GB2550192A - Pipework Fatigue Lifetime Measurement - Google Patents

Abstract

A method for measuring stress in a structure is provided, wherein the structure is a subsea structure. The method comprises receiving acceleration data captured at each of a series of time points from each of one or more accelerometers 11, each of the one or more accelerometers being attached to a respective position on the subsea structure; applying the acceleration data to a virtual model of the subsea structure; and calculating, from the virtual model, a respective stress resulting from the applied acceleration data at one or more locations on the subsea structure. An apparatus, computer program and computer readable medium are also provided.

Description

PIPEWORK FATIGUE LIFETIME MEASUREMENT

Background

Though the evidence of pipework failure subsea is rare, the consequences can be catastrophic. Until a few years ago, vibration induced fatigue was not considered a major threat to the integrity of subsea systems, but as flow rates increase, and the need for flexibility and mobility in the piping to accommodate the impact of HPHT (High Pressure, High Temperature) becomes a key design requirement, so vibration is now being carefully considered, with subsea engineers taking the dilemma back to the drawing board.

There are a number of different aspects and challenges associated with vibration induced fatigue as an integrity issue subsea. Assessment of subsea systems has largely been limited to vortex induced vibration (VIV) of riser systems and unsupported pipeline spans (i.e. vibration caused by environmental loading) due to flow past the outside of a riser, conductor or pipeline. Piping vibration due to process excitation has only now started to become a recognised issue on manifolds and jumpers, in part associated with increasing production rates leading to higher fluid velocities. As well as piping integrity issues, additional vibration related problems have also been experienced with valves and instrumentation.

Published data suggest around 20% of pipework failures (topsides) which lead to hydrocarbon release may be caused by vibration induced fatigue. To date, on subsea systems, the number of actual failures has been much lower, although there have been a number of instances of high levels of vibration being experienced which have resulted in a lowering of production rates until a fix was put in place. Though the likelihood of a failure is low, the consequences of a failure can be high, resulting in an unacceptable level of risk.

There is currently no known method to continuously monitor subsea fatigue and predict fatigue lifetime. Convention and regulation currently dictate that fatigue must be evaluated and predicted before deployment. A simple spreadsheet technique is used when a pipeline is commissioned to assess any potentially at risk areas on the build. Operating data and data from Piping and Instrumentation Diagrams (P&IDs) are entered and the data is screened against industry standards and Likelihood Of Failure (LOF) is highlighted. The estimate of fatigue is rarely updated and it is manifestly inaccurate. Such an approach is inadequate for such high risk deployments and, as indicated above, the consequences of failure of the build could be catastrophic.

Typically in order to estimate the fatigue lifetime of a structure one must consider the dynamic stresses on that structure. Piping design and construction can present a number of unique challenges to this, particularly in a subsea environment given its remoteness and complexity to access. Vibration issues may occur subsea without any obvious sign topsides and subsea estimation must compensate for external factors such as water loading which will affect the natural frequency of the structure. It has previously been proposed to detect fatigue in subsea pipeline structures by applying variable vibration monitors in-situ and then inferring fatigue damage by linking the measurement data with a suitable simulation. However known techniques are expensive and inaccurate as they may miss the location of the vibration and the sensors are difficult to retrieve data from. Another challenge relates to the often limited real-time capability of the measurement instrumentation. Fatigue damage can be accrued quickly given the relatively high response frequencies in subsea pipework, and the delay which often occurs between a measurement being taken and the subsequent recovery and analysis of vibration data. In some cases the analysis is completed weeks after the measurements have been obtained which can build in an unacceptable level of risk.

Vibration monitoring techniques have also been used in above-water systems to estimate fatigue. These techniques typically involve a two-step calculation. A strain gauge is first attached to a structure near the position where the stress is to be determined and the measured strain is converted into stress by multiplying the measurement by the Young’s modulus of the structure material. This calculated stress is then multiplied by an appropriate stress concentration factor to determine the stress at a particular location such as a weld toe. The stress concentration factor takes into account the structure and weld geometries, and any other appropriate factors. These techniques are inadequate for complex subsea piping structures because, for example: in order to use a single strain gauge the strain (and stress) must be uniaxial; the transducers are difficult to mount and surface preparation is generally required; the transducers and wiring can be sensitive to measurement errors; and the transducers can be easily damaged. However perhaps most importantly in the present scenario such systems are inadequate because the transducers are not suitable for subsea installation and the transducers would need to be mounted before submersion which may not be practicable and the installation may be damaged during submersion.

An alternative method used for fatigue estimation in above-water structures is to monitor the displacement of a structure using GPS. This is typically performed on large, fixed structures such as bridges. GPS variations are recorded to build up a picture of the displacements of the sensors on the structure. These displacement measurements can be used to provide an indication of stress on the structure and potential fatigue. Due to signal attenuation and the need for line of sight in GPS systems such an approach is not suitable for subsea deployments.

Subsea deployments therefore introduce a degree of complexity when attempting to accurately estimate fatigue which not previously been overcome.

There also does not currently exist a practicable system that considers the stresses on a piping structure caused by the internal fluid. Known systems for fatigue lifetime analysis are aimed at above water, fixed structures such as bridges where the stresses are consistent and are caused by external forces. It is known to monitor corrosion and erosion using specific sensors however these can only monitor effects at particular locations and are problematic to install.

Known methods of fatigue lifetime analysis are inadequate since the complexities of piping structures and subsea piping structures have not been addressed. Improvements are needed, especially as the risks are high as the industry adapts to cope with increased flow rates and HPHT.

Summary of the invention

The present invention demonstrates that dynamic stress calculations can be measured or calculated from in-service measurements to monitor and predict fatigue, particularly in subsea environments. Various aspects of the present invention, either in combination or in isolation, can provide an online, dynamic fatigue monitoring and prediction system which can be based on continuous data.

