INTERNALLY PROFILED TUBES

Abstract

The present invention relates to internally profiled variable pitch tubes or pipes made of steel. The terms tube and pipe are used synonymously in the context of this invention. These tubes are used in the petrochemical industry to crack oil, gas and shale feedstocks into simple hydrocarbons such as ethylene and similar products.

Claims

1: A steel tube for use in cracking hydrocarbons at high temperature, wherein the steel tube has a fin formed on the inner wall of the tube, the fin extending continuously in a helical direction across at least a portion of an axial length of the tube, the fin having a region of varying helical pitch.

2: The steel tube of claim 1, wherein the fin extends for an entire axial length of the tube.

3: The steel tube of claim 1, wherein the fin comprises an initial region of constant helical pitch.

4: The steel tube of claim 1, wherein the fin comprises a final region of constant helical pitch.

5: The steel tube of claim 3, wherein the initial region of constant helical pitch is between 1 D and 40 D in length (where D is an internal diameter of the tube).

6: The steel tube of claim 4, wherein the final region of constant helical pitch is between 1 D and 40 D in length (where D is an internal diameter of the tube).

7: The steel tube of claim 1, wherein the region of variable helical pitch is a length that is at least 80% of the axial length of the tube.

8: The steel tube of claim 1, wherein the region of variable helical pitch is a length that is at least 50% of the axial length of the tube.

9: The steel tube of claim 1, wherein the region of variable helical pitch has a length that is from 0.5 to 1.0 times the length of the tube.

10: The steel tube of claim 1, wherein a pitch of the fin in the region of varying helical pitch increases from its beginning to its end.

11: The steel tube of claim 10, wherein the increase in pitch is constant along the axial length of the region of varying helical pitch.

12: The steel tube of claim 1, wherein a cross-sectional profile of the walls of the tubes are circular in shape.

13: The steel tube of claim 1, wherein an height of the fin is approximately constant along its axial length.

14: The steel tube of claim 1, wherein the tube has a diameter in the range of 20 mm to 100 mm.

15: The steel tube of claim 1, wherein the tube has a diameter in the range of 40 or 50 mm to 75 or 80 mm.

16: The steel tube of claim 1, wherein an cross-section of the fin is semi-circular.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Embodiments of the invention are further described hereinafter with reference to the accompanying drawings, in which:

[0059] FIG. 1 demonstrates fluid flow through three tube designs, as modelled by the CFD software described herein: a) a bare tube, with no internal fin, b) a tube with a discontinuous/intermittent fin of constant pitch, and c) a tube according to the present invention, having a continuous fin of varying pitch.

[0060] FIG. 2 charts the core temperature of gas flowing through the tubes of RUN06, RUN07, and RUN08 as a gas passes along the axial length of the tube.

[0061] FIG. 3 charts the core pressure of a gas flowing through tubes of RUN06, RUN07, and RUN08 as a gas passes along the axial length of the tube.

[0062] FIG. 4 depicts an example of a Pareto plot that results from the modelling experiments detailed herein.

[0063] FIG. 5 is a flow diagram representing the method used to determine the optimal design parameters of tubes according to the present invention.

[0064] FIG. 6 demonstrates fluid flow through tubes according to RUN36 and RUN37.

[0065] FIG. 7 charts the core pressure of a gas flowing through tubes of RUN36 and RUN37 as a gas passes along the axial length of the tube.

[0066] FIG. 8 demonstrates fluid flow through tubes according to RUN01 and RUN02.

[0067] FIG. 9 depicts the internal profile of an exemplary tube according to the present invention.

DETAILED DESCRIPTION

[0068] The current invention is designed to achieve the maximum mixing of a fluid passing through a tube to facilitate an efficient chemical reaction. The tube comprises a continuous fin with a varied pitch helical shape, starting with a length or without a length of constant helical pitch at a defined initial pitch, and finishing with a length or without length of constant pitch at a defined final pitch. In other words, the initial and final regions of constant helical pitch are optional.

[0069] In the context of the present invention, a ‘continuous’ fin is a fin that extends from a first point to a second point without interruption. It may be that the first point is the first end of the tube and the second point is the second end of the tube.

[0070] We have found that there are four parameters of the tube which may be defined in order to calculate the appropriate region of variable helical pitch of the tube in order to maximise the efficiency of the cracking reaction while minimising pressure drop across the length of the tube. These are: [0071] Fin pitch of the initial constant helical pitch region [0072] Length of the initial constant helical pitch region [0073] Fin pitch of the final constant helical pitch region [0074] Length of the final constant helical pitch region

[0075] These parameters were used by us to model the pressure and temperature of the fluid flowing through the tube. This was done using computational fluid dynamics (CFD) software as described below.

[0076] Accordingly, it will be appreciated that tubes according to the present invention have a region of varying helical fin pitch, wherein the length of the varying helical pitch region is a result of the lengths of the initial and final constant helical pitch regions.

[0077] The four parameters described above are determined such that the furnace outlet temperature is maximised and such that the pressure drop across the tube is minimised. Each of these parameters are defined for a tube having a specific tube length and with a specific internal diameter. The software enables optimum values to be determined from our realisation of the four key parameters.

