ABS TECHNICAL PAPERS 2005 NON-LINEAR TIME DEPENDENT CORROSION WASTAGE OF DECK PLATES OF BALLAST AND CARGO TANKS OF TANKERS

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1 ABS TECHNICAL PAPERS 5 Proceedings of OMAE5 4 th International Conference on Offshore Mechanics and Arctic Engineering June 1-17, 5, Halkidiki, Greece OMAE NON-LINEAR TIME DEPENDENT CORROSION WASTAGE OF DECK PLATES OF BALLAST AND CARGO TANKS OF TANKERS Y. Garbatov Unit of Marine Technology and Engineering, Technical University of Lisbon, Instituto Superior Técnico, Av. Rovisco Pais, Lisboa, Portugal yordan.garbatov@mar.ist.utl.pt G. Wang American Bureau of Shipping ABS Plaza, Northchase Drive Houston, Texas , USA GWang@eagle.org C. Guedes Soares Unit of Marine Technology and Engineering, Technical University of Lisbon, Instituto Superior Técnico, Av. Rovisco Pais, Lisboa, Portugal guedess@mar.ist.utl.pt Originally published by American Society of Mechanical Engineers (ASME), New York, NY and reprinted with their kind permission. ABSTRACT The corrosion wastage of deck plates of ballast and cargo tanks is analyzed based on a non-linear corrosion model. This model is able to describe an initial period without corrosion due to the presence of a corrosion protection system, a transition period with a nonlinear increase of wastage up to a steady state of long-term corrosion wastage. This model is applied to corrosion wastage data of deck plates collected by the American Bureau of Shipping. The objective of this work is to fit this corrosion wastage model to the service measured data, determining the values of the model parameters that represent the best fit to the data so as to describe how corrosion wastage varies in time as a result of generalized corrosion. INTRODUCTION Corrosion is one of the most critical degrading mechanisms of the structural strength of ships and offshore structures. Various theoretical approaches are available to determine the strength of corroded structures as well as their reliability. All of these approaches depend on corrosion wastage models that describe how the structural degradation evolves with time. The conventional models of corrosion wastage assume a constant corrosion rate, leading to a linear relationship between the material lost and time (e.g. Guedes Soares, 1988). Southwell et al., (1979) proposed a linear and a bilinear model for corrosion wastage which were considered appropriate for design purposes and both are conservative in the early stages of corrosion, and overestimate the corrosion depth at the initial phases of corrosion progress. Melchers, (1998) suggested a steady-state tri linear and another power for corrosion wastage thickness. In fact, experimental evidence of corrosion reported by various authors shows that nonlinear models are more appropriate. Yamamoto and Ikegami, (1998) proposed a corrosion model based on analyzing collected from plate thickness measurements. The corrosion wastage process was considered in three periods: period when the anticorrosive paint coating is effective (including the period of generation of active pitting points), period when pitting points are progressed and period when corrosion process stops and corrosion rate becomes zero. In this model corrosion and wear seen in structural members are assumed to be the consequence of an extremely Non-Linear Time Dependent Corrosion Wastage of Deck Plates of Ballast and Cargo Tanks of Tankers 67

