Probability-Based Sentencing Criteria for Volumetric In-Line Inspection Data

Author(s):  
James Mihell ◽  
J. P. Lemieux ◽  
Samah Hasan

ASME B31.8S, Figure 7.2.1-1 (referred to as Figure 4 in earlier editions of the Standard) is used by many operators of natural gas transmission pipelines to schedule the remediation of corrosion features found via in-line inspection (ILI). The underlying philosophy of this approach is that wall loss features should be repaired before the calculated failure pressure falls below 110% of the maximum allowable operating pressure (MAOP). ASME B31.8S Figure 7.2.1-1 provides a basis for establishing maximum response times as a function of pipeline operating stress level, based in part on assumed corrosion growth rates. The corrosion rates assumed in the derivation of ASME B31.8S Figure 7.2.1-1 depend on the wall thickness of the pipe and the operating stress level as a percent of SMYS. As documented in PHMSA’s March 17, 2016 Notice of Proposed Rulemaking, the 1.1xMAOP repair criterion that forms the basis of Figure 7.2.2-1 has a demonstrated successful history of use in response management for wall loss ILI data. Despite this successful record, some potential exists for the underlying corrosion growth rate assumptions that are incorporated within that criterion to be non-conservative. Under some circumstances, the underlying corrosion growth rate assumption that is incorporated in Figure 7.2.1-1 can be significantly less than that which is provided in the guidance provided in NACE SP0502 (referenced in Appendix B of ASME B31.8S). Therefore, operators should ideally take measures to verify that the growth rate assumptions incorporated within Figure 7.2.1-1 are appropriate for their circumstances before adopting the scheduled response criteria from that Figure. On the other hand, for the majority of circumstances, it could be demonstrated that the Figure 7.2.1-1 criteria may represent overly-conservative response times, particularly where feature-specific information related to corrosion rates are available, and/or can be inferred from ILI data. A desirable solution would be to employ a response time threshold that utilizes the 1.1xMAOP repair criterion that has been demonstrated to be successful through industry’s widespread adoption of the Figure 7.2.2-1 criteria, along with some basis for incorporating feature-specific corrosion growth rates (from ILI data), and additionally, some basis for accounting for tool measurement error. Techniques for estimating the relative probability of failure (Pf) exist that employ ILI data and account for tool measurement error, model error, and tolerances in pipe dimensions and material properties. The problem to date is that probability targets have not been available for use in conjunction with a Pf analysis. Building on previous work done by Kiefner and Kolovich, this paper derives an approach for expressing Pf targets in terms of the 1.1xMAOP repair criterion adopted by ASME B31.8S, Figure 7.2.1-1. The Pf targets are derived using stochastic modeling, and incorporate probability density functions on tool error for feature depth and length, wall thickness, yield strength, and model error. Using a wide range of pipeline material and design parameters, a relationship for establishing lower-bound Pf targets is developed for broad application.

Homeopathy ◽  
2021 ◽  
Author(s):  
Tim Jäger ◽  
Sandra Würtenberger ◽  
Stephan Baumgartner

Abstract Background A bioassay with severely mercury-stressed duckweed (Lemna gibba L.) had revealed growth-inhibiting effects of homeopathically potentised mercury(II) chloride (Mercurius corrosivus, Merc-c.). We hypothesised that effects of potentised preparations are dependent on the stress level of the organisms used in the bioassay. The aim of the present investigation was to examine the response of duckweed to potentised Merc-c. at a lower stress level. Methods Duckweed was moderately stressed with 2.5 mg/L mercury(II) chloride for 48 hours. Afterwards plants grew in either Merc-c. (seven different potency levels, 24x–30x) or water controls (unsuccussed or succussed water) for 7 days. Growth rates of the frond (leaf) area were determined using a computerised image-analysis system for day 0–3 and 3–7. Three independent experiments with potentised Merc-c. and three systematic negative control experiments were performed. All experiments were randomised and blinded. Results Unsuccussed and succussed water did not significantly differ in their effects on duckweed growth rate. The systematic negative control experiments did not yield any significant effects, thus providing evidence for the stability of the experimental system. Data from the two control groups and the seven treatment groups (Merc-c. 24x–30x) were each pooled to increase statistical power. Duckweed growth rates for day 3–7 were enhanced (p < 0.05) after application of Merc-c. compared with the controls. Growth rates for day 0–3 were not influenced by the homeopathic preparations. Conclusions Moderately mercury-stressed Lemna gibba L. yielded evidence of growth-enhancing specific effects of Merc-c. 24x–30x in the second observation period (day 3–7). This observation is complementary to previous experiments with severely mercury-stressed duckweed, in which a decrease in growth was observed in the first observation period (day 0–3). We hypothesise that the differing results are associated with the level of stress intensity (moderate vs. severe).


