OTC-27808-MS

Validation of Global Riser/Wellhead Analysis using Data from a Full-scale Measurement Campaign Puneet Agarwal, Scot McNeill, Kenneth Bhalla, Stress Engineering Services; Karen Walker, ExxonMobil Upstream Research Company

Copyright 2017, Offshore Technology Conference This paper was prepared for presentation at the Offshore Technology Conference held in Houston, Texas, USA, 1–4 May 2017. This paper was selected for presentation by an OTC program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Offshore Technology Conference and are subject to correction by the author(s). The material does not necessarily reflect any position of the Offshore Technology Conference, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Offshore Technology Conference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of OTC copyright.t.

Abstract

Fatigue damage predictions of risers and wellhead/casing systems due to drilling operations require predictive modeling techniques for load calculation/estimation. This work attempts to address the uncertainty as to whether the global riser analyses are overly conservative due to model idealizations, analytical assumptions, the use of time- or frequency-domain techniques, and incorporation of certain linear or non-linear behavior. To address these questions, a field measurement program was executed to obtain vessel, riser and stack motions data, which were used to validate analytical models and procedures.

A real-time monitoring system was deployed on a 6th generation semi-submersible mobile offshore drilling unit operating in a shallow water, harsh environment region. Accelerations and angular rates were captured on the Lower Marine Riser Package (LMRP), drilling riser and vessel. The metocean data consisting of measured seastates and full-depth current profiles, as well as riser tensions, mud weights, and vessel offsets were also concurrently recorded. The global models of the riser, wellhead, stack, casing and soils were created using two in-house software, DERP (frequency-domain) and RAMS (both frequency- and time-domain), using “as-designed” input information.

Analytically predicted motions (displacements and rotations) of the LMRP, riser, and vessel were compared with the measured motions. It was found that the frequency-domain analytical results match the measured data well over all the measured significant wave heights, which ranged from 6.5-ft to 26-ft. Since the riser and LMRP RMS motions are well predicted by models, it follows that wellhead loads are well estimated from analytical models. The frequency-domain analytical results were further verified for a few cases by time-domain analyses. Both measured and analytical spectra generally exhibit peaks at similar frequencies. While the first analytical riser mode is clearly identified in the measured data, the analytical blow out preventer (BOP) stack/riser mode is not as evident in the measured data. Further, the measured peak close to the analytical stack/riser frequency is very broad. These observations and additional sensitivity studies showed that further investigation for sources of damping due to soil and/or stack hydrodynamics is required.

This work shows that the modeling techniques used presently for analyzing the global riser/stack response in frequency-domain are reasonably accurate for the analyzed conditions.

Introduction Estimation and management of the wellhead fatigue is required to insure the well integrity during offshore drilling operations. The criticality of this topic has increased recently as the fatigue demand due to loads on wellheads have increased with larger BOP/LMRP stacks, in addition to drilling operations being performed in harsher metocean environments. The term “wellhead fatigue” refers to the fatigue damage at the hotspots in the wellhead and casing system. Cyclic loads are imparted to the wellhead by the connected riser, as the riser experiences dynamic motions from waves, vessel motions, and by vortex-induced-vibrations due to currents. The hotspots in the wellhead/casing system include welds, connectors, and also the geometrical features in the wellhead itself.

A number of papers addressing the well system fatigue for offshore environment were published through the 1980s; e.g., Hopper [1], Singeetham [2], King [3], and Valka and Fowler [4]. Again, in recent years, wellhead fatigue has been a topic of significant research and development [5, 6]. A Joint Industry Project was launched in 2014 to address the analysis procedures, and a Recommended Practice DNVGL-RP-0142 [7] on wellhead fatigue analysis was issued in 2015. The RP

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provides a framework for assessing the wellhead fatigue, calling-out the major considerations while avoiding being prescriptive on how to address them. San Pedro et. al. [8] presented a qualititative summary of the uncertainties in analytical predictions of wellhead fatigue life, while considering both the load (i.e., demand) and resistance (i.e., capacity).

Field measurement is another approach that has been used to address the wellhead fatigue. Russo et. al. [9] and Myhre et. al. [10] discussed a comprehensive monitoring campaign conducted during 2014. This real-time campaign directly measured forces and stresses in the wellhead/casing by using strain gages; additional loggers measured stack and riser motions. Grytøyr et. al. [11] showed that the bending moments at the wellhead are directly correlated with the BOP/LMRP motions, especially with rotations, and thus bending moments can be indirectly derived from the measured motions. Similar findings were reported by Russo et. al. [9]. This is an important learning for situations when the wellhead system had already been installed prior to designing a measurement campaign, which is the case for the work presented in this paper, or the implementation of a more instrusive instrumentation system is cost and schedule prohibitive.

Monitoring using only one or two motion sensors installed on the BOP/LMRP, with or without the facility to communicate to the surface, is becoming increasingly popular since it is provides a relatively inexpensive way to monitor well integrity. McNeill et. al. [12] presented an example of using data from stand-alone accelerometers to estimate wellhead fatigue. However, such data are often of limited utility to broader research since insufficient data are being collected.

While monitoring provides real-time or after-the-fact estimates of the wellhead fatigue, predictive analysis for wellhead fatigue is always required for planning and managing drilling operations. The typical analysis procedure used for the wellhead fatigue assessment involves the following number of steps, which are briefly summarized below:

1. Run global riser analysis for the design seastatesthe global model consists of the vessel, drilling riser, BOP/LMRP

stack, wellhead, casings, and soilsand obtain dynamic loads imparted to the wellhead. 2. Combine global loads with results from a detailed finite element (FE) sub-model consisting of wellhead, casings, and

soils to obtain stresses at critical locations. 3. Compute fatigue damage at critical locations using the appropriate Stress Amplification Factors (SAF) and S-N

fatigue curves using Miner’s rule. Clearly, any uncertainties in the global riser analysis will impact the wellhead loads and thus wellhead fatigue estimates.

The industry uses a number of global riser analysis software packages, which have been developed and used since 1980s. One of the first publications on the global riser analysis was in 1978 by Young and Fowler [13]. In 2002, Garrett [14] published the coupled analysis of the floating systems, in which coupling between the riser(s) and vessel has been considered. These two publications provide some of the basis for the riser analysis software DERP [15] and RAMS [16], which have been used extensively for the industry and which are also used for analysis summarized in this paper.

The work presented in this paper validates the global riser analysis procedures with full-scale field data. The objective is to quantify any possible conservatism in the riser analyses and thus in wellhead loads and fatigue estimates. In other words, the focus is to address the “load” side of the wellhead fatigue equation, the “resistance” side being out of scope. Any conservatism in loads due to the design metocean conditions is not the focus of this paper. With this goal, a real-time measurement campaign that was conducted from a 6th generation mobile offshore drilling unit (MODU) was designed and executed. The project site was in a shallow water location (water depth of 85 – 95 m) with harsh environmental conditions. Vessel, riser and stack response was measured using synchronized vibration loggers. All the inputs required in the riser analysis were concurrently measured, which include items such as riser tension variation, and the metocean data. The analytical models were driven both in frequency-domain and time-domain with measured input parameters, and the analytical predictions of riser and stack motions were compared with motions measured in the field. Approximately six weeks of measured data were used for the data analysis and model validation. Another objective of the monitoring system was to provide real-time information to the rig-crew on the riser/stack motions and on wellhead fatigue response and management; these aspects are not discussed in this paper.