2 ABS TECHNICAL PAPERS 5 large number of pits growing progressively and individually. Guedes Soares and Garbatov (1999) proposed one model that describes the growth of corrosion wastage by a non-linear function of time in three phases. In the first phase, it is assumed that there is no corrosion because a corrosion protection system is effective. Failure of the protection system will occur at a random point of time and the corrosion wastage will start a nonlinear process of growth with time, which levels off asymptotically at a long-term value of corrosion wastage. Since then, several authors have proposed some variants of this model or have compared it with other modifications. Sun and Bai, (1) suggested a time-variant corrosion rate model, adapting the model of Guedes Soares and Garbatov, (1999), to describe the corrosion rate instead of the corrosion wastage thickness. In their model, the corrosion rate increases as an exponential function of time and finally tends to be a constant value in the third phase. Qin and Cui, () assumed that the coating protection system (CPS) deteriorates gradually so that corrosion may start as pitting corrosion before the CPS loses completely its effectiveness. The corrosion rate was defined by equating the volume of pitting corrosion to uniform corrosion. This was regarded as the transition period in which the corrosion rate increases. After the CPS loses its complete effectiveness, general corrosion starts and the corrosion rate decreases due to the increasing thickness of the corroded product. The whole corrosion process was divided into three stages: no corrosion when the CPS is fully effective, corrosion accelerating when the pitting corrosion generates and progresses, and corrosion decelerating. This model is flexible and can describe different other models of corrosion rate using the same format. For a particular value of one of its parameters (β = 1), it becomes the model of Guedes Soares and Garbatov, (1999). The corrosion model of Paik et al., (3) also categorizes the corrosion behavior into three phases, durability of coating, transition to visibly obvious corrosion, and progress of such corrosion. The coating life is assumed to follow the log-normal distribution and the transition time is considered to be an exponentially distributed random variable. A probabilistic model is currently being developed by Melchers, (3), which divides the corrosion process into four stages: initial corrosion, oxygen diffusion controlled by corrosion products and micro-organic growth, limitation on food supply for aerobic activity and anaerobic activity. The proposed model consists of a number of phases, each represent a different corrosion controlling process. To allow the data from the various sites to be compared for preliminary analysis, it was necessary to correct the data for water temperature. Wang et al., (3) collected a corrosion database from measurements made in ships in service and they performed a statistical analysis of the data leading to values of corrosion rate of deck plates in cargo tanks of oil tankers. They derived regression relations of corrosion wastage as a function of time which provide a consistent fitting to the data analyzed. The model of Ivanov et al., (3) model assumes three phases of corrosion wear as the one of Guedes Soares and Garbatov, (1999). However it substitutes the transition phase of nonlinear thickness increase with time by a linear relation. It is seen that in the literature several authors adopt the basic ideas of the model proposed by Guedes Soares and Garbatov, (1999), and modify some details. Therefore it is worthwhile to consider again the adequacy of the model of Guedes Soares and Garbatov, (1999), by comparing it with full scale measured data. The main objective of this work is to fit this corrosion wastage model to a corrosion wastage data set of deck plates collected by American Bureau of Shipping (Wang et al., (3) and determine the values of the model parameters that represent the best fit to the data so as to describe how corrosion wastage varies in time as a result of generalized corrosion. NON-LINEAR CORROSION WASTAGE MODEL The non-linear corrosion wastage model proposed by Guedes Soares and Garbatov (1999) describes the growth of corrosion wastage by a non-linear function of time in three phases. In the first phase, it is assumed that there is no corrosion because a corrosion protection system is effective. Failure of the protection system will occur at a random point of time and the corrosion wastage will start a non-linear process of growth with time, which levels off asymptotically at a long-term value of corrosion wastage. Figure 1 illustrates the time dependent model of corrosion degradation, separated into four phases, where in the first one there is no corrosion ( t [ O, O], in Figure 1). The second phase corresponds to the initiation of failure of the corrosion protection system, which leads to corrosion with the decrease of thickness of the plate (OB-fast growing corrosion). The third phase, BC, corresponds slowly growing corrosion and the last one, (t>c), corresponds to a stop in the corrosion process when the corrosion rate becomes zero. 68 Non-Linear Time Dependent Corrosion Wastage of Deck Plates of Ballast and Cargo Tanks of Tankers

3 ABS TECHNICAL PAPERS 5 dt ( ) τ c τ t plates from ballast tanks with original nominal thicknesses varying from 13.5 to 35 mm on ships with lengths between perpendiculars in the range of to 41 m (see Figure 3). A The second set of data (see Figure 3) includes 4665 measurements of deck plates from cargo tank with original nominal thicknesses varying from 1.7 to 35 mm on ships with lengths between perpendiculars in the range of to 41 m (see Figure 5). d O O B C t 14 Figure 1. Thickness of corrosion wastage as a function of time The model is based on the solution of a differential equation of the corrosion wastage: d () t d = d 1 e t τ c τ () t = t τ c t, t > τ c (1) where d is the long- corrosion wastage, d ( t) is the corrosion wastage at time t, τ c is the time without corrosion which corresponds to the start of failure of the corrosion protection coating (when there is one), and τ t is the transition time duration, which may be calculated as: d τ t = () tgα where α is the angle defined by OA and OB in Figure 1. Although this model has been validated with some corrosion data, it is the purpose of this work to validate it against measured data supplied by ABS, particularly measured corrosion wastage for ship deck plates of ballast and cargo tanks. Since corrosion data has a very large variability, the approach taken has been to model separately the time variation of the mean corrosion wastage and of the standard deviation. This allows the main tendency of the data (mean) to be described by the above corrosion model and the uncertainty of the model to be described by the standard deviation of the errors as a function of time. DATA ANALYSIS Two sets of corrosion data, deck plates of ballast and cargo tanks of tankers provided by ABS, are analyzed here (ABS, and Wang et al., 3a, b). The first set (see Figure 3) includes 1168 measurements of deck No of obs As-built thickness, mm Figure. Data of deck plates of ballast tanks, as-built thickness No of obs <= 14 (16,18] (,] (4,6] (8,3] (3,34] (36,38] (4,4] (14,16] (18,] (,4] (6,8] (3,3] (34,36] (38,4] > 4 Ship length between perpendiculars, m Figure 3. Data of deck plates of ballast tanks, versus ship length between perpendiculars Non-Linear Time Dependent Corrosion Wastage of Deck Plates of Ballast and Cargo Tanks of Tankers 69

