Field of the invention

The invention relates to the field of hydrocarbon cracking, such as by thermal cracking, steam cracking and/or pyrolysis. More specifically it relates to a reactor for cracking hydrocarbons, a system for cracking hydrocarbons and a method for producing light olefins from a hydrocarbon feedstock.

Background of the invention

Hydrocarbon cracking is an approach, known in the art, for producing light olefins, such as, for example, ethene, propene, benzene and/or butadiene. Such light olefins are typically used as essential building blocks in the chemical industry, and may be commonly referred to as platform molecules. Due to the high demand for such platform molecules and for the sake of efficiency, hydrocarbon cracking processes may typically be performed at very large industrial scales. For example, a light olefin production capacity of a plant may be in the range of 300 kta to 2000 kta, and even higher capacities may be realistic. Steam cracking is such an industrial process that is commonly applied at a large scale.

In a steam cracking process as known in the art, a hydrocarbon feedstock material, such as ethane, propane, butane, naphtha, a light gas oil or even hydrotreated crude oil, is heated in a tubular reactor to a reactor temperature, e.g. in the range of 600°C to 1000 °C. The tubular reactor may have a length of, for example, about 10 m to about 100 m. The tubular reactor or, typically, a plurality of such tubular reactors may be suspended in a large furnace, e.g. a gas-fired furnace, to supply the heat for bringing the feedstock material up to the reactor temperature.

When a sufficiently high temperature is reached, the hydrocarbon feedstock undergoes cracking reactions. In such a free-radical process, large hydrocarbon molecules are broken down to smaller molecules and unsaturated bonds are formed. Process conditions such as temperature, residence time, dilution, etc. may be tuned to maximize the ethene yield.

It is a disadvantage of such prior art processes that a coke residue is deposited on the inner wall of the tubular reactor. Coke is a carbonaceous, graphite-like deposit with a relatively low thermal conductivity. Due to this low thermal conductivity, an efficient heat transfer from the furnace to the process gas inside the reactor is impeded. This can be compensated by increasing the fuel flow rate to the furnace to maintain a constant level of production, which, however, lowers the thermal efficiency of the process. The coke deposit also reduces the cross-sectional area of the tubular reactor that is available for the process gas, which results in a higher process gas flow velocity and hence a higher pressure drop over the tube. The outlet pressure may typically be constrained or determined by downstream processing steps, e.g. such as by the operational parameters of a cracked gas compressor. Therefore, an inlet pressure has to be increased to compensate for the higher pressure drop. Moreover, due to the higher average pressure in the tube, selectivity towards light olefins decreases as the secondary reactions between those olefins are favored over the primary reactions.

As another disadvantage, the deposition of coke also decreases the carbon yield of the process, since the carbon atoms that are incorporated in the coke do not end up in the process products, i.e. are typically lost for producing the intended products.

It is known in the art to regularly shut a steam cracking installation down to remove the deposited coke from the inner wall of the reactor. For example, a decoking procedure may comprise the feeding of a steam/air mixture through the reactor to oxidize the carbon to carbon dioxide. This process may also be referred to as 'burning of the coke'. A shutdown of the furnace is required for such a decoking process to avoid damage to the reactor, since the oxidation process is exothermic.

Depending on the reactor geometry, process conditions and the feedstock material, the reactor may require a shutdown and decoking when the furnace heat output is increased to a level where a reactor temperature approaches a maximum, e.g. a maximum tube metal temperature, and/or when a maximum pressure drop over the reactor tube is reached. When one such shutdown criterium is met for at least one reactor coil in the furnace, the whole furnace may typically be taken offline for decoking.

Since the reactor coils may be directly exposed to the open flames in the furnace, cooling of the reactor material is essentially provided by the endothermic cracking reactions. As coke is deposited, the reactor wall temperature needs to increase to maintain a sufficient heat transfer to the feedstock gas in the reactor. Therefore, to prevent damage, the outer wall temperature of the reactor needs to be limited, for example, depending on the coil metallurgy, to a maximum in the range of 1050 °C to 1200 °C.

The maximum pressure drop may be determined by the maximum pressure at the inlet. The feed distribution may rely on Venturi nozzles for maintaining a fixed mass flow rate to the reactor coils, e.g. independent of the backpressure. However, once the inlet pressure exceeds a critical threshold, the backpressure can be too high to guarantee an equal flow distribution to all coils. This could result in damage to the coils due to the formation of hot spots.

Typical intervals between subsequent decoking shutdowns, i.e. run lengths, may range from 15 days to 60 days, while a decoking procedure may typically take 2 days to complete. Since decoking decreases the efficiency and profitability of the steam cracking process, the run length of a furnace is preferably as long as possible.

Various furnace and reactor geometries are known in the art. For example, internal enhancements to the reactor coil design are known in the art for improving the heat transfer of the reactor, e.g. relative to a similar coil without such internal enhancements. However, such enhancements may also disadvantageously increase the pressure drop over the coil, relative to a similar unenhanced coil, which, as mentioned hereinabove, could lead to a loss in the product selectivity.

For example, US 7,963,318 discloses a tube comprising fins that increase the internal surface area to improve the convective heat transfer.

US 5,950,718 and US 2006/0102327 disclose another type of reactor enhancement known in the art. A single semi-circular rib spirals along the axis of the tube to systematically break down the thermal laminar boundary layer by flow of the feedstock gas over the rib with a subsequent region of reversed flow, thus achieving an improved heat transfer.

US 9,359,560 discloses discrete mixing elements that are positioned at discrete locations along the length of the reactor, e.g. every few meters. These baffles transversally intersect the tube and make a 180° to 360° twist to bring substantially the entirety of the flow into a swirling motion. Advantageously, this allows a good heat transfer improvement relative to an unenhanced tube design, at the cost of only a limited additional pressure drop.

WO 2017/178551 discloses a reactor inner wall comprising cavities rather than protrusions. In this design, spherical or oval cavities are introduced at the surface, similar to the surface of golf balls. These cavities may reduce drag forces in operation of the reactor by making the boundary layer more turbulent and by suppressing flow separation.

Summary of the invention

It is an object of embodiments of the present invention to provide a good and efficient reactor for cracking hydrocarbons, a system comprising such reactor and a related method for the production of light olefins. The above objective is accomplished by a method and device according to the present invention.

It is an advantage of embodiments of the present invention that the run length, e.g. the time interval between shutdowns for decoking, can be longer, on average, compared to at least one approach for cracking hydrocarbons, e.g. steam cracking, known in the art.

