| Title: | Diagnostics, Reliability and Predictive Maintenance of Pipeline Systems |
|---|---|
| Description: | Functions that represent some useful empirical and data-driven models for heat loss, corrosion diagnostics, and predictive maintenance of pipeline systems. The package is designed for engineers who are involved in exploratory or routine calculations. Methods are described in Timashev et al. (2016) <doi:10.1007/978-3-319-25307-7>, A.C.Reddy (2017) <doi:10.1016/j.matpr.2017.07.081>, Minenergo (2008) <https://docs.cntd.ru/document/902148459>, Minenergo (2005) <https://docs.cntd.ru/document/1200035568>, Xing LU. (2014) <doi:10.1080/23744731.2016.1258371>. |
| Authors: | Yuri Possokhov [aut, cre] |
| Maintainer: | Yuri Possokhov <[email protected]> |
| License: | GPL-3 |
| Version: | 0.2.1 |
| Built: | 2024-11-04 04:19:07 UTC |
| Source: | https://github.com/omega1x/pipenostics |
Functions that represent some useful empirical and data-driven models for heat loss, corrosion diagnostics, and predictive maintenance of pipeline systems. The package is designed for engineers who are involved in exploratory or routine calculations. Methods are described in Timashev et al. (2016) doi:10.1007/978-3-319-25307-7, A.C.Reddy (2017) doi:10.1016/j.matpr.2017.07.081, Minenergo (2008) https://docs.cntd.ru/document/902148459, Minenergo (2005) https://docs.cntd.ru/document/1200035568, Xing LU. (2014) doi:10.1080/23744731.2016.1258371.
Maintainer: Yuri Possokhov [email protected] (ORCID)
Useful links:
Data represents specified minimum yield strength (SMYS) and ultimate tensile strength (UTS) both achieved when producing line pipes according to regulatory specifications.
api5l3tdataapi5l3tdata
A data frame with 57 rows and 4 variables:
designation of standard grade of manufactured pipe. Type: assert_character.
SMYS - specified minimum yield strength, [psi]. Type: assert_double.
UTS - ultimate tensile strength, [psi]. Type: assert_double.
Identifier for the information origin regarding the specifications of pipe, []:
10API SPECIFICATION 5L. Table 3A
3GOST 20295-85. Table 7
11GOST 31443-2012. Tables 6, 7
Type: assert_integer.
API SPECIFICATION 5L. Specification for Line Pipe
GOST 20295-85. Steel welded pipes for main gas-and-oil pipelines. Specifications
GOST 31443-2012. Steel pipes for crafts pipelines. Specifications
Imitation of CVRL.BAS computer program presented in ASME B31G-1991 Appendix A for determining allowable length and allowable operating pressure
b31crvl(maop, d, wth, smys, def = 0.72, depth, l)b31crvl(maop, d, wth, smys, def = 0.72, depth, l)
maop |
maximum allowable operating pressure - MAOP, [PSI]. Type: |
d |
nominal outside diameter of pipe, [inch]. Type: |
wth |
nominal wall thickness of pipe, [inch]. Type: |
smys |
specified minimum yield of stress (SMYS) as a
characteristics of steel strength, [PSI]. Type: |
def |
appropriate (combined) design factor from
ASME B31.4,
ASME B31.8,
or ASME B31.11,
[]. Type: |
depth |
measured maximum depth of the corroded area, [inch]. Type: |
l |
measured maximum longitudinal length of the corroded area, [inch]. Type: |
Columns maop, d, wth, smys, def, depth, l in the output data.frame come from function's input, other columns are calculated.
For univariate case (when lengths of all input vectors are one) messages that imitate CRVL.BAS console output are printed.
Object of S3-class crvl which is a data.frame with the next numeric columns:
maximum allowable operating pressure - MAOP, [PSI]. Type: assert_double.
nominal outside diameter of pipe, [inch]. Type: assert_double.
nominal wall thickness of pipe, [inch]. Type: assert_double.
specified minimum yield of stress (SMYS) as a
characteristics of steel strength, [PSI]. Type: assert_double.
appropriate (combined) design factor from
ASME B31.4,
ASME B31.8,
or ASME B31.11, [].
Type: assert_double.
measured maximum depth of the corroded area, [inch]. Type: assert_double.
measured maximum longitudial length of corroded area, [inch]. Type: assert_double.
Operational status of pipe:
1 - excellent,
2 - monitoring is recommended,
3 - alert! replace the pipe immediately!
Type: assert_numeric.
design pressure of pipe, [PSI]. Type: assert_double.
safe maximum pressure for the corroded area, [PSI]. Type: assert_double.
whether operator's action is required to reduce
MOAP lower than the maximum safe pressure
of the corroded area. Type: assert_logical.
allowable depth of the corroded area, [inch]. Type: assert_double.
intermediate factor related to the geometry of the corroded area, []. Type: assert_double.
allowable length of the corroded area, [inch]. Type: assert_double.
another intermediate factor related to the geometry of the corroded area, []. Type: assert_double.
ASME B31 G-1991. Manual for determining the remaining strength of corroded pipelines. A supplement to ASME B31G code for pressure piping.
Other ASME B31G functions:
b31gacd(),
b31gacl(),
b31gafr(),
b31gdep(),
b31gmodpf(),
b31gops(),
b31gpf(),
b31gsap()
library(pipenostics) ## Further examples are inspired by those used in Appendix A of ## ASME B31G-1991 to verify correct entry of CRVL.BAS source code ## Example 1 b31crvl(maop = 910, d = 30, wth = .438, smys = 52000, def = .72, depth = .1, l = 7.5) # # -- Calculated data -- # Intermediate factor (A) = 1.847 # Design pressure = 1093 PSI; Safe pressure = 1093 PSI # Pipe may be operated safely at MAOP, 910 PSI # With corrosion length 7.500 inch, maximum allowed corrosion depth is 0.2490 inch; A = 1.847 # With corrosion depth 0.100 inch, maximum allowed corrosion length is Inf inch; A = 5.000 ## Example 2 b31crvl(maop = 400, d = 20, wth = .25, smys = 35000, def = 0.5, depth = 0.18, l = 10) # # -- Calculated data -- # Intermediate factor (A) = 3.993 # Design pressure = 438 PSI; Safe pressure = 284 PSI # Reduce operating pressure so it will not exceed 284 PSI, and so operate legally and safely # With corrosion length 10.000 inch, maximum allowed corrosion depth is 0.0790 inch; A = 3.993 # With corrosion depth 0.180 inch, maximum allowed corrosion length is 2.0180 inch; A = 0.806 ## Example 3 b31crvl(maop = 910, d = 24, wth = .432, smys = 52000, def = .72, depth = 0.13, l = 30) # # -- Calculated data -- # Intermediate factor (A) = 8.320 # Design pressure = 1348 PSI; Safe pressure = 1037 PSI # Pipe may be operated safely at MAOP, 910 PSI # With corrosion length 30.000 inch, maximum allowed corrosion depth is 0.1670 inch; A = 8.320 # With corrosion depth 0.130 inch, maximum allowed corrosion length is Inf inch; A = 5.000 ## Example 4 b31crvl(maop = 910, d = 24, wth = .432, smys = 52000, def = .72, depth = .3, l = 30) # # -- Calculated data -- # Intermediate factor (A) = 8.320 # Design pressure = 1348 PSI; Safe pressure = 453 PSI # Reduce operating pressure so it will not exceed 453 PSI, and so operate legally and safely # With corrosion length 30.000 inch, maximum allowed corrosion depth is 0.1670 inch; A = 8.320 # With corrosion depth 0.300 inch, maximum allowed corrosion length is 12.8670 inch; A = 3.568 ## Example 5 b31crvl(maop = 731, d = 24, wth = .281, smys = 52000, def = 0.72, depth = 0.08, l = 15) # # -- Calculated data -- # Intermediate factor (A) = 5.158 # Design pressure = 877 PSI; Safe pressure = 690 PSI # Reduce operating pressure so it will not exceed 690 PSI, and so operate legally and safely # With corrosion length 15.000 inch, maximum allowed corrosion depth is 0.0680 inch; A = 5.158 # With corrosion depth 0.080 inch, maximum allowed corrosion length is 11.6340 inch; A = 4.000 ## Example 6 b31crvl(maop = 1e3, d = 36, wth = .5, smys = 52000, def = 0.72, depth = 0.41, l = 100) # Alert! Corrosion depth exceeds 80 % of pipe wall! Pipe must be replaced! # -- Calculated data -- # Intermediate factor (A) = 21.048 # Design pressure = 1040 PSI; Safe pressure = 206 PSI # Repair or replace pipe because corrosion depth exceeds 80 % of pipe wall! # Reduce operating pressure so it will not exceed 206 PSI, and so operate legally and safely # With corrosion length 100.000 inch, maximum allowed corrosion depth is 0.0630 inch; A = 21.048 # With corrosion depth 0.410 inch, maximum allowed corrosion length is 2.5560 inch; A = 0.538 # But 0.410 inch exceeds allowable corrosion depth!!! ## Example 7 b31crvl(maop = 877, d = 12.625, wth = .5, smys = 35000, def = .4, depth = .035, l = 3) # Corrosion depth is less than 10 % of pipe wall. No resrictions on operation # -- Calculated data -- # Intermediate factor (A) = 1.066 # Design pressure = 1109 PSI; Safe pressure = 1109 PSI # Pipe may be operated safely at MAOP, 877 PSI # With corrosion length 3.000 inch, maximum allowed corrosion depth is 0.4000 inch; A = 1.066 # With corrosion depth 0.035 inch, maximum allowed corrosion length is Inf inch; A = 5.000 ## Example 8 b31crvl(maop = 790, d = 24, wth = .5, smys = 42000, def = .5, depth = .125, l = 12) # # -- Calculated data -- # Intermediate factor (A) = 3.093 # Design pressure = 875 PSI; Safe pressure = 845 PSI # Pipe may be operated safely at MAOP, 790 PSI # With corrosion length 12.000 inch, maximum allowed corrosion depth is 0.1790 inch; A = 3.093 # With corrosion depth 0.125 inch, maximum allowed corrosion length is 15.5190 inch; A = 4.000 ## TEST #1 b31crvl(maop = 790, d = 24, wth = .5, smys = 42000, def = .5, depth = .179, l = 12) # #-- Calculated data -- # Intermediate factor (A) = 3.093 # Design pressure = 875 PSI; Safe pressure = 791 PSI # Pipe may be operated safely at MAOP, 790 PSI # With corrosion length 12.000 inch, maximum allowed corrosion depth is 0.1790 inch; A = 3.093 # With corrosion depth 0.179 inch, maximum allowed corrosion length is 12.1820 inch; A = 3.140 ## TEST #1A b31crvl(maop = 790, d = 24, wth = .5, smys = 42000, def = .5, depth = .179, l = 12.182) # # -- Calculated data -- # Intermediate factor (A) = 3.140 # Design pressure = 875 PSI; Safe pressure = 790 PSI # Pipe may be operated safely at MAOP, 790 PSI # With corrosion length 12.182 inch, maximum allowed corrosion depth is 0.1780 inch; A = 3.140 # With corrosion depth 0.179 inch, maximum allowed corrosion length is 12.1820 inch; A = 3.140 ## TEST #1B b31crvl(maop = 790, d = 24, wth = .5, smys = 42000, def = .5, depth = .180, l = 12.182) # # -- Calculated data -- # Intermediate factor (A) = 3.140 # Design pressure = 875 PSI; Safe pressure = 789 PSI # Reduce operating pressure so it will not exceed 789 PSI, and so operate legally and safely # With corrosion length 12.182 inch, maximum allowed corrosion depth is 0.1780 inch; A = 3.140 # With corrosion depth 0.180 inch, maximum allowed corrosion length is 11.9610 inch; A = 3.083 ## TEST #2 b31crvl(maop = 790, d = 24, wth = .5, smys = 42000, def = .5, depth = .179, l = 12.297) # # -- Calculated data -- # Intermediate factor (A) = 3.170 # Design pressure = 875 PSI; Safe pressure = 789 PSI # Reduce operating pressure so it will not exceed 789 PSI, and so operate legally and safely # With corrosion length 12.297 inch, maximum allowed corrosion depth is 0.1780 inch; A = 3.170 # With corrosion depth 0.179 inch, maximum allowed corrosion length is 12.1820 inch; A = 3.140 ## All examples at once: data(b31gdata) examples <- with(b31gdata, b31crvl(maop, d, wth, smys, def, depth, l))library(pipenostics) ## Further examples are inspired by those used in Appendix A of ## ASME B31G-1991 to verify correct entry of CRVL.BAS source code ## Example 1 b31crvl(maop = 910, d = 30, wth = .438, smys = 52000, def = .72, depth = .1, l = 7.5) # # -- Calculated data -- # Intermediate factor (A) = 1.847 # Design pressure = 1093 PSI; Safe pressure = 1093 PSI # Pipe may be operated safely at MAOP, 910 PSI # With corrosion length 7.500 inch, maximum allowed corrosion depth is 0.2490 inch; A = 1.847 # With corrosion depth 0.100 inch, maximum allowed corrosion length is Inf inch; A = 5.000 ## Example 2 b31crvl(maop = 400, d = 20, wth = .25, smys = 35000, def = 0.5, depth = 0.18, l = 10) # # -- Calculated data -- # Intermediate factor (A) = 3.993 # Design pressure = 438 PSI; Safe pressure = 284 PSI # Reduce operating pressure so it will not exceed 284 PSI, and so operate legally and safely # With corrosion length 10.000 inch, maximum allowed corrosion depth is 0.0790 inch; A = 3.993 # With corrosion depth 0.180 inch, maximum allowed corrosion length is 2.0180 inch; A = 0.806 ## Example 3 b31crvl(maop = 910, d = 24, wth = .432, smys = 52000, def = .72, depth = 0.13, l = 30) # # -- Calculated data -- # Intermediate factor (A) = 8.320 # Design pressure = 1348 PSI; Safe pressure = 1037 PSI # Pipe may be operated safely at MAOP, 910 PSI # With corrosion length 30.000 inch, maximum allowed corrosion depth is 0.1670 inch; A = 8.320 # With corrosion depth 0.130 inch, maximum allowed corrosion length is Inf inch; A = 5.000 ## Example 4 b31crvl(maop = 910, d = 24, wth = .432, smys = 52000, def = .72, depth = .3, l = 30) # # -- Calculated data -- # Intermediate factor (A) = 8.320 # Design pressure = 1348 PSI; Safe pressure = 453 PSI # Reduce operating pressure so it will not exceed 453 PSI, and so operate legally and safely # With corrosion length 30.000 inch, maximum allowed corrosion depth is 0.1670 inch; A = 8.320 # With corrosion depth 0.300 inch, maximum allowed corrosion length is 12.8670 inch; A = 3.568 ## Example 5 b31crvl(maop = 731, d = 24, wth = .281, smys = 52000, def = 0.72, depth = 0.08, l = 15) # # -- Calculated data -- # Intermediate factor (A) = 5.158 # Design pressure = 877 PSI; Safe pressure = 690 PSI # Reduce operating pressure so it will not exceed 690 PSI, and so operate legally and safely # With corrosion length 15.000 inch, maximum allowed corrosion depth is 0.0680 inch; A = 5.158 # With corrosion depth 0.080 inch, maximum allowed corrosion length is 11.6340 inch; A = 4.000 ## Example 6 b31crvl(maop = 1e3, d = 36, wth = .5, smys = 52000, def = 0.72, depth = 0.41, l = 100) # Alert! Corrosion depth exceeds 80 % of pipe wall! Pipe must be replaced! # -- Calculated data -- # Intermediate factor (A) = 21.048 # Design pressure = 1040 PSI; Safe pressure = 206 PSI # Repair or replace pipe because corrosion depth exceeds 80 % of pipe wall! # Reduce operating pressure so it will not exceed 206 PSI, and so operate legally and safely # With corrosion length 100.000 inch, maximum allowed corrosion depth is 0.0630 inch; A = 21.048 # With corrosion depth 0.410 inch, maximum allowed corrosion length is 2.5560 inch; A = 0.538 # But 0.410 inch exceeds allowable corrosion depth!!! ## Example 7 b31crvl(maop = 877, d = 12.625, wth = .5, smys = 35000, def = .4, depth = .035, l = 3) # Corrosion depth is less than 10 % of pipe wall. No resrictions on operation # -- Calculated data -- # Intermediate factor (A) = 1.066 # Design pressure = 1109 PSI; Safe pressure = 1109 PSI # Pipe may be operated safely at MAOP, 877 PSI # With corrosion length 3.000 inch, maximum allowed corrosion depth is 0.4000 inch; A = 1.066 # With corrosion depth 0.035 inch, maximum allowed corrosion length is Inf inch; A = 5.000 ## Example 8 b31crvl(maop = 790, d = 24, wth = .5, smys = 42000, def = .5, depth = .125, l = 12) # # -- Calculated data -- # Intermediate factor (A) = 3.093 # Design pressure = 875 PSI; Safe pressure = 845 PSI # Pipe may be operated safely at MAOP, 790 PSI # With corrosion length 12.000 inch, maximum allowed corrosion depth is 0.1790 inch; A = 3.093 # With corrosion depth 0.125 inch, maximum allowed corrosion length is 15.5190 inch; A = 4.000 ## TEST #1 b31crvl(maop = 790, d = 24, wth = .5, smys = 42000, def = .5, depth = .179, l = 12) # #-- Calculated data -- # Intermediate factor (A) = 3.093 # Design pressure = 875 PSI; Safe pressure = 791 PSI # Pipe may be operated safely at MAOP, 790 PSI # With corrosion length 12.000 inch, maximum allowed corrosion depth is 0.1790 inch; A = 3.093 # With corrosion depth 0.179 inch, maximum allowed corrosion length is 12.1820 inch; A = 3.140 ## TEST #1A b31crvl(maop = 790, d = 24, wth = .5, smys = 42000, def = .5, depth = .179, l = 12.182) # # -- Calculated data -- # Intermediate factor (A) = 3.140 # Design pressure = 875 PSI; Safe pressure = 790 PSI # Pipe may be operated safely at MAOP, 790 PSI # With corrosion length 12.182 inch, maximum allowed corrosion depth is 0.1780 inch; A = 3.140 # With corrosion depth 0.179 inch, maximum allowed corrosion length is 12.1820 inch; A = 3.140 ## TEST #1B b31crvl(maop = 790, d = 24, wth = .5, smys = 42000, def = .5, depth = .180, l = 12.182) # # -- Calculated data -- # Intermediate factor (A) = 3.140 # Design pressure = 875 PSI; Safe pressure = 789 PSI # Reduce operating pressure so it will not exceed 789 PSI, and so operate legally and safely # With corrosion length 12.182 inch, maximum allowed corrosion depth is 0.1780 inch; A = 3.140 # With corrosion depth 0.180 inch, maximum allowed corrosion length is 11.9610 inch; A = 3.083 ## TEST #2 b31crvl(maop = 790, d = 24, wth = .5, smys = 42000, def = .5, depth = .179, l = 12.297) # # -- Calculated data -- # Intermediate factor (A) = 3.170 # Design pressure = 875 PSI; Safe pressure = 789 PSI # Reduce operating pressure so it will not exceed 789 PSI, and so operate legally and safely # With corrosion length 12.297 inch, maximum allowed corrosion depth is 0.1780 inch; A = 3.170 # With corrosion depth 0.179 inch, maximum allowed corrosion length is 12.1820 inch; A = 3.140 ## All examples at once: data(b31gdata) examples <- with(b31gdata, b31crvl(maop, d, wth, smys, def, depth, l))
Calculate allowable depth of the corroded area in the pipe.
b31gacd(dep, maop, d, wth, l)b31gacd(dep, maop, d, wth, l)
dep |
design pressure of pipe, [PSI]. Type: |
maop |
maximum allowable operating pressure - MAOP, [PSI]. Type: |
d |
nominal outside diameter of pipe, [inch]. Type: |
wth |
nominal wall thickness of pipe, [inch]. Type: |
l |
measured maximum longitudinal length of corroded area, [inch].
Type: |
allowable depth of the corroded area in the pipe, [inch]. Type: assert_double.
ASME B31G-1991. Manual for determining the remaining strength of corroded pipelines. A supplement to ASTME B31 code for pressure piping.
Other ASME B31G functions:
b31crvl(),
b31gacl(),
b31gafr(),
b31gdep(),
b31gmodpf(),
b31gops(),
b31gpf(),
b31gsap()
library(pipenostics) b31gacd(1093, 910, 30, .438, 7.5) # [1] 0.249 # [inch]library(pipenostics) b31gacd(1093, 910, 30, .438, 7.5) # [1] 0.249 # [inch]
Calculate allowable length of the corroded area in the pipe.
b31gacl(dep, maop, d, wth, depth, l)b31gacl(dep, maop, d, wth, depth, l)
dep |
design pressure of pipe, [PSI]. Type: |
maop |
maximum allowable operating pressure - MAOP, [PSI].
Type: |
d |
nominal outside diameter of pipe, [inch]. Type: |
wth |
nominal wall thickness of pipe, [inch]. Type: |
depth |
measured maximum depth of the corroded area, [inch].
Type: |
l |
measured maximum longitudinal length of the corroded area, [inch].
Type: |
allowable length of the corroded area in the pipe, [inch].
Type: assert_double.
ASME B31G-1991. Manual for determining the remaining strength of corroded pipelines. A supplement to ASTME B31 code for pressure piping.
Other ASME B31G functions:
b31crvl(),
b31gacd(),
b31gafr(),
b31gdep(),
b31gmodpf(),
b31gops(),
b31gpf(),
b31gsap()
library(pipenostics) b31gacl(1093, 910, 30, .438, .1, 7.5) # [1] Inf # [inch] - corrosion is low, no limit for the corroded area length b31gacl(438, 400, 20, .25, .18, 10) # [1] 2.018 # [inch] - finite allowed length of the corroded arealibrary(pipenostics) b31gacl(1093, 910, 30, .438, .1, 7.5) # [1] Inf # [inch] - corrosion is low, no limit for the corroded area length b31gacl(438, 400, 20, .25, .18, 10) # [1] 2.018 # [inch] - finite allowed length of the corroded area
Calculate intermediate factor related to the geometry of the corroded area.
b31gafr(d, wth, l)b31gafr(d, wth, l)
d |
nominal outside diameter of pipe, [inch]. Type: |
wth |
nominal wall thickness of pipe, [inch]. Type: |
l |
measured maximum longitudinal length of the corroded area, [inch].
Type: |
Intermediate factor related to the geometry of the corroded area, [].
Type: assert_double.
ASME B31G-1991. Manual for determining the remaining strength of corroded pipelines. A supplement to ASTME B31 code for pressure piping.
