Use of DOE methodology for Investigating Conditions that Influence the Tension in Marine Risers for FPSO Ships

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1 st International Structural Specialty Conference 1ère Conférence internationale sur le spécialisée sur le génie des structures Calgary, Alberta, Canada May 23-26, 2006 / 23-26 Mai 2006 Use of DOE

1 1 st International Structural Specialty Conference 1ère Conférence internationale sur le spécialisée sur le génie des structures Calgary, Alberta, Canada May 23-26, 2006 / Mai 2006 Use of DOE methodology for Investigating Conditions that Influence the Tension in Marine Risers for FPSO Ships D. Hawkins 1 and L. M. Lye 2 1 Flexible Design Ltd, St. John s, NL, Canada 2 Faculty of Engineering and Applied Science, Memorial University of Newfoundland, St. John s, NL, Canada, A1B 3X5. Abstract: This paper examined the potential of utilizing the Design of Experiments or DOE methodology for exploring the design parameters and environmental conditions that influence the tension in marine risers for Floating Production Storage and Offloading (FPSO) ships. A resolution IV, fractional (1/8 th ) factorial, was first used to screen the initial design parameters, and then two foldover design augmentation techniques were used to resolve the aliased two-factor interactions effects. The responses for the fractional factorial design were gathered from OrcaFlex, the world's leading package for the dynamic analysis of offshore marine systems. It was found that riser tension is most affected by: vessel offset, wave height, water depth, interaction of wave period and water depth, and interaction of wave height and vessel offset. The resulting predictive model based on these important effects was validated by out of sample testing at design points other than those used in model development. From 20 test cases, the average deviation was about 1.7%, and the highest deviation between the full finite element model and the model developed using DOE was only 3.4%. This paper has shown that by using DOE methodology, a predictive model and the conditions that influence the tension in marine risers for FPSO ships can be examined objectively and accurately, with minimal experimental runs. 1. Introduction FPSO stands for Floating Production, Storage and Offloading. An FPSO system is an offshore production facility that is typically ship-shaped. Oil in the submarine oil field is drawn from the ocean bottom oil wellhead through riser pipes to the surface platform. On the platform, the oil is processed and then stored in onboard storage tanks located in the hull of the vessel. The crude oil is periodically offloaded to shuttle tankers or ocean-going barges for transport to shore. In this paper, the potential of utilizing Design of Experiments or DOE methodology to examine the design parameters and environmental conditions that most influence the tension in marine risers for FPSO ships is presented. An efficient, resolution IV, fractional (1/8 th ) factorial design, was first used to screen the initial design parameters, and then two foldover design augmentation techniques were used to resolve the aliased two-factor interactions effects. The important factor effects were identified and a predictive model was developed and validated. The responses for the fractional factorial design were gathered by ST