It is an advantage of embodiments of the present invention that an advantageously long run length of a cracking furnace can reduce costs and improve economic profitability, e.g. in a large scale industrial application.

It is an advantage of embodiments of the present invention that turbulence of the process gas being treated in a hydrocarbon cracking process is promoted to obtain a good convective heat transfer.

It is an advantage of embodiments of the present invention that a good convective heat transfer to the process gas in hydrocarbon cracking can be achieved.

It is an advantage of embodiments of the present invention that a good convective heat transfer may lead to lower temperatures at the inner surface of the reactor in a hydrocarbon cracking process.

It is an advantage of embodiments of the present invention that a lower temperature of the reactor wall can lead to a lower coking rate, and hence to a longer run length of the furnace.

It is an advantage of embodiments of the present invention that a lower temperature of the reactor wall and a good convective heat transfer in the reactor can advantageously reduce thermal stresses inside the reactor wall.

It is an advantage of embodiments of the present invention that a good heat transfer from the furnace to the process gas can be obtained without incurring a large pressure drop over the reactor, i.e. between a process gas inlet and a process gas outlet of the reactor.

It is an advantage of embodiments of the present invention that a good light olefin selectivity can be maintained in the hydrocarbon cracking process.

It is an advantage of embodiments of the present invention that a stable and good heat transfer is achieved, e.g. without (locally) strongly fluctuating over time due to transient effects, such as transient vortex structures.

It is an advantage of embodiments of the present invention that a stable heat transfer may avoid damage to and/or reduce the wearing down of the reactor. It is an advantage of embodiments of the present invention that only a limited (i.e. a relatively small) increase (i.e. relative to a conventional reactor without specific geometry augmentations) of the internal surface area of the reactor wall may be required. For example, while a substantial increase of the internal surface area, such as by including fins in the reactor, may achieve a reduction of the metal temperature of the reactor wall, such a substantial increase of the internal surface area also disadvantageously increases the surface area available for cokes deposition, e.g. which may lead to a similar total coke yield in a design with fins as in a design without fins. This is not limited to prior-art approaches where rib structures are used. For example, in prior art approaches where baffles are placed in the core of the flow, coke deposition may also occur on such baffles. The depth of internal surface features of the reactor in accordance with embodiments of the present invention may be substantially smaller than the height of a typical fin in a prior-art reactor.

It is an advantage of embodiments of the present invention that only a limited (i.e. a relatively small) variation (i.e. relative to a conventional reactor without specific geometry augmentations) of the temperature over the internal surface area of the reactor can be achieved. It is a further advantage that low thermal stresses due to variations in temperature in the reactor can be achieved. It is a further advantage that a good durability, e.g. a good life span, can be achieved for a reactor in hydrocarbon cracking.

For example, a prior-art design that includes fins in the reactor may have a significant temperature variation over the internal surface of the reactor in operation, e.g. due to the large size of such fins. In a prior-art approach, the valley between two adjacent fins can be, for example, 10 K to 30 K higher in temperature than the temperature on the peak of the fins. This can lead to an increase in the thermal stresses inside the reactor material and this can significantly influence the lifetime of the coils.

It is an advantage of embodiments of the present invention that flow separation, such as a zone of separated flow downstream of a reactor augmentation feature or even a complete separation between the flow in the fins and the flow near the reactor tube axis, can be reduced or avoided. Such flow separation may cause a substantial pressure drop over the reactor. It is therefore also an advantage that a pressure drop over the reactor can be kept relatively low.

In accordance with embodiments of the present invention, a flow separation between a bulk flow and a flow in the outer regions of the reactor tube are avoided or reduced, e.g. due to a good radial mixing, e.g. by interaction between flow between the tube axis and the near wall regions. It is an advantage of embodiments of the present invention that blockages due to cokes spalling can be avoided or reduced. In prior-art approaches, the cross-section in some parts of the coil can be substantially narrower, thus increasing the risk for blockages. For example, if baffles are present in the core of the flow, in accordance with a prior-art approach, coke can be deposited on both the baffle and the internal surface of the reactor, such that this region of the reactor may be particularly susceptible to blockages due to cokes spalling, i.e. relatively large pieces of the coke may break off from a coke layer due to shear stresses on the cokes and cause a blockage downstream. Such blockages may arise during operation, which may result in a premature decoking of the furnace, but also during decoking, which may cause the cokes to burn up too rapidly and may thus potentially lead to melting of the entire reactor tube. It is therefore also an advantage of embodiments of the present invention that damage to the reactor during decoking due to blockages can be reduced or avoided.

It is an advantage of embodiments of the present invention that stagnant zones, i.e. of reduced or even zero flow during operation, in at least a part of a cavity in the reactor wall can be avoided or reduced. For example, stagnant zones in hydrocarbon cracking reactor tubes may lead to high temperatures and hence fast coking.

It is an advantage of embodiments of the present invention, that a cavity in a reactor wall can simultaneously support two flow vortices inside the cavity in operation of the reactor.

In a first aspect, the present invention relates to a reactor for use in cracking hydrocarbons of a hydrocarbon material. The reactor comprises an inlet, an outlet and a flow conduit between the inlet and the outlet for transporting the hydrocarbon material in a flow from the inlet to the outlet. The flow conduit comprises a tubular wall having an inner surface and an outer surface, in which the inner surface has a plurality of indentations provided in the tubular wall. Each indentation has an edge defining a circumferential shape of said indentation. Each indentation of the plurality of indentations comprises an elongated surface feature of the part of the inner surface forming the indentation, said elongated surface feature being distinct from the edge of the indentation, and/or a concavity of the edge of the indentation. The elongated surface feature and/or the concavity, in operation of the reactor, causes the flow to separate into at least two distinct flow vortices in and/or near the indentation.

In a preferred reactor in accordance with embodiments of the present invention, at least one indentation of the plurality of indentations may comprise a concavity of the edge of the indentation. In such a reactor, at least one indentation (which may be the same or a different indentation) of the plurality of indentations may comprise an elongated surface feature of the part of the inner surface forming the indentation.

In a reactor in accordance with embodiments of the present invention, the concavity may be formed by a cusp of the edge.

In a reactor in accordance with embodiments of the present invention, the elongated surface feature may comprise a ridge.

In a reactor in accordance with embodiments of the present invention, said ridge may be oriented substantially along, e.g. parallel to, an axis that is substantially aligned with an axial direction of the flow conduit.

In a reactor in accordance with embodiments of the present invention, the edge may be symmetrical when mirrored with respect to the said axis.