Other ASME B31G functions:
b31crvl(),
b31gacd(),
b31gacl(),
b31gdep(),
b31gmodpf(),
b31gops(),
b31gpf(),
b31gsap()
library(pipenostics) b31gafr(30, .438, 7.5) # [1] 1.847 # A-factor is less than 5, so the corrosion is not criticallibrary(pipenostics) b31gafr(30, .438, 7.5) # [1] 1.847 # A-factor is less than 5, so the corrosion is not critical
Data represents examples used for verification of computer program CRVL.BAS listed in Appendix A of ASME B31G-1991.
b31gdatab31gdata
A data frame with 12 rows and 15 variables:
maximum allowable operating pressure - MAOP, [PSI]. Type: assert_double.
nominal outside diameter of pipe, [inch]. Type: assert_double.
nominal wall thickness of pipe, [inch]. Type: assert_double.
specified minimum yield of stress (SMYS) as a
characteristics of steel strength, [PSI]. Type: assert_double.
appropriate (combined) design factor from
ASME B31.4,
ASME B31.8,
or ASME B31.11,
[]. Type: assert_double.
measured maximum depth of the corroded area, [inch].
Type: assert_double.
measured maximum longitudinal length of corroded area, [inch].
Type: assert_double.
Operational status of pipe:
1 - excellent,
2 - monitoring is recommended,
3 - alert! replace the pipe immediately!
Type: assert_numeric.
design pressure of pipe, [PSI]. Type: assert_double.
safe maximum pressure for the corroded area, [PSI]. Type: assert_double.
whether operator's action is required to reduce
MOAP lower than the maximum safe pressure
of the corroded area. . Type: assert_logical.
allowable depth of the corroded area, [inch]. Type: assert_double.
intermediate factor related to the geometry of the corroded area, []. Type: assert_double.
allowable length of the corroded area, [inch]. Type: assert_double.
another intermediate factor related to the geometry of the corroded area, []. Type: assert_double.
https://law.resource.org/pub/us/cfr/ibr/002/asme.b31g.1991.pdf
Calculate the design pressure that according to ASME B31G-1991 is the conditioned construction characteristic that should not in no way exceeded.
b31gdep(d, wth, smys, def)b31gdep(d, wth, smys, def)
d |
nominal outside diameter of pipe, [inch]. Type: |
wth |
nominal wall thickness of pipe, [inch]. Type: |
smys |
specified minimum yield of stress (SMYS) as a
characteristics of steel strength, [PSI]. Type: |
def |
appropriate (combined) design factor from
ASME B31.4,
ASME B31.8,
or ASME B31.11, [].
Type: |
Design pressure of pipe, [PSI]. Type: assert_double.
ASME B31G-1991. Manual for determining the remaining strength of corroded pipelines. A supplement to ASTME B31 code for pressure piping.
Other ASME B31G functions:
b31crvl(),
b31gacd(),
b31gacl(),
b31gafr(),
b31gmodpf(),
b31gops(),
b31gpf(),
b31gsap()
library(pipenostics) b31gdep(30, .438, 52e3, .72) # [1] 1093.748 # [PSI]library(pipenostics) b31gdep(30, .438, 52e3, .72) # [1] 1093.748 # [PSI]
Calculate failure pressure of the corroded pipe according to Modified B31G, Level-1 algorithm listed in ASME B31G-2012.
The next assumption of corrosion shape is adopted by Modified B31G:
There dcor represents argument depth.
b31gmodpf(d, wth, smys, depth, l)b31gmodpf(d, wth, smys, depth, l)
d |
nominal outside diameter of pipe, [inch]. Type: |
wth |
nominal wall thickness of pipe, [inch]. Type: |
smys |
specified minimum yield of stress (SMYS) as a
characteristics of steel strength, [PSI]. Type: |
depth |
measured maximum depth of the corroded area, [inch]. Type: |
l |
measured maximum longitudinal length of corroded area, [inch]. Type: |
Since the definition of flow stress, Sflow, in ASME B31G-2012 is recommended with Level 1 as follows:
no other possibilities of its evaluation are incorporated.
For this code we avoid possible semantic optimization to preserve readability and correlation with original text description in ASME B31G-2012. At the same time source code for estimated failure pressure preserves maximum affinity with its semantic description in ASME B31G-2012.
Numeric NAs may appear in case prescribed conditions of
use are offended.
Estimated failure pressure of the corroded pipe, [PSI]. Type: assert_double.
ASME B31G-2012. Manual for determining the remaining strength of corroded pipelines: supplement to B31 Code for pressure piping.
S. Timashev and A. Bushinskaya, Diagnostics and Reliability of Pipeline Systems, Topics in Safety, Risk, Reliability and Quality 30, DOI 10.1007/978-3-319-25307-7
Other fail pressure functions: b31gpf, dnvpf,
shell92pf, pcorrcpf
Other ASME B31G functions:
b31crvl(),
b31gacd(),
b31gacl(),
b31gafr(),
b31gdep(),
b31gops(),
b31gpf(),
b31gsap()
library(pipenostics) ## Example: maximum percentage disparity of original B31G ## algorithm and modified B31G showed on CRVL.BAS data with(b31gdata, { original <- b31gpf(d, wth, smys, depth, l) modified <- b31gmodpf(d, wth, smys, depth, l) round(max(100*abs(1 - original/modified), na.rm = TRUE), 4) }) ## Output: #[1] 32.6666 ## Example: plot disparity of original B31G algorithm and ## modified B31G showed on CRVL data with(b31gdata[-(6:7),], { b31g <- b31gpf(depth, wth, smys, depth, l) b31gmod <- b31gmodpf(depth, wth, smys, depth, l) axe_range <- range(c(b31g, b31gmod)) plot(b31g, b31g, type = 'b', pch = 16, xlab = 'Pressure, [PSI]', ylab = 'Pressure, [PSI]', main = 'Failure pressure method comparison', xlim = axe_range, ylim = axe_range) inc <- order(b31g) lines(b31g[inc], b31gmod[inc], type = 'b', col = 'red') legend('topleft', legend = c('B31G Original', 'B31G Modified'), col = c('black', 'red'), lty = 'solid') })library(pipenostics) ## Example: maximum percentage disparity of original B31G ## algorithm and modified B31G showed on CRVL.BAS data with(b31gdata, { original <- b31gpf(d, wth, smys, depth, l) modified <- b31gmodpf(d, wth, smys, depth, l) round(max(100*abs(1 - original/modified), na.rm = TRUE), 4) }) ## Output: #[1] 32.6666 ## Example: plot disparity of original B31G algorithm and ## modified B31G showed on CRVL data with(b31gdata[-(6:7),], { b31g <- b31gpf(depth, wth, smys, depth, l) b31gmod <- b31gmodpf(depth, wth, smys, depth, l) axe_range <- range(c(b31g, b31gmod)) plot(b31g, b31g, type = 'b', pch = 16, xlab = 'Pressure, [PSI]', ylab = 'Pressure, [PSI]', main = 'Failure pressure method comparison', xlim = axe_range, ylim = axe_range) inc <- order(b31g) lines(b31g[inc], b31gmod[inc], type = 'b', col = 'red') legend('topleft', legend = c('B31G Original', 'B31G Modified'), col = c('black', 'red'), lty = 'solid') })
Determine the operational status of pipe: is it excellent? or is technological control required? or is it critical situation?
b31gops(wth, depth)b31gops(wth, depth)
wth |
nominal wall thickness of pipe, [inch]. Type: |
depth |
measured maximum depth of the corroded area, [inch]. Type: |
Operational status of pipe as an integer value:
1 - excellent
2 - monitoring is recommended
3 - alert! replace the pipe immediately!
Type: assert_numeric and assert_subset.
ASME B31G-1991. Manual for determining the remaining strength of corroded pipelines. A supplement to ASTME B31 code for pressure piping.
Other ASME B31G functions:
b31crvl(),
b31gacd(),
b31gacl(),
b31gafr(),
b31gdep(),
b31gmodpf(),
b31gpf(),
b31gsap()
library(pipenostics) b31gops(.438, .1) # [1] 2 # typical status for the most of pipes b31gops(.5, .41) # [1] 3 # alert! Corrosion depth is too high! Replace the pipe!library(pipenostics) b31gops(.438, .1) # [1] 2 # typical status for the most of pipes b31gops(.5, .41) # [1] 3 # alert! Corrosion depth is too high! Replace the pipe!
Calculate failure pressure of the corroded pipe according to Original B31G, Level-1 algorithm listed in ASME B31G-2012.
The next assumption of the corrosion shape is adopted by ASME B31G-2012:
There (a) is a parabolic and (b) is a rectangular idealizations of a corroded area.
b31gpf(d, wth, smys, depth, l)b31gpf(d, wth, smys, depth, l)
d |
nominal outside diameter of pipe, [inch]. Type: |
wth |
nominal wall thickness of pipe, [inch]. Type: |
smys |
specified minimum yield of stress (SMYS) as a
characteristics of steel strength, [PSI]. Type: |
depth |
measured maximum depth of the corroded area, [inch]. Type: |
l |
measured maximum longitudinal length of corroded area, [inch]. Type: |
Since the definition of flow stress, Sflow, in ASME B31G-2012 is recommended with Level 1 as follows:
no other possibilities of its evaluation are incorporated.
For this code we avoid possible semantic optimization to
preserve readability and correlation with original text description
in ASME B31G-2012.
At the same time source code for estimated failure pressure preserves
maximum affinity with its semantic description in ASME B31G-2012
and slightly differs from that given by Timashev et al. The latter
deviates up to 0.7
(b31gdata).
Numeric NAs may appear in case prescribed conditions of
use are offended.
Estimated failure pressure of the corroded pipe, [PSI].
Type: assert_double.
ASME B31G-2012. Manual for determining the remaining strength of corroded pipelines: supplement to B31 Code for pressure piping.
S. Timashev and A. Bushinskaya, Diagnostics and Reliability of Pipeline Systems, Topics in Safety, Risk, Reliability and Quality 30, DOI 10.1007/978-3-319-25307-7
Other fail pressure functions: b31gmodpf, dnvpf,
shell92pf, pcorrcpf
Other ASME B31G functions:
b31crvl(),
b31gacd(),
b31gacl(),
b31gafr(),
b31gdep(),
b31gmodpf(),
b31gops(),
b31gsap()
library(pipenostics) ## Example: maximum percentage disparity of original B31G ## algorithm and modified B31G showed on CRVL.BAS data with(b31gdata, { original <- b31gpf(d, wth, smys, depth, l) modified <- b31gmodpf(d, wth, smys, depth, l) round(max(100*abs(1 - original/modified), na.rm = TRUE), 4) }) ## Output: #[1] 32.6666 ## Example: plot disparity of original B31G algorithm and ## modified B31G showed on CRVL data with(b31gdata[-(6:7),], { b31g <- b31gpf(depth, wth, smys, depth, l) b31gmod <- b31gmodpf(depth, wth, smys, depth, l) axe_range <- range(c(b31g, b31gmod)) plot(b31g, b31g, type = 'b', pch = 16, xlab = 'Pressure, [PSI]', ylab = 'Pressure, [PSI]', main = 'Failure pressure method comparison', xlim = axe_range, ylim = axe_range) inc <- order(b31g) lines(b31g[inc], b31gmod[inc], type = 'b', col = 'red') legend('topleft', legend = c('B31G Original', 'B31G Modified'), col = c('black', 'red'), lty = 'solid') })library(pipenostics) ## Example: maximum percentage disparity of original B31G ## algorithm and modified B31G showed on CRVL.BAS data with(b31gdata, { original <- b31gpf(d, wth, smys, depth, l) modified <- b31gmodpf(d, wth, smys, depth, l) round(max(100*abs(1 - original/modified), na.rm = TRUE), 4) }) ## Output: #[1] 32.6666 ## Example: plot disparity of original B31G algorithm and ## modified B31G showed on CRVL data with(b31gdata[-(6:7),], { b31g <- b31gpf(depth, wth, smys, depth, l) b31gmod <- b31gmodpf(depth, wth, smys, depth, l) axe_range <- range(c(b31g, b31gmod)) plot(b31g, b31g, type = 'b', pch = 16, xlab = 'Pressure, [PSI]', ylab = 'Pressure, [PSI]', main = 'Failure pressure method comparison', xlim = axe_range, ylim = axe_range) inc <- order(b31g) lines(b31g[inc], b31gmod[inc], type = 'b', col = 'red') legend('topleft', legend = c('B31G Original', 'B31G Modified'), col = c('black', 'red'), lty = 'solid') })
Calculate safe maximum pressure for the corroded area of pipe.
b31gsap(dep, d, wth, depth, l)b31gsap(dep, d, wth, depth, l)
dep |
design pressure of pipe, [PSI]. Type: |
d |
nominal outside diameter of pipe, [inch]. Type: |
wth |
nominal wall thickness of pipe, [inch]. Type: |
depth |
measured maximum depth of the corroded area, [inch]. Type: |
l |
measured maximum longitudinal length of the corroded area, [inch]. Type: |
Safe maximum pressure for the corroded area of pipe, [PSI]. Type: assert_double.
ASME B31G-1991. Manual for determining the remaining strength of corroded pipelines. A supplement to ASTME B31 code for pressure piping.
Other ASME B31G functions:
b31crvl(),
b31gacd(),
b31gacl(),
b31gafr(),
b31gdep(),
b31gmodpf(),
b31gops(),
b31gpf()
library(pipenostics) b31gsap(1093, 30, .438, .1, 7.5) # [1] 1093 # [PSI], safe pressure is equal to design pressure b31gsap(877, 24, .281, .08, 15) # [1] 690 # [PSI], safe pressure is lower than design pressure due corrosionlibrary(pipenostics) b31gsap(1093, 30, .438, .1, 7.5) # [1] 1093 # [PSI], safe pressure is equal to design pressure b31gsap(877, 24, .281, .08, 15) # [1] 690 # [PSI], safe pressure is lower than design pressure due corrosion
Estimate mass or geometric specifications of the manufactured pipes
b36mass(d, wth, len = 1, rho = 7.85, origin = NULL) b36d(wth, mass, len = 1, rho = 7.85) b36wth(d, mass, len = 1, rho = 7.85)b36mass(d, wth, len = 1, rho = 7.85, origin = NULL) b36d(wth, mass, len = 1, rho = 7.85) b36wth(d, mass, len = 1, rho = 7.85)
d |
nominal outside diameter of pipe, [mm]. Type: |
wth |
nominal wall thickness of pipe, [mm]. Type: |
len |
pipe length, [m]. Type: |
rho |
mass density of pipe material, [g/cm^3]. Type: |
origin |
identifier for the information origin regarding the specifications of pipe.
Type: |
mass |
actual mass of pipe, [kg]. Type: |
The mass of a one-meter pipe segment is determined by linear interpolation based on
the tabular data provided in the specified origins (see b36pipedata). If
the origin of the initial data is NULL (default), the mass of the pipe is calculated using a formula:
where
- mass of a pipe, [kg]
- mass density of pipe material, [g/cm^3]
- nominal wall thickness of the manufactured pipe, [mm]
- nominal outside diameter of the manufactured pipe, [mm]
- actual pipe length, [m]
For origin in c(1, 2, 4, 5) the values provided in the
b36pipedata match the calculated values obtained from the formula
with an accuracy of 1 %.
Inverse calculations b36wth and b36d are performed using
algebraically derived formulas.
b36mass
pipe mass, [kg]
b36wth
pipe wall thickness, [mm]
b36d
outside diameter of pipe, [mm]
Other utils:
b36pipedata,
geoarea(),
meteos(),
mgtdhid(),
wth_d()
library(pipenostics) # Since some specification origins provide the mass of a one-meter pipe segment taking # into account possible deviations during its production process, when the user # specifies the origin ID directly, the mass values are calculated using linear # interpolation: b36mass(68, 13, rho = 7.9, origin = 7L) # [1] 16.43 # The discrepancy with the calculations based on the formula can be more than 7 %: b36mass(68, 13, rho = 7.9, origin = NULL) # [1] 17.74529 # For origins which are ASME B36 standards such differences should be minimal: b36mass(965, 10.31, origin = 1L) - b36mass(965, 10.31, origin = NULL) # [1] 0.0004356046 # The calculations of diameter and wall thickness are straightforward and use # only inverse formulas without origin references: b36d(10.31, 242.74) # [1] 965.0017 b36wth(965, 242.74) # [1] 10.31002library(pipenostics) # Since some specification origins provide the mass of a one-meter pipe segment taking # into account possible deviations during its production process, when the user # specifies the origin ID directly, the mass values are calculated using linear # interpolation: b36mass(68, 13, rho = 7.9, origin = 7L) # [1] 16.43 # The discrepancy with the calculations based on the formula can be more than 7 %: b36mass(68, 13, rho = 7.9, origin = NULL) # [1] 17.74529 # For origins which are ASME B36 standards such differences should be minimal: b36mass(965, 10.31, origin = 1L) - b36mass(965, 10.31, origin = NULL) # [1] 0.0004356046 # The calculations of diameter and wall thickness are straightforward and use # only inverse formulas without origin references: b36d(10.31, 242.74) # [1] 965.0017 b36wth(965, 242.74) # [1] 10.31002
Data represents the nominal specifications of steel pipes produced by the industry according to regulatory standards.
b36pipedatab36pipedata
A data frame with 6064 rows and 5 variables:
Nominal outside diameter of the manufactured pipe, [mm]. Type: assert_double.
Nominal wall thickness of the manufactured pipe, [mm]. Type: assert_double.
Nominal mass density of the steel rank applied in the pipe manufacturing, [g/cm³]. Type: assert_double.
Nominal mass of one-meter length pipe segment, [kg]. Type: assert_double.
Identifier for the information origin regarding the specifications of pipe, []:
123GOST 20295-85. Table 1
4GOST 33229-2015. Table 1
5GOST 33229-2015. Table 2
6GOST R 57423-2017. Table 1
7GOST R 57423-2017. Table 2
8GOST R 57423-2017. Table 3
9GOST R 57423-2017. Table 4
Type: assert_integer.
NOTE! Due to numerous typos in origins with identifiers 4, 5 all mass values in those origins are the recalculations made with formula
where
- mass of one-meter pipe segment, [kg]
- nominal outside diameter of the manufactured pipe, [mm]
(wth) - nominal wall thickness of the manufactured pipe, [mm]
ASME B36.10M-2018. Welded and seamless wrought steel pipe
ASME B36.19M-2018. Stainless steel pipe
GOST 20295-85. Steel welded pipes for main gas-and-oil pipelines. Specifications
GOST 33229-2015. Tubes for boiler and heat exchanging equipment. Technical specifications. Part 1. Seamless steel pipes to work under pressure not more than 6,4 MPa and at temperatures not exceeding 400°C
GOST R 57423-2017. Tubes for boiler and heat exchanging equipment. Part 2. Seamless steel tubes for pressure purposes more 6,4 MPa and temperatures exceeding 400°C. Specifications
Other utils:
b36mass(),
geoarea(),
meteos(),
mgtdhid(),
wth_d()
Convert temperature measured in Kelvin- or Fahrenheit-scale to Celsius (°C).
c_k(x) c_f(x)c_k(x) c_f(x)
x |
temperature in initial scale:
Type: |
temperature in Celsius-scale, [°C]. Type: assert_double.
k_c and f_c for converting from Celsius-scale.
Other units:
f_k(),
inch_mm(),
k_c(),
kgf_mpa(),
loss_flux(),
mm_inch(),
mpa_kgf(),
mpa_psi(),
psi_mpa()
library(pipenostics) # Convert from Kelvin to Celsius: c_k(c(0, 373.15)) # [1] -273.15 100 # Convert from Fahrenheit to Celsius: c_f(c(-459.67, 212)) # [1] -273.15 100library(pipenostics) # Convert from Kelvin to Celsius: c_k(c(0, 373.15)) # [1] -273.15 100 # Convert from Fahrenheit to Celsius: c_f(c(-459.67, 212)) # [1] -273.15 100
Calculate failure pressure of the corroded pipe according to Section 8.2 of in DNV-RP-F101. The estimation is valid for single isolated metal loss defects of the corrosion/erosion type and when only internal pressure loading is considered.
The next assumption of the corrosion shape is adopted by DNV-RP-F101:
There dcor represents argument depth.
dnvpf(d, wth, uts, depth, l)dnvpf(d, wth, uts, depth, l)
d |
nominal outside diameter of pipe, [mm]. Type: |
wth |
nominal wall thickness of pipe, [mm]. Type: |
uts |
ultimate tensile strength (UTS) or
specified minimum tensile strength (SMTS) as a
characteristic of steel strength, [MPa]. Type: |
depth |
measured maximum depth of the corroded area, [mm]. Type: |
l |
measured maximum longitudinal length of corroded area, [mm]. Type: |
In contrast to
ASME B31G-2012
property of pipe metal is characterized by specified minimum tensile
strength - SMTS, [], and SI
is default unit system. SMTS is given in the linepipe steel
material specifications (e.g. API 5L)
for each material grade.
At the same time Timashev et al. used ultimate tensile strength - UTS in place of SMTS. So, for the case those quantities may be used in interchangeable way.
Numeric NAs may appear in case prescribed conditions of
use are offended.
Estimated failure pressure of the corroded pipe, [MPa].
Type: assert_double.
Recommended practice DNV-RP-F101. Corroded pipelines. DET NORSKE VERITAS, October 2010.
ASME B31G-2012. Manual for determining the remaining strength of corroded pipelines: supplement to B31 Code for pressure piping.
S. Timashev and A. Bushinskaya, Diagnostics and Reliability of Pipeline Systems, Topics in Safety, Risk, Reliability and Quality 30, DOI 10.1007/978-3-319-25307-7.
Other fail pressure functions: b31gpf, b31gmodpf,
shell92pf, pcorrcpf
Other DNV-RP-F101 functions:
strderate()
library(pipenostics) d <- c(812.8, 219.0) # [mm] wth <- c( 19.1, 14.5) # [mm] uts <- c(530.9, 455.1) # [N/mm^2] l <- c(203.2, 200.0) # [mm] depth <- c( 13.4, 9.0) # [mm] dnvpf(d, wth, uts, depth, l) # [1] 15.86626 34.01183library(pipenostics) d <- c(812.8, 219.0) # [mm] wth <- c( 19.1, 14.5) # [mm] uts <- c(530.9, 455.1) # [N/mm^2] l <- c(203.2, 200.0) # [mm] depth <- c( 13.4, 9.0) # [mm] dnvpf(d, wth, uts, depth, l) # [1] 15.86626 34.01183
Calculate drop or recovery of flow rate in pipe using geometric factors.
The calculated value may be positive or negative. When it is positive they have the drop, i.e. the decrease of flow rate in the outlet of pipe under consideration. When the calculated value is negative they have the recovery, i.e. the increase of flow rate in the outlet of pipe under consideration. In both cases to calculate flow rate on the outlet of pipe under consideration simply subtract the calculated value from the sensor-measured flow rate on the inlet.
dropg(adj = 0, d = 700, flow_rate = 250)dropg(adj = 0, d = 700, flow_rate = 250)
adj |
diameters of adjacent pipes through which discharges to and recharges from network occur, [mm]. Types:
Positive values of diameters of adjacent pipes correspond to discharging process through those pipe, whereas negative values of diameters mean recharging. See Details and Examples for further explanations. |
d |
diameter of pipe under consideration, [mm]. Type: |
flow_rate |
sensor-measured amount of heat carrier (water) that is transferred through
the inlet of pipe during a period, [ton/hour]. Type: |
It is common that sensor-measured flow rate undergoes discharges to network and recharges from it. For calculation of flow rate drop or recovery the next configuration of district heating network segment is assumed:
Usually, there are no additional sensors that could measure flow rate in each flow fork. In that case they only may operate with geometric factors, i.e. assuming that flow rate is proportional to square of pipe diameter.
