U.S. patent application number 15/599927 was filed with the patent office on 2017-11-30 for u-bends with the reduced pressure losses to fluid distributing networks.
This patent application is currently assigned to NOVA Chemicals (International) S.A.. The applicant listed for this patent is NOVA Chemicals (International) S.A.. Invention is credited to Eric Clavelle, Grazyna Petela, Edgar Yajure.
Application Number | 20170343300 15/599927 |
Document ID | / |
Family ID | 58737696 |
Filed Date | 2017-11-30 |
United States Patent
Application |
20170343300 |
Kind Code |
A1 |
Petela; Grazyna ; et
al. |
November 30, 2017 |
U-BENDS WITH THE REDUCED PRESSURE LOSSES TO FLUID DISTRIBUTING
NETWORKS
Abstract
Provided herein are components for a fluid network modified for
one or more objective functions of interest such as pressure drop,
erosion rate, fouling, coke deposition and operating costs.
Inventors: |
Petela; Grazyna; (Calgary,
CA) ; Clavelle; Eric; (Calgary, CA) ; Yajure;
Edgar; (Calgary, CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
NOVA Chemicals (International) S.A. |
Fribourg |
|
CH |
|
|
Assignee: |
NOVA Chemicals (International)
S.A.
Fribourg
CH
|
Family ID: |
58737696 |
Appl. No.: |
15/599927 |
Filed: |
May 19, 2017 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
F28F 1/02 20130101; F28D
1/0477 20130101; F28F 1/00 20130101; F28F 2210/10 20130101; F16L
43/005 20130101; F28D 7/06 20130101; F28F 1/006 20130101; F15D 1/04
20130101 |
International
Class: |
F28F 1/02 20060101
F28F001/02; F28F 1/00 20060101 F28F001/00; F28D 7/06 20060101
F28D007/06 |
Foreign Application Data
Date |
Code |
Application Number |
May 25, 2016 |
CA |
2930824 |
Claims
1. A U-bend for a fluid network said U-bend having individually or
in co-operative arrangement an internal flow passage having a
continuously smooth and differentiable perimeter and centerline and
a smoothly varying cross-section along the flow passage such that
in the 5% of the flow passage from the inlet and the 5% of the flow
passage from the outlet ARQ is from 1.0 to 1.02 and over the
remaining 90% of the length of the flow passage not less than 5% of
the flow passage has an ARQ from 1.02 to 1.15 and further wherein
the presence of one or more of the U-bends reduces the overall
pressure drop within the fluid network by 10% or more when compared
to the calculated pressure drop for fluid network having a flow
passage with an ARQ along its length from 1.00 to 1.02.
2. The U-bend of claim 1 wherein the bend between about 90 and
about 180 degrees.
3. The U-bend of claim 1 wherein the bend between about 95 and
about 180 degrees.
4. The U-bend of claim 1 wherein the bend between about 90 and
about 175 degrees.
5. The U-bend of claim 1 wherein the fluid network comprises one or
more U-bends connected by pipes.
6. The U-bend of claim 1 wherein the fluid network comprises 5 or
more U-bends connected by pipes.
7. The U-bend of claim 1 wherein the fluid network comprises 50 or
more U-bends connected by pipes.
8. The U-bend of claim 5 wherein L is the pipe length and D is the
inner diameter of the pipe and further wherein L/D of the pipe
connecting the U-bend is greater than 0 and less than 55.
9. The U-bend of claim 5 wherein L is the pipe length and D is the
inner diameter of the pipe and further wherein L/D of the pipe
connecting the U-bend is greater than 0 and less than 45.
10. The U-bend of claim 5 wherein L is the pipe length and D is the
inner diameter of the pipe and further wherein L/D of the pipe
connecting the U-bend is greater than 0 and less than 20.
11. The U-bend of claim 5 wherein Rb is half the distance between
the center of two pipes being connected by the U-bend and D is the
inner diameter of the pipe and further wherein Rb/D is greater than
1 and less than 4.
12. The U-bend of claim 5 wherein Rb is half the distance between
the center of two pipes being connected by the U-bend and D is the
inner diameter of the pipe and further wherein Rb/D is greater than
1 and less than 3.
13. The U-bend according to claim 1, wherein over the remaining 90%
of the length of the flow passage not less than 10% of the flow
passage has an ARQ from 1.02 to 1.15
14. The U-bend according to claim 1, wherein erosion rate of the
fluid network is decreased by not less than 10% compared to the
erosion rate for a fluid network having a flow passage with an ARQ
along its length from 1.00 to 1.02.
15. The U-bend according to claim 1, wherein fouling or
sedimentation rate of the fluid network is decreased by not less
than 10% compared to the fouling or sedimentation rate for a fluid
network having a flow passage with an ARQ along its length from
1.00 to 1.02.
16. The U-bend according to claim 1, wherein the flow passage has
smoothly varying walls in its flow direction which although may
change rapidly, does not include abrupt, sharp changes of internal
section (steps).