[0078] For example. A tube having a 50 mm internal diameter (ID) and a tube length of 6 m, the following four parameters may maximise the outlet temperature while minimising pressure drop: [0079] Fin pitch of the initial constant pitch region: 100 mm [0080] Length of the initial constant pitch region: 1516 mm [0081] Fin pitch of the final constant pitch region: 128.57 mm [0082] Length of the final constant pitch region: 763 mm

[0083] ‘Pitch’ as described herein refers to the axial length along the tube required for one complete revolution of the helical fin. In other words, the pitch is the distance between equivalent points on two adjacent helical rotations of the fin, for example, between points A and B on FIG. 9. The reference to increasing pitch, or reducing pitch, means that the amount of curvature i.e. gradient of the fin increases or reduces respectively. A constant pitch fin has the same amount of curvature at any point on its length. Similarly, a varying pitch fin has a varying amount of curvature at different points along its axial direction. The fins are generally helical.

[0084] Tubes according to the present invention therefore aim to maximise the efficiency of heat transfer at a key location within the furnace and minimise as much as possible the pressure drop. Accordingly, the tubes of the present invention may apply to the full length of the entire furnace tube, but preferably to only a portion of the entire furnace tube length.

EXAMPLES

Example 1

[0085] Table 1 shows comparative data for simulations conducted for a series of tubes having an internal fin. The experiment calculated the outlet temperature and pressure drop across the tube for a hydrocarbon cracking reactor. The simulation study comprised four tubes, each with a 50 mm internal diameter and a total axial length of 6 m.

TABLE-US-00001 TABLE 1 RUN02 RUN03 RUN05 RUN06 Description 200 mm Pitch 100 mm Pitch 200-100 150 mm-100 mm Varying Bitch Varying Pitch Constant Pitch Length FallTube FaTube 10D at either None end of sot Total Pressure Drop (barg) 0.514 0.840 0.655 0.570 Outlet Temperature (° C.) 982.3 1003.9 983.9 993.5 Hteating Efficiency (° C./bar) 199.2 147.5 158.5 199.2

[0086] RUN02 relates to a tube with a continuous internal fin having a constant 200 mm pitch across the entire length of the tube, i.e. not a tube according to the present invention. This configuration results in a low pressure drop (0.514 bar), but also a low outlet temperature at the furnace exit (982.3° C.).

[0087] RUN03 corresponds to a similar tube having a continuous internal fin with a constant pitch of 100 mm across the entire length of the tube, i.e. not a tube according to the present invention. This configuration results in a high outlet temperature at the furnace exit (1003.9° C.), but also a high pressure drop (0.840 bar).

[0088] RUN05 relates to a tube having an initial region of 200 mm constant pitch and final region of 100 mm constant pitch, each region corresponding to a length of 10 tube diameters. The tube of RUN05 also has a region of varying pitch positioned between the initial and final constant pitch regions. The pitch in the varying pitch region varies from 200 mm at the start of the varying pitch region to 100 mm at the end of the varying pitch region.

[0089] RUN06 corresponds to a tube having no constant pitch region, i.e. a tube in which the initial and final constant pitch regions each have a length of 0 D. Therefore, the tube comprising a region of varying pitch extending along the full length of the tube. The pitch varies from 150 mm at the start of the tube to 100 mm at the end of the tube.

[0090] RUN05 shows a noticeable increase in pressure drop (0.655 bar) and almost no temperature increase relative to RUN02. RUN06 shows a noticeable temperature increase at tube exit (993.5° C.), corresponding to a 10° C. increase relative to a tube having a continuous pitch of 200 mm (RUN02), with only a small increase in pressure drop (0.570 bar).

[0091] The simulations also studied the heating efficiency of each RUN. Table 1 shows that tubes having only a constant pitch region with a 200 mm pitch (RUN02) and tubes having only a variable pitch region with the pitch varying from 150 mm to 100 mm (RUN06) exhibit the best heating efficiency.

Example 2

[0092] A comparative study of the velocity of the fluid inside a 6 m tube length with a 50 mm internal diameter was performed via the simulation methods described herein. The study compared a tube with no internal fin (RUN07) i.e. a ‘reference tube’, a tube with a discontinuous/intermittent fin of constant pitch such as those disclosed in EP1561795 (RUN08), and a tube comprising a region or varying helical pitch, wherein the pitch varies from 150 mm to 100 mm across the length of the tube, i.e. a tube according to the present invention (RUN06).

[0093] The study showed that a laminar fluid motion in the reference tube (RUN07), with the fluid in the centre moving faster than near the tube wall, as can be seen in FIG. 1a. This is typical and expected behaviour of fluid in a tube without an internal fin. Accordingly, the fluid in centre of the tube is much cooler than near the tube wall. The tube comprising a discontinuous fin (RUN08) involves a fluid velocity much higher in the centre of the tube than the reference (RUN07), as can be seen in FIG. 1b. FIG. 1b also demonstrates that fluid flowing through the tube in RUN08 is bouncing on the discontinuous helical fin, with the warn fluid near the tube wall being redirected in several directions and creating turbulence towards the centre of the tube.

[0094] FIG. 1c demonstrates that a tube according to the present invention (RUN06), where continuous fin having a varying pitch, produces a fluid velocity in the centre of the tube that is much higher than reference tube (RUN07). However, in contrast to the tube comprising a discontinuous fin (RUN08), the higher fluid velocity is not only concentrated in the tube centre, but across the full internal area of the tube (tube wall to centre) by the time that the fluid has reached the second half of the tube.