According to a first aspect of the invention, there is provided a method for measuring stress in a structure, wherein the structure is a subsea structure. The method comprises: receiving acceleration data captured at each of a series of time points from each of one or more accelerometers, each of the one or more accelerometers being attached to a respective position on the subsea structure; applying the acceleration data to a virtual model of the subsea structure; and calculating, from the virtual model, a respective stress resulting from the applied acceleration data at one or more locations on the subsea structure.

The invention provides an accurate, optionally real-time, method of understanding and measuring the fatigue in a subsea structure. The use of accelerometers to determine stress is advantageous as they are easy to install and can be clamped to the structure prior to submersion or subsea, for example retrofitted. Moreover the equipment is generally robust. When the stresses are applied within a virtual model, the fatigue lifetime can be accurately evaluated at substantially all portions of the structure to significantly mitigate the risk of failure. The use of accelerometers to adjust a virtual model allows for the sensors to be effectively calibrated and positioned to improve the detection of stress data relative to known systems.

Applying the acceleration data to the virtual model may comprise: deriving displacement data from the received acceleration data; and applying the displacement data to the virtual model of the subsea structure. The stress can then be determined from the displacements rather than directly from the acceleration data. Both are computationally contemplated. The method adopted could be user-selectable or set at installation for example based on the requirements of the operator or the environment in which the sensors are to be deployed.

Deriving displacement data may comprise deriving a displacement of each respective position on the subsea structure based on the acceleration data and applying the displacement data to the virtual model of the subsea structure may comprise updating the virtual model of the subsea structure by virtually displacing, for each respective position of the subsea structure, a corresponding position of the virtual model by the derived displacement for that respective position. This ‘virtual displacement method’ at a static point requires few calculation steps to derive a model of the stresses. Such a method is highly accurate and can derive a large amount of detail from the results.

The step of applying the acceleration data to the virtual model may comprise: optionally, deriving velocity or displacement data from the received acceleration data; converting the received acceleration data, or the derived velocity or displacement data, for the series of time points into the frequency domain, for example by fourier transform; and updating the virtual model by applying a plurality of virtual vibrations to the virtual model at a respective plurality of different frequencies, each frequency corresponding to a vibration mode of the virtual model, either sequentially or simultaneously; and calculating the respective stress from the virtual model comprises, for each of the at one or more locations on the subsea structure: summing stress data calculated from the virtual model for each vibration mode; wherein either the magnitudes of the virtual vibrations applied to the virtual model are weighted, or the stress data calculated from the virtual model for each vibration mode is weighted before summing, in each case the weighting being based on the converted acceleration, velocity or displacement data. In this aspect, the summing step could be automatically performed in the output from the model, if for example all vibrations are applied simultaneously, or could be performed in a second step for example by integrating over the frequency space. Such an analysis allows the virtual model to consider the stresses resulting from multiple different frequencies of vibration simultaneously. Each mode of vibration will have a different effect on the structure to a greater or lesser extent and will each contribute together. The application of acceleration data described allows for the model to consider how each vibration frequency will stress and fatigue the structure. This analysis method is computationally efficient and therefore faster for deriving the desired stress data as compared with the virtual displacement method, but ultimately provides a lower level of detail as to the local of the stresses experienced by the structure.

The virtual model may be a structural model, preferably a finite element model, a finite volume model or a finite difference model. Such models provide for an accurate indication of the stresses on the structure.

The acceleration data may comprise one or more of: (a) substantially real time data received from the one or more accelerometers; and (b) historic data previously recorded from the one or more accelerometers. It is contemplated that data from only one accelerometer needs to be used, whether real-time data or historical, however preferably data from a plurality of accelerometers may be used to improve accuracy. Real-time data may improve the accuracy of the system and historic data may be more readily available and open to detailed analysis. A combination of both data types may allow for calibration, efficiency benefits and also accuracy benefits as the model may be able to build up a complete picture of the stresses on the structure over time in order to better understand fatigue lifetime. Historic data may need to be used where the output from the sensors cannot be linked directly to the necessary processing equipment, for example in remote areas, or if the accelerometers have already been in-situ for other purposes. In this latter scenario, previously recorded data can be analysed and processed to derive the virtual model.

It is strongly preferable that the one or more accelerometers may be attached to respective positions on the subsea structure which positions are underwater. The positions may be determined or recommended automatically from an initial virtual model to provide an accurate picture of the stress on the structure. In some embodiments the positions may be either side of a curvature of the structure whereas in some embodiments, where the analysis considers the frequencies of vibrations, a single sensor may be placed proximate to a point of curvature. The acceleration data may be captured from a plurality of accelerometers. It may be preferable if the model is to be derived from the summing of stress data calculated from the virtual model for each vibration mode to position the sensors at the ‘anti-node(s)’ of interest, that is, a sensor between each pair of nodes in each vibration mode. This can be considered to be at the point at which the sensor will receive the most displacement or movement for each frequency to be summed. It may be preferable to provide one sensor for each known vibration mode.

The method may be performed repeatedly, with each subsequent repetition being performed using respective acceleration data captured at at least one subsequent time point. The acceleration data may be captured substantially continuously and the method may be performed substantially continuously on the received acceleration data so as to calculate respective stresses at the one or more locations on the subsea structure at a substantially continuous series of time points. Thus the accuracy of the model is improved over time.

The subsea structure may be a subsea pipe structure, which introduces complexities into the modelling relative to above-water and subsea structures of fixed or substantially fixed nature and those not carrying fluid.