The outline of this paper is as follows: the measurement campaign is briefly described; statistical and spectral analyses of data are presented; main sources of model nonlinearities including tension variation and soils are investigated; measured-analytical comparisons are performed; statistical comparisons using the entire of data are first presented followed by the detailed spectral comparison to investigate reasons for similartities and differences; the dynamics of the combined riser/BOP mode is investigated in detail; and finally, wellhead loads and fatigue damages are presented. This paper shows that the presently used modeling techniques for global riser analyses in both the frequency and time domains are reasonably accurate for the analyzed conditions. Important findings on the frequency and damping of the combined riser/BOP mode are summarized.

Description of the Measurement Campaign

The measurement campaign was designed to facilitate comparison between analytical and measured riser and stack response. Subsea Vibration Data Loggers (SVDLs) record the riser and stack response data. Analytical models require a number of inputs which include, mud weight, slip ring tension, vessel offsets, riser tension variation, and the metocean data including wave and current profile data. The measurement system was designed to concurrently record all critical data variables.

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Riser and Stack Vibration Data A real-time wellhead fatigue monitoring system (WFMS) was designed for this site. The system is based on the previous riser fatigue monitoring system (RFMS) developed by SES, which was described by Kluk et al [17] and McNeill et al [18]. The monitoring system consists primarily of a number of Subsea Vibration Data Logger (SVDL) “bottles,” an armored subsea cable containing copper wires, and a portable power/control system. The portable system consisted of a real-time controller, an Ethernet switch, power conditioning, and UPS. The interface control for the SVDLs is performed from a touch-screen interface in the portable enclosure while a remote laptop with a Human-Machine Interface (HMI) provided the user with the results of the online data analysis. Each SVDL is a pressure housing consisting of an accelerometer and angular rate sensor. Electronics within the SVDL perform low-pass filtering, digitize, and record the data. The data from each SVDL is synchronized and combined on the real-time controller. The SVDL data is measured at a sampling frequency of 25.6 Hz. The riser and stack motions occur at frequencies below 1.0 Hz, therefore, sampling rate of the data is quite adequate.

A schematic of a real-time wellhead fatigue monitoring system is shown in Figure 1. For this project, two SVDLs were mounted on the LMRP, one on the riser adapter above the LFJ, one toward the top of the riser and finally one on the vessel.

Figure 1: Schematic of a Real-time Wellhead Fatigue Monitoring System

Tensioner Pressure Data In order to capture dynamic tension variations imparted on the riser and wellhead system by the direct acting tensioners

(DATs), the team utilized pressure transducers close to the tensioner anti-recoil valves to provide an indirect means (through calculation) for determining dynamic tension variation. While strain gauges on the riser or perhaps on the tensioner shackles would be more direct, this method was deemed too intrusive and thus utilizing pressure transducers in the cylinders was deemed to be the least intrusive way for evaluating dynamic tension variation on the MODU.

Tensions (15-min mean) were computed as part of the monitoring system from pressure measurements at the anti-recoil valves. To obtain the mean tension applied to the slip ring (which is used in riser models), the measured tensions from the rod side pressures were adjusted by the weight of the rod, weight of the ring, and known pressure on the blind side of the piston. Mean tensions were relatively constant during the campaign. Note that while this approach provides accurate mean tensions at the slip ring, the dynamic tension variations at the slip ring cannot be captured, as pressure variations that occur in the

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piping between each anti-recoil valve and the rod side of the corresponding tensioner were not measured. Furthermore, the tension variation caused by mechanical friction in the tensioner is unknown. A detailed study was performed using models to quantify the actual tension variation in the riser and its effects on the lateral riser response; this is discussed later in the paper. The vessel position data was measured using dedicated GPS units, from which the magnitude and direction of the vessel offset w.r.t. the well were computed. Vessel offsets were quite small and the vessel was positioned close to the well center. Values of the tension, mud weight, and vessel offset averaged over 15-minutes are used as inputs to the global riser analyses.

Metocean Data Wave and current measurements were captured as part of this monitoring project. A Datawell DWR4/ACM directional

wave rider buoy with integral acoustic current meter was utilized to capture the wave characteristics and surface current data on-site. From the wave rider buoy, wave height, period, and direction were derived. Through water column current direction and speed were captured using acoustic Doppler current profilers (ADCPs).

Raw time series from the buoy were processed by the metocean vendor providing significant wave height, direction, peak period and surface currents. These resulting metocean parameters were taken as the input for the analytical simulations. This paper considers an approximately six-week period timeframe where significant wave heights (Hs) were found to vary from 6 ft to 26 ft. Figure 2a shows the variation of significant wave height during this phase of the campaign. Wave period varied

from 5.7 sec to 20.0 sec. Wave direction and JONSWAP peakedness parameter, γ, were also provided. Points highlighted by red dots in Figure 2a indicate the time segments that were selected for the detailed analysis presented later in the paper. Current speeds at the site were relatively small with near-surface and bottom currents of up to 1.4-knots and 0.6-knots, respectively, as shown in Figure 2b.

All the data (i.e., SVDL, metocean, and vessel offset) were transformed so that direction conventions are consistent. The Cartesian coordinate system of the global riser model is used as the common coordinate and direction system. In this, the Z-axis is upwards, and the X-axis is from aft to fore of the vessel. Planar angles are positive when measured counter-clockwise from the +X direction.

(a) Wave Heights

(b) Current Speeds Figure 2: Measured Wave and Current Data

Analysis of SVDL Data

Data Quality Checks The availability of good-quality data is paramount to the use and interpretation of the vessel, riser and BOP stack motions. Therefore, the recorded acceleration and rotational rate data were extensively checked for quality. In general, vibration data may often contain gross errors such as outliers, segments of constant value, clipping of data, sudden discontinuities, repeated values, missing values, and mean drift. Though the measured motion data in this application were relatively error-free, automated algorithms were run on the data to identify the presence of any such errors. Raw time series of the entire data (i.e., 26 channels of accelerations and angular rates) were plotted and visually examined for errors. The SVDL data were found to be of good quality and free of major errors. The only issue found was that the Logger 9 (one of the two loggers on the LMRP) did not record any data for about a week; the logger was later restarted and the data logging continued. However, this incident demonstrated the importance of building redundancy in stack motion measurements by using two loggers, especially since wellhead response is most directly related to the stack motions.