[0095] FIG. 1c demonstrates that fluid passing through the second half of the tube section, is submitted to a centrifugal force with spinning turbulence orientated more in the axial direction of the tube. This creates less pressure drop relative to it the tube of RUN08, where the fluid bouncing creates turbulence resulting in a pressure drop across the tube. The results of this comparative study are summarised in Table 2.

TABLE-US-00002 TABLE 2 RUN06 RUN07 RUN08 Description 150 mm-100 m Bare (Unwelded) Discontinuous Pitch Spiral Tube 90.5 mm Pitch Spiral Total Pressure 0.570 0.340 0.794 Drop (barg) Outlet 993.5 976.2 996.9 Temperature (° C.) Heating Efficiency 199.2 283.0 147.1 (° C./bar)

[0096] The average streamwise velocity and average in plane velocity of each tube was determined, as shown in Table 3. The average streamwise velocity is almost the same for each of the three tube designs. However, the average in-plane velocity of the tube of RUN07, which has no internal fin, is almost non-existent (0.13 m/s). Conversely, the tube of RUN08, which has a constant but discontinuous pitch, is significantly higher (33.85 m/s), however tubes according to the present invention, i.e. RUN06, demonstrate a drastically increased in-plane velocity (52.83 m/s). This is 18.43 m/s higher than the discontinuous design of RUN08. Therefore, tubes according to the present invention demonstrate an increase in the spinning/stirring/mixing of the gas within the tube. This allows a better distribution of the temperature across the entire contents of the tube and therefore a more efficient cracking reaction can occur.

TABLE-US-00003 TABLE 3 RUN06 RUN07 RUN08 Description 150 mm-100 m Bare (Unwelded) Discontinuous Varied 90.5 mm Pitch Spiral Tube Pitch Spiral Average 165.55 164.31 167.06 streamwise velocity (Ux − m/s)) Average in-plane 52.28 0.13 33.85 velocity magnitude (Uy Uz − m/s) Ratio of in plane to 0.314 7.8E−5 0.203 streamwise velocity

[0097] FIG. 2 plots the distribution temperature along each of the tubes of RUN06, RUN07, and RUN08 at their core. FIG. 2 clearly shows that the core exit temperature of the tube of RUN07 (no fin) is over 20° C. lower than the core exit temperature of the tubes of RUN06 and RUN08. The temperature distribution pattern of the tube of RUN06 (i.e. a tube of the invention) falls between the temperature in the tubes of RUN07 and RUN08, until the last 500 mm of the tube, where the central temperature of RUN06 is slightly above that of RUN08. In this regard, one aim of the invention is to bring the fluid to its highest temperature just before exiting the tube to maximise cracking but to minimise secondary reactions due to long exposure at a cracking temperature, where formation of aromatics and soot decrease the yield of the desired cracked products, such as ethylene.

[0098] Similarly, FIG. 3 shows that the starting pressure in the tube of RUN08 has to be much higher than for tubes of the invention (RUN06) in order to reach a similar exit pressure. Whilst the pressure drop is linear after 1000 mm up to the exit for the tubes of RUN07 and RUN08, this is not the case for the RUN06, where the pressure drops mostly in the last 1000 mm of the tube, where it is expected that the velocity will be much higher because of increased spinning/mixing of the gas, and where the temperature increase is the highest.

[0099] Another way to understand the temperature distribution of the gas across and along the tube length is to evaluate the volume of total gas reaching a given temperature or to evaluate the length of tube needed for the gas to reach a given temperature (slide 7). The chosen temperatures been 927° C., 955° C., 975° C., it was determined the portion of gas above these temperatures and the length of tube in which the gas need to travel to reach these temperatures. If the average exit temperature of the concurrent and the invention are nearly identical, the length of tube needed to a gas above 975° C. which is nearly the same than the exit temperature of the reference, is longer for the invention (104.5×internal diameter=5225 mm) than the competitor (98.3×internal diameter=4915 mm), which means that the extra nearly 20° C. increase temperature before tube exit are reach in a shorter distance and therefore with less secondary reactions. It can observe that the volume of fluid reaching the given temperature are below the competitor with 2%, 5% and finally 6%, but these results have to be considered with the pressure drop results. As if the volume is higher and as if the exit temperature of the invention is slightly lower than the competitor, in other hand, the pressure drop is much smaller (slide 08), so this means that the current invention is impressively efficient to heat the fluid (199.2° C./bar) than the concurrent (147.1° C./bar), with 52.1° C./bar more heating efficiency.

Invention Design Optimisation

[0100] The axial length of the initial and final regions of constant helical pitch determines the length of the region of varying helical pitch. The length of the region of varying helical pitch is the length of the tube that is remaining once the initial and final regions of constant helical pitch have been determined.

[0101] Therefore, it will be appreciated that in some embodiments where the initial and final regions of constant helical pitch are absent, the total axial length of the fin is the same as the axial length of the tube.

Example 3

[0102] A number of simulations were performed by the methods described herein, to determine the influence of each of the tube parameters on the pressure drop and gas outlet temperature. The results of these simulations are given in Table 4.

