HEAT EXCHANGER BAFFLE ASSEMBLY AND TUBE PATTERN FOR RADIAL FLOW HEAT EXCHANGER AND FLUID HEATING SYSTEM INCLUDING THE SAME

Abstract

A fluid heating system assembly includes a first tube sheet, a second tube sheet opposite the first sheet, a plurality heat exchanger tubes, which connect the first tube sheet and the second tube sheet, and a plurality of baffles, comprising at least one plate baffle and at least one annular baffle disposed between the first tube sheet and the second tube sheet, wherein the heat exchanger tubes sealingly pass through the baffles, and wherein the tubes are arranged in a staggered ring configuration and the baffles have a baffle spacing, such that there is a substantially uniform temperature distribution and efficient exchange of thermal energy across the heat exchanger tube walls.

Description

BACKGROUND

Field

This disclosure relates to fluid heating systems using shell and tube heat exchangers.

Description of the Related Art

Fluid heating systems, including steam, hydronic (water), and thermal fluid boilers, constitute a broad class of devices for producing a heated fluid for use in domestic, industrial, and commercial applications. Because of the desire for improved energy efficiency, compactness, reliability, and cost reduction, there remains a need for improved fluid heating systems, as well as improved methods of manufacture thereof.

SUMMARY

A fluid heating system or heat exchanger baffle assembly comprising: a first tube sheet; a second tube sheet opposite the first sheet; one or more heat exchanger tubes, which connects the first tube sheet and the second tube sheet; and one or more plate baffles and/or one or more annular baffles disposed between the first tube sheet and the second tube sheet, wherein the heat exchanger tubes sealingly pass through the baffles.

Also, disclosed is a heat exchanger tube assembly comprising a first tube sheet, a second tube sheet opposite the first sheet, a plurality of heat exchanger tubes, each independently connects the first tube sheet and the second tube sheet, wherein the tubes are in a staggered ring configuration that comprises a concentric sequence of rings of decreasing diameter wherein adjacent tubes on the same ring are separated by a fixed radial separation.

Also disclosed is a fluid heating system including a heat exchanger comprising: a pressure vessel; a baffle assembly disposed in the pressure vessel, the baffle assembly comprising a first tube sheet, a second tube sheet opposite the first tube sheet, one or more heat exchanger tubes which connect the first tube sheet and the second tube sheet, an annular baffle and/or a plate baffle disposed between the first tube sheet and the second tube sheet.

Also disclosed is a fluid heating system including a heat exchanger comprising: a pressure vessel; a first tube sheet; a second tube sheet opposite the first sheet; one or more heat exchanger tubes, which connects the first tube sheet and the second tube sheet; one or more plate baffle assemblies disposed between the first tube sheet and the second tube sheet, wherein the heat exchanger tube sealingly passes through the plate baffles; and one or more annular baffle assemblies sealing disposed between the first tube sheet and the second tube sheet, wherein the heat exchanger tubes sealingly pass through the annular baffle.

Also disclosed is a method of producing radial flow in a fluid heating system or heat exchanger heat exchanger, the method comprising: providing a heat exchanger comprising a baffle assembly comprising a pressure vessel shell comprising an inlet and outlet; a baffle assembly entirely disposed in the pressure vessel shell; the baffle assembly comprising a first tube sheet, a second tube sheet opposite the first sheet, one or more heat exchanger tubes which connects the first tube sheet and the second tube sheet; at least one plate baffle disposed between the first tube sheet and the second tube sheet, wherein the heat exchanger tube sealingly passes through the baffle; at least one annular baffle and/or at least one plate baffle sealingly disposed between the first tube sheet and the second tube sheet, wherein the heat exchanger tube sealingly passes through the baffle; and directing a production fluid from the first inlet to the first outlet to provide a flow of the production fluid through the pressure vessel shell to produce the radial flow.

Also disclosed is a heat exchanger tube assembly comprising a first tube sheet, a second tube sheet opposite the first sheet, a plurality of heat exchanger tubes, each independently connects the first tube sheet and the second tube sheet, wherein the tubes are in a staggered ring configuration that comprises a concentric sequence of rings of decreasing diameter wherein adjacent tubes on the same ring are separated by a fixed radial separation angle, and adjacent tubes on adjacent rings are staggered by rotating all the tubes within an inner ring by a fixed radial index angle, IA, relative to the next outermost tube ring.

Also disclosed is a heat exchanger comprising: a pressure vessel; a heat exchanger tube assembly disposed in the pressure vessel, the tube assembly comprising a first tube sheet; a second tube sheet opposite the first sheet; a plurality of heat exchanger tubes, each independently connects the first tube sheet and the second tube sheet, wherein the tubes are in a staggered ring configuration that comprises a concentric sequence of rings of decreasing diameter and wherein adjacent tubes on the same ring are separated by a fixed radial separation angle, RA.

Also disclosed is a heat exchanger comprising: a pressure vessel; a heat exchanger tube assembly disposed in the pressure vessel, the tube assembly comprising a first tube sheet; a second tube sheet opposite the first sheet; a plurality of heat exchanger tubes, each independently connects the first tube sheet and the second tube sheet, wherein the tubes are in a staggered ring configuration that comprises a concentric sequence of rings of decreasing diameter and wherein adjacent tubes on the same ring are separated by a fixed radial separation angle, RA, and adjacent tubes on adjacent rings are staggered by rotating all the tubes within an inner ring by a fixed radial index angle, IA, relative to the next outermost tube ring.

Also disclosed is a fluid heating system comprising: a pressure vessel shell comprising a first inlet and first outlet, a shell, a first top head and a first bottom head, wherein the shell is disposed between the first top head and the first bottom head, and wherein the first inlet and the first outlet are each independently on the shell, the first top head, or the first bottom head; a heat exchanger tube assembly disposed in the pressure vessel shell, the heat exchanger tube assembly comprising, a first tube sheet, a second tube sheet opposite the first sheet, a plurality of heat exchanger tubes, each independently connects the first tube sheet and the second tube sheet, wherein the tubes are in a staggered ring configuration that comprises a concentric sequence of rings of decreasing diameter and wherein adjacent tubes on the same ring are separated by a fixed radial separation angle, RA; a conduit, which penetrates the pressure vessel shell, wherein a first end of the conduit is connected to the first tube sheet wherein the conduit is in fluid communication with the heat exchanger tubes and wherein a second end of the conduit is on the outside of the pressure vessel shell; a burner disposed in the conduit; and a blower, which is in fluid communication with the second end of the conduit.

Also disclosed is a fluid heating system comprising: a pressure vessel shell comprising a first inlet and first outlet, a shell, a first top head and a first bottom head, wherein the shell is disposed between the first top head and the first bottom head, and wherein the first inlet and the first outlet are each independently on the shell, the first top head, or the first bottom head; a heat exchanger tube assembly disposed in the pressure vessel shell, the heat exchanger tube assembly comprising, a first tube sheet, a second tube sheet opposite the first sheet, a plurality of heat exchanger tubes, each independently connects the first tube sheet and the second tube sheet, wherein the tubes are in a staggered ring configuration that comprises a concentric sequence of rings of decreasing diameter and wherein adjacent tubes on the same ring are separated by a fixed radial separation angle, RA, and wherein adjacent tubes on adjacent rings are staggered by rotating all the tubes within an inner ring by a fixed radial index angle, IA, relative to the next outermost tube ring; a conduit, which penetrates the pressure vessel shell, wherein a first end of the conduit is connected to the first tube sheet wherein the conduit is in fluid communication with the heat exchanger tubes and wherein a second end of the conduit is on the outside of the pressure vessel shell; a burner disposed in the conduit; and a blower, which is in fluid communication with the second end of the conduit.

Also disclosed is a method for computing the radial separation angle and the radial stagger index angle for a staggered ring heat exchanger tube configuration, using the design diameter of the tube configuration, the required gap between the design diameter and the first tube ring, the tube element clearance diameter required for each ring of tubes, and the rounding threshold to be applied to the tube count calculation.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other advantages and features of this disclosure will become more apparent by describing in further detail exemplary embodiments thereof with reference to the accompanying drawings, in which:

FIG. 1A is a schematic diagram of an embodiment of a fluid heating system which includes an embodiment of a combustion gas supply system in accordance with embodiments of the present disclosure.

FIG. 1B is a perspective view of an embodiment of a shell-and-tube heat exchanger incorporating a plate baffle assembly that directs production fluid back-and-forth across the surfaces of adjacent baffle plates in accordance with embodiments of the present disclosure.

FIG. 1C is a view of a circular plate baffle where the production fluid is directed across the surface of the plate baffle along a chord in accordance with embodiments of the present disclosure.

FIG. 2A is a longitudinal cross-sectional view of an embodiment of a shell-and-tube heat exchanger incorporating plate baffle and annular baffle assemblies generating radial production fluid flow in accordance with embodiments of the present disclosure.

FIG. 2B is a longitudinal view of a heat exchanger comprising a plate baffle in accordance with embodiments of the present disclosure.

FIG. 2C is a perspective view of an embodiment of a plate baffle showing the heat exchanger tube holes and the mounting flanges in accordance with embodiments of the present disclosure.

FIG. 3 is a side view of an embodiment of a plate baffle assembly showing the plate baffle, the gasket and the retainer with fasteners in accordance with embodiments of the present disclosure.

FIG. 4 shows a cross-sectional schematic of an embodiment of a plate baffle assembly showing the gasket seal between the baffle and the outer wall of a heat exchanger tube in accordance with embodiments of the present disclosure.

FIG. 5 is a longitudinal cross-sectional view of a shell-and-tube heat exchanger incorporating an annular baffle assembly in accordance with embodiments of the present disclosure.

FIG. 6 is a perspective view of an embodiment of an annular baffle showing the heat exchanger tube holes and the mounting flanges in accordance with embodiments of the present disclosure.

FIG. 7 shows a cross-sectional schematic of an embodiment of an annular baffle assembly showing the gasket seal between the baffle and the outer wall of a heat exchanger tube, and the gasket seal between the baffle and the inner wall of the pressure vessel in accordance with embodiments of the present disclosure.

FIG. 8 is a longitudinal cross-sectional view of an embodiment of a shell-and-tube heat exchanger incorporating an alternating plate and annular baffle assembly in accordance with embodiments of the present disclosure.

FIG. 9 is a perspective view of an embodiment of a shell-and-tube heat exchanger incorporating an alternating plate and annular baffle assembly in accordance with embodiments of the present disclosure.

FIG. 10 is a schematic drawing of the cross-section of the region near a heat exchanger tube wall showing the modeling elements used in the calculation model for baffle-to-baffle spacing assembly in accordance with embodiments of the present disclosure.

FIG. 11 is a generalize plot of the temperature profile along the length of the heat exchanger in accordance with embodiments of the present disclosure.

FIG. 12 provides a flow diagram for a method to compute the radial separation angle and the radial stagger index angle for a staggered ring heat exchanger tube configuration, using the design diameter of the tube configuration, the required gap between the design diameter and the first tube ring, the tube element clearance diameter required for each ring of tubes, and the rounding threshold to be applied to the tube count calculation in accordance with embodiments of the present disclosure.

FIG. 13 shows the heat exchanger tube distribution pattern that results from applying the method described in the flow diagram shown in FIG. 12 in accordance with embodiments of the present disclosure.

FIG. 14 is a cross-sectional diagram showing the staggered ring tube distribution pattern in a plate baffle with mounting flanges to the pressure vessel wall in accordance with embodiments of the present disclosure.

FIG. 15 shows the velocity flow field results from a computational fluid dynamic (CFD) simulation of a full-scale fluid heating system using a standard hexagonal heat exchanger tube configuration in accordance with embodiments of the present disclosure.

FIG. 16 shows the velocity flow field results from a computational fluid dynamic (CFD) simulation of a full-scale fluid heating system using a staggered ring heat exchanger tube configuration in accordance with embodiments of the present disclosure.

FIG. 17 shows a computational fluid dynamics (CFD) numerical simulation of the flow field across the baffle with a staggered ring tube pattern distribution closest to the upper tube sheet with a baffle spacing of 0.75 inches between the baffle and the tube sheet in accordance with embodiments of the present disclosure.

FIG. 18A shows a computational fluid dynamics (CFD) numerical simulation of the flow field through the pressure vessel of an embodiment of a shell-and-tube heat exchanger incorporating an alternating plate and annular baffle assembly and illustrating the temperature field contour lines for radial flow created by the baffle assembly in accordance with embodiments of the present disclosure.

FIG. 18B shows a computational fluid dynamics (CFD) numerical simulation of the flow field through the pressure vessel of an embodiment of a shell-and-tube heat exchanger incorporating an alternating plate and annular baffle assembly and illustrating the velocity field for radial flow created by the baffle assembly in accordance with embodiments of the present disclosure.

FIG. 19 shows a computational fluid dynamics (CFD) numerical simulation of the flow field across the baffle closest to the upper tube sheet with a baffle spacing of 1.25 inches between the baffle and the tube sheet in accordance with embodiments of the present disclosure.

DETAILED DESCRIPTION

There remains a need for fluid heating systems which provide more thermally compact designs, e.g., configurations that provide an increased ratio between the power and volume or footprint of the fluid heating systems (FHS), and which can be manufactured at a reasonable cost, with satisfactory material requirements, and reduced complexity. Improvements in the state-of-the-art for fluid heating system design, methods, and manufacture that enable increases in the thermal power achievable for a prescribed size or, conversely, enable a reduction in size for a prescribed thermal power level, accomplished for the same or lower manufacturing cost and complexity, are desirable.

It has been unexpectedly discovered that methods for reducing the size of fluid heating systems incorporating shell-and-tube heat exchangers achieved by increasing the bulk heat flux can exacerbate issues created by the non-uniform temperatures. Areas within the heat exchanger where heat is concentrated can lead to material failures, corrosion, and fouling. Where the temperature exceeds the boiling point of the production fluid, adverse effects may accumulate, particularly near structural joints or cracks that precipitate a production fluid phase change. Not only is the magnitude of the temperature non-uniformity generally increased, but the number of locations or sites has also increased.

Methods for promoting a uniform velocity field within the flow of production fluid through the pressure vessel promote a uniform temperature distribution and efficient exchange of thermal energy across the walls of the heat exchanger tubes. This is achieved in classical heat exchanger design through some form of baffling to direct the production fluid flow, or some other means for controlling the fluid flow in a predictable manner. Baffling may be done in only a few discreet locations to address known issues, or they can be systemic, closely controlling the fluid flow throughout the entire heat exchanger.

Disclosed in FIG. 1A is a schematic of a fluid heating system 100. Ambient air is forced under pressure by a blower 102 through a conduit into a combustor 104, which comprises a furnace 106. In the furnace 106, a sustained combustion of a combination of fuel and air is maintained, releasing heat energy and combustion gases that travel through the upper tube sheet 105 and into a plurality of heat exchanger tubes 115. After traversing the heat exchanger tubes, the hot combustion gases pass through the lower tube sheet 110, into the exhaust plenum 112 bounded by the exhaust plenum shell 114, and through the exhaust port to be conveyed out of the fluid heating system by an exhaust flue (not shown).