17. A fluid network comprising at least one pipe connected to at
least one U-bend, wherein said U-bend has individually or in
co-operative arrangement an internal flow passage having a
continuously smooth and differentiable perimeter and centerline and
a smoothly varying cross-section along the flow passage such that
in the 5% of the flow passage from the inlet and the 5% of the flow
passage from the outlet ARQ is from 1.0 to 1.02 and over the
remaining 90% of the length of the flow passage not less than 5% of
the flow passage has an ARQ from 1.02 to 1.15 and wherein the
presence of one or more of the U-bends reduces the overall pressure
drop within the fluid network by 10% or more when compared to the
calculated pressure drop for fluid network having a flow passage
with an ARQ along its length from 1.00 to 1.02.
18. The fluid network of claim 17 wherein the overall pressure drop
within the fluid network is 15% or more.
19. The fluid network of claim 17 wherein the overall pressure drop
within the fluid network is 20% or more.
20. The fluid network of claim 17 wherein the pipes are straight or
essentially straight.
21. The fluid network of claim 17 wherein the fluid network is a
heat exchanger.
22. The fluid network of claim 17 wherein the fluid network is a
fluid transporting network.
23. The fluid network of claim 17 wherein the fluid network is a
fluid transporting network selected from pipelines and hydraulic
systems.
24. The fluid network of claim 17 wherein the fluid network is
fluid processing equipment or is a fluid processing device wherein
fluid condenses or evaporates when in contact with the fluid
network.
25. The fluid network of claim 17 wherein the fluid network is
fluid processing equipment or is a fluid processing device wherein
fluid changes its temperature when in contact with the fluid
network.
26. The fluid network of claim 17 wherein the fluid network is
fluid processing equipment or is a fluid processing device wherein
fluid undergoes a chemical reaction with or without participation
of other substances/components when in contact with the fluid
network.
27. The fluid network of claim 17 wherein the fluid network is a
fluid distribution network.
28. The fluid network of claim 17 wherein the bend in the U-tube is
between about 90 and about 180 degrees.
29. The fluid network of claim 17 wherein L is the pipe length and
D is the inner diameter of the pipe and further wherein L/D of the
pipe connecting the U-bend is greater than 0 and less than 55.
30. The fluid network of claim 17 wherein Rb is half the distance
between the center of two pipes being connected by the U-bend and D
is the inner diameter of the pipe and further wherein Rb/D is
greater than 1 and less than 4 where.
31. The fluid network of claim 17 wherein erosion rate of the fluid
network is decreased by not less than 10% compared to the erosion
rate for a fluid network having a flow passage with an ARQ along
its length from 1.00 to 1.02.
32. The fluid network of claim 17 wherein fouling or sedimentation
rate of the fluid network is decreased by not less than 10%
compared to the fouling or sedimentation rate for a fluid network
having a flow passage with an ARQ along its length from 1.00 to
1.02.
33. The fluid network of claim 17 wherein the flow passage has
smoothly varying walls in its flow direction which although may
change rapidly, does not include abrupt, sharp changes of internal
section (steps).
34. A method to reduce the overall pressure drop within a fluid
network by 10% or more when compared to the calculated pressure
drop for fluid network having a flow passage with an ARQ along its
length from 1.00 to 1.02, the method comprising using in the fluid
network comprising at least one pipe connected to at least one
U-bend, wherein said U-bend has individually or in co-operative
arrangement an internal flow passage having a continuously smooth
and differentiable perimeter and centerline and a smoothly varying
cross-section along the flow passage such that in the 5% of the
flow passage from the inlet and the 5% of the flow passage from the
outlet ARQ is from 1.0 to 1.02 and over the remaining 90% of the
length of the flow passage not less than 5% of the flow passage has
an ARQ from 1.02 to 1.15.
35. The method of claim 34 wherein the fluid network is a heat
exchanger.
36. The method of claim 34 wherein the fluid network is a fluid
transporting network.
37. The method of claim 34 wherein the overall pressure drop within
the fluid network is 15% or more.
38. The method of claim 34 wherein the overall pressure drop within
the fluid network is 20% or more.
39. The method of claim 34 further wherein erosion rate of the
fluid network is decreased by not less than 10% compared to the
erosion rate for a fluid network having a flow passage with an ARQ
along its length from 1.00 to 1.02.
40. The method of claim 34 further wherein fouling or sedimentation
rate of the fluid network is decreased by not less than 10%
compared to the fouling or sedimentation rate for a fluid network
having a flow passage with an ARQ along its length from 1.00 to
1.02.
Description
[0001] Disclosed herein are components for fluid networks that
include curved conduits such as branches, bends, by-passes, etc.
which enforce multiple turns and direction changes on a flowing
fluid stream. The fluid could be a liquid, gas, or multiphase flow
such as a liquid-gas, liquid-solid (slurry) or gas-solid mixture.
This network could be for fluid transport, distribution or
recycling the working fluid in heating or cooling systems.
[0002] To date the pipe components for fluid networks have been
circular in cross-section. The consideration of the cost of
manufacture relative to efficiency of the components in terms of
pressure drop and erosion rate has been largely weighted to
minimize the cost of manufacturing. Hence the components have
circular cross sections. With the increase in the price of
feedstocks, the concern about greenhouse gas emissions, and desire
to improve overall efficiencies in fluid systems the weighting of
the factors in the design of components is starting to move toward
the efficiency of the process. Several factors to be considered in
the efficiency of the fluid network include the pressure drop
across (i.e. along the length of) the fluid network the erosion
rate of the components of the fluid network and the degree of
sedimentation or forming deposit during the flow, which relates to
fouling.