TABLE-US-00004 TABLE 4 Outputs Input Parameters Pressure Outlet Initial Final Initial Final Drop Temperature Run Pitch Pitch Length Length (bar) (° C.) 11 194.7 144.75 1579 1684 0.4256 985.98 12 247.4 55.25 526 421 0.5439 987.24 13 131.6 102.65 2000 1158 0.6393 996.66 14 110.5 134.2 421 842 0.6064 996.42 15 257.9 128.95 632 211 0.3917 983.14 16 278.9 118.4 1158 1895 0.4311 984.64 17 300 76.3 1263 947 0.4612 983.90 18 173.7 150 1474 526 0.4891 986.53 19 152.6 50 1368 632 0.8451 994.26 20 163.2 81.6 211 316 0.6594 990.98 21 226.3 86.85 1684 105 0.4732 984.42 22 100 113.15 947 1789 0.7098 999.79 23 205.3 71.05 1789 1579 0.6460 992.32 24 236.8 65.8 737 2000 0.7543 994.37 25 289.5 97.35 105 1053 0.4759 984.07 26 268.4 123.7 1895 737 0.4059 982.28 27 215.8 139.45 315 1263 0.4741 985.99 28 184.2 92.1 0 1368 0.6053 993.77 29 121.1 60.55 842 1474 0.9863 998.03 30 142.1 107.9 1053 0 0.5854 994.77 31 240.40 119.80 2000 470 0.3987 983.28 32 174.50 127.80 2000 1056 0.4633 988.10 33 142.10 119.50 1685 980 0.5536 993.41 34 100.00 122.00 524 467 0.7033 1000.17

[0103] As evident from Table 4, the highest gas outlet temperature can be achieved with an initial pitch in the region of constant helical pitch that is smaller than the pitch in the final region of constant helical pitch (see RUN14, RUN22 and RUN34).

[0104] Accordingly, the axial length of the region final region of constant helical pitch has a greater impact on the pressure drop across the tube than the initial region of constant helical pitch. We have found that the longer the axial length of the region of constant helical pitch, the large the pressure drop across the tube. However, the increase of the axial length of the initial region of constant helical pitch on its own does not have a notable influence on the pressure drop. The initial region of constant helical pitch only appears to influence pressure drop when combined with an increasing axial length of the region of final constant helical pitch.

[0105] This means that relatively short, or non-existent, initial and final regions of constant helical pitch are most effective. We also found that the influence of the axial length of the initial and final constant pitches are similar on the gas exit/outlet temperature as on the pressure drop.

Methodology for Modelling Fluid Flow

[0106] To simulate the fluid flow inside tubes of the invention, computational fluid dynamics (CFD) software was used to solve a series of equations that describe how the fluid behaves within a given geometry and set of flow conditions.

[0107] The CFD solver used to determine the performance characteristics of each tube design is based on OpenFOAM (an open source CFD solver). However, there are several commercial CFD solvers available that would be capable of simulating the gas flow through the tube design and outputting pressure drop and gas exit temperature. For example, the CFD solver used to determine the characteristics of the tube may be ANSYS Fluent, ANSYS CFX, or Star CCM+.

[0108] The following assumptions are made when setting up the CFD model: [0109] The flow is compressible, unsteady, turbulent and single phase [0110] There are no significant geometric features directly upstream or downstream of the region of interest [0111] The tube wall is held at a fixed temperature [0112] The incoming flow enters at a fixed temperature [0113] The mass flow rate entering the tube is fixed [0114] The chemical reactions within the tube are not modelled.

[0115] The code used to determine the performance envelope for the design can be replicated using one of the following commercial optimisation codes: [0116] Mode Frontier (https://www.esteco.com/modefrontier) [0117] Noesis (https://www.noesissolutions.com/our-products/optimys/engineering-optimization) [0118] The type of optimisation used is an ‘expensive objective function’ and using meta-modelling methods (https:en.wikipedia.org/wiki/Metamodeling). [0119] The results are assessed with a response surface approach, in particular this uses a type of analysis known as kriging (https://en.wikipedia.org/wiki/Kriging).

[0120] We have undertaken a kriging process that takes a set of points that populate a design space, each of which consist of geometric parameters and desired outputs and fits a response surface to the input data. This response surface then gives a method for predicting how the outputs will respond to any change of the design within the limits of the input parameters. In the case of tubes of the present invention, each point in the design space consists of the following:

TABLE-US-00005 Fin pitch of the initial region of constant helical pitch Parametric Input Fin pitch of the final region of constant helical pitch Parametric Input Axial length of the initial region of constant helical pitch Parametric Input Axial length of the final region of constant helical pitch Parametric Input Pressure Drop Simulation Output Outlet Temperature Simulation Output

[0121] Therefore, each output design point provides a predicted performance and the combination of the four design parameters that achieve it.

[0122] The optimisation code produces a Pareto plot that defines the predicted limits of the design space, based on the input parameters. FIG. 4 shows an example of a Pareto plot. The red points are CFD simulation results that have been used in the optimisation code to predict the performance envelope (bounded by the blue points). In this example the green line shows the favourable frontier of the Pareto. Further details on the Pareto plot can be found on the following webpage: https://en.wikipedia.org/wiki/Multi-objective optimization.

Optimisation Procedure

[0123] The method used to determine the optimal parameters of the tube is depicted in the flow diagram of FIG. 5.

[0124] In a first step, initial CFD runs are undertaken to scope out a suitable range of helix shape parameters to be used for the optimisation study. These runs consist of a series of tubes comprising a fin of constant pitch or varying pitch.

[0125] In a second step, limits for the four design parameters are chosen based on the stage 1 results, with the aim of providing a relatively wide parameter range around the current best constant pitch fin geometry. Performance is judged on pressure drop and outlet temperature. The design parameters are ‘initial pitch’, ‘final pitch’, ‘length that initial pitch is held constant’ and ‘length that final pitch is held constant’, as described herein.