2 using the OcraFlex Design and Analysis software, a world's leading commercial software package for the dynamic analysis of offshore marine systems that has been used to design and analyze risers in several countries around the world. At the heart of the software, is a finite element analysis engine that has been specially tailored to suit the unique requirement for design and analysis of marine risers. The seven factors chosen were determined by the input parameters used in the software. The factors chosen for analysis were: drag coefficient for the riser; current speed; wave height; wave period; vessel offset; riser added mass coefficient; and water depth. The response of the system for various combinations of the seven factors was the riser tension, in kilonewton (kn) as measured at the FPSO. In the next section, a brief introduction to experimentation and DOE methodology will be described. This will be followed by the analysis of the fractional factorial design used to investigate the effects of the seven factors on the riser tension. The final model and interpretation of the results will be discussed next and finally some conclusions from this study will be presented. 2. DOE Methodology Civil engineers carry out a fair amount of experimentation in laboratories and in design offices in areas of structural engineering, hydraulic engineering, geotechnical engineering, environmental engineering, etc. We carry out experiments to 1) evaluate and compare basic design configurations, 2) evaluate material alternatives, 3) select design parameters so that the design will work well under a wide variety of field conditions (robust design), and 4) determine the key design parameters that impact performance. The experiments may be computer simulations, laboratory or field experiments. As with most engineering problems, we are often faced with limited time and budget. Hence we would like to gain as much information as possible and do so as efficiently as possible. How would one proceed to conduct such an experiment? In engineering, one often-used approach is the best-guess (with engineering judgment) approach. Another strategy of experimentation that is prevalent in practice is the one-factor-at-a-time or OFAT approach. The OFAT method was once considered as the standard, systematic, and accepted method of scientific experimentation. Both of these methods have been shown to be inefficient and in fact can be disastrous (Lye, 2002; Montgomery, 2005). These methods of experimentation became outdated in the early 1920s when Ronald A. Fisher discovered much more efficient methods of experimentation based on factorial designs. These were further developed to include fractional factorial designs, orthogonal arrays, and response surface methodology. These statistical methods are now simply called design of experiment methods or DOE methods. Basically, DOE is a methodology for systematically applying statistics to experimentation. DOE lets experimenters develop a mathematical model that predicts how input variables interact to create output variables or responses in a process or system. DOE can be used for a wide range of experiments for various purposes including nearly all fields of engineering and science and even in marketing studies. The use of statistics is important in DOE but not absolutely necessary. In general, by using DOE, we can: learn about the process we are investigating; screen important factors; determine whether factors interact; build a mathematical model for prediction; and optimize the response(s) if required. DOE methods are also very useful as a strategy for building mechanistic models, and they have the additional advantage that no complicated calculations are needed to analyze the data produced from the designed experiment. It has been recognized for many years that the factorial-based DOE is the correct and the most efficient method of doing multi-factored experiments; they allow a large number of factors to be investigated in few experimental runs. The efficiency stems from using settings of the independent factors that are completely uncorrelated with each other. That is, the experimental designs are orthogonal. The consequence of the orthogonal design is that the main effect of each experiment factor, and also the ST

3 interactions between factors, can be estimated independent of the other effects (Berthouex and Brown, 2002). Factorial designs in which each of the factors has exactly two levels (a low and a high) are among the most commonly used in industrial experiments. These designs work very well as screening tools. If performed properly, they can reveal the vital few factors that significantly affect the system under study. A two-level design having k factors requires a minimum of 2 k test runs to accommodate all possible combinations of the factor levels, i.e. a full factorial. A full factorial design with seven factors would require 2 7 runs or 128 runs. To save on costly runs, only a fraction of all the possible combinations can be performed. These are called fractional factorial designs and are symbolized as 2 k-p, where k refers to the number of factors and p is the fraction. While cutting out runs saves on costs, it reduces the ability of the design to resolve all possible effects, specifically the higher order interactions. How well the design can resolve the interactions depends on the resolution of the design. For example, a design with seven factors in eight runs (2 7-4 ) a 1/16 th fraction, can only estimate main effects. These designs are known as resolution III designs to indicate that main effects will be aliased with two-factor interactions (2FIs). For screening purposes, resolution IV designs work much better than resolution III designs because of their ability to more clearly reveal main effects. However, two-factor interactions remain aliased with each other. To improve design resolution, a complete foldover can be done when results look significant. It is well known that a complete foldover of a resolution III fractional factorial makes it resolution IV. However, a complete foldover of a resolution IV fractional factorial may not improve matter much as this may create a replicate of the existing runs, rather than a unique fraction. For cases like this, it is better to do a single factor foldover where a second fraction is added in which the signs for only one factor are reversed. This de-aliases the 2FIs involving the foldover factor from other 2FIs, but at double the original runs. A more efficient method is to do a semifoldover that involves only half the original block of runs (Mee and Peralta, 2000). For example, a resolution IV fractional factorial requires only 16 runs, and with a foldover and subsequent semi-foldover, a total of = 48 runs would be required. Details of factorial and fractional factorial designs can be found in Montgomery (2005), among others. 3. Tension in Marine Riser Experiment Flexible risers are the connections between the wellhead on the ocean floor and the surface production vessel. They are used for oil extraction, gas extraction as well as water re-injection to maintain reservoir pressure. Figure 1 shows several riser configurations, The riser is designed to have low bending stiffness and high axial stiffness. This is achieved through a series of helical armor layers and polymer sealing layers, which allows for smaller radius of curvature than steel pipe designed for equivalent pressure. Each riser is custom designed for its particular field application which allows it to be optimized for cost and performance. The riser design process requires input from many different aspects of the overall field development. In some cases there are over 20 variables that are input into the analysis program to determine if the maximum allowable stresses are exceeded. The case selected for this paper was a flexible riser in service that was being analyzed to determine the impact of the environment on riser tension. The factors, and their values, were chosen for this analysis based on actual field conditions, and are given below: A. Drag Coefficient for the Riser ( ); B. Current Speed ( m/s); C. Wave Height (15 25 m); D. Wave Period (12-15 s); E. Vessel Offset (15 25 m); F. Riser Added Mass Coefficient ( ); and ST