The simple summation of flow rates over all adjacent pipes produces the required flow rate drop or recovery located on the outlet of the pipe under consideration. Since there is concurrency between discharges and recharges the diameters of discharge pipes are regarded positive whereas diameters of recharge pipes must be negative.
Be careful when dealing with geometric factors for large amount of recharges from network: there are no additional physical constraints and thus the calculated value of recovery may have non-sense.
flow rate drop or recovery at the outlet of pipe,
[ton/hour], numeric vector. The value is positive for drop,
whereas for recovery it is negative. In both cases to calculate
flow rate on the outlet of pipe under consideration simply subtract the
calculated value from the sensor-measured flow rate on the inlet.
Type: assert_double.
Other district heating:
dropp(),
dropt()
library(pipenostics) # Let consider pipes according to network segment scheme depicted in figure # in [?dropg] help-page. # Typical large diameters of pipes under consideration, [mm]: d <- as.double(unique(subset(pipenostics::m325nhldata, diameter > 700)$diameter)) # Let sensor-measured flow rate in the inlet of pipe # under consideration be proportional to d, [ton/hour]: flow_rate <- .125*d # Let consider total diameter case when total diameters of adjacent pipes are no # more than d, [mm]: adj <- c(450, -400, 950, -255, 1152) # As at may be seen for the second and fourth cases they predominantly have # recharges from network. # Let calculate flow rate on the outlet of the pipe under consideration, # [ton/hour] result <- flow_rate - dropg(adj, d, flow_rate) print(result) # [1] 75.96439 134.72222 65.70302 180.80580 78.05995 # For more clarity they may perform calculations in `data.table`.library(pipenostics) # Let consider pipes according to network segment scheme depicted in figure # in [?dropg] help-page. # Typical large diameters of pipes under consideration, [mm]: d <- as.double(unique(subset(pipenostics::m325nhldata, diameter > 700)$diameter)) # Let sensor-measured flow rate in the inlet of pipe # under consideration be proportional to d, [ton/hour]: flow_rate <- .125*d # Let consider total diameter case when total diameters of adjacent pipes are no # more than d, [mm]: adj <- c(450, -400, 950, -255, 1152) # As at may be seen for the second and fourth cases they predominantly have # recharges from network. # Let calculate flow rate on the outlet of the pipe under consideration, # [ton/hour] result <- flow_rate - dropg(adj, d, flow_rate) print(result) # [1] 75.96439 134.72222 65.70302 180.80580 78.05995 # For more clarity they may perform calculations in `data.table`.
Calculate pressure drop in straight cylidrical steel pipe of district heating system (where water is a heat carrier) that is a result of pipe orientation in space (hydrostatic component), and friction between water and internal wall of pipe.
dropp( temperature = 130, pressure = mpa_kgf(6), flow_rate = 1276, d = 1, len = 1, roughness = 0.006, inlet = 0, outlet = 0, method = "romeo" )dropp( temperature = 130, pressure = mpa_kgf(6), flow_rate = 1276, d = 1, len = 1, roughness = 0.006, inlet = 0, outlet = 0, method = "romeo" )
temperature |
temperature of heat carrier (water) inside the pipe, [°C].
Type: |
pressure |
absolute pressure
of heat carrier (water) measured at the
entrance (inlet) of pipe, [MPa]. Type: |
flow_rate |
amount of heat carrier (water) that is transferred by pipe during a period,
[ton/hour]. Type: |
d |
internal diameter of pipe, [m]. Type: |
len |
pipe length, [m]. Type: |
roughness |
roughness of internal wall of pipe, [m]. Type: |
inlet |
elevation of pipe inlet, [m]. Type: |
outlet |
elevation of pipe outlet, [m]. Type: |
method |
method of determining Darcy friction factor.
Type: |
The underlying engineering model for calculation of pressure drop considers only two contributions (components):
Pressure drop due to gravity (hydrostatic component).
Pressure drop due to friction.
The model does not consider any size changes of pipe and presence of fittings.
For the first component that depends on pipe position in space the next figure illustrates adopted disposition of pipe.
So, the expression for the first component can be written as:
where g - is gravity factor, , and - density
of water (heat carrier), ; inlet and outlet
are appropriate pipe elevations (under sea or any other adopted level),
.
The second component comes from
Darcy–Weisbach equation
and is calculated using heating carrier regime parameters (temperature,
pressure, flow_rate). Temperature and pressure values of
heat carrier define water properties according to
IAPWS formulation.
Several methods for calculating of Darcy friction factor are possible and limited to the next direct approximations of Colebrook equation:
Romeo, Royo and Monzon, 2002
Vatankhan and Kouchakzadeh, 2009
Buzzelli, 2008
According to Brkic, 2011 approximations errors of those methods do not
exceed 0.15 % for the most combinations of
Reynolds numbers and
actual values of internal
wall roughness of pipe.
pressure drop at the outlet of pipe, [MPa]. Type: assert_double.
W.Wagner et al. The IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam, J. Eng. Gas Turbines Power. Jan 2000, 122(1): 150-184 (35 pages)
M.L.Huber et al.New International Formulation for the
Viscosity of , Journal of Physical and Chemical Reference Data
38, 101 (2009);
D.Brkic. Journal of Petroleum Science and Engineering, Vol. 77, Issue 1, April 2011, Pages 34-48.
Romeo, E., Royo, C., Monzon, A., 2002. Improved explicit equation for estimation of friction factor in rough and smooth pipes. Chem. Eng. J. 86 (3), 369–374.
Vatankhah, A.R., Kouchakzadeh, S., 2009. Discussion: Exact equations for pipeflow problems, by P.K. Swamee and P.N. Rathie. J. Hydraul. Res. IAHR 47 (7), 537–538.
Buzzelli, D., 2008. Calculating friction in one step. Mach. Des. 80 (12), 54–55.
dropt for calculating temperature drop in pipe
Other district heating:
dropg(),
dropt()
library(pipenostics) # Typical pressure drop for horizontal pipeline segments # in high-way heating network in Novosibirsk dropp(len = c(200, 300)) #[1] 0.0007000666 0.0010500999library(pipenostics) # Typical pressure drop for horizontal pipeline segments # in high-way heating network in Novosibirsk dropp(len = c(200, 300)) #[1] 0.0007000666 0.0010500999
Calculate temperature drop in steel pipe of district heating system (where water is a heat carrier) that is a result of heat loss through pipe wall and insulation.
dropt( temperature = 130, pressure = mpa_kgf(6), flow_rate = 250, loss_power = 7000 )dropt( temperature = 130, pressure = mpa_kgf(6), flow_rate = 250, loss_power = 7000 )
temperature |
temperature of heat carrier (water) inside the pipe measured at the
inlet of pipe, [°C]. Type: |
pressure |
absolute pressure
of heat carrier (water) inside the pipe, [MPa]. Type: |
flow_rate |
amount of heat carrier (water) that is transferred by pipe during a period,
[ton/hour]. Type: |
loss_power |
power of heat loss - heat loss through area of pipe wall per hour, [kcal/hour].
Type: |
Specific isobaric heat capacity used in calculations is calculated according to IAPWS R7-97(2012) for Region 1 since it is assumed that state of water in district heating system is always in that region.
temperature drop at the outlet of pipe, [°C]. Type: assert_double.
Other district heating:
dropg(),
dropp()
library(pipenostics) # Calculate normative temperature drop based on Minenergo-325 for pipe segment pipeline <- list( year = 1968, laying = "channel", d = 700, # [mm] len = 1000 # [m] ) regime <- list( temperature = c(130, 150), # [°C] pressure = .588399, # [MPa] flow_rate = 250 # [ton/hour] ) pipe_loss_power <- do.call( m325nhl, c(pipeline, temperature = list(regime[["temperature"]]), duration = 1) # [kcal/hour] ) temperature_drop <- dropt( temperature = regime[["temperature"]], # [°C] loss_power = pipe_loss_power # [kcal/hour] ) # [°C] print(temperature_drop) # [1] 1.366806 1.433840library(pipenostics) # Calculate normative temperature drop based on Minenergo-325 for pipe segment pipeline <- list( year = 1968, laying = "channel", d = 700, # [mm] len = 1000 # [m] ) regime <- list( temperature = c(130, 150), # [°C] pressure = .588399, # [MPa] flow_rate = 250 # [ton/hour] ) pipe_loss_power <- do.call( m325nhl, c(pipeline, temperature = list(regime[["temperature"]]), duration = 1) # [kcal/hour] ) temperature_drop <- dropt( temperature = regime[["temperature"]], # [°C] loss_power = pipe_loss_power # [kcal/hour] ) # [°C] print(temperature_drop) # [1] 1.366806 1.433840
Convert temperature measured in Kelvin- or Celsius-scale to Fahrenheit (°F).
f_k(x) f_c(x)f_k(x) f_c(x)
x |
temperature in initial scale: Type: |
temperature in Fahrenheit-scale, [°F]. Type: assert_double.
k_f and c_f for converting from Fahrenheit-scale.
Other units:
c_k(),
inch_mm(),
k_c(),
kgf_mpa(),
loss_flux(),
mm_inch(),
mpa_kgf(),
mpa_psi(),
psi_mpa()
library(pipenostics) # Convert from Kelvin to Fahrenheit: f_k(c(0, 373.15)) # [1] -459.67 212 # Convert from Celsius to Fahrenheit: f_c(c(-273.15, 100)) # [1] -459.67, 212library(pipenostics) # Convert from Kelvin to Fahrenheit: f_k(c(0, 373.15)) # [1] -459.67 212 # Convert from Celsius to Fahrenheit: f_c(c(-273.15, 100)) # [1] -459.67, 212
Find and list all possible paths of heat carrier flow (water) in the given topology of district heating system.
flowls(sender = "A", acceptor = "B", use_cluster = FALSE)flowls(sender = "A", acceptor = "B", use_cluster = FALSE)
sender |
identifier of the node which heat carrier flows out.
Type: any type that can be painlessly coerced to character by
|
acceptor |
identifier of the node which heat carrier flows in. According to topology
of test bench considered this identifier should be unique.
Type: any type that can be painlessly coerced to character by
|
use_cluster |
utilize functionality of parallel processing on multi-core CPU.
Type: |
Only branched topology without cycles is considered where no more than one
incoming edge exists for every acceptor node. For instance,
m325nxdata has permitted topology.
Though input arguments are natively vectorized their individual values
all relate to common part of district heating network, i.e. associated with
common object. It is due to isomorphism between vector representation and
directed graph of this network. For more details of isomorphic topology
description see m325nxdata.
named list that contains integer vectors as its elements. The name
of each element in the list is the name of acceptor associated
with terminal node of district heating network. Each vector in the
list represents an ordered sequence of indexes in acceptor
that enumerates incoming edges from starting node to terminal one. The
length of returned list is equal to number of terminal nodes for
topology considered. Type: assert_list.
m325nxdata for example of topology of district heating
system
library(pipenostics) # Find path from A to B in trivial line topology: flowls("A", "B") # $B # [1] 1 # More complex example with two terminal nodes D and E: flowls(c("A", "B", "B"), c("B", "D", "E")) #$D #[1] 1 2 # #$E #[1] 1 3 # All possible flow paths in test bench illustrated in `?m325nxdata`: all_paths <- list( c(12, 13, 11, 8, 4, 1), # hereinafter indexes of acceptor nodes c(12, 13, 11, 8, 4, 2), c(12, 13, 11, 8, 6, 5, 3), c(12, 13, 11, 8, 6, 7), c(12, 13, 11, 8, 6, 9), c(12, 13, 11, 10), c(12, 13, 14, 15), c(12, 13, 16, 17), c(12, 13, 16, 18, 20, 19), c(12, 13, 16, 18, 20, 21), c(12, 13, 16, 18, 22, 24), c(12, 13, 16, 18, 22, 25), c(12, 13, 16, 18, 20, 23, 26) ) # find those paths: path <- with(pipenostics::m325nxdata, { flowls(sender, acceptor) }) path[[4]] # [1] 12 13 11 8 6 7library(pipenostics) # Find path from A to B in trivial line topology: flowls("A", "B") # $B # [1] 1 # More complex example with two terminal nodes D and E: flowls(c("A", "B", "B"), c("B", "D", "E")) #$D #[1] 1 2 # #$E #[1] 1 3 # All possible flow paths in test bench illustrated in `?m325nxdata`: all_paths <- list( c(12, 13, 11, 8, 4, 1), # hereinafter indexes of acceptor nodes c(12, 13, 11, 8, 4, 2), c(12, 13, 11, 8, 6, 5, 3), c(12, 13, 11, 8, 6, 7), c(12, 13, 11, 8, 6, 9), c(12, 13, 11, 10), c(12, 13, 14, 15), c(12, 13, 16, 17), c(12, 13, 16, 18, 20, 19), c(12, 13, 16, 18, 20, 21), c(12, 13, 16, 18, 22, 24), c(12, 13, 16, 18, 22, 25), c(12, 13, 16, 18, 20, 23, 26) ) # find those paths: path <- with(pipenostics::m325nxdata, { flowls(sender, acceptor) }) path[[4]] # [1] 12 13 11 8 6 7
Estimate Darcy friction factor explicitly with extremely accurate Buzelli approximation of Colebrook equation.
fric_buzelli(reynolds, roughness = 0, strict = FALSE)fric_buzelli(reynolds, roughness = 0, strict = FALSE)
reynolds |
Reynolds number, []. Type: |
roughness |
relative roughness, []. Type: |
strict |
calculate only inside the precision region. Type: |
Buzelli's formula is reported to be extremely accurate in the region:
3.0e3 <= reynolds <= 3.0e8
0 <= roughness <= 0.05
In strict = TRUE mode argument values outside this precision region
are not allowed, whereas in strict = FALSE either NAs are
generated in that case or calculation for laminar flow is performed when
reynolds < 2100.0.
pipe friction factor, []. Type: assert_double.
Offor, U. and Alabi, S. (2016) An Accurate and Computationally Efficient Explicit Friction Factor Model. Advances in Chemical Engineering and Science, 6, pp. 237-245. doi:10.4236/aces.2016.63024.
Buzzelli, D. (2008) Calculating friction in one step. Machine Design, 80 (12), pp. 54–55.
Other Fluid properties:
fric_romeo(),
fric_vatankhan(),
re_u()
library(pipenostics) fric_buzelli(c(2118517, 2000, 2118517), c(1e-6, 70e-3/1, 7e-3/1)) # [1] 0.01031468 0.03200000 0.03375076 # [] fric_buzelli(c(2118517, 5500, 2118517), c(1e-6, 50e-3/1, 7e-3/1), TRUE) # [1] 0.01031468 0.07556734 0.03375076library(pipenostics) fric_buzelli(c(2118517, 2000, 2118517), c(1e-6, 70e-3/1, 7e-3/1)) # [1] 0.01031468 0.03200000 0.03375076 # [] fric_buzelli(c(2118517, 5500, 2118517), c(1e-6, 50e-3/1, 7e-3/1), TRUE) # [1] 0.01031468 0.07556734 0.03375076
Estimate Darcy friction factor explicitly with extremely accurate Romeo-Royo-Monzón approximation of Colebrook equation.
fric_romeo(reynolds, roughness = 0, strict = FALSE)fric_romeo(reynolds, roughness = 0, strict = FALSE)
reynolds |
Reynolds number, []. Type: |
roughness |
relative roughness, []. Type: |
strict |
calculate only inside the precision region. Type: |
Romeo's formula is reported to be extremely accurate in the region:
3.0e3 <= reynolds <= 1.5e8
0.0 <= roughness <= 0.05
In strict = TRUE mode argument values outside this precision region
are not allowed, whereas in strict = FALSE either NAs are
generated in that case or calculation for laminar flow is performed when
reynolds < 2100.0.
pipe friction factor, []. Type: assert_double.
Offor, U. and Alabi, S. (2016) An Accurate and Computationally Efficient Explicit Friction Factor Model. Advances in Chemical Engineering and Science, 6, pp. 237-245. doi:10.4236/aces.2016.63024.
Eva Romeo, Carlos Royo, Antonio Monzón, Improved explicit equations for estimation of friction factor in rough and smooth pipes, Chemical Engineering Journal, Volume 86, Issue 3, 2002, Pages 369-374, ISSN 1385-8947. doi:10.1016/S1385-8947(01)00254-6.
Other Fluid properties:
fric_buzelli(),
fric_vatankhan(),
re_u()
library(pipenostics) fric_romeo(c(2118517, 2000, 2118517), c(0, 70e-3/1, 7e-3/1)) # [1] 0.01028473 0.03200000 0.03373215 # [] fric_romeo(c(2118517, 3030, 2118517), c(0, 50e-3/1, 7e-3/1), TRUE) # [1] 0.01028473 0.07859636 0.03373215 # []library(pipenostics) fric_romeo(c(2118517, 2000, 2118517), c(0, 70e-3/1, 7e-3/1)) # [1] 0.01028473 0.03200000 0.03373215 # [] fric_romeo(c(2118517, 3030, 2118517), c(0, 50e-3/1, 7e-3/1), TRUE) # [1] 0.01028473 0.07859636 0.03373215 # []
Estimate Darcy friction factor explicitly with extremely accurate Vatankhah-Kouchakzadeh approximation of Colebrook equation.
fric_vatankhan(reynolds, roughness = 0, strict = FALSE)fric_vatankhan(reynolds, roughness = 0, strict = FALSE)
reynolds |
Reynolds number, []. Type: |
roughness |
relative roughness, []. Type: |
strict |
calculate only inside the precision region. Type: |
Vatankhah's formula is reported to be extremely accurate in the region:
5.0e3 <= reynolds <= 1.0e8
1e-6 <= roughness <= 0.05
In strict = TRUE mode argument values outside this precision region
are not allowed, whereas in strict = FALSE either NAs are
generated in that case or calculation for laminar flow is performed when
reynolds < 2100.0.
pipe friction factor, []. Type: assert_double.
Offor, U. and Alabi, S. (2016) An Accurate and Computationally Efficient Explicit Friction Factor Model. Advances in Chemical Engineering and Science, 6, pp. 237-245. doi:10.4236/aces.2016.63024.
Ali R. Vatankhah, Salah Kouchakzadeh (2009) Exact equations for pipe-flow problems. Journal of Hydraulic Research, 47:4, pp. 537-538, DOI: doi:10.1080/00221686.2009.9522031
Other Fluid properties:
fric_buzelli(),
fric_romeo(),
re_u()
library(pipenostics) fric_vatankhan(c(2118517, 2000, 2118517), c(1e-6, 70e-3/1, 7e-3/1)) # [1] 0.01031665 0.03200000 0.03375210 # [] fric_vatankhan(c(2118517, 5500, 2118517), c(1e-6, 50e-3/1, 7e-3/1), TRUE) # [1] 0.01031665 0.07556163 0.03375210library(pipenostics) fric_vatankhan(c(2118517, 2000, 2118517), c(1e-6, 70e-3/1, 7e-3/1)) # [1] 0.01031665 0.03200000 0.03375210 # [] fric_vatankhan(c(2118517, 5500, 2118517), c(1e-6, 50e-3/1, 7e-3/1), TRUE) # [1] 0.01031665 0.07556163 0.03375210
Calculate geographical metrics (distance, area) for two or three geographical locations.
geoarea(lat1, lon1, lat2, lon2, lat3, lon3, earth = 6371008.7714) geodist(lat1, lon1, lat2, lon2, earth = 6371008.7714)geoarea(lat1, lon1, lat2, lon2, lat3, lon3, earth = 6371008.7714) geodist(lat1, lon1, lat2, lon2, earth = 6371008.7714)
lat1 |
latitude of the first geographical location, [DD].
Type: |
lon1 |
longitude of the first geographical location, [DD].
Type: |
lat2 |
latitude of the second geographical location, [DD].
Type: |
lon2 |
longitude of the second geographical location, [DD].
Type: |
lat3 |
latitude of the third geographical location, [DD].
Type: |
lon3 |
longitude of the third geographical location, [DD].
Type: |
earth |
Earth radius, [m]. See Details.
Type: |
geodist calculates distance between two geographical locations on Earth,
whereas geoarea calculates the area of spherical triangle between
three geographical locations.
Both functions use absolute positions of geographical locations described by
geographical coordinate system
in
decimal degrees
units denoted as DD. The
haversine formula
is applied to calculate the distance, and so the spherical model of
Earth is considered in both functions.
Since several variants of Earth radius can be accepted,
the user is welcome to provide its own value.
WGS-84
mean radius of semi-axes,
, is the default value.
The resulting distance is expressed in metres (m), whereas the area is expressed in square kilometers(km^2).
geodist:distance between two geographical locations, [m].
geoarea:area of spherical triangle between three geographical locations, [km^2].
Type: assert_double.