The production fluid is forced under pressure into an inlet 116, through the space 155 bounded by the pressure vessel 150 surrounding the heat exchanger tubes and out through the outlet 118. A baffle 108 can be placed around the heat exchanger tubes to direct the flow of production fluid.

The capacity of the fluid heating system is total heat transferred from the thermal transfer fluid to the production fluid under standard conditions. By convention, when the production fluid consists of a liquid (e.g., water, thermal fluid, or thermal oil) the capacity is expressed in terms of British thermal units per hour (BTU/hr); and when the production fluid comprises a gas or vapor (e.g., steam) the standard unit of measurement is expressed in horsepower (HP). In an embodiment wherein the production fluid is a liquid (e.g., water, thermal fluid or thermal oil), the capacity of the fluid heating system may be between 100,000 BTU/hr, or 150,000 BTU/hr, or 200,000 BTU/hr, or 250,000 BTU/hr, or 300,000 BTU/hr, or 350,000 BTU/hr, or 400,000 BTU/hr, or 450,000 BTU/hr, or 500,000 BTU/hr, or 550,000 BTU/hr, or 600,000 BTU/hr, or 650,000 BTU/hr, or 700,000 BTU/hr, or 750,000 BTU/hr, or 800,000 BTU/hr, or 850,000 BTU/hr, or 900,000 BTU/hr to 50,000,000 BTU/hr, or 40,000,000 BTU/hr, or 30,000,000 BTU/hr, or 20,000,000 BTU/hr, or 15,000,000 BTU/hr, or 14,000,000 BTU/hr or 13,000,000 BTU/hr, or 12,000,000 BTU/hr, or 10,000,000 BTU/hr, or 8,000,000 BTU/hr, or 6,000,000 BTU/hr, or 5,000,000 BTU/hr, or 4,000,000 BTU/hr, or 3,000,000 BTU/hr, or 2,000,000 BTU/hr, or 1,000,000 BTU/hr, wherein the foregoing upper and lower bounds can be independently combined. Specifically mentioned is the range from 750,000 BTU/hr to 12,000,000 BTU/hr.

In the fluid heating system, where the production fluid temperature exceeds its heat of vaporization, the production fluid will boil and provide a vapor. This can occur where the flow velocity is low and the production fluid remains in extended contact with the hot surface; for example, near the heat exchanger tubes, or upper or lower tube sheets. While not wanting to be bound by theory, production fluid boiling is understood to cause a loss of thermal efficiency, and sites that regularly experience boiling are also regions where material failure, corrosion and fouling are likely.

It has been unexpectedly discovered that the temperature and mass flow distribution from the furnace into the tubesheet are not homogenous. In all burner configurations, but particularly true for those utilizing premixed surface combustion, there exists temperature and flow gradients. The flow exiting the burner, and driven closest to the furnace will transfer more of its thermal energy into the furnace wall. The resulting temperature boundary layer will flow down the wall, and primarily enter the tubes closest to the perimeter. This results in a mass flow concentration near the perimeter. Contrarily, the rest of the combustion flow will be insulated from the furnace wall, and therefore will retain more of its heat, and generally this hot flow will prefer tubes closest to the center, the magnitude of which was extremely surprising when discovered during CFD modeling of the flow field. This result is so surprising since conventional design practice predicts the turbulence of combustion would promote more even mixing. Additionally, the pressure drop through the length of the tubes would be expected to be much larger in magnitude than the dynamic effects from confined flow, and the flow inside the tubes in highly turbulent. This would be expected to even out the effect on the flow field. Lastly, conventional practice would predict that radiant heat transfer from the hottest gasses in the center (and indeed from the flame itself) would also contribute to increasing the uniformity of the temperature field.

The magnitude of the deviation within gas side temperature field creates uneven heat transfer requirements on the water side of the boiler. Specifically, higher water side heat transfer coefficients (and thus velocity and turbulence) are required near these concentrations of high temperature gas containing tubes.

Most heat exchangers are designed with round cross sections, commonly cylinders. In an embodiment where the production fluid flows across the face of each baffle surface along a chord of the surface, alternating direction across the surface of adjacent baffles (a “back and forth” baffle pattern design), the cross section of flow is small at the entry of a given section (defined by a chord length which is less than the diameter), then increases as it reaches the center of the tube bundle (chord length equal to diameter) and is then reduced again as the fluid reaches the opposite side of the baffle section. FIG. 1B illustrates the production fluid flow corresponding to the configuration described. Production fluid moves through the pressure vessel 150 back-and-forth across the heat exchanger tubes 115, alternating direction in regions between adjacent baffles by turning the flow 160 at the edges of the baffle plates. FIG. 1C illustrates how the production average fluid flow 165 is directed along geometrical chords 166 across the baffles plate through the spaces between adjacent heat exchanger tubes 115. While such abrupt velocity changes at the edges of the baffles plates to turn the flow direction are not in and of themselves detrimental, the design results in two primary disadvantages:

Firstly, flow momentum dictates that the fluid will try to flow in a straight line. The result is that the tubes at the outside edges 170 tend to receive less flow than those at the center. Secondly, even when the outside tubes are included in the flow (through smart tube patterns, or additional baffling to force flow into these regions), the increase in cross sectional area means that flow velocity is reduced in the center of the bundle. Depending on the configuration of the furnace and heat exchanger tube top sheet, these center tubes are typically the hottest and already at the highest risk of failure.

While not wanting to be bound by theory, these effects are especially pronounced in single-pass, in-line heat exchangers incorporating conventional mesh burners for firetube boilers. Particularly in such design applications, the temperature of the thermal transfer fluid exiting the furnace is highest at the center as it impinges on the upper tube sheet and enters the heat exchanger tubes closest to the centerline, and coolest near the walls of the furnace as it impinges on the top tube sheet and enters the heat exchanger tubes along the circumference. In such applications, avoiding high temperatures near the centerline that can cause boiling of the production fluid and material failure is an important limiting design constraint.

It has also been unexpectedly discovered that radial flow of production fluid through the collection of heat exchanger tubes is effective at promoting a uniform, distribution of temperature and flow velocity within the heat exchanger. Radial flow of the production fluid can be arranged by design in a fluid heating system using arrangements of baffles that cause the flow to alternate between inward-directed radial flow towards the longitudinal axis and outward-directed radial flow towards the pressure vessel inner wall. Additionally, the geometry of alternating radial flows ensures that peak velocities occur at the center of the tube bundle, where they are most needed, as confirmed by computational fluid dynamic (CFD) modeling simulation.

Furthermore, it has been unexpectedly discovered that sealing the baffles to the heat exchanger tubes and the pressure vessel inner surface substantially contribute to the creation of a uniform temperature and velocity production fluid flow field. Sealing the heat exchanger tubes to the baffles eliminates gaps where production fluid can leak through a baffle, degrading the desired radial flow and creating regions where low flow velocities and high temperatures can concentrate. The disclosed configuration provides unexpectedly improved uniformity in the production fluid velocity and temperature field.

The flow pattern induced by the alternating plate and annular baffles is illustrated in the rendering shown in FIG. 2A, where production fluid entering 201 the inlet 200 flows through the center region 202 of the first annular baffle assembly 204, turns outward and flows radially 206 to the outer perimeter of the first plate baffle assembly 208 where it is turned inward 210 to again flow radially to the center region 212 of the second annular baffle assembly 214. This alternating radial flow pattern continues until the production fluid passes through the outlet (not shown) and out of the pressure vessel.

An embodiment of a baffle assembly 220 deposed on the heat exchanger upper tube sheet 222, lower tube sheet 224, and tube structure 226 promoting uniform radial production flow conditions shown in FIG. 2B. In this embodiment, the assembly comprising an upper tube sheet 222, a lower tube sheet 224, and a plurality of heat exchanger tubes 228, which connects the upper tube sheet 222 and the lower tube sheet 224. A baffle assembly 220 is disposed between the upper tube sheet 222 and the lower tube sheet 224, wherein the heat exchanger tubes sealingly passes through the baffle 250. The baffle assembly is secured to the pressure vessel using a mounting flange 245.

As used herein, “sealingly” means that a seal is provided between adjacent members to substantially or effectively preclude fluid flow between the adjacent members. In an embodiment, a region between the adjacent members is 80% to 100%, 90% to 99%, or 95% to 98% obscured, and preferably 95% to 100% obscured, wherein the foregoing percentage is determined as a percentage of the area between the adjacent members. For example, the seal can be formed merely from the close proximity of the adjacent members or the seal can be formed, for example, using a gasket.

As shown in FIG. 2C, the plate baffle 260 may be in the shape of a plate with a perimeter having any suitable geometry. The plate may be rectilinear or curvilinear, and may have a disk shape, an elliptical shape, a lobular shape, a square shape, a rectangular shape, or any combination thereof. Each heat exchanger tube passes through a hole 262 in the plate baffle. The baffle assembly may be secured to the pressure vessel using a fastener that passes through a hole 264 in a mounting flange 266, although any equivalent method of securing the plate baffle is contemplated and claimed herein.

The components comprising the baffle assembly may each independently comprise any suitable material, and may comprise a metal such as iron, aluminum, magnesium, titanium, nickel, cobalt, zinc, silver, copper, an alloy comprising at least one of the foregoing, or a combination thereof. Representative metals include carbon steel, mild steel, cast iron, wrought iron, stainless steel (e.g., 304, 316, or 439 stainless steel), Monel, Inconel, bronze, and brass. Specifically mentioned is an embodiment in which the baffle assembly components are mild steel.

The plate baffle assembly is sealed to the heat exchanger tubes to prevent production fluid flow in the gap between the baffle and the tubes, thereby forcing the fluid across the perimeter of the baffle assembly. The baffle assembly may be sealed to the heat exchanger tubes using any suitable method, for example by welding the heat exchanger tubes to the plate baffle, or sealing the gap using an adhesive.

In another embodiment, the plate baffle may be sealed to the heat exchanger tubes using a gasket, as shown in FIG. 3. In this embodiment, the plate baffle assembly comprises a rigid plate baffle element 302, secured to the pressure vessel by a flange 310, and a gasket 304 is disposed on a surface of the plate baffle and between the rigid element and the heat exchanger tube, wherein a gasket seals the baffle to the heat exchanger tube where the heat exchanger tube passes through the baffle. The gasket may be secured to the plate baffle using an adhesive. A retainer 306 may also be used to secure the retainer to the plate baffle using adhesive or fasteners 308. Any suitable adhesive may be used. Representative adhesives include a vinyl ester, an epoxy, a phenolic, a silicone, a polyurethane, and a fluorinated rubber.

The gasket used to seal the baffle to the heat exchanger tubes may comprise an elastomer. Specifically mentioned is an embodiment where the elastomer is an ethylene propylene diene terpolymer.

An embodiment of the plate baffle assembly incorporating a gasket and a retainer 416 is shown in FIG. 4, where the gasket 400 is disposed between the plate baffle 402 and the retainer 404. In the embodiment shown in FIG. 4, the retainer outer diameter is smaller than the plate baffle diameter so that the gasket protrudes 406 from the baffle assembly and contacts the outer wall of the heat exchanger tube 408, preferentially in the direction of the retainer. As a result, fluid flow pressure in the space 412 between the heat exchanger tube 408 and the pressure vessel wall 410 forces the gasket against the heat exchanger tube outer wall 414, promoting the seal. The shape of the plate baffle and the seal between the baffle and the heat exchanger tube forces the production fluid to flow across the perimeter of the baffle assembly, between the edge of the baffle assembly and the inner surface of the pressure vessel 410.

As a result, the plate baffle assembly forces the production fluid to flow radially, outward from the longitudinal centerline of the heat exchanger and around the perimeter of the baffle.

Another embodiment of a baffle assembly promoting uniform production flow conditions is shown in FIG. 5, the baffle assembly comprising a pressure vessel 500 and an annular baffle assembly 502. The baffle assembly is sealingly disposed in the pressure vessel, the sealed baffle assembly comprising an upper tube sheet 504; a lower tube sheet 506 opposite the upper tube sheet; a heat exchanger tube 508 which connects the upper tube sheet and the second tube sheet; an annular baffle 510 disposed between the first tube sheet and the second tube sheet, wherein the heat exchanger tube passes through the annular baffle, the annular baffle has a first side 512 and an opposite second side 514, and the annular baffle has an annular shape, wherein the sealed baffle assembly is sealingly disposed 516 in the pressure vessel such that least 51% of fluid communication between the first side and the second side of the baffle is through the center region bounded by the inner diameter of the baffle annulus.

As shown in FIG. 6, the annular baffle 620 may be in the shape of an annulus with an inner perimeter 600 and outer perimeter 601. The inner diameter 600 and outer perimeter 601 can each independently have any suitable geometry, can be a rectilinear or curvilinear, and can have a circular shape, an elliptical shape, a lobular shape, a square shape, a rectangular shape, or any combination thereof. The heat exchanger tube passes through a hole 610 in the annular baffle. The baffle assembly may be secured to the pressure vessel using a fastener that passes through the hole 615 and is secured to a mounting flange on the pressure vessel wall.

The circumference of the annular baffles is designed to be disposed on the inner surface of the pressure vessel and may be sealed by a weld or gasket or unsealed and mounted to the pressure vessel at attachment points. The annular opening is a major factor in specifying the fluid pressure drop in that heat exchanger section. It has been discovered that the size of the annulus can be chosen so that the first 1-3 inner rows of heat exchanger tubes pass through the annulus. Thus, the dimensions of the annulus is determined by the pressure drop characteristics of the flow through the annulus, and not a fixed fraction of the baffle surface. For plate baffles, the diameter is typically selected so that the outermost tube row sealingly passes through the plate baffle.

The components comprising the annular baffle assembly may each independently comprise any suitable material, and may comprise a metal such as iron, aluminum, magnesium, titanium, nickel, cobalt, zinc, silver, copper, and an alloy comprising at least one of the foregoing. Representative metals include carbon steel, mild steel, cast iron, wrought iron, stainless steel (e.g., 304, 316 or 439 stainless steel), Monel, Inconel, bronze, and brass. Specifically mentioned is an embodiment in which the baffle assembly components are mild steel.

The annular baffle assembly is sealed to the inner surface of the pressure vessel to prevent production fluid flow in the gap between the annular baffle and the pressure vessel, thereby forcing the fluid across the inner perimeter of the baffle assembly and through the center region bounded by the inner diameter of the baffle annulus. The baffle assembly may be sealed to the pressure vessel in any suitable way, including welding the annular baffle to the pressure vessel inner surface, or sealing the gap using an adhesive.