4 ABS TECHNICAL PAPERS No of obs No of obs, 1st year As-built thickness, mm Figure 4. Data of deck plates of cargo tanks, as-built thickness No of obs <= 14 (16,18] (,] (4,6] (8,3] (3,34] (36,38] (4,4] (14,16] (18,] (,4] (6,8] (3,3] (34,36] (38,4] > 4 Ship length between perpendiculars, m Figure 5. Data of deck plates of cargo tanks versus ship length between perpendiculars No of obs, 5th year Figure 7. Histograms of corrosion wastage of deck plates of ballast tanks for 1st year Figure 8. Histograms of corrosion wastage of deck plates of ballast tanks for 5th year No of obs, 19th year No of obs, 19th year Figure 6. Histograms of corrosion wastage of deck plates of ballast tanks for 19 th year Figure 9. Histograms of corrosion wastage of deck plates of cargo tanks for 19 th year 7 Non-Linear Time Dependent Corrosion Wastage of Deck Plates of Ballast and Cargo Tanks of Tankers

5 ABS TECHNICAL PAPERS 5 No of obs, 1st year Figure 1. Histograms of corrosion wastage of deck plates of cargo tanks for 1 st year 1 or the time of initiation of corrosion τ c, and the transition time, τ t are defined based on performing a least squares fit to the data using a quasi-newton algorithm, which determines the direction to search used at each iteration considering the mean value of corrosion depth taken from the yearly subset of data histograms (see Figure 6 to 11).! The judgment of the adequacy of approximation is done by: n d l n i R = 1 d / d n i 1 ( i µ = i) i (3) i= 1 i= 1 where n is the total number of measurements, l is the total number of classified years of observation, µ i is the mean value of observations during each year No of obs, 5th year Figure 11. Histograms of corrosion wastage of deck plates of cargo tanks for 5 th year In order to provide a detailed description of the variability of the data, it has been grouped by year and histograms of the measurements in each year are presented in Figure 6 to 11. The frequency scatter diagrams of corrosion wastage, d, are shown in Figure 1 for deck plates of ballast tanks and in Figure 13 for deck plates of cargo tanks respectively. The scatter plots display the frequencies of overlapping points between time and corrosion wastage in order to visually represent the frequencies of the overlapping points and categorize those frequencies according to the number specified in the right hand side of figures as for an example (min=, max=4). The sizes of the point markers in the plots represent the frequencies. The long-term wastage d is defined as the maximum value in the observed time interval for ballast tanks and cargo tanks respectively. The period without corrosion, Figure 1. Frequency scatter diagram of corrosion wastage of deck plates of ballast tanks. There is some variability of the yearly mean values of the data around the regressed line, as can be seen in Figure 14 and Figure 15, which is smaller for the deck plates of ballast tanks ( R =.9) than for the deck plates of cargo tanks ( R =.85). The larger value of R does not necessarily imply that the model will provide accurate prediction. Non-Linear Time Dependent Corrosion Wastage of Deck Plates of Ballast and Cargo Tanks of Tankers 71