Other utils:
b36mass(),
b36pipedata,
meteos(),
mgtdhid(),
wth_d()
library(pipenostics) # Consider the longest linear pipeline segment in Krasnoyarsk, [DD]: pipe <- list( lat1 = 55.98320350, lon1 = 92.81257226, lat2 = 55.99302417, lon2 = 92.80691885 ) # and some official Earth radii, [m]: R <- c( nominal_zero_tide_equatorial = 6378100.0000, nominal_zero_tide_polar = 6356800.0000, equatorial_radius = 6378137.0000, semiminor_axis_b = 6356752.3141, polar_radius_of_curvature = 6399593.6259, mean_radius_R1 = 6371008.7714, same_surface_R2 = 6371007.1810, same_volume_R3 = 6371000.7900, WGS84_ellipsoid_axis_a = 6378137.0000, WGS84_ellipsoid_axis_b = 6356752.3142, WGS84_ellipsoid_curvature_c = 6399593.6258, WGS84_ellipsoid_R1 = 6371008.7714, WGS84_ellipsoid_R2 = 6371007.1809, WGS84_ellipsoid_R3 = 6371000.7900, GRS80_axis_a = 6378137.0000, GRS80_axis_b = 6356752.3141, spherical_approx = 6366707.0195, meridional_at_the_equator = 6335439.0000, Chimborazo_maximum = 6384400.0000, Arctic_Ocean_minimum = 6352800.0000, Averaged_center_to_surface = 6371230.0000 ) # Calculate length of the pipeline segment for different radii: len <- with( pipe, vapply( R, geodist, double(1), lat1 = lat1, lon1 = lon1, lat2 = lat2, lon2 = lon2 ) ) print(range(len)) # [1] 1140.82331483 1152.37564656 # [m] # Consider some remarkable objects on Earth, [DD]: objects <- rbind( Mount_Kailash = c(lat = 31.069831297551982, lon = 81.31215667724196), Easter_Island_Moai = c(lat =-27.166873910247862, lon =-109.37092217323053), Great_Pyramid = c(lat = 29.979229451772856, lon = 31.13418110843685), Antarctic_Pyramid = c(lat = -79.97724194984573, lon = -81.96170583068950), Stonehendge = c(lat = 51.179036665131870, lon =-1.8262150017463086) ) # Consider all combinations of distances between them: path <- t(combn(rownames(objects), 2)) d <- geodist( lat1 = objects[path[, 1], "lat"], lon1 = objects[path[, 1], "lon"], lat2 = objects[path[, 2], "lat"], lon2 = objects[path[, 2], "lon"] )*1e-3 cat( paste( sprintf("%s <--- %1.4f km ---> %s", path[, 1], d, path[, 2]), collapse = "\n" ) ) # Consider two areas # * Bermuda triangle * Polynesian Triangle lat1 <- c(Miami = 25.789106, Hawaii = 19.820680) lon1 <- c(Miami = -80.226529, Hawaii = -155.467989) lat2 <- c(Bermuda = 32.294887, NewZeland = -43.443219) lon2 <- c(Bermuda = -64.781380, NewZeland = 170.271360) lat3 <- c(SanJuan = 18.466319, EasterIsland = -27.112701) lon3 <- c(SanJuan = -66.105743, EasterIsland = -109.349668) # Area provided by manually operated Google Earth: GETriangleArea <- c( Bermuda = 1147627.48, # [km^2] Polynesian = 28775517.77 # [km^2] ) # Show the discrepancy in calculations, [km^2]: print(geoarea(lat1, lon1, lat2, lon2, lat3, lon3)) # Bermuda Polynesian # 0.4673216 11.1030971library(pipenostics) # Consider the longest linear pipeline segment in Krasnoyarsk, [DD]: pipe <- list( lat1 = 55.98320350, lon1 = 92.81257226, lat2 = 55.99302417, lon2 = 92.80691885 ) # and some official Earth radii, [m]: R <- c( nominal_zero_tide_equatorial = 6378100.0000, nominal_zero_tide_polar = 6356800.0000, equatorial_radius = 6378137.0000, semiminor_axis_b = 6356752.3141, polar_radius_of_curvature = 6399593.6259, mean_radius_R1 = 6371008.7714, same_surface_R2 = 6371007.1810, same_volume_R3 = 6371000.7900, WGS84_ellipsoid_axis_a = 6378137.0000, WGS84_ellipsoid_axis_b = 6356752.3142, WGS84_ellipsoid_curvature_c = 6399593.6258, WGS84_ellipsoid_R1 = 6371008.7714, WGS84_ellipsoid_R2 = 6371007.1809, WGS84_ellipsoid_R3 = 6371000.7900, GRS80_axis_a = 6378137.0000, GRS80_axis_b = 6356752.3141, spherical_approx = 6366707.0195, meridional_at_the_equator = 6335439.0000, Chimborazo_maximum = 6384400.0000, Arctic_Ocean_minimum = 6352800.0000, Averaged_center_to_surface = 6371230.0000 ) # Calculate length of the pipeline segment for different radii: len <- with( pipe, vapply( R, geodist, double(1), lat1 = lat1, lon1 = lon1, lat2 = lat2, lon2 = lon2 ) ) print(range(len)) # [1] 1140.82331483 1152.37564656 # [m] # Consider some remarkable objects on Earth, [DD]: objects <- rbind( Mount_Kailash = c(lat = 31.069831297551982, lon = 81.31215667724196), Easter_Island_Moai = c(lat =-27.166873910247862, lon =-109.37092217323053), Great_Pyramid = c(lat = 29.979229451772856, lon = 31.13418110843685), Antarctic_Pyramid = c(lat = -79.97724194984573, lon = -81.96170583068950), Stonehendge = c(lat = 51.179036665131870, lon =-1.8262150017463086) ) # Consider all combinations of distances between them: path <- t(combn(rownames(objects), 2)) d <- geodist( lat1 = objects[path[, 1], "lat"], lon1 = objects[path[, 1], "lon"], lat2 = objects[path[, 2], "lat"], lon2 = objects[path[, 2], "lon"] )*1e-3 cat( paste( sprintf("%s <--- %1.4f km ---> %s", path[, 1], d, path[, 2]), collapse = "\n" ) ) # Consider two areas # * Bermuda triangle * Polynesian Triangle lat1 <- c(Miami = 25.789106, Hawaii = 19.820680) lon1 <- c(Miami = -80.226529, Hawaii = -155.467989) lat2 <- c(Bermuda = 32.294887, NewZeland = -43.443219) lon2 <- c(Bermuda = -64.781380, NewZeland = 170.271360) lat3 <- c(SanJuan = 18.466319, EasterIsland = -27.112701) lon3 <- c(SanJuan = -66.105743, EasterIsland = -109.349668) # Area provided by manually operated Google Earth: GETriangleArea <- c( Bermuda = 1147627.48, # [km^2] Polynesian = 28775517.77 # [km^2] ) # Show the discrepancy in calculations, [km^2]: print(geoarea(lat1, lon1, lat2, lon2, lat3, lon3)) # Bermuda Polynesian # 0.4673216 11.1030971
Convert length measured in millimeters (mm) to inches
inch_mm(x)inch_mm(x)
x |
length measured in millimeters, [mm].
Type: |
length in inches, [inch].
Type: assert_double.
mm_inch for converting inches to mm
Other units:
c_k(),
f_k(),
k_c(),
kgf_mpa(),
loss_flux(),
mm_inch(),
mpa_kgf(),
mpa_psi(),
psi_mpa()
library(pipenostics) inch_mm(c(25.4, 1)) # [1] 1.00000000 0.03937008 # [inch]library(pipenostics) inch_mm(c(25.4, 1)) # [1] 1.00000000 0.03937008 # [inch]
Convert temperature measured in Celsius- or Fahrenheit-scale to Kelvin (K).
k_c(x) k_f(x)k_c(x) k_f(x)
x |
temperature in initial scale:
Type: |
temperature in Kelvin-scale, [K]. Type: assert_double.
c_k and f_k for converting from Kelvin-scale.
Other units:
c_k(),
f_k(),
inch_mm(),
kgf_mpa(),
loss_flux(),
mm_inch(),
mpa_kgf(),
mpa_psi(),
psi_mpa()
library(pipenostics) # Convert from Celsius to Kelvin: k_c(c(-273.15, 100)) # [1] 0 373.15 # Convert from Fahrenheit to Kelvin: k_f(c(-459.67, 212)) # [1] 0 373.15library(pipenostics) # Convert from Celsius to Kelvin: k_c(c(-273.15, 100)) # [1] 0 373.15 # Convert from Fahrenheit to Kelvin: k_f(c(-459.67, 212)) # [1] 0 373.15
Convert pressure (stress) measured in megapascals (MPa)
to kilogram-force per square cm ().
kgf_mpa(x)kgf_mpa(x)
x |
pressure (stress) measured in megapascals,
[MPa]. Type: |
pressure (stress) in
kilogram-force per square cm, [kgf/cm^2].
Type: assert_double.
mpa_kgf for converting kilogram-force per square cm to megapascals
Other units:
c_k(),
f_k(),
inch_mm(),
k_c(),
loss_flux(),
mm_inch(),
mpa_kgf(),
mpa_psi(),
psi_mpa()
library(pipenostics) kgf_mpa(c(0.0980665, 1)) # [1] 1.00000 10.19716library(pipenostics) kgf_mpa(c(0.0980665, 1)) # [1] 1.00000 10.19716
Convert heat flux measured for a cylindrical steel pipe to specific heat loss power of pipe.
loss_flux(x, d, wth = 0) flux_loss(x, d, wth = 0)loss_flux(x, d, wth = 0) flux_loss(x, d, wth = 0)
x |
value of
Type: |
d |
outside (if wth = 0) or internal (if wth > 0) diameter of cylindrical pipe, [m].
Type: |
wth |
wall thickness of pipe, [mm], or 0 if argument d is an outside diameter of pipe.
Type: |
value of
specific heat loss power, [kcal/m/h], for loss_flux(x, d, wth)
heat flux, [W/m^2], for flux_loss(x, d, wth)(x)
Type: assert_double.
Other units:
c_k(),
f_k(),
inch_mm(),
k_c(),
kgf_mpa(),
mm_inch(),
mpa_kgf(),
mpa_psi(),
psi_mpa()
library(pipenostics) # Consider pipes: diameter <- c(998, 1395) # [mm] wall_thikness <- c( 2, 5) # [mm] # Then maximum possible normative neat loss according (Minenergo-325) for # these pipe diameters are loss_max <- c(218, 1040) # [kcal/m/h] # The appropriate flux is flux <- flux_loss(loss_max, diameter * 1e-3, wall_thikness) print(flux) # [1] 80.70238 275.00155 # [W/m^2] stopifnot( all.equal(loss_flux(flux, diameter * 1e-3, wall_thikness), loss_max, tolerance = 5e-6) )library(pipenostics) # Consider pipes: diameter <- c(998, 1395) # [mm] wall_thikness <- c( 2, 5) # [mm] # Then maximum possible normative neat loss according (Minenergo-325) for # these pipe diameters are loss_max <- c(218, 1040) # [kcal/m/h] # The appropriate flux is flux <- flux_loss(loss_max, diameter * 1e-3, wall_thikness) print(flux) # [1] 80.70238 275.00155 # [W/m^2] stopifnot( all.equal(loss_flux(flux, diameter * 1e-3, wall_thikness), loss_max, tolerance = 5e-6) )
Calculate normative heat loss of the open-air supplying pipe as a function of construction, operation, and technical condition specifications according to Appendix 5.1 of Minenergo Method 278.
This type of calculations is usually made on design stage of district heating network (where water is a heat carrier) and is closely related to building codes and regulations.
m278hlair( t1 = 110, t2 = 60, t0 = 5, insd1 = 0.1, insd2 = insd1, d1 = 0.25, d2 = d1, lambda1 = 0.09, lambda2 = 0.07, k1 = 1, k2 = k1, lambda0 = 26, len = 1, duration = 1 )m278hlair( t1 = 110, t2 = 60, t0 = 5, insd1 = 0.1, insd2 = insd1, d1 = 0.25, d2 = d1, lambda1 = 0.09, lambda2 = 0.07, k1 = 1, k2 = k1, lambda0 = 26, len = 1, duration = 1 )
t1 |
temperature of heat carrier (water) inside the supplying pipe, [°C].
Type: |
t2 |
temperature of heat carrier (water) inside the returning pipe, [°C].
Type: |
t0 |
temperature of environment, [°C]. In case of open-air pipe this is
the ambient temperature. Type: |
insd1 |
thickness of the insulator which covers the supplying pipe, [m].
Type: |
insd2 |
thickness of the insulator which covers the returning pipe, [m].
Type: |
d1 |
outside diameter of supplying pipe, [m].
Type: |
d2 |
outside diameter of returning pipe, [m].
Type: |
lambda1 |
thermal conductivity of insulator which covers the supplying pipe
[W/m/°C]. Type: |
lambda2 |
thermal conductivity of insulator which covers the returning pipe
[W/m/°C]. |
k1 |
technical condition factor for insulator of supplying pipe, [].
Type: |
k2 |
technical condition factor for insulator of returning pipe, [].
Type: |
lambda0 |
thermal conductivity of environment, [W/m/°C]. In case of overhead
laying this is the thermal conductivity of open air.
Type: |
len |
length of supplying pipe, [m]. Type: |
duration |
duration of heat loss, [hour]. Type: |
Details on using k1 and k2 are the same as for
m278hlcha.
Normative heat loss of the open-air layed supplying cylindrical pipe
during duration, [kcal].
If len of pipe is 1 m (meter) as well as duration is set to
1 h (hour) (default values) then the return value is also the
specific heat loss power, [kcal/m/h] and so comparable with those
prescribed by Minenergo Order 325.
Type: assert_double.
Other Minenergo:
m278hlcha(),
m278hlund(),
m278insdata,
m278inshcm(),
m278soildata,
m325beta(),
m325nhl(),
m325nhldata,
m325nxdata
library(pipenostics) m278hlair() # [1] 138.7736library(pipenostics) m278hlair() # [1] 138.7736
Calculate normative heat loss of the supplying pipe mounted in underground channel as a function of construction, operation, and technical condition specifications according to Appendix 5.1 of Minenergo Method 278.
This type of calculations is usually made on design stage of district heating network (where water is a heat carrier) and is closely related to building codes and regulations.
m278hlcha( t1 = 110, t2 = 60, t0 = 5, insd1 = 0.1, insd2 = insd1, d1 = 0.25, d2 = d1, lambda1 = 0.09, lambda2 = 0.07, k1 = 1, k2 = k1, lambda0 = 1.74, z = 2, b = 0.5, h = 0.5, len = 1, duration = 1 )m278hlcha( t1 = 110, t2 = 60, t0 = 5, insd1 = 0.1, insd2 = insd1, d1 = 0.25, d2 = d1, lambda1 = 0.09, lambda2 = 0.07, k1 = 1, k2 = k1, lambda0 = 1.74, z = 2, b = 0.5, h = 0.5, len = 1, duration = 1 )
t1 |
temperature of heat carrier (water) inside the supplying pipe, [°C].
Type: |
t2 |
temperature of heat carrier (water) inside the returning pipe, [°C].
Type: |
t0 |
temperature of environment, [°C]. In case of channel laying this is
the temperature of subsoil. Type: |
insd1 |
thickness of the insulator which covers the supplying pipe, [m].
Type: |
insd2 |
thickness of the insulator which covers the returning pipe, [m].
Type: |
d1 |
outside diameter of supplying pipe, [m]. Type: |
d2 |
outside diameter of returning pipe, [m]. Type: |
lambda1 |
thermal conductivity of insulator which covers the supplying pipe
[W/m/°C]. Type: |
lambda2 |
thermal conductivity of insulator which covers the returning pipe
[W/m/°C]. Type: |
k1 |
technical condition factor for insulator of supplying pipe, [].
Type: |
k2 |
technical condition factor for insulator of returning pipe, [].
Type: |
lambda0 |
thermal conductivity of environment, [W/m/°C]. In case of channel
laying this is the thermal conductivity of subsoil. Type: |
z |
channel laying depth, [m]. Type: |
b |
channel width, [m]. Type: |
h |
channel height, [m]. Type: |
len |
length of supplying pipe, [m]. Type: |
duration |
duration of heat loss, [hour]. Type: |
k1 and k2 factor values equal to 1 mean the best technical
condition of insulation of appropriate pipes, whereas for poor technical
state factor values tends to 5 or more.
Nevertheless, when k1 and k2 both equal to 1 the calculated
specific heat loss power [kcal/m/h] is sometimes higher than that listed in
Minenergo Order 325.
One should consider that situation when choosing method for heat loss
calculations.
Normative heat loss of supplying cylindrical pipe mounted in channel during duration, [kcal].
If len of pipe is 1 m (meter) as well as duration is set to
1 h (hour) (default values) then the return value is also the
specific heat loss power, [kcal/m/h] and so comparable with those
prescribed by Minenergo Order 325.
Type: assert_double.
Other Minenergo:
m278hlair(),
m278hlund(),
m278insdata,
m278inshcm(),
m278soildata,
m325beta(),
m325nhl(),
m325nhldata,
m325nxdata
library(pipenostics) m278hlcha() # ## Naive way to find out technical state (factors k1 and k2) for pipe ## segments constructed in 1980: optim( par = c(1.5, 1.5), fn = function(x) { # functional to optimize abs( m278hlcha(k1 = x[1], k2 = x[2]) - m325nhl(year = 1980, laying = "channel", d = 250, temperature = 110) ) }, method = "L-BFGS-B", lower = 1.01, upper = 4.4 )$par # [1] 4.285442 4.323628library(pipenostics) m278hlcha() # ## Naive way to find out technical state (factors k1 and k2) for pipe ## segments constructed in 1980: optim( par = c(1.5, 1.5), fn = function(x) { # functional to optimize abs( m278hlcha(k1 = x[1], k2 = x[2]) - m325nhl(year = 1980, laying = "channel", d = 250, temperature = 110) ) }, method = "L-BFGS-B", lower = 1.01, upper = 4.4 )$par # [1] 4.285442 4.323628
Calculate normative heat loss of the supplying underground pipe as a function of construction, operation, and technical condition specifications according to Appendix 5.1 of Minenergo Method 278.
This type of calculations is usually made on design stage of district heating network (where water is a heat carrier) and is closely related to building codes and regulations.
m278hlund( t1 = 110, t2 = 60, t0 = 5, insd1 = 0.1, insd2 = insd1, d1 = 0.25, d2 = d1, lambda1 = 0.09, lambda2 = 0.07, k1 = 1, k2 = k1, lambda0 = 1.74, z = 2, s = 0.55, len = 1, duration = 1 )m278hlund( t1 = 110, t2 = 60, t0 = 5, insd1 = 0.1, insd2 = insd1, d1 = 0.25, d2 = d1, lambda1 = 0.09, lambda2 = 0.07, k1 = 1, k2 = k1, lambda0 = 1.74, z = 2, s = 0.55, len = 1, duration = 1 )
t1 |
temperature of heat carrier (water) inside the supplying pipe, [°C].
Type: |
t2 |
temperature of heat carrier (water) inside the returning pipe, [°C].
Type: |
t0 |
temperature of environment, [°C]. For underground pipe this is
the temperature of subsoil. Type: |
insd1 |
thickness of the insulator which covers the supplying pipe, [m].
Type: |
insd2 |
thickness of the insulator which covers the returning pipe, [m].
Type: |
d1 |
outside diameter of supplying pipe, [m]. Type: |
d2 |
outside diameter of returning pipe, [m]. Type: |
lambda1 |
thermal conductivity of insulator which covers the supplying pipe
[W/m/°C]. Type: |
lambda2 |
thermal conductivity of insulator which covers the returning pipe
[W/m/°C]. Type: |
k1 |
technical condition factor for insulator of supplying pipe, [].
Type: |
k2 |
technical condition factor for insulator of returning pipe, [].
Type: |
lambda0 |
thermal conductivity of environment, [W/m/°C]. For underground pipe this is
the thermal conductivity of subsoil.
Type: |
z |
underground laying depth of supplying pipe, [m].
Type: |
s |
distance between supplying and returning pipes, [m].
Type: |
len |
length of supplying pipe, [m].
Type: |
duration |
duration of heat loss, [hour].
Type: |
Details on using k1 and k2 are the same as for
m278hlcha.
Normative heat loss of supplying underground cylindrical pipe during duration, [kcal].
If len of pipe is 1 m (meter) as well as duration is set to
1 h (hour) (default values) then the return value is also the
specific heat loss power, [kcal/m/h] and so comparable with those
prescribed by Minenergo Order 325.
Type: assert_double.
Other Minenergo:
m278hlair(),
m278hlcha(),
m278insdata,
m278inshcm(),
m278soildata,
m325beta(),
m325nhl(),
m325nhldata,
m325nxdata
library(pipenostics) m278hlund() # [1] 102.6226library(pipenostics) m278hlund() # [1] 102.6226
Data represent values of terms (intercept and factor) for calculating thermal conductivity of pipe insulation as a linear function of temperature of heat carrier (water). Those values are set for different insulation materials in Appendix 5.3 of Minenergo Method 278 as norms.
m278insdatam278insdata
A data frame with 39 rows and 4 variables:
Number of insulation material table 5.1 of Appendix 5.3 in
Minenergo Method 278.
Type: assert_integerish.
Designation of insulation material more or less similar
to those in table 5.1 of Appendix 5.3 in
Minenergo Method 278.
Type: assert_character.
Value for intercept, [mW/m/°C].
Type: assert_integer.
Value for factor. Type: assert_integer.
Usually the data is not used directly. Instead use function m278inshcm.
https://docs.cntd.ru/document/1200035568
Other Minenergo:
m278hlair(),
m278hlcha(),
m278hlund(),
m278inshcm(),
m278soildata,
m325beta(),
m325nhl(),
m325nhldata,
m325nxdata
Get normative values of thermal conductivity of pipe insulation materials affirmed by Minenergo Method 278 as a function of temperature of heat carrier (water).
m278inshcm(temperature = 110, material = "aerocrete")m278inshcm(temperature = 110, material = "aerocrete")
temperature |
temperature of heat carrier (water) inside the pipe, [°C].
Type: |
material |
designation of insulation material as it stated in |
Thermal conductivity of insulation materials at given
set of temperatures, [W/m/°C], [W/m/K].
Type: assert_double.
Other Minenergo:
m278hlair(),
m278hlcha(),
m278hlund(),
m278insdata,
m278soildata,
m325beta(),
m325nhl(),
m325nhldata,
m325nxdata
library(pipenostics) # Averaged thermal conductivity of pipe insulation at 110 °C print(m278insdata) mean(m278inshcm(110, m278insdata[["material"]])) # [1] 0.09033974 # [\emph{W/m/°C}]library(pipenostics) # Averaged thermal conductivity of pipe insulation at 110 °C print(m278insdata) mean(m278inshcm(110, m278insdata[["material"]])) # [1] 0.09033974 # [\emph{W/m/°C}]
Data represent normative values of thermal conductivity of subsoils which can surround pipes according to Table 5.3 of Appendix 5.3 in Minenergo Method 278.
m278soildatam278soildata
A data frame with 15 rows and 3 variables:
Geological name of subsoil. Type: assert_character.
The degree of water penetration to the subsoil. Type: assert_character.
Value of thermal conductivity of subsoil regarding water penetration, [W/m/°C].
Type: assert_double.
https://docs.cntd.ru/document/1200035568
Other Minenergo:
m278hlair(),
m278hlcha(),
m278hlund(),
m278insdata,
m278inshcm(),
m325beta(),
m325nhl(),
m325nhldata,
m325nxdata
Calculate - local heat loss coefficient according to rule 11.3.3
of Minenergo Order 325.
Local heat loss coefficient is used to increase normative heat loss
of pipe by taking into account heat loss of fittings (shut-off valves,
compensators and supports). This coefficient is applied mostly as a factor
during the summation of heat losses of pipes in pipeline leveraging
formula 14 of Minenergo Order 325.
m325beta(laying = "channel", d = 700)m325beta(laying = "channel", d = 700)
laying |
type of pipe laying depicting the position of pipe in space:
Type: |
d |
internal diameter of pipe, [mm]. Type: |
Two possible values of : 1.2 or 1.15 depending on
pipe laying and its diameter. Type: assert_double.
Other Minenergo:
m278hlair(),
m278hlcha(),
m278hlund(),
m278insdata,
m278inshcm(),
m278soildata,
m325nhl(),
m325nhldata,
m325nxdata
library(pipenostics) norms <- within(m325nhldata, { beta <- m325beta(laying, as.double(diameter)) }) unique(norms$beta) # [1] 1.15 1.20library(pipenostics) norms <- within(m325nhldata, { beta <- m325beta(laying, as.double(diameter)) }) unique(norms$beta) # [1] 1.15 1.20
Calculate normative heat loss of pipe that is legally affirmed by Minenergo Order 325.
m325nhl( year = 1986, laying = "underground", exp5k = TRUE, insulation = 0, d = 700, temperature = 110, len = 1, duration = 1, beta = FALSE, extra = 2 )m325nhl( year = 1986, laying = "underground", exp5k = TRUE, insulation = 0, d = 700, temperature = 110, len = 1, duration = 1, beta = FALSE, extra = 2 )
year |
year when the pipe is put in operation after laying or total overhaul.
Type: |
laying |
type of pipe laying depicting the position of pipe in space:
Type: |
exp5k |
pipe regime flag: is pipe operated more that 5000 hours per year?
Type: |
insulation |
insulation that covers the exterior of pipe:
Type: |
d |
internal diameter of pipe, [mm]. Type: |
temperature |
temperature of heat carrier (water) inside the pipe, [°C].