[0126] In a third step, a set of CFD runs with various combinations of each design parameter is then assessed, to populate the design space. The parameter values for these runs is determined using a Latin hypercube method, to ensure an efficient number of design points (https://en.wikipedia.orgiwiki/Latin_hypercube_sampling). In this case with these four parameters, this results in 20 simulations being run.

[0127] Subsequently, in a fourth step, a time averaged pressure drop and outlet temperature is extracted from all of the CFD runs from stage 3.

[0128] In a fifth step, a response surface approach is used to analyse the output data (pressure drop and outlet temperature). This uses a kriging process, as discussed elsewhere herein. Analysis of the response surface results in a Pareto plot, which displays the predicted limits of performance in terms of pressure drop and outlet temperature over the limits of the shape parameters.

[0129] In a sixth step, a series of design points of interest are chosen, these are on the Pareto front of the design envelope that produces the desired performance i.e. they have a high outlet temperature and low pressure drop. The chosen design points are then simulated in CFD.

[0130] In a seventh step, the kriging process is repeated including the new runs to further refine the fit of the response surface in the region of interest.

[0131] If the Pareto front of the design envelope changes significantly after the seventh step, then the fit of the response surface is deemed not to have sufficient resolution on the Pareto front of the design envelope. A new series of design points is taken from the Pareto front of the design envelope and are then simulated in CFD.

[0132] If the Pareto front of the design envelope does not change significantly, then the fit of the response surface is deemed to have a high enough resolution on the Pareto front of the design envelope, and an optimal design is chosen from the frontier.

FURTHER EXAMPLES

Example 4

12 m Length Tube—50 mm Inside Diameter:

[0133] Tubes according to the present invention may be 6 m in length. However, conventional cracking furnaces comprise a cracking tube that is 12 m in length. We have therefore investigated the present invention wherein the tube has an axial length of 12 m.

[0134] A comparative study between a 12 m tube of the present invention (RUN36) and a 12 m tube comprising a discontinuous fin of constant helical pitch (RUN37). The tube of RUN36 comprises a fin having a region of varying pitch, wherein the fin having a region of varying pitch extends across the final 6 m portion of the tube. In other words, the tube of RUN36 has an initial 6 m axial length in which there is no fin.

[0135] FIG. 6 depicts the gas stream velocity profiles of the tubes of RUN36 (FIG. 6a) and RUN37 (FIG. 6b). It is clear from FIG. 6 that the gas velocity in the 12 m tube of the invention is better distributed across and along the entire tube length when compared to the tube of RUN37. Accordingly, the tube of RUN36 will have an improved heating efficiency and less pressure drop compared to RUN37.

[0136] The summary of the gas stream velocity shown in Table 5 demonstrates that the average in-plane velocity of a 12 m tube of the invention and that of a 12 m tube comprising a discontinuous fin of constant pitch are very similar to the average in-plane velocity of the 6 m tubes detailed in Table 3. Therefore, we have found that despite an initial finless 6 m region in a 12 m tube of the invention (compared to a 12 m discontinuous fin in RUN37), a 12 m tube of the invention still creates a higher in-plane velocity of the gas stream. Accordingly, a 12 m tube of the invention having a 6 m fin provides enhanced spinning/stirring/mixing of the gas within the tube.

TABLE-US-00006 TABLE 5 RUN36 RUN37 Description Partially Welded 100 mm- Discontinuous 90.5 mm 128.6 m Pitch Spiral Pitch Spiral Average streamwise 170.897 171.479 velocity (Ux − m/s)) Average in-plane velocity 49.307 34.459 magnitude (Uy Uz − m/s) Ratio of in-plane to 0.289 0.201 streamwise velocity

[0137] FIG. 6a shows that the core gas temperature in the tube of RUN 36 does not increase too early in the tube, but instead only begins to increase after around 8.46 m (169.2×ID, where ID=50 mm). This is an essential part of the invention, as this prevents the gas from heating up and cracking too early, which in turn avoids the formation of unwanted secondary reactions.

[0138] We have found that the temperature distribution of the core gas between 8.0 m (160×ID) and the tube exit at 12 m (240×ID), is the most critical region of the tube for efficient cracking. It can be seen in FIG. 6a that the gas temperature increase is drastic in this region of tubes of the invention. In fact, in this short length of the tube of RUN36, the temperature increases to match the temperature of the tube of RUN37.

[0139] More specifically, the core gas temperature in the tube of RUN36 is at 988.5° C. at a point 8 m along the tube, while the temperature of the tube of RUN37 is already 1007.35° C. by this point (i.e. 18.85° C. higher). Accordingly, the tube of RUN 37 is more likely to produce side products than the tube of RUN36. In addition, the core gas temperature in tubes of the invention is 1026.15° C. when it exits the tube, compared to a temperature of 1029.45° C. in the tubes of RUN37 (i.e. only 3.3° C. more than the invention). It follows that the targeted and more efficient mixing resulting from the tubes of the present invention give rise to a more efficient cracking reaction.

[0140] Furthermore, as can be seen from FIG. 7, the increased temperature of the gas at the outlet of the tube of RUN37 comes at a cost of increased pressure drop. Accordingly, the tube of RUN37 requires a higher starting gas core pressure (0.4 bar higher) than tubes according to the present invention.