6 ABS TECHNICAL PAPERS Deck Plates - Cargo Tanks d =1.91mm τ t =11.5 years τ c = years Figure 13. Frequency scatter diagram of corrosion wastage of deck plates of cargo tanks Deck Plates - Ballast Tanks d =5 mm τ t = years τ c =1.541 years Figure 14. Time dependent mean corrosion wastage of deck plates of ballast tanks The parameters of the regressed line of corrosion depth as a function of time were determined under the assumption that it is approximated by the exponential function given in equation 1. It can be noted that the long-term corrosion wastage for deck plates of ballast tanks is d,ballast = 5 mm and d,cargo = 1.91 mm for cargo tanks respectively. The time without corrosion is τ = 1.54 years in deck plates of ballast tanks and c,ballast τ c,cargo = years for cargo tanks, respectively. Finally, the transition period for deck plates of ballast tanks is τ t,ballast = years and the one for deck plates of cargo tanks is τ t,cargo = 11.3 years. Figure 15. Time dependent mean corrosion wastage of deck plates of cargo tanks The comparison between the corrosion wastage of deck plates of ballast and cargo tanks as a function of time is given in Figure 16. It can be seen that there is a different starting point of corrosion as a result of the different time duration without corrosion. There is also a different final point related to the long-term corrosion wastage already observed during the analysis Ballast Tanks Cargo Tanks % % 8% 6% 4% % % -% -4% Figure 16. Comparative analysis of corrosion wastage of deck plates of ballast and cargo tanks If the service life of ship is split into 5 time zones it can be observed that in the first one from to 1.54 or years there is no corrosion, which is the zone without corrosion. In the second zone that is limited in the time interval between 1.54 or year to year of the 7 Non-Linear Time Dependent Corrosion Wastage of Deck Plates of Ballast and Cargo Tanks of Tankers

7 ABS TECHNICAL PAPERS 5 service life of ship the difference between the corrosion wastage of deck plates of ballast and cargo tanks varies between 1 and percent. In the third zone between and year the difference between the corrosion depth varies between and -9 percent and in the fourth zone between and 8.1 year the difference varies between -9 and which is its minimum and in the time interval between 8.1 to 3 years the difference is reduced up to -3.1 at the 3nd year. Another important statistical descriptor of the data set is the standard deviation, which is given in Figure 17 and 18 for each yearly subset of data. The standard deviation as a function of time is fit to a logarithmic function: St Dev (t) = a Ln (t) - b, (4) which is shown in Figures 17 and 18. Although the figures show a regression line, the correlation coefficient is very low and the regression is not significant. In fact there is a large variability in the data, which is the dominant feature a =.834 b= Figure 17. Standard deviation of the yearly data of corrosion wastage of deck plates of cargo tanks a =.384 b= t, years Figure 18. Standard deviation of the yearly data of corrosion wastage of deck plates of ballast tanks To define the probability density function of the corrosion wastage depth, the observed distribution is fit by a theoretical distribution by comparing the frequencies observed in the data to the expected frequencies of the theoretical distribution and for that purpose the Kolmogorov-Smirnov of fit test is applied here. Several distributions were evaluated and it was concluded that corrosion wastage depth is the best fit by the Log-normal distribution. The mean value and the variance of the long-normal distribution for the corrosion wastage of deck plates of ballast tanks are and.919 and for the corrosion wastage of deck plates of cargo tanks are and 1.46 respectively (see Figure 19 and ). No. of observations Figure 19. Log-normal probability density function of the corrosion wastage of deck plates of ballast tanks for the entire period of 3 years Non-Linear Time Dependent Corrosion Wastage of Deck Plates of Ballast and Cargo Tanks of Tankers 73

8 ABS TECHNICAL PAPERS 5 45 No. of observations Figure. Log-normal probability density function of the corrosion wastage of deck plates of cargo tanks for entire the period of 3 years Corrosion Depth, mm Figure. Time dependent probability density function of corrosion wastage of deck plates of ballast tanks Considering that the corrosion wastage depth can be described by a log-normal distribution function with a mean value and standard deviation changing yearly as indicated in Figure 14 to Figure 18, the probability density function as a function of time of corrosion wastage for cargo and ballast tank are given in Figure 1 and The corrosion rate defined as the first derivative of the corrosion wastage is also analyzed, and presented in Figure 3. The initial values of corrosion rate are determined when the corrosion process start, which is earlier for the plates of cargo tanks in this data set. It can also be observed that the corrosion rate is higher for cargo than for ballast tanks. The corrosion rate is less aggressive in ballast tanks than in cargo tanks for the first 8 years, but after that point the contrary is true. It is also apparent from the figure that the rate of decrease of the corrosion rate is higher for cargo than for ballast tanks Corrosion Depth, mm Figure 1. Time dependent probability density function of corrosion wastage of deck plates of cargo tanks Corrosion rate,mm/year Ballast Tanks Cargo Tanks Figure 3. Comparative analysis of corrosion rate of deck plates of ballast and cargo tanks 74 Non-Linear Time Dependent Corrosion Wastage of Deck Plates of Ballast and Cargo Tanks of Tankers