Type: |
len |
length of pipe, [m]. Type: |
duration |
duration of heat loss, [hour]. Type: |
beta |
should they consider additional heat loss of fittings?
Type: |
extra |
number of points used for temperature extrapolation: |
Temperature extrapolation and pipe diameter interpolation are leveraged
for better accuracy. Both are linear as it dictated by
Minenergo Order 325.
Nevertheless, one could control the extrapolation behavior by extra
argument: use lower values of extra for soft curvature near extrapolation
edges, and higher values for more physically reasoned behavior in far regions
of extrapolation.
Normative heat loss of cylindrical pipe during duration, [kcal].
If len of pipe is 1 m (meter) as well as duration is set to
1 h (hour) (default values) then the return value is also the
specific heat loss power, [kcal/m/h], prescribed by
Minenergo Order 325.
Type: assert_double.
Other Minenergo:
m278hlair(),
m278hlcha(),
m278hlund(),
m278insdata,
m278inshcm(),
m278soildata,
m325beta(),
m325nhldata,
m325nxdata
library(pipenostics) ## Consider a 1-meter length pipe with pipe_diameter <- 700.0 # [mm] pipe_dating <- 1980 pipe_laying <- "underground" ## Linear extrapolation adopted in Minenergo's Order 325 using last two points: operation_temperature <- seq(0, 270, 10) qs <- m325nhl( year = pipe_dating, laying = pipe_laying, d = pipe_diameter, temperature = operation_temperature ) # [kcal/m/h] plot( operation_temperature, qs, type = "b", main = "Minenergo's Order 325. Normative heat loss of pipe", sub = sprintf( "%s pipe of diameter %i [mm] laid in %i", pipe_laying, pipe_diameter, pipe_dating ), xlab = "Temperature, [°C]", ylab = "Specific heat loss power, [kcal/m/h]" ) ## Consider heat loss due fittings: operation_temperature <- 65 # [°C] fittings_qs <- m325nhl( year = pipe_dating, laying = pipe_laying, d = pipe_diameter, temperature = operation_temperature, beta = c(FALSE, TRUE) ) # [kcal/m/h] print(fittings_qs); stopifnot(all(round(fittings_qs ,1) == c(272.0, 312.8))) # [1] 272.0 312.8 # [kcal/m/h] ## Calculate heat flux: operation_temperature <- c(65, 105) # [°C] qs <- m325nhl( year = pipe_dating, laying = pipe_laying, d = pipe_diameter, temperature = operation_temperature ) # [kcal/m/h] print(qs) # [1] 272.00 321.75 # [kcal/m/h] pipe_diameter <- pipe_diameter * 1e-3 # [m] factor <- 2.701283 # [kcal/h/W] flux <- qs/factor/pipe_diameter -> a # heat flux, [W/m^2] print(flux) # [1] 143.8470 170.1572 # [W/m^2] ## The above line is equivalent to: flux <- flux_loss(qs, pipe_diameter) -> b stopifnot(all.equal(a, b, tolerance = 5e-6))library(pipenostics) ## Consider a 1-meter length pipe with pipe_diameter <- 700.0 # [mm] pipe_dating <- 1980 pipe_laying <- "underground" ## Linear extrapolation adopted in Minenergo's Order 325 using last two points: operation_temperature <- seq(0, 270, 10) qs <- m325nhl( year = pipe_dating, laying = pipe_laying, d = pipe_diameter, temperature = operation_temperature ) # [kcal/m/h] plot( operation_temperature, qs, type = "b", main = "Minenergo's Order 325. Normative heat loss of pipe", sub = sprintf( "%s pipe of diameter %i [mm] laid in %i", pipe_laying, pipe_diameter, pipe_dating ), xlab = "Temperature, [°C]", ylab = "Specific heat loss power, [kcal/m/h]" ) ## Consider heat loss due fittings: operation_temperature <- 65 # [°C] fittings_qs <- m325nhl( year = pipe_dating, laying = pipe_laying, d = pipe_diameter, temperature = operation_temperature, beta = c(FALSE, TRUE) ) # [kcal/m/h] print(fittings_qs); stopifnot(all(round(fittings_qs ,1) == c(272.0, 312.8))) # [1] 272.0 312.8 # [kcal/m/h] ## Calculate heat flux: operation_temperature <- c(65, 105) # [°C] qs <- m325nhl( year = pipe_dating, laying = pipe_laying, d = pipe_diameter, temperature = operation_temperature ) # [kcal/m/h] print(qs) # [1] 272.00 321.75 # [kcal/m/h] pipe_diameter <- pipe_diameter * 1e-3 # [m] factor <- 2.701283 # [kcal/h/W] flux <- qs/factor/pipe_diameter -> a # heat flux, [W/m^2] print(flux) # [1] 143.8470 170.1572 # [W/m^2] ## The above line is equivalent to: flux <- flux_loss(qs, pipe_diameter) -> b stopifnot(all.equal(a, b, tolerance = 5e-6))
Data represent values of specific heat loss power officially accepted by
Minenergo Order 325 as
norms. Those values are maximums which are legally
affirmed to contribute to normative heat loss of
district heating systems with water as a heat carrier.
m325nhldatam325nhldata
A data frame with 17328 rows and 8 variables:
Identifier of data source: identifiers suited with
glob t?p? mean appropriate table ?.? in
Minenergo Order 325;
identifier sgc means that values are additionally
postulated (see Details).
Type: assert_character.
Year depicting the epoch when the pipe is put in operation after laying or total overhaul.
Type: assert_integer.
Type of pipe laying depicting the position of pipe in space. Only five types of pipe laying are considered:
air,
channel,
room,
tunnel,
underground.
Type: assert_character.
Logical indicator for pipe regime: if TRUE pipe is
operated more that 5000 hours per year.
Type: assert_logical.
Identifier of insulation that covers the exterior of pipe:
0no insulation
1foamed polyurethane or analogue
2polymer concrete
Type: assert_integerish.
Nominal internal diameter of pipe, [mm]. Type: assert_double.
Operational temperature of pipe, [°C]. Type: assert_double.
Normative value of specific heat loss power equal to heat flux output by
1 meter length steel pipe during an hour,
[kcal/m/hour].
Type: assert_double.
Data is organized as a full factorial design, whereas for some factorial combinations Minenergo Order 325 does not provide values. For that cases values are postulated by practical reasons in Siberian cities and marked with source label sgc.
Usually the data is not used directly. Instead use function m325nhl.
https://docs.cntd.ru/document/902148459
Other Minenergo:
m278hlair(),
m278hlcha(),
m278hlund(),
m278insdata,
m278inshcm(),
m278soildata,
m325beta(),
m325nhl(),
m325nxdata
Data describes a virtual test bench of branched district heating network by exposing parameters associated with Minenergo Order 325. They treat data as a snapshot of network state and use it primarily for static thermal-hydraulic computations and topology effects.
m325nxdatam325nxdata
A data frame with 22 rows (number of nodes and incoming edges) and 15 variables:
An identifier of node which heat carrier flows out.
Type: any type that can be painlessly coerced to character
by as.character.
An identifier of node which heat carrier flows in. According to topology
of test bench considered this identifier should be unique for every row.
Type: any type that can be painlessly coerced to
character by as.character.
Snapshot of thermal-hydraulic regime state: temperature of heat carrier
(water) sensor-measured on terminal acceptor node, [°C].
Type: assert_double. NAs are introduced for nodes
without temperature sensor.
Snapshot of thermal-hydraulic regime state:
sensor-measured
absolute pressure
of heat carrier (water) inside the pipe (i.e. acceptor's incoming edge),
[MPa].
Type: assert_double. NAs are introduced for nodes
without pressure sensor.
Snapshot of thermal-hydraulic regime state:
sensor-measured amount of heat carrier (water) on terminal node that is
transferred by pipe (i.e. acceptor's incoming edge) during a period,
[ton/hour]. Type: assert_double.
NAs are introduced for nodes without flow rate sensor.
internal diameter of pipe (i.e.diameter of acceptor's incoming edge),
[m].
Type: assert_double.
pipe length (i.e. length of acceptor's incoming edge), [m].
Type: assert_double.
year when the pipe (i.e. acceptor's incoming edge) is put in operation after
laying or total overhaul.
Type: assert_integerish.
identifier of insulation that covers the exterior of pipe (i.e. acceptor's incoming edge):
0no insulation
1foamed polyurethane or analogue
2polymer concrete
Type: assert_integerish.
type of pipe laying depicting the position of pipe in space. Only five types of pipe laying are considered:
air,
channel,
room,
tunnel,
underground.
Type: assert_character.
logical indicator: should they consider additional heat loss of fittings
located on this pipe (i.e. acceptor's incoming edge)?
Type: assert_logical.
logical indicator for regime of pipe (i.e. acceptor's incoming edge): if
TRUE pipe is operated more that 5000 hours per year.
Type: assert_logical.
roughness of internal wall of pipe (i.e. acceptor's incoming edge),
[m].
Type: assert_double.
elevation of pipe inlet, [m].
Type: assert_double.
elevation of pipe outlet, [m].
Type: assert_double.
The test bench has the next configuration:
As it may be seen from the figure there is a particularity in topology of
the provided directed graph: each node has only single ancestor. Hence one
of isomorphic representation of such directed graph is a
data.frame in which each row describes a node along with its
incoming edge and each column contains an attribute value for that node or
an attribute value for its incoming edge.
Since they deal with incoming edges and hence nodes are all flow acceptors the natural enumeration of nodes is by acceptor id.
Note that to leverage igraph functionality for plotting there is a zero sender of flow.
Other Minenergo:
m278hlair(),
m278hlcha(),
m278hlund(),
m278insdata,
m278inshcm(),
m278soildata,
m325beta(),
m325nhl(),
m325nhldata
library(pipenostics) # Do not hesitate to use `data.table` and `igraph` for larger chunks of network. # Check for declared topology isomorphism: stopifnot( all(!duplicated(m325nxdata$acceptor)) ) # Do all terminal nodes have sensor-measured regime parameters?: terminal_nodes <- subset(m325nxdata, !(acceptor %in% sender)) stopifnot( all(!is.na(subset(terminal_nodes, select = c(temperature, pressure, flow_rate)))) )library(pipenostics) # Do not hesitate to use `data.table` and `igraph` for larger chunks of network. # Check for declared topology isomorphism: stopifnot( all(!duplicated(m325nxdata$acceptor)) ) # Do all terminal nodes have sensor-measured regime parameters?: terminal_nodes <- subset(m325nxdata, !(acceptor %in% sender)) stopifnot( all(!is.na(subset(terminal_nodes, select = c(temperature, pressure, flow_rate)))) )
Trace values of thermal-hydraulic regime (temperature, pressure, flow rate, and other) in the bunched pipeline against the flow direction using norms of heat loss values prescribed by Minenergo Order 325.
Algorithm also suits for partially measurable district heating network with massive data lack conditions, when there are no temperature and pressure sensor readings on the majority of terminal nodes.
m325tracebw( sender = 6, acceptor = 7, temperature = 70, pressure = pipenostics::mpa_kgf(6), flow_rate = 20, d = 100, len = 72.446, year = 1986, insulation = 0, laying = "tunnel", beta = FALSE, exp5k = TRUE, roughness = 0.001, inlet = 0.5, outlet = 1, method = "romeo", opinion = "median", verbose = TRUE, csv = FALSE, file = "m325tracebw.csv" )m325tracebw( sender = 6, acceptor = 7, temperature = 70, pressure = pipenostics::mpa_kgf(6), flow_rate = 20, d = 100, len = 72.446, year = 1986, insulation = 0, laying = "tunnel", beta = FALSE, exp5k = TRUE, roughness = 0.001, inlet = 0.5, outlet = 1, method = "romeo", opinion = "median", verbose = TRUE, csv = FALSE, file = "m325tracebw.csv" )
sender |
identifier of the node which heat carrier flows out.
Type: any type that can be painlessly coerced to character by
|
acceptor |
identifier of the node which heat carrier flows in. According to topology
of test bench considered this identifier should be unique for every row.
Type: any type that can be painlessly coerced to character by
|
temperature |
Sensor-measured temperature of heat carrier (water) sensor-measured on
the terminal acceptor node, [°C].
Use |
pressure |
Sensor-measured
absolute pressure
of heat carrier (water) inside the pipe (i.e. acceptor's incoming edge),
[MPa].
Type: |
flow_rate |
Sensor-measured amount of heat carrier (water) on terminal node that is
transferred by pipe (i.e. acceptor's incoming edge) during a period, [ton/hour].
Type: |
d |
internal diameter of pipe (i.e.diameter of acceptor's incoming edge),
[mm].
Type: |
len |
pipe length (i.e. length of acceptor's incoming edge), [m].
Type: |
year |
year when the pipe (i.e. acceptor's incoming edge) is put in operation
after laying or total overhaul.
Type: |
insulation |
identifier of insulation that covers the exterior of pipe (i.e. acceptor's incoming edge):
Type: |
laying |
type of pipe laying depicting the position of pipe in space. Only five types of pipe laying are considered:
Type: |
beta |
logical indicator: should they consider additional heat loss of fittings
located on this pipe (i.e. acceptor's incoming edge)?
Type: |
exp5k |
logical indicator for regime of pipe (i.e. acceptor's incoming edge): if
|
roughness |
roughness of internal wall of pipe (i.e. acceptor's incoming edge), [m].
Type: |
inlet |
elevation of pipe inlet, [m]. Type: |
outlet |
elevation of pipe outlet, [m]. Type: |
method |
method of determining Darcy friction factor:
Type: |
opinion |
method for aggregating values of regime parameters on each node for the next tracing step:
Type: |
verbose |
logical indicator: should they watch tracing process on console?
Type: |
csv |
logical indicator: should they incrementally dump results to csv-
file while tracing?
Type: |
file |
name of csv-file which they dump results to.
Type: |
They consider the topology of district heating network represented by
m325nxdata:
The network may be partially sensor-equipped too:
In latter case no more than two nodes must be equipped with pressure and temperature sensors whereas for other nodes only flow rate sensors must be installed.
Tracing starts from sensor-equipped nodes and goes backwards, i.e against the flow direction.
Though some input arguments are natively vectorized their individual values
all relate to common part of district heating network, i.e. associated with
common object. It is due to isomorphism between vector representation and
directed graph of this network. For more details of isomorphic topology
description see m325nxdata.
Before tracing starts for the next node, previously calculated values of thermal-hydraulic parameters are aggregated by either averaging or by median. The latter seems more robust for avoiding strong influence of possible outliers which may come from actual heating transfer anomalies, erroneous sensor readings or wrong pipeline specifications.
Aggregation for values of flow rate at the node is always sum.
data.frame containing results (detailed log) of tracing in
narrow format:
nodeTracing job. Identifier of the node which regime parameters is
calculated for. Values in this vector are identical to those in
argument acceptor.
Type: assert_character.
tracingTracing job. Identifiers of nodes from which regime parameters
are traced for the given node. Identifier sensor is used when
values of regime parameters for the node are sensor readings.
Type: assert_character.
backwardTracing job. Identifier of tracing direction. It constantly
equals to TRUE.
Type: assert_logical.
aggregationTracing job. Identifier of aggregation method: span, median, mean, or identity. Type: assert_character.
lossTraced thermal hydraulic regime. Normative specific heat loss power of adjacent pipe, [kcal/m/h]. Type: assert_double.
fluxTraced thermal hydraulic regime. Normative heat flux of adjacent pipe, [W/m^2]. Type: assert_double.
QTraced thermal hydraulic regime. Normative heat loss of adjacent pipe per day, [kcal].
Type: assert_character.
temperatureTraced thermal hydraulic regime. Traced temperature of heat
carrier (water) that is associated with the node, [°C].
Type: assert_double.
pressureTraced thermal hydraulic regime. Traced pressure of heat
carrier (water) that is associated with the node, [MPa].
Type: assert_double.
flow_rateTraced thermal hydraulic regime. Traced flow rate of heat
carrier (water) that is associated with the node, [ton/hour].
Type: assert_double.
jobTracing job. Value of tracing job counter.
Type: assert_count.
Type: assert_data_frame.
Other Regime tracing:
m325tracefw(),
m325traceline(),
tracebw(),
tracefw(),
traceline()
library(pipenostics) ## It is possible to run without specification of argument values: m325tracebw() ## Consider isomorphic representation of District Heating Network graph: DHN <- pipenostics::m325nxdata DHN$d <- 1e3*DHN$d # convert [m] to [mm] ## When tracing large network graphs put screen log to file output <- do.call("m325tracebw", c(as.list(DHN), verbose = TRUE)) ## Distinct options for opinion aggregation lead to distinct traced ## temperature and pressure: ## * When aggregation is by mean: output_mean <- do.call( "m325tracebw", c(as.list(DHN), verbose = FALSE, opinion = "mean") ) ## * When aggregation is by median: output_median <- do.call( "m325tracebw", c(as.list(DHN), verbose = FALSE, opinion = "median") ) ## The differences between aggregations should be: aggregation_differences <- c(delta_t = 0.03732, delta_p = 0.00139, delta_g = 0) print(aggregation_differences) ## Check: stopifnot( round( subset( output_mean, node == 13 & aggregation == "median", c("temperature", "pressure", "flow_rate") ) - subset( output_median, node == 13 & aggregation == "median", c("temperature", "pressure", "flow_rate") ), 5 # difference between aggregation options ) == aggregation_differences ) ## It is possible to process partially measurable District Heating Network: ## * Simulate lack of temperature and pressure sensors: DHN[c(7, 10, 21, 24), c("temperature", "pressure")] <- NA_real_ ## Trace thermal-hydraulic regime output <- do.call("m325tracebw", c(as.list(DHN))) print(output)library(pipenostics) ## It is possible to run without specification of argument values: m325tracebw() ## Consider isomorphic representation of District Heating Network graph: DHN <- pipenostics::m325nxdata DHN$d <- 1e3*DHN$d # convert [m] to [mm] ## When tracing large network graphs put screen log to file output <- do.call("m325tracebw", c(as.list(DHN), verbose = TRUE)) ## Distinct options for opinion aggregation lead to distinct traced ## temperature and pressure: ## * When aggregation is by mean: output_mean <- do.call( "m325tracebw", c(as.list(DHN), verbose = FALSE, opinion = "mean") ) ## * When aggregation is by median: output_median <- do.call( "m325tracebw", c(as.list(DHN), verbose = FALSE, opinion = "median") ) ## The differences between aggregations should be: aggregation_differences <- c(delta_t = 0.03732, delta_p = 0.00139, delta_g = 0) print(aggregation_differences) ## Check: stopifnot( round( subset( output_mean, node == 13 & aggregation == "median", c("temperature", "pressure", "flow_rate") ) - subset( output_median, node == 13 & aggregation == "median", c("temperature", "pressure", "flow_rate") ), 5 # difference between aggregation options ) == aggregation_differences ) ## It is possible to process partially measurable District Heating Network: ## * Simulate lack of temperature and pressure sensors: DHN[c(7, 10, 21, 24), c("temperature", "pressure")] <- NA_real_ ## Trace thermal-hydraulic regime output <- do.call("m325tracebw", c(as.list(DHN))) print(output)
Trace values of thermal-hydraulic regime (temperature, pressure, flow rate, and other) in the bunched pipeline along the flow direction using norms of heat loss values prescribed by Minenergo Order 325.
m325tracefw( sender = c(0, 1), acceptor = c(1, 2), temperature = c(70, NA_real_), pressure = c(pipenostics::mpa_kgf(6), NA_real_), flow_rate = c(20, NA_real_), d = rep_len(100, 2), len = rep_len(72.446, 2), year = rep_len(1986, 2), insulation = rep_len(0, 2), laying = rep_len("tunnel", 2), beta = rep_len(FALSE, 2), exp5k = rep_len(TRUE, 2), roughness = rep_len(0.001, 2), inlet = c(0.5, 1), outlet = c(1, 1), elev_tol = 0.1, method = "romeo", verbose = TRUE, csv = FALSE, file = "m325tracefw.csv", use_cluster = FALSE )m325tracefw( sender = c(0, 1), acceptor = c(1, 2), temperature = c(70, NA_real_), pressure = c(pipenostics::mpa_kgf(6), NA_real_), flow_rate = c(20, NA_real_), d = rep_len(100, 2), len = rep_len(72.446, 2), year = rep_len(1986, 2), insulation = rep_len(0, 2), laying = rep_len("tunnel", 2), beta = rep_len(FALSE, 2), exp5k = rep_len(TRUE, 2), roughness = rep_len(0.001, 2), inlet = c(0.5, 1), outlet = c(1, 1), elev_tol = 0.1, method = "romeo", verbose = TRUE, csv = FALSE, file = "m325tracefw.csv", use_cluster = FALSE )
sender |
identifier of the node which heat carrier flows out.
Type: any type that can be painlessly coerced to character by
|
acceptor |
identifier of the node which heat carrier flows in. According to topology
of test bench considered this identifier should be unique for every row.
Type: any type that can be painlessly coerced to character by
|
temperature |
Sensor-measured temperature of heat carrier (water) sensor-measured on
the root node, [°C].
Use |
pressure |
Sensor-measured
absolute pressure
of heat carrier (water) inside the pipe on the root node, [MPa].
Use |
flow_rate |
Sensor-measured amount of heat carrier (water) on root node that is
transferred by pipe during a period, [ton/hour].
Type: |
d |
internal diameter of pipe (i.e.diameter of acceptor's incoming edge),
[mm].
Type: |
len |
pipe length (i.e. length of acceptor's incoming edge), [m].
Type: |
year |
year when the pipe (i.e. acceptor's incoming edge) is put in operation
after laying or total overhaul.
Type: |
insulation |
identifier of insulation that covers the exterior of pipe (i.e. acceptor's incoming edge):
Type: |
laying |
type of pipe laying depicting the position of pipe in space. Only five types of pipe laying are considered:
Type: |
beta |
logical indicator: should they consider additional heat loss of fittings
located on this pipe (i.e. acceptor's incoming edge)?
Type: |
exp5k |
logical indicator for regime of pipe (i.e. acceptor's incoming edge): if
|
roughness |
roughness of internal wall of pipe (i.e. acceptor's incoming edge), [m].
Type: |
inlet |
elevation of pipe inlet, [m]. Type: |
outlet |
elevation of pipe outlet, [m]. Type: |
elev_tol |
maximum allowed discrepancy between adjacent outlet and inlet elevations
of two subsequent pipes in the traced path, [m].
Type: |
method |
method of determining Darcy friction factor:
Type: |
verbose |
logical indicator: should they watch tracing process on console?
Type: |
csv |
logical indicator: should they incrementally dump results to csv-
file while tracing?
Type: |
file |
name of csv-file which they dump results to.
Type: |
use_cluster |
utilize functionality of parallel processing on multi-core CPU.
Type: |
The calculated (values of) regime may be considered as representation of district heating process in conditions of hypothetically perfect technical state of pipe walls and insulation.
They consider the topology of district heating network represented by
m325nxdata:
Tracing starts from sensor-equipped root node and goes forward, i.e along
the flow direction. Function m325traceline serves under the
hood for tracing identified linear segments from root node to every
terminal node. Hence they only need root node to be equipped with sensors.
Sensors at other nodes are redundant in forward tracing, since the tracing
algorithm by no means consider them for tracing.