In another embodiment, the annular baffle may be sealed to the inner surface of the pressure vessel using a gasket, as shown in FIG. 7. In this embodiment, the annular baffle assembly comprises a rigid annular baffle element 702, and a gasket 704 is disposed on a surface of the annular baffle and between the baffle and the pressure vessel 706, wherein the gasket 710 seals the baffle to the pressure vessel. The gasket may be secured to the annular baffle using an adhesive. Fluid flow in the space 712 between the heat exchanger tube 714 and the inner wall of the pressure vessel 706 presses the gasket material to the outer wall 710 of the heat exchanger tube 714, and also seals the annual baffle gasket 714 to the inner wall of the pressure vessel 706. A retainer 708 may also be used to secure the retainer to the annular baffle using adhesive or fasteners.

The gasket used to seal the baffle to the heat exchanger tubes may comprise an elastomer. Any suitable elastomer may be used. Specifically mentioned is an embodiment where the elastomer is an ethylene propylene diene terpolymer.

The retainer outer diameter is smaller than the plate baffle diameter so that the gasket protrudes 710 from the baffle assembly and contacts the inner wall of the pressure vessel 706, preferentially in the direction of the retainer. As a result, fluid pressure forces the gasket against the pressure vessel inner wall, promoting the seal. The shape of the annular baffle and the seal between the baffle and the pressure vessel forces the production fluid to flow across the inner perimeter of the baffle assembly annulus through the center region bounded by the inner diameter of the baffle annulus.

The annular baffle assembly may further be sealed to the heat exchanger tubes to prevent production fluid flow in the gap between the baffle and the tubes, thereby forcing the fluid across the inner perimeter of the annular baffle assembly. The baffle assembly may be sealed to the heat exchanger tubes in a variety of ways including welding the heat exchanger tubes to the annular baffle, or sealing the gap using an adhesive.

As a result, the annular baffle assembly forces the production fluid to flow radially, inward towards the longitudinal centerline of the heat exchanger and through the center region bounded by the inner diameter of the baffle annulus.

An another embodiment, the plate and annular baffle assembly can be used in conjunction to maintain a predominately radial flow pattern in the production fluid along the length of the fluid heating system heat exchanger.

An embodiment where the plate and annular baffles alternate along the length of the heat exchanger is further shown in FIG. 8. In this embodiment three annular baffles 802 alternate with two plate baffles 804. A plurality of heat exchanger tubes 806 are disposed between the heat exchanger top tube sheet 808 and the bottom tube sheet 810. The heat exchanger tubes sealingly pass through both types of baffles alternatively, and the annular baffles are sealed to the pressure vessel inner surface (not shown). The sequence of alternating plate baffles 804 and annular baffles 802 direct the production fluid flow radially through the plurality of heat exchanger tubes in six distinct flow regions of differing spacing, from narrow spacing near the heat exchanger top head in the region T₁ defined by the top tube sheet and the first annular baffle, to the region T₆ defined by the heat exchanger bottom sheet and the last annular baffle.

A perspective drawing of the embodiment shown in FIG. 9 where the plate and annular baffles alternate along the length of the heat exchanger to induce radial flow is shown in FIG. 9. Three annular baffles 802 alternate with two plate baffles 804. The heat exchanger tubes 806 sealingly pass through both types of baffles, and the annular baffles are sealed to the pressure vessel inner surface (not shown). As used herein, a plate baffle is a baffle that has a first side and an opposite second side, and wherein fluid communication between the first side and the second side is across a perimeter of the plate baffle. As used herein, an annular baffle is baffle that has a first side and an opposite second side, and wherein fluid communication between the first side and the second side of the annular baffle is through the annulus of the baffle.

The selection of the number of baffles, and the spacing between them is highly dependent on the performance and fluid desired for the product. The measure of optimality for this design process can be stated as: minimizing the fluid side pressure drop as the fluid moves from pressure vessel inlet to the outlet (subject to operational constraints, where larger pressure drops result in larger pumping requirements and overall reduction in system efficiencies once installed), while simultaneously minimizing the number and magnitude of local tube temperature outliers, subject to a given threshold temperature. Most often the temperature threshold selected is the vaporization temperature for the given fluid, at the given operating pressure, but can be selected based on any number of measures, durability or otherwise, including but not limited to material temperature limits, production fluid temperature limits, thermal stress limits, or any other suitable measure.

Variables important for the optimization of the baffle spacing, attachment and design geometry are many including, but not limited to: the production fluid viscosity, boiling point, density, specific heat, and thermal conductivity; the heat exchanger tube geometry, heat exchanger tube material; and the pressure drop constraints. Also important is the design flow rate of production fluid from the pressure vessel inlet to outlet which is often specified by a temperature change from the inlet to outlet, at a given heat input.

Standard heat exchanger design references recommend the minimum spacing between the baffles be 20% of the shell diameter. (Shah, Ramesh K., and Dusan P. Sekulic. “Fundamentals of heat exchanger design”, John Wiley & Sons, 2003.) In products with high heat flux, the flow velocity may be insufficient to keep the metals temperatures below the production fluid boiling temperature which creates an important constraint. Reducing the baffle separation distance does not solve the problem since the pressure gradient promotes the leakage flow rather than the main cross flow. Sealing the baffle provides an approach to exceed conventional design limits since it enables flow velocities and heat transfer coefficients required to avoid local boiling temperatures without the leakage side effects.

In an embodiment wherein the production fluid is a liquid (e.g., water, thermal fluid or thermal oil), the temperature difference between the pressure vessel inlet and outlet can be between 180 degrees centigrade (° C.), or 170° C., or 160° C., or 150° C., or 140° C., or 130° C., or 120° C., or 110° C., or 105° C., or 100° C., or 95° C., or 90° C., or 85° C., or 80° C., or 75° C., or 70° C., or 65° C., or 60° C., or 55° C., or 50° C., or 45° C., or 40° C., or 35° C., or 30° C., or 25° C., or 20° C., or 15° C., or 10° C. The temperature difference range 110° C. to 30° C. is specifically mentioned. Depending upon the geometric, thermal, fluid and material properties of the embodiment, the separation distance between baffle plates may be between 300 centimeters (cm), or 250 cm, or 200 cm, or 150 cm, or 100 cm, or 90 cm, or 80 cm, or 70 cm, or 60 cm, or 50 cm, or 40 cm, or 35 cm, or 30 cm, or 26 cm, or 24 cm, or 22 cm, or 20 cm, or 18 cm, or 16 cm, or 14 cm, or 12 cm, or 10 cm, or 8 cm to 6 cm, or 5 cm, or 4 cm, or 3 cm, or 2 cm, or 1.5 cm, or 1 cm, or 0.5 cm or 0.25 cm, wherein the foregoing upper and lower bounds can be independently combined. The gap distance range from 1.5 cm to 50 cm is specifically mentioned.

An optimum spacing can be determined for combinations of design variables and fluid properties. Computation Fluid Dynamic (CFD) numerical simulation can be used to design the baffle system and, in particular, the spacing between the baffle plates accounting for each of the design variables. For instance, a baffle set designed for a hydronic fluid heating systems with a 20 degrees Fahrenheit (° F.) temperature difference between the pressure vessel inlet and outlet, will have significantly different optimal spacing requirements than one designed for a 40° F. temperature difference, where the production fluid is glycol or a combined glycol and water mixture.

However, it has been unexpectedly discovered that the baffles can be arranged where the baffles are sealed to the tubes, or where the baffles are unsealed, with similar results at the beginning of life. Where the baffles are unsealed, the small amount of leakage flow where the heat exchanger tubes pass through the baffle holes acts to break up vortices and stagnant flow areas, whereas if the baffles are sealed, more baffles are required to ensure these areas of low, or cyclical flow are managed so as not to cause a durability issue.

Also surprising is the discovery that unsealed baffles have radically different performance characteristics over their life span. Specifically, the result can be a solution, which is indeterminate with respect to time. In other words, the system can be designed such that extreme changes in performance and symmetry can present themselves over time during the systems life in the field. Once a radial flow pattern has been selected, the system is inherently designed with a high degree of axial symmetry. During system operation, small amounts of debris tend to get caught in the gap between the baffle and the tube and corrosion material will build-up over time. A loss of leakage flow through a given baffle to tube space is irrelevant in a local sense; however, as the debris does not deposit symmetrically around the axis, the blocked local leakage flow can have a major impact on the flow symmetry which has a significant effect downstream in the heat exchanger.

The effects of symmetry on the dynamics and stability of fluid flow systems has been established in many engineering fields. (e.g., Holmes, Lumley, Berkooz and Rowley, “Turbulence, Coherent Structures, Dynamical Systems and Symmetry”, Cambridge Monographs on Mechanics, 2^nd Edition, Cambridge University Press, 2012.) In the case of unsealed baffles, when the flow symmetry surrounding the tubes and around the circumference of the plate baffles is broken where debris or corrosion material clogs the gaps, the production fluid flow is disrupted causing a new flow field and resulting temperature distribution. The perturbations in the flow and temperature fields can be dramatic, even for small changes in the geometry caused by particulate clogging of the gaps. In fact, this sensitive dependence upon flow conditions were observed during instrumented prototype testing where a single test rig would exhibit significantly different temperature field behavior from test to test as debris accumulated and sifted in the unsealed gaps. This sensitive dependence on the precise geometry of the gaps was eliminated by sealing.

New generation of hydronic boilers are more compact than the older boilers and have higher efficiencies. For example, the Fulton EDR+6000 has a foot print that is equal to almost one third of the Fulton Vantage 6000, both examples of state-of-the-art boilers in their eras. Both boilers have the same heat capacity. This means that same amount of heat is transferred from the fire side to the heat transfer fluid in a smaller surface area. This drives the surface heat fluxes up considerably, where heat flux is defined as the heat transferred per unit surface area (q″=q/A, where q″ is the heat flux, q is the total heat transferred in a time interval and A is the surface area across which the heat is transferred). A result of the increased heat flux is that the operational temperature at the fluid-metal interface(s) is higher.

Without being bound by theory or the specifics of a particular embodiment, consider the heat transfer fluid in hydronic (water) boilers at liquid phase. Those skilled in the art design the pressures and temperatures of hydronic boilers so that the fluid remains in liquid phase over the range of operations heat fluxes. An important consideration is that, with high heat fluxes in the new generation boilers, the temperature at the metal-water interface risks exceeding the boiling temperature of the fluid (water). If so, then local boiling at the boundary layer next to the wall becomes a factor, even if the average volumetric water temperature is well below the fluid boiling point.

Local boiling is detrimental to the boiler and may result in structural, mechanical and operational failure. Boiling leaves deposits on the hot metal surface. The deposit acts as an insulation and reduces the heat removal so the tube temperature keeps going up which causes more boiling and more deposit. The cascading effect eventually can drive metal and weld temperatures above the allowable service temperature and damage the boiler structure.

Moreover, as the boiler becomes more compact, the power density of the heat exchanger also increases, resulting in higher operational heat flux through the metal-fluid interfaces of the exchanger heat transfer surfaces. The heat generated at the gas (thermal transfer fluid) side must be absorbed at the production fluid (water) side fast enough so the metal temperatures do not exceed the boiling temperature.

While the rate of heat removal is a function of water temperature, velocity, and the thermo-physical are all important design properties, selection of water velocity is key to water management and avoiding local boiling. Baffles can be used to make the water in the heat exchanger move at a faster velocity and reach all heat transfer surfaces to ensure proper cooling. In such designs, varying the spacing between the baffles allows a designer skilled in the art to match the local water velocities to ensure operation within design limits. This increases the heat removal capacity of the water and keeps the metal temperatures below boiling temperature.

The inventors have unexpectedly discovered an effective procedure for approximately determining the operationally effective baffle spacing in a system of one or more baffles, and the procedure yields a deterministic solution (that is, the procedure results in efficient spacing that produces regular, deterministic temperature and flow conditions in the resulting production fluid flow under normal operating conditions) if the tubes are sealed to the baffles. The water velocities required for heat removal from the water side are high. This makes the baffle spacing at the critical locations very small. This creates a large pressure gradient between the top and the bottom of the baffle.

The tubes are corrugated and there are manufacturing tolerances on the baffle. Water could leak through the openings and bypass the main path. The leakage flow is usually negligible in large boilers but with a large pressure gradient between the top and the bottom of the baffle up to 60% of the flow could leak through the baffle and bypass the heat transfer areas. Thus, sealing the baffles is required to ensure deterministic flow velocities and direction.

The calculation procedure is iterative (like Newton's method) and entails four steps:

Step 1: The operational limits of the water baffle system as a subsystem in the heat exchanger are determined. In this step, the maximum allowable surface or mean metal temperature is determined and several factors may be significant. Typically, the limiting factor will be vaporization of the fluid being heated, which results in deposits which accelerate failure. Another possible limiting factor may be service temperature of the metal being used for the heat exchanger tubes.

Step 2. Determine fire (Transfer Fluid) side temperature profile, and heat transfer coefficient profile. Typically, this step is accomplished analytically, through fluid and heat transfer analysis techniques known to those skilled in the art of heat exchanger design and manufacture. To accomplish this objective, the heat exchanger is conceptually separated into segments, and a profile is determined applying standard methods within each segment. Once the system heat transfer coefficient profile is established, an estimate of the heat flux profile along the length of the heat exchanger can be determined. Since in a typical fuel fired boiler, heating water, the heat flux through the wall is strongly dependent on the flue side heat transfer coefficient, and only weakly dependent on the water side heat transfer coefficient, an estimated fixed water side heat transfer coefficient can be used for the initial analysis.

Step 3. This step involves the calculation of temperature and flow conditions for each baffle spacing in turn. Beginning at the hot end of the heat exchanger, for each baffle section determine the minimum water side heat transfer coefficient that would be sufficient to satisfy the metal temperature limits determined prior. Conceptually, the basic problem being solved is that of the composite wall, with fluid convection on either side, and a thin metallic (or others solid tube material) interface and can be represented as a thermal resistance diagram shown in FIG. 10.

The problem being solved is that of the composite wall, with fluid convection on either side, and a thin metallic (or others solid tube material) interface and can be represented as a thermal resistance diagram as illustrated in FIG. 10. The figure illustrates the conceptual framework for computing the baffle spacing, modeling the heat transfer from a bulk region of thermal transfer fluid 1002, across the solid heat exchanger tube wall material 1004, and into a region of bulk production fluid 1006. Electrical resistance provides useful theoretical analogue for the material resistance of heat transfer: In the region of thermal transfer fluid 1004, the resistance 1008 to heat transfer, R_t,tf, equals the inverse of the product of the heat transfer coefficient h_t,tf times the surface area A; in the region of heat exchanger tube wall material 1002, the resistance 1010 to heat transfer, R_t,w equals the wall thickness divided by the product of the heat transfer coefficient k_t,w times the surface area A; and in the region of heat exchanger tube wall material 1006, the resistance 1012 to heat transfer, R_t,pf equals the inverse of the product of the heat transfer coefficient h_t,pf times the surface area A. This model yields a temperature profile that is highest in the thermal transfer fluid bulk flow 1014; decreases near the tube wall and through the boundary layer to the tube wall outer surface 1016; decreases as energy is transferred through the tube material 1018 to the interface between the wall and the production fluid flow boundary layer 1020; and decreases to an average asymptotic value in the production fluid bulk flow 1022.