Batch Statistical and Spectral Analysis Overall statistics, i.e., average, standard deviation, skewness, kurtosis, maximum, and minimum, are computed for each

15-minute data file. Such batch statistics help to visualize overall trends and data quality. They also point to files that need closer examination. For example, a very high kurtosis value may indicate significant outliers in a 15-min segment; raw time trace of such segments would need examination in more detail. Statistics also help perform “sense-checks” on the accuracy of the measured data. For example, SVDL 9 and SVDL 10 provided exactly the same statistics since they are measuring motion

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of a rigid stack on opposite sides. The RMS of vessel heave acceleration was found to be almost perfectly correlated with the significant wave height, which is expected for long-period waves, and this confirms that both the Hs and acceleration data are consistent. Figure 3 shows the RMS accelerations and rotational rates for the logger on LMRP and on the riser flange (on the topmost slick joint).

The spectral content of the data was examined by computing the power spectral densities (PSDs) of accelerations and angular rates. Time-frequency plots showing PSDs for the entire measurement duration are shown in Figure 4. PSDs show several important characteristics of the riser and stack motions. There are three main bands of energy: a 0.1-0.2 Hz band which corresponds to the wave energy, a 0.20-0.25 Hz which corresponds to the first riser mode, and a 0.4-0.5 Hz band which correspond to the combined riser/stack mode. These system modes are discussed in detail later in the paper. PSDs also show that the frequency content is generally similar over the entire six week period.

(a) Logger on LMRP

(b) Logger on the Riser Flange

Figure 3: Plot of RMS Accelerations and Rotational Rate at the Logger on LMRP and on the Riser Flange on Topmost Slick Joint

(a) PSD of Acceleration – Y (b) PSD of Rotational Rate – X Figure 4: Power Spectral Densities (PSD) of Accelerations and Rotational Rate at the LMRP Logger

Integration of SVDL Data Wellhead stresses are more directly related to displacements and rotations than to accelerations and angular rates. Thus,

the measured acceleration and rotational rate data is integrated to obtain displacements and rotations, which are then compared to the model predictions. Integration of data at low frequencies (close to zero) is prone to integration errors. This is because the time integration in the frequency domain is equivalent to multiplication of the ith frequency component by 1/ωi. A small amount of low frequency noise in the acceleration spectrum blows up when converted to displacement since double integration is required. Therefore, a suitable lower cut-off frequency applicable for all data is required. The spectra of the measured SVDL data from all loggers were investigated in detail, and it was found that 0.05 Hz is a suitable lower-cut off frequency. An upper cut-off frequency of 0.5 Hz was used since there is negligible energy in the measured data at higher frequencies. Also, the relative importance of energy at higher frequencies diminishes because of integration; the wave frequency band (<0.15 Hz) is found to contribute almost the entire energy to displacements and rotations.

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Figure 5: Simulated Pressure and Measured Pressure near the

Anti-Recoil Valve

Figure 6: Comparison of the Lateral Response at LMRP with

and without Tensioner

Checks for Main Sources of Nonlinearities The main goal of the measurement campaign is to validate the analytical modeling techniques for the global riser response analysis. Frequency domain (FD) dynamic analysis is appealing for the riser analyses since it captures the stochastic nature of the offshore environment well, and it is computationally very efficient allowing numerous design load cases to be run quickly. However, the frequency domain analysis can only be linear (or linearized to be more precise). Therefore, it is important to check for the effect of nonlinearities in the system. Two sources most relevant for this project are identified to be the dynamic tension variation and potential nonlinearities in soils. These are discussed next. Note that hydrodynamic drag is accurately linearized using statistical linearization.

Dynamic Tension Variation As noted earlier, the applied mean riser tension has been calculated from pressures measured at the anti-recoil valve

(a.k.a. Olmsted valve) on each DAT, known pressures on the blind (low pressure) side of the tensioner piston, and weight of the appropriate tensioner components. Measured pressures correlate well with vessel heave, as would be expected. An example of the pressure variation for each tensioner cylinder is given in Figure 5; the selected time segment corresponds to the time when tensioner pressure variation was largest over the measurement campaign. As a check to ensure that the calculated tension variation is reasonable, a detailed model of the riser tensioning system was built in the SES in-house software STARR and the model driven using measured vessel heave motions. An example of the modeled pressure variations at the anti-recoil valve is shown in Figure 5, along with measured pressures. The simulated and measured pressures correlate well with one another, giving confidence that the observed pressure fluctuations in the field are realistic and explained by the physical processes modeled in the simulation. Pressures were measured at the anti-recoil valves, thus the additional pressure variation that occurs in the piping between the each anti-recoil valve and the rod side of the corresponding tensioner was not measured. This additional pressure variation can be significant. For the case being discussed here, the RMS pressure in the tensioner cylinders predicted by the simulations was approximately 50% larger than the RMS pressure predicted at the location corresponding to the anti-recoil valve. In addition, tension variation caused by mechanical friction in the tensioner cylinder seals was not measured.

An examination of the complete data set shows that the coefficient of variation in measured pressure is less than 4%. Therefore, for the global modeling, a constant mean top tension (over 15-minutes) can be used when comparing the analytical riser and BOP response to measurements. Note that at this shallow water depth site, only four tensioners were used.

To further verify the suitability of a constant top tension boundary condition for the global riser analysis model, another coupled model was built in which the tensioners were explicitly modeled using nonlinear stiffness and damping properties that approximate the mechanical friction, hydraulic pressure drops, fluid inertia, and gas compression effects that are in the tensioner simulation model. Time domain analysis during the time of maximum tension variation showed that the lateral response of the riser and stack with and without these tensioner properties is almost identical, as shown in Figure 6. This confirms that these modeled axial tension variation effects do not affect the lateral riser response for this case.

Note that the effort to determine tensioner properties for use in the global model showed that, in addition to the tensioner properties that correlate with heave and heave velocity, the inertia of the tensioner fluid from the DATs to the tensioner accumulators produces a significant influence on tension variation that correlates with vessel heave acceleration. Time and resource limitations did not permit a detailed assessment of this component of tension variation. Although this analysis shows

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reasonable agreement between measured and modeled riser and BOP stack response, the effect of fluid inertia in this type of riser tensioner system may have a more significant influence on riser and stack response for longer risers and/or more compliant wellhead/casing/soil systems.

Soils Since the frequency domain analysis is linear, the nonlinearity of soil P-Y curves can influence the accuracy of results.

Wellhead and casing response, which is the focus of this project, can be especially sensitive to soils. Therefore, a detailed static nonlinear analysis of the global riser/stack/casing/soil model was performed to evaluate whether the soils are in the linear or nonlinear range.

The nonlinear P-Y springs over the length of casings are derived from the API RP-2A [19] formulation for sand, using site-specific soil properties. Nonlinear static analysis of the global riser/wellhead/casing/soil model was performed for the vessel offsets of 0%, 1%, 2%, and 5% of water depth. The analysis also considered the 95%-non exceedance environment from the site-specific design metocean criteria, which included a current profile with surface speed of 0.6-knots. From the nonlinear static analysis, casing displacements at various depths below mudline were obtained. Corresponding to the displacement at each depth, the “actual” lateral stiffness of soil from the slope of P-Y curve at that displacement at that depth was computed. The actual lateral soil stiffness was then compared to the initial linear stiffness from the P-Y curve. Results are shown in Figure 7, and it is found that the actual lateral soil stiffness is practically the same as the initial linear soil stiffness for small vessel offsets, which are most likely to occur in field. Even for a large offset of 5% of water depth, the differences between the actual and linear soil are not large. This is mainly because the soils at this site are relatively stiff.