Moreover in the forward tracing algorithm they assume the flow of heat carrier is distributed proportionally to the cross-sectional area of the outgoing pipeline. Actually, a lot of reasons may cause significant deviations from this assumption. As a result, the sequence of paired backward/forward tracing may be divergent for regime parameters.
Though some input arguments are natively vectorized their individual values
all relate to common part of district heating network, i.e. associated with
common object. It is due to isomorphism between vector representation and
directed graph of this network. For more details of isomorphic topology
description see m325nxdata.
They are welcome to couple the algorithm with functionality of data.table.
data.frame containing results (detailed log) of tracing in
narrow format:
nodeTracing job. Identifier of the node which regime parameters is
calculated for. Values in this vector are identical to those in
argument acceptor.
Type: assert_character.
tracingTracing job. Identifiers of nodes from which regime parameters
are traced for the given node. Identifier sensor is used when
values of regime parameters for the node are sensor readings.
Type: assert_character.
backwardTracing job. Identifier of tracing direction. It constantly
equals to FALSE.
Type: assert_logical.
aggregationTracing job. Identifier of the aggregation method associated
with traced values. For forward tracing the only option is
identity.
Type: assert_character.
temperatureTraced thermal hydraulic regime. Traced temperature of heat
carrier (water) that is associated with the node, [°C].
Type: assert_double.
pressureTraced thermal hydraulic regime. Traced pressure of heat
carrier (water) that is associated with the node, [MPa].
Type: assert_double.
flow_rateTraced thermal hydraulic regime. Traced flow rate of heat
carrier (water) that is associated with the node, [ton/hour].
Type: assert_double.
jobTracing job. Value of tracing job counter.
For forward tracing value of job counts the number of traced paths from root node.
Type: assert_count.
Type: assert_data_frame.
Other Regime tracing:
m325tracebw(),
m325traceline(),
tracebw(),
tracefw(),
traceline()
library(pipenostics) # Minimum two nodes should be in district heating network graph: m325tracefw(verbose = FALSE) # Consider isomorphic representation of District Heating Network graph: DHN <- pipenostics::m325nxdata # * avoid using numeric identifiers for nodes: DHN$sender <- sprintf("N%02i", DHN$sender) DHN$acceptor <- sprintf("N%02i", DHN$acceptor) # * alter units: DHN$d <- 1e3 * DHN$d # convert [m] to [mm] # Perform backward tracing to get regime on root node: bw_report <- do.call("m325tracebw", c(as.list(DHN), verbose = FALSE)) # Put the traced values to the root node of test bench: root_node_idx <- 12 root_node <- sprintf("N%02i", root_node_idx) regime_param <- c("temperature", "pressure", "flow_rate") DHN[root_node_idx, regime_param] <- subset(bw_report, node == root_node & aggregation == "median", regime_param) rm(root_node, root_node_idx) # Trace the test bench forward for the first time: fw_report <- do.call("m325tracefw", c(as.list(DHN), verbose = FALSE, elev_tol = .5)) # Let's compare traced regime at terminal nodes back to test bench: report <- subset( rbind(bw_report, fw_report), node %in% subset(DHN, !(acceptor %in% sender))$acceptor & aggregation == "identity" ) regime_delta <- colMeans( subset(report, backward, regime_param) - subset(report, !backward, regime_param) ) print(regime_delta) stopifnot(sqrt(regime_delta %*% regime_delta) < 0.5)library(pipenostics) # Minimum two nodes should be in district heating network graph: m325tracefw(verbose = FALSE) # Consider isomorphic representation of District Heating Network graph: DHN <- pipenostics::m325nxdata # * avoid using numeric identifiers for nodes: DHN$sender <- sprintf("N%02i", DHN$sender) DHN$acceptor <- sprintf("N%02i", DHN$acceptor) # * alter units: DHN$d <- 1e3 * DHN$d # convert [m] to [mm] # Perform backward tracing to get regime on root node: bw_report <- do.call("m325tracebw", c(as.list(DHN), verbose = FALSE)) # Put the traced values to the root node of test bench: root_node_idx <- 12 root_node <- sprintf("N%02i", root_node_idx) regime_param <- c("temperature", "pressure", "flow_rate") DHN[root_node_idx, regime_param] <- subset(bw_report, node == root_node & aggregation == "median", regime_param) rm(root_node, root_node_idx) # Trace the test bench forward for the first time: fw_report <- do.call("m325tracefw", c(as.list(DHN), verbose = FALSE, elev_tol = .5)) # Let's compare traced regime at terminal nodes back to test bench: report <- subset( rbind(bw_report, fw_report), node %in% subset(DHN, !(acceptor %in% sender))$acceptor & aggregation == "identity" ) regime_delta <- colMeans( subset(report, backward, regime_param) - subset(report, !backward, regime_param) ) print(regime_delta) stopifnot(sqrt(regime_delta %*% regime_delta) < 0.5)
Trace values of thermal-hydraulic regime (temperature, pressure, flow_rate, and other) along the adjacent linear segments of pipeline using norms of heat loss values prescribed by Minenergo Order 325.
m325traceline( temperature = 130, pressure = mpa_kgf(6), flow_rate = 250, g = 0, d = 700, len = c(600, 530, 300, 350), year = 1986, insulation = 0, laying = "underground", beta = FALSE, exp5k = TRUE, roughness = 0.006, inlet = 0, outlet = 0, elev_tol = 0.1, method = "romeo", forward = TRUE, absg = TRUE )m325traceline( temperature = 130, pressure = mpa_kgf(6), flow_rate = 250, g = 0, d = 700, len = c(600, 530, 300, 350), year = 1986, insulation = 0, laying = "underground", beta = FALSE, exp5k = TRUE, roughness = 0.006, inlet = 0, outlet = 0, elev_tol = 0.1, method = "romeo", forward = TRUE, absg = TRUE )
temperature |
Traced thermal hydraulic regime. Sensor-measured temperature of heat
carrier (water)
inside the pipe sensor-measured at the inlet
(forward tracing) or at the outlet (backward tracing) of path, [°C].
Type: |
pressure |
Traced thermal hydraulic regime. Sensor-measured
absolute
pressure of heat carrier (water) sensor-measured at the inlet
(forward tracing) or at the outlet (backward tracing) of path, [MPa].
Type: |
flow_rate |
Traced thermal hydraulic regime. Amount of heat carrier (water)
sensor-measured at the inlet (forward tracing) or at the outlet (backward
tracing) of path, [ton/hour]. Type: |
g |
amount of heat carrier discharge to network for each pipe segment in the
tracing path enumerated along the direction of flow. If flag |
d |
internal diameters of subsequent pipes in tracing path that are enumerated
along the direction of flow, [mm].
Type: |
len |
length of subsequent pipes in tracing path that are enumerated
along the direction of flow, [m].
Type: |
year |
year when pipe is put in operation after laying or total overhaul for
each pipe in tracing path enumerated along the direction of flow.
Type: |
insulation |
insulation that covers the exterior of pipe:
for each pipe in tracing path enumerated along the direction of flow.
Type: |
laying |
type of pipe laying depicting the position of pipe in space:
for each pipe in tracing path enumerated along the direction of flow.
Type: |
beta |
logical indicator: should they consider additional heat loss of fittings?
Logical value for each pipe in tracing path enumerated along the direction
of flow. Type: |
exp5k |
logical indicator for regime of pipe: is pipe operated more that
|
roughness |
roughness of internal wall for each pipe in tracing path enumerated along
the direction of flow, [m]. Type: |
inlet |
elevation of pipe inlet for each pipe in tracing path enumerated along
the direction of flow, [m]. Type: |
outlet |
elevation of pipe outlet for each pipe in tracing path enumerated along
the direction of flow, [m]. Type: |
elev_tol |
maximum allowed discrepancy between adjacent outlet and inlet elevations of
two subsequent pipes in the traced path, [m].
Type: |
method |
method of determining Darcy friction factor
Type: |
forward |
tracing direction flag: is it a forward direction of tracing?
If |
absg |
Whether argument |
The calculated (values of) regime may be considered as representation of district heating process in conditions of hypothetically perfect technical state of pipe walls and insulation.
They consider only simple tracing paths which do not contain rings and any kind of parallelization. At the same time bidirectional (forward and backward) tracing is possible in accordance with sensor position. They also may consider discharges to network at the inlet of each pipeline segment as an approximation of actual forks of flows. Relevant illustration of adopted assumptions for 4-segment tracing path is depicted on the next figure.
They make additional check for consistency of inlet and outlet
values for subsequent pipe segments. Discrepancy of appropriate elevations
cannot be more than elev_tol.
Since inner diameter of the pipe is used as input, the the thickness of the pipe wall additionally considered in heat flux calculations. Pipe wall thickness is derived from pipe diameter using GOST 30732 specifications.
list containing results (detailed log) of tracing for each pipe
in tracing path enumerated along the direction of flow:
temperatureTraced thermal hydraulic regime. Traced temperature of heat
carrier (water), [°C]. Type: assert_double.
pressureTraced thermal hydraulic regime. Traced pressure of heat
carrier (water) for each pipe in tracing path enumerated along the
direction of flow, [MPa]. Type: assert_double.
flow_rateTraced thermal hydraulic regime. Traced flow rate of heat
carrier (water) for each pipe in tracing path enumerated along the
direction of flow, [ton/hour]. Type: assert_double.
lossTraced thermal hydraulic regime. Normative specific heat
loss power for each pipe in tracing path enumerated along the direction
of flow, [kcal/m/h]. Type: assert_double.
fluxTraced thermal hydraulic regime. Normative heat flux for each pipe
in tracing path enumerated along the direction of flow, [W/m^2].
Type: assert_double.
QTraced thermal hydraulic regime. Normative heat loss for each
pipe in tracing path enumerated along the direction of flow per day,
[kcal]. Type: assert_double.
Type: assert_list.
Other Regime tracing:
m325tracebw(),
m325tracefw(),
tracebw(),
tracefw(),
traceline()
library(pipenostics) # Consider 4-segment tracing path depicted in ?m325regtrace help page. # First, let sensor readings for forward tracing: t_fw <- 130 # [°C] p_fw <- mpa_kgf(6)*all.equal(.588399, mpa_kgf(6)) # [MPa] g_fw <- 250 # [ton/hour] # Let discharges to network for each pipeline segment are somehow determined as discharges <- seq(0, 30, 10) # [ton/hour] # Then the calculated regime (red squares) for forward tracing is regime_fw <- m325traceline(t_fw, p_fw, g_fw, discharges, forward = TRUE) print(regime_fw) # $temperature # [1] 129.1799 128.4269 127.9628 127.3367 # # $pressure # [1] 0.5878607 0.5874226 0.5872143 0.5870330 # # $flow_rate # [1] 250 240 220 190 # # $loss # [1] 348.0000 347.1389 346.3483 345.8610 # # $flux # [1] 181.9600 181.5097 181.0963 180.8415 # # $Q # [1] 5011200 4415607 2493707 2905232 # Next consider values of traced regime as sensor readings for backward tracing: t_bw <- 127.3367 # [°C] p_bw <- .5870330 # [MPa] g_bw <- 190 # [ton/hour] # Then the calculated regime (red squares) for backward tracing is regime_bw <- m325traceline(t_bw, p_bw, g_bw, discharges, forward = FALSE) print(regime_bw) # $temperature # [1] 129.9953 129.1769 128.4254 127.9619 # # $pressure # [1] 0.5883998 0.5878611 0.5874228 0.5872144 # # $flow_rate # [1] 250 250 240 220 # # $loss # [1] 347.1358 346.3467 345.8599 345.2035 # # $flux # [1] 181.5081 181.0955 180.8410 180.4978 # # $Q # [1] 4998755 4405529 2490192 2899710 # Let compare sensor readings with backward tracing results: tracing <- with(regime_bw, { lambda <- function(val, constraint) c(val, constraint, constraint - val, abs(constraint - val)*100/constraint) first <- 1 structure( rbind( lambda(temperature[first], t_fw), lambda(pressure[first], p_fw), lambda(flow_rate[first], g_fw) ), dimnames = list( c("temperature", "pressure", "flow_rate"), c("sensor.value", "traced.value", "abs.discr", "rel.discr") ) ) }) print(tracing) # sensor.value traced.value abs.discr rel.discr # temperature 129.9952943 130.000000 4.705723e-03 0.0036197868 # pressure 0.5883998 0.588399 -8.215938e-07 0.0001396321 # flow_rate 250.0000000 250.000000 0.000000e+00 0.0000000000library(pipenostics) # Consider 4-segment tracing path depicted in ?m325regtrace help page. # First, let sensor readings for forward tracing: t_fw <- 130 # [°C] p_fw <- mpa_kgf(6)*all.equal(.588399, mpa_kgf(6)) # [MPa] g_fw <- 250 # [ton/hour] # Let discharges to network for each pipeline segment are somehow determined as discharges <- seq(0, 30, 10) # [ton/hour] # Then the calculated regime (red squares) for forward tracing is regime_fw <- m325traceline(t_fw, p_fw, g_fw, discharges, forward = TRUE) print(regime_fw) # $temperature # [1] 129.1799 128.4269 127.9628 127.3367 # # $pressure # [1] 0.5878607 0.5874226 0.5872143 0.5870330 # # $flow_rate # [1] 250 240 220 190 # # $loss # [1] 348.0000 347.1389 346.3483 345.8610 # # $flux # [1] 181.9600 181.5097 181.0963 180.8415 # # $Q # [1] 5011200 4415607 2493707 2905232 # Next consider values of traced regime as sensor readings for backward tracing: t_bw <- 127.3367 # [°C] p_bw <- .5870330 # [MPa] g_bw <- 190 # [ton/hour] # Then the calculated regime (red squares) for backward tracing is regime_bw <- m325traceline(t_bw, p_bw, g_bw, discharges, forward = FALSE) print(regime_bw) # $temperature # [1] 129.9953 129.1769 128.4254 127.9619 # # $pressure # [1] 0.5883998 0.5878611 0.5874228 0.5872144 # # $flow_rate # [1] 250 250 240 220 # # $loss # [1] 347.1358 346.3467 345.8599 345.2035 # # $flux # [1] 181.5081 181.0955 180.8410 180.4978 # # $Q # [1] 4998755 4405529 2490192 2899710 # Let compare sensor readings with backward tracing results: tracing <- with(regime_bw, { lambda <- function(val, constraint) c(val, constraint, constraint - val, abs(constraint - val)*100/constraint) first <- 1 structure( rbind( lambda(temperature[first], t_fw), lambda(pressure[first], p_fw), lambda(flow_rate[first], g_fw) ), dimnames = list( c("temperature", "pressure", "flow_rate"), c("sensor.value", "traced.value", "abs.discr", "rel.discr") ) ) }) print(tracing) # sensor.value traced.value abs.discr rel.discr # temperature 129.9952943 130.000000 4.705723e-03 0.0036197868 # pressure 0.5883998 0.588399 -8.215938e-07 0.0001396321 # flow_rate 250.0000000 250.000000 0.000000e+00 0.0000000000
Calculate probability of failure (POF) of the corroded pipe taking into account its actual level of defectiveness and exploiting Monte-Carlo simulation within Principle of maximum entropy.
Consistent estimate of POF for pipeline systems plays a critical role in optimizing their operation. To prevent pipeline failures due to actively growing defects it is necessary to be able to assess the pipeline system failure operation probability during a certain period, taking into account its actual level of defectiveness. The pipeline limit state comes when the burst pressure, considered as a random variable, reaches an unacceptable level, or when the defect depth, also a random variable, exceeds the predetermined limit value.
That is why in the method they consider two possible failures for a single pipeline cross section with the on-surface and longitudinally oriented defect of metal-loss type:
a decrease of value of failure pressure down to the operating pressure.
increase of corrosion depth (defect) up to the specified ultimate permissible fraction of pipe wall thickness.
Since up to now no methods existed which would give absolutely correct POF assessments they suggest simple fiddling with random values of affecting factors without deeping into intrinsic mechanisms of corrossion. For this purpose they choose classical Monte-Carlo simulation within the Principle of maximum entropy. The latter allows to avoid doubtful and excessive preferences and detalization when choosing probability distribution models for failure factors and for inline inspection measurements.
mepof( depth = seq(0, 10, length.out = 100), l = seq(40, 50, length.out = 100), d = rep.int(762, 100), wth = rep.int(10, 100), strength = rep.int(358.5274, 100), pressure = rep.int(0.588, 100), temperature = rep.int(150, 100), rar = function(n) stats::runif(n, 0.01, 0.3)/365, ral = function(n) stats::runif(n, 0.01, 0.3)/365, days = 0, k = 0.8, method = "b31g", n = 1e+06 )mepof( depth = seq(0, 10, length.out = 100), l = seq(40, 50, length.out = 100), d = rep.int(762, 100), wth = rep.int(10, 100), strength = rep.int(358.5274, 100), pressure = rep.int(0.588, 100), temperature = rep.int(150, 100), rar = function(n) stats::runif(n, 0.01, 0.3)/365, ral = function(n) stats::runif(n, 0.01, 0.3)/365, days = 0, k = 0.8, method = "b31g", n = 1e+06 )
depth |
maximum depth of the corroded area measured during inline inspection,
[mm]. Type: |
l |
maximum longitudinal length of corroded area measured during
inline inspection, [mm]. Type: |
d |
nominal outside diameter of pipe, [mm]. Type: |
wth |
nominal wall thickness of pipe, [mm]. Type: |
strength |
one of the next characteristics of steel strength, [MPa]:
Type: |
pressure |
absolute pressure
of substance (i.e. heat carrier) inside the pipe measured near defect
position, [MPa]. In most cases this is a nominal operating pressure.
Type: |
temperature |
temperature of substance (i.e. heat carrier) inside the pipe measured near
defect position, [°C]. In case of district heating network this is
usually a calculated value according to actual or normative thermal-hydraulic
regime. Type: |
rar |
random number generator for simulating of distribution of radial corrosion
rate in pipe wall, [mm/day]. The only
argument |
ral |
random number generator for simulating of distribution of longitudinal corrosion
rate in pipe wall, [mm/day]. The only
argument |
days |
number of days that have passed after or preceded the inline inspection, [].
Negative values are for retrospective assumptions whereas positives are for
failure prognosis. Type: |
k |
alarm threshold for leakage failure. It usually |
method |
method for calculating failure pressure:
Type: |
n |
number of observations to generate for
Monte-Carlo simulations,
Type: |
Since for all influence factors they can more or less assume range limits,
the uniform distribution gets the maximum entropy in this context
(see JCGM 101:2008).
That is why parameters of corrosion defects measured during the
inline inspection as well as regime parameters and engineering
characteristics of pipe segment - all they are simulated by
runif.
runif-limits for depth of corrosion defect are associated
with precision of commonly applied measurement instruments. For traditionally
exploited ultrasonic control those limits are well-known and can reach up to
10 % of pipe wall thickness. Whereas uncertainty of defect longitudinal
length may be more than enough constrained with 5 %.
Recommendations for choosing stochastic characteristics of pipe
engineering factors (i.e. crossection diameter, wall thickness and material
strength) are taken from aggregated review of Timashev et al. but
gently transformed for compatibility with
Principle of maximum entropy,
i.e. runif.
Uncertainties of regime parameters in stohastic models are set minimized by regarding only precision of metering devices which commonly applied in district heating networks. For temperature it is about 2 °C.
Since the rate of corrosion processes in the pipe wall is a consequence of physical and chemical processes occurring at the atomic scale, it depends on a large number of environmental factors differently and ambiguously. That is why various deterministic and stochastic models can be potentially involved in POF assessment. For that purpose radial and longitudinal corrosion rate can be independently formulated as random value generation functions. They only admit that change in depth and length of corrosion defects in time is close to linear for the generated value of corrosion rate.
Probability of pipe failure for each corroded area measured during
inline inspection. Type: assert_double.
If NAs returned use another method
for calculating failure pressure.
S. Timashev and A. Bushinskaya, Diagnostics and Reliability of Pipeline Systems, Topics in Safety, Risk, Reliability and Quality 30, DOI 10.1007/978-3-319-25307-7.
BIPM. Guides in Metrology (GUM). JCGM 101:2008. Evaluation of measurement data – Supplement 1 to the Guide to the expression of uncertainty in measurement – Propagation of distributions using a Monte Carlo method.
library(pipenostics) # Let's consider a pipe in district heating network with diameter <- 762 # [mm] wall_thickness <- 10 # [mm] UTS <- 434.3697 # [MPa] # which transfers heat-carrier (water) at operating_pressure <- 0.588399 # [MPa]. temperature <- 95 # [°C] # During inline inspection four corroded areas (defects) are detected with: depth <- c(2.45, 7.86, 7.93, 8.15) # [mm] # whereas the length of all defects is not greater 200 mm: length <- rep(200, 4) # [mm] # Corrosion rates in radial and in longitudinal directions are not well-known and # may vary in range .01 - .30 mm/year: rar = function(n) stats::runif(n, .01, .30) / 365 ral = function(n) stats::runif(n, .01, .30) / 365 # Then POFs related to each corroded area are near: pof <- mepof(depth, length, rep(diameter, 4), rep(wall_thickness, 4), rep(UTS, 4), rep(operating_pressure, 4), rep(temperature, 4), rar, ral, method = "dnv") print(pof) # 0.000000 0.252510 0.368275 0.771595 # So, the POF of pipe is near print(max(pof)) # 0.771595 # The value of POF changes in time. So, in a year after inline inspection of # the pipe we can get something near pof <- mepof(depth, length, rep(diameter, 4), rep(wall_thickness, 4), rep(UTS, 4), rep(operating_pressure, 4), rep(temperature, 4), rar, ral, method = "dnv", days = 365) print(pof) # 0.000000 0.525539 0.648359 0.929099 # for entire pipe we get something near: print(max(pof)) # 0.929099 # Two years ago before inline inspection the pipe state was rather good: pof <- mepof(depth, length, rep(diameter, 4), rep(wall_thickness, 4), rep(UTS, 4), rep(operating_pressure, 4), rep(temperature, 4), rar, ral, method = "dnv", days = -2 * 365) print(pof) # 0.000000 0.040780 0.072923 0.271751 # for entire pipe we get something near: print(max(pof)) # 0.271751library(pipenostics) # Let's consider a pipe in district heating network with diameter <- 762 # [mm] wall_thickness <- 10 # [mm] UTS <- 434.3697 # [MPa] # which transfers heat-carrier (water) at operating_pressure <- 0.588399 # [MPa]. temperature <- 95 # [°C] # During inline inspection four corroded areas (defects) are detected with: depth <- c(2.45, 7.86, 7.93, 8.15) # [mm] # whereas the length of all defects is not greater 200 mm: length <- rep(200, 4) # [mm] # Corrosion rates in radial and in longitudinal directions are not well-known and # may vary in range .01 - .30 mm/year: rar = function(n) stats::runif(n, .01, .30) / 365 ral = function(n) stats::runif(n, .01, .30) / 365 # Then POFs related to each corroded area are near: pof <- mepof(depth, length, rep(diameter, 4), rep(wall_thickness, 4), rep(UTS, 4), rep(operating_pressure, 4), rep(temperature, 4), rar, ral, method = "dnv") print(pof) # 0.000000 0.252510 0.368275 0.771595 # So, the POF of pipe is near print(max(pof)) # 0.771595 # The value of POF changes in time. So, in a year after inline inspection of # the pipe we can get something near pof <- mepof(depth, length, rep(diameter, 4), rep(wall_thickness, 4), rep(UTS, 4), rep(operating_pressure, 4), rep(temperature, 4), rar, ral, method = "dnv", days = 365) print(pof) # 0.000000 0.525539 0.648359 0.929099 # for entire pipe we get something near: print(max(pof)) # 0.929099 # Two years ago before inline inspection the pipe state was rather good: pof <- mepof(depth, length, rep(diameter, 4), rep(wall_thickness, 4), rep(UTS, 4), rep(operating_pressure, 4), rep(temperature, 4), rar, ral, method = "dnv", days = -2 * 365) print(pof) # 0.000000 0.040780 0.072923 0.271751 # for entire pipe we get something near: print(max(pof)) # 0.271751
Get a list of weather stations located primarily in the central and northern parts of Eurasia. For each weather station, the following information is provided: an integer station ID, geographic coordinates, altitude, and the mean annual ground temperature averaged over depth.
meteos()meteos()
list of weather stations (meteos) with the next fields:
station_idWeather station unique identifier. Type: assert_integer.
nameHuman-readable name of weather station. Type: assert_character.
latGeographical position of wether station. Latitude, [DD]. Type: assert_double.
lonGeographical position of wether station. Longitude, [DD]. Type: assert_double.
altAltitude - position of weather station above sea level, [m]. Type: assert_double.
avgMean annual ground temperature averaged over depth, [°C]. Type: assert_double.