Author(s):  
Khalid A. Farrag

External corrosion growth rate is an essential parameter to establish the time interval between successive pipe integrity evaluations. Actual corrosion rates are difficult to measure or predict. NACE Standard RP0502 [1] recommends several methods including comparison with historical data, buried coupons, electrical resistance (ER), and Linear Polarization Resistance (LPR) measurements. This paper presents a testing program and procedure to validate the use of the LPR and ER methods to enhance the estimation of corrosion growth rates and improve the selection of reassessment intervals of gas transmission pipelines. Laboratory and field tests were performed using the LPR and ER technologies. The evaluation of soil parameters that affect localized corrosion included its type, moisture content, pH, resistivity, drainage characteristics, chloride and sulfite levels, and soil Redox potential. The results show that the LPR device provides instantaneous measurement of corrosion potential and it may be used to reflect the variations of corrosion rates with the changes of soil conditions, moisture, and temperature. However, LPR measurements are more efficient in saturated soils with uncertainty about its validity in partially and totally dry soils. Consequently, seasonal changes in soil conditions make it difficult to estimate total corrosion growth rate. On the other hand, the measurements using the ER method provided consistent estimates for long-term corrosion growth rates. Corrosion growth rates were also evaluated from a previous study by the National Institute of Standards (NIST) [2]. A procedure was developed to correlate soil properties to corrosion rates from the ER measurements and NIST data. The procedure was implemented in a computer program to provide an estimate of corrosion rate based on the soil input data and allows the operator to use the ER probes to improve the reliability of corrosion rate estimates.


Author(s):  
Maher Nessim ◽  
Jane Dawson ◽  
Rafael Mora ◽  
Sherif Hassanein

The ability to accurately determine the rate of corrosion growth along a pipeline is an essential input into a number of key integrity management decisions. For example, corrosion rates are needed to predict pipeline reliability (probability of failure and/or probability of exceedance) as a function of time, to identify the need for and timing of field investigations and/or repairs and to determine optimum re-inspection intervals to name just a few applications. As more and more pipelines are now being inspected using intelligent in-line inspection (ILI) tools for a second or even third or fourth time, pipeline operators require reliable guidelines for comparing repeat ILI data sets to obtain valid corrosion growth rates. Because of the measurement uncertainties associated with corrosion size estimated from a single ILI run, the corrosion growth rate calculated from consecutive ILI runs has a degree of uncertainty that needs to be considered in determining valid and accurate corrosion growth rates. The ratio between the measured corrosion growth and the measurement error is an important parameter in determining a meaningful distribution of the corrosion growth rate either when performing defect to defect comparisons or when comparing the defect populations in pipeline segments. When this ratio is small the associated uncertainty can be too large to make meaningful probabilistic inferences. As the ratio increases, the effect of measurement uncertainty becomes more manageable, allowing growth rate distributions to be calculated with reasonable confidence. This paper describes an approach to define the probability distribution of corrosion growth rates as a function of a simple parameter that characterizes the ratio between the ILI-observed corrosion growth and the ILI measurement error. This approach has been developed as part of an ongoing PRCI-sponsored research project to produce procedures for determining and validating corrosion growth rates from repeat ILI runs. The paper also provides examples using sample data from repeat ILI runs showing the application of these procedures, the treatment of measurement uncertainty, the resulting corrosion growth rate information that can be obtained and the associated level of confidence in the results.


