SOLID SHAPED BODY AND USE OF THE SOLID SHAPED BODY

Abstract

The invention relates to a solid shaped body (1) having a cylindrical form with a first base area (3), a second base area (5) and a lateral area (7), wherein the solid shaped body (1) comprises a first number of flutes (9) with at least one flute radius (13) in the lateral area (7), each extending from the first base area (3) to the second base area (5), and a second number of openings (11), each extending from the first base area (3) to the second base area (5), wherein the solid shaped body (1) has a cross-sectional area in form of a rholoid (2). The invention further relates to a use of the solid shaped body (1).

Claims

1-15. (canceled)

16. Solid shaped body (1) having a cylindrical form with a first base area (3), a second base area (5) and a lateral area (7), wherein the solid shaped body (1) comprises a first number of flutes (9) with at least one flute radius (13) in the lateral area (7), each extending from the first base area (3) to the second base area (5), and a second number of openings (11), each extending from the first base area (3) to the second base area (5), wherein the solid shaped body (1) has a cross-sectional area in form of a rholoid (2).

17. Solid shaped body (1) according to claim 16, wherein the second number of openings (11) is in a range from 2 to 8.

18. Solid shaped body (1) according to claim 16, wherein the first number of flutes (9) is larger than the second number of openings (11).

19. Solid shaped body (1) according to claim 16, wherein a ratio between the first number of flutes (9) and the second number of openings (11) is 2.

20. Solid shaped body (1) according to claim 16, wherein the solid shaped body (1) comprises 6 flutes (9) and 3 openings (11).

21. Solid shaped body (1) according to claim 16, wherein a ratio between a diameter (17) of the solid shaped body (1) and a height (19) of the solid shaped body (1) is in a range from 0.5 to 4.0.

22. Solid shaped body (1) according to claim 16, wherein at least one opening (11) has a second radius (15) and a ratio between the second radius (15) of the at least one opening (11) and the diameter (17) of the solid shaped body (1) is in a range from 0.01 to 0.50.

23. Solid shaped body (1) according to claim 16, wherein the first number of flutes (9) comprises a third number of first flutes (21) with a third radius (25) and a fourth number of second flutes (23) with a fourth radius (27), wherein the third radius (25) is smaller than the fourth radius (27).

24. Solid shaped body (1) according to claim 23, wherein a ratio between the third radius (25) of the first flutes (21) and the diameter (17) of the solid shaped body (1) is in a range from 0.05 to 0.45 and/or a ratio between the fourth radius (27) of the second flutes (23) and the diameter (17) of the solid shaped body (1) is in a range from 0.075 to 0.50.

25. Solid shaped body (1) according to claim 23, wherein the third number of first flutes (21) is equal to the fourth number of second flutes (23).

26. Solid shaped body (1) according to claim 23, wherein each of the openings (11) is arranged between two second flutes (23).

27. Solid shaped body (1) according to claim 16, wherein a ratio between a first distance (29) from a central axis (30) of the solid shaped body (1) to at least one first centre (31) of the openings (11) and the diameter (17) of the solid shaped body (1) is in a range from 0.00 to 0.40.

28. Solid shaped body (1) according to claim 16, wherein the first base area (3) and/or the second base area (5) are domed and a ratio between a dome height (35) and the diameter (17) of the solid shaped body (1) is in a range from 0.01 to 0.40.

29. Solid shaped body (1) according to claim 16, wherein the solid shaped body (1) comprises a mixed oxide and the mixed oxide comprises oxygen, aluminum, cobalt and at least one rare earth metal such as lanthanum or the mixed oxide comprises oxygen, aluminum, nickel and at least one alkaline earth metal such as magnesium.

30. Use of the solid shaped body (1) according to claim 16 as a catalyst.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0080] The present invention is described in more detail at hand of the accompanying drawings, in which:

[0081] FIG. 1 shows a longitudinal section of a solid shaped body with a cylindrical form,

[0082] FIG. 2 shows a cross-section of a solid shaped body having a cross-sectional area in form of a rholoid,

[0083] FIG. 3 shows a cross-section of a solid shaped body having a cross-sectional area in form of a rholoid and comprising openings and flutes,

[0084] FIGS. 4 to 6 show test set-ups for determination of side crushing strength,

[0085] FIGS. 7 and 8 show a perspective view and a cross-section, respectively, of a solid shaped body according to the state of the art,

[0086] FIG. 9 shows a perspective view of a further solid shaped body according to the state of the art and

[0087] FIGS. 10 to 12 show different embodiments of solid shaped bodies having a cross-sectional area in form of a rholoid and comprising openings and flutes.

[0088] FIG. 1 shows a longitudinal section of a solid shaped body 1 having a cylindrical form. The solid shaped body 1 comprises a first base area 3 and a second base area 5, which are connected by a lateral area 7. In the illustrative embodiment of FIG. 1, the first base area 3 and the second base are 5 are domed with a dome height 35. Further, the solid shaped body 1 has a height 19 and a diameter 17.