It was thus concluded that the initial linear stiffness can be used in static or dynamic models without losing any accuracy. It is noted here that all nonlinearities, including soil stiffness, are accounted for in the static step of the frequency-domain dynamic analysis; the static solutions becomes the configuration about which to linearize for the linear dynamic solution. Furthermore, time-domain nonlinear dynamic analysis was also performed to verify the frequency domain analysis; these results are discussed later in the paper.

Figure 7: Static Casing Displacement and Soil Stiffness at Various Vessel Offsets

Measured-Analytical Correlation

In this section, the measured riser motions (i.e., displacements and rotations) are compared to the motions predicted by the analytical model when the models are driven by inputs recorded at the same time as the riser motions. Recorded inputs consist of waves (height, period, direction, and the JONSWAP peakedness-parameter), currents (speed and direction over the entire depth), riser mud weight, tension, and vessel offset (magnitude and direction). The purpose of this comparison is to validate the analytical models and thus establish the level of confidence/conservatism in the loads applied to the wellhead.

Model Description The global analysis model consists of the entire drilling riser system, comprising the telescopic joint, pup joints, slick

joints, riser adapter, LMRP, BOP, wellhead, casing, and soils. Mean (over 15-minute) tension is used; it has been shown earlier in this paper that the effects of the tension variations due to DATs are small. Soils are modeled using the distributed

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springs based on P-Y curves. The vessel was modeled using its response amplitude operators (RAOs). RAOs were provided at 22.5 deg heading intervals; for other headings, linear interpolation of complex RAO amplitudes was performed.

SES in-house programs RAMS [12] and DERP [13] were used for the global response analysis. Both RAMS and DERP have been used for the industry for nearly two decades. RAMS is a specialized finite element program designed for the efficient static and dynamic analysis of floating systems. In global analysis, large-volume bodies that are typically characterized as being rigid (e.g., the vessel) are modeled in RAMS using rigid body elements. Slender elastic members (e.g., risers) are modeled in RAMS using elastic, nonlinear rod elements which allow for large deflections, finite rotations, and axial stretch. Both the frequency-domain and time-domain analyses can be performed in RAMS. DERP is a planar, small displacement, frequency domain riser analysis program. DERP makes the conservative assumption that wave and current velocities act in the same plane at every point along the length of the riser. Both RAMS and DERP can model both the linear and distributed non-linear soil springs for the static solution. For frequency domain analysis, the hydrodynamic drag term is linearized using statistical linearization as is common practice. In the frequency domain, both programs first solve the statics problem accounting for all modeled nonlinearities. The static solution becomes the configuration about which to linearize for the linearized frequency domain dynamic solution.

The DERP and RAMS models were compared and they provided nearly the same static and dynamic responses. Another global model was also built in the general purpose finite element software ABAQUS [20] using beam elements. The static response from the ABAQUS model was found to be nearly the same as that from the DERP and RAMS software. All the analytical models were built using the “as-designed” model properties prior to the measurement campaign, and no changes were made to models in order to facilitate a better match with measurements.

(a) RMS Displacements

(b) RMS Rotations

Figure 8: Comparison of the RMS Displacements and Rotations Predicted by DERP and RAMS Analysis with Measured Data for

All Seastates at SVDL Locations

Statistical Motion Comparisons for the Entire Data Both RAMS and DERP were run in the frequency-domain using the measured input data, over the entire six weeks of

measurement campaign. One simulation every hour was run, resulting in 938 simulations. Sensitivity checks showed that a 1-hour duration, compared to a longer or a shorter duration, provided a good balance between the computational time utilized and capturing the variability in the environment and the riser motions. The measured seastate parameters were used at each time interval, including using the interpolated RAO corresponding to the measured wave headings.

RMS displacements and rotations at SVDL locations predicted by analysis are compared to measured values. The resultants of the horizontal X and Y directions are used for comparison. Results are presented in Figure 8 and they show that

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RAMS and DERP results match each other very closely as well as match the measured RMS response well. Noise was present in the displacement data for the SVDL on the riser adapter, which tends to artificially increase the RMS during a few time periods. Rotations for the same logger were free of noise, and as seen in Figure 8, measured and analytical rotations for the riser adapter match very well.

These results show that the presently used modeling techniques for analyzing the global riser/stack/wellhead/casing/soil response in RAMS and DERP appear to be reasonably adequate. The close match between the measured and analytical results is obtained using the frequency-domain runs, and the analysis period covers a wide range of seastates (Hs = 6 ft to 26 ft). This shows that the frequency-domain analysis is accurate for the analyzed cases. If statistics (e.g., RMS of motions and stresses, and fatigue) of the resultant direction are of interest, the planar DERP analysis provides results as good as those calculated by the more detailed 3D RAMS model. When the orthogonal components (e.g., X and Y) of motions in the horizontal plane are desired, then 3D RAMS analysis is required. The slight discrepancies in the measured versus analytical (DERP or RAMS) results can be primarily attributed to the inaccuracies in the measured seastates and using the idealized wave spectra.

While the statistics of the measured and analytical motions match reasonable well, the detailed spectral comparison of the measurements and analytical results is performed next in order to understand reasons for similarities and differences.

(a) RMS Displacements (b) RMS Rotations Figure 9: Comparison of the Predicted and Measured RMS Vessel Motions for Each Degree-of-Freedom

Vessel Motion Comparisons Since the drilling riser is excited both by direct wave/current loading along the riser and vessel motions on top of the riser,

it is important to ensure that the analytical vessel motions resulting from measured seastate parameters and provided RAOs match the measured vessel motions reasonably well.

The gravity component, g*sin(θ), was removed from measured acceleration data prior to integration to obtain displacement. The gravitational correction, while always important for low-frequency motion, was found to be critical for surge/sway comparisons for this site. This was because a notch was observed in the measured spectrum precisely where a peak is observed in the analytical spectrum, i.e., at the peak frequency of the wave spectrum. This notch was replaced with a peak in the gravity-corrected spectra, which implies that the g*sin(θ) term was canceling the energy due to the motion of the vessel in the measured data.

Analytical vessel response was computed from vessel RAOs and measured seastate data (Hs, Tp, Heading, γ) using a JONSWAP spectrum, and transferred to the SVDL location. Note that RAOs were provided over 2.5 – 40.0 seconds. Vessel motion outside this range is assumed to be zero. It was found that better correlation between the measured and analytical vessel directional response (e.g., ratio of surge to sway or roll to pitch) could be achieved by slightly adjusting the wave heading values from the “measured” values to the “used” values; the adjustments were generally less than 15 deg. It is important to use the refined heading value when comparing surge, sway, roll and pitch spectra, because the division of energy between surge/sway and roll/pitch is highly sensitive to the heading. However, when resultant offset and tilt statistics are compared, there is less sensitivity to variation in the wave heading.