1990 ◽  
Vol 55 (7) ◽  
pp. 1691-1707 ◽  
Author(s):  
Miloslav Karel ◽  
Jiří Hostomský ◽  
Jaroslav Nývlt ◽  
Axel König

Crystal growth rates of copper sulphate pentahydrate (CuSO4.5 H2O) determined by different authors and methods are compared. The methods included in this comparison are: (i) Measurement on a fixed crystal suspended in a streaming solution, (ii) measurement on a rotating disc, (iii) measurement in a fluidized bed, (iv) measurement in an agitated suspension. The comparison involves critical estimation of the supersaturation used in measurements, of shape factors used for data treatment and a correction for the effect of temperature. Conclusions are drawn for the choice of values to be specified when data of crystal growth rate measurements are published.


1989 ◽  
Vol 54 (11) ◽  
pp. 2951-2961 ◽  
Author(s):  
Miloslav Karel ◽  
Jaroslav Nývlt

Measured growth and dissolution rates of single crystals and tablets were used to calculate the overall linear rates of growth and dissolution of CuSO4.5 H2O crystals. The growth rate for the tablet is by 20% higher than that calculated for the single crystal. It has been concluded that this difference is due to a preferred orientation of crystal faces on the tablet surface. Calculated diffusion coefficients and thicknesses of the diffusion and hydrodynamic layers in the vicinity of the growing or dissolving crystal are in good agreement with published values.


2021 ◽  
pp. 0272989X2110222
Author(s):  
Yuwen Gu ◽  
Elise DeDoncker ◽  
Richard VanEnk ◽  
Rajib Paul ◽  
Susan Peters ◽  
...  

It is long perceived that the more data collection, the more knowledge emerges about the real disease progression. During emergencies like the H1N1 and the severe acute respiratory syndrome coronavirus 2 pandemics, public health surveillance requested increased testing to address the exacerbated demand. However, it is currently unknown how accurately surveillance portrays disease progression through incidence and confirmed case trends. State surveillance, unlike commercial testing, can process specimens based on the upcoming demand (e.g., with testing restrictions). Hence, proper assessment of accuracy may lead to improvements for a robust infrastructure. Using the H1N1 pandemic experience, we developed a simulation that models the true unobserved influenza incidence trend in the State of Michigan, as well as trends observed at different data collection points of the surveillance system. We calculated the growth rate, or speed at which each trend increases during the pandemic growth phase, and we performed statistical experiments to assess the biases (or differences) between growth rates of unobserved and observed trends. We highlight the following results: 1) emergency-driven high-risk perception increases reporting, which leads to reduction of biases in the growth rates; 2) the best predicted growth rates are those estimated from the trend of specimens submitted to the surveillance point that receives reports from a variety of health care providers; and 3) under several criteria to queue specimens for viral subtyping with limited capacity, the best-performing criterion was to queue first-come, first-serve restricted to specimens with higher hospitalization risk. Under this criterion, the lab released capacity to subtype specimens for each day in the trend, which reduced the growth rate bias the most compared to other queuing criteria. Future research should investigate additional restrictions to the queue.


Geosciences ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 187
Author(s):  
Rolf Vieten ◽  
Francisco Hernandez

Speleothems are one of the few archives which allow us to reconstruct the terrestrial paleoclimate and help us to understand the important climate dynamics in inhabited regions of our planet. Their time of growth can be precisely dated by radiometric techniques, but unfortunately seasonal radiometric dating resolution is so far not feasible. Numerous cave environmental monitoring studies show evidence for significant seasonal variations in parameters influencing carbonate deposition (calcium-ion concentration, cave air pCO2, drip rate and temperature). Variations in speleothem deposition rates need to be known in order to correctly decipher the climate signal stored in the speleothem archive. StalGrowth is the first software to quantify growth rates based on cave monitoring results, detect growth seasonality and estimate the seasonal growth bias. It quickly plots the predicted speleothem growth rate together with the influencing cave environmental parameters to identify which parameter(s) cause changes in speleothem growth rate, and it can also identify periods of no growth. This new program has been applied to multiannual cave monitoring studies in Austria, Gibraltar, Puerto Rico and Texas, and it has identified two cases of seasonal varying speleothem growth.


