Scot McNeill and Kenneth Bhalla, of Stress Engineering Services, show how measured data coupled with engineering analysis can increase asset utilization.
To date, the oil and gas industry has struggled to employ structural monitoring data in meaningful way. The missing link has been the ability to extract and interpret useful information from the data and apply it in a manner that has a significant impact on productivity and utilization.
To design and install successful monitoring systems, engineers with knowledge and experience in signal processing and data acquisition, as well as the mechanics of offshore systems, are needed throughout the entire program.
Some approaches to incorporating measured data into an engineering assessment are highlighted by using an S-N based fatigue analysis as an example. In this type of analysis, fatigue damage is determined using an empirical stress (S) vs. number of cycles (N) relationship. A typical fatigue analysis consists of modeled environmental loads, the structural model that takes in applied loads and outputs stresses, and the fatigue assessment, which computes fatigue damage from structural stresses.
The process for S-N fatigue of offshore structures is:
- Develop environmental loads from limited offshore measured data, using statistical models;
- Apply the environmental loads to a structural model to determine stresses;
- Perform fatigue analysis at critical locations using the calculated stress.
Uncertainty in each of the above is typically dealt with in a conservative manner by engineers, leading to uncertainty stack-up in the fatigue life estimate. The uncertainty is magnified even further by applying large factors of safety (e.g. 10) to the fatigue life estimate, prior to comparing to allowable values. In this way, uncertainty in the environmental load, for example, propagates in a multiplicative manner to the factored fatigue life estimate.
Uncertainty can be reduced in a fatigue assessment by introducing measured data. The data may take the form of environmental loads (waves, wind, current), structural response (motions, vibrations, stresses). Depending on the type of measurements made, the data can be incorporated in a fatigue assessment in different ways, representing different levels of assessment:
- Driven by indirect environmental data – Apply measured environmental data to structural models to determine stresses.
- Driven by indirect motion data – Apply measured structural vibration/motion data to structural transfer functions to determine stresses.
- Direct – Use measured stress/strain data directly in S-N fatigue assessment.
Modeling requirements are highest for level 1 and decrease going down the list, while data requirements (accuracy, completeness and relevance) are highest for level 3. If a level 2 assessment is performed, the uncertainty associated with environmental loads is eliminated, as well as some of the uncertainty associated with the structural model (the portion associated with calculating motions from applied loads), for example. The approach is illustrated in the following examples.
TLP tendon fatigue demand
With continuous metocean and floating production system (FPS) response monitoring the design environment and structural response can be assessed. To maximize the impact of the data measurement program, knowledge of the environment and FPS response with proper data cleansing and analysis techniques need to be integrated. In this example, measured waves and tendon tensions at a tension leg platform (TLP) in the Gulf of Mexico (GOM) were compared with design data to determine the level of conservatism in design. Results were fed into a continued service assessment.
Figure 1: Comparison of measured and design wave data |
The wave time series data and tendon tensions on the TLP were measured over a five-year period, 2006-2011. Figure 1 (left) compares the design wave and measured wave data. In this case, the design wave is very consistent with the measured data at the site. Figure 1 (right) compares measured significant wave height exceedance probability (from five years of FPS data and 14 years of wave buoy data) to metocean design data. Though the wave size in large, low-probability seastates is slightly under predicted in the design data, due to several large hurricanes in the GOM during that period of time, the high probability seastates that are the primary contributors to fatigue are conservative (larger at a given probability level) in the design data.
Figure 2: Comparison of measured and design tendon tension data |
Figure 2 (left) shows the relationship of normalized tendon tension standard deviation to significant wave height over the five-year period, along with analytical RAMS coupled analysis software [1] predictions from the design scatter diagram. It can be seen that the analytical predictions show the same relationship between tendon dynamic response and wave height as the measured data. The scatter in the relationship is primarily due to the wave heading, quartering seas or beam seas, compared to the tendon location, up or down wave. Figure 2 (right) shows (normalized) measured TLP tendon tension standard deviation exceedance probability, along with tensions resulting from the design scatter diagram. In this case, it is clear that the dynamic tendon tension values used in design are conservative compared to the measured values. This is not particularly surprising, considering that conservative assumptions are often made in design. Such a result paves the way for life extension efforts.