In a reactor in accordance with embodiments of the present invention, each indentation of the plurality of indentations may be droplet-shaped or heart-shaped. In a reactor in accordance with embodiments of the present invention, each indentation of the plurality of indentations may be heart-shaped. A narrow end of the droplet or heart shape may be substantially directed toward the inlet.

In a reactor in accordance with embodiments of the present invention, an area coverage, defined as a total area of the inner surface that is covered by the plurality of indentations over a total area of the inner surface, may lie in a range of 5% to 90%.

In a reactor in accordance with embodiments of the present invention, the indentations may be arranged in a plurality of rows, each row being substantially arranged along a cross-section of the tubular wall. Each row may be separated from each neighboring row in an axial direction of the tubular wall by a distance in the range of 0 to 5 times the cross- sectional diameter of the inner surface.

In a reactor in accordance with embodiments of the present invention, at least one of the rows may comprise a number of the plurality of indentations, in which this number lies in the range of 1 to 20.

In a reactor in accordance with embodiments of the present invention, a maximum width of the circumferential shape of each of the number N of indentations may lie in the range of nD/8N to nD/N, where D refers to the cross-sectional diameter of the inner surface and N refers to the number of indentations in said row.

In a reactor in accordance with embodiments of the present invention, neighboring rows of the plurality of rows in the axial direction may be aligned such that corresponding indentations in each of the rows are positioned substantially at a same angular position on the tubular wall.

In a reactor in accordance with embodiments of the present invention, neighboring rows of the plurality of rows in the axial direction may be staggered such that corresponding indentations in each of the neighboring rows are angularly shifted with respect to each other.

In a reactor in accordance with embodiments of the present invention, the indentations of at least one row of the plurality of rows may be spread out unevenly in the row, such that the inner surface of the tubular wall is devoid of indentations over an angular region. The angular region may cover an angle around the axial direction of the tubular wall in the range of 10° to 180°.

In a reactor in accordance with embodiments of the present invention, at least one of the plurality of indentations may extend for a maximum depth into the tubular wall, in which the maximum depth lies in the range of 0.1 mm to 10 mm and/or in which the maximum depth lies in the range of 0.01 to 0.15 times the cross-sectional diameter of the inner surface.

In a second aspect, the present invention relates to a furnace for producing light olefins from a hydrocarbon feedstock material, the furnace comprising a reactor in accordance with embodiments of the present invention.

In a third aspect, the present invention relates to a method for producing light olefins using a reactor in accordance with embodiments of the present invention and/or using a furnace in accordance with embodiments of the present invention.

In a fourth aspect, the present invention relates to a reactor for use in cracking hydrocarbons of a hydrocarbon material. The reactor comprises an inlet, an outlet and a flow conduit between the inlet and the outlet for transporting the hydrocarbon material in a flow from the inlet to the outlet. The flow conduit comprises a tubular wall having an inner surface and an outer surface, in which the inner surface has a plurality of indentations provided in the tubular wall. The indentations are arranged in a plurality of rows, each row being substantially arranged along a cross-section of the tubular wall. The indentations of at least one row, e.g. of each row, of the plurality of rows may be spread out unevenly in that row, such that the inner surface of the tubular wall is devoid of indentations over an angular region. The angular region devoid of indentations covers an angle around the axial direction of the tubular wall in the range of 45° to 225°, e.g. in the range of 90° to 180°. In a reactor in accordance with embodiments of the present invention, each indentation of the plurality of indentations may be spherical, ovoid, droplet-shaped and/or heart-shaped.

In a reactor in accordance with embodiments of the present invention, an area coverage, defined as a total area of the inner surface that is covered by the plurality of indentations over a total area of the inner surface, may lie in a range of 5% to 90%.

In a reactor in accordance with embodiments of the present invention, each row may be separated from each neighboring row in an axial direction of the tubular wall by a distance in the range of 0 to 5 times the cross-sectional diameter of the inner surface.

In a reactor in accordance with embodiments of the present invention, at least one of the rows may comprise a number of the plurality of indentations, in which this number lies in the range of 1 to 20.

In a reactor in accordance with embodiments of the present invention, a maximum width of the circumferential shape of each of the number N of indentations may lie in the range of nD/8N to nD/N, where D refers to the cross-sectional diameter of the inner surface and N refers to the number of indentations in said row.

In a reactor in accordance with embodiments of the present invention, neighboring rows of the plurality of rows in the axial direction may be aligned such that corresponding indentations in each of the rows are positioned substantially at a same angular position on the tubular wall.

In a reactor in accordance with embodiments of the present invention, neighboring rows of the plurality of rows in the axial direction may be staggered such that corresponding indentations in each of the neighboring rows are angularly shifted with respect to each other.

In a reactor in accordance with embodiments of the present invention, at least one of the plurality of indentations may extend for a maximum depth into the tubular wall, in which the maximum depth lies in the range of 0.1 mm to 10 mm and/or in which the maximum depth lies in the range of 0.01 to 0.15 times the cross-sectional diameter of the inner surface.

Particular and preferred aspects of the invention are set out in the accompanying independent and dependent claims. Features from the dependent claims may be combined with features of the independent claims and with features of other dependent claims as appropriate and not merely as explicitly set out in the claims.

These and other aspects of the invention will be apparent from and elucidated with reference to the embodiment(s) described hereinafter. Brief description of the drawings

FIG 1 shows a schematic overview of a first exemplary reactor in accordance with embodiments of the present invention.

FIG 2 shows a schematic overview of a second exemplary reactor in accordance with embodiments of the present invention.

FIG 3 shows an edge of an indentation in a reactor in accordance with embodiments of the present invention, which edge comprises a cusp that forms a concavity of the edge.

FIG 4 shows an indentation in a reactor in accordance with embodiments of the present invention, in which the surface of the inner wall in the indentation comprises an elongate surface feature.

FIG 5 shows an edge of an indentation in a reactor in accordance with embodiments of the present invention, which edge is substantially wider in a direction toward the outlet than toward the inlet.

FIG 6 shows an exemplary configuration of a reactor in accordance with embodiments of the present invention in which indentations are evenly distributed over cross-sections of the tubular wall.

FIG 7 shows an exemplary configuration of a reactor in accordance with embodiments of the present invention in which indentations are spread out unevenly over cross-sections of the tubular wall.

FIG 8 shows an exemplary three-dimensional shape of an indentation in a reactor in accordance with embodiments of the present invention.

FIG 9 illustrates a furnace for producing light olefins from a hydrocarbon feedstock material in accordance with embodiments of the present invention.

FIG 10 shows an exemplary heat transfer map for reactor having a staggered row design in accordance with embodiments of the present invention.