We can solve for a baffle spacing separation length iterative by assuming a production fluid side heat transfer coefficient, computing the resulting thermal flux conditions, and then updating the separation distance to meet the operation limit requirements defined in Step 1.

The thermal resistance presented by the thermal transfer fluid (e.g., combustion gas), the tube wall and the production fluid (e.g., liquid water), R_t,tf, R_t,w and R_t,pf respectively, can be calculated as:

R _t,tf=1/(k_t,tf·A)

R _t,w =t/(k_t,w·A)

R _t,pf=1/(h_t,pf·A)

where h_t,tf and h_t,pf are the heat transfer coefficients of the thermal transfer fluid and the production fluid, respectively, k_t,w is the conductivity of the tube wall, and t and A are the tube wall thickness and the surface area of the tube spanned by the baffle section under consideration, respectively. Empirically, it has been discovered that the length of the tube spanned by the baffle section should be chosen so that the local average temperatures of the thermal transfer fluid and the production fluid should not change substantially over the baffle section. A change of about one Kelvin over the length of the baffle section is specifically mentioned. Then the total thermal resistance to heat flux can be determined:

R _t,total =R _t,tf +R _t,w +R _t,pf

The total heat transfer for this baffle section is:

q=(1/R_t,total)·ΔT

where ΔT is the temperature gradient between the bulk of the transfer fluid and production fluid, and the total heat flux is given by:

q″=q/A

Knowing the heat flux and the target wall temperatures to avoid local the heat transfer coefficient of production fluid could be calculated to evaluate the initial assumption,

h _t,pf =q″/(T_surface−T_bulk,pf)

where q″ is the heat flux, T_surface is the target temperature to avoid boiling and T_bulk,pf is the bulk temperature production fluid.

If this computed value of the heat transfer coefficient does not match the assumed value, the assumed value is iteratively adjusted until convergence in h_t,pf is achieved.

Step 4. Determine the minimum production fluid velocity required. To determine the fluid velocity, a correlation based on the specific boiler geometry must be used, at the worst case point. For this example, the outer row (or two rows) of heat exchanger tubes will be the worst case, as the flow is radial, and this will be the point of minimum velocity. Thus, the outer two rows of tubes can be used and approximated by know correlations for a staggered tube bundle (Incropera, Frank P., et al. Fundamentals of heat and mass transfer. Wiley, 2007, pps. 438-440., which is incorporated herein by reference to the extent necessary to understand the present invention).

Using equations for tube flow and Reynolds number,

$V_{\mathrm{ma}x}=\frac{\mathrm{Nu}*\mu }{C*{{\mathrm{Pr}}^{0.36}\left(\frac{\mathrm{Pr}}{\mathrm{Prs}}\right)}^{0.25}*\rho *D}$

which can be solved for the mean flow velocity:

$V_{\mathrm{pf}}=\frac{\mathrm{St}}{\mathrm{St}-D}*V_{\mathrm{ma}x}$

Combining and rearranging for mean velocity,

$V_{\mathrm{pf}}=\frac{\mathrm{Nu}*\mu *\left(\mathrm{St}-D\right)}{C*{{\mathrm{Pr}}^{0.36}\left(\frac{\mathrm{Pr}}{\mathrm{Prs}}\right)}^{0.25}*\rho *D*\mathrm{St}}$

In these equations, Nu is the Nusselt number of production fluid, Pr and Prs are the Prandtl Number at the production fluid balk and surface temperature, respectively, ρ and μ are the density and viscosity of the production fluid and D is the tube diameter and St is the transverse pitch of the tube bundle. The coefficient C is a geometry factor that could be extracted from heat exchanger design tables such as Table 7.5 in the reference mentioned above.

Once the mean velocity is determined, the baffle separation distance can be computed. In case of radial flow, the area bounded by the circumference at the outermost tubes A_required, and the design flow rate of production fluid, {dot over (V)}_pf, are related:

$A_{\mathrm{required}}=\frac{{\stackrel{.}{V}}_{\mathrm{pf}}}{V_{\mathrm{pf}}}$

The baffle spacing is the required area divided by the circumference at the outermost tubes.

Steps 1 through 4 are then repeated and applied to the next baffle section. The thermal transfer fluid temperature used in the procedure for the next baffle section is the temperature at the termination of the prior baffle (i.e., hottest cross-section of the new region spanned by a baffle section).

To illustrate the procedure outlined above with an example, we can define an example hydronic fluid heating system comprising a tube-and-shell heat exchanger using combustion gases as the thermal transfer fluid. Then, in Step 1, an operational limit of 240 degrees Fahrenheit may be specified throughout the water baffle system to prevent local boiling on the water side under mild pressure.

In Step 2, approximately 3,000 W/m²K is a typical starting point. As a result, in a configuration where flue gas is traveling through 275 tubes, each of which is corrugated, at an excess air rate of 15%, the overall heat input equals 3,000,000 BTU/hr, and the unit is 96% efficient, with the water side conditions being 80 degrees Fahrenheit into the heat exchanger and 180 degrees Fahrenheit out.

In Step 3, the iterative procedure begins with the baffle section closest to the inlet (equivalently, the upper tube sheet). Then, incorporating the detailed design parameters,

	Flue Gas Temperature	2800 F.	(1811 K)
	Water Temperature	175 F.	(353 K)
	Thickness of the wall	0.049″
	Conductivity of the wall	16
	Tube diameter	0.5″
	Flue gas heat transfer coefficient	77.75
	in the first 0.25″ of the tube
	Design Flow Rate of Water	3.668 kg/s	(58.6 GPM)
	Design Water Inlet Temperature	80	(300 K)
	Design Water Outlet Temperature	180	(355 K)

Assuming in water side heat transfer coefficient estimate of 3,000 W/m²K,

R _t,total =R _t,tf +R _t,w +R _t,pf

R _t,total=0.338 K/W+0.0029 K/W+0.0334 K/W=0.3744 K/W

The heat transfer for this section is given by:

q=(1/R_t,total)*ΔT=(1/1.3306 K/W)*(1,811 K−353 K)=1096 W

q″=q/A=427,752 W/m²

Knowing the heat flux, we can determine the wall temperature from the basic heat transfer equations.

For this example, the desired metal temp is known, so we will solve for a new water side h_t,pf that would guarantee the desired temperature:

h _t,pf =q″/(T_surface−T_bulk,pf)=427,752(W/m²)/(389 K−353K)=11,982 W/m²K

At this point, it has been determined that original assumption of 3,000 W/m²K must be adjusted, and iteration of the steps with an updated heat transfer coefficient choice on the water side is repeated until convergence is reached (that is, h_t,pf doesn't change over with subsequent iterations).

After convergence the final value of the heat transfer coefficient is determined:

h _t,pf,final=10,000W/m²K

In Step 4, using standard equations for tube flow and Reynolds number,

$V_{\mathrm{pf}}=\frac{\mathrm{Nu}*\mu *\left(\mathrm{St}-D\right)}{C*{{\mathrm{Pr}}^{0.36}\left(\frac{\mathrm{Pr}}{\mathrm{Prs}}\right)}^{0.25}*\rho *D*\mathrm{St}}=0.1665\text{m/s}$

Once the velocity is known, the height can be computed:

A _required=0.022 m² yielding a height(baffle spacing of 0.0156 m or 0.6145 inches.

Thus, the separation distance for the first baffle section is 0.625 inches.

The 4-step iterative procedure is then be used for the next section. The flue gas temperature to be used would be the one at the termination of the prior baffle (i.e, hottest section of the new region to be baffled).

Computational fluid dynamics (CFD) software (for example, the CFD/FEA software packages by ANSYS or COMSOL) can also be used for determining the optimal spacing for the sealed tube radial flow design. Moreover, use of CFD methods permits the analysis of local temperature and flow conditions in the sealed baffle system that the analytical procedure above based on macroscopic parameters does not permit.

For instance, each tube blocks some portion of flow, which must navigate around the tube. The path that flow takes, and the resulting eddies and turbulence formed, will be dependent on the specific geometry, as well as nearby geometries (i.e., other tubes, fasteners, baffles, etc.).

The exact details of the geometry can lead to result which differ from the first principles look taken previously. This difference can lead to either better thermal performance than expected (which could perhaps lead the designer to space the baffles slightly further apart, resulting in lower production fluid side pressure drop, which is advantageous to the market) or worse than expected (which could lead the designer to shrink the baffle spacing slightly to account for local outliers).

That said, the four-step analytical procedure defined above provides a very effective approach to determining initial geometry for a detailed analysis using CFD methods.

The general procedure for baffle spacing determination using CFD methods is:

Step A: Utilize the analytical baffle spacing process defined above to generate CFD model initial geometry.

Step B. Solve the temperature and flow conditions for the thermal fluid side of the heat exchanger tube operating conditions. Several options exist including: (i) Utilize the same relationships as defined above to set the heat flux through the wall; (ii) Utilize CFD to simultaneously solve the Transfer Fluid side and the Production Fluid Side heat transfer characteristics and temperatures; (iii) Use some iterative combination of both approaches to determine the Thermal Transfer Fluid side temperature and heat flux profile.

Step C. Calculate the thermal transfer fluid wall temperature. In this step, CFD software is used to predict the fluid flow and heat transfer throughout the baffle system.

Step D. Identify local areas of high and low temperature and stagnant flow.

Starting at the top of the heat exchanger, identify locations which exceed the desired material temperature. Determine by what amount the velocity needs to increase in this region (use methods from original baffle spacing work), then adjust the bottom baffle (and all subsequent baffles, so that those spacings are held constant) up by the desired change

Starting at the top of the heat exchanger, identify locations which have suitable metal temperatures, but may have too much pressure drop. Determine by what amount velocity can be allowed to decrease (use methods from original baffle spacing work), then adjust bottom baffle (and all subsequent baffles, so that those spacings are held constant) down by the desired change.

Step E. Iterate on baffle spacing adjustments. Once adjustments have been made to all baffles, run the simulation model until the temperature and flow conditions meet all the operating requirements and local areas of excessive temperature and stagnant flow are eliminated. Results will be iterative, as adjusting any given baffle up or down changes the temperature profile applied to that segment.

One feature of the present disclosure is that, in exchanger systems where baffle sealing is used between the baffle elements (e.g., plate and annulus elements), the above procedures yield a deterministic solution for optimal spacing between the baffle elements.

A second feature, surprisingly discovered by the inventors, is that the deterministic optimized spacing procedure typically yields a baffle spacing that is uneven—that is, the spacing between baffle elements is not equal from element to element from the entrance of the thermal transfer fluid inlet to the thermal transfer fluid outlet. This unequal spacing optimally accommodates the temperature gradient along the fluid path.

As the thermal transfer fluid moves through the heat exchanger from the heat exchanger inlet to the outlet, heat it transferred from the thermal transfer fluid (e.g., hot combustion gas) to the production fluid (e.g., water or oil) across the thermal transfer surfaces. As a result, the temperature of the thermal transfer fluid decreases as it moves towards the outlet (or exhaust, in the case of combustion gas).

In an efficient fluid heating system (or boiler) the outlet temperature of the thermal transfer fluid is very close to the inlet temperature of the production fluid. In typical embodiments for commercial or industrial applications, the temperature of the thermal transfer fluid may drop 1,500 Kelvin while the production fluid gains less than 56 Kelvin.

At the locations close to the inlet of the thermal transfer fluid the temperature gradient between the thermal transfer fluid and the production fluid is the highest as illustrated in FIG. 11. The temperature gradient drops sharply 1102 as the fluid approaches the outlet of the thermal transfer fluid. This implies that higher heat transfer coefficients are required at locations closer to the thermal transfer fluid inlet compared with the outlet. Therefore, to maintain even temperature distributions and prevent excessive local heating conditions that could impair system performance (e.g., local boiling) and mechanical longevity (e.g., prevent material fatigue, corrosion and thermal stresses), higher velocities and tighter baffle spacings are required closer to the thermal transfer fluid inlet compare to locations nearer the outlet where, near the outlet, the rate of change in temperature 1104 slows as the temperature gradient is smaller. The temperature profile shown in FIG. 11 is juxtaposed with the baffle spacing shown in FIG. 8 to illustrate this point, although this is only one specific example of the general principle.

Thus, baffle spacings are typically tighter at the top of the boiler and it becomes wider at the bottom part of the boiler. This effect is most pronounced in baffle section near the hot inlet end; for baffle sections closer to the outlet end of the heat exchanger, the moderate temperatures and flows permit one skilled in the art design flexibility to address other objectives—such as desirable flow properties near the lower tube sheet or cost constraints—since tolerances needed to respect the temperature thresholds are less stringent and more easily achieved. This means that—far from the inlet end—strict adherence to an increasing pattern of spacing may be relaxed to safely meet other design objectives. As a result, baffle spacing patterns where the distal spacing is relaxed to equal spacing—or even narrower spacing at the distal end such as that shown in FIG. 8—are contemplated and claimed in the present disclosure.

As is discussed above, an advantage of the disclosed system is that it can provide a more uniform production fluid flow field which is predominately radial, minimizing areas of high temperature that are understood to cause material failures, fluid boiling, and loss of thermal efficiency. The disclosed baffle assembly and heat exchanger provides for improvement in the management of production fluid flow of fluid heating systems and heat exchangers that enable greater compactness, reliability and performance in these systems.

However, it has further been unexpectedly discovered that methods for reducing the size of fluid heating systems incorporating shell-and-tube heat exchangers achieved by increasing the bulk heat flux can exacerbate issues created by the non-uniform temperatures. Areas within the heat exchanger where heat is concentrated can lead to material failures, corrosion, and fouling. Where the temperature exceeds the boiling point of the production fluid, adverse effects may accumulate, particularly near structural joints or cracks that precipitate a production fluid phase change.

A fundamental objective in the design of a compact tube-and-shell heat exchanger for a fluid heating system is to determine an arrangement of a specific number of heat exchanger tubes in the smallest cross-sectional area while ensuring a production fluid temperature distribution that is as close to uniform as possible within prescribed design limits. Since the temperature distribution is partly determined by the production fluid flow field, in practical terms this means determining a tube arrangement and flow field so that the flow velocities in each fluid control volume around the heat exchanger tubes ensures a uniform opportunity for heat transfer. Regions where the flow velocity is too low (or where it may re-circulate) produce areas of high temperature since the dwell time near the heat exchanger tubes are too long, while regions where the flow velocity is too high implies too little time for heat transfer to occur across the heat transfer surfaces to the production fluid. Additionally, opportunities for the flow to go around heat exchanger elements, allowing for little or no exchange, rob flow from areas which need it. Different tube pattern geometries produce different production fluid flow patterns and velocity fields, and an important objective is to choose tube distribution patterns that, for a prescribed number of tubes, result in a relatively uniform cross-sectional temperature field produced by a flow field through an optimally-compact the tube arrangement that minimizes “hallways” (areas of high-velocity fluid flow resulting in incomplete heat-transfer) and stagnation zones (regions of low-velocity flow resulting in excessive temperature buildup).

