Non-Linear Corrosion Growth: A More Appropriate and Accurate Model for Predicting Corrosion Growth Rate

2016 ◽  
Author(s):  
M. Al-Amin ◽  
S. Kariyawasam ◽  
S. Zhang ◽  
W. Zhou
Keyword(s):  
Growth Rate ◽  
Case Studies ◽  
Growth Model ◽  
Measurement Errors ◽  
Linear Growth ◽  
Management Program ◽  
Linear Growth Rate ◽  
Metal Loss ◽  
Contributing Factors ◽  
Non Linear

External metal-loss corrosion is one of the major contributing factors for pipeline failures in North America. Corrosion growth rate plays a crucial role in managing corrosion hazard for gas and liquid pipelines. Quantifying the growth of corrosion over time is critically important for the risk and reliability analysis of pipelines, planning for corrosion mitigation and repair, and determination of time intervals for corrosion inspections. Conservatism in predicting the growth rate has significant engineering implication as non-conservatism can lead to critical anomalies being missed by mitigation actions and may cause pipeline failure; whereas, over conservatism can lead to unnecessary inspections and anomaly mitigations that may result in significant unnecessary cost to pipeline operators. As more and more pipelines are now being inspected by in-line inspection (ILI) tools on a regular basis, the ILI data from multiple inspections provide valuable information about the growth of corrosion anomalies on the pipeline. Although the application of linear growth rate calculated by comparing depths from two successive ILI is a common practice in the pipeline industry, research has shown that the growth of corrosion anomaly is non-linear and anomaly-specific. The authors of this paper have previously developed anomaly-specific non-linear corrosion growth model based on multiple ILI data. The objectives of this paper are to demonstrate the appropriateness of anomaly-specific non-linear corrosion growth model, and to illustrate the advantages of using non-linear corrosion growth model in the integrity management program. Two case studies were performed to illustrate the application of non-linear growth model by incorporating the measurement errors associated with the ILI tools, which include both the bias (constant and non-constant) and random scattering error. The findings of these case studies are presented in this paper.

scholarly journals Validating the methodology for constraining the linear growth rate from clustering anisotropies

2020 ◽  
Vol 494 (2) ◽  
pp. 1658-1674
Author(s):  
Jorge Enrique García-Farieta ◽  
Federico Marulli ◽  
Lauro Moscardini ◽  
Alfonso Veropalumbo ◽  
Rigoberto A Casas-Miranda
Keyword(s):  
Growth Rate ◽  
Correlation Function ◽  
Measurement Errors ◽  
Linear Growth ◽  
Dispersion Model ◽  
Linear Growth Rate ◽  
Small Scale ◽  
Point Correlation ◽  
Point Correlation Function ◽  
The Impact

ABSTRACT Redshift-space clustering distortions provide one of the most powerful probes to test the gravity theory on the largest cosmological scales. We perform a systematic validation study of the state-of-the-art statistical methods currently used to constrain the linear growth rate from redshift-space distortions in the galaxy two-point correlation function. The numerical pipelines are tested on mock halo catalogues extracted from large N-body simulations of the standard cosmological framework. We consider both the monopole and quadrupole multipole moments of the redshift-space two-point correlation function, as well as the radial and transverse clustering wedges, in the comoving scale range 10 < r[$h^{-1}\, \mbox{Mpc}$] < 55. Moreover, we investigate the impact of redshift measurement errors on the growth rate and linear bias measurements due to the assumptions in the redshift-space distortion model. Considering both the dispersion model and two widely used models based on perturbation theory, we find that the linear growth rate is underestimated by about $5\!-\! 10\, {\rm {per\ cent}}$ at $z$ < 1, while limiting the analysis at larger scales, r > 30 $h^{-1}\, \mbox{Mpc}$, the discrepancy is reduced below $5\, {\rm {per\ cent}}$. At higher redshifts, we find instead an overall good agreement between measurements and model predictions. Though this accuracy is good enough for clustering analyses in current redshift surveys, the models have to be further improved not to introduce significant systematics in RSD constraints from next-generation galaxy surveys. The effect of redshift errors is degenerate with the one of small-scale random motions, and can be marginalized over in the statistical analysis, not introducing any statistically significant bias in the linear growth constraints, especially at $z$ ≥ 1.