FIG 11 shows a thermal enhancement factor (TEF) obtained in exemplary simulations illustrating embodiments of the present invention.

FIG 12 shows a relative heat transfer enhancement (Nusselt number ratio Nu/Nuo) w.r.t. the relative pressure drop (pressure drop ratio DR/DRo) obtained in the exemplary simulations of FIG 11, illustrating embodiments of the present invention.

FIG 13 shows a shape of an indentation as described by four Bezier curves, relating to a reactor in accordance with embodiments of the present invention. FIG 14 shows exemplary simulations of the circumferentially averaged wall temperature and the pressure, at the start of a run, as function of axial position along the reactor for two reactors in accordance with embodiments of the present invention and for a reference prior-art reactor. FIG 15 shows an evolution in time over a run of the maximum TMT and the pressure drop over the reactor for the two reactors in accordance with embodiments of the present invention and for the reference prior-art reactor.

FIG 16 shows the evolution in time over a run of the produced ethylene and propylene fractions for the two reactors in accordance with embodiments of the present invention and for the reference prior-art reactor.

FIG 17 shows exemplary simulation data of the pressure drop ratio Dr/Dro in function of the Nusselt number ratio Nu/Nuo, demonstrating the impact of the number and the geometrical configuration of the indentations in a cross-sectional row of a reactor in accordance with embodiments of the present invention on the thermal enhancement and the pressure drop enhancement, relative to a conventional reactor as known in the art.

FIG 18 shows a third-order Bezier curve defined by four points, for illustrating embodiments of the present invention.

FIG 19 illustrates slope angles cii to ct ₄ in a plane through a downstream point, a central point and an upstream point of an indentation in a reactor in accordance with embodiments of the present invention.

FIG 20 shows two exemplary three-dimensional shapes of indentation in a reactor in accordance with embodiments of the present invention.

FIG 21 shows heat transfer maps with the local Nusselt number ratio Nu/Nuo for the two exemplary indentations of FIG 20.

The drawings are only schematic and are non-limiting. In the drawings, the size of some of the elements may be exaggerated and not drawn on scale for illustrative purposes.

Any reference signs in the claims shall not be construed as limiting the scope.

In the different drawings, the same reference signs refer to the same or analogous elements.

Detailed description of illustrative embodiments

The present invention will be described with respect to particular embodiments and with reference to certain drawings but the invention is not limited thereto but only by the claims. The drawings described are only schematic and are non-limiting. In the drawings, the size of some of the elements may be exaggerated and not drawn on scale for illustrative purposes. The dimensions and the relative dimensions do not correspond to actual reductions to practice of the invention.

Furthermore, the terms first, second and the like in the description and in the claims, are used for distinguishing between similar elements and not necessarily for describing a sequence, either temporally, spatially, in ranking or in any other manner. It is to be understood that the terms so used are interchangeable under appropriate circumstances and that the embodiments of the invention described herein are capable of operation in other sequences than described or illustrated herein.

Moreover, the terms top, under and the like in the description and the claims are used for descriptive purposes and not necessarily for describing relative positions. It is to be understood that the terms so used are interchangeable under appropriate circumstances and that the embodiments of the invention described herein are capable of operation in other orientations than described or illustrated herein.

It is to be noticed that the term "comprising", used in the claims, should not be interpreted as being restricted to the means listed thereafter; it does not exclude other elements or steps. It is thus to be interpreted as specifying the presence of the stated features, integers, steps or components as referred to, but does not preclude the presence or addition of one or more other features, integers, steps or components, or groups thereof. Thus, the scope of the expression "a device comprising means A and B" should not be limited to devices consisting only of components A and B. It means that with respect to the present invention, the only relevant components of the device are A and B.

Reference throughout this specification to "one embodiment" or "an embodiment" means that a particular feature, structure or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, appearances of the phrases "in one embodiment" or "in an embodiment" in various places throughout this specification are not necessarily all referring to the same embodiment, but may. Furthermore, the particular features, structures or characteristics may be combined in any suitable manner, as would be apparent to one of ordinary skill in the art from this disclosure, in one or more embodiments.

Similarly it should be appreciated that in the description of exemplary embodiments of the invention, various features of the invention are sometimes grouped together in a single embodiment, figure, or description thereof for the purpose of streamlining the disclosure and aiding in the understanding of one or more of the various inventive aspects. This method of disclosure, however, is not to be interpreted as reflecting an intention that the claimed invention requires more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive aspects lie in less than all features of a single foregoing disclosed embodiment. Thus, the claims following the detailed description are hereby expressly incorporated into this detailed description, with each claim standing on its own as a separate embodiment of this invention.

Furthermore, while some embodiments described herein include some but not other features included in other embodiments, combinations of features of different embodiments are meant to be within the scope of the invention, and form different embodiments, as would be understood by those in the art. For example, in the following claims, any of the claimed embodiments can be used in any combination.

In the description provided herein, numerous specific details are set forth. Flowever, it is understood that embodiments of the invention may be practiced without these specific details. In other instances, well-known methods, structures and techniques have not been shown in detail in order not to obscure an understanding of this description.

In a first aspect, the present invention relates to a reactor for cracking hydrocarbons. The reactor is adapted for transporting a hydrocarbon material in a flow from an inlet to an outlet. The reactor comprises an inlet, and outlet and a flow conduit between the inlet and the outlet for transporting the hydrocarbon material in a flow from the inlet to the outlet. This flow conduit comprises (or consists of) a tubular wall having an inner surface and an outer surface. The inner surface has a plurality of indentations provided in the wall, e.g. cavities that extend into the tubular wall without extending through the tubular wall, e.g. such as not to perforate the tubular wall. For example, in each of the indentations, the inner surface locally recedes from a central longitudinal axis of the flow conduit.

Each indentation of the plurality of indentations comprises at least one elongated surface feature of a part of the inner surface that forms the indentation and/or at least one concavity of the edge of the indentation that, in operation of the reactor, causes the flow to form at least two distinct flow vortices, e.g. non-transient flow vortices, in and/or near the indentation. For example, the at least two distinct flow vortices may alternate to achieve a good mass and thermal mixing. Referring to FIG 1 and FIG 2, reactors 1 for cracking hydrocarbons in accordance with embodiments of the present invention is shown. The reactor 1 is adapted for transporting a hydrocarbon material in a flow from an inlet 2 to an outlet 3.

The reactor 1 may be adapted for, in operation, being exposed to a high temperature environment, e.g. being placed in a hydrocarbon cracking furnace.