Disclosed is a pattern for tube layout which is “staggered” relative to the direction of flow. Tube spacing is defined as the center-to-center arc length separation of consecutive tubes in the same radial row. Tube stagger is defined as the fraction of the tube spacing between two consecutive tubes that the tube centers are shifted in the same row where a tube stagger of zero indicates no shift and a tube stagger of one indicates that the row is shifted the full length of the tube separation distance. For the purposes of designing heat exchanger tube distribution patterns relative to the face of the tube sheets, the range of tube stagger is 1.0, or 0.99, or 0.98, or 0.97, or 0.96, or 0.95, or 0.94, or 0.93, or 0.92, or 0.91, or 0.90, or 0.85, or 0.80, or 0.75, or 0.70, or 0.65, or 0.6, or 0.55 to 0.5, or 0.45, or 0.4, or 0.35, or 0.3, or 0.25, or 0.20, or 0.15, or 0.10, or 0.09, or 0.08, or 0.07, or 0.06, or 0.05, or 0.04, or 0.03, or 0.02, or 0.01, or 0.00 wherein the foregoing upper and lower bounds can be independently combined. The range from 0.0 to 1.0 is specifically mentioned. The range from 0.01 to 0.99 is also specifically mentioned. The range from 0.1 to 0.9 is also specifically mentioned. In a symmetrical pattern, this means that a line connecting the centers of all tubes in a given row is perpendicular to the flow, and that each subsequent row is offset by a tube stagger, for example, one-half the tube spacing. Thus the passage between two consecutive tubes in a given row is all or partially occluded by another tube in the direction of the production fluid flow. This provides an improved amount of flow impingement and turning, which is responsible for enhancing turbulence, and raising heat transfer coefficients.

Furthermore, the magnitude of this effect is dependent upon constraints created by the tube diameter, the tube spacing, and the row spacing, and additionally can be quantified in terms of ratios of those parameters.

Heat exchangers which rely on cross flow can be rectangular in shape. However, there is an advantage in arranging heat exchangers into circular cross sections, as this allows the exchanger to exist within a shell of circular cross section. Having a shell with a circular cross section is not only labor and material efficient for construction, but it allows the shell to hold more pressure than flat planes arranged into a rectangular section and can have more compact overall physical dimensions.

Cross flow in circular sections is more challenging, as the flow needs to distribute as it makes its way across a tube bundle, then contracted again on the other side, as the chord which defined the flow area changes length as one moves across the diameter of a circle. This tends to create flow imbalance.

Methods for promoting a uniform velocity field within the flow of production fluid through the pressure vessel promote a uniform temperature distribution and efficient exchange of thermal energy across the walls of the heat exchanger tubes. Towards this end, it has also been unexpectedly discovered that radial and spiral flow of production fluid through the collection of heat exchanger tubes is effective at promoting a uniform, distribution of temperature and flow velocity within the heat exchanger. Radial flow of the production fluid can be arranged by design in a fluid heating system using arrangements of baffles that cause the flow to alternate between inward-directed radial flow towards the longitudinal axis and outward-directed radial flow towards the pressure vessel inner wall.

In preferable arrangements, which direct the flow radially, the flow can either be radially inward, or radially outward. As used herein, the term radially inward means that the fluid flow is from an outer edge of the tube arrangement inward towards a center point of the tube arrangement; and the term radially outward means that the fluid flow is from a center point of the tube arrangement outward towards an outer edge of the tube arrangement. In such cases the “flow area” is defined by the height of a section, and the circumference at each point. The typical staggered tube arrangement known to those skilled in the art of boiler and heat exchanger design are difficult to implement, as each row contains a different number of tubes.

Furthermore, the staggered tube arrangement typically results in “hexagonally shaped” patterns. These Hexagonal patterns, when placed in a radial flow arrangement, create alternating sections of aligned tubes, and staggered tubes. The result is that the pressure drop is not equally distributed among all radii, and thus most of the flow will proceed through the “aligned” sections, resulting in inefficient heat transfer overall, and more specifically the unit will experience high temperature zones on certain tubes, which could ultimately lead to heat exchanger failure.

Useful and novel methods for inducing radial production fluid flow in a heat exchanger and fluid heating system are described in the U.S. Provisional Application Ser. No. 62,281,534, filed on Jan. 21, 2016, “Baffle Assembly for a Heat Exchanger, Heat Exchanger Including a the Baffle Assembly, Fluid Heating System Including the Same, and Methods of Manufacture Thereof,” the content of which is incorporated herein by reference in its entirety. U.S. Provisional Application 62/281,534 describes methods for inducing radial production fluid flow using alternating plate and annular baffles.

The capacity of the fluid heating system is total heat transferred from the thermal transfer fluid to the production fluid under standard conditions. By convention, when the production fluid consists of a liquid (e.g., water, thermal fluid, or thermal oil) the capacity is expressed in terms of British thermal units per hour (BTU/hr); and when the production fluid comprises a gas or vapor (e.g., steam) the standard unit of measurement is expressed in horsepower (HP). In an embodiment wherein the production fluid is a liquid (e.g., water, thermal fluid or thermal oil), the capacity of the fluid heating system may be between 100,000 BTU/hr, or 150,000 BTU/hr, or 200,000 BTU/hr, or 250,000 BTU/hr, or 300,000 BTU/hr, or 350,000 BTU/hr, or 400,000 BTU/hr, or 450,000 BTU/hr, or 500,000 BTU/hr, or 550,000 BTU/hr, or 600,000 BTU/hr to 50,000,000 BTU/hr, or 40,000,000 BTU/hr, or 30,000,000 BTU/hr, or 20,000,000 BTU/hr, or 15,000,000 BTU/hr, or 14,000,000 BTU/hr or 13,000,000 BTU/hr, or 12,000,000 BTU/hr, or 10,000,000 BTU/hr, 9,000,000 BTU/hr, 8,000,000 BTU/hr, or 7,000,000 BTU/hr wherein the foregoing upper and lower bounds can be independently combined.

As is further discussed above, an advantage of the alternating plate and annular baffle system is that it can provide a more uniform production fluid flow field which is predominately radial, minimizing areas of high temperature that are understood to cause material failures, fluid boiling, and loss of thermal efficiency. The disclosed baffle assembly and heat exchanger provides for improvement in the management of production fluid flow of fluid heating systems and heat exchangers that enable greater compactness, reliability and performance in these systems.

It has been unexpectedly discovered that certain heat exchanger tube arrangements further promote the generation of uniform flow velocity and temperature fields in predominately radial production fluid flows. In contrast, it has been further discovered that conventional tube arrangements known to those skilled in the art of heat exchanger and boiler design: (a) are unable to fully exploit the benefits of radial production fluid flow, particularly where induced by alternating plate and annular baffle systems; (b) create extended hallways in the pressure vessel flow field where radial flow of production fluid does not impinge on heat exchange surfaces for significant distances, degrading the bulk heat transfer and creating regions of high-velocity flow; and, (c) fail to optimize the packing density of heat exchange surfaces within compact heat exchanger volumes.

In radial production fluid flows induced by alternating plate and annular baffle systems, regions of lower fluid velocity are located near the perimeter of the upper and lower tube sheets and the baffle assemblies; that is, in areas of the flow that are radially further from the heat exchanger longitudinal centerline. Conversely, regions of higher fluid velocity are located radially closer to the heat exchanger longitudinal centerline.

Standard tube configuration methods distribute the heat exchanger tubes in regular patterns; for example, in configurations where adjacent tubes are organized in equilateral triangles or squares, which produce regular polygonal configurations. Moreover, methods that produce regular polygonal tube configurations ignore the predominately circular symmetry of the fluid flow, leaving vertices and edges in the tube arrangements that cause local irregularities in the flow, temperature and velocity fields.

Disclosed is a method for optimizing the heat exchanger tube configuration that provides for one or both of: (a) capitalizes the advantages of production fluid radial and spiral flow and the structural tube configurations that result from applying the method; (b) reduces or eliminates extended straight, or nearly straight, paths (“hallways”) in the production fluid flow field near the heat exchange surfaces; improve or optimize the packing density of heat exchange surfaces within a design boundary for the collection of heat exchanger tubes. One aspect of the method and resulting tube configurations is that they are approximately circularly symmetric; that is, tubes are approximately configured in concentric rings relative to the heat exchanger longitudinal centerline. Tubes within a ring of diameter, D, relative to the longitudinal centerline are separated by a fixed radial tube Separation Angle (RA). The Separation Angle can be 0 to 180 degrees, or 1 to 179 degrees, or 1 to 90 degrees.

A second aspect of the disclosed method and the resulting tube configurations is that the tube arrangement is dense at radial distances further from the centerline and the tube density is sparse along the centerline.

A third aspect of the disclosed method and the resulting tube configuration is that the tube arrangement is staggered between adjacent rings. This ensures that radial fluid streamlines cannot travel far without impinging upon a heat transfer tube, thereby improving heat transfer, overall thermal efficiency and producing a more uniform radial flow and temperature field. This is accomplished by staggering tubes on adjacent rings, for example, from a first ring to an adjacent ring. More precisely, if T_k(i) denotes the i^th tube center on the k^th tube ring located at a distance D_k/2 from the centerline (for 1≤i≤N_k, where N_k is the number of tubes on ring k), then the radial angle between T_k(1) and T_k-1(1) is the Index Angle for the k^th row, (IA_k). Alternatively, this is equivalent to rotating the k^th ring relative to ring k−1 by a ring-specific angle, IA_k. The Index Angle can be 0 to 180 degrees, or 1 to 179 degrees, or 1 to 90 degrees.

A fourth aspect is that the disclosed method and resulting tube pattern improves or optimizes the packing density of the tube collection within a prescribed design boundary. This promotes increased bulk heat transfer of a compact heat exchanger. There are four, sometimes competing, measures of optimality.

Firstly, the alignment of tubes provides a measure of optimality measures how close to a staggered arrangement a given tube is, as compared to the two closest tubes in the next row. In a radial flow pattern, we can assume that the two closet tubes in the next row are simply the next two closest tube along the flow path, and do not necessarily need to be arranged in concentric rings, although the pattern presented here is indeed arranged on concentric rings.

Secondly, row-wise optimality is an indicator of how many consecutive rows, along one, or a narrow band of radii have low scoring staggering of the tubes. This seeks to ensure that tubes don't align to provide a single “hallway” which allows flow imbalance.

Thirdly, optimality of the stagger (or aligned) pattern provides a measure of optimality of the stagger pattern. Heat transfer is largely governed by Nusselt number, Nu, which, when evaluating Nu over a bank of tubes, the solution takes the form Nu=1.13 C1 Re^mPr^1/3. Evaluations of C1 and m have been conducted in academia, and tabulated results are available, and determined by two ratios: (a) SL/D, which is the ratio of distance between tube rows divided by the diameter of the tube, and (b) ST/D, which is the ratio of the tube spacing along a row divided by the diameter. There exists optimum combinations of both parameters. In general increasing SL will always result in lower values for C1. The effect of ST is less linear, and depends largely on the SL selected.

Fourthly, the packing fraction provides a measure of tube layout concerns packing fraction, or packing density, and is a measure of how many tubes can be fit inside a given area, specifically in this case, an area defined by a circle. Said another way, how large a circle is required to encompass all the tubes in a given tube bundle. In practical applications, the packing density must accommodate some of the constraints, calculated using the diameter of the tube, plus the minimum ligament distance, so that the packing fraction represents the full element size, with constraints, as opposed to being penalized for manufacturing considerations. Here, the meaning of “ligament distance” (or “ligament”) is the clearance required from the heat exchanger tube outside surface to allow for the structural attachment of the tube to the tube sheet (e.g., the clearance for a weld joint.).

The inventors have discovered a tube pattern and a method for specifying the pattern provided the required heat exchanger and boiler physical and performance requirements that is ideally suited for radial flow, in which the baffles which direct the flow exterior to the tubes are arranged such they direct the flow first from the center outward, in a radial sense, and then from the outer perimeter to the center in a radial sense.

Tube patterns for this flow regime need to provide roughly equal flow resistance across all radius line, in order to ensure that flow is balanced. In one embodiment, a tube pattern which is ideal for this flow consists of: (i) A plurality of N tubes are arranged in k concentric rings; (ii) the diameter of the tubes can be expressed as D; (iii) the minimum space between tubes is the ligament, and is expressed as l; (iv) the number of rings, k, is determined such that there is D+1 distance between the rings, guaranteeing that there will be at least l distance between any tubes in consecutive rings which land on the same radius line; (v) the distance from any tube on the outermost ring to the edge of the tube sheet is expressed as c; (vi) the tube sheet diameter can be expressed as D_t. The outermost ring diameter can then be determined by D_t−D−2*c; (vii) all subsequent rings are then fully determined. Ring diameters can be expressed as RD_k, where k indicates the ring number, with the first ring being the innermost ring; (viii) the maximum number of tubes on a given row is determined π*RD_k/(D+1). This value should be rounded down to the nearest whole number, so as not to compromise the ligament distance; (ix) one tube in each row is arbitrarily considered the “first tube”. Each first tube can be “clocked” by a number of degrees, a, as compared to horizontal plane when looking at a tubesheet. The maximum change in orientation is determined by the angle formed by two consecutive tubes in a single row; finally, each row of tubes is clocked by some ak until optimality constraints are met or exceeded.

The number of tubes can vary, according to the design requirements, from 50 tubes to 1,000 tubes, or 75 tubes to 750 tubes, or 150 tubes to 600 tubes. The number of rings can be 2 rings to 100 rings, or 10 rings to 50 rings, or 5 rings to 20 rings. The tube diameter can vary from 0.5 cm to 30 cm, or 1 cm to 20 cm, or 1.25 cm to 6 cm. The diameter of the tube sheet can be 10 cm to 400 cm, or 20 cm to 200 cm, or 35 cm to 120 cm.

The circumference of the annular baffles is designed to be disposed on the inner surface of the pressure vessel and may be sealed by a weld or gasket (sealingly attached) or unsealed and mounted to the pressure vessel at attachment points. The annular opening is a major factor in specifying the fluid pressure drop in that heat exchanger section. It has been discovered that in typical embodiments the size of the annulus is appropriately chosen so that the first 1 to 3 inner rows of heat exchanger tubes pass through the annulus. Thus the dimensions of the annulus can be determined by the pressure drop characteristics of the flow through the annulus, and not a fixed fraction of the baffle surface, using methods known to practitioners skilled in the art. For plate baffles, the diameter is typically selected so that the outermost tube row sealingly passes through the plate baffle.

FIG. 12 shows a flow diagram for computing the tube Separation Angle (RA) and Index Angle (IA) for a tube configuration of concentric rings (indexed by the subscript, k). The method uses as input the design diameter, D_t, of the tube configuration; the required gap, GAP, between the design diameter and the first (outermost) tube ring, the tube element clearance diameter which limits the closest separation distance between two adjacent tubes in a ring, CD_k, required for each ring, k, of tubes; and a rounding threshold, RT, to be applied to the tube count to obtain integer values in the numerical rounding process.

