalence of the specific embodiments and features that have been described and illustrated.