The reactor in accordance with embodiments of the present invention may be a pyrolysis, thermal cracking, or steam cracking reactor.

The reactor defines a flow conduit between the inlet 2 and the outlet 3, in which this flow conduit comprises a tubular wall 4 having an inner surface 5 and an outer surface 6.

The flow conduit, e.g. the tubular wall 4, may have a length in the range of 10m to

500m.

The inner surface 5 may have a cross-sectional diameter in the range of 2 cm to 25 cm, e.g. in the range of 3 cm to 15 cm.

The outer surface 6 may have a cross-sectional diameter, larger than the cross- sectional diameter of the inner surface, in the range of 3 cm to 27 cm, e.g. in the range of 5 cm to 17 cm.

The tubular wall 4 may have a thickness in the range of 3 mm to 25 mm, e.g. in the range of 5 mm to 10 mm.

In a reactor in accordance with embodiments of the present invention, the tubular wall 4 may comprise a metal, a metal alloy, a ceramic, and/or a combination thereof. For example, the tubular wall may be composed of aluminium, stainless steel, carbon steel, a glass-lined material, a polymer-based material, a nickel-base metal alloy, a cobalt-base metal alloy and/or a combination thereof.

The tubular wall 4 may have a cylindrical shape. Flowever, embodiments of the present invention are not limited to straight cylindrical shapes. For example, each cross section of the tubular wall may be substantially circular, yet the tubular wall may be curved along its axis A, e.g. may be bent or curved. For example, the tubular wall may follow an undulating or helicoidal path, e.g. to promote a swirling of a feedstock gas in the conduit in operation, e.g. as known in the art. The cross section of the tubular wall may also have a different shape, such as elliptical, oval, square or rectangular or a combination thereof.

The inner surface 5 has a plurality of indentations 7 provided in the wall, e.g. cavities that extend into the tubular wall without extending through the tubular wall, e.g. such as not to perforate the tubular wall. Thus, in each of the indentations 7, the inner surface 5 locally recedes from a central longitudinal axis A of the flow conduit.

It is an advantage of embodiments of the present invention that the plurality of indentations may reduce or avoid a flow separation, e.g. on at least a large scale, may provide a good radial mixing and/or may decrease the thermal boundary layer at the reactor wall, e.g. when compared to at least one prior-art reactor. Another advantage may be a relatively low pressure drop, in operation, between the inlet and the outlet, e.g. such that operation at lower pressures may be feasible and/or such that a selectivity towards the desired products may be advantageously high. Another advantage may be a good heat transfer, e.g. which may allow a longer run length on average.

The outer surface 6 may also have protrusions corresponding to the indentations 7 of the inner surface 5, e.g. as shown in FIG 1. For example, the protrusions may be formed by stamping (or otherwise deforming) the material of the tubular wall 4, e.g. such that the tubular wall is locally deformed outward to form each of the indentations. It is an advantage that a substantially uniform thickness of the tubular wall 4 can be obtained. Flowever, embodiments of the present invention are not limited thereto. For example, the indentations may also be formed by locally removing, e.g. by drilling, etching or another known subtractive manufacturing technique, the material of the tubular wall. Thus, as shown in FIG 2, the indentations 7 are not necessarily perceivable on the outer surface 6. It is to be noted that other manufacturing methods may be used to achieve substantially the same volumetric shape, e.g. a molding or additive manufacturing process may be used to integrally form the tubular wall as having substantially the same properties as are obtainable by stamping or deforming a basic geometry and/or as are obtainable by a subtractive manufacturing technique to locally remove material from such a basic geometry. For example, a reactor in accordance with embodiments of the present invention may be manufactured by a process comprising steps of molding, centrifugal casting, excavation and/or deposition.

The indentations may be composed of the same material as the tubular wall, but embodiments of the present invention are not necessarily limited thereto. For example, the (wall of the) indentations may be composed of aluminium, stainless steel, carbon steel, a glass- lined material, a polymer-based material, a nickel-base metal alloy, a cobalt-base metal alloy and/or a combination thereof.

The tubular wall 4 may have a dominant geometrical shape, such as a cylindrical shape, that is locally modified by the indentations 7. For example, each indentation has an edge 8. Where reference is made to the circumferential shape of the indentation, reference is made to the shape of this edge 8.

For example, at least a portion of the inner surface may be smooth, e.g. not covered by any of the indentations.

An area coverage, e.g. defined as a total area of the inner surface covered by the indentations over a total area of the inner surface, may lie in the range of 10% to 99%, e.g. in the range of 30% to 90%, e.g. about 40%, about 50%, about 60%, about 70% or about 80%.

However, in a preferred embodiment, the indentations may be provided in only a section of the reactor. This section may be, but is not necessarily, an end part of the reactor proximal to the outlet, e.g. may be a section close to or including the outlet. For example, the section may extend over a length of the reactor in the longitudinal direction. The length of the section may lie in a range of 1 m to 20 m, e.g. 1 m to 10 m, e.g. 1 m to 5 m.

An area coverage, e.g. defined as a total area of the inner surface covered by the indentations over a total area of the inner surface of that section of the reactor that comprises the indentations, may lie in the range of 10% to 99%, e.g. in the range of 30% to 90%, e.g. about 40%, about 50%, about 60%, about 70% or about 80%.

For example, another section, e.g. the complement of the aforementioned section, such as an end part of the reactor proximal to the inlet, may be devoid of the indentations.

For example, at least one, e.g. preferably a plurality of, cross-section of the tubular wall, e.g. perpendicular to the longitudinal axis A, may intersect a number N of indentations of the plurality of indentations, in which this number lies in the range of 1 to 30, e.g. in the range of 3 to 20.

At least a portion of the plurality of indentations may be arranged in one or more patterns, e.g. preferably wherein the pattern is linear, staggered and/or crossed.

Referring to FIG 6, rows of indentations, in which each row 19 is substantially arranged along a cross-section of the tubular wall, may be separated from each neighboring row in the axial direction, e.g. along the longitudinal axis A, by a distance in the range of 0 to 5 times the cross-sectional diameter of the inner surface.

Neighboring rows in the axial direction may be aligned, e.g. such that corresponding indentations 18 in each of the rows are substantially at a same angular position on the tubular wall. It is an advantage that such configuration may favor a higher heat transfer efficiency.

Neighboring rows in the axial direction may be staggered, e.g. such that corresponding indentations in each of the rows are angularly shifted, e.g. over an angle that substantially corresponds to half of the angular separation between two neighboring indentations in a same row. It is an advantage that such configuration may favor a lower pressure drop over the reactor. For example, the exemplary heat transfer map of FIG 10 shows such a staggered configuration.