[0089] FIG. 2 shows a cross-section of a solid shaped body 1 having a cross-sectional area in form of a rholoid 2. The rholoid 2 is geometrically formed by intersection of three superposed circles 4, each with a circle radius 6, and comprises three edges 8 and three corners 10. The three corners 10 lie on an embracing circle 12 with a diameter 17. The diameter 17 is understood to be the diameter 17 of the solid shaped body 1. The diameter 17 and the circle radius 6 are of a same length.

[0090] FIG. 3 shows a cross-section of a solid shaped body 1 having a cross-sectional area in form of a rholoid 2 and comprising four openings 11 and six flutes 9 with at least one flute radius 13. The four openings 11 with a second radius 15 comprise one central opening 14. The central opening 14 is located on a central axis 30 of the solid shaped body 1. The flutes 9 are located at the lateral surface 7 of the solid shaped body 1. Further, the flutes 9 and the openings 11 extend from the first base area 3 to the second base area 5 of the solid shaped body 1. First flutes 21 have a third radius 25, which is smaller than a fourth radius 27 of second flutes 23.

[0091] Each second flute 23 is arranged between two first flutes 21 and vice versa. Two adjacent second flutes 23 are separated from each other by a lobe 37, which comprises one of the first flutes 21 and also one of the openings 11. Thus, the solid shaped body 1 according to FIG. 3 comprises three lobes 37.

[0092] A first distance 29 from the central axis 30 of the solid shaped body 1 to first centers 31 of three of the openings 11 is represented as radius of a circle, on which the first centers 31 are located.

[0093] In addition, a second distance 43 from the central axis 30 of the solid shaped body 1 to second centers 33 of the first flutes 21 is equal to a third distance 46 from the central axis 30 of the solid shaped body 1 to third centers 45 of the second flutes 23, in this illustrative embodiment.

[0094] The second distance 43 is represented as radius of a circle, on which the second centers 33 of the first flutes 21 are located. The second centers 33 refer to a fictive circle, respectively, of which an arc forms the first flutes 21. Further, the third distance 46 is represented as radius of a circle, on which the third centers 45 of the second flutes 23 are located. The third centers 45 refer to a fictive circle, respectively, of which an arc forms the second flutes 23.

[0095] FIGS. 4 to 6 show three different test set-ups for determination of side crushing strength of a solid shaped body 1 with three different positions of the solid shaped body 1 in a testing machine 47. According to FIG. 4 determination of a side crushing strength A is represented. Here, the sample solid shaped body 1 is in a test position standing on a flute 9, specifically on a second flute 23. FIG. 5 illustrates determination of a side crushing strength B, wherein the sample solid shaped body 1 stands on a lobe 37 and is turn by 45° or 60°, respectively, compared the set-up shown in FIG. 4. In case of an odd number of lobes the side crushing strength B corresponds to the side crushing strength A as each lobe is opposing one flute. According to FIG. 6, a side crushing strength C is determined and refers to a position where openings 11 of the solid shaped body 1 are orientated in parallel to the direction of the force applied on the sample solid shaped body 1 during the test by the testing machine 47.

[0096] FIG. 7 shows a perspective view of a solid shaped body 1 according to the state of the art and FIG. 8 shows a cross-section of the solid shaped body 1 according to FIG. 7. The solid shaped body 1 comprises four flutes 9 and four openings 11 extending from a first base area 3 through the solid shaped body 1.

[0097] FIG. 9 shows a perspective view of a further solid shaped body 1 according to the state of the art, which also comprises the same number of flutes 9 as openings 11.

[0098] FIGS. 10 to 12 show different embodiments of solid shaped bodies 1 having a cross-sectional area in form of a rholoid 2. Each of the solid shaped bodies comprises three openings 11 and six flutes 9, wherein three flutes 9 are first flutes 21 and three flutes 9 are second flutes 23. All openings 11 have a circular cross-section. Third radii 25 of the first flutes 21 are smaller than fourth radii 27 of the second flutes 23. Further, the openings 11 are arranged in equidistance to adjacent openings 11 and the first flutes 21 and the second flutes 23 are arranged in an alternating manner in the lateral area 7 of the solid shaped body 1.

EXAMPLES AND COMPARATIVE EXAMPLES

[0099] Dimensions of solid shaped bodies according to comparative examples 1.1, 1.2, 1.2.1 and 1.2.2 are summarized in table 1. The given reference numerals refer to FIGS. 1 and 3, respectively.