Several seastates, shown by red dots in Figure 2a, were selected for detailed comparisons of vessel and riser/BOP stack motion spectra. Seastates were selected such that they are approximately stationary within a 1-3 hour period. Measured and analytical vessel motion RMS values for each degree of freedom are compared in Figure 9. In general, the overall comparison between predicted and measured vessel response is found to be good, with analytical RMS values being slightly larger than the measured values.

Vessel motion PSDs were also generally similar between the analysis and measurements. Figure 10a shows an example when the measured vessel motion PSD matches very well with the analytical PSD derived from the JONSWAP spectra and

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vessel RAOs. However, the comparison is less favorable for certain seastates. Discrepancies are more prominent when there are two or more independent components in the vessel motion spectra. An example of this behavior is shown in Figure 10b; on closer inspection of wave data, bi-directional seas were found in this case and the JONSWAP spectrum with long-crested assumption does not model these waves well using a single heading.

(a) Seastate with Hs = 16.4 ft, Tp = 15.4 sec, exhibiting

unidirectional seas

(b) Seastate with Hs = 19.9 ft, Tp = 11.8 sec, exhibiting

bidirectional seas Figure 10: Measured (“Meas.”) and Analytical (“An.”) Vessel Motion PSDs for two Seastates

Figure 11: Comparison of Analytical (“An”) and Measured

(“Meas”) Motion PSDs at LMRP Logger

Figure 12: Comparison of Analytical (“An”) and Measured

(“Meas”) Mode Shapes

Modal Identification for Riser and Stack Modes From the analytical model, natural frequencies and mode shapes of the system are calculated. The two system modes

extracted from the model in the frequency range of interest are the primary riser mode and combined riser/BOP mode (a.k.a. the flagpole mode). The response frequencies for these modes are 0.24 Hz and 0.37 Hz respectively (4.2 sec and 2.7 sec). Comparison of these response frequencies with frequency content in the measured data is of primary interest.

The measured acceleration and rotational rate PSDs at the LMRP logger for the entire campaign are shown in Figure 4. The analytical and measured displacement and rotation PSDs are also shown in Figure 11 for a 15-minute time segment. It can be seen that the measured peak due to the first riser mode at 0.24 Hz is distinct, while the measured peak due to the combined riser/BOP mode is very broad (0.4-0.5 Hz).

To further verify the modes, the mode shapes were identified from the measured data using a simple “peak-picking” method. The Cross Spectral Density (CSD) of motions was computed for one seastate. The CSD was evaluated at the peak spectral frequencies (0.2 Hz and 0.4 Hz). The complex modal vectors were realized using the standard method for mode shapes. The resulting shapes are compared to the analytical mode shapes in Figure 12, and the analytical and measured mode shapes are found to match reasonably well.

The measured riser and LMRP motion PSDs show that the combined riser/BOP mode is highly damped. Such damping of the riser/BOP mode is not typically considered in the analysis and should be a topic for further investigation. The shift in

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OTC-27808-MS 11

measured vs analytical riser/BOP mode frequencies may indicate that the model may not correctly capture the stiffness and/or the added mass of the BOP, wellhead, casing, soil system.

Note that the first riser mode at this site has a smaller natural period than those found in [25]. This can be attributed to the: shallow water depth of 85-95m outside of the critical range of 100-150 m identified in [25], the large and heavy BOP found on 6th generation MODUs (typically 600-700 kips), and relatively high riser tension utilized at the site.

(a) Logger at LMRP (b) Logger at Riser Flange on Topmost Slick Joint

Figure 13: Measured (“Meas.”) and Analytical (“An.”) PSDs for Hs = 16.4 ft and Tp = 15.4 sec

(a) Logger at LMRP (b) Logger at Riser Flange on Topmost Slick Joint Figure 14: Measured (“Meas.”) and Analytical (“An.”) PSDs for Hs = 19.9 ft and Tp = 11.8 sec

Spectral Riser and Stack Motion Comparisons Detailed comparison of the measured and analytical riser and BOP/LMRP stack response was performed for a number of

selected seastates. These seastates are indicated by red dots in Figure 2a. The models were run in both the frequency domain (with appropriate linearization) and time domain (fully non-linear). The resulting analytical responses are compared to measured results. In the comparisons, the analytical results are labeled as:

• FDO - original frequency domain results driven by measured Hs, Tp, Heading, Gamma (JONSWAP Spectrum) and vessel RAOs,

• FD - frequency domain analysis driven by measured vessel motions and wave spectra estimated from measured vessel motions,

• TD - time domain driven by measured vessel motions and wave time series estimated from measured vessel motions. Note that the wave time traces were estimated using measured vessel motions and analytical RAOs. The measured and analytical (FDO) motion spectra are shown in Figure 13 for the loggers on LMRP and on the riser

flange (on the topmost slick joint), for a seastate with Hs = 16.4 ft and Tp = 15.4 sec. It can be seen that the shapes as well as the location of peaks match well between the measured and analytical spectra. The bulk of energy over the wave frequencies (~0.05-0.15 Hz) is captured well in both the measured and analytical spectra. A relatively small amount of energy is present at the first riser mode (around 0.2-0.25 Hz). The combined riser/BOP mode (0.4-0.5 Hz) sees almost negligible energy. As mentioned previously, the measured peak due to the combined riser/BOP mode is very broad while the analytical peak is distinct and narrow-banded. The PSDs also show the global riser response at this site is essentially quasi-static, which is expected for such shallow water sites with long-period waves. Figure 14 shows the measured and analytical (FDO) motion spectra for another seastate (Hs = 19.9 ft and Tp = 11.8 sec); this was the seastate that was found to be bidirectional. For this seastate consisting of two components, discrepancies between the measured and analytical motion PSDs for riser/LMRP are as prominent as they were for the vessel motion PSDs (see Figure 10b).

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12 OTC-27808-MS

Figure 15: Wave Time Trace and Spectrum Estimated from the Measured Vessel Motions. Hs = 21.6 ft, Tp = 18.2 sec

Figure 16: Comparison of Motion PSDs at LMRP Logger for the Seastate with Hs = 21.6 ft, Tp = 18.2 sec.

While the results so far have shown that the frequency-domain (FDO) predictive modeling provides reasonably accurate

riser and stack response, time domain (TD) analysis was performed to further check for effects of any nonlinearities that are not captured in the FDO analysis. The time domain analysis was run using the measured vessel motions (measured by SVDL data) and by the wave time-trace/spectra estimated from the measured vessel motions and analytical RAOs. The sea surface elevation was estimated from the measured vessel displacement and RAOs by inverting the RAO matrix at each wave frequency using a regularization technique to combat the ill-conditioning inherent in the problem. Calculations were performed in the frequency domain. Using the spectra of the measured waves, the frequency domain (FD) analysis was also performed to check the effect of using the idealized (JONSWAP) versus the measured wave spectra.