In a row, the indentations may be spread out evenly (i.e. uniformly), e.g. as schematically illustrated in FIG 6 for eight indentations per row. For example, each pair of neighboring indentations in a row may be separated by an angle of 45°, for the example of eight indentations per row, or, generally, by an angle of 360°/N where the row contains N indentations.

For example, FIG 17 illustrates the impact of the number N on the thermal enhancement Nu/NuO (Nusselt number ratio Nu/Nuo) and the pressure drop enhancement ff/ffO (pressure drop ratio Dr/Dro), as obtained by simulations of reactors in accordance with embodiments of the present invention.

Referring to FIG 7, the indentations may also be spread out unevenly (i.e. not uniformly) in a row. For example, the inner surface of the tubular wall may be devoid of indentations in an angular region, e.g. a cylinder segment. This angular region may cover an arc around the longitudinal axis A in the range of 10° to 300°, e.g. in the range of 45° to 225°, e.g. in the range of 90° to 180°, e.g. about 90°. It is to be noted that the schematic representation and the three-dimensional rendering shown in FIG 7 do not relate to identical reactors, i.e. the number of indentations differ, even though both representations illustrate a non-uniform angular distribution of the indentations.

For example, referring again to FIG 17, by spacing the N (in this example N = 4) indentations in a row over an arc of less than 360°, e.g. of about 180°, while leaving the remaining part, e.g. about 180°, of the circumference of the reactor uncovered by indentations, a surprising increase in the heat transfer enhancement Nu/Nuo can be achieved without a corresponding substantial change in the pressure drop enhancement Dr/Dro, as indicated by the marker 170.

A straight continuation 9 of the inner surface 5 over each indentation 7 and along the tangent of the inner surface, i.e. the tangent on the edge 8 and in accordance with the surface orientation outside of the indentation (or, more precise, the limit of the tangent when approaching the edge from outside the area circumscribed by the edge), may describe a closed and continuous surface that completes the dominant geometrical shape. While the meaning of the circumferential shape and/or edge of the indentation is clear on its own, the edge may also be defined as that closed curve over the inner surface that would form such continuous closure of the inner surface when the interior of the closed curve is excluded and replaced by a tangential continuation of the inner surface. Where reference is made to the volume of the indentation, reference is made to the volume enclosed by the indented inner surface and such tangential continuation of the inner surface.

In a reactor in accordance with embodiments of the present invention, at least one, e.g. each, indentation 7 may extend for a maximum depth into the wall, e.g. relative to the straight continuation 9 of the inner surface, that lies in the range of 0.1 mm to 10 mm, e.g. preferably in the range of 0.2 mm to about 2.0 mm, e.g. in the range of 0.2 mm to 1.0 mm.

The maximum depth of the (or each) indentation 7 into the wall may lie in the range of 0.01 to 0.15 times the (average) cross-sectional diameter of the inner surface. The point where the maximum depth is reached will be referred to herein as the 'point of maximal depth'.

In a reactor in accordance with embodiments of the present invention, at least one, e.g. each, indentation 7 may have a diameter in the range of 0.1 cm to 5.0 cm, e.g. preferably in the range of 0.5 cm to 2.0 cm. For example, this diameter may refer to a diameter of the smallest circle encompassing the edge 8 of the indentation.

In a reactor in accordance with embodiments of the present invention, at least one, e.g. each, indentation 7 may have a depth-to-diameter ratio of the maximum depth mentioned hereinabove over the diameter mentioned hereinabove that lies in the range of 0.01 to 0.5, e.g. preferably in the range of 0.05 to 0.4, e.g. even more preferred in the range of 0.1 to 0.3.

Each indentation 7 of the plurality of indentations comprises at least one elongated surface feature 14 of a part of the inner surface that forms the indentation and/or at least one concavity 13 of the edge 8 of the indentation that, in operation of the reactor, causes the flow to form at least two distinct flow vortices, e.g. non-transient flow vortices, in and/or near the indentation 7.

Referring to FIG 3, an indentation 7 of the plurality of indentations may comprise a concavity 13 of the edge 8 of the indentation that, in operation of the reactor, causes the flow to form at least two distinct flow vortices, e.g. non-transient flow vortices, e.g. flow vortices that are counterrotating with respect to each other, in and/or near the indentation. This concavity 13 may be formed by a cusp, e.g. a spinode, of the edge.

Referring to FIG 4, an indentation 7 of the plurality of indentations may comprise an elongated surface feature 14, e.g. a ridge, of a part of the inner surface that forms the indentation that, in operation of the reactor, causes the flow to form at least two distinct flow vortices, e.g. non-transient flow vortices, e.g. flow vortices that are counterrotating with respect to each other, in and/or near the indentation. For example, such elongated surface feature 14 may locally extend along (e.g. may be parallel to) the central longitudinal axis A of the flow conduit, e.g. forming a ridge.

For example, such elongated surface feature 14 may comprise a ridge along an axis B (e.g. a centerline B) of the indentation 7. For example, such axis B may be substantially aligned with, e.g. substantially parallel to or parallel to, the longitudinal axis A of the flow conduit.

For example, the depth of the indentation may comprise two local maxima on, respectively, either side of the axis B, e.g. caused by a ridge along the axis B.

Referring to FIG 5, each indentation of the plurality of indentations 7 may have a circumferential shape, i.e. a shape of the edge 8 of the indentation on the inner surface 5, that is substantially wider in a direction B toward the outlet 3 than toward the inlet 2, e.g. where such width wi,W is expressed in a direction perpendicular to that direction B and substantially tangential to the shape of inner surface 5.

For example, each indentation of the plurality of indentations may be droplet-shaped or heart-shaped, where a narrow end of the droplet or heart shape may be substantially directed toward the inlet.

It shall be understood that the edge being a closed curve may imply that such width may approaches zero on both extremes 11 in respectively the direction B toward the outlet and in the inverse direction toward the inlet. Flowever, when dividing the shape in two complementary parts on either side of the midpoint 12 between these extremes 11, the width W on the side toward the outlet may be on average larger than the width wi on the side toward the inlet. Alternatively or additionally, a maximum of the width W may be located in the part on the side between the midpoint 12 and the extreme point 11 in the direction toward the outlet 3.

Referring again to FIG 3, the concavity 13 of the edge 8 may be located in the part on the side between the midpoint 12 and the extreme point 11 in the direction toward the outlet 3.

The direction B from the inlet 2 and toward the outlet 3 may be substantially parallel with the longitudinal axis A. The circumferential shape may be symmetrical when mirrored with respect to the direction B through a geometrical center of the shape.