scholarly journals Theoretical wind clumping predictions of OB supergiants from line-driven instability simulations across the bi-stability jump

2019 ◽  
Vol 631 ◽  
pp. A172 ◽  
Author(s):  
F. A. Driessen ◽  
J. O. Sundqvist ◽  
N. D. Kee
Keyword(s):  
Growth Rate ◽  
Mass Loss ◽  
Linear Growth ◽  
Massive Stars ◽  
Linear Growth Rate ◽  
Linear Perturbation ◽  
Lower Growth ◽  
Lower Velocity ◽  
Non Linear ◽  
Loss Rates

Context. The behaviour of mass loss across the so-called bi-stability jump, where iron recombines from Fe IV to Fe III, is a key uncertainty in models of massive stars. Specifically, while an increase in mass loss is theoretically predicted, this has not yet been observationally confirmed. However, radiation-driven winds of hot massive stars are known to exhibit clumpy structures triggered by the line-deshadowing instability (LDI). This wind clumping severely affects empirical mass-loss rates inferred from ρ2-dependent spectral diagnostics. Thus, if clumping properties differ significantly for O and B supergiants across the bi-stability jump, this may help alleviate current discrepancies between theory and observations. Aims. We investigated with analyt ical and numerical tools how the onset of clumpy structures behave in the winds of O supergiants (OSG) and B supergiants (BSG) across the bi-stability jump. Methods. We derived a scaling relation for the linear growth rate of the LDI for a single optically thick line and applied it in the OSG and BSG regime. We ran 1D time-dependent line-driven instability simulations to study the non-linear evolution of the LDI in clumpy OSG and BSG winds. Results. Linear perturbation analysis for a single line shows that the LDI linear growth rate Ω scales strongly with stellar effective temperature and terminal wind speed: Ω∝v∞2Teff4. This implies significantly lower growth rates for (the cooler and slower) BSG winds than for OSG winds. This is confirmed by the non-linear simulations, which show significant differences in OSG and BSG wind structure formation, with the latter characterized by significantly weaker clumping factors and lower velocity dispersions. This suggests that lower correction factors due to clumping should be employed when deriving empirical mass-loss rates for BSGs on the cool side of the bi-stability jump. Moreover, the non-linear simulations provide a theoretical background towards explaining the general lack of observed intrinsic X-ray emission in single B-star winds.

scholarly journals On the non-axisymmetric fragmentation of rings generated by the Secular Gravitational Instability

2021 ◽  
Author(s):  
Arnaud Pierens
Keyword(s):  
Growth Rate ◽  
Growth Rates ◽  
Linear Growth ◽  
Gravitational Instability ◽  
Dust Particles ◽  
Linear Growth Rate ◽  
Stability Parameters ◽  
Dust Density ◽  
Linear Evolution ◽  
Non Linear

Abstract Ringed structures have been observed in a variety of protoplanetary discs. Among the processes that might be able to generate such features, the Secular Gravitational Instability (SGI) is a possible candidate. It has also been proposed that the SGI might lead to the formation of planetesimals during the non-linear phase of the instability. In this context, we employ two-fluid hydrodynamical simulations with self-gravity to study the non-axisymmetric, non-linear evolution of ringed perturbations that grow under the action of the SGI. We find that the non-linear evolution outcome of the SGI depends mainly on the initial linear growth rate. For SGI growth rates smaller than typically σ ≳ 10−4 − 10−5Ω, dissipation resulting from dust feedback introduces a m = 1 spiral wave in the gas, even for Toomre gas stability parameters Qg > 2 for which non-axisymmetric instabilities appear in a purely gaseous disc. This one-armed spiral subsequently traps dust particles until a dust-to-gas ratio ε ∼ 1 is achieved. For higher linear growth rates, the dust ring is found to undergo gravitational collapse until the bump in the surface density profile becomes strong enough to trigger the formation of dusty vortices through the Rossby Wave Instability (RWI). Enhancements in dust density resulting from this process are found to scale with the linear growth rate, and can be such that the dust density is higher than the Roche density, leading to the formation of bound clumps. Fragmentation of axisymmetric rings produced by the SGI might therefore appear as a possible process for the formation of planetesimals.