Type: assert_data_frame.
Climate Change Investigation Laboratory. Description of the array of daily data on soil temperature at depths up to 320 centimeters by meteorological stations of the Russian Federation.
mgtdhid to get hourly ground temperature values at different
depths measured at the listed weather stations.
Other utils:
b36mass(),
b36pipedata,
geoarea(),
mgtdhid(),
wth_d()
library(pipenostics) head(meteos())library(pipenostics) head(meteos())
Get the undisturbed (median) value of ground temperature at different depths at a specified time leveraging Modified Ground Temperature Double Harmonic Model (MGTDH-model).
mgtdhid(id, tau = 1440L, depth = 2.4) mgtdhidt(tau, id = 28434L, depth = 2.4) mgtdhgeo(lat, lon, tau = 1440L, depth = 2.4, use_cluster = FALSE) mgtdhgeot(tau, lat = 57, lon = 57, depth = 2.4)mgtdhid(id, tau = 1440L, depth = 2.4) mgtdhidt(tau, id = 28434L, depth = 2.4) mgtdhgeo(lat, lon, tau = 1440L, depth = 2.4, use_cluster = FALSE) mgtdhgeot(tau, lat = 57, lon = 57, depth = 2.4)
id |
weather station unique identifier. Only identifiers from |
tau |
time point for which it is necessary to obtain the value of the soil
temperature; it can be specified as an integer, representing the
number of hours that have passed since the beginning of the year, or
as a value of |
depth |
depth at which the ground temperature is calculated, [m]. Type: |
lat |
latitude of the geographical location where the value of soil temperature needs to be determined, [DD].
Type: |
lon |
longitude of the geographical location where the value of soil temperature needs to be determined, [DD].
Type: |
use_cluster |
utilize functionality of parallel processing on multi-core CPU.
Type: |
The MGTDH-model is a modified solution of the thermal conductivity equation for soil and can be expressed by the formula
where
undisturbed (median) ground temperature [°C] at specified depth [m], and time [hour].
time point (tau) calculated in hours since the beginning of the year, [hour].
depth (depth) at which the ground temperature should be calculated, [m].
shift constant, [].
temperature diffusivity factors, [].
rate of rotation of the Earth, expressed with an accuracy equal to the inverse of an hour, [1/hour].
soil diffusivity, [mm^2/s].
constant that represents the number of seconds in one day, [s/day].
harmonic temperature amplitudes, [°C].
phase shifts, depending on the geographical location, [].
Soil diffusivity, , harmonic temperature amplitudes, , ,
and phase shifts , are geographically dependant parameters which values
were established for each weather station listed in meteos-dataset.
For the convenience of using the MGTDH-model, several interface
functions have been provided. Each function generates a vector of type
assert_double as an output.
The mgtdhid and mgtdhidt functions are used to obtain
ground temperature data from specific meteorological stations.
The functions mgtdhgeo and mgtdhgeot provide ground temperatures
at any geographical location, but note that their usage is primarily limited
to the Northern Asian part of Eurasia, as most meteorological stations
and parameters for the MGTDH-model are established there. Ground temperature
at the specified location is obtained by linear interpolation using barycentric
coordinates formed in the system of the three nearest meteorological stations.
Undisturbed (median) ground temperature value calculated with
the MGTDH-model, specifically for the location of the
user-specified meteorological station, at specified depth, and time, [°C].
Type: assert_double.
Lu Xing & Jeffrey D. Spitler (2017) Prediction of undisturbed ground temperature using analytical and numerical modeling. Part I: Model development and experimental validation. Science and Technology for the Built Environment, 23:5, 787-808, doi:10.1080/23744731.2016.1258371.
geodist and geoarea for calculating geographical metrics.
Other utils:
b36mass(),
b36pipedata,
geoarea(),
meteos(),
wth_d()
# Let consider the next geographical positions: lat <- c(s28434 = 56.65, s28418 = 56.47, s23711 = 62.70, ControlPoint = 57) lon <- c(s28434 = 57.78, s28418 = 53.73, s23711 = 56.20, ControlPoint = 57) # * ground temperatures at first three locations on 02 March 2023 at depth 3 m: mgtdhgeo(head(lat, 3), head(lon, 3), tau = as.POSIXct("2023-03-02"), depth = 3) # * it is the same as obtaining ground temperatures from weather stations: mgtdhid(id = c(28434L, 28418L, 23711L), tau = as.POSIXct("2023-03-02"), depth = 3) # * undisturbed ground temperature plot at Control Point: days <- as.POSIXct("2023-01-01") + 3600*24*(seq.int(1, 365) - 1) plot( days, mgtdhgeot(days, lat[["ControlPoint"]], lon[["ControlPoint"]]), type = "l", ylab = "Temperature, °C" )# Let consider the next geographical positions: lat <- c(s28434 = 56.65, s28418 = 56.47, s23711 = 62.70, ControlPoint = 57) lon <- c(s28434 = 57.78, s28418 = 53.73, s23711 = 56.20, ControlPoint = 57) # * ground temperatures at first three locations on 02 March 2023 at depth 3 m: mgtdhgeo(head(lat, 3), head(lon, 3), tau = as.POSIXct("2023-03-02"), depth = 3) # * it is the same as obtaining ground temperatures from weather stations: mgtdhid(id = c(28434L, 28418L, 23711L), tau = as.POSIXct("2023-03-02"), depth = 3) # * undisturbed ground temperature plot at Control Point: days <- as.POSIXct("2023-01-01") + 3600*24*(seq.int(1, 365) - 1) plot( days, mgtdhgeot(days, lat[["ControlPoint"]], lon[["ControlPoint"]]), type = "l", ylab = "Temperature, °C" )
Convert length measured in inches to millimeters (mm)
mm_inch(x)mm_inch(x)
x |
length measured in inches, [inch].
Type: |
length in millimeters, [mm].
Type: assert_double.
inch_mm for converting mm to inches
Other units:
c_k(),
f_k(),
inch_mm(),
k_c(),
kgf_mpa(),
loss_flux(),
mpa_kgf(),
mpa_psi(),
psi_mpa()
library(pipenostics) mm_inch(c(0.03937008, 1)) # [1] 1.0 25.4 # [mm]library(pipenostics) mm_inch(c(0.03937008, 1)) # [1] 1.0 25.4 # [mm]
Convert pressure (stress) measured in kilogram-force per square cm ()
to megapascals (MPa)
mpa_kgf(x)mpa_kgf(x)
x |
pressure (stress) measured in kilogram-force per square cm,
[kgf/cm^2]. Type: |
pressure (stress) in megapascals, [MPa].
Type: assert_double.
kgf_mpa for converting megapascals to kilogram-force per square cm
Other units:
c_k(),
f_k(),
inch_mm(),
k_c(),
kgf_mpa(),
loss_flux(),
mm_inch(),
mpa_psi(),
psi_mpa()
library(pipenostics) mpa_kgf(c(10.1971619998, 1)) # [1] 1.0000000 0.0980665 # [MPa]library(pipenostics) mpa_kgf(c(10.1971619998, 1)) # [1] 1.0000000 0.0980665 # [MPa]
Convert pressure (stress) measured in pounds per square inch (PSI) to megapascals (MPa)
mpa_psi(x)mpa_psi(x)
x |
pressure (stress) measured in pounds per square inch (PSI).
Type: |
pressure (stress) in megapascals (MPa).
Type: assert_double.
psi_mpa for converting megapascals to pounds per square inch
Other units:
c_k(),
f_k(),
inch_mm(),
k_c(),
kgf_mpa(),
loss_flux(),
mm_inch(),
mpa_kgf(),
psi_mpa()
library(pipenostics) mpa_psi(c(145.03773800721814, 1)) # [1] 1.000000000 0.006894757 # [MPa]library(pipenostics) mpa_psi(c(145.03773800721814, 1)) # [1] 1.000000000 0.006894757 # [MPa]
Calculate failure pressure of the corroded pipe according to PCORRC model.
PCORRC methodology was developed on the basis of studying the mechanism of destruction of pipes, material of which has improved or high fracture toughness, and on the high-precision modeling of the finite element pipe models performed at the Battelle Institute. According to field test results of a large number of actual pipe segments, the destruction mechanism for defective pipeline segment depends on the pipe material fracture toughness. These tests also showed that only pipes made out of steel with improved or high fracture toughness fail a result of plastic fracture. In determining the Folias factor the effect of increased stress concentration and steel hardening in the plastic deformation zone at the start of the defect failure process was taken into account.
This code should be applied only to
a single cross section of the pipeline containing a longitudinally oriented, flat bottom surface defect of corrosion/erosion type;
pipelines, which operate at temperatures exceeding the temperature of pipe material ductile–brittle transition, and for pipematerial with the impact energy of Charpy 61 [J] and above.
pcorrcpf(d, wth, uts, depth, l)pcorrcpf(d, wth, uts, depth, l)
d |
nominal outside diameter of pipe, [mm].
Type: |
wth |
nominal wall thickness of pipe, [mm].
Type: |
uts |
ultimate tensile strength (UTS) or
specified minimum tensile strength (SMTS) as a
characteristic of steel strength, [ |
depth |
measured maximum depth of the corroded area, [mm].
Type: |
l |
measured maximum longitudinal length of corroded area, [mm].
Type: |
Estimated failure pressure of the corroded pipe, [].
Type: assert_double.
S. Timashev and A. Bushinskaya, Diagnostics and Reliability of Pipeline Systems, Topics in Safety, Risk, Reliability and Quality 30, DOI 10.1007/978-3-319-25307-7
A.C.Reddy, Safety Failure Criteria of Fluorocarbon Plastic Pipes for Dry Chlorine Transport using Finite Element Analysis Materials today: proceedings, Vol. 4(8), 2017, pp. 7498-7506. DOI 10.1016/j.matpr.2017.07.081
Other fail pressure functions: b31gpf, b31gmodpf,
dnvpf, shell92pf
library(pipenostics) d <- c(812.8, 219.0) # [mm] wth <- c( 19.1, 14.5) # [mm] uts <- c(530.9, 455.1) # [N/mm^2] l <- c(203.2, 200.0) # [mm] depth <- c( 13.4, 9.0) # [mm] pcorrcpf(d, wth, uts, depth, l) # [1] 16.35449 33.01288library(pipenostics) d <- c(812.8, 219.0) # [mm] wth <- c( 19.1, 14.5) # [mm] uts <- c(530.9, 455.1) # [N/mm^2] l <- c(203.2, 200.0) # [mm] depth <- c( 13.4, 9.0) # [mm] pcorrcpf(d, wth, uts, depth, l) # [1] 16.35449 33.01288
Convert pressure (stress) measured in megapascals (MPa) to pounds per square inch (PSI)
psi_mpa(x)psi_mpa(x)
x |
pressure (stress) measured in megapascals. [MPa].
Type: |
pressure (stress) in pounds per square inch,
[PSI]. Type: assert_double.
mpa_psi for converting pounds per square inch to megapascals
Other units:
c_k(),
f_k(),
inch_mm(),
k_c(),
kgf_mpa(),
loss_flux(),
mm_inch(),
mpa_kgf(),
mpa_psi()
library(pipenostics) psi_mpa(c(6.89475728e-3, 1)) # [1] 1.0000 145.0377 # [PSI]library(pipenostics) psi_mpa(c(6.89475728e-3, 1)) # [1] 1.0000 145.0377 # [PSI]
Estimate Reynolds number for fluid flow in a cylindrical pipe.
re_u(d, mu, u, rho) re_v(d, mu, v, rho) re_m(d, mu, m)re_u(d, mu, u, rho) re_v(d, mu, v, rho) re_m(d, mu, m)
d |
internal diameter of pipe, [m]. Type: |
mu |
dynamic viscosity of fluid in pipe, [kg/m/s]. Type: |
u |
mean velocity of fluid in pipe, [m/s]. Type: |
rho |
mass density of fluid in pipe, [kg/m^3]. Type: |
v |
volumetric flow rate of fluid in pipe, [m^3/s]. Type: |
m |
mass flow rate of fluid in pipe, [kg/s]. Type: |
The calculation of Reynolds number is bounded by physically reasonable limits of fluid properties found in domain specificity of the package.
Reynolds number - a dimensionless quantity that reveals the ratio
between inertial and viscous forces in the fluid, []. Type: assert_double.
Other Fluid properties:
fric_buzelli(),
fric_romeo(),
fric_vatankhan()
library(pipenostics) # Reynolds numbers for typical district heating water flows at temperature # near 25 C in a set of pipes with different sizes: range(re_u(seq(.25, 1, 0.05), .89, 1, 1000)) # [1] 280.8989 1123.5955library(pipenostics) # Reynolds numbers for typical district heating water flows at temperature # near 25 C in a set of pipes with different sizes: range(re_u(seq(.25, 1, 0.05), .89, 1, 1000)) # [1] 280.8989 1123.5955
Calculate failure pressure of the corroded pipe according to Shell92 code.
This code should be applied only to
single cross section of the pipeline containing a longitudinally oriented, flat bottom surface defect of corrosion/erosion type;
defects which depth is less than 85 % of pipe wall thickness.
The estimation is valid for single isolated metal loss defects of the corrosion/erosion type and when only internal pressure loading is considered.
As in the case of dnvpf, the defect is approximated by a
rectangular form.
shell92pf(d, wth, uts, depth, l)shell92pf(d, wth, uts, depth, l)
d |
nominal outside diameter of pipe, [mm].
Type: |
wth |
nominal wall thickness of pipe, [mm].
Type: |
uts |
ultimate tensile strength (UTS) or
specified minimum tensile strength (SMTS) as a
characteristic of steel strength, [MPa].
Type: |
depth |
measured maximum depth of the corroded area, [mm].
Type: |
l |
measured maximum longitudinal length of corroded area, [mm].
Type: |
Numeric NAs may appear in case prescribed conditions of
use are offended.
Estimated failure pressure of the corroded pipe, [MPa].
Type: assert_double.
Timashev and A. Bushinskaya, Diagnostics and Reliability of Pipeline Systems, Topics in Safety, Risk, Reliability and Quality 30, DOI 10.1007/978-3-319-25307-7
Other fail pressure functions: b31gpf, b31gmodpf,
dnvpf, pcorrcpf
library(pipenostics) d = c(812.8, 219.0) # [mm] wth = c( 19.1, 14.5) # [mm] uts = c(530.9, 455.1) # [N/mm^2] l = c(203.2, 200.0) # [mm] depth = c( 13.4, 9.0) # [mm] shell92pf(d, wth, uts, depth, l) # [1] 11.09262 25.27286library(pipenostics) d = c(812.8, 219.0) # [mm] wth = c( 19.1, 14.5) # [mm] uts = c(530.9, 455.1) # [N/mm^2] l = c(203.2, 200.0) # [mm] depth = c( 13.4, 9.0) # [mm] shell92pf(d, wth, uts, depth, l) # [1] 11.09262 25.27286
Temperature is highly influence on pipe material properties and especially on its strength. Since in API SPECIFICATION 5L values of SMYS or UTS are postulated at room conditions, in case of higher temperature magnitudes they should be corrected. For that purpose DNV-RP-F101 offers linear de-rating for SMYS or SMYS according to figure 2-3.
strderate(x, temperature = 24.3)strderate(x, temperature = 24.3)
x |
specified minimum yield of stress (SMYS), or ultimate tensile
strength (UTS), or specified minimum tensile strength (SMTS)
as a characteristic of steel strength at room temperature,
[MPa]. Type: |
temperature |
temperature of pipe wall, [°C]. Type: |
de-rated value of x, i.e. of appropriate pipe material property,
[MPa] .
Type: assert_double.
Other DNV-RP-F101 functions:
dnvpf()
library(pipenostics) pipe_specs <- api5l3tdata[api5l3tdata$origin == 10,] with(pipe_specs, { print(strderate(mpa_psi(smys), 53)) print( strderate(mpa_psi(uts),seq(0, 250, length.out = length(smys))) ) }) # [1] 170.5689 205.0427 239.5165 287.7798 315.3588 356.7274 384.3064 411.8854 446.3592 480.8330 # [11] 549.7806 # [1] 310.2641 330.9483 413.6854 398.6854 404.3697 415.0540 439.5278 457.1068 460.8963 485.3701 # [11] 530.5282library(pipenostics) pipe_specs <- api5l3tdata[api5l3tdata$origin == 10,] with(pipe_specs, { print(strderate(mpa_psi(smys), 53)) print( strderate(mpa_psi(uts),seq(0, 250, length.out = length(smys))) ) }) # [1] 170.5689 205.0427 239.5165 287.7798 315.3588 356.7274 384.3064 411.8854 446.3592 480.8330 # [11] 549.7806 # [1] 310.2641 330.9483 413.6854 398.6854 404.3697 415.0540 439.5278 457.1068 460.8963 485.3701 # [11] 530.5282
Trace values of thermal-hydraulic regime (temperature, pressure, flow rate, and other) in the bunched pipeline against the flow direction using user-provided values of specific heat loss power.
Algorithm also suits for partially measurable district heating network with massive data lack conditions, when there are no temperature and pressure sensor readings on the majority of terminal nodes.
tracebw( sender = 6, acceptor = 7, temperature = 70, pressure = pipenostics::mpa_kgf(6), flow_rate = 20, d = 100, len = 72.446, loss = 78.4, roughness = 0.001, inlet = 0.5, outlet = 1, method = "romeo", opinion = "median", verbose = TRUE, csv = FALSE, file = "tracebw.csv" )tracebw( sender = 6, acceptor = 7, temperature = 70, pressure = pipenostics::mpa_kgf(6), flow_rate = 20, d = 100, len = 72.446, loss = 78.4, roughness = 0.001, inlet = 0.5, outlet = 1, method = "romeo", opinion = "median", verbose = TRUE, csv = FALSE, file = "tracebw.csv" )
sender |
identifier of the node which heat carrier flows out.
Type: any type that can be painlessly coerced to character by
|
acceptor |
identifier of the node which heat carrier flows in. According to topology
of test bench considered this identifier should be unique for every row.
Type: any type that can be painlessly coerced to character by
|
temperature |
Sensor-measured temperature of heat carrier (water) sensor-measured on
the terminal acceptor node, [°C].
Use |
pressure |
Sensor-measured
absolute pressure
of heat carrier (water) inside the pipe (i.e. acceptor's incoming edge),
[MPa].
Type: |
flow_rate |
Sensor-measured amount of heat carrier (water) on terminal node that is
transferred by pipe (i.e. acceptor's incoming edge) during a period, [ton/hour].
Type: |
d |
internal diameter of pipe (i.e.diameter of acceptor's incoming edge),
[mm].
Type: |
len |
pipe length (i.e. length of acceptor's incoming edge), [m].
Type: |
loss |
user-provided value of specific heat loss power for each pipe,
[kcal/m/h]. Values of the argument can be obtained experimentally,
or taken from regulatory documents.
Type: |
roughness |
roughness of internal wall of pipe (i.e. acceptor's incoming edge), [m].
Type: |
inlet |
elevation of pipe inlet, [m]. Type: |
outlet |
elevation of pipe outlet, [m]. Type: |
method |
method of determining Darcy friction factor:
Type: |
opinion |
method for aggregating values of regime parameters on each node for the next tracing step:
Type: |
verbose |
logical indicator: should they watch tracing process on console?
Type: |
csv |
logical indicator: should they incrementally dump results to csv-
file while tracing?
Type: |
file |
name of csv-file which they dump results to.
Type: |
They consider the topology of district heating network represented by
m325nxdata:
The network may be partially sensor-equipped too:
In latter case no more than two nodes must be equipped with pressure and temperature sensors whereas for other nodes only flow rate sensors must be installed.
Tracing starts from sensor-equipped nodes and goes backwards, i.e against the flow direction.
Though some input arguments are natively vectorized their individual values
all relate to common part of district heating network, i.e. associated with
common object. It is due to isomorphism between vector representation and
directed graph of this network. For more details of isomorphic topology
description see m325nxdata.
Before tracing starts for the next node, previously calculated values of thermal-hydraulic parameters are aggregated by either averaging or by median. The latter seems more robust for avoiding strong influence of possible outliers which may come from actual heating transfer anomalies, erroneous sensor readings or wrong pipeline specifications.
Aggregation for values of flow rate at the node is always sum.
data.frame containing results (detailed log) of tracing in
narrow format:
nodeTracing job. Identifier of the node which regime parameters is
calculated for. Values in this vector are identical to those in
argument acceptor.
Type: assert_character.
tracingTracing job. Identifiers of nodes from which regime parameters
are traced for the given node. Identifier sensor is used when
values of regime parameters for the node are sensor readings.
Type: assert_character.
backwardTracing job. Identifier of tracing direction. It constantly
equals to TRUE.
Type: assert_logical.
aggregationTracing job. Identifier of aggregation method: span, median, mean, or identity. Type: assert_character.
lossTraced thermal hydraulic regime. Normative specific heat loss power of adjacent pipe, [kcal/m/h]. Type: assert_double.
fluxTraced thermal hydraulic regime. Normative heat flux of adjacent pipe, [W/m^2]. Type: assert_double.
QTraced thermal hydraulic regime. Normative heat loss of adjacent pipe per day, [kcal].
Type: assert_character.
temperatureTraced thermal hydraulic regime. Traced temperature of heat
carrier (water) that is associated with the node, [°C].
Type: assert_double.
pressureTraced thermal hydraulic regime. Traced pressure of heat
carrier (water) that is associated with the node, [MPa].
Type: assert_double.
flow_rateTraced thermal hydraulic regime. Traced flow rate of heat
carrier (water) that is associated with the node, [ton/hour].
Type: assert_double.
jobTracing job. Value of tracing job counter.
Type: assert_count.
Type: assert_data_frame.