[0003] In one embodiment, the present disclosure seeks to provide
the components individually and collectively for a fluid network
which is fabricated to minimize any one of or combinations of
pressure drop, fouling, erosion in the component(s), the assembled
fluid network, or both, thus minimizing the cost (operating,
capital or both).
[0004] Provided herein is a U-bend for a fluid network said U-bend
having individually or in co-operative arrangement an internal flow
passage having a continuously smooth and differentiable perimeter
and centerline and a smoothly varying cross-section along the flow
passage such that in the 5% of the flow passage from the inlet and
the 5% of the flow passage from the outlet ARQ (as herein after
defined) is from 1.0 to 1.02 and over the remaining 90% of the
length of the flow passage not less than 5% of the flow passage has
an ARQ from 1.02 to 1.15 and further wherein the presence of one or
more of the U-bends reduces the overall pressure drop within the
fluid network by 10% or more when compared to the calculated
pressure drop for fluid network having a flow passage with an ARQ
along its length from 1.00 to 1.02.
[0005] Also provided herein is a fluid network comprising at least
one pipe connected to at least one U-bend, wherein said U-bend has
individually or in co-operative arrangement an internal flow
passage having a continuously smooth and differentiable perimeter
and centerline and a smoothly varying cross-section along the flow
passage such that in the 5% of the flow passage from the inlet and
the 5% of the flow passage from the outlet ARQ is from 1.0 to 1.02
and over the remaining 90% of the length of the flow passage not
less than 5% of the flow passage has an ARQ from 1.02 to 1.15 and
wherein the presence of one or more of the U-bends reduces the
overall pressure drop within the fluid network by 10% or more when
compared to the calculated pressure drop for fluid network having a
flow passage with an ARQ along its length from 1.00 to 1.02.
[0006] Also provided herein is a method to reduce the overall
pressure drop within a fluid network by 10% or more when compared
to the calculated pressure drop for fluid network having a flow
passage with an ARQ along its length from 1.00 to 1.02, the method
comprising using in the fluid network comprising at least one pipe
connected to at least one U-bend, wherein said U-bend has
individually or in co-operative arrangement an internal flow
passage having a continuously smooth and differentiable perimeter
and centerline and a smoothly varying cross-section along the flow
passage such that in the 5% of the flow passage from the inlet and
the 5% of the flow passage from the outlet ARQ is from 1.0 to 1.02
and over the remaining 90% of the length of the flow passage not
less than 5% of the flow passage has an ARQ from 1.02 to 1.15.
BRIEF DESCRIPTION OF THE DRAWINGS
[0007] The features, benefits and aspects of the present disclosure
are best understood in the context of the attached figures in which
like parts or features are designated by like numbers.
[0008] FIG. 1 shows different cross sections of a flow passage
having an ARQ greater than 1.
[0009] FIG. 2 shows a series of overlays of equal perimeter
ellipses having different ARQ equal to or greater than 1.
[0010] FIG. 3 is an isometric view of a typical fluid network as an
example of prior art.
[0011] FIG. 4 shows multiple views of a U-bend or 180 degree bend
in accordance with the present disclosure
[0012] FIG. 5 is a sectional view along the flow passage of FIG. 4
and cross sections at A, B, C, D and E.
[0013] FIG. 6 is a graph of network system pressure drop
improvement vs. network length and the number of U-bends.
[0014] As used in this specification "fluid network" means piping
systems, tube heat exchangers, coolers, heaters, fluid conduits,
installations where the flowing medium, which is gas or liquid or
slurry or multiphase fluid, is forced to change a direction by an
angle of 90.degree. to 200.degree., in multiple passes.
[0015] As used in this specification "ARQ" means the ratio of
aspect ratio (AR) to isoperimetric quotient (Q) of a section or
segment of the flow passage perpendicular to the direction of flow
(AR/Q), which is described in more detail herein below.
[0016] As used in this specification "relatively smoothly" or
"smoothly varying" in relation to the ARQ means the quotient does
not change by more than about 7% over a about 5% length of the flow
passage.
[0017] As used in this specification "smooth in relation to the
perimeter of the flow passage" means the perimeter at an angle
perpendicular to the flow is a differentiable continuous smooth
line (i.e., having no kinks or discontinuities). As a result the
perimeter of the flow passage will not be a geometric shape having
straight sides and "corners" or "angles" such as a square, a
parallelogram or a triangle. Rather the perimeter of the flow
passage is defined by a continuous smooth curved line.
[0018] As used in this specification "smooth in relation to the
center line of the flow passage" means the center line of the flow
passage is a differentiable continuous smooth line (i.e. having no
kinks or discontinuities). While the center line of the flow
passage may change rapidly, it will not include abrupt, sharp
changes of internal section (steps).
[0019] As used in this specification "Rb" is the half the distance
between the center of the two tubes or pipes being connected by the
U-bend. D is the internal diameter of the tube or pipe.
[0020] As used in this specification "building a computational
model" means creating a virtual three dimensional geometric model
of one or more component(s) or a reactor and filling it with a
three dimensional computational mesh to create cells (e.g. 5,000
cells to greater than 100,000 cells).