Microborings and growth in Late Ordovician halysitids and other corals

1993 ◽  
Vol 67 (6) ◽  
pp. 922-934 ◽  
Author(s):  
Robert J. Elias ◽  
Dong-Jin Lee
Keyword(s):  
Growth Rate ◽  
Linear Growth ◽  
Inverse Correlation ◽  
Weight Percent ◽  
Late Ordovician ◽  
Coral Growth ◽  
Linear Growth Rate ◽  
Skeletal Density ◽  
Rugose Coral ◽  
Endolithic Algae

Microborings in the Late Ordovician tabulate corals Catenipora rubra (a halysitid) and Manipora amicarum (a cateniform nonhalysitid) and in an epizoic solitary rugose coral differ from nearly all of those previously reported in Paleozoic corals. These microborings were formed within the coralla by endolithic algae and fungi located beneath living polyps. Comparable structures in the Late Ordovician tabulate Quepora ?agglomeratiformis (a halysitid) represent algal microborings, not spicules, and halysitids are corals, not sponges as suggested by Kaźmierczak (1989).Endolithic algae in cateniform tabulates relied primarily on light entering through the outer walls of the ranks rather than through the polyps; lacunae within coralla permitted appropriate levels of light to reach many corallites. The direction of boring was determined by corallum microstructure and possibly also by the distribution of organic matter within the skeleton. There is an apparent inverse correlation between boring activity and coral growth rate.The location and relative abundance of pyritized microborings within calcareous coralla can be established quantitatively and objectively from electron microprobe determinations of weight percent sulfur along appropriate traverses of the coral skeleton. The distribution of such microborings in Catenipora rubra and Manipora amicarum is comparable to algal banding in modern corals; this is the first report of such banding in the interiors of Paleozoic corals. Change in the intensity of boring within each corallum was evidently a response to variation in the linear growth rate of the coral, or to fluctuation in an environmental factor (perhaps light intensity) that could control both algal activity and growth rate in these corals. Change in the algal boring intensity and linear growth rate of the coral was generally but not always seasonal and usually but not invariably associated with change in the density of coral skeletal deposition.Cyclic bands of boring abundance maxima within fossil colonial corals provide a measure of annual linear growth comparable to the widely accepted method based on skeletal density bands. Algal bands are more sporadically developed than density bands within and among coralla, thus increasing the difficulty of interpretation. Fluctuations in the abundance of algal microborings apparently provide a detailed record of changes in the linear growth rate of colonies and of individuals within colonies. Combined analyses of microboring abundance and skeletal density will contribute significantly to our understanding of the biological and environmental factors involved in endolithic activity and coral growth.

scholarly journals <sup>210</sup>Pb-<sup>226</sup>Ra chronology reveals rapid growth rate of <i>Madrepora oculata</I> and <i>Lophelia pertusa</i> on world's largest cold-water coral reef

2011 ◽  
Vol 8 (6) ◽  
pp. 12247-12283
Author(s):  
P. Sabatier ◽  
J.-L. Reyss ◽  
J. M. Hall-Spencer ◽  
C. Colin ◽  
N. Frank ◽  
...  
Keyword(s):  
Growth Rate ◽  
Coral Reef ◽  
Linear Growth ◽  
Cold Water ◽  
Optimal Growth ◽  
Growth Conditions ◽  
Age And Growth ◽  
Linear Growth Rate ◽  
Lophelia Pertusa ◽  
Water Coral