Plants ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 31 ◽  
Author(s):  
Maria N. Metsoviti ◽  
George Papapolymerou ◽  
Ioannis T. Karapanagiotidis ◽  
Nikolaos Katsoulas

In this research, the effect of solar irradiance on Chlorella vulgaris cultivated in open bioreactors under greenhouse conditions was investigated, as well as of ratio of light intensity in the 420–520 nm range to light in the 580–680 nm range (I420–520/I580–680) and of artificial irradiation provided by red and white LED lamps in a closed flat plate laboratory bioreactor on the growth rate and composition. The increase in solar irradiance led to faster growth rates (μexp) of C. vulgaris under both environmental conditions studied in the greenhouse (in June up to 0.33 d−1 and in September up to 0.29 d−1) and higher lipid content in microalgal biomass (in June up to 25.6% and in September up to 24.7%). In the experiments conducted in the closed bioreactor, as the ratio I420–520/I580–680 increased, the specific growth rate and the biomass, protein and lipid productivities increased as well. Additionally, the increase in light intensity with red and white LED lamps resulted in faster growth rates (the μexp increased up to 0.36 d−1) and higher lipid content (up to 22.2%), while the protein, fiber, ash and moisture content remained relatively constant. Overall, the trend in biomass, lipid, and protein productivities as a function of light intensity was similar in the two systems (greenhouse and bioreactor).


1974 ◽  
Vol 11 (03) ◽  
pp. 437-444 ◽  
Author(s):  
Benoit Mandelbrot

Luria and Delbrück (1943) have observed that, in old cultures of bacteria that have mutated at random, the distribution of the number of mutants is extremely long-tailed. In this note, this distribution will be derived (for the first time) exactly and explicitly. The rates of mutation will be allowed to be either positive or infinitesimal, and the rate of growth for mutants will be allowed to be either equal, greater or smaller than for non-mutants. Under the realistic limit condition of a very low mutation rate, the number of mutants is shown to be a stable-Lévy (sometimes called “Pareto Lévy”) random variable, of maximum skewness ß, whose exponent α is essentially the ratio of the growth rates of non-mutants and of mutants. Thus, the probability of the number of mutants exceeding the very large value m is proportional to m –α–1 (a behavior sometimes referred to as “asymptotically Paretian” or “hyperbolic”). The unequal growth rate cases α ≠ 1 are solved for the first time. In the α = 1 case, a result of Lea and Coulson is rederived, interpreted, and generalized. Various paradoxes involving divergent moments that were encountered in earlier approaches are either absent or fully explainable. The mathematical techniques used being standard, they will not be described in detail, so this note will be primarily a collection of results. However, the justification for deriving them lies in their use in biology, and the mathematically unexperienced biologists may be unfamiliar with the tools used. They may wish for more details of calculations, more explanations and Figures. To satisfy their needs, a report available from the author upon request has been prepared. It will be referred to as Part II.


1978 ◽  
Vol 14 (1) ◽  
pp. 1-5 ◽  
Author(s):  
J. L. Monteith

SUMMARYFigures for maximum crop growth rates, reviewed by Gifford (1974), suggest that the productivity of C3 and C4 species is almost indistinguishable. However, close inspection of these figures at source and correspondence with several authors revealed a number of errors. When all unreliable figures were discarded, the maximum growth rate for C3 stands fell in the range 34–39 g m−2 d−1 compared with 50–54 g m−2 d−1 for C4 stands. Maximum growth rates averaged over the whole growing season showed a similar difference: 13 g m−2 d−1 for C3 and 22 g m−2 d−1 for C4. These figures correspond to photosynthetic efficiencies of approximately 1·4 and 2·0%.


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