[0021] "ARQ" is defined as the ratio of aspect ratio (AR) to
isoperimetric quotient (Q) of a section or segment of the flow
passage perpendicular to the direction of flow (AR/Q). The aspect
ratio (AR) is defined as the ratio of long to short side of the
smallest-area rectangle into which a particular section can be
circumscribed. This ratio, for the case of a convex ovoid section
symmetric about one axis, is equal to the ratio of the major chord
to minor chord. The major chord is the length of the longest
straight line between two points in the perimeter of a closed
section which may or may not cross the centroid of the section. The
minor chord for such a section is the longest distance
perpendicular to the major chord between two points along the
perimeter of the section. It will appear clear to those skilled in
the art that thus defined the aspect ratio is greater than one.
AR=Long/Short
[0022] The isoperimetric quotient is defined as four times Pi
(.pi.) times the Area of the section of the flow passage divided by
the square of that section's perimeter. At a cross section of the
flow path if the area of the cross section is A and the perimeter
is L, then the isoperimetric quotient Q, is defined by
Q = 4 .pi. A L 2 ##EQU00001##
[0023] The isoperimetric quotient is a measure of circularity. This
is illustrated in FIG. 1 and FIG. 2. A circle is the only
cross-sectional shape with an isoperimetric quotient of one and all
other cross-sectional shapes have an isoperimetric quotient less
than one.
[0024] Since the ARQ ratio is the aspect ratio (AR) divided by the
isoperimetric quotient (Q) and as defined AR is greater than one
and Q is less than one, ARQ is also greater than one and greater
than or equal to the aspect ratio.
[0025] FIGS. 1 and 2 demonstrate that even an ARQ near but not
equal to 1 can be noticeably non-circular.
[0026] Sample calculation of an ARQ ratio:
[0027] An ellipse with a major radius "a" and a minor radius "b"
has a cross sectional area A=Pi*a*b. The perimeter of such an
ellipse can be approximated by Ramanujan's formula which states the
perimeter of an ellipse being approximately:
L.apprxeq..pi.[3(a+b)- {square root over ((3a+b)(3b+a))}]
[0028] For a particular example of an ellipse having a major radius
"a" equals four times the minor radius "b", it would have an Area
A=4*Pi*b.sup.2. This four-to-one ellipse has a perimeter L
L.apprxeq..pi.[3(5b)- {square root over ((12b+b)(3b+4b))}]
L.apprxeq..pi.[15b- {square root over
(91b.sup.2)}].apprxeq.5.461.pi.b
[0029] So a four-to-one ellipse has an isoperimetric quotient Q
equal
Q .apprxeq. 16 .pi. 2 b 2 29.822 .pi. 2 b 2 .apprxeq. 0.537
##EQU00002##
[0030] And since the aspect ratio of this section is 4, the ARQ of
such a section is 7.45
[0031] In comparison, standard pipe has an out-of round tolerance
of plus or minus 1.5% and as such, the maximum ARQ of a nominally
round section is approximately 1.0151.
[0032] The pipes useful with the embodiments disclosed herein are
straight, or are substantially straight, meaning the pipe may have
some curves or bends, but over the length of the pipe the direction
does not change by more than 20 degrees. In some embodiments the
pipes may be composed of multiple sections connected by such
methods as welding, threaded joints or flanges. In some
embodiments, the L/D of the pipe connecting the U-bend is greater
than 0 and less than 55. In some embodiments, the L/D of the pipe
connecting the U-bend is greater than 0 and less than 45. In some
embodiments, the L/D of the pipe connecting the U-bend is greater
than 0 and less than 20. In some embodiments, the Rb/D is greater
than 1 and less than 4. In some embodiments, the Rb/D is greater
than 1 and less than 3 where. In some embodiments, the Rb/D is
greater than 1 and less than 2.
[0033] The embodiments of this disclosure may work with any number
of U-bends connected by an appropriate number of pipes to create a
fluid network system. In some embodiments, the fluid networks of
this disclosure comprise one or more U-bends connected by pipes. In
some embodiments, the fluid network comprises five (5) or more
U-bends connected by pipes. In some embodiments, the fluid network
comprises fifty (50) or more U-bends connected by pipes. In some
embodiments, the fluid network comprises 100 or more, or 150 or
more, or 200 or more, U-bends connected by pipes. The number of
U-bends connected by pipes is one factor taken into consideration
when designing the overall shape and size of a fluid network.
[0034] FIG. 3 is an isometric drawing of a fluid network (in this
case a heat exchanger) in which a gas or liquid flowing within the
tubes is cooled by a gas flowing over the outside of the tubes. The
fluid network comprises one or more inlets 1, multiple straight
tubes or pipes 2, multiple U-bends or 180 degree bends 3, a flow
combining manifold 4 and an outlet or exit 5. U-bend, 3, is an
example of a U-bend whose modification is the subject of this
disclosure.
[0035] In FIG. 3 cross sections at all positions along fluid
network length are circular typically having an out-of round
tolerance of plus or minus 1.5% and as such, the maximum ARQ of a
nominally round section is approximately 1.0151.