TABLE-US-00001 Comparative example No. Reference numeral Unit 1.1 1.2 1.2.1 1.2.2 Diameter 17 mm 13.00 16.50 14.03 12.87 Height 19 mm 17.00 10.00 8.50 7.80 Dome height 35 mm 1.10 1.10 Flute radius 13 mm 1.50 2.05 Second distance 43 mm 6.50 8.25 First distance 29 mm 3.40 4.10 Second radius 15 mm 1.65 1.90

[0100] Dimensions of solid shaped bodies according to examples 2.1 to 2.3, as illustrated in FIGS. 10 to 12, respectively, are summarized in table 2.

TABLE-US-00002 Reference numeral Unit 2.1 2.2 2.2.1 2.2.2 2.3 Diameter 17 mm 19.04 19.99 16.18 14.85 19.60 Height 19 mm 9.14 9.84 7.77 7.13 11.42 Dome height 35 mm 1.68 1.13 1.13 Second radius 15 mm 1.90 2.14 2.14 Third radius 25 mm 1.90 2.14 2.14 Fourth radius 27 mm 4.74 4.74 4.23 First distance 29 mm 3.42 3.42 3.76 Second distance 43 mm 9.52 9.99 9.80 Third distance 46 mm 9.52 9.99 9.80

[0101] For all examples and comparative examples the surface, volume and relative weight of the respective solid shaped body were calculated and are summarized in table 3. The volume indicates the volume, which is filled with material, thus the total outer volume of the solid shaped body subtracting an inner volume of the openings and flutes.

[0102] The geometric surface and geometric volume of each solid shaped body were determined from CFD (Computational Fluid Dynamics) simulations based on CAD (Computer Aided Design) models of each solid shaped body geometry.

TABLE-US-00003 Nb. Surface (m.sup.2) Volume (m.sup.3) Relative weight 1.1 1.53.Math.10.sup.-3 1.36.Math.10.sup.-6 1.07 1.2 1.19.Math.10.sup.-3 1.26.Math.10.sup.-6 1.00 1.2.1 0.86.Math.10.sup.-3 0.80.Math.10.sup.-6 0.63 1.2.2 0.72.Math.10.sup.-3 0.62.Math.10.sup.-6 0.49 2.1 1.29.Math.10.sup.-3 1.38.Math.10.sup.-6 1.09 2.2 0.98.Math.10.sup.-3 0.96.Math.10.sup.-6 0.76 2.2.1 0.71.Math.10.sup.-3 0.59.Math.10.sup.-6 0.47 2.2.2 0.60.Math.10.sup.-3 0.46.Math.10.sup.-6 0.36 2.3 1.15.Math.10.sup.-3 1.16.Math.10.sup.-6 0.92

[0103] Resulting properties of the solid shaped bodies are summarized in table 4, which represent calculated values.

[0104] The pressure drop for each solid shaped body geometry was calculated via numerical flow simulation, which describes the flow in spaces between solid shaped bodies of a bed of solid shaped bodies. The procedure comprised three consecutive steps. First, a CAD model of each solid shaped body was created. A tube with an internal diameter of a typical technical reactor of ca. 100 mm was assumed as an outer container comprising the bed of the solid shaped bodies. Both the digital container geometry and the digital geometry of the solid shaped body were fed into a simulation program which allowed to calculate the arrangement of the solid shaped bodies as filled into the container, using Newton’s equations of motion.

[0105] Pressure drop calculations were performed with air at ambient temperature and Pressure drop calculations were performed with air at ambient temperature and at a superficial velocity of 1 m/s in a DN100 tube. Literature values for air at a constant operating pressure of 1 bar and a temperature of 20° C. were used for the thermodynamic and transport properties of the gas.

[0106] In order to calculate the side crush strength (SCS), also referred to as crushing strength, of each solid shaped body, a numerical method such as Finite Element Analysis was used to simulate a side crush strength test applying each CAD model of the solid shaped bodies, based on alumina.

[0107] For the minimum SCS/particle volume, the lowest of the determined crushing strength was divided by the volume of the solid shaped body. The axial dispersion coefficient was calculated according to Levenspiel, The Chemical Reactor Omnibook, 4. Edition, Chapter 64, 1993 using “Small Deviation from Plug Flow”, wherein for an ideal plug flow reactor D.sub.ax .fwdarw. 0.