Referring to FIG 8, an exemplary three-dimensional shape of the indentation 7 is illustrated. In this example, the edge of the indentation may also have a concavity 13, e.g. a cusp point. The circumferential shape may be symmetrical when mirrored with respect to the direction B, e.g. a direction B substantially parallel with the longitudinal axis A of the flow conduit. The volume of the indentation 7 may be symmetrical when mirrored with respect to a plane through the direction B and substantially normal to the inner surface.

A maximum width W of the circumferential shape of the indentation, e.g. the maximum distance between any two points on the edge in the direction perpendicular to the direction B, may lie in the range of nD/8N to nD/N, where D refer to the (average) cross- sectional diameter of the inner surface and N refers to the number of indentations in a row 19.

A distance between the point of maximal depth 21 and a downstream point 23 on the edge 8 may lie in the range of 0.01 to 0.50 times the (average) cross-sectional diameter D of the inner surface.

A distance between the point of maximal depth 21 and an upstream point 22 on the edge 8 may lie in the range of 0.05 to 1 times the (average) cross-sectional diameter D of the inner surface.

A maximum distance in between the point of maximal depth 21 and that part of the edge 8 of the indentation that lies in the direction of the outlet with respect to the point of maximal depth 21, i.e. the downstream edge, may lie in the range of 0.01 to 0.50 of the (average) cross-sectional diameter of the inner surface. This maximum distance may be equal to, or may not be equal to, the distance between the point of maximal depth 21 and the downstream point 23 on the edge 8.

The downstream point 22 and the upstream point 23 may be defined as the points where the edge 8 of the indentation intersects a plane through the point of maximal depth 21 that is that oriented along the direction B and oriented substantially normal to the inner surface, in which the downstream point 22 is closer to the outlet than the upstream point 23.

A slope cii of the indentation 7 leading from the upstream point 23 to the point of maximal depth 21 may lie in the range of 0° to 70°.

A slope ci of the indentation 7 leading from the point maximal depth 21 to the point of maximal depth 21 may lie in the range of 0° to 70°.

A slope ci of the indentation 7 leading from the point of maximal depth 21 to the downstream point 22 may lie in the range of 5° to 90°.

A slope a ₄ of the indentation 7 leading from the downstream point 22 to the point of maximal depth 21 may lie in the range of 5° to 90°. These slopes cii, ci2, a^, a ₄ may be defined relative to a reference plane formed by the continuation of the inner surface 9 as described hereinabove.

The point of maximum depth will be, for the sake of simplicity, be referred to as the central point, without thereby implying that this point corresponds to, for example, a geometrical center. The shape of the indentation may be described by four Bezier curves, e.g. third-order Bezier curves, as illustrated in FIG 13, e.g. a first curve from the upstream point 23 to the central point 21, a second curve from the central point 21 to the downstream point 22, a third curve from a first lateral point 132 to the central point 21, and a fourth curve from a second lateral point 134 (on the side opposite of the side of the first lateral point) to the central point 21.

Referring to FIG 18, as known in the art, a Bezier curve can be defined by four points, namely a start point A, an end point B, a point C defining a slope at the start point, and a point D defining a slope at the end point. A smooth curve is defined by these four points, and the combination of the four Bezier curves referred to hereinabove may thus define a smooth indentation. For example, a Bezier curve of order 3, constructed from four points Po,Pi,P2,P3 may be expressed by:

Bit ) = (1 — tfP ₀ + 3t(l— t) ² Pi + 3t ² (l— t)P ₂ + t ³ P ₂ , where t is a parameter in the range of 0 to 1.

Thus, eight slopes, e.g. corresponding to the points C and D for each of the four Bezier curves, may be used to characterize the geometrical shape of the indentation. Furthermore, to form a smooth indentation, the C and/or D points defining the slope in the central point 21 may lie in a same plane for the first curve from the upstream point 23 to the central point 21 and for the second curve from the central point 21 to the downstream point 22. Likewise, the C and/or D points defining the slope in the central point 21 may lie in a same plane for the third curve from the first lateral point 132 to the central point 21 and for the fourth curve from the central point 21 to the second lateral point 134. The plane in which the upstream point 23, the central point 21 and the downstream point 22 lie may be a plane of symmetry of the indentation.

Under the constraints referred to hereinabove, six slope values may define the geometrical shape of the indentation, in combination with predetermined positions of the points 23,132,21,134,22: a slope at point 23 towards point 21, a slope at point 22 towards point 21, a slope at point 21 towards point 22, a slope at point 21 towards point 23, a slope at point 21 towards point 132 (being equal to the slope at point 21 towards point 134) and a slope at point 132 towards point 21 (being equal to the slope at point 134 towards point 21). These six degrees of freedom can be expressed by six slope values cii to ci ₆ . For example, FIG 19 illustrates the slope angles cii to a ₄ in the plane through the downstream point 22, the central point 21 and the upstream point 23.

In a second aspect, the present invention also relates to a furnace for producing light olefins from a hydrocarbon feedstock material, the furnace comprising a reactor 1 in accordance with embodiments of the first aspect of the present invention.

Referring to FIG 9, such furnace 10 is schematically illustrated. The furnace comprises one or more reactors 1 in accordance with embodiments of the present invention. Fleat Q is supplied by the furnace to heat a hydrocarbon material, e.g. transported by a steam flow, introduced via the inlet 2 in the reactor 1.

The furnace 10 is adapted for providing light olefins, e.g. C FI and C H , at the outlet 3 of the reactor 1.

In a third aspect, the present invention relates to a method for producing light olefins using a reactor in accordance with embodiments of the first aspect of the present invention and/or using a furnace in accordance with embodiments of the second aspect of the present invention. For example, the method may comprise cracking a hydrocarbon feedstock material into light olefins at a temperature in the range of 700°C to 900°C.

In a fourth aspect, the present invention relates to a reactor for use in cracking hydrocarbons of a hydrocarbon material. The reactor comprises an inlet, an outlet and a flow conduit between the inlet and the outlet for transporting the hydrocarbon material in a flow from the inlet to the outlet. The flow conduit comprises a tubular wall having an inner surface and an outer surface, in which the inner surface has a plurality of indentations provided in the tubular wall. The indentations are arranged in a plurality of rows, each row being substantially arranged along a cross-section of the tubular wall. The indentations of at least one row, e.g. of each row, of the plurality of rows may be spread out unevenly in that row, such that the inner surface of the tubular wall is devoid of indentations over an angular region. The angular region devoid of indentations covers an angle around the axial direction of the tubular wall in the range of 45° to 225°, e.g. in the range of 90° to 180°.