[0141] Table 6 summarises the average gas pressure drop and the average exit/outlet gas temperature (note that this is the average gas temperature and pressure, not the core), shows that tubes having a fin present on the final 6 m portion of a 12 m tube is still more efficient tubes having a discontinuous fin of constant pitch across the full 12 m length of a tube.

TABLE-US-00007 TABLE 6 RUN36 RUN37 Description Partially Welded Discontinuous 100 mm-128.6 m 90.5 mm Pitch Spiral Pitch Spiral Total Pressure 1.000 1.480 Drop (barg) Outlet 1027.95 1031.99 Temperature (° C.) Heating 147.89 102.70 Efficiency (° C./bar)

[0142] We have found that the heating efficiency of tubes of the present invention (RUN36) is around 45° C./bar (44%) higher than the tubes of RUN36. Therefore, even if tubes according to RUN37 demonstrate a slightly higher (around 4° C.) average exit gas temperature, the pressure drop is drastically lower (0.480 bar). This means that the pressure drop in tubes of the invention is nearly 50% less than the tubes of RUN37, which have a discontinuous fin of fixed pitch. Considering that a plain tube, without any internal fin, has a pressure drop of 0.764 bar, tubes according to the present invention exhibit a pressure drop increase of only 0.236 bar relative to a bare tube (a 31% increase). Conversely, tubes according to RUN37 exhibit a 94% increase pressure drop across the tube.

Example 5

13.26 m Length—44 mm Inside Diameter:

[0143] The experiments of Example 4 were repeated for a tube having an axial length of 13.26 m and an internal diameter of 44 mm. A tube with these dimensions closely resembles those used in millisecond ethylene steam cracker furnaces.

[0144] FIG. 8 shows the gas velocity distribution for a tube according to the present invention (RUN01—FIG. 8a) and a 13.26 m tube comprising a discontinuous fin of constant helical pitch (RUN02—FIG. 8b). The tube of RUN01 comprises a fin having a region of varying pitch, wherein the fin having a region of varying pitch extends across the final 6 m portion of the tube. In other words, the tube of RUN36 has an initial 7.26 m axial length in which there is no fin.

[0145] FIG. 8 shows that the tube according to the present invention exhibits a fast and homogeneously distributed gas flow, even very close of the tube wall. This is not the case for the tube of RUN02, where a thick layer near a large portion of the tube wall has a slower velocity. From this study and findings, it can expected that the pressure drop across tubes of the invention should be significantly lower than the tubes of RUN02.

[0146] Table 7 shows that the average in plane velocity of tubes according to the invention is 57.88 m/s compared to only 33.57 m/s for tubes according to RUN02 (i.e. a 24.31 m/s (72%) increase in velocity. Therefore, a 13.26 m tube according to the invention provides enhanced spinning/stirring/mixing of the gas within the tube. The result is a tube that gives rise to fewer side products and a more efficient cracking reaction.

TABLE-US-00008 TABLE 7 RUN01 RUN02 Description Partially Welded 88 mm- Discontinuous 113.14 mm 79.64 mm Pitch Spiral Pitch Spiral Average streamwise 173.36 172.40 velocity (Ux − m/s)) Average in-plane velocity 57.88 33.57 magnitude (UyUz − m/s) Ratio of in-plane to 0.3339 0.1947 stream wise velocity

[0147] The Core Temperature distribution along the 13.26 m is similar to the 12 m tubes described in Example 4, and show the same drastic core temperature increase, in this case in the region from 7.7 m (175×ID of 44 mm), and more from 8.8 m (210×ID), with the difference between the exit core temperature of the RUN01 and RUN02 being smaller than for the 12 m tubes described in Example 4 (only 1.3° C., compared to 3.3° C. for the 12 m tubes).

[0148] Whilst the core gas exit temperature is nearly the same for RUN01 and RUN02, tubes of RUN02 need a starting gas core pressure that is even higher than the increased starting pressure required for the 12 m/50 mm ID tubes of Example 4 (0.4 bar in Example 4, 0.662 bar in the present example). This represents a requirement of a 66% increase in starting pressure to achieve a similar core gas exit temperature.

[0149] Table 8 shows that the average gas pressure drop and the average exit/outlet gas temperature (note that average gas temperature and pressure, not the core) of the 13.26 m tubes of the present invention are even more efficient. Tubes of the present invention (RUN01) are 34.88° C./bar more efficient that the tubes of RUN02. This is an efficiency increase of 46.4%.

TABLE-US-00009 TABLE 8 RUN01 RUN02 Description Partially Welded Discontinuous 88 mm-113.14 mm 79.64 mm Pitch Spiral Pitch Spiral Total Pressure Drop (barg) 1.41 2.09 Outlet Temperature (° C.) 1035.3 1037.1 Heating Efficiency (° C./bar) 110.13 75.25

Example 6

13.26 m Length—44 mm Inside Diameter—Fin Region Extending Across the Full Axial Length of the Tube

[0150] The above experiments were repeated to provide a comparison between a 13.26 m tube having a discontinuous fin of fixed pitch (RUN02) and a tube according to the present invention where the fin also extends across the full axial length of the tube (RUN03).

[0151] We found that the velocity distribution for tubes according to RUN03 were slightly more turbulent near the tube exit when the fin is applied across the full length, compared to when the fin only extends across the final 6 m axial region of the tube (RUN01), and still more homogeneous temperature distribution near the ID wall in comparison to the tubes of RUN02, which have a discontinuous fin of fixed helical pitch.