The basic method involves three steps The basic geometrical constraints of the tube pattern required given the heat exchanger dimensions 1200 are used in an iterative process 1202, beginning with the outermost ring: (a) The tube count 1204 for the particular ring is calculated, and rounded either up 1208 or down 1210 to an integer based on the residual; (b) The actual ring diameter is calculated based on the revised ring count and whether the count was rounded up 1212 or down 1214; and (c) the ring tube separation angle 1216 and index angle 1218 are calculated.

An embodiment of tube configuration that results from the method detailed in FIG. 12 is shown in FIG. 13. The heat exchanger tubes within ring k are centered in a region defined by the clearance diameter, PD_k, defined as diameter of the tube plus the Clearance (equivalently, ligament) which is the straight-line distance from tube edge to tube edge (OD). Tubes within a ring are separated by the ring separation angle, RA_k, and are non-overlapping, for example, tubes 1300 and 1310 are located in an outermost ring and are separated by ring separation angle RA₁. The Radial Separation Angle varies from 0.1 degrees (0.1°), or 0.2°, or 0.3°, or 0.4°, or 0.5°, or 1°, or 2°, or 3°, or 4°, or 5°, or 6°, or 7°, or 8°, or 9°, or 10° to 180°, wherein the foregoing upper and lower bounds can be independently combined. The Radial Separation Angle Range of 0.5° to 180° is specifically mentioned. Tubes in two adjacent rows, k and k−1, are staggered rotating the two rings relative to each other by the ring-specific Index angle, IA_k, for example, tubes 1320 and 1330 in ring 2 are separated from tubes 500 and 510 in ring 1 by Index angle IA₂ and Index angle IA₂, respectively.

FIG. 14 shows a plate baffle with a tube configuration produced using the method detailed in FIG. 12. The baffle is secured to the pressure vessel using mounting flanges 1410 held into position by fasteners. The heat exchanger tube apparatus includes 274 heat exchanger tubes 1400 arranged in nine concentric rings (1≤k≤9). In the outermost tube ring, each pair of adjacent tube centers are separated by a fixed, ring-specific separation angle; the ring separation angle for the outermost row (RA₁) is shown.

Improvement of the flow and temperature characteristics due to the optimized staggered tube configuration can be analyzed using computational fluid dynamic (CFD) simulation. FIG. 15 shows a CFD simulation under typical operating conditions for a hexagonal tube configuration. Note the region of high velocity 1500 located near the longitudinal centerline 1502. A characteristic of many tube pattern distributions with regular geometries is that they create fluid flow paths (alternatively, channels, or corridors, or hallways) that are relatively unimpeded by heat exchanger tubes. Along these corridors, local fluid velocity may be high and the efficiency of heat transfer from the thermal transfer fluid (e.g., combustion gas) to the product fluid (e.g., water or oil) degraded, particularly where such patterns are applied to the radial flow created by the alternating plate and annulus design. The hexagonal heat exchanger tube pattern shown in FIG. 15 shows this characteristic disadvantage since a corridor, C, is created by each pair of adjacent tube rows.

CFD simulation under the same operational conditions using a staggered tube configuration produced by the method detailed in FIG. 12 is shown in FIG. 16. Note the more spatially uniform velocity distribution 1600, particularly near the longitudinal centerline 1602.

Presented below are non-limiting examples of the present disclosure.

EXAMPLES

Example 1

Two fluid heating systems with alternating annular and plate baffles configurations were constructed and instrumented based on the embodiment illustrated in FIG. 9 for the purpose of comparing the advantages of sealing the baffles to the heat exchanger tubes and pressure vessel compared to leaving these areas unseal and allowing flow the gaps formed between these structures.

The first of the two fluid heating test systems comprises a heat exchanger with five baffle plates and 275 heat exchanger tubes in a boiler that is supplied with a heat input of 3 million BTU/hr. The production fluids tested were water and various mixtures of water and glycol. The gaps formed between the openings in the baffles where the heat exchanger tubes penetrate the baffles were between 0.0 cm (contact surfaces) and 0.5 cm and were unsealed, allowing a flow of production fluid through the gaps.

The first (unsealed) fluid heating test system was instrumented with thermocouples at various positions in each region, T₂ through T₅ shown in FIG. 9, between the set of five baffles to measure the evolution of production fluid temperatures over time as the test units were operated under installed conditions. The system was operated under normal installation conditions for 118 days and the temperatures at each of the measurement points was recorded at the beginning and end of the test period. The second and third columns of TABLE 1 show the results. For each fluid region, the average of the temperature difference range from the beginning to the end of the test period is shown, together with the standard deviation of the temperature ranges measured. These data provide a measurement of the average temperature deviation of the test period together with the variance of the temperature deviations. These data show large variations in the temperature measurements over the test period, due to the accumulation of debris and corrosion in the unsealed gaps between the baffles and heat exchanger tubes which changes the production fluid flow pattern over (relatively short) time periods away from the target design conditions.

The second of the two fluid heating test systems comprises a heat exchanger with seven baffle plates and 275 heat exchanger tubes in a system configuration that is supplied with a heat input of 3 million BTU/hr. Heat exchanger tubes pass through the alternating sequence of plate and annular baffles assemblies, sealed by gaskets and held in place by retainers as shown in previously described embodiments. The production fluids tested were water and various mixtures of water and glycol. The gaps formed between the openings in the baffles where the heat exchanger tubes penetrate the baffles were between 0 cm (contact surfaces) and 0.3 cm and were sealed, preventing the flow of production fluid through the baffle plates where the heat exchanger tubes sealingly pass through the baffles.

The second (sealed) fluid heating test system was instrumented with thermocouples at various positions in each region, T₂ through T₅ shown in FIG. 8, between the set of seven baffles to measure the evolution of production fluid temperatures over time as the test units were operated under installed conditions. The system was operated under normal installation conditions for 16 days and the temperatures at each of the measurement points was recorded at the beginning and end of the test period. The fourth and fifth columns of TABLE 1 show the results. For each fluid region, the average of the temperature difference range from the beginning to the end of the test period is shown, together with the standard deviation of the temperature ranges measured. These data provide a measurement of the average temperature deviation of the test period together with the variance of the temperature deviations. These data reduced variations in the temperature measurements over the test period, since debris and corrosion can no longer accumulate in the gaps between the baffles and heat exchanger tubes. As a result, the production fluid flow pattern over is stabilized at or near the target design conditions.

	TABLE 1
	Fluid Heating Test System 1	Fluid Heating Test System 2
	(Unsealed Gaps)	(Sealed Gaps)
		Std. Dev.		Std. Dev.
Test	Average Temp	Of Temp	Average Temp	Of Temp
Region	Range (° F.)	Range (° F.)	Range (° F.)	Range (° F.)
T2	4.8	2.0	2.9	1.8
T3	21.3	13.4	3.4	1.2
T4	15.2	6.9	6.4	4.3
T5	7.0	3.9	11.5	8.5

Example 2

A computational fluid dynamics (CFD) simulation of the fluid heating system prototype shown in FIG. 9 was performed.

	Operating Conditions:
	Input:	3,000,000 BTU/hr	(878.4 kW)
	Inlet Temperature:	80° F.	(26.6° C.)
	Outlet Temperature:	180° F.	(82.2° C.)
	Geometry:
	Tube Length:	40 inches	(1.016 m)
	Tube Outside Diameter:	0.5 inches	(12.7e−3 m)

Number of Tubes	275
Inlet Inside Diameter:	4 inches	(1.016e−1 m)
Pressure Vessel Inside Diameter:	23.5 inches	(5.969e−1 m)
Baffle Spacing:	2, 5, 8, 8, 8, 9 inches
Plate Baffle Diameter:	19⅝ inches	(4.985e−1 m)
Annular Baffle Inside Diameter:	6⅛ in	(1.555e−1 m)
(Annulus Outside Diameter Equals
Pressure Vessel Shell Inside
Diameter)

FIG. 17 shows the approximately uniform flow velocity field 1700 generated by the radial flow across an annular baffle using the staggered ring heat exchanger tube pattern

Example 3

A computational fluid dynamics (CFD) simulation of the fluid heating system prototype corresponding to FIG. 8 was performed.

	Operating Conditions:
	Input:	3,000,000 BTU/hr	(878.4 kW)
	Inlet Temperature:	80° F.	(26.6° C.)
	Outlet Temperature:	120° F.	(48.9° C.)

In this simulation, the separation distance between the heat exchanger top sheet and the first baffle plate (forming the region T₁ in FIG. 8) was varied to illustrate the changes in production flow field uniformity as a function of baffle separation distance.

For these design parameters, when the separation between the top sheet and the first baffle was set to 0.75 inches, the flow field shows a pronounced region of reduced flow velocity near the centerline. FIG. 18A shows the flow temperature field, and FIG. 18B shows the flow velocity field, for a simulation with the same geometry and operating conditions, but the separation between the top sheet and the first baffle has been increased to 1.25 inches. At this increased separation distance, the flow field is more uniform including the flow velocity near the centerline 1810. A design objective is to minimize the separation distance while achieving a relatively uniform flow field across the face of the baffle. In many cases the uniformity of flow must be weighed against the specific temperature needs of the tubes in that flow region. As a result, either spacing could be considered “optimal” pending the specific case in question.

Example 4

A computational fluid dynamics (CFD) simulation of the fluid heating system prototype shown in FIG. 9 was performed using the baffle spacing CFD method described above.

Operating Conditions:
Input:	3,000,000 Btu/hr	(878.4 kW)
Inlet Temperature:	80 F.	(26.6 C.)
Outlet Temperature:	180 F.	(82.2 C.)
Geometry:
Tube Length:	40 inches	(1.016 m)
Tube Outside Diameter:	0.5 inches	(12.7e−3 m)
Number of Tubes	274
Inlet Inside Diameter:	4 inches	(1.016e−1 m)
Pressure Vessel Inside Diameter:	23.5 inches	(5.969e−1 m)
Baffle Spacing:	2, 5, 8, 8, 8, 9 inches
Plate Baffle Diameter:	19⅝ inches	(4.985e−1 m)
Annular Baffle Inside Diameter:	6⅛ in	(1.555e−1 m)
(Annulus Outside Diameter Equals
Pressure Vessel Shell Inside
Diameter)

FIG. 19 shows the nearly uniform flow velocity field at the topmost (T₁) section generated by the alternating sequence of plate and annular baffles.

Set forth below are non-limiting embodiments of the present disclosure.

An embodiment is disclosed with a baffle assembly comprising: a first tube sheet; a second tube sheet opposite the first sheet; a heat exchanger tube, which connects the first tube sheet and the second tube sheet; and a baffle disposed between the first tube sheet and the second tube sheet, wherein the heat exchanger tube passes through the baffle; wherein the baffle is a plate baffle, and wherein the plate baffle has a disk shape, an elliptical shape, a lobular shape, a square shape, a rectangular shape, a rectilinear shape, or a curvilinear shape, or any combination thereof; wherein the baffle has a disk shape; wherein the baffle has a first side and an opposite second side, and wherein fluid communication between the first side and the second side is across a perimeter of the baffle; wherein a maximum distance between an outer surface of the heat exchanger tube and the baffle is between 0 centimeters and 3 centimeters; wherein the sealed baffle assembly comprises a plurality of heat exchanger tubes, and wherein each heat exchanger tube independently penetrates the baffle; wherein the plurality of heat exchanger tubes comprises 50 to 5000 heat exchanger tubes; wherein the baffle assembly comprises a plurality of baffles, and wherein each heat exchanger tube penetrates each baffle; wherein the plurality of baffles comprises 1 to 100 baffles; wherein the baffle has an aspect ratio of 5 to 10,000, wherein the aspect ratio is a largest dimension of a major surface of the baffle divided by a thickness of the baffle.

An embodiment is disclosed with a baffle assembly comprising: a first tube sheet; a second tube sheet opposite the first sheet; a heat exchanger tube, which connects the first tube sheet and the second tube sheet; and a baffle disposed between the first tube sheet and the second tube sheet, wherein the heat exchanger tube sealingly passes through the baffle; wherein the baffle is a plate baffle, and wherein the plate baffle has a disk shape, an elliptical shape, a lobular shape, a square shape, a rectangular shape, a rectilinear shape, or a curvilinear shape, or any combination thereof; wherein the baffle has a disk shape; wherein the baffle has a first side and an opposite second side, and wherein fluid communication between the first side and the second side is exclusively across a perimeter of the baffle; wherein a maximum distance between an outer surface of the heat exchanger tube and the baffle is between 0 centimeters and 3 centimeters; further comprising a continuous weld, which sealingly connects the baffle to the heat exchanger tube; wherein the continuous weld which sealingly connects the baffle to the heat exchanger tube is disposed on a circumference of the tube; further comprising an adhesive, which adhesively and sealingly connects the baffle to the heat exchanger tube, and wherein the adhesive is disposed between the heat exchanger tube passes and the baffle; wherein the baffle comprises a rigid element, and a gasket disposed on a surface of the rigid element and between the rigid element and the heat exchanger tube, wherein the gasket seals the baffle to the heat exchanger tube where the heat exchanger tube passes through the baffle; wherein the gasket is attached to the rigid element by an adhesive; further comprising a retainer, which is attached to the rigid element by a fastener, and wherein the gasket is disposed between the rigid element and the retainer; wherein the gasket comprises an elastomer; wherein the elastomer is ethylene propylene diene monomer; wherein the gasket comprises a metal plate with a maximum thickness between 0.002 millimeters to 6 millimeters; wherein the sealed baffle assembly comprises a plurality of heat exchanger tubes, and wherein each heat exchanger tube independently sealingly penetrates the baffle; wherein the plurality of heat exchanger tubes comprises 50 to 5000 heat exchanger tubes; wherein the sealed baffle assembly comprises a plurality of baffles, and wherein each heat exchanger tube sealingly penetrates each baffle; wherein the plurality of baffles comprises 3 to 100 baffles; wherein the baffle has an aspect ratio of 5 to 10,000, wherein the aspect ratio is a largest dimension of a major surface of the baffle divided by a thickness of the baffle

An embodiment is disclosed with a baffle assembly comprising: a first tube sheet; a second tube sheet opposite the first sheet; a heat exchanger tube, which connects the first tube sheet and the second tube sheet; and a baffle disposed between the first tube sheet and the second tube sheet, wherein the heat exchanger tube passes through the baffle; wherein the baffle is a plate baffle, and wherein the plate baffle has a disk shape, an elliptical shape, a lobular shape, a square shape, a rectangular shape, a rectilinear shape, or a curvilinear shape, or any combination thereof; wherein the baffle has a disk shape; wherein the baffle has a first side and an opposite second side, and wherein fluid communication between the first side and the second side is across a perimeter of the baffle; wherein a maximum distance between an outer surface of the heat exchanger tube and the baffle is between 0 centimeters and 3 centimeters; wherein the sealed baffle assembly comprises a plurality of heat exchanger tubes, and wherein each heat exchanger tube independently penetrates the baffle; wherein the plurality of heat exchanger tubes comprises 50 to 5000 heat exchanger tubes; wherein the baffle assembly comprises a plurality of baffles, and wherein each heat exchanger tube penetrates each baffle; wherein the plurality of baffles comprises 1 to 100 baffles; wherein the baffle has an aspect ratio of 5 to 10,000, wherein the aspect ratio is a largest dimension of a major surface of the baffle divided by a thickness of the baffle.