Abstract. Here we show the use of the 210Pb-226Ra excess method to determine the growth rate of corals from one of the world's largest known cold-water coral reef, the Røst Reef off Norway. Two large branching framework-forming cold-water coral specimens, one Lophelia pertusa and one Madrepora oculata were collected alive at 350 m water depth from the Røst Reef at ~67° N and ~9° E. Pb and Ra isotopes were measured along the major growth axis of both specimens using low level alpha and gamma spectrometry and the corals trace element compositions were studied using ICP-QMS. Due to the different chemical behaviors of Pb and Ra in the marine environment, 210Pb and 226Ra were not incorporated the same way into the aragonite skeleton of those two cold-water corals. Thus to assess of the growth rates of both specimens we have here taken in consideration the exponential decrease of initially incorporated 210Pb as well as the ingrowth of 210Pb from the decay of 226Ra. Moreover a~post-depositional 210Pb incorporation is found in relation to the Mn-Fe coatings that could not be entirely removed from the oldest parts of the skeletons. The 226Ra activities in both corals were fairly constant, then assuming constant uptake of 210Pb through time the 210Pb-226Ra chronology can be applied to calculate linear growth rate. The 45.5 cm long branch of M. oculata reveals an age of 31 yr and a~linear growth rate of 14.4 ± 1.1 mm yr−1, i.e. 2.6 polyps per year. However, a correction regarding a remaining post-depositional Mn-Fe oxide coating is needed for the base of the specimen. The corrected age tend to confirm the radiocarbon derived basal age of 40 yr (using 14C bomb peak) with a mean growth rate of 2 polyps yr−1. This rate is similar to the one obtained in Aquaria experiments under optimal growth conditions. For the 80 cm-long specimen of L. pertusa a remaining contamination of metal-oxides is observed for the middle and basal part of the coral skeleton, inhibiting similar accurate age and growth rate estimates. However, the youngest branch was free of Mn enrichment and this 15 cm section reveals a growth rate of 8 mm yr−1 (~1 polyp every two to three years). However, the 210Pb growth rate estimate is within the lowermost ranges of previous growth rate estimates and may thus reflect that the coral was not developing at optimal growth conditions. Overall, 210Pb-226Ra dating can be successfully applied to determine the age and growth rate of framework-forming cold-water corals, however, removal of post-depositional Mn-Fe oxide deposits is a prerequisite. If successful, large branching M. oculata and L. pertusa coral skeletons provide unique oceanographic archive for studies of intermediate water environmentals with an up to annual time resolution and spanning over many decades.

scholarly journals Generation of Wave Groups by Shear Layer Instability

Fluids ◽  
2019 ◽  
Vol 4 (1) ◽  
pp. 39 ◽  
Author(s):  
Roger Grimshaw
Keyword(s):  
Growth Rate ◽  
Group Velocity ◽  
Linear Growth ◽  
Linear Stability Theory ◽  
Linear Growth Rate ◽  
Wave Groups ◽  
Weakly Nonlinear ◽  
Complex Valued ◽  
Fundamental Requirement ◽  
Temporal Growth Rate

The linear stability theory of wind-wave generation is revisited with an emphasis on the generation of wave groups. The outcome is the fundamental requirement that the group move with a real-valued group velocity. This implies that both the wave frequency and the wavenumber should be complex-valued, and in turn this then leads to a growth rate in the reference frame moving with the group velocity which is in general different from the temporal growth rate. In the weakly nonlinear regime, the amplitude envelope of the wave group is governed by a forced nonlinear Schrödinger equation. The effect of the wind forcing term is to enhance modulation instability both in terms of the wave growth and in terms of the domain of instability in the modulation wavenumber space. Also, the soliton solution for the wave envelope grows in amplitude at twice the linear growth rate.

scholarly journals Wavelength dependence of the linear growth rate of the <I>E<sub>s</sub></I> layer instability

2007 ◽  
Vol 25 (6) ◽  
pp. 1311-1322 ◽  
Author(s):  
R. B. Cosgrove
Keyword(s):  
Growth Rate ◽  
Electric Fields ◽  
Large Scale ◽  
Linear Growth ◽  
Three Dimensional ◽  
Generalized Derivation ◽  
Wavelength Dependence ◽  
Meridional Wind ◽  
Linear Growth Rate ◽  
Significant Wavelength

Abstract. It has recently been shown, by computation of the linear growth rate, that midlatitude sporadic-E (Es) layers are subject to a large scale electrodynamic instability. This instability is a logical candidate to explain certain frontal structuring events, and polarization electric fields, which have been observed in Es layers by ionosondes, by coherent scatter radars, and by rockets. However, the original growth rate derivation assumed an infinitely thin Es layer, and therefore did not address the short wavelength cutoff. Also, the same derivation ignored the effects of F region loading, which is a significant wavelength dependent effect. Herein is given a generalized derivation that remedies both these short comings, and thereby allows a computation of the wavelength dependence of the linear growth rate, as well as computations of various threshold conditions. The wavelength dependence of the linear growth rate is compared with observed periodicities, and the role of the zeroth order meridional wind is explored. A three-dimensional paper model is used to explain the instability geometry, which has been defined formally in previous works.

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