In a second aspect of the invention, a method is provided for measuring stress in a structure, wherein the structure is a pipe structure. The method comprises: receiving measurement(s) of at least one property of a fluid contained within the pipe structure, the measurement(s) indicating value(s) for the at least one property of the fluid at at least one respective position(s) at a point in time, the at least one property including a flow rate of the fluid; updating a first virtual model of the fluid contained within the pipe structure by setting, for each of the at least one respective position(s), virtual fluid properties at a corresponding position of the virtual model to the value(s) indicated by the received measurement(s) for that respective position; calculating, from the updated first virtual model of the fluid contained within the pipe structure, respective static and dynamic pressures of the fluid at one or more points within the pipe structure; deriving a forcing function representing the force applied by the fluid on the pipe structure based on the calculated respective static and dynamic pressures of the fluid at the one or more points within the pipe structure; applying the forcing function to a virtual model of the pipe structure; and calculating, from the virtual model of the pipe structure, a respective stress resulting from the applied forcing function at one or more locations on the pipe structure. The fluid could be liquid, gas or multiphase fluid. This aspect of the invention allows for the internal forces exerted on pipework by the internal fluid in the pipe to be effectively evaluated and fatigue estimated in a hitherto unknown manner. Previous solutions have focussed on the external effects of the pipework such as corrosion or erosion but this solution allows for specific at risk areas to be identified and risk mitigated. This approach is well suited to subsea environments but can also be applied above water and in non-marine environments such as the chemical industry.

The first virtual model of the fluid contained within the pipe structure may be a one-dimensional or three-dimensional computational fluid dynamics model. The at least one property of the fluid of which measurement(s) are received may further comprise: a pressure of the fluid, a temperature of the fluid and/or a density of the fluid; wherein the respective positions at which each property is measured may be the same or different. The additional measurements will thus improve the accuracy of the first virtual model and ultimately the stress calculations. Preferably the flow is measured at a single location upstream in the pipe, that is, at the beginning of the pipeline, and the pressure at a single downstream location. If the fluid is multi-phase then it is preferably important to measure the pressure as it is typically difficult to estimate.

The measurement(s) of the at least one property of the fluid contained within the pipe structure may comprise one or more of: (a) substantially real time measurements received from one or more sensors within the pipe structure at the at least one position; and (b) historic data previously recorded from one or more sensors within the pipe structure at the at least one position. It is contemplated that data from only one fluid or pressure sensor needs to be used, whether real-time data or historical, however preferably data from a plurality of sensors may be used to improve accuracy. Real-time data may improve the accuracy of the system and historic data may be more readily available and open to detailed analysis. A combination of both data types may allow for calibration, efficiency benefits and also accuracy benefits as the model may be able to build up a complete picture of the forces on the structure over time in order to better understand stresses and fatigue lifetime. Historic data may need to be used where the output from the sensors cannot be linked directly to the necessary processing equipment, for example in remote areas, or if the accelerometers have already been in-situ for other purposes. In this latter scenario, previously recorded data can be analysed and processed to derive the virtual model. Typical pipework already comprises pressure and flow sensors and these may be used to provide the analysis.

All of the above may be performed using a single virtual model of fluid but preferably the method uses two virtual models, in the manner described below.

Calculating the respective static and dynamic pressure of the fluid at one or more points within the pipe structure may comprise: calculating, from the first virtual model of the fluid contained within the pipe structure, a flow rate of the fluid at at least one point within the pipe structure; updating a second virtual model of the fluid contained within the pipe structure by setting, for the or each point, a virtual flow rate at a corresponding point of the second virtual model to the calculated flow rate for that point; calculating, from the second virtual model of the fluid contained within the pipe structure, the respective static and dynamic pressure of the fluid at the one or more points within the pipe structure. The first virtual model thus considers the effects of the fluid over time and at different points along the course of the fluid. It could be described as a ‘virtual flow meter’. The second virtual model can be considered to calculate pressure acting on the walls of the pipeline based on the flow measurements provided by the virtual flow meter. A resolution of the first virtual model of the fluid contained within the pipe structure may be lower than a resolution of the second virtual model of the fluid contained within the pipe structure.

The second virtual model of the fluid contained within the pipe structure may be a computational fluid dynamics model, preferably a three-dimensional computational fluid dynamics model.

The method may be performed repeatedly, with each subsequent repetition being performed using respective measurements of the at least one property of the fluid contained within the pipe structure at the at least one respective position at a subsequent point in time. The method may further comprise: storing the calculated respective static and dynamic pressure of the fluid at the one or more points within the pipe structure for the calculated flow rate of the fluid at the at least one position within the pipe structure; and for a subsequent calculation of a subsequent respective static and dynamic pressure of the fluid at the one or more points within the subsea structure based on a subsequently calculated flow rate of the fluid at the two or more points within the pipe structure, determining whether a calculation of the respective static and dynamic pressure of the fluid at the one or more points within the pipe structure has previously been stored, and, if so, calculating the respective static and dynamic pressure of the fluid at the one or more points within the pipe structure by retrieving the previously calculated value. Computational fluid dynamics can be computationally expensive. This sophisticated approach allows for computation to be performed on an as needed basis thus improving the speed and efficiency of the system.

The pipe structure may be a subsea pipe structure, which introduces complexities into the modelling relative to above-water and subsea structures of fixed or substantially fixed nature. The above aspects may be performed together to produce a more effective, accurate and complete model of the stresses on and the fatigue of subsea pipework structures both internally and externally. Such a combined method may be performed using acceleration data captured over substantially the same period of time as that in which the measurement(s) of the at least one property of the fluid are made.

The combined method may compare the respective stress at the one or more locations within the subsea pipe structure calculated by the first aspect with the respective stress at the one or more locations within the subsea pipe structure calculated by the second aspect. This may result in a more complete model of the stress at that location.

Additionally, the model of the method of the first aspect may be used to calibrate the model of the method of the second aspect and vice versa. For example when the measurements are taken over the same time period in each method, then the stresses derived in the two methods can be compared to adjust the model and/or sensors of the other. Further the models and stresses derived from each method above may be compared to the model of the other aspect over the same time period and the differences analysed to examine the stresses and forces on the structure, which may be of interest in itself. For example, the method of the first aspect will be influenced by external forces (such as water pressure) whilst that of the second aspect will not. Therefore any difference between the results of the two methods can be attributed to external influences and may provide useful data relating thereto.