Results for a seastate with large Hs of 21.6 ft are discussed here. The time trace and spectrum of the estimated waves are provided in Figure 15. It can be seen that the waves are in phase with heave and roughly double the amplitude, as expected from examining the vessel heave RAOs in the expected range of wave energy. The wave spectral shape deviates from the JONSWAP shape somewhat. The peak frequency is lower in the estimated wave spectrum and a small secondary peak is visible. The significant wave height and peak period from the estimated wave spectrum is 22.0 ft and 19.2 seconds, respectively. Note that the significant wave height is slightly higher than the value of 21.6 from the wave buoy, used to construct the JONSWAP spectrum. In addition, the peak period is one second longer. Besides different Hs and Tp values, more energy exists at the natural frequencies. It should be noted that the wave spectrum beyond 0.2 Hz is very difficult to estimate, due to lack of vessel response.

A comparison of the spectra from the three different analytical methods (FDO, FD, and TD) is presented in Figure 16. The measured spectra are also shown for comparison. The features of the analytical motion spectra match the measured spectra better when measured motions and estimated waves are used either in the time-domain (TD) or in the frequency-domain (FD). The FD and TD spectra are similar, which shows the lack of any significant nonlinearities in the system, even for this large Hs of 21.6 ft. The differences in the FD and TD response compared to FDO are primarily due to differences in Hs and Tp, wave spectral shape and motion spectral shape. Differences between FD and TD analysis are primarily due to the fact that wave phases were not retained in in the (smoothed) wave spectrum in FD analysis, while they were retained in TD analysis. In addition for the TD analysis, the fully nonlinear drag formulation has a small effect.

An important observation from PSD comparisons is that the resonant peak due to the combined riser/BOP mode (0.4-0.5 Hz band) is not broadened and flattened due to nonlinearities in time domain analysis. Therefore, the stack mode is likely

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OTC-27808-MS 13

flattened due to a significant amount of damping which could come from BOP hydrodynamics or/and soils. This is investigated next by sensitivities on input parameters.

Investigation of Damping of the Combined Riser/BOP Mode

Recall that the measured peak (over 0.4-0.5 Hz) in LMRP motion PSDs due to the combined riser/BOP mode is very broad. The corresponding analytical peak at 0.37 is distinct and narrow-banded. This implies that the analytical models are not capturing the damping inherent in the combined riser/BOP mode. For this site, these differences at the combined riser/BOP mode did not result in significant differences in the statistics (RMS) of LMRP motions computed from measurements and versus analytical predictions. Therefore, the wellhead loads and fatigue estimates are also not expected to be affected significantly. However, for other sites/conditions, such as deeper waters, or softer soils when there may be significant energy at the combined riser/BOP mode, the analytical RMS predictions may be quite different than the measurements. The wellhead loads and wellhead fatigue predictions would also then be adversely affected. Therefore, it is important to investigate for the potential sources of damping in the combined riser/BOP mode. Two potential sources investigated here are the stack hydrodynamics and soils.

(a) Entire Spectra

(b) Zoomed over BOP Mode

Figure 17: Effect of the BOP Hydrodynamic Coefficients on Damping in the LMRP Displacement Spectra. “Original” Cd = 1.0,

Dhyd =232 in, “Alternate:” Cd = 15, Dhyd = 80.5 in. Hs = 21.6 ft, Tp = 18.2 sec

Damping due to BOP Hydrodynamics

Recently, Holmes et. al. [21] published new hydrodynamic coefficients (i.e., the drag coefficient Cd and the added mass coefficient Ca) based on scaled model tests and CFD analysis of two BOP types; this work is part of the DNV GL Structural Well Integrity JIP. Based on [21], “Alternate” coefficients were chosen for comparison such that Cd = 15 and Ca = 2, along with a hydrodynamic diameter of 80.5 inches (volume equivalent diameter). The standard values typically used in the industry, and which were used in all results discussed so far, are Cd = 1 and Ca = 0.75 (denoted as “Original” case in plots), along with a hydrodynamic diameter of 232 inches (diagonal dimension). The alternate drag properties result in an increased drag loading by a factor of 5.2.

LMRP displacement spectra for the Original and Alternate hydrodynamic coefficients are shown in Figure 17; the measured spectrum is also shown. The increased drag loading from waves due to Cd = 15 (D = 80.5 in) increases the wave excitation on the BOP stack, increasing the response at frequencies below the combined riser/BOP mode. The RMS displacement with Cd = 15 increases by 28% w.r.t. the Original analytical results. The RMS displacement with original properties was 16% lower than the measured value, and it becomes 8% higher than the measured values when the alternate properties are used. Therefore, the alternate properties provide a slightly better match with the measured RMS response.

The resonant response is zoomed-in in Figure 17b. The natural frequency and damping of the first system mode (0.22 Hz) have not changed much because it is primarily a riser mode and riser properties have not changed. Conversely, the decrease in BOP stack added mass has caused the combined riser/BOP mode (0.37 Hz) to increase to 0.42 Hz and the increased damping has caused its spectral peak to become broadened and flattened. It thus seems that the BOP hydrodynamics could be one of sources for damping of the BOP mode as seen from the measured spectra. However, further work is needed to quantify this effect.

It is noted here that if the damping of the combined riser/BOP mode is only due to the drag loading on the BOP/LMRP stack, the damping effect should be seastate-dependent. Such an effect was not obvious in the measured data, though there is some ambiguity due to the broad, flat peak at 0.4 Hz.

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14 OTC-27808-MS

Damping due to Soils The possibility of soil damping leading to the broadening and flattening of the measured spectral peak for the combined

riser/BOP mode is investigated for one seastate (Hs = 7.6 ft and Tp = 11.8 sec). Since the analysis software does not directly model soil damping, structural (hysteretic) damping was added to the beam elements below the seafloor. The values of the

structural damping parameter, η, used for this sensitivity study included 0.01, 0.016, and 0.2. LMRP motion spectra for the

case η = 0.016 are compared to the original η = 0 case and the measured data for rotations about the X-axis in Figure 18. The analytical spectral peaks at the wave frequency (0.08 Hz) and the first system mode (0.24 Hz) are nearly unaltered, while the peak for the second system mode (0.37 Hz) has been broadened and flatted to the point of being barely identifiable. The reason for this is that the shape of the quasistatic response and the first system mode have little motion below the seafloor, where damping is applied. On the other hand, the second system mode (the combined riser/BOP mode) has significantly more motion below the seafloor, engaging the soil significantly. It can be seen that the spectral shape of the analytical peak is now as broad and flat as the measured peak, though the amplitude is smaller.

This indicates that the soil damping could also be one of the sources for damping of the BOP mode as seen from the measured spectra. However, further work is needed to quantify this effect.

(a) Entire Spectra (b) Zoomed over BOP Mode

Figure 18: Effect of the Soil Damping on the LMRP Displacement Spectra; Plot shown for Damping Parameter ηηηη =0 and 0.016. Hs

= 21.6 ft, Tp = 18.2 sec; “An:” Analytical, “Meas:” Measured.