TABLE-US-00004 Nb. Crushing strength A (N) Crushing strength B (N) Minimum SCS/particle volume (N/m.sup.3) Relative packed bed density Pressure drop (Pa/m) Specific surface area (m.sup.2/m.sup.3) Axial dispersion coefficient (m.sup.2/s) 1.1 389 174 1.28.Math.10.sup.+8 0.94 851 423 1.55.Math.10.sup.-2 1.2 301 139 1.10.Math.10.sup.+8 1.00 816 371 1.18.Math.10.sup.-2 1.2.1 228 105 1.31.Math.10.sup.+8 1.02 949 452 1.02.Math.10.sup.-2 1.2.2 204 96 1.56.Math.10.sup.+8 1.01 975 486 1.23.Math.10.sup.-2 2.1 228 - 1.65.Math.10.sup.+8 0.92 795 347 1.43.Math.10.sup.-2 2.2 183 - 1.91.Math.10.sup.+8 0.92 856 381 1.21.Math.10.sup.-2 2.2.1. 140 - 2.37.Math.10.sup.+8 0.94 1160 457 1.05.Math.10.sup.-2 2.2.2 125 - 2.74.Math.10.sup.+8 0.95 1414 504 1.01.Math.10.sup.-2 2.3 198 - 1.71.Math.10.sup.+8 0.90 817 362 1.29.Math.10.sup.-2

[0108] Results according to table 4, which were derived from the modeled solid shaped bodies, show that the axial dispersion coefficient was enhanced for the examples with respect to the comparative examples, corresponding the same geometric scale, whereas examples 2.2.1 and 2.2.2 are scale-downs of example 2.2 to represent different levels of shrinkage. Further, the pressure drop was decreased for examples 2.1 and 2.3. The axial dispersion coefficient was increased over comparative example 1.2, 1.2.1 and 1.2.2, respectively.

[0109] Resulting properties of the solid shaped bodies were further studied at hand of 3D-printed representative solid shaped bodies prepared from CaSO.sub.4.

[0110] The 3D-printed solid shaped bodies were manufactured with a 3D-printer using a Z Corporation Spectrum Z510 model. The solid shaped bodies of a constant composition, also referred to as tablets, were made of a mixture comprising gypsum (CaSO.sub.4) using commercial VisiJet PXL Core by 4Dconcepts and a binder using commercial VisiJet PXL Binder by 4Dconcepts. During the 3D-printing process individual solid shaped bodies were not in contact with neighboring solid shaped bodies and all shaped bodies were oriented in such a way that the openings of the solid shaped bodies extended vertically through the shaped bodies. 3D-printing was carried out with a 3D-printing layer thickness of 0.1 mm. Typically, around 200 layers were applied to complete one solid shaped body and around 100 solid shaped bodies were 3D-printed in one experiment. After completing the 3D-printing process, the printed solid shaped bodies were allowed to stay for 1 h in the printing chamber and the build envelope, respectively. Afterwards the solid shaped bodies were removed individually by hand and cleaned from residual powder.

[0111] The 3D-printed solid shaped bodies were analyzed according to the following measurement methods. Results of the measurements are summarized in table 5. For comparative example 1.2, three different sizes of the solid shaped body, were investigated. The respective solid shaped bodies were scaled down to different levels of shrinkage.

[0112] The side crush strength of the 3D-printed shaped bodies was determined experimentally using a commercial material testing machine of the type BZ2.5/TS1S from Zwick, which allowed testing of the mechanical properties according to DIN EN ISO 7500-1:2018-06. For each type of solid shape body, 10 individual solid shape bodies were investigated. The applied analysis method included a preload of 0.5 N and a preload velocity of 10 mm/min. Analysis velocity was 1.6 mm/min. The solid shaped bodies were tested, whereby three positions were investigated allowing determination of side crushing strength A, side crushing strength B and side crushing strength C, as illustrated in FIGS. 4 to 6.

[0113] The diameter and the height of the individual solid shaped bodies were determined by means of a caliper. The weight of the solid shaped bodies was determined by an analysis balance. Typically, 10 shaped bodies were analyzed and the average value was considered.

TABLE-US-00005 Nb. Diameter (mm) Height (mm) Weight (g) Crushing strength A (N) Crushing strength B (N) Crushing strength C (N) 1.2 16.69 9.96 1.52 38 28 243 1.2.1 14.20 8.72 1.12 76 33 162 1.2.2 13.03 7.97 0.87 70 37 150 2.1 15.35 11.61 1.96 73 - 244 2.2. 14.70 9.27 1.27 33 - 178

[0114] The analysis of the 3D-printed samples showed an improvement of at least one of the three tested side crushing strengths for example 2.1, whereas example 2.2 is characterized by a high minimum SCS/particle volume as shown in table 4.

TABLE-US-00006 Reference numerals 1 Solid shaped body 2 Rholoid 3 First base area 4 Circle 5 Second base area 6 Circle radius 7 Lateral area 8 Edge 9 Flute 10 Corner 11 Opening 12 Embracing circle 13 Flute radius 14 Central opening 15 Second radius 17 Diameter of the solid shaped body 1 19 Height of the solid shaped body 1 21 First flute 23 Second flute 25 Third radius of first flutes 21 27 Fourth radius of second flutes 23 29 First distance 30 Central axis of the solid shaped body 1 31 First center of openings 11 33 Second center of first flutes 21 35 Dome height 37 Lobe 43 Second distance 45 Third center of second flutes 23 46 Third distance 47 Testing machine