One or either of the first aspect or the second aspect may be used to calculate the respective stress at the one or more locations on the subsea pipe structure based on previously recorded historic data and the other of either the first method or the second method may be used to calculate the respective stress at the one or more locations on the subsea pipe structure based on substantially real time data.

The following features apply to the method of the first aspect, the method of the second aspect and/or the combined method.

For each repetition, the method may comprise recording the respective stress of the one or more locations on the structure in association with a timestamp, so as to generate time-series stress data for the one or more locations on the structure. An accurate picture of the stress over time can thus be derived. The combined method may further comprise: determining a stress cycle count or frequency from the time-series stress data. The combined method may further comprise: comparing the stress cycle count or frequency to a predetermined threshold and taking a predetermined action if the stress cycle count or frequency is above the predetermined threshold. The method is thus able to proactively mitigate risk in subsea pipework environments. The predetermined action may be triggering an alarm, thus alerting operators to a potentially catastrophic situation or a potential fatigue related issue.

The method may further comprise determining a remaining fatigue life of the structure based at least in part on the time-series stress data. Determining the remaining fatigue life of the structure may comprise comparing the stress cycle count or frequency to a predetermined maximum stress cycle count or frequency for the structure. The method may further comprise outputting an indication of the remaining fatigue life of the structure. The indication may be a qualitative indication, such as a traffic light warning system, or a quantitative indication, such as an estimate of the fatigue lifetime in months or years, or both qualitative and quantitative indications. In this way the method is able to accurately and efficiently alert operators to an expected fatigue lifetime such that actions can be taken in advance of pipe failure.

In any of the above aspects, the virtual model of the structure may be a calibrated virtual model representing the characteristics of the structure when the structure is under operating conditions. The accelerometers and virtual model provide for improved calibration relative to vibration monitoring or strain based monitoring solutions and thus the virtual model is able to more accurately reflect the real-time conditions than other known monitoring and measuring solutions.

The method may further comprise calibrating the virtual model to generate the calibrated virtual model by: receiving vibration data for the structure captured while the structure is under operating conditions; determining modal properties of the structure while the structure is under operating conditions based on the vibration data; and modifying the virtual model so that the modal properties of the virtual model substantially match those of the structure while the structure is under operating conditions, wherein modifying the virtual model comprises one or more of: modifying one or more boundary conditions of the virtual model; and modifying one or more values representing a mass of a respective one or more elements of the virtual model. The vibration data may be received from the one or more accelerometers.

The structure may be a pipeline. In the second and combined aspects the fluid contained within the structure may comprise oil, gas, water or any combination thereof.

In a further aspect, there may be provided an apparatus adapted to carry out the method of any of the above aspects. In a further aspect, there may be provided a computer program which, when executed by a processor, causes the processor to carry out a method according to any of the above aspects. In a further aspect, there may be provided a computer-readable medium storing the computer program.

Detailed Description

Examples of systems and methods in accordance with the invention will now be described with reference to the accompanying drawings, in which:-

Figure 1 shows a high-level process diagram of a first embodiment;

Figure 2 shows a part of an exemplary finite element model;

Figure 3 shows a lower-level process diagram of the embodiment of Figure 1; Figure 4 shows two exemplary mathematical outputs;

Figures 5 and 6 shows exemplary processes of two methods of determining stress;

Figure 7 shows exemplary accelerometer placement on a pipeline structure; Figure 8 shows an exemplary calibration process;

Figure 9 shows exemplary stress prediction overtime;

Figure 10 shows exemplary measured acceleration time history;

Figure 11 shows exemplary decomposed modes of acceleration time history; Figure 12 shows frequency content of the three decomposed modes of Figure 11;

Figures 13A-I show an exemplary finite element model being displaced by a series of modes;

Figure 14 shows an exemplary finite element model being displaced;

Figure 15 shows a process diagram of an exemplary method of determining fatigue based on internal forces exerted on a pipe;

Figures 16A-B show a computational fluid dynamics model; and,

Figure 17 shows a force time history for a bend in the computational fluid dynamics model of Figure 16.

The following are examples of systems and methods for estimating fatigue. Throughout the following description it will be noted that there is particularly utility for the described concepts in subsea pipeline structures. Flowever, it will be understood that the principles may be applied to above surface structures equally. References to subsea structures are merely exemplary.

The process of structural analysis involves identifying the behaviour of a physical structure when subjected to force. Structural dynamics is a type of structural analysis which covers the behaviour of structures subjected to dynamic loading which are actions having high acceleration. Dynamic loads include people, wind, waves, traffic, earthquakes and blasts. Indeed any structure can be subjected to dynamic loading. The following is a structural dynamics process for estimating structure fatigue. A high-level process diagram is illustrated in Figure 1 to provide an overview of the logical blocks that operate together to provide the functionality of the system. Such logical or functional blocks are of course merely exemplary and the system may operate in a variety of different ways to provide the described functionality. The terms model, engine and logical block will be used throughout the description interchangeably. A logical computational software block 10 is illustrated as containing a series of distinct logical functional entities 12, 13, 14. The computational software 10 receives data directly from a set of accelerometers 11 which have been placed on the pipeline structure to provide real-time, dynamic data of the acceleration of that point of the structure. The output 15 of the computational software 10 is a visual representation of dynamic stresses on a structure and the fatigue associated with stresses.

Accelerometer placement will be described in more detail below, however at a high level, accelerometer placement (step 17) may be based on a finite element virtual model of the system (step 18) and the method by which the data is to be modelled. The finite element model is initially created using isometric data or a process flow diagram (step 16) in a known manner.

Principles are described herein for determining fatigue based on measurements from sensors placed on the structure. The dynamic stresses exerted on the structure are determined in order to accurately predict fatigue. For all methods, after the dynamic stress is determined, standard fatigue analyses can be conducted (BS7608). These analyses will be well known to the skilled person and we will not comment further here.