9 ABS TECHNICAL PAPERS 5 CONCLUSION The non-linear corrosion wastage proposed by Guedes Soares and Garbatov, (1999) was used to describe the corrosion wastage of deck plates of ballast and cargo tanks of the ABS database. The corrosion wastage of deck plates was examined with respect to how the corrosion wastage varies in time. The parameters of this corrosion wastage model were obtained. A non-linear function of time applied here describes the growth of corrosion wastage in three different phases. In the first phase, it was assumed that there is no corrosion. Failure of the protection system occurs at a random point of time and the corrosion wastage will start a non-linear growing process with time. The formulation presented here used the measurements of corrosion wastage as input for creating an exponential function of time that describes the effect of corrosion and thus can be applied for the reliability assessment of different plate elements. The model of corrosion wastage applied to analyze the corrosion wastage of deck plate is flexible enough to represent realistic situations. It was found that there were different corrosion initiation times for plates of ballast and cargo tanks and that the corrosion rates were different as well as the rate by which the corrosion rates decreased with time. ACKNOWLEDGEMENTS This work has been funded by American Bureau of Shipping under the project Condition Assessment of Ageing Ship Strutures. REFERENCES ABS (), ABS Database of Corrosion Wastage for Oil Tankers, ABS RD 7. Guedes Soares, C. 1988, Uncertainty Modeling in Plate Buckling, Structural Safety, Vol. 5, pp Guedes Soares, C. and Garbatov, Y., 1999, Reliability of Maintained, Corrosion Protected Plate Subjected to Non-linear Corrosion and Compressive Loads, Marine Structures, Vol. 1, pp Ivanov, L., Spencer J., and Wang G., 3, Probabilistic Evaluation of Hull Structure Renewals for Aging Ships, Proceedings of the 8th International Marine Design Conference (IMDC), Athens, Greece, pp Melchers, R., 1998, Probabilistic Modeling of Immersion Marine Corrosion, Structural Safety and Reliability, Shiraishi, N.; Shinozuka, M., and Wen, Y. K., (Eds), A. A. Balkema, pp Melchers, R., 3, Probabilistic Models for Corrosion in Structural Reliability Assessment, Part : Models Based on Mechanics. Journal of Offshore Mechanics and Arctic Engineering, Vol. 15, pp Paik, J., Jae L., Joon H. and Young P., 3, A Time- Dependent Corrosion Wastage Model for the Structures of Single and Double Hull Tankers and FSOs and FPSOs, Marine Technology, Vol. 4, No. 3, pp Qin, S., and Cui, W.,, Effect of Corrosion Models on the Time-Dependent Reliability of Steel Plated Elements, Marine Structures, Vol. 15, pp Southwell, R., Bultman, D., and Hummer, Jr., 1979, Estimating of Service Life of Steel in Seawater, Seawater Corrosion Handbook, New Jersey, Noyes Data Corporation, pp Sun, H., and Bai, Y., 1. Time-Variant Reliability of FPSO Hulls. Transactions SNAME, Vol. 19, pp Wang, G., Spencer, J., Sun, H., 3a, Assessment of Corrosion Risks to Aging Ships using an Experience Database, Proceedings of the nd International Conference on Offshore Mechanics and Arctic Engineering, ASME, Paper OMAE Wang, G., Spencer, J., Elsayed, T., 3b, Estimation of Corrosion Rates of Oil Tankers, Proceedings of the nd International Conference on Offshore Mechanics and Arctic Engineering, ASME, Paper OMAE Yamamoto, N., and Ikegami, K., 1998, A Study on the Degradation of Coating and Corrosion of Ship s Hull Based on the Probabilistic Approach, Journal of Offshore Mechanics and Arctic Engineering, Vol. 1, pp Non-Linear Time Dependent Corrosion Wastage of Deck Plates of Ballast and Cargo Tanks of Tankers 75

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