[0152] Table 9 shows that the average in the plane velocity of the tubes of RUN03 is 4.08 m/s lower (53.80 m/s) than the tubes of the invention having an equivalent fin across only the final 6 m region of the tube (57.88 m/s). However, this in-plane velocity is still 20.23 m/s higher than the discontinuously finned tubes of RUN02 (33.57 m/s). This represents a 60.3% increase in velocity for the tubes of RUN03 over RUN02. Accordingly, tubes according to the present invention in RUN03 provide much higher mixing for a more efficient cracking reaction.

TABLE-US-00010 TABLE 9 RUN02 RUN03 Description Discontinuous Fully Welded 79.64 mm 88 mm-113.14 mm Pitch Spiral Pitch Spiral Average 172.40 174.00 streamwise velocity (Ux − m/s)) Average in-plane 33.57 53.80 velocity magnitude (Uy Uz − m/s) 0.1947 0.3092 Ratio of in-plane to streamwise velocity)

[0153] This ability of tubes of the invention to exhibit a high velocity of the gas in the plane of the tube can explain why when the fin extends across the full length of the tube, the core gas temperature is significantly higher (10° C.) than the tubes of RUN02. This 10° C. difference is maintained for 1.72 m, to decrease at 7.1° C. average up to 7.83 m length (178×ID) so during 5.71 m, to decrease in average to 4.5° C. average from 7.83 m length to exit 13.26 m (301×ID), so during 5.43 m. In other words, when the tube of the invention comprises a continuous fin extending across the full length of the tube, the gas temperature is increased along the full length of the tube, relative to the tubes having a discontinuous fin of fixed helical pitch across the full length of the tube. This performance can be of great advantage when the gas to crack is a heavy feedstock, which are more difficult to crack. Such heavy feedstocks undergo a slower kinetic cracking reaction and so need more time and an increased temperature to reach a better cracking yield.

Tube

[0154] Tubes according to the present invention may be prepared by centrifugal casting or by extrusion.

[0155] In preferred embodiments, the steel tube is an extruded steel tube.

[0156] In embodiments, the fin formed on the inner wall of the tube is a steel fin. The fin may be welded directly to the inner wall of the tube. The fin may be a shaped spring wire that is spot welded to the inner wall of the tube

Example 7

[0157] An exemplary tube according to the present invention, having a variable pitch fin and an internal diameter of 50 mm, is depicted in FIG. 9. The exemplary tube was prepared by centrifugal casting. The fin on the inner wall of the tube was welded using Automatic Tungsten Inert Gas (TIG) welding. This technique uses a filler wire to produce the internal fin profile. The welding parameters were such that the weld profile was semi-circular and has an average height of 2 mm and an average width of 3.5 mm.

[0158] Tubes according to the present invention may be prepared from an alloy comprising:

from 0.15 to 0.35 wt % carbon,
from 2.5 to 5.0 wt % aluminium,
from 40 to 45 wt % nickel,
from 25 to 35 wt % chromium,
from 0.50 to 1.50 wt % niobium and/or vanadium,
from 0.01 wt % to 0.25 wt % yttrium,
from 0.01 wt % to 0.25 wt % tungsten and/or tantalum,
from 0.01 wt % to 0.25 wt % in total of one or more of titanium and/or zirconium and/or hafnium,
up to 0.9 wt % manganese,
up to 0.9 wt % silicon, and
up to 0.10 wt % nitrogen,
with the balance of the composition being iron and incidental impurities
optionally wherein between 1 wt % and 75 wt % by weight of the nickel is replaced with cobalt.

[0159] Tubes according to the present invention may be prepared from an alloy comprising:

from 0.15 to 0.35 wt % carbon,
from 2.5 to 5.0 wt % aluminium,
from 40 to 45 wt % nickel,
from 25 to 35 wt % chromium,
from 0.50 to 1.50 wt % niobium and/or vanadium,
from 0.01 wt % to 0.05 wt % yttrium,
from 0.05 wt % to 0.25 wt % tungsten and/or tantalum,
from 0.04 wt % to 0.15 wt % in total of one or more of titanium and/or zirconium and/or hafnium,
an amount of up to 0.9 wt % manganese,
an amount of up to 0.6 wt % silicon, and
an amount of up to 0.10 wt % nitrogen,
with the balance of the composition being iron and incidental impurities optionally wherein between 5 wt % and 15 wt % by weight of the nickel is replaced with cobalt.

[0160] Tubes of the invention may be prepared from the above alloys, wherein carbon is present in an amount of from 0.20 wt % to 0.35 wt %.

[0161] Tubes of the invention may be prepared from the above alloys, wherein aluminium is present in an amount of from 3.5 wt % to 4.5 wt %.

[0162] Tubes of the invention may be prepared from the above alloys, wherein nickel is present in an amount of from 42 wt % to 45 wt %.

[0163] Tubes of the invention may be prepared from the above alloys, wherein chromium is present in an amount of from 28 wt % to 30 wt %.

[0164] Tubes of the invention may be prepared from the above alloys, wherein niobium is present in an amount of from 0.80 wt % to 1.50 wt %.

[0165] Tubes of the invention may be prepared from the above alloys, wherein silicon is present in an amount of from 0.3 wt % to 0.6 wt %.