The present process begins by creating or otherwise obtaining a finite element model of a structure such as that illustrated in part in Figure 2. A finite element model is the result of finite element analysis and the terms will be used interchangeably throughout the present specification to represent the particular model or modelling steps. The principles behind the finite element analysis are well understood and will not be discussed in detail here. It should be noted that other known types of virtual structural model, such as a finite volume model or a finite difference model, could be used in place of a finite element model. A more detailed, low-level diagram of the computational software 10 is illustrated in Figure 3 where reference numerals in Figure 1 are replicated to show correspondence between the Figures. The steps of each of the process data model 12, the process engine model 13 and the analysis engine fatigue prediction model 14 are expanded.

The process data model 12 serves to format and filter the data received from the accelerometers and (in this embodiment) to translate this data into displacement data. The process engine model 13 serves to optionally calibrate the finite element model already derived (steps 31, 32 and 33) and generates stress time history from the finite element model (steps 34 and 35). The analysis engine fatigue prediction model 14 serves to generate the estimate of fatigue life (step 36) and further outputs 15 such as integral remaining fatigue life (step 38) or an instantaneous fatigue alarm if the fatigue is determined to be above a certain threshold (step 37). The steps described may be performed periodically or continuously as set by the operator.

Two methods are presented for determining dynamic stress from measured accelerations. The first method predicted will be termed the ‘modal stress method’ which uses modal analysis. Modal analysis aims to identify modal properties of a structure based on data collected when the structure is operating under its operating conditions, that is, no initial excitation or artificial excitation. The modal properties of a structure include primarily natural frequency, damping ratios and mode shapes. The object of the modal analysis is to extract frequencies, damping and/or operating shapes of a structure. The present ‘modal stress method’ decomposes the measured accelerations into separate modal components and integrates the components to obtain modal displacements. The modal displacements can then be used to determine modal stresses from finite element analysis.

The second method presented is referred to as the ‘static displacement method’ in which the measured accelerations are integrated directly to obtain a set of displacements. The displacements are then directly applied to the finite element model to determine stresses incurred at each point over time.

Although in the detailed examples described herein, the ultimate stresses are derived from displacement data in both methods, it will be clear that in the modal analysis method described the displacement data is not necessary. The steps of deriving displacement data from acceleration data may be omitted and the stresses calculated directly from acceleration data. Nevertheless, in the detailed example, displacement data is used as an intermediate step in order to derive the stresses on the structure and update the finite element model.

To derive displacement data from the acceleration data, a mathematical process of integration occurs in the process data model 12. The displacement data in modal component or directly determined form is passed to the process engine model. To determine displacement, acceleration is first converted to velocity which is in turn converted to displacement as illustrated in Figure 4. Due to the nature of integration, errors in the accelerometers are compounded during the integration from acceleration to displacement. The errors may be due to the characteristics and inaccuracy of the accelerometers used. Errors can be caused by for example accelerometer bias (fixed offset), vibration rectification (amplitude dependent bias), accelerometer sensitivity, accelerometer noise and error and change in accelerometer orientation. Errors introduced in acceleration usually show up in drift in the integrated displacements which is removed by signal processing in the process data model 12 before the displacement data is passed to the process engine model 13.

Figures 5 and 6 demonstrate the two methods in flow diagram form. In both methods, the acceleration data over time is recorded and measured and integrated to obtain displacement. In Figure 5 this is illustrated at item 51 and in Figure 6 this is illustrated at steps 61 and 62. As above, signal processing has been performed to remove displacement drift errors.

In the modal stress method, the displacement data is decomposed to modal displacements (steps 52 and 64). Each modal component corresponds to a particular frequency of vibration. The accelerometer data is passed through a Fourier transform to identify the modes and their respective frequency, and to identify which frequencies are present in the signal and with what relative intensities. This modal analysis can be considered equivalent to performing the finite element analysis in the frequency space. The displacement data for each frequency is obtained and therefore the displacement data at each mode of vibration is derived. As above, this is considered equivalent to the derivation of the displacement of each modal component. The accelerometer data can be integrated before or after the Fourier transform is performed.

In the static displacement method, the displacement data from the accelerometers is passed from the process data model 12 post signal processing (step 51) to the process engine model 13. In the modal stress method the modal displacements (step 52, the displacement of each of a set of frequencies that comprise the received data derived by Fourier transform) are passed to the process engine model 13.

In the static displacement method, the displacement data is directly applied to the already determined finite element model (steps 53 and 65). The static solution is then solved at each measured time step to obtain equivalent stress time history (steps 54 and 66). The stress is then added to time history (step 55) and the data passed to the analysis engine fatigue prediction model 14.

In the modal stress method, the decomposed modal displacements are applied to corresponding scaled finite element mode shapes in order to generate modal stresses from which the modal stress time histories can be calculated (steps 56 and 67). In other words, the FE model is caused to vibrate in each one of the detected modes, sequentially or simultaneously, with a magnitude based on the corresponding modal displacement. Effectively displacement data is plotted over time for each frequency or vibration. The respective modal stresses will be intrinsically weighted relative to one another in accordance with the different intensities of each modal frequency in the measured data. The modal stresses at the detected frequencies are then summed to obtain an overall stress time history (steps 57 and 68). As illustrated in Figure 5, both methods may be used to generate an accurate model.

Once the stress time history has been determined, a cycle counting of stress time history and fatigue life can be calculated by the analysis engine fatigue prediction model (step 69). For all methods, after the dynamic stress is determined over time, standard fatigue analyses can be conducted (BS7608). This analysis will be well known to the skilled person and we will not comment further here.

For both methods it would be beneficial if the finite element model were accurate to determine accurate stresses. To ensure the model matches the constructed pipework it may be be updated to measurements recorded on the pipework. Generally updating will be conducted by matching analytical modal properties (mode shapes and frequencies) with their experimental counterparts. In addition, stresses are very sensitive to accurate modelling of boundary conditions. Ideally the finite modal properties and boundary conditions match measurements.