An embodiment is disclosed with a baffle assembly comprising: a first tube sheet; a second tube sheet opposite the first sheet; a heat exchanger tube, which connects the first tube sheet and the second tube sheet; and a baffle disposed between the first tube sheet and the second tube sheet, wherein the heat exchanger tube sealingly passes through the baffle; wherein the baffle is a plate baffle, and wherein the plate baffle has a disk shape, an elliptical shape, a lobular shape, a square shape, a rectangular shape, a rectilinear shape, or a curvilinear shape, or any combination thereof; wherein the baffle has a disk shape; wherein the baffle has a first side and an opposite second side, and wherein fluid communication between the first side and the second side is exclusively across a perimeter of the baffle; wherein a maximum distance between an outer surface of the heat exchanger tube and the baffle is between 0 centimeters and 3 centimeters; further comprising a continuous weld, which sealingly connects the baffle to the heat exchanger tube; wherein the continuous weld which sealingly connects the baffle to the heat exchanger tube is disposed on a circumference of the tube; further comprising an adhesive, which adhesively and sealingly connects the baffle to the heat exchanger tube, and wherein the adhesive is disposed between the heat exchanger tube passes and the baffle; wherein the baffle comprises a rigid element, and a gasket disposed on a surface of the rigid element and between the rigid element and the heat exchanger tube, wherein the gasket seals the baffle to the heat exchanger tube where the heat exchanger tube passes through the baffle; wherein the gasket is attached to the rigid element by an adhesive; further comprising a retainer, which is attached to the rigid element by a fastener, and wherein the gasket is disposed between the rigid element and the retainer; wherein the gasket comprises an elastomer; wherein the elastomer is ethylene propylene diene monomer; wherein the gasket comprises a metal plate with a maximum thickness between 0.002 millimeters to 6 millimeters; wherein the sealed baffle assembly comprises a plurality of heat exchanger tubes, and wherein each heat exchanger tube independently sealingly penetrates the baffle; wherein the plurality of heat exchanger tubes comprises 50 to 5000 heat exchanger tubes; wherein the sealed baffle assembly comprises a plurality of baffles, and wherein each heat exchanger tube sealingly penetrates each baffle; wherein the plurality of baffles comprises 3 to 100 baffles; wherein the baffle has an aspect ratio of 5 to 10,000, wherein the aspect ratio is a largest dimension of a major surface of the baffle divided by a thickness of the baffle.

Set forth below are non-limiting embodiments of the present disclosure.

Embodiment 1

A baffle assembly comprising: a first tube sheet; a second tube sheet opposite the first sheet; a heat exchanger tube, which connects the first tube sheet and the second tube sheet; and a baffle disposed between the first tube sheet and the second tube sheet, wherein the heat exchanger tube passes through the baffle, optionally, wherein the heat exchanger tube sealingly passes through the baffle.

Embodiment 2

The baffle assembly of embodiment 1, wherein the baffle has a disk shape, an elliptical shape, a lobular shape, a square shape, a rectangular shape, a rectilinear shape, or a curvilinear shape, or any combination thereof.

Embodiment 3

The baffle assembly of any of embodiments 1 or 2, wherein the baffle has a disk shape.

Embodiment 4

The baffle assembly of any of embodiments 1 to 3, wherein the baffle comprises a plate baffle that has a first side and an opposite second side, and wherein fluid communication between the first side and the second side is across a perimeter of the baffle. At least 51%, or at least 90%, or at least 99% by weight of fluid communication between the first side and the second side of the baffle can be through the perimeter of the baffle.

Embodiment 5

The baffle assembly of any of embodiments 1 to 4, wherein the baffle comprises an annular baffle that has a first side and an opposite second side, and wherein fluid communication between the first side and the second side is across an annulus of the baffle. At least 51%, or at least 90%, or at least 99% by weight of fluid communication between the first side and the second side of the baffle can be through the annulus of the annular baffle.

Embodiment 6

The baffle assembly of any of embodiments 1 to 5, wherein a maximum distance between an outer surface of the heat exchanger tube and the baffle is between 0 centimeters and 3 centimeters.

Embodiment 7

The baffle assembly of any of embodiments 1 to 6, further comprising a continuous weld, which sealingly connects the baffle to the heat exchanger tube; or wherein a seal is formed between the heat exchanger tubes and the baffle based on a close proximity of the heat exchanger tubes and the baffle.

Embodiment 8

The baffle assembly of embodiment 7, further comprising the weld; wherein the continuous weld which sealingly connects the baffle to the heat exchanger tube is disposed on a circumference of the tube.

Embodiment 9

The baffle assembly of any of embodiments 1 to 8, further comprising an adhesive, which adhesively and sealingly connects the baffle to the heat exchanger tube, and wherein the adhesive is disposed between the heat exchanger tube passes and the baffle.

Embodiment 10

The baffle assembly of any of embodiments 1 to 9, wherein the baffle comprises a rigid element, and a gasket disposed on a surface of the rigid element and between the rigid element and the heat exchanger tube, wherein the gasket seals the baffle to the heat exchanger tube where the heat exchanger tube passes through the baffle.

Embodiment 11

The baffle assembly of embodiment 10, wherein the gasket is attached to the rigid element by an adhesive.

Embodiment 12

The baffle assembly of any of embodiments 10 to 11, further comprising a retainer, which is attached to the rigid element by a fastener, and wherein the gasket is disposed between the rigid element and the retainer.

Embodiment 13

The baffle assembly of any of embodiments 10 to 12, wherein the gasket comprises an elastomer.

Embodiment 14

The baffle assembly of any of embodiments 10 to 13, wherein the elastomer is ethylene propylene diene monomer.

Embodiment 15

The baffle assembly of any of embodiments 10 to 14, wherein the gasket comprises a metal plate with a maximum thickness between 0.002 millimeters to 6 millimeters.

Embodiment 16

The baffle assembly of any of embodiments 1 to 15, wherein the baffle assembly comprises a plurality of heat exchanger tubes, and wherein each heat exchanger tube independently sealingly penetrates the baffle.

Embodiment 17

The baffle assembly of any of embodiments 1 to 16, wherein the plurality of heat exchanger tubes comprises 50 to 5000 heat exchanger tubes.

Embodiment 18

The baffle assembly of any of embodiments 1 to 17, wherein the baffle assembly comprises a plurality of baffles, and wherein each heat exchanger tube sealingly penetrates each baffle.

Embodiment 19

The baffle assembly of any of embodiments 1 to 18, wherein the plurality of baffles comprises 3 to 100 baffles.

Embodiment 20

The baffle assembly of any of embodiments 1 to 19, wherein the baffle has an aspect ratio of 5 to 10,000, wherein the aspect ratio is a largest dimension of a major surface of the baffle divided by a thickness of the baffle.

Embodiment 21

The baffle assembly of any one of embodiments 1-20, wherein the baffle assembly comprises a plurality of baffles comprising at least one plate baffle and at least one annular baffle.

Embodiment 22

The baffle assembly of any one of embodiments 1 to 21, wherein a fluid flow through the baffle assembly encounters an alternating route of plate baffles and annular baffles.

Embodiment 23

A heat exchanger comprising: a pressure vessel; and a baffle assembly disposed in the pressure vessel such as the one described in any one of embodiments 1 to 22, the baffle assembly comprising a first tube sheet, a second tube sheet opposite the first tube sheet, a heat exchanger tube, which connects the first tube sheet and the second tube sheet, a baffle disposed between the first tube sheet and the second tube sheet, wherein the heat exchanger tube passes through the baffle.

Embodiment 24

The heat exchanger of embodiment 23, wherein a maximum distance between an inner surface of the pressure vessel and an edge surface of the baffle is between 0 centimeters and 3 centimeters.

Embodiment 25

The heat exchanger of any of embodiments 23 to 24, further comprising a continuous weld, which sealingly connects the annular baffle to the pressure vessel.

Embodiment 26

The heat exchanger of any of embodiments 23 to 25, wherein the continuous weld which sealingly connects the annular baffle to the heat exchanger tube is disposed on a perimeter of the baffle.

Embodiment 27

The heat exchanger of any of embodiments 23 to 26, further comprising an adhesive, which adhesively and sealingly connects the baffle to the pressure vessel, and wherein the adhesive is disposed on the perimeter of the baffle.

Embodiment 28

The heat exchanger of any of embodiments 23 to 27, wherein the baffle comprises a rigid element, and a gasket disposed on the surface of the rigid element, wherein the gasket seals the annular baffle to the pressure vessel on the perimeter of the annular baffle.

Embodiment 29

The heat exchanger of embodiment 28, wherein the gasket is attached to the rigid element by an adhesive.

Embodiment 30

The heat exchanger of any of embodiments 28 to 29, further comprising a retainer, which is attached to the rigid element by a fastener, and wherein the gasket is disposed between the rigid element and the retainer.

Embodiment 31

The heat exchanger of any of embodiments 28 to 30, wherein the gasket comprises an elastomer.

Embodiment 32

The heat exchanger of embodiment 31, wherein the elastomer is ethylene propylene diene monomer.

Embodiment 33

The heat exchanger of any of embodiments 28 to 32, wherein the gasket comprises a metal plate having a maximum thickness between 0.002 millimeters to 6.35 millimeters.

Embodiment 34

The heat exchanger of any of embodiments 23 to 33, wherein the heat exchanger tube sealingly passes through the baffle, wherein the baffle comprises an annular baffle, and wherein fluid communication between the first side and the second side of the annular baffle is through the annulus of the baffle, for example, exclusively across.

Embodiment 35

The heat exchanger of any of embodiments 23 to 34, wherein the heat exchanger tube sealingly passes through the baffle, wherein the baffle comprises a plate baffle, and wherein fluid communication between the first side and the second side of the plate baffle is across the perimeter of the baffle, for example, exclusively across.

Embodiment 36

The heat exchanger of any of embodiments 23 to 35, wherein a maximum distance between an outer surface of the heat exchanger tube and the baffle is between 0 centimeters and 3 centimeters.

Embodiment 37

The heat exchanger of any of embodiments 23 to 36, further comprising a continuous weld, which sealingly connects the baffle to the heat exchanger tube.

Embodiment 38

The heat exchanger of any of embodiments 23 to 37, wherein the continuous weld which sealingly connects the baffle to the heat exchanger tube is disposed on a circumference of the tube.

Embodiment 39

The heat exchanger of any of embodiments 23 to 38, further comprising an adhesive, which adhesively and sealingly connects the baffle to the heat exchanger tube, wherein the adhesive is disposed between the heat exchanger tube and the baffle where the heat exchanger tube passes through the baffle.

Embodiment 40

The heat exchanger of any of embodiments 23 to 39, wherein the baffle comprises a rigid element, and a gasket disposed on the surface of the rigid element, wherein the gasket seals the baffle to the heat exchanger tube where the heat exchanger tube passes through the baffle, and wherein the gasket seals the baffle to the pressure vessel on the perimeter of the baffle.

Embodiment 41

The heat exchanger of embodiment 40, wherein the gasket is attached to the rigid element by the adhesive.

Embodiment 42

The heat exchanger of any of embodiments 40 to 41, further comprising a retainer, which is attached to the rigid element by a fastener, and wherein the gasket is disposed between the rigid element and the retainer.

Embodiment 43

The heat exchanger of any of embodiments 40 to 42, wherein the gasket comprises an elastomer.

Embodiment 44

The heat exchanger of any of embodiments 40 to 43, wherein the elastomer is ethylene propylene diene monomer.

Embodiment 45

The heat exchanger of any of embodiments 40 to 44, wherein the gasket comprises a metal plate having a maximum thickness between 0.002 millimeters to 6 millimeters.

Embodiment 46

The heat exchanger of any of embodiments 23 to 45, wherein the heat exchanger assembly comprises a plurality of heat exchanger tubes, and wherein each heat exchanger tube independently and penetrates the baffle.

Embodiment 47

The heat exchanger of embodiment 46, wherein the plurality of heat exchanger tubes comprises 50 to 5000 heat exchanger tubes.

Embodiment 48

The heat exchanger of embodiments 23 to 47, comprising a plurality of annular baffles and/or plate baffles, wherein each baffle is sealingly disposed between the first tube sheet and the second tube sheet.

Embodiment 49

The heat exchanger of any of embodiments 23 to 48, wherein the heat exchanger comprises a plurality of annular baffles and/or plate baffles, and wherein each heat exchanger tube penetrates each baffle.

Embodiment 50

The heat exchanger of any of embodiments 23 to 49, wherein the plurality of baffles comprises 3 to 100 baffles.

Embodiment 51

A baffle assembly, such as any one of the preceding embodiments, comprising: a first tube sheet; a second tube sheet opposite the first sheet; a heat exchanger tube, which connects the first tube sheet and the second tube sheet; and a plate baffle disposed between the first tube sheet and the second tube sheet, wherein the heat exchanger tube sealingly passes through the plate baffle, and an annular baffle sealingly disposed between the first tube sheet and the second tube sheet, wherein the heat exchanger tube sealingly passes through the annular baffle.

Embodiment 52

The baffle assembly of embodiment 51, wherein the plate baffles and the annular baffles alternate from the first tube sheet to the second tube sheet.

Embodiment 53

The baffle assembly of any of embodiments 1 to 52, wherein a separation distance between adjacent baffles is between 0.2 centimeters and 5,200 centimeters.

Embodiment 54

The baffle assembly of any of embodiments 1 to 53, wherein the heat exchanger tube has a first end and an opposite second end, wherein the first end of the heat exchanger tube is disposed on the first tube sheet, and wherein the second end of the heat exchanger tube is disposed on the second tube sheet, wherein a perimeter of the first end of the heat exchanger tube is sealingly connected to the first tube sheet, and wherein a perimeter of the second end of the heat exchanger tube is sealingly connected to the second tube sheet.

Embodiment 55

A method of producing radial flow in a heat exchanger, the method comprising: providing a heat exchanger comprising a baffle assembly, such as that of any one of embodiments 1-54, comprising a pressure vessel shell comprising an inlet and outlet, a baffle assembly entirely disposed in the pressure vessel shell, the baffle assembly comprising a first tube sheet, a second tube sheet opposite the first sheet, a heat exchanger tube, which connects the first tube sheet and the second tube sheet; and at least one plate baffle disposed between the first tube sheet and the second tube sheet, wherein the heat exchanger tube sealingly passes through the baffle; and at least one annular baffle sealingly and/or at least one plate baffle disposed between the first tube sheet and the second tube sheet, wherein the heat exchanger tube sealingly passes through the baffle; and directing a production fluid from the first inlet to the first outlet to provide a flow of the production fluid through the pressure vessel shell to produce the radial flow.