[0036] In the components of the prior art the flow passage was
circular along its entire length albeit expanding as described
below and the ARQ along the serpentine reactor is essentially 1
(e.g. from 1.0 to 1.02).
[0037] The cross sectional area of the flow passage varies along
the length of the components in the direction of flow of the gas
but all cross-sections are substantially round with an ARQ of 1
other than by unintentional variations of tolerance plus or minus
2% (Maximum ARQ of 1.02).
[0038] In some embodiments, provided herein is a U-bend for a fluid
network said U-bend having individually or in co-operative
arrangement an internal flow passage having a continuously smooth
and differentiable perimeter and centerline and a smoothly varying
cross-section along the flow passage such that in the 5% of the
flow passage from the inlet and the 5% of the flow passage from the
outlet ARQ is from 1.0 to 1.02 and over the remaining 90% of the
length of the flow passage not less than 5% of the flow passage has
an ARQ from 1.02 to 1.15 and further wherein the presence of one or
more of the U-bends reduces the overall pressure drop within the
fluid network by 10% or more when compared to the calculated
pressure drop for fluid network having a flow passage with an ARQ
along its length from 1.00 to 1.02.
[0039] The embodiments disclosed herein may work with a U-bend of
any degree of bending. In some embodiments, the bend in the U-bend
is between about 90 and about 180 degrees. In some embodiments, the
bend in the U-bend is between about 95 and about 180 degrees. In
some embodiments, the bend in the U-bend is between about 120 and
about 180 degrees. In some embodiments, the bend in the U-bend is
between about 90 and about 175 degrees. In some embodiments, the
bend in the U-bend is between about 90 and about 160 degrees. In
some embodiments, the bend in the U-bend is between about 90 and
about 120 degrees. In some embodiments, the bend in the U-bend is
about 90 degrees, or about 120 degrees or about 180 degrees. In
some embodiments, in a fluid network the U-bends may all have the
same degree of bending. In some embodiments, some or all of the
U-bends in the fluid network may have different degrees of bending.
The degree of bending is one factor taken into consideration when
designing the overall shape and size of a fluid network.
[0040] FIG. 4 has several views of a component, a "U" bend.
[0041] The U-bend 30 an inlet 31 a body 32, and exit or outlet 33.
The gas or liquid enters at the inlet 31, passes through the body
32 turns through 180 degrees and exits at 33. The inlet 31 and exit
33 of the "U" bend is circular or substantially circular. 32 is a
side view, 34 is a bottom view, 35 an isometric view, and 36 is and
end view of the component ("U" bend").
[0042] FIG. 5 shows a sectional view of the component ("U" bend) of
FIG. 4 in accordance with the various embodiments of this
disclosure. The cross sections at A-A, B-B, C-C, D-D and E-E as
well as the inlet and outlet are also shown. The cross section at
the inlet 31 and exit 33 in FIG. 4 of the "U" bend are essentially
circular. However, the cross sections as A-A, B-B, C-C, D-D, and
E-E have respective ARQ values of 1.02, 1.114, 1.94, 1.12, and
1.02. Clearly, cross sections, B-B, C-C, and D-D are not circular.
Arguably cross sections A-A and E-E are not circular.
[0043] In this embodiment, the ARQ varies smoothly from 1 at either
end (inlet 31 and exit 33 (round furnace pipe at both ends)) but
reaches a maximum non-roundness with a maximum ARQ of 1.94 at
C-C.
[0044] The shape of the cross section of the flow passage may be
elliptical, ovoid, segmented or asymmetric in nature. The area of
the cross-section may also be held constant, increase or decrease
according to the function to be achieved. A twist may optionally be
imposed on adjacent cross sections either by means of interior
swirling vanes or beads (e.g. a welded bead on the interior of the
pipe) within the fluid network or by the bulk twisting of the cross
sections relative to each other.
[0045] However, it should be noted that different shapes may have a
comparable ARQ and that a low change in the quotient may in fact
result in a significant change in the cross section shape of the
flow passage such as from a near ellipse to a "flattened egg
shape". This is demonstrated in FIGS. 1 and 2. A 1% change in ARQ
can have a profound effect on the flow characteristics as indicated
by pressure drop, for example.
[0046] The cross section of the component within the last 5% of the
flow passage from the inlet and 5% of the flow passage from the
exit or outlet of the component have an ARQ approaching unity from
above, typically from 1.02 to 1.0, for example from 1.01 to 1. This
helps with component assembly and reduces redundancy of comparable
components.
[0047] In the remaining 90% of the flow passage, there are one or
more sections where the ARQ is from 1.02 to 1.50, for example from
1.02 to 1.3, and for example, from 1.02 to 1.12, and for example,
from 1.05 to 1.12, and for example, from 1.10 to 1.15. The interior
of the flow passage is "smooth" in the sense that the change in the
ARQ in 5% sections of the remaining flow passage does not change by
more than 7%, or for example, less than 5%. In some embodiments,
over the remaining 90% of the length of the flow passage not less
than 10% of the flow passage has an ARQ from 1.02 to 1.15. In some
embodiments, over the remaining 90% of the length of the flow
passage the ARQ does not change by more than 7% over a 5% length of
the flow passage. In some embodiments, the ARQ of about 80% of the
length of the flow passage does not change by more than 5% over a
5% length of the flow passage.