The process engine model 13 may optionally first identify if the previously determined finite element model of the system has been calibrated (step 31), as shown in Figure 3. If calibration has not been performed, the finite element model may be calibrated based on the measurements received (step 32) and this calibration is then fed into the step of using the finite element analysis to generate the stress time history (step 34) and improve the result. If the analysis has already been calibrated, then the analysis may be updated based on the measurements (step 33) and used to obtain the stress time history (step 34) without using a calibrated model.

Figure 8 illustrates this calibration in a flow diagram. The measured mode shapes and natural frequencies 62 are compared with those predicted in the model (step 81). If they are not well correlated (step 82) then the finite element model is updated using boundary conditions and added mass (step 83) before the test is re-run and a calibrated finite element model (step 84) is produced for use in the subsequent calculations.

In the high level diagram of Figure 1, it was shown that the finite element model of the system may be used to inform and determine the appropriate placement for sensors such that an appropriate stress time history can be determined (step 17). An exemplary placement of sensors is shown in Figure 7 on a finite element model. The virtual model illustrated in Figure 7 shows 10 accelerometers 70-79 placed adjacent each curvature.

For the modal stress method, determining the accelerations of each mode is a key requirement. In this case the best locations for the sensors would be the anti-nodes of the modes of interest, that is, the point at which displacement is largest for a particular frequency. These locations can be approximated by an FE analysis. In practice, it is likely that the anti-node will be missed. It is desirable that the ratio of the modal amplitude and the anti-node is known; otherwise it is not possible to correctly scale the modal displacements. The error in this ratio will be the same as the error in modal stress. Therefore, it is desirable to describe the mode shape with high spatial resolution.

One measurement per mode should be measured to robustly decompose the response into its modal components. In addition, an accurate estimation of the mode shape is required - a higher spatial resolution will generally give better results. However, it may be possible to combine a coarse mode shape estimation using operational modal analysis techniques with the FE model to give an improved spatial resolution.

Typically only the direction of acceleration needs to be determined for each mode shape to enable the calculation of stress; however, the orientation of the accelerometer should also be known to make the calculation more accurate.

In the ‘static displacement method’, the acceleration data is integrated twice to obtain displacements. The displacements are then directly applied to the FE model to determine stresses. For the static displacement method, determining the dynamic displacements and the curvature to the stress location are key requirements. Two measurement points either side of the stress location are preferred to define the curvature. The measurements are desirably triaxial to correctly define the deflected shape. If too few points are measured the results become inaccurate, as demonstrated in Figure 9. The plot shows the stress response of a simulated subsea jumper with 8 measurement points (top) and 5 measurement points (bottom). The 8 measurement points matched the original stress time history almost exactly. It is clear that in both cases the amplitudes are similar, but the characteristics of the response are very different. This shows that using too few measurement locations will not give a good stress estimate.

An accurate FE model is required in this method, but less so than the modal stress method. There are also less calculation steps than the modal stress method. More accelerometers are required in the static displacement method since it is required to have two accelerometers either side of a stress location to appropriately approximate the curve of the pipe. In the FE model, a static solution is solved at each measured time step to generate an equivalent stress time history.

As outlined above, the FE model first estimated can be used to indicate appropriate positions for the sensors. The sensor positions proposed should be sufficient to determine the dynamic stresses at the required locations. The key issues for sensor locations are different depending on the method of determining stress.

The proposed measurement system is of sufficient specification to determine the dynamic displacements with sufficient accuracy and have a power consumption low enough to run on battery power. This section briefly discusses the effects of sensor specification on the result which is based on analytical and laboratory studies. Due to the low frequency modes expected, accelerometers that can measure down to DC (0 Hz) should be used.

Three accelerometers are considered here, and some of their properties are shown in the following table.

Accelerometer 1 has considerably less noise in the measured signal and is capable of resolving very low levels of acceleration, which is required to determine low frequency displacements. When double integrating to derive displacement, accelerometer 1 had the lowest drift, which reduces the amount of post processing required. Accelerometer 3 gives acceptable results, but significantly more drift in the integrated displacements then accelerometer 1. It is possible to determine the displacements, but requires more time post processing. The sensitivity and noise of accelerometer 2 does not give acceptable performance at low levels of vibration. In addition, the drift on the integrated displacements for accelerometer 2 is significant.

As an example, Figure 4 shows integrated displacements for accelerometers 1 and 2 with no post processing. It is clear that the noisier accelerometer has significantly more drift. Accelerometer 1 is illustrated with an unbroken line and accelerometer 2 with a dotted line.

Choosing an appropriate accelerometer is a trade-off between power consumption, sensitivity, robustness and price. As a minimum, it would be recommended that an accelerometer with similar properties to accelerometer 3 should be used; but the best accelerometer possible should be used. If an accelerometer with a lower sensitivity or higher noise is proposed, it should be shown that adequate displacements can be calculated.

The response of individual modes may be determined using band pass filtering. However, this is only suitable for well-spaced modes. For low frequency modes and modes that are not well-spaced, this method is not appropriate. In this case, a modal decomposition method may be used. The accuracy of modal decomposition is reliant on accurate mode shapes.

An example of modal decomposition is shown in Figures 10 and 11, where a measured acceleration time history of walking on a concrete slab is decomposed into three separate modal components. Figure 12 shows the frequency content of Figure 11 (obtained by fourier transform), which clearly shows the modal response. The proposed solution decomposes the signal into its modal components.

Figures 13A-I and 14 illustrate a finite element model being displaced at a particular mode. Each of the Figures in Figure 13 illustrates the displacement of the model at a particular frequency step. Figure 14 illustrates a more complicated structure under stress at one particular frequency.