Embodiment 56

The method of embodiment 55, wherein the production fluid comprises water, a substituted or unsubstituted C1 to C30 hydrocarbon, a thermal fluid, a glycol, or a combination thereof.

Embodiment 57

A heat exchanger tube assembly comprising: a first tube sheet; a second tube sheet opposite the first sheet; a plurality of heat exchanger tubes, wherein each heat exchanger tube of the plurality of heat exchanger tubes independently connects the first tube sheet and the second tube sheet, and wherein the heat exchanger tubes are in a staggered ring configuration that comprises a plurality of concentric rings of tubes, wherein adjacent tubes on a ring are separated by a radial separation angle RA.

Embodiment 58

The heat exchanger tube assembly of embodiment 1, wherein the radial separation angle is 1 to 90 degrees.

Embodiment 59

The heat exchanger tube assembly of any one or more of the preceding embodiments, wherein neighboring tubes on adjacent rings are separated by rotating all the tubes within an inner ring by a radial index angle, IA, relative to the next outermost tube ring.

Embodiment 60

The heat exchanger tube assembly of any one or more of the preceding embodiments, further comprising a baffle located between the first tube sheet and the second tube sheets, wherein the plurality of heat exchanger tubes traverses through the baffle.

Embodiment 61

The heat exchanger tube assembly of embodiment 4, wherein the baffle comprises at least one plate baffle; wherein fluid communication between a first side and a second side of the plate baffle is across a perimeter of the plate baffle.

Embodiment 62

The heat exchanger tube assembly of any one or more of embodiments 4 to 5, wherein the baffle comprises at least one annular baffle; wherein fluid communication between a first side and a second side of the annular baffle is through the annulus of the baffle.

Embodiment 63

The heat exchanger tube assembly of any one or more of embodiments 4 to 6, wherein the baffle comprises at least two plate baffles and at least two annular baffles; wherein a fluid flow traverses an alternating path of plate baffles and annular baffles.

Embodiment 64

The heat exchanger tube assembly of any one or more of the preceding embodiments, wherein neighboring tubes on adjacent rings are separated by rotating all the tubes within an inner ring by a radial index angle, IA, relative to the next outermost tube ring.

Embodiment 65

A heat exchanger comprising: a pressure vessel; and the heat exchanger tube assembly of any one or more of the preceding embodiments; wherein the heat exchanger tube assembly is disposed in the pressure vessel.

Embodiment 66

The heat exchanger of embodiment 9, wherein neighboring tubes on adjacent rings are separated by rotating all the tubes within an inner ring by a radial index angle, IA, relative to the next outermost tube ring.

Embodiment 67

A fluid heating system comprising: the heat exchanger of any one or more of embodiments 9 to 10; wherein the pressure vessel comprises a pressure vessel shell comprising a first inlet and first outlet, a shell, a first top head and a first bottom head, wherein the shell is disposed between the first top head and the first bottom head, and wherein the first inlet and the first outlet are each independently on the shell, the first top head, or the first bottom head; a conduit, which penetrates the pressure vessel shell, wherein a first end of the conduit is connected to the first tube sheet wherein the conduit is in fluid communication with the heat exchanger tubes and wherein a second end of the conduit is on the outside of the pressure vessel shell; a burner disposed in the conduit; and a blower, which is in fluid communication with the second end of the conduit.

Embodiment 68

The heat exchanger tube assembly of embodiment 11, wherein neighboring tubes on adjacent rings are separated by rotating all the tubes within an inner ring by a radial index angle, IA, relative to the next outermost tube ring.

Embodiment 69

A method of calculating the radial separation angle RA, and the radial stagger index angle IA, for a staggered ring heat exchanger tube configuration, for example, of any one or more of the preceding embodiments, using the design diameter DD of the tube configuration, a gap GAP between the design diameter and the first tube ring, the tube element clearance diameter CD_k for each row k of tubes, and the rounding threshold RT to be applied to the tube count, the method comprising: computing a diameter of an outer row RD₁ using the Formula 1 RD₁=DD−(2×GAP)−CM; (1) computing the diameter RDk of the interior rows k using the Formula 2 RDk=RDk−1−CDk−1−CDk (2) for each row diameter where RDk≥0; computing the tube count for each row k using Formula 3 CTk=360/2 sin−1(CDk/RDk); (3) computing the integer tube count by rounding using the rounding threshold RT, where RT is between 0.001 and 0.99, wherein: if the fractional part of the computed tube count CTk is greater than the rounding threshold RT, round the tube count using Formula 4 Ck=ceil(CTk), (4), and compute the final ring diameter using Formula 5 Dk=CDk/sin(360/2Ck); (5) otherwise round the tube count using Formula 6 Ck=floor(CTk), and (6) compute the final ring diameter using Formula 7 D1=OD−(2×GAP)−CD1 (8) if the computation is for the first row or Formula 9 Dk=Dk−1−CDk−1−CDk (9) if for an inner row with k>1; computing the fixed row separation angle RAk for tubes in each row from k=1 to the innermost row using Formula 10 RAk=360/Ck; (10) computing the fixed tube stagger index angle IAk for adjacent tubes in adjacent rows, k and k−1, using Formula 11 IAk=(RAk+RAk−1)/2 (11) for each inner row and setting IA1=0 for the first row, k=1.

Embodiment 70

A heat exchanger tube assembly for example, of any one or more of the preceding embodiments, comprising: a first tube sheet; a second tube sheet opposite the first sheet; a plurality of heat exchanger tubes, wherein each heat exchanger tube of the plurality of heat exchanger tubes independently connects the first tube sheet and the second tube sheet, and wherein the heat exchanger tubes are in a staggered ring configuration that comprises a plurality of concentric rings of tubes, the heat exchange tubes in each ring have approximately the same tube diameter and ligament; the radial distance separating two adjacent rings is between one half and three times the sum of the minimum ligament and minimum tube diameter for any tube on the two adjacent rings; wherein adjacent tubes on a ring are separated by a radial separation angle between 0.5 degrees and 180 degrees; and each concentric ring contains a designated first tube.

The disclosure has been described with reference to the accompanying drawings, in which various embodiments are shown. This disclosure may, however, be embodied in many different forms, and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art. Like reference numerals refer to like elements throughout.

It will be understood that when an element is referred to as being “on” another element, it can be directly on the other element or intervening elements may be present there between. In contrast, when an element is referred to as being “directly on” another element, there are no intervening elements present. Also, the element may be on an outer surface or on an inner surface of the other element, and thus “on” may be inclusive of “in” and “on.”

It will be understood that, although the terms “first,” “second,” “third,” etc. may be used herein to describe various elements, components, regions, layers, and/or sections, these elements, components, regions, layers, and/or sections should not be limited by these terms. These terms are only used to distinguish one element, component, region, layer, or section from another element, component, region, layer or section. Thus, “a first element,” “component,” “region,” “layer,” or “section” discussed below could be termed a second element, component, region, layer, or section without departing from the teachings herein.

The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting. As used herein, the singular forms “a,” “an,” and “the” are intended to include the plural forms, including “at least one,” unless the content clearly indicates otherwise. “Or” means “and/or.” As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items. It will be further understood that the terms “comprises” and/or “comprising,” or “includes,” and/or “including” when used in this specification, specify the presence of stated features, regions, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, regions, integers, steps, operations, elements, components, and/or groups thereof.

Furthermore, relative terms, such as “lower” or “bottom” and “upper” or “top,” may be used herein to describe one element's relationship to another element as illustrated in the Figures. It will be understood that relative terms are intended to encompass different orientations of the device in addition to the orientation depicted in the Figures. For example, if the device in one of the figures is turned over, elements described as being on the “lower” side of other elements would then be oriented on “upper” sides of the other elements. The exemplary term “lower,” can therefore, encompasses both an orientation of “lower” and “upper,” depending on the particular orientation of the figure. Similarly, if the device in one of the figures is turned over, elements described as “below” or “beneath” other elements would then be oriented “above” the other elements. The exemplary terms “below” or “beneath” can, therefore, encompass both an orientation of above and below.

Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and the present disclosure, and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.

Exemplary embodiments are described herein with reference to cross section illustrations that are schematic illustrations of idealized embodiments. As such, variations from the shapes of the illustrations as a result, for example, of manufacturing techniques and/or tolerances, are to be expected. Thus, embodiments described herein should not be construed as limited to the particular shapes of regions as illustrated herein but are to include deviations in shapes that result, for example, from manufacturing. For example, a region illustrated or described as flat may, typically, have rough and/or nonlinear features. Moreover, sharp angles that are illustrated may be rounded. Thus, the regions illustrated in the figures are schematic in nature and their shapes are not intended to illustrate the precise shape of a region and are not intended to limit the scope of the present claims.

Claims

1. A fluid heating system having a heat exchanger baffle assembly and tube pattern for radial flow heat exchanger, comprising: a first tube sheet;a second tube sheet opposite the first sheet;a plurality of heat exchanger tubes, wherein each heat exchanger tube of the plurality of heat exchanger tubes independently connects the first tube sheet and the second tube sheet, and wherein the heat exchanger tubes are in a staggered ring configuration that comprises a plurality of concentric rings of tubes; andwherein adjacent tubes on a ring are separated by a radial separation angle RA, such that there is a substantially uniform temperature distribution and efficient exchange of thermal energy across the heat exchanger tube walls.

2. The heat exchanger tube assembly of claim 1, wherein the radial separation angle is 1 to 90 degrees.

3. The heat exchanger tube assembly of claim 1, wherein neighboring tubes on adjacent rings are separated by rotating all the tubes within an inner ring by a radial index angle, IA, relative to the next outermost tube ring.

4. The heat exchanger tube assembly of claim 1, further comprising a baffle located between the first tube sheet and the second tube sheets, wherein the plurality of heat exchanger tubes traverses through the baffle.

5. The sealed baffle assembly of claim 4, wherein the baffle is a plate baffle, and wherein the plate baffle has a disk shape, an elliptical shape, a lobular shape, a square shape, a rectangular shape, a rectilinear shape, or a curvilinear shape, or any combination thereof.

6. The sealed baffle assembly of any of claim 4, wherein the baffle has a disk shape.

7. The sealed baffle assembly of any of claim 4, wherein the baffle has a first side and an opposite second side, and wherein fluid communication between the first side and the second side is exclusively across a perimeter of the baffle.

8. The sealed baffle assembly of any of claim 4, wherein a maximum distance between an outer surface of the heat exchanger tube and the baffle is between 0 centimeters and 3 centimeters.

9. The sealed baffle assembly of any of claim 4, further comprising a continuous weld, which sealingly connects the baffle to the heat exchanger tube.

10. The sealed baffle assembly of any of claim 4, wherein the continuous weld which sealingly connects the baffle to the heat exchanger tube is disposed on a circumference of the tube.

11. A method of producing radial flow in a heat exchanger, the method comprising: providing a heat exchanger having a baffle assembly, the heat exchanger comprising: a pressure vessel shell comprising a vessel inlet and a vessel outlet,a baffle assembly, comprising: a first tube sheet;a second tube sheet opposite the first sheet;a heat exchanger tube, which connects the first tube sheet and the second tube sheet;at least one plate baffle disposed between the first tube sheet and the second tube sheet, wherein the heat exchanger tube sealingly passes through the baffle; andat least one annular baffle sealingly disposed between the first tube sheet and the second tube sheet, wherein the heat exchanger tube sealingly passes through the baffle; anddirecting using the baffle assembly a production fluid from the vessel inlet to the vessel outlet to provide alternating radial flow of the production fluid through the sealed baffle assembly.

12. The method of claim 11, wherein the production fluid comprises water, a substituted or unsubstituted C1 to C30 hydrocarbon, a thermal fluid, a glycol, or a combination thereof.

13. The heat exchanger of claim 11, wherein neighboring tubes on adjacent rings are separated by rotating all the tubes within an inner ring by a radial index angle, IA, relative to the next outermost tube ring.

14. The heat exchanger tube assembly of claim 11, wherein neighboring tubes on adjacent rings are separated by rotating all the tubes within an inner ring by a radial index angle, IA, relative to the next outermost tube ring.

15. The heat exchanger of claim 11, wherein the heat exchanger tubes are in a staggered ring configuration that comprises a plurality of concentric rings of tubes, the heat exchange tubes in each ring have approximately the same tube diameter and ligament, the radial distance separating two adjacent rings is between one half and three times the sum of the minimum ligament and minimum tube diameter for any tube on the two adjacent rings; and wherein adjacent tubes on a ring are separated by a radial separation angle between 0.5 degrees and 180 degrees; and each concentric ring contains a designated first tube.

16. The heat exchanger of claim 11, further comprising a plurality of baffles located between the first tube sheet and the second tube sheets, wherein the number of baffles and baffle spacing is set to that provides a substantially uniform temperature distribution and efficient exchange of thermal energy across the heat exchanger tube walls, and to minimize production fluid pressure drop from vessel inlet to vessel outlet while simultaneously minimizing the number and magnitude of local temperature outliers.

17. The heat exchanger of claim 16, wherein the baffle spacing increases from vessel outlet toward the vessel inlet for at least the first two baffle spacings.

18. The heat exchanger of claim 16, wherein the baffle spacing is determined by an iterative baffle spacing calculation process.

19. The heat exchanger of claim 11, wherein the annular baffles and plate baffles alternate long the length of the heat exchanger tubes.

20. A method of calculating a radial separation angle RA, and the radial stagger index angle IA, for a staggered ring heat exchanger tube configuration, using a design diameter (DD) of the tube configuration, a gap (GAP) between the design diameter (DD) and a first tube ring, the tube element clearance diameter CDk for each row k of tubes, and a rounding threshold (RT) to be applied to the tube count, the method comprising: computing a diameter of an outer row RD1 using the Formula 1, RD1=DD−(2×GAP)−CD1;  (1)computing the diameter RDk of the interior rows 2≤k using the Formula 2, RDk=RDk-1−CDk-1−CDk  (2)for each row diameter where RDk≥0;computing the tube count for each row k using Formula 3, CTk=360/2 sin−1(CDk/RDk);  (3)computing the integer tube count by rounding using the rounding threshold RT, where RT is between 0.001 and 0.99, wherein if the fractional part of the computed tube count CTk is greater than the rounding threshold (RT), rounding the tube count using Formula 4, Ck=ceil(CTk);  (4)computing the final ring diameter using Formula 5, Dk=CDk/sin(360/2Ck);  (5)otherwise, rounding the tube count using Formula 6, Ck=floor(CTk);  (6)computing the final ring diameter using Formula 7, D1=OD−(2×GAP)−CD1  (7)if the computation is for the first row, or using Formula 8, Dk=Dk-1−CDk-1−CDk  (8)if for an inner row with k>1;computing the fixed row separation angle RAk for tubes in each row from k=1 to the innermost row using Formula 9, RAk=360/Ck  (9); andcomputing the fixed tube stagger index angle IAk for adjacent tubes in adjacent rows, k and k−1, using Formula 10, IAk=(RAk+RAk-1)/2  (10)for each inner row, and setting IA1=0 for the first row, k=1.