[0166] Tubes of the invention may be prepared from the above alloys, wherein manganese is present in an amount of from 0.4 wt % to 0.8 wt %.

[0167] Tubes of the invention may be prepared from the above alloys, wherein tungsten is present in an amount of from 0.05 wt % to 0.15 wt %.

[0168] Tubes of the invention may be prepared from the above alloys, wherein titanium is present in an amount of from 0.08 wt % to 0.15 wt %.

[0169] Tubes of the invention may be prepared from the above alloys, wherein yttrium is present in an amount of from 0.01 wt % to 0.03 wt %.

[0170] Tubes of the invention may be prepared from the above alloys, wherein nitrogen is present in an amount of from 0.03 wt % to 0.06 wt %

[0171] Tubes according to the present invention may be prepared from an alloy according to Table 10:

TABLE-US-00011 TABLE 10 C Ni Cr Nb Si Mn W Ti Y Al wt 0.25 43.3 29.6 0.81 0.56 0.54 0.05 0.11 0.01 3.86 %

Comparative Example 1

[0172] A number of simulations were performed by the methods described herein, to determine the influence of each of the tube parameters on the pressure drop and gas outlet temperature on tubes having a length of 6 m and a diameter of 75 mm. Tubes having a diameter of 75 mm fall outside the scope of the present invention and therefore provide a useful comparison of the beneficial properties of the tubes of the invention. The results of these simulations are given in Table 11.

TABLE-US-00012 TABLE 11 Outputs Input Parameters Pressure Outlet Initial Final Initial Final Drop Temperature Run Pitch Pitch Length Length (bar) (° C.) 1 292.050 217.125 1579 1684 0.2537 954.15 2 371.100 82.875 526 421 0.2968 953.93 3 197.400 153.975 1000 1158 0.3147 957.27 4 165.750 201.300 421 842 0.3058 957.43 5 386.850 193.425 632 211 0.2401 952.83 6 418.350 177.600 1158 1895 0.2591 953.67 7 450.000 114.450 1263 947 0.2740 953.15 8 260.550 225.000 1474 526 0.2556 954.44 9 228.900 75.000 1368 632 0.3848 958.73 10 244.800 122.400 211 316 0.3133 956.53 11 339.450 130.275 1684 105 0.2571 953.51 12 150.000 169.725 947 1789 0.3750 959.81 13 307.950 106.575 1789 1579 0.3385 955.26 14 355.200 98.700 737 2000 0.3519 956.55 15 434.250 146.025 105 1053 0.2654 953.69 16 402.600 185.550 1895 737 0.2416 952.68 17 323.700 209.175 516 1263 0.2527 953.99 18 276.300 138.150 0 1368 0.3181 955.93 19 181.650 90.825 842 1474 0.5079 966.10 20 213.150 161.850 1053 0 0.3206 956.75 22 176.330 145.743 103 510 0.3502 959.55 23 179.202 129.635 350 312 0.3695 960.70

[0173] It can be seen from the above results that larger diameter pipes, such as those over 70 mm, do not obey the same rules as the pipes of the invention. The experimental results appear to show that that pipes having diameters larger than 70 mm, i.e. those falling outside the scope of the present invention, are less affected by the profile of the internal fin. In other words, the gas flow appears to be less affected by the fin in these pipes.

[0174] As evident from Table 11, tubes having a diameter of 75 mm do not provide the same beneficial temperature and pressure drop properties. In addition, the relative effects of the initial and final helical portions on the overall properties, i.e. temperature and pressure of the fluid stream within the pipe, appear to be different from the pipes of the invention. This is evident from at least RUN9, RUN12, RUN19, RUN22, and RUN23, which demonstrate that tubes having an initial region of constant helical pitch with a higher pitch than the pitch in the final region of constant helical pitch result in higher outlet temperatures. This is the complete opposite to tubes according to the invention, where a lower pitch in the initial region of constant helical pitch than in the final region of constant helical pitch gives the highest outlet temperatures. As can be seen from RUN4, 75 mm diameter tubes having a lower pitch in the initial region of constant helical pitch results in a lower outlet temperature.

[0175] Throughout the description and claims of this specification, the words “comprise” and “contain” and variations of them mean “including but not limited to”, and they are not intended to (and do not) exclude other moieties, additives, components, integers or steps. Throughout the description and claims of this specification, the singular encompasses the plural unless the context otherwise requires. In particular, where the indefinite article is used, the specification is to be understood as contemplating plurality as well as singularity, unless the context requires otherwise.

[0176] Features, integers, characteristics, compounds, chemical moieties or groups described in conjunction with a particular aspect, embodiment or example of the invention are to be understood to be applicable to any other aspect, embodiment or example described herein unless incompatible therewith. All of the features disclosed in this specification (including any accompanying claims, abstract and drawings), and/or all of the steps of any method or process so disclosed, may be combined in any combination, except combinations where at least some of such features and/or steps are mutually exclusive. The invention is not restricted to the details of any foregoing embodiments. The invention extends to any novel one, or any novel combination, of the features disclosed in this specification (including any accompanying claims, abstract and drawings), or to any novel one, or any novel combination, of the steps of any method or process so disclosed.

[0177] The reader's attention is directed to all papers and documents which are filed concurrently with or previous to this specification in connection with this application and which are open to public inspection with this specification, and the contents of all such papers and documents are incorporated herein by reference.