The above method considers the stresses experienced by a structure taking into account all applied forces including those due to external effects. In an alternative approach for assessing the stresses expected or suffered by a structure, it is further proposed to consider the internal forces exerted on the structure by fluid flowing through the pipeline. An exemplary process diagram is illustrated in Figure 15. The process begins by taking measurements of the system (step 156). These measurements may be from sensors already positioned on the pipe and that are already included in the system in standard deployments. These will comprise at least one flow meter but could also include for example one or more additional flow meters, pressure sensors, temperature sensors, valve positions and/or fluid composition recordings. Whilst the method can be performed based on measurements from a single flow meter, the accuracy will be improved by supplementing this with data from additional sensors. Preferably at least one flow meter and one pressure sensor are deployed, especially if the fluid is multi-phase. The measurements derived from these sensor(s) can then be used to populate a virtual flow meter which predicts the flow conditions throughout the system (step 152a).

As in the model above, the computational software 10 is split into three logical entities, a process data model 152, a process engine model 153 and an analysis engine fatigue prediction model 154. The high level functionalities are the same in this method, the process data model serves to format and filter the real world data, the process engine model serves to analyse the data and determine stress and the analysis engine fatigue model serves to provide an analysis of this data depending on operator requirements and provide an output 155.

Once the virtual flow meter 152a has been derived from the sensor measurements, it is optionally considered whether there is a stored process condition in a database (step 153d). If one exists for this process then the stress (which has already been calculated for that process condition) can be added to the time history to calculate fatigue. This step may be effectively a look up table of the process condition against stress since the next step may take a long time to process.

If, as is at least likely in the initial stages and before a historical database can be populated, historical data does not exist then a computational fluid dynamic model (CFD) can be produced (step 157) for the sections of the pipeline of interest. It is optionally not proposed to model the entire structure due to computational efficiencies but only on sections of interest.

Figure 16 illustrates an exemplary CFD model of a simple pipeline structure. An extracted view is shown in Figure 16A and a flow is shown in Figure 16B. In the flow of Figure 16B, the darker areas illustrate an increase in velocity of the fluid whereas the lighter areas show where the velocity is less.

The inputs from the virtual flow meter are then combined with the CFD model to derive a CFD model for the particular process conditions (step 153a). The inputs may include mass flow, temperature and compositional data at upstream boundary conditions, liquid and/or gas properties and pressure at the downstream boundary conditions. The process of computational fluid dynamics modelling is well known and will not be discussed in detail here for the purposes of brevity. The CFD model is used to calculate the static and dynamic pressure applied to the pipeline structure by the fluid. From this, a forcing function can be derived describing the forces on the pipeline structure arising from the calculated pressure.

Hence, once the CFD for the process condition has been determined, this CFD can be combined with all or parts of the FE model 158 determined in the earlier described process (step 153b) to apply the forcing function to the FE model. Using FE analysis, the stress at each point can then be determined (step 153c) and it can be added to the time history for the model (153e) to enable fatigue to be calculated in the conventional manner.

Figure 17 illustrates the results of applying a forcing function derived from the CFD model of Figure 16 to an already generated FE model at one bend of the structure. The force time history charts at the bend is plotted over time and the force converted into a predicted stress at that location in the FE model. Each trace shows a different force time history for a different operating condition.

Whichever of the above methods is utilised, once the stress has been determined, this can be directly output to the operator, however as above, additional analysis may be desirable and may be performed by the analysis engine fatigue prediction model 154. For example, the time history and cycle count could be used to determine the damage fraction (step 154c). From this, the integral remaining fatigue life could be determined (step 154a) and/ or an instantaneous fatigue alarm could be triggered if the fatigue is determined to be above a predetermined threshold. Any analysis and/or output described above could be combined with this method.

It will of course be understood that the method of determining externally caused fatigue and the internally caused fatigue may be performed independently or in conjunction with one another.

The flow charts and descriptions thereof herein should not be understood to prescribe a fixed order of performing the method steps described therein. Rather, the method steps may be performed in any order that is practicable. Although the present invention has been described in connection with specific exemplary embodiments, it should be understood that various changes, substitutions, and alterations apparent to those skilled in the art can be made to the disclosed embodiments.

Methods and processes described herein can be embodied as code (e.g., software code) and/or data. Such code and data can be stored on one or more computer-readable media, which may include any device or medium that can store code and/or data for use by a computer system. When a computer system reads and executes the code and/or data stored on a computer-readable medium, the computer system performs the methods and processes embodied as data structures and code stored within the computer-readable storage medium. In certain embodiments, one or more of the steps of the methods and processes described herein can be performed by a processor (e.g., a processor of a computer system or data storage system). It should be appreciated by those skilled in the art that computer-readable media include removable and non-removable structures/devices that can be used for storage of information, such as computer-readable instructions, data structures, program modules, and other data used by a computing system/environment. A computer-readable medium includes, but is not limited to, volatile memory such as random access memories (RAM, DRAM, SRAM); and non-volatile memory such as flash memory, various read-only-memories (ROM, PROM, EPROM, EEPROM), magnetic and ferromagnetic/ferroelectric memories (MRAM, FeRAM), and magnetic and optical storage devices (hard drives, magnetic tape, CDs, DVDs); network devices; or other media now known or later developed that is capable of storing computer-readable information/data. Computer-readable media should not be construed or interpreted to include any propagating signals.

Claims (42)

1. A method for measuring stress in a structure, wherein the structure is a subsea structure, the method comprising: receiving acceleration data captured at each of a series of time points from each of one or more accelerometers, each of the one or more accelerometers being attached to a respective position on the subsea structure; applying the acceleration data to a virtual model of the subsea structure; and calculating, from the virtual model, a respective stress resulting from the applied acceleration data at one or more locations on the subsea structure.

2. The method of claim 1, wherein applying the acceleration data to the virtual model comprises: deriving displacement data from the received acceleration data; and applying the displacement data to the virtual model of the subsea structure.