In a reactor in accordance with embodiments of the present invention, each indentation of the plurality of indentations may be spherical, ovoid, droplet-shaped and/or heart-shaped. In a reactor in accordance with embodiments of the present invention, an area coverage, defined as a total area of the inner surface that is covered by the plurality of indentations over a total area of the inner surface, may lie in a range of 5% to 90%.

In a reactor in accordance with embodiments of the present invention, each row may be separated from each neighboring row in an axial direction of the tubular wall by a distance in the range of 0 to 5 times the cross-sectional diameter of the inner surface.

In a reactor in accordance with embodiments of the present invention, at least one of the rows may comprise a number of the plurality of indentations, in which this number lies in the range of 1 to 20.

In a reactor in accordance with embodiments of the present invention, a maximum width of the circumferential shape of each of the number N of indentations may lie in the range of nD/8N to nD/N, where D refers to the cross-sectional diameter of the inner surface and N refers to the number of indentations in said row.

In a reactor in accordance with embodiments of the present invention, neighboring rows of the plurality of rows in the axial direction may be aligned such that corresponding indentations in each of the rows are positioned substantially at a same angular position on the tubular wall.

In a reactor in accordance with embodiments of the present invention, neighboring rows of the plurality of rows in the axial direction may be staggered such that corresponding indentations in each of the neighboring rows are angularly shifted with respect to each other.

In a reactor in accordance with embodiments of the present invention, at least one of the plurality of indentations may extend for a maximum depth into the tubular wall, in which the maximum depth lies in the range of 0.1 mm to 10 mm and/or in which the maximum depth lies in the range of 0.01 to 0.15 times the cross-sectional diameter of the inner surface.

Various advantageous effects of embodiments of the present invention may be simultaneously evaluated by the thermal enhancement factor TEF, which may be defined as a

Nu/Nu ₀ relative heat transfer improvement over a relative pressure drop increase, TEF =

Al/3'

⁽ Ap ₀ ^J where Dr ₀ and Nu ₀ refer to the pressure drop between the inlet and outlet, respectively the heat transfer (Nusselt number), for a conventional reactor without specific optimizations, e.g. a bare and smooth cylindrical reactor without inserts or surface modifications, and Dr and Nu refer to the pressure drop, respectively the heat transfer (Nusselt number), for an augmented reactor design at hand, e.g. a reactor in accordance with embodiments of the present invention. For example, FIG 10 shows a map of the heat transfer improvement Nu/Nu ₀ , for a configuration in accordance with embodiments of the present invention.

Simulations of the reactor design in accordance with embodiments of the present invention, for a set of 1500 different geometrical configurations of the indentations, were performed with a customized solver based on the CFD software package OpenFOAM that is produced by OpenCFD Ltd. and released free and open source to the general public. The customized solver has been implemented for the detailed evaluation of heat transfer and friction characteristics in generic tubular geometries while another solver incorporates the chemical kinetics to perform full-scale reactive simulations.

An optimization routine was performed with the Dakota (Design Analysis Kit for Optimization and Terascale Applications) Toolkit. Reactive simulations can be performed with OpenFOAM. Evaluation of expected yields, TMTs and coking rates was performed using a purpose-specific simulation algorithm 'COILSIM1D'.

Information on the averaged pressure drop and heat transfer was implemented in a one-dimensional reactive simulation package, COILSIM1D, to estimate the TMT temperatures in an industrial furnace as well as assessing yields, coke formation and run length. These results showed a decrease of the maximum TMT of over 30 degrees, relative to a conventional reactor tube.

FIG 11 shows the thermal enhancement factor TEF, computed for the simulations in this example. As can be observed, an improvement of 16.6% over the reference bare tube performance can be obtained by a reactor in accordance with embodiments of the present invention.

FIG 12 shows the relative heat transfer improvement, computed for the simulations in this example.

FIG 14 shows simulations of the wall temperature and the pressure, at the start of a run, as function of axial position along the reactor for two reactors 141,142 in accordance with embodiments of the present invention, and a reference prior-art reactor 140 comprising a bare tubular reactor. FIG 15 shows the evolution over a run, i.e. as function of the onstream time, of the maximum TMT and the pressure drop over the reactor. FIG 16 shows the evolution over a run, i.e. as function of the onstream time, of the produced ethylene and propylene fractions.

FIG 20 shows two exemplary three-dimensional shapes of indentations: both have similar dimensions, but one is droplet-shaped (FIG 20A) and the other has a concavity 13 of its edge 8 in the form of a cusp, thereby being heart-shaped (FIG 20B). These indentation shapes correspond to designs 704 and 718 as marked on FIG 11. Heat transfer maps, showing the local Nusselt number ratio Nu/Nuo, for the droplet-shaped indentation and the heart-shaped indentation are depicted in FIG 21A and 21B respectively. For a bulk temperature of 726.9 °C, this corresponds to an average wall temperature of 754 °C, a maximum wall temperature of 767 °C and an overall Nusselt number ratio of 1.13 for the droplet-shaped indentation (A).

Under the same conditions, the average wall temperature is 752.8 °C, the maximum wall temperature is 765.5 °C and the overall Nusselt number ratio is 1.20 for the heart-shaped indentation (B). A generally improved heat transfer, with lower average and maximum wall temperatures and a higher Nusselt number ratio, is thus observed for the heart-shaped indentation compared to the droplet-shaped indentation. Both indentations were furthermore seen to have a similar pressure drop value, so that overall the thermal enhancement factor (TEF) of the heart-shaped indentation was higher than that of the droplet-shaped indentation.

To rationalize this difference, large eddy simulations were performed, which show that two separate vortices co-exist at all times for the heart-shaped indentation. These vortices do not display the transient behavior seen in spherical indentations, where a vortex alternates between two positions at opposite sides of the axial centerline of the dimple, as for example reported by Voskoboinick et al. (V. Voskoboinick, N. Kornev, and J. Turnow, "Study of Near Wall Coherent Flow Structures on Dimpled Surfaces Using Unsteady Pressure Measurements," Flow Turbulence and Combustion , vol. 90, pp. 709-722, Jun 2013.). Without being bound by theory, it is believed that these separate vortices lead to the observed improvement in heat transfer. These experiments therefore illustrate the improvements obtained with embodiments of the present invention in general, where an elongated surface feature and/or a concavity causes the flow to separate into at least two distinct flow vortices in and/or near the indentation; and the improvements obtained with embodiments comprising at least a concavity in particular.