4 G. Water Depth ( m). The range of values for each factor was determined in consultation with a lead engineer of the riser analysis group in the first author s company. The response chosen for measurement was the riser tension, in kilonewtons (kn) as measured at the FPSO. A full-factorial two-level design would require 128 runs of the finite element program mentioned above. To save time and cost of running so many runs, a fractional factorial design was used. All statistical analysis was conducted using Design-Expert version 6 software by Stat-Ease, Inc ( 3.1 Fractional Factorial Design A resolution IV fractional factorial experiment was conducted and then a semi-foldover was carried out to resolve any ambiguities arising from the aliasing structure. The fractional factorial (1/8 th ) design summary is shown below: Table 1: Screening Design Summary Factor Name Low Actual High Actual Low Coded High Coded A Riser Drag Coefficient B Current Speed (m/s) C Wave Height (m) D Wave Period (s) E Vessel Offset (m) F Added Mass Coefficient G Water Depth (m) Table 2 gives the aliasing structure for the initial screening experiment. All of the main effects are aliased with 3FIs which is good, but all of the 2FIs are aliased with other 2FIs. It was anticipated that a foldover, or semi-foldover, would be required to resolve any ambiguities of the 2FIs. It is normally assumed that 3FIs and above effects are assumed to be negligible. Table 2 Aliasing structure for initial screening experiment Factorial Effects Defining Contrast I = ABCE = ABFG = ACDG = ADEF = BCDF = BDEG = CEFG Factorial Effects Aliases [Est. Terms] Aliased Terms [A] = A + BCE + BFG + CDG + DEF [B] = B + ACE + AFG + CDF + DEG [C] = C + ABE + ADG + BDF + EFG [D] = D + ACG + AEF + BCF + BEG [E] = E + ABC + ADF + BDG + CFG [F] = F + ABG + ADE + BCD + CEG [G] = G + ABF + ACD + BDE + CEF [AB] = AB + CE + FG [AC] = AC + BE + DG [AD] = AD + CG + EF [AE] = AE + BC + DF [AF] = AF + BG + DE [AG] = AG + BF + CD [BD] = BD + CF + EG ST