[0048] The shape of the cross sections of the flow passage is
optimized to obtain a local beneficial minimum or maximum (known
collectively as extrema) of an objective function. Such objective
function may be any parameter affecting the economics of the
operation of the transfer line including the cost (capital and or
operating) itself include but is not limited to pressure drop,
erosion rate of the fluid-contacting surfaces, weight of the
component, temperature profile, residence time and rate of fouling
(or coke deposition).
[0049] There are a number of software applications available which
are useful in the design of optimized network elements disclosed
herein. These include SOLIDWORKS software for the creation and
parametric manipulation of the flow geometry, ANSYS MECHANICAL
software for the calculation of material stress and ANSYS FLUENT
software to determine the flow pattern, pressure drop and erosion
rate used in calculating the objective function corresponding to a
particular geometry.
[0050] Procedurally, one way to find a local objective function
extremum is by sequentially applying a small perturbation to a
parameter affecting the shape of the component and determining the
resulting value of the objective function by either analytical
techniques, experiments or numerical computation. A deformation
parameter is defined as a value which can be uniquely mapped to a
change in geometry by means of scaling, offsetting or deforming any
or all of the sections in a deterministic fashion. Each parameter
may also be bounded to prevent geometric singularities, unphysical
geometries or to remain within the boundaries of a physical
solution space. After each of a finite and arbitrary number of
parameters has been perturbed, any one of a series of mathematical
techniques may be used to find the local extremum. In one such
technique a vector of steepest approach to the objective function
extremum is determined as a linear combination of parameter
changes. The geometry is progressively deformed in the direction of
steepest approach and the value of the objective function
determined for each deformation until a local extremum is found.
The process is then restarted with a new set of perturbations of
the parameter set. Other techniques that may be used to advance the
search for a local extremum include Multi-objective genetic
algorithms, Metamodeling techniques, the Monte Carlo Simulation
method or Artificial Neural Networks.
[0051] For example, a model of the original design is built. That
is a three dimensional finite model of the component is created.
The model must include the internal flow passage (void) within the
component. The model may also include the external surface of the
component. The model is then divided into (filled with) cells,
typically from 5,000 to more than 100,000 (e.g. 150,000). To some
extent this is dependent on computing power available and how long
it will take to run the programs for each deformation of the
original model. There are a number of computer programs which may
be used to build the original model such as for example finite
element analysis software (e.g. ANSYS MECHANICAL software).
[0052] Then the model needs to be "initialized". That is a fluid
dynamics and energy (of mass, energy and momentum etc.) dynamics
computer program is applied to each cell of the model to solve the
operation of that cell at given operating conditions for the
component (e.g. mass of gas passing through the component, flow
velocity, temperature, and pressure, erosion rate, fouling rate,
recirculation rate etc.) to calculate one or more objective
functions. The sum of the results of each cell operation describes
the overall operation of the component. This is run iteratively
until the model and its operation approach, or closely match actual
plant data. Generally the model should be initialized so that for
one or more of objective functions, the simulation is within 5%, or
for example, within 2%, or for example, within 1.5% of the actual
plant operating data for that objective function of the transfer
line exchanger. One fluid and/or energy dynamics program which is
suitable for the simulation is ANSYS FLUENT software.
[0053] Once the design of the component and its operation is
initialized the model of the component is iteratively deformed, for
example in a small manner but incremental manner and the simulated
operation of the deformed part is run to determine the one or more
objective functions for the deformed component (for the cells and
the sum of the cells or even cells in specified location or regions
(at the internal radius of curvature of a bend). Typically the
deformation is applied to all or part of the flow channel of the
component within 5% of the flow channel downstream of the inlet to
5% of the flow channel upstream of the exit (i.e. 90% of the
component is available for deformation). In some instances the
deformation may occur in one or more sections or parts within 10%
of the flow channel downstream of the inlet to 10% of the flow
channel upstream of the exit (i.e. 80% of the component is
available for deformation). While the deformation could be applied
to the whole length of component available for deformation it may
be useful to apply the deformation to sections or portions of the
component. For example the last or first half, third or quarter or
combinations thereof could be deformed. The results (e.g. one or
more objective functions and the sum of each such objective
function) of the simulated operation of the deformed component are
stored in the computer.
[0054] The deformation of the component may be accomplished by
applying a further computer program to the design which
incrementally deforms the part. One such commercially available
deformation and optimization software is sold under the trademark
SCULPTOR. However, it may be desirable to use a neural network to
optimize the location and degree of deformation to speed up or
focus the iterative process.
[0055] The stored calculated objective function(s) for the
operation of the deformed component are then compared until
either:
[0056] 1) the extrema of one or more objective functions is
reached; or
[0057] 2) the rate of change in the one or more objective functions
is approaching zero.