Many operators have realized the importance of continuously monitoring metocean conditions and the FPS response to support design verification efforts, evaluate future expansion capacity, and extend the service life of the asset. The value of data from existing monitoring systems can be fully realized when the measurements are integrated into engineering analysis.
Subsea jumper vibration
Figure 3: FE model of subsea jumper with applied force locations (yellow dots) |
Flow induced vibration (FIV) of piping systems is generated by flow restrictions such as elbows, tees and partially closed valves. Vibrations can be severe enough to cause restrictions on production rates. Predictive analysis of subsea piping is limited, due to lack of empirical data for common geometries and flow conditions. An alternative analysis approach, combining in-field measured data and finite element (FE) models can be taken to assess stress and fatigue damage. To obtain accurate results, understanding the nature of random response and applying appropriate data analysis methods are imperative.
Many of the analytical tools and techniques developed for random vibration induced fatigue assume that the dynamic stresses are stationary, narrow-banded and normally distributed. These assumptions must be validated before application of such methods. Measured acceleration power spectral density (PSD) data from a well jumper at a subsea installation is shown in Figure 4 (left). Three vertical, three horizontal in-plane and three horizontal out-of-plane channels were recorded. The data revealed that the dominant direction of vibration was vertical (green, red and yellow lines). Though many modes were excited, only two modes contributed significantly to vertical acceleration (4.5 Hz and 6 Hz modes). Computation of the statistics, including bandwidth parameter, skewness and kurtosis confirmed that the vibration is classified as narrow banded and normally distributed.
Figure 4: Acceleration spectrum for subsea jumper in FIV |
Under the assumptions, the peaks or cycles in the vibration time history should follow the Rayleigh distribution. This is confirmed by comparing the measured acceleration cycles to the theoretical Rayleigh distribution in Figure 5.
Figure 5: Measured (rainflow) acceleration cycles with theoretical Rayleigh distribution. |
After verifying the nature of the random vibration and building the FE model (Figure 3), the forcing function was determined such that the predicted acceleration PSD matches the measured acceleration PSD for all peaks (vibration modes) and all sensors. In the process, the true natural frequencies and mode shapes are identified from the measured data, using operational modal analysis techniques.
The FE model is then refined such that the FE natural frequencies and mode shapes are in close agreement with the measured values. The predicted acceleration PSD, from FE analysis, is shown in Figure 4 (right). The resulting analytical stress PSD is then re-examined to ensure that it is narrow-banded before applying the classical spectral fatigue damage calculations. By merging the measured subsea vibration data into the fatigue assessment, FIV effects on subsea piping can be accurately assessed. More information on the method and applications can be found in the paper co-authored by BP [2], including discussion on handling nonstationary and non-Gaussian vibration.
Conclusion
The industry has started to take advantage of measured data for analysis of offshore structures. The case for incorporating measured data will strengthen over time, as the benefits of doing so are continually demonstrated. Enterprising companies will be quick to embrace the heightened safety and efficiencies gained by utilizing measured data, rather than waiting for competitive pressures or regulatory decree to provide the impetus.
References
_{1. Garrett, D.L., Gordon, R.B. and Chappell, J.F., “Global Performance of Floating Production Systems,” May 2002, OTC 14230.}
_{2. Urthaler, Y., Breaux, L., McNeill, S., Luther, E., Austin, J. and Tognarelli, M., “A Methodology for Assessment of Internal Flow-Induced Vibration (FIV) in Subsea Piping Systems,” June 2011.}
Kenneth Bhalla is a principal at Stress Engineering Services in Houston, where he has worked for 18 years, and leads the drilling systems group. Bhalla holds a B.Sc (Eng) and M.Sc (Eng) in aeronautical engineering with fluid and structural mechanics, and mathematics, from Imperial College University of London. He also holds a PhD in theoretical and applied mechanics from Cornell University.
Scot McNeill is a principal at Stress Engineering Services. He specializes in dynamics, vibrations, signal processing, dynamics and random processes and has been working on structural monitoring systems. McNeill holds BS and MS degrees in engineering mechanics from the University of Wisconsin at Madison and a PhD in mechanical engineering from the University of Houston.