5 3.1.1 Effects and Aliases The half-normal plot of effects is given in Figure 2. Points that deviate significantly from the straight line are considered as significant effects. A review of the half normal plot suggested that C, E, G, AB, and AC should be included in the model. However, as this is a resolution IV design, the aliasing structure resulted in all 2FIs being aliased with other 2FIs. A review of the aliasing structure revealed that AB is aliased with CE and FG, and AC is aliased with BE and DG. It is likely that the effect of AB is really the effect of CE as both of these main effects were already present in the model. The effect of AC was more puzzling, as AC is aliased with BE and DG, and neither B nor D were included as contributing main effects. In order to resolve the ambiguity with these 2FIs, a foldover was required. In this case, a single factor foldover was used. It was anticipated that a second foldover (or semi-foldover) would be required, as there are 2 aliased terms, AC and AB. Either factor C or G could be used for the foldover. Factor G was chosen over C because of the fact that G appeared in both alias structures, and was aliased with other main effects that were thought to be more significant. The foldover on G removed all aliases with the factor G and its 2FIs, so it was assumed that DG is a valid contributing effect. The resulting half-normal plot of effects after the single-factor foldover is shown in Figure 3. The presence of AB was still a source of uncertainty as neither A nor B was present as main effects. The new alias structure is given in Table 3. Terms that were not of interest were deleted from the table. Table 3 Aliasing Structure for Factor G Foldover experiment [Est. Terms] Aliased Terms [A] = A + BCE + DEF [B] = B + ACE + CDF [C] = C + ABE + BDF [D] = D + AEF + BCF [E] = E + ABC + ADF [F] = F + ADE + BCD [G] = G [AB] = AB + CE + ACDF + BDEF [DG] = DG + AEFG + BCFG Table 3 shows that factors G and the 2FI [DG] were completely de-aliased, but AB was still aliased with CE. However, since C and E were the strongest main effects, it was concluded that AB was actually CE. It was decided to perform a semi-foldover on factor C, as this required only 16 of the 32 runs of a full foldover on factor C, as the current model included 32 runs resulting from the factor G foldover Semi-Foldover (C) After performing the foldover on Factor G only the runs where C was high (Wave Height = 25 m) were selected. As shown in Figure 4, the half-normal plot of effects after the semi-foldover, CE was the actual effect being represented by AB. The ANOVA table given in Table 4 shows that the model is statistically significant, and the only term that is not statistically significant is D which was included under the hierarchy requirement. The predicted R-Squared value of is in very good agreement with the Adjusted R-Squared value of ST

6 Table 4 : ANOVA for additional design augmentation Factor (C) Semi-Foldover Sum of Mean F Source Squares DF Square Value Prob > F Block C <0.01 D E <0.01 G <0.01 CE <0.01 DG <0.01 Residual Cor Total The resulting regression model in coded factors using the significant effects and the effect D to preserve hierarchy is given by: [1] Riser Tension = C D E G CE DG The final equation in actual factors is: [2] Riser Tension = Wave Height Wave Period Vessel Offset Water Depth (Wave Height)(Vessel Offset) (Wave Period)(Water Depth) This equation was validated by testing a design point midpoint of all the values. The equation predicted a tension of 96.6 kn, and the finite element model produced an answer of 95.2 kn, a difference of less than 2%. This model was further validated using test cases that were not used for model development. In particular, the effect of ignoring the Riser Drag Coefficient and Added Mass Coefficient, that is, A and F, respectively, from the predictive model. Figure 6 shows the comparison for 20 test cases, between the simple predictive model and the finite element program with different combinations of factors A and F. The average percentage error between the finite element program and predictive model was 1.7%, and the highest deviation was 3.4%. In general, the simple predictive model gave a more conservative prediction in that it tends to over predict the riser tension on average by about 1.7%. 4. Interpretation and Discussion This experiment revealed that the tension in this particular riser was a function of wave height, wave period, vessel offset, and water depth. As main effects, all of these factors have a positive effect on tension, as they increase, so does the tension. This is very logical as they all serve to increase the distance between FPSO and the subsea attachment for the riser. The same applies to factor CE (Wave Height * Vessel Offset). As both main effects have a positive effect on the tension, it is consistent that the interaction also has a positive impact on tension. However, the interaction DG (Wave Period * Water Depth) is puzzling. This interaction plot is shown in Figure 5. It has a larger negative effect than the interaction CE has positive effect, yet, wave period was not present as a significant main effect. At the lower water depth, the effect is positive, but at the higher water depth, the effect is negative. The probable physical explanation for this reversal of effect is that there may be some sort of effect involving the natural frequency of a seakeeping response, such as heave or pitch. There may well be other effects that are not being captured as this is still a fractional factorial, and only 48 of the possible 128 runs have been analyzed. It is more likely that the former is more probable than the latter. Despite these minor concerns the model is quite accurate and is a reliable model for navigation of the design space. ST