Other Regime tracing:
m325tracebw(),
m325tracefw(),
m325traceline(),
tracefw(),
traceline()
library(pipenostics) # It is possible to run without specification of argument values: m325tracebw() # Consider isomorphic representation of District Heating Network graph: DHN <- pipenostics::m325nxdata # * Adapt units: DHN$d <- 1e3*DHN$d # convert [m] to [mm] # * Adapt node identifiers for ordering representation simplification: DHN[["sender"]] <- sprintf("N%02i", DHN[["sender"]]) DHN[["acceptor"]] <- sprintf("N%02i", DHN[["acceptor"]]) # * Provided actual values of specific heat loss power (say, field measurements) for each # pipe in DHN, [kcal/m/h]: actual_loss <- c( # acceptor: 96.236, # 1 96.288, # 2 70.584, # 3 116.045, # 4 70.734, # 5 96.211, # 6 78.400, # 7 116.016, # 8 28.115, # 9 24.918, # 10 116.679, # 11 0.000, # 12, may be unmeasured! 153.134, # 13 96.733, # 14 96.600, # 15 116.667, # 16 24.960, # 17 115.923, # 18 28.166, # 19 96.123, # 20 77.824, # 21 115.946, # 22 70.690, # 23 96.184, # 24 96.236, # 25 70.540 # 26 ) # * Remove inappropriate attributes of the graph: DHN.1 <- DHN[, setdiff(colnames(DHN), c("year", "insulation", "laying", "beta", "exp5k"))] # * Trace thermal-hydraulic regime for DHN: tracebw_report <- do.call("tracebw", c(as.list(DHN.1), list(loss = actual_loss))) # * If the actual values of specific heat loss power presented above are close # to those in Minenergo-325, then the results of regime tracing match the # normative procedure: m325_report <- do.call("m325tracebw", DHN) stopifnot( all.equal(tracebw_report$temperature, m325_report$temperature, tolerance = 1e-4), all.equal(tracebw_report$pressure , m325_report$pressure , tolerance = 1e-4), all.equal(tracebw_report$flow_rate , m325_report$flow_rate , tolerance = 1e-4) )library(pipenostics) # It is possible to run without specification of argument values: m325tracebw() # Consider isomorphic representation of District Heating Network graph: DHN <- pipenostics::m325nxdata # * Adapt units: DHN$d <- 1e3*DHN$d # convert [m] to [mm] # * Adapt node identifiers for ordering representation simplification: DHN[["sender"]] <- sprintf("N%02i", DHN[["sender"]]) DHN[["acceptor"]] <- sprintf("N%02i", DHN[["acceptor"]]) # * Provided actual values of specific heat loss power (say, field measurements) for each # pipe in DHN, [kcal/m/h]: actual_loss <- c( # acceptor: 96.236, # 1 96.288, # 2 70.584, # 3 116.045, # 4 70.734, # 5 96.211, # 6 78.400, # 7 116.016, # 8 28.115, # 9 24.918, # 10 116.679, # 11 0.000, # 12, may be unmeasured! 153.134, # 13 96.733, # 14 96.600, # 15 116.667, # 16 24.960, # 17 115.923, # 18 28.166, # 19 96.123, # 20 77.824, # 21 115.946, # 22 70.690, # 23 96.184, # 24 96.236, # 25 70.540 # 26 ) # * Remove inappropriate attributes of the graph: DHN.1 <- DHN[, setdiff(colnames(DHN), c("year", "insulation", "laying", "beta", "exp5k"))] # * Trace thermal-hydraulic regime for DHN: tracebw_report <- do.call("tracebw", c(as.list(DHN.1), list(loss = actual_loss))) # * If the actual values of specific heat loss power presented above are close # to those in Minenergo-325, then the results of regime tracing match the # normative procedure: m325_report <- do.call("m325tracebw", DHN) stopifnot( all.equal(tracebw_report$temperature, m325_report$temperature, tolerance = 1e-4), all.equal(tracebw_report$pressure , m325_report$pressure , tolerance = 1e-4), all.equal(tracebw_report$flow_rate , m325_report$flow_rate , tolerance = 1e-4) )
Trace values of thermal-hydraulic regime (temperature, pressure, flow rate, and other) in the bunched pipeline along the flow direction using user-provided values of specific heat loss power.
tracefw( sender = c(0, 1), acceptor = c(1, 2), temperature = c(70, NA_real_), pressure = c(pipenostics::mpa_kgf(6), NA_real_), flow_rate = c(20, NA_real_), d = rep_len(100, 2), len = rep_len(72.446, 2), loss = rep_len(78.4, 2), roughness = rep_len(0.001, 2), inlet = c(0.5, 1), outlet = c(1, 1), elev_tol = 0.1, method = "romeo", verbose = TRUE, csv = FALSE, file = "tracefw.csv", use_cluster = FALSE )tracefw( sender = c(0, 1), acceptor = c(1, 2), temperature = c(70, NA_real_), pressure = c(pipenostics::mpa_kgf(6), NA_real_), flow_rate = c(20, NA_real_), d = rep_len(100, 2), len = rep_len(72.446, 2), loss = rep_len(78.4, 2), roughness = rep_len(0.001, 2), inlet = c(0.5, 1), outlet = c(1, 1), elev_tol = 0.1, method = "romeo", verbose = TRUE, csv = FALSE, file = "tracefw.csv", use_cluster = FALSE )
sender |
identifier of the node which heat carrier flows out.
Type: any type that can be painlessly coerced to character by
|
acceptor |
identifier of the node which heat carrier flows in. According to topology
of test bench considered this identifier should be unique for every row.
Type: any type that can be painlessly coerced to character by
|
temperature |
Sensor-measured temperature of heat carrier (water) sensor-measured on
the root node, [°C].
Use |
pressure |
Sensor-measured
absolute pressure
of heat carrier (water) inside the pipe on the root node, [MPa].
Use |
flow_rate |
Sensor-measured amount of heat carrier (water) on root node that is
transferred by pipe during a period, [ton/hour].
Type: |
d |
internal diameter of pipe (i.e.diameter of acceptor's incoming edge),
[mm].
Type: |
len |
pipe length (i.e. length of acceptor's incoming edge), [m].
Type: |
loss |
user-provided value of specific heat loss power for each pipe in tracing
path, [kcal/m/h]. Values of the argument can be obtained experimentally,
or taken from regulatory documents.
Type: |
roughness |
roughness of internal wall of pipe (i.e. acceptor's incoming edge), [m].
Type: |
inlet |
elevation of pipe inlet, [m]. Type: |
outlet |
elevation of pipe outlet, [m]. Type: |
elev_tol |
maximum allowed discrepancy between adjacent outlet and inlet elevations
of two subsequent pipes in the traced path, [m].
Type: |
method |
method of determining Darcy friction factor:
Type: |
verbose |
logical indicator: should they watch tracing process on console?
Type: |
csv |
logical indicator: should they incrementally dump results to csv-
file while tracing?
Type: |
file |
name of csv-file which they dump results to.
Type: |
use_cluster |
utilize functionality of parallel processing on multi-core CPU.
Type: |
They consider the topology of district heating network represented by
m325nxdata:
Tracing starts from sensor-equipped root node and goes forward, i.e along
the flow direction. Function traceline serves under the
hood for tracing identified linear segments from root node to every
terminal node. Hence they only need root node to be equipped with sensors.
Sensors at other nodes are redundant in forward tracing, since the tracing
algorithm by no means consider them for tracing.
Moreover in the forward tracing algorithm they assume the flow of heat carrier is distributed proportionally to the cross-sectional area of the outgoing pipeline. Actually, a lot of reasons may cause significant deviations from this assumption. As a result, the sequence of paired backward/forward tracing may be divergent for regime parameters.
Though some input arguments are natively vectorized their individual values
all relate to common part of district heating network, i.e. associated with
common object. It is due to isomorphism between vector representation and
directed graph of this network. For more details of isomorphic topology
description see m325nxdata.
They are welcome to couple the algorithm with functionality of data.table.
data.frame containing results (detailed log) of tracing in
narrow format:
nodeTracing job. Identifier of the node which regime parameters is
calculated for. Values in this vector are identical to those in
argument acceptor.
Type: assert_character.
tracingTracing job. Identifiers of nodes from which regime parameters
are traced for the given node. Identifier sensor is used when
values of regime parameters for the node are sensor readings.
Type: assert_character.
backwardTracing job. Identifier of tracing direction. It constantly
equals to FALSE.
Type: assert_logical.
aggregationTracing job. Identifier of the aggregation method associated
with traced values. For forward tracing the only option is
identity.
Type: assert_character.
temperatureTraced thermal hydraulic regime. Traced temperature of heat
carrier (water) that is associated with the node, [°C].
Type: assert_double.
pressureTraced thermal hydraulic regime. Traced pressure of heat
carrier (water) that is associated with the node, [MPa].
Type: assert_double.
flow_rateTraced thermal hydraulic regime. Traced flow rate of heat
carrier (water) that is associated with the node, [ton/hour].
Type: assert_double.
jobTracing job. Value of tracing job counter.
For forward tracing value of job counts the number of traced paths from root node.
Type: assert_count.
Type: assert_data_frame.
Other Regime tracing:
m325tracebw(),
m325tracefw(),
m325traceline(),
tracebw(),
traceline()
library(pipenostics) # Minimum two nodes should be in district heating network graph: tracefw(verbose = FALSE) # Consider isomorphic representation of District Heating Network graph: DHN <- pipenostics::m325nxdata # * remove irrelevant parameters from the test bench DHN[c("year", "insulation", "laying", "beta", "exp5k")] <- NULL DHN[c("temperature", "pressure", "flow_rate")] <- NA_real_ # * avoid using numeric identifiers for nodes: DHN$sender <- sprintf("N%02i", DHN$sender) DHN$acceptor <- sprintf("N%02i", DHN$acceptor) # * alter units: DHN$d <- 1e3 * DHN$d # convert [m] to [mm] # * provide current regime parameters for root node root_node <- 12 DHN[root_node, "temperature"] <- 70.4942576978 # [°C] DHN[root_node, "pressure"] <- 0.6135602014 # [MPa] DHN[root_node, "flow_rate"] <- 274.0 # [ton/hour] # * provide actual values of specific heat loss power, [kcal/m/h], for each # segment N01 - N26. Since N12 is a root node, the specific heat loss # power for this acceptor is set to 0 (or may be any other numeric value). actual_loss <- c( 96.8, 96.8, 71.2, 116.7, 71.3, 96.8, 78.5, 116.7, 28.6, 24.5, 116.7, 0.0, 153.2, 96.8, 96.8, 116.7, 24.5, 116.7, 28.6, 96.8, 78.5, 116.7, 71.3, 96.8, 96.8, 71.1 ) # Trace the test bench forward for the first time: fw_report <- do.call( "tracefw", c(as.list(DHN), list(loss = actual_loss), verbose = FALSE, elev_tol = .5) )library(pipenostics) # Minimum two nodes should be in district heating network graph: tracefw(verbose = FALSE) # Consider isomorphic representation of District Heating Network graph: DHN <- pipenostics::m325nxdata # * remove irrelevant parameters from the test bench DHN[c("year", "insulation", "laying", "beta", "exp5k")] <- NULL DHN[c("temperature", "pressure", "flow_rate")] <- NA_real_ # * avoid using numeric identifiers for nodes: DHN$sender <- sprintf("N%02i", DHN$sender) DHN$acceptor <- sprintf("N%02i", DHN$acceptor) # * alter units: DHN$d <- 1e3 * DHN$d # convert [m] to [mm] # * provide current regime parameters for root node root_node <- 12 DHN[root_node, "temperature"] <- 70.4942576978 # [°C] DHN[root_node, "pressure"] <- 0.6135602014 # [MPa] DHN[root_node, "flow_rate"] <- 274.0 # [ton/hour] # * provide actual values of specific heat loss power, [kcal/m/h], for each # segment N01 - N26. Since N12 is a root node, the specific heat loss # power for this acceptor is set to 0 (or may be any other numeric value). actual_loss <- c( 96.8, 96.8, 71.2, 116.7, 71.3, 96.8, 78.5, 116.7, 28.6, 24.5, 116.7, 0.0, 153.2, 96.8, 96.8, 116.7, 24.5, 116.7, 28.6, 96.8, 78.5, 116.7, 71.3, 96.8, 96.8, 71.1 ) # Trace the test bench forward for the first time: fw_report <- do.call( "tracefw", c(as.list(DHN), list(loss = actual_loss), verbose = FALSE, elev_tol = .5) )
Trace values of thermal-hydraulic regime (temperature, pressure, flow_rate, and other) along the adjacent linear segments of pipeline using user-provided values of specific heat loss power.
traceline( temperature = 130, pressure = mpa_kgf(6), flow_rate = 250, g = 0, d = 700, len = c(600, 530, 300, 350), loss = c(348, 347.1389, 346.3483, 345.861), roughness = 0.006, inlet = 0, outlet = 0, elev_tol = 0.1, method = "romeo", forward = TRUE, absg = TRUE )traceline( temperature = 130, pressure = mpa_kgf(6), flow_rate = 250, g = 0, d = 700, len = c(600, 530, 300, 350), loss = c(348, 347.1389, 346.3483, 345.861), roughness = 0.006, inlet = 0, outlet = 0, elev_tol = 0.1, method = "romeo", forward = TRUE, absg = TRUE )
temperature |
Traced thermal hydraulic regime. Sensor-measured temperature of heat
carrier (water)
inside the pipe sensor-measured at the inlet
(forward tracing) or at the outlet (backward tracing) of path, [°C].
Type: |
pressure |
Traced thermal hydraulic regime. Sensor-measured
absolute
pressure of heat carrier (water) sensor-measured at the inlet
(forward tracing) or at the outlet (backward tracing) of path, [MPa].
Type: |
flow_rate |
Traced thermal hydraulic regime. Amount of heat carrier (water)
sensor-measured at the inlet (forward tracing) or at the outlet (backward
tracing) of path, [ton/hour]. Type: |
g |
amount of heat carrier discharge to network for each pipe segment in the
tracing path enumerated along the direction of flow. If flag |
d |
internal diameters of subsequent pipes in tracing path that are enumerated
along the direction of flow, [mm].
Type: |
len |
length of subsequent pipes in tracing path that are enumerated
along the direction of flow, [m].
Type: |
loss |
user-provided value of specific heat loss power for each pipe in tracing
path enumerated along the direction of flow, [kcal/m/h]. Values of the
argument can be obtained experimentally, or taken from regulatory documents.
Type: |
roughness |
roughness of internal wall for each pipe in tracing path enumerated along
the direction of flow, [m]. Type: |
inlet |
elevation of pipe inlet for each pipe in tracing path enumerated along
the direction of flow, [m]. Type: |
outlet |
elevation of pipe outlet for each pipe in tracing path enumerated along
the direction of flow, [m]. Type: |
elev_tol |
maximum allowed discrepancy between adjacent outlet and inlet elevations of
two subsequent pipes in the traced path, [m].
Type: |
method |
method of determining Darcy friction factor
Type: |
forward |
tracing direction flag: is it a forward direction of tracing?
If |
absg |
Whether argument |
They consider only simple tracing paths which do not contain rings and any kind of parallelization. At the same time bidirectional (forward and backward) tracing is possible in accordance with sensor position. They also may consider discharges to network at the inlet of each pipeline segment as an approximation of actual forks of flows. Relevant illustration of adopted assumptions for 4-segment tracing path is depicted on the next figure.
They make additional check for consistency of inlet and outlet
values for subsequent pipe segments. Discrepancy of appropriate elevations
cannot be more than elev_tol.
Since inner diameter of the pipe is used as input, the the thickness of the pipe wall additionally considered in heat flux calculations. Pipe wall thickness is derived from pipe diameter using GOST 30732 specifications.
list containing results (detailed log) of tracing for each pipe
in tracing path enumerated along the direction of flow:
temperatureTraced thermal hydraulic regime. Traced temperature of heat
carrier (water), [°C]. Type: assert_double.
pressureTraced thermal hydraulic regime. Traced pressure of heat
carrier (water) for each pipe in tracing path enumerated along the
direction of flow, [MPa]. Type: assert_double.
flow_rateTraced thermal hydraulic regime. Traced flow rate of heat
carrier (water) for each pipe in tracing path enumerated along the
direction of flow, [ton/hour]. Type: assert_double.
lossUser-provided specific heat
loss power for each pipe in tracing path enumerated along the direction
of flow, [kcal/m/h], - copy of input. Type: assert_double.
fluxHeat flux for each pipe
in tracing path enumerated along the direction of flow, [W/m^2].
Type: assert_double.
QHeat loss for each
pipe in tracing path enumerated along the direction of flow per day,
[kcal]. Type: assert_double.
Type: assert_list.
Other Regime tracing:
m325tracebw(),
m325tracefw(),
m325traceline(),
tracebw(),
tracefw()
library(pipenostics) # Consider 4-segment tracing path. # First, let sensor readings for forward tracing: t_fw <- 130 # [°C] p_fw <- mpa_kgf(6)*all.equal(.588399, mpa_kgf(6)) # [MPa] g_fw <- 250 # [ton/hour] # Let discharges to network for each pipeline segment are somehow determined as discharges <- seq(0, 30, 10) # [ton/hour] # Experimentally obtained values of specific heat loss power are actual_loss <- c(348.0000, 347.1389, 346.3483, 345.8610) # Then the calculated regime (red squares) for forward tracing is regime_fw <- traceline(t_fw, p_fw, g_fw, discharges, loss = actual_loss, forward = TRUE) print(regime_fw) # $temperature # [1] 129.1799 128.4269 127.9628 127.3367 # # $pressure # [1] 0.5878607 0.5874226 0.5872143 0.5870330 # # $flow_rate # [1] 250 240 220 190 # # $loss # [1] 348.0000 347.1389 346.3483 345.8610 # # $flux # [1] 181.9600 181.5097 181.0963 180.8415 # # $Q # [1] 5011200 4415607 2493707 2905232 # Next consider values of traced regime as sensor readings for backward tracing: t_bw <- 127.3367 # [°C] p_bw <- .5870330 # [MPa] g_bw <- 190 # [ton/hour] # Then the calculated regime (red squares) for backward tracing is regime_bw <- traceline(t_bw, p_bw, g_bw, discharges, loss = actual_loss, forward = FALSE) print(regime_bw) # $temperature # [1] 130.000893685 129.180497939 128.427226907 127.963046346 # # $pressure # [1] 0.588399833660 0.587861095778 0.587422779315 0.587214377798 # # $flow_rate # [1] 250 250 240 220 # # $loss # [1] 348.0000 347.1389 346.3483 345.8610 # # $flux # [1] 181.959958158 181.509711836 181.096328092 180.841531863 # # $Q # [1] 5011200.000 4415606.808 2493707.760 2905232.400 # Let compare sensor readings with backward tracing results: tracing <- with(regime_bw, { lambda <- function(val, constraint) c(val, constraint, constraint - val, abs(constraint - val)*100/constraint) first <- 1 structure( rbind( lambda(temperature[first], t_fw), lambda(pressure[first], p_fw), lambda(flow_rate[first], g_fw) ), dimnames = list( c("temperature", "pressure", "flow_rate"), c("sensor.value", "traced.value", "abs.discr", "rel.discr") ) ) }) print(tracing) # sensor.value traced.value abs.discr rel.discr # temperature 130.00089368526 130.0000000000 -8.93685255676e-04 0.000687450196674 # pressure 0.58839983366 0.5883990075 -8.26160099998e-07 0.000140408139624 # flow_rate 250.00000000000 250.0000000000 0.00000000000e+00 0.000000000000000library(pipenostics) # Consider 4-segment tracing path. # First, let sensor readings for forward tracing: t_fw <- 130 # [°C] p_fw <- mpa_kgf(6)*all.equal(.588399, mpa_kgf(6)) # [MPa] g_fw <- 250 # [ton/hour] # Let discharges to network for each pipeline segment are somehow determined as discharges <- seq(0, 30, 10) # [ton/hour] # Experimentally obtained values of specific heat loss power are actual_loss <- c(348.0000, 347.1389, 346.3483, 345.8610) # Then the calculated regime (red squares) for forward tracing is regime_fw <- traceline(t_fw, p_fw, g_fw, discharges, loss = actual_loss, forward = TRUE) print(regime_fw) # $temperature # [1] 129.1799 128.4269 127.9628 127.3367 # # $pressure # [1] 0.5878607 0.5874226 0.5872143 0.5870330 # # $flow_rate # [1] 250 240 220 190 # # $loss # [1] 348.0000 347.1389 346.3483 345.8610 # # $flux # [1] 181.9600 181.5097 181.0963 180.8415 # # $Q # [1] 5011200 4415607 2493707 2905232 # Next consider values of traced regime as sensor readings for backward tracing: t_bw <- 127.3367 # [°C] p_bw <- .5870330 # [MPa] g_bw <- 190 # [ton/hour] # Then the calculated regime (red squares) for backward tracing is regime_bw <- traceline(t_bw, p_bw, g_bw, discharges, loss = actual_loss, forward = FALSE) print(regime_bw) # $temperature # [1] 130.000893685 129.180497939 128.427226907 127.963046346 # # $pressure # [1] 0.588399833660 0.587861095778 0.587422779315 0.587214377798 # # $flow_rate # [1] 250 250 240 220 # # $loss # [1] 348.0000 347.1389 346.3483 345.8610 # # $flux # [1] 181.959958158 181.509711836 181.096328092 180.841531863 # # $Q # [1] 5011200.000 4415606.808 2493707.760 2905232.400 # Let compare sensor readings with backward tracing results: tracing <- with(regime_bw, { lambda <- function(val, constraint) c(val, constraint, constraint - val, abs(constraint - val)*100/constraint) first <- 1 structure( rbind( lambda(temperature[first], t_fw), lambda(pressure[first], p_fw), lambda(flow_rate[first], g_fw) ), dimnames = list( c("temperature", "pressure", "flow_rate"), c("sensor.value", "traced.value", "abs.discr", "rel.discr") ) ) }) print(tracing) # sensor.value traced.value abs.discr rel.discr # temperature 130.00089368526 130.0000000000 -8.93685255676e-04 0.000687450196674 # pressure 0.58839983366 0.5883990075 -8.26160099998e-07 0.000140408139624 # flow_rate 250.00000000000 250.0000000000 0.00000000000e+00 0.000000000000000
Use GOST 30732 specifications to derive the value of the pipe wall thickness if only its diameter is known for the pipe.
wth_d(x)wth_d(x)
x |
outside diameter of pipe, [mm]. Type: |
Utility should be used only in cases where the actual value of the pipe wall thickness cannot be determined by any other means. In many cases internal diameter may be used instead of outside one without significant loss in precision. The wall thickness value is derived only for the diameters mentioned in Minenergo Order 325.
Unfortunately, the inverse function cannot be constructed in any reliable way due to significant ambiguity.
GOST 30732. Steel pipes and shaped products with foamed polyurethane thermal insulation in protective sheath. Specifications.
Other utils:
b36mass(),
b36pipedata,
geoarea(),
meteos(),
mgtdhid()
library(pipenostics) # Guess pipe widths for some frequently met diameters wth_d(as.double(c(57, 76, 89))) # [1] 3 7 11 # [mm]library(pipenostics) # Guess pipe widths for some frequently met diameters wth_d(as.double(c(57, 76, 89))) # [1] 3 7 11 # [mm]