Differences in the Frequency of the Combined Riser/BOP Mode

The analytical estimate of the natural frequency of the combined riser/BOP mode (a.k.a. the flagpole mode) is 0.37 Hz. However, the measured data show a broad-banded peak over 0.4-0.5 Hz corresponding to the combined riser/BOP mode; while it is hard to pinpoint the exact measured frequency over the 0.4-0.5 Hz band of this mode, a frequency of 0.45 Hz is considered for comparisons here. This implies that the soil stiffness and/or the mass of the stack/wellhead/casing/soil system are not representative of the field conditions. The effect of the different values of the stack added mass and soil stiffness on the analytical natural frequency is investigated in this section.

Added Mass Coefficient of Stack

The “Original” added mass coefficient, Ca, for the BOP/LMRP stack used in this work is Ca = 0.75 along with an inertial diameter, D, of 232 inches, which is the largest diagonal dimension for the frame of this stack. The stack hydrodynamics are quite complex and a precise added mass for lateral vibrations is generally not available. It is common practice to treat the

stack as a prismatic section. Since the outer footprint of the stack is rectangular, the added mass is computed as �� =

0.19�� for the flow along the diagonal of a rectangular section, as given in Sarpkaya [22]; here, � is the density of seawater. If the cross-section is treated as circular with diameter, D, then the equivalent added mass coefficient works out to be approximately 0.75.

Based on a Ca = 2.0 (along with a volume equivalent diameter of 80.5 inches) the added mass decreases by 68% compared to the base case. The analytical natural frequencies of the combined riser/BOP mode for different choices of the added mass are shown in Figure 19a. It can be seen that by using Ca = 2 and D = 80.5 inches increases the natural frequency to 0.42 Hz, which is closer to the measured frequency of 0.45 Hz. In other words, the analytical frequency matches better with the measured frequency when the alternate added mass properties are used. As a lower-bound sensitivity, Ca is set to be zero. The analytical frequency with Ca = 0 increases to 0.46 Hz, which is pretty close to the measured frequency of 0.45 Hz; however, this seems to be serendipitous since the added mass is not expected to be zero.

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OTC-27808-MS 15

(a) Effect of the Added Mass (b) Effect of Soil Spring Stiffness

Figure 19: Effect of Different Assumptions for the Added Mass and Soil Spring Stiffness on the Natural Frequency of the

Combined Riser/BOP Mode

Stiffness of Soil Springs

In this project, the nonlinear P-Y springs over the length of casings are used. These springs are derived from the API RP-2A [19] formulation, using the site-specific soil properties. It was demonstrated earlier that the casing displacements for practical ranges of vessel offsets and current speeds are so small that the soil springs are always in the linear range. This is mainly because the soils at this site are relatively stiff sands. Because of soils being in the linear range, the analytical natural frequencies do not suffer from any inaccuracies due to linearization inherent in the eigensolution.

A simple approach is taken to assess the effect of soil spring stiffness on the natural frequency of the combined riser/BOP mode. The soil stiffness values at each depth throughout the casing are multiplied by assumed multipliers ranging from 1.2 to 5.0. The objective is to find how much stiffer soil springs should be such that the analytical frequency (0.37 Hz with no multiplier) matches the measured frequency of 0.45 Hz. Results shown in Figure 19b indicate that the soil springs have be stiffer by more than a factor of 5 for the analytical frequency to match the measured frequency of the combined riser/BOP mode. It is, however, not known if such a multiplier on the P-Y curves reported in the API RP-2A is realistic.

It is noted that alternate P-Y curves for sands have been published recently by Zakeri et. al. [23]. Computations were performed using Zakeri’s P-Y curves for this site to determine if they provide an improved comparison with the analytical frequency for the riser/BOP mode. The natural frequencies found were almost identical to that using the API approach for this case, therefore detailed results are not presented here.

Load versus Resistance

One of the main objectives for the offline analysis performed in this project has been to address any conservatism in the global riser analyses, from which motions and loads at the stack or wellhead are determined for the wellhead fatigue assessment. The results show that the RMS motions of the riser and stack predicted by analysis using existing modeling techniques match well with measurements. It is therefore a good assumption to conclude that the wellhead loads would also be very well estimated from analytical models; recall that Grytøyr [11] showed that the bending moments at the wellhead can be adequately determined from the motions of the BOP/LMRP. This is true for the analyzed conditions, which correspond to the shallow water depth, stiff soils, mild to harsh wave environment, and small current speeds (no vortex-induced-vibrations). It is noted that any conservatism in loads due to conservatisms in the design metocean conditions is not focus of this paper.

Therefore, the next logical step will be to address any conservatism in the resistance side. The main variables on the resistance side include characterization of the material properties, estimation of the SAFs for the hotspots in welds and connectors, and choice of the appropriate S-N fatigue curves. Furthermore, mechanism of the load transfer in the wellhead and the methodology for the fatigue estimation (S-N approach or fracture mechanics or initiation life) may also need to be addressed. Baker and Walker [24] discuss many of these factors that affect the well system fatigue.

Loads on the Wellhead

For the estimation of wellhead fatigue, loads (bending moments and shear forces) at the top of the wellhead are required. Bending moments for this campaign are not directly measured; instead, they are computed via an indirect method which involves computing the bending moments at the wellhead datum from RAMS simulations from all the analyzed seastates corresponding to six weeks of measurements. Since RMS motions predicted by models match well with measurements, it can be assumed that the wellhead loads would also be very well estimated from analytical models. Bending moment histograms are then computed from these simulation results. For each seastate, Gaussian random bending moment time traces are synthesized from the corresponding spectra and rainflow cycles are counted. Histograms are developed from the results of the rainflow cycle count over all seastates. The bending moment range histograms are shown in Figure 20. The loading levels shown here follow similar trends as those presented by Grytoyr et.al. in [25]. Magnitudes of loads are somewhat

16 OTC-27808-MS

different between the two cases; however, the water depth, riser, and weather were also different for the two cases. Importantly for the case analyzed in [25], the first riser natural frequency was predicted to be 0.125 Hz (8-second period), which often falls within the band of high wave energy. As shown in Figure 20, the largest bending moment range observed is in the order of 2,500 kips-ft. Such a large load level is primarily due to the use of the 6th generation MODU with very large stack in a shallow water depth. Grytoyr [25] notes that no evidence is seen of the BOP mode being triggered in the measurements taken for the 130 m case, an observation which holds true for this measurement campaign also.