[0058] In one embodiment, a method to optimize one or more of the
operating characteristics of a fixed industrial flow passage
defined by a continuous metal envelope, selected from pressure
drop, heat transfer rate, erosion rate, and coke deposition rate is
provided, the method comprising:
[0059] 1. building a numerical model comprising not less than
5,000, or for example, more than 100,000, computational cells of
the portion of the flow channel typically from 5% of the flow
channel downstream of the inlet and to 5% of the flow channel
upstream of the outlet (e.g. 90% of the of the flow channel of the
transfer line) of the initial design;
[0060] 2. simulating (on a computational cell level and summed) the
operation of the model design from step 1 using fluid and energy
dynamics software under the industrial pressure, temperature, and
flow rate conditions of operation to numerically determine one or
more of the functions of interest (pressure drop, heat transfer
rate, erosion rate, fouling rate and cost (capital and operating))
approach (within 5%) or match actual operating conditions;
[0061] 3. iteratively;
[0062] a) deforming said numerical model comprising not less 5,000
computational cells by defaulting the geometry such that the
resulting ARQ of the section is materially greater than 1.02;
[0063] b) simulating the operation of the deformed model under the
plant operating conditions used in step 2 to determine one or more
objective functions of interest (e.g. pressure drop, heat transfer
rate, erosion rate, fouling rate, and cost (capital and/or
operating);
[0064] c) calculating and storing said one or more of functions of
interest calculated in step b);
[0065] d) using some or all of the stored results from step 3c)
with an optimization algorithm to estimate a deformation that will
improve the objective function;
[0066] e) comparing the stored objective functions of interest
until one or both of the following conditions are met: [0067] i)
the objective function reaches the desirable local extrema; or
[0068] ii) the objective function ceases to change in the
parameterized direction.
[0069] Some objective function value, for example pressure drop,
erosion rate and heat transfer rate, at each evaluation stage in
the process of finding the local extremum can be obtained via
Computational Fluid Dynamics. If the change in transfer line
cross-sections along the flow passage is selected so that the
calculated total pressure drop across the line decreases by 10%
from the baseline condition made of standard components (i.e. where
the ARQ is from 1 to 1.02 along the 90% or 80% of transfer line
flow passage) which is used as a comparison benchmark and the heat
transfer rate of the line is decreased by more than 5% compared to
the baseline calculated using a combination of structural finite
element analysis software; computational fluid dynamics simulation
of the flow rate and a geometry manipulating software that alters
the shape of the transfer line in a parametric fashion. In some
embodiments the models will be run until the change in objective
function between successive iterations is less than 10% or, for
example, less than 1%.
[0070] Also provided herein are methods to reduce the overall
pressure drop within a fluid network by 10% or more when compared
to the calculated pressure drop for fluid network having a flow
passage with an ARQ along its length from 1.00 to 1.02, in one
embodiment, the method comprising using in the fluid network
comprising at least one pipe connected to at least one U-bend,
wherein said U-bend has individually or in co-operative arrangement
an internal flow passage having a continuously smooth and
differentiable perimeter and centerline and a smoothly varying
cross-section along the flow passage such that in the 5% of the
flow passage from the inlet and the 5% of the flow passage from the
outlet ARQ is from 1.0 to 1.02 and over the remaining 90% of the
length of the flow passage not less than 5% of the flow passage has
an ARQ from 1.02 to 1.15.
[0071] In some embodiments, provided herein is a fluid network
comprising at least one pipe connected to at least one U-bend,
wherein said U-bend has individually or in co-operative arrangement
an internal flow passage having a continuously smooth and
differentiable perimeter and centerline and a smoothly varying
cross-section along the flow passage such that in the 5% of the
flow passage from the inlet and the 5% of the flow passage from the
outlet ARQ is from 1.0 to 1.02 and over the remaining 90% of the
length of the flow passage not less than 5% of the flow passage has
an ARQ from 1.02 to 1.15 and wherein the presence of one or more of
the U-bends reduces the overall pressure drop within the fluid
network by 10% or more when compared to the calculated pressure
drop for fluid network having a flow passage with an ARQ along its
length from 1.00 to 1.02.
[0072] In some embodiments, the fluid network comprising pipes and
U-bends displays an overall pressure drop within the fluid network
of 15% or more. In some embodiments the fluid network comprising
pipes and U-bends displays an overall pressure drop within the
fluid network of 20% or more. In some embodiments the fluid network
comprising pipes and U-bends displays an overall pressure drop
within the fluid network of 50% or more. In some embodiments the
fluid network comprising pipes and U-bends displays an overall
pressure drop within the fluid network of less than 5%. In some
embodiments the fluid network comprising pipes and U-bends displays
an overall pressure drop within the fluid network of less than 10%.
In some embodiments the fluid network comprising pipes and U-bends
displays an overall pressure drop within the fluid network of less
than 15%.
[0073] In some embodiments, the fluid network is a heat exchanger,
such as e.g. a shell-tube heat exchanger which comprises multiple
tube passes, forced draft exchangers comprising tube bundles,
U-tube waste heat boilers, etc.
[0074] In some embodiments, the fluid network is a fluid
transporting network. In some embodiments the fluid network is a
fluid transporting network selected from pipelines and hydraulic
systems, such as water supply distribution or wastewater collection
systems. Particular application could be for compact liquid
distribution systems such as liquid handling and dosing,
dissolving/blending or conditioning systems in
food/beverages/juices processing plants.