7 5. Conclusions This paper examined the potential of utilizing the Design of Experiments or DOE methodology for exploring the design parameters and environmental conditions that influence the tension in marine risers for Floating Production Storage and Offloading (FPSO) ships. A resolution IV, fractional (1/8 th ) factorial, was first used to screen the initial design parameters. A single factor foldover followed by a semi-foldover design augmentation technique was used to resolve the aliased two-factor interactions effects. It was found that riser tension is most affected by the vessel offset and wave height, followed by water depth, interaction of wave period and water depth, and interaction of wave height and vessel offset. The resulting predictive model based on these important effects has a predicted R-Square value of and an adjusted R-Square of The model was validated at design points other than those used in model development. From 20 test cases, the average deviation was about 1.7%, and the highest deviation between the full finite element model and the model developed using DOE was only 3.4% although the DOE model generally over predicted the riser tension. This paper has shown that by using DOE methodology, a predictive model and the conditions that influence the tension in marine risers for FPSO ships can be examined objectively and accurately, with minimal experimental runs as compared with say a Monte Carlo analysis. It is likely that if the range of the factors used were larger, there may be nonlinearity effects as well. In this case, the experimental runs can easily be further augmented to form a response surface design which will then be able to model the nonlinearity using a higher order regression model. Other applications of response surface models in civil engineering is given in Lye (2003) and Kandil and Lye (2005). An application in structural engineering is given in Ebead et al (2002). 6. References Berthouex, P. M. and Brown, L. C Statistics for Environmental Engineers, 2 nd Publishers. Edition, Lewis Ebead, U., Marzouk, H. and L. M. Lye Strengthening of Two-Way Slabs Using FRP Materials: A Simplified Analysis Based on Response Surface Methodology, Proceedings 2 nd World Engineering Congress, Kuching, Malaysia. Kandil, K. and Lye, L. M A Design of Experiment Approach to Pavement Responses Evaluation, Proceedings of the 6 th Transportation Specialty Conference, Toronto Ontario, June. Lye, L. M Design of Experiments in Civil Engineering: Are we still in the 1920s?, Proceedings of the 30 th Annual Conference of the Canadian Society for Civil Engineering, Montreal, Quebec, June. Lye, L. M Some Applications of Design of Experiment Methodology in Civil Engineering, Proceedings of the 32 nd Annual Conference of the Canadian Society for Civil Engineering, Moncton, NB, June. Mee, R. W. and Peralta, M Semifolding 2 k-p Designs, Technometrics, Vol. 42, No. 2 (May): Montgomery, D. C Design and Analysis of Experiments, 6 th Edition, John Wiley and Sons, Inc. ST

8 Figure 1 : Several variations of flexible riser configurations (Source : American Petroleum Institute Recommend Practice for Flexible Pipe 17B March 2002) Figure 2 : Half-Normal plot for Resolution IV experiment ST

9 Figure 3 : Half-Normal plot on Data after Single Factor (G) Foldover Figure 4: Half-Normal plot on Data after Factor (C) Semi-Foldover ST

10 Figure 5 : Interaction graph for Wave Period and Water Depth 110 FE Predicted Tension (kn) Line of Perfect Agreement DOE Predicted Tension (kn) Figure 6: Comparison of finite element model with DOE model ST

SOME APPLICATIONS OF STATISTICAL DESIGN OF EXPERIMENT METHODOLOGY IN CIVIL ENGINEERING

SOME APPLICATIONS OF STATISTICAL DESIGN OF EXPERIMENT METHODOLOGY IN CIVIL ENGINEERING Congrès annuel de la Société canadienne de génie civil Annual Conference of the Canadian Society for Civil Engineering Moncton, Nouveau-Brunswick, Canada 4-7 juin 2003 / June 4-7, 2003 SOME APPLICATIONS