Figure 20: Histogram of the Bending Moment Ranges at the

Wellhead

Figure 21: Cumulative Fatigue Damage at the Critical Location

in the Wellhead/Casing System

Wellhead Fatigue Estimation

A finite element (FE) submodel of the wellhead/casing/soils is then driven by the RMS wellhead loads obtained from RAMS analysis. Stresses at the hotspots in the wellhead and casings are computed from a static FE analysis. It is assumed that all the dynamic effects are captured in the loads, and thus the stresses obtained from the static FE analysis can be considered as the RMS stresses. This assumption is valid in this case since the global riser/stack response has been found to be quasistatic from the measured data. There is insignificant energy at the first global riser mode, and at the combined riser/BOP mode. Even if the first riser mode and the combined riser/BOP mode were excited, the static FE analysis may be appropriate since the mode shape of the combined riser/BOP mode over the wellhead and casing essentially mimics their static deflection shape from the BOP stack downward. In situations when higher riser and BOP modes are excited, the assumption of the static analysis of the submodel may need to be revisited (while also accounting for the inherent damping in the combined riser/BOP mode).

Using the RMS stress, Tz (of the loads), corresponding Stress Amplification Factor (SAF), and S-N fatigue curve, the damage rate (per hour) is calculated. The damage rate is cumulated over the six-week duration of all analyzed seastates to obtain the cumulative fatigue damage or cumulative fatigue life.

The stresses are computed by two analysis types, namely “planar” and “directional.” In the planar analysis, the effect of changing wave direction at each time is ignored. Stresses at each location are computed from the planar ABAQUS analysis. It is assumed that the same location on the pipe circumference is most stressed irrespective of the direction of waves or wellhead loads. In the directional analysis, stresses at a location are considered to be in the plane of the wave direction. For each seastate, stresses are resolved along the pipe circumference by projecting the computed stresses (in the plane of wave direction) to 72 points (at 5-degree increments) on the pipe circumference. Fatigue damage is computed and cumulated at each of the 72 circumferential points. The directional analysis thus accounts for changing wave direction at each time.

The cumulative fatigue damage at the most critical hotspot in the wellhead/casing system is shown in Figure 21. It can be seen that the fatigue damages from the two methods are on the same order of magnitude, with directional analysis providing slightly lower damage. The planar analysis is more conservative since the directionality is not accounted for and loading at all the time steps is applied in one plane. In the directional analyses, the point on the pipe circumference perpendicular to the wave direction experiences the largest stress.

Figure 21 can also be considered as the so-called “fatigue-meter,” since it provides the accumulation of fatigue damage with time. The monitoring system developed for this project provided relevant information on the stack motion and wellhead fatigue estimates in real-time; it thus helped the project team with operational decisions relating to the wellhead integrity.

OTC-27808-MS 17

Summary and Conclusions

A comprehensive measurement campaign was designed and deployed on a 6th generation semi-submersible mobile offshore drilling unit. The measurement campaign was conducted in a shallow water region and was subjected to a harsh wave environment. The campaign consisted of a real-time wellhead fatigue monitoring system (WFMS) that measured vessel, riser, and stack motions with synchronized accelerometers and angular rate sensors. The metocean data including wave and current data, mud weight, slip ring tension, vessel offsets, and the tensioner pressures were concurrently measured.

This comprehensive measurement campaign had the following two objectives: 1. Perform offline data analysis and validate the analytical models for global riser analysis, in order to estimate the

accuracy or conservatism in the wellhead motions and loads. 2. Provide real-time information to the rig-crew on the riser and stack motions and on wellhead fatigue estimates in

order to assist the project team make operational decisions relating to the wellhead integrity. Both the project objectives were successfully achieved. For the model validation, measured motions on vessel, riser, and stack were compared with the analytical predictions.

Analytical models were driven by inputs (metocean, tension, mud weight, offsets) recorded at the same time. The analytical models were built a-priori using design information; no changes to models were made. Existing modeling techniques for the global riser analysis in frequency and time domains were utilized. Statistics were compared for the entire duration of the campaign, while the detailed spectral comparison of motions was performed for a number of selected seastates. Sensitivities were performed for a few model parameters to better understand the dynamics of the combined riser/BOP mode.

The overall conclusions from the measured-analytical comparison are as follows: 1. The RMS response of riser and stack motions obtained from the frequency-domain analysis match the measured data

well. The match is obtained over the full campaign of approximately six weeks when significant wave heights ranged from 6.4 ft to 26.0 ft.

2. The planar DERP analysis is found to be as accurate as the more detailed 3D RAMS analysis. The 3D RAMS analysis is obviously required when the orthogonal components of response in the horizontal plane are desired.

3. Including the tensioner stiffness and damping in the global model did not change the lateral riser response. Therefore, using mean top tension in the global riser models is appropriate.

4. The measured and analytical spectra of motions are generally similar. Both the measured and analytical displacement and rotation spectra generally exhibit peaks at: wave frequency, first riser mode, and the combined riser/BOP mode.

5. Discrepancies between the measured and analytical spectra are more prominent when there are two (or more) independent components in the seastates.

6. The match between the measured and analytical spectra improves when the measured vessel motions and estimated waves are used to drive models (either in time or in frequency domain) instead of using the measured seastates and a JONSWAP spectrum.

7. The frequency- and time-domain results are almost identical. While frequency-domain analysis is linearized, the time-domain analysis included nonlinearities due to soils, tensioner, and flex joints. The match between the two shows a lack of any significant nonlinearities in the system, even for large seastates.

8. The analytical resonant peaks due to the first riser mode and the combined riser/BOP mode are distinct and typically narrow-banded. The measured peak due to the first riser mode is distinct, while the measured peak due to the combined riser/BOP mode is very broad. The analytical riser/BOP mode peak does not significantly broaden due to nonlinearities in the time-domain analysis, compared to linearized frequency-domain analysis,

9. Measured data showed a significant amount of damping in the combined riser/BOP (a.k.a. the flagpole mode). The alternate drag coefficient, Cd, of 15 along with the volume equivalent diameter increases the damping of the combined riser/BOP mode significantly, causing the spectral peak to be flatter and broader, similar to the 0.4-0.5 Hz peak in the measured data; however, adding soil damping has a similar effect. Further work is needed to quantify this damping effect.

10. The analytical frequency of the combined riser/BOP mode matches better with the measured frequency when the alternate added mass properties (Ca = 2 along with the volume equivalent diameter) are used.

11. Sensitivity analyses showed that the soil springs have to be much stiffer, or the added mass of stack has to be close to zero, for the analytical frequency to precisely match the measured frequency of the combined riser/BOP mode. Further work is needed to determine suitable added mass values for the stack and possibly to determine appropriate P-Y springs for relatively stiff sands.

This paper showed that the RMS riser and stack motions predicted by analysis using existing modeling techniques match well with the measurements. By extension, the wellhead loads would be accurately estimated from analytical models. This is valid for the analyzed conditions, which correspond to the shallow water depth (85-95 m), stiff sandy soils, mild to harsh wave environment, and small current speeds (no vortex-induced-vibrations). In other words, for given metocean conditions, the load side of the wellhead fatigue equation appears to be reasonably predicted by existing analytical techniques both in frequency and time domain.

18 OTC-27808-MS

Acknowledgements

Authors sincerely acknowledge numerous colleagues who provided valuable assistance over the course of this project. Authors also thank Maderra Engineering and Hibernia Management and Development Company Ltd. (HMDC) for their support.

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