[0075] In some embodiments, the fluid network is fluid processing
equipment or is a fluid processing device wherein fluid condenses
or evaporates when in contact with the fluid network. In some
embodiments the fluid network is fluid processing equipment or is a
fluid processing device wherein fluid changes its temperature when
in contact with the fluid network. In some embodiments the fluid
network is fluid processing equipment or is a fluid processing
device wherein fluid undergoes a chemical reaction with or without
participation of other substances or components when in contact
with the fluid network. In some embodiments the fluid network is a
part of a larger fluid processing network. In some embodiments the
fluid network is a fluid distribution network.
[0076] In one embodiment, when compared to a baseline of a
conventionally designed component, a decrease in total pressure
drop of over 10% is observed and the subsequent, sedimentation
rate, or erosion rate or fouling rate is also affected and
decreased when compared to the baseline conditions.
[0077] In some embodiments, either the erosion rate, or the fouling
rate or sedimentation rate (or any combination thereof) in the
fluid network is decreased by not less than 10% compared to the
fouling or sedimentation rate for a fluid network having a flow
passage with an ARQ along its length from 1.00 to 1.02.
Demonstration:
[0078] Provided, by way of example only, is a modification of NOVA
Chemicals commercial ethylene cracking furnace convection section
piping (i.e., a heat exchanger) at Joffre and Corunna.
[0079] The commercial finite element analysis software and
computational fluid dynamic software have been used to model the
convection section with the sufficient accuracy to generally
predict the commercial operation of industrial plants.
[0080] First, the numerical model of the convection section with
conventional U-bends as shown in FIG. 3, was created. The pressure
drop and erosion rate were determined using ANSYS FLUENT
software.
[0081] Using the shape deformation and optimization software,
SCULPTOR, the circular cross section of the conventional U-bend or
180 degree bend component computational or numerical model was
modified into an arbitrary shape independently at several
transverse planes of the original connecting pipe to generate a
"deformed" shape based on a series of deformation parameters per
section. The ARQ of the resulting sections having a maximum ARQ
substantially greater than 1.02. The metallurgy of the pipe was
maintained constant for these models. The pressure drop and erosion
rate were also calculated for the "deformed" pipe.
[0082] The process was applied iteratively until no further
improvements in pressure drop or erosion rate were found. The
resulting geometry and ARQ values are shown in FIG. 4 and FIG. 5.
Table 1 is a summary of representative data from the computer
modeling.
TABLE-US-00001 TABLE 1 Simulation or Iteration Reduction in U-Bend
Reduction in Number Pressure Drop Erosion Rate 1 (Initial U-bend in
FIG. 3) 0% 0% 2 39% 24% 3 41% 23% 4 47% 26% 5 49% 32% 6 49% 30%
[0083] The numerical results show that although the change in ARQ
of the modified U-bends appears to be moderate, as FIG. 5
indicates, the resulting change in pressure drop and erosion rate
performance, which are summarized in Table 1, has been
dramatic.
[0084] More generally, a fluid network composed of one or more
modified U-bends described herein, connected by straight or
essentially straight pipes can be evaluated in terms of the
reduction in overall pressure drop relative to the same fluid
network with the conventional U-bends having the circular
cross-section. FIG. 6 shows, a plot of the pressure drop reduction
in a fluid network composed of one to eleven U-bends (though the
various embodiments disclosed herein need not be limited to eleven
U-bends) interconnected by straight tubes. The bottom axis of the
graph is the pipe length made non-dimensional and hence universally
comparable by dividing through by the internal diameter. This is
called the tube or pipe L/D. The vertical axis is the ratio of the
calculated overall pressure drop with optimized U-bends and the
overall pressure drop with standard U-bends. The ratio value of 1.0
indicates that there is no benefit in terms of pressure reduction
resulting from U-bend modification. Lower ratio values on the
vertical axis indicate the improvement, i.e. pressure loss
reduction resulting from the U-bend modification. The different
curves show the impact of the number of U-bends that are
incorporated into the considered network/heat exchanger. The
U-bends in this example have a non-dimensional bend radius Rb/D of
1.5 which is typical for compact and efficient heat exchangers. Rb
is the half the distance between the center of the two tubes or
pipes being connected by the U-bend. D is the internal diameter of
the tube or pipe. However, the conclusions of the example are not
limited to a bend radius Rb/D of 1.5, nor is the application of
optimized U-bends to heat exchangers limited to a bend radius Rb/D
of 1.5.
[0085] It can be seen that for all combinations of number of
U-bends and tube L/D, the use of modified U-bends shows a definite
benefit. The most significant benefit is in exchangers with a lower
L/D and larger number of U-bends. Marked on the plot is the
pressure drop reduction of a typical ethylene cracking furnace such
as described in US 2014178256A1. The reduction in pressure drop is
approximately 8% due to u-bend modification. Also indicated is the
reduction in pressure drop for a typical convection section heat
exchanger (example discussed above) and a typical cooler similar to
the one shown in FIG. 3. It can be seen that with these heat
exchangers the L/D in particular is lower and that the benefit of
pressure drop reduction after u-bend modification is significant.
For the convection section heat exchanger indicated, the pressure
drop reduction is 15%. For the cooler indicated the pressure drop
reduction is 35%.
[0086] The present invention has been described with reference to
certain details of particular embodiments thereof. It is not
intended that such details be regarded as limitations upon the
scope of the invention except insofar as and to the extent that
they are included in the accompanying claims.
* * * * *