3. The method of claim 2, wherein deriving displacement data comprises deriving a displacement of each respective position on the subsea structure based on the acceleration data and wherein applying the displacement data to the virtual model of the subsea structure comprises updating the virtual model of the subsea structure by virtually displacing, for each respective position of the subsea structure, a corresponding position of the virtual model by the derived displacement for that respective position.

4. The method of claim 1 or 2, wherein applying the acceleration data to the virtual model comprises: optionally, deriving velocity or displacement data from the received acceleration data; converting the received acceleration data, or the derived velocity or displacement data, for the series of time points into the frequency domain; and updating the virtual model by applying a plurality of virtual vibrations to the virtual model at a respective plurality of different frequencies, each frequency corresponding to a vibration mode of the virtual model, either sequentially or simultaneously; and calculating the respective stress from the virtual model comprises, for each of the at one or more locations on the subsea structure: summing stress data calculated from the virtual model for each vibration mode; wherein either the magnitudes of the virtual vibrations applied to the virtual model are weighted, or the stress data calculated from the virtual model for each vibration mode is weighted before summing, in each case the weighting being based on the converted acceleration, velocity or displacement data.

5. The method of any of the preceding claims, wherein the virtual model is a structural model, preferably a finite element model, a finite volume model or a finite difference model.

6. The method of any of the preceding claims, wherein the acceleration data comprises one or more of: (a) substantially real time data received from the one or more accelerometers; and (b) historic data previously recorded from the one or more accelerometers.

7. The method of any of the preceding claims, wherein the one or more accelerometers are attached to respective positions on the subsea structure which positions are underwater.

8. The method of any of the preceding claims, wherein the acceleration data is captured from a plurality of accelerometers.

9. The method of any of the preceding claims, wherein the method is performed repeatedly, with each subsequent repetition being performed using respective acceleration data captured at at least one subsequent time point.

10. The method of claim 9, wherein the acceleration data is captured substantially continuously and the method is performed substantially continuously on the received acceleration data so as to calculate respective stresses at the one or more locations on the subsea structure at a substantially continuous series of time points.

11. The method of any of the preceding claims, wherein the subsea structure is a subsea pipe structure.

12. A method for measuring stress in a structure, wherein the structure is a pipe structure, the method comprising: receiving measurement(s) of at least one property of a fluid contained within the pipe structure, the measurement(s) indicating value(s) for the at least one property of the fluid at at least one respective position(s) at a point in time, the at least one property including a flow rate of the fluid; updating a first virtual model of the fluid contained within the pipe structure by setting, for each of the at least one respective position(s), virtual fluid properties at a corresponding position of the virtual model to the value(s) indicated by the received measurement(s) for that respective position; calculating, from the updated first virtual model of the fluid contained within the pipe structure, respective static and dynamic pressures of the fluid at one or more points within the pipe structure; deriving a forcing function representing the force applied by the fluid on the pipe structure based on the calculated respective static and dynamic pressures of the fluid at the one or more points within the pipe structure; applying the forcing function to a virtual model of the pipe structure; and calculating, from the virtual model of the pipe structure, a respective stress resulting from the applied forcing function at one or more locations on the pipe structure.

13. The method of claim 12, wherein the first virtual model of the fluid contained within the pipe structure is a one-dimensional or three-dimensional computational fluid dynamics model.

14. The method of claim 12 or claim 13, wherein the at least one property of the fluid of which measurement(s) are received further comprises: a pressure of the fluid, a temperature of the fluid and/or a density of the fluid; wherein the respective positions at which each property is measured may be the same or different.

15. The method of any of claims 12 to 14, wherein the measurement(s) of the at least one property of the fluid contained within the pipe structure comprise one or more of: (a) substantially real time measurements received from one or more sensors within the pipe structure at the at least one position; and (b) historic data previously recorded from one or more sensors within the pipe structure at the at least one position.

16. The method of any of claims 12 to 15, wherein calculating the respective static and dynamic pressure of the fluid at one or more points within the pipe structure comprises: calculating, from the first virtual model of the fluid contained within the pipe structure, a flow rate of the fluid at at least one point within the pipe structure; updating a second virtual model of the fluid contained within the pipe structure by setting, for the or each point, a virtual flow rate at a corresponding point of the second virtual model to the calculated flow rate for that point; calculating, from the second virtual model of the fluid contained within the pipe structure, the respective static and dynamic pressure of the fluid at the one or more points within the pipe structure.

17. The method of claim 16, wherein a resolution of the first virtual model of the fluid contained within the pipe structure is lower than a resolution of the second virtual model of the fluid contained within the pipe structure.

18. The method of claim 16 or 17, wherein the second virtual model of the fluid contained within the pipe structure is a computational fluid dynamics model, preferably a three-dimensional computational fluid dynamics model.

19. The method of any of claims 12 to 18, wherein the method is performed repeatedly, with each subsequent repetition being performed using respective measurements of the at least one property of the fluid contained within the pipe structure at the at least one respective position at a subsequent point in time.

20. The method of claim 19, when dependent upon any of claims 16 to 18, further comprising: storing the calculated respective static and dynamic pressure of the fluid at the one or more points within the pipe structure for the calculated flow rate of the fluid at the at least one position within the pipe structure; and for a subsequent calculation of a subsequent respective static and dynamic pressure of the fluid at the one or more points within the subsea structure based on a subsequently calculated flow rate of the fluid at the two or more points within the pipe structure, determining whether a calculation of the respective static and dynamic pressure of the fluid at the one or more points within the pipe structure has previously been stored, and, if so, calculating the respective static and dynamic pressure of the fluid at the one or more points within the pipe structure by retrieving the previously calculated value.

21. The method of any of claims 12 to 20, wherein the pipe structure is a subsea pipe structure.

22. A method for measuring stress in a subsea pipe structure comprising performing a first method according to claiml 1 and performing a second method according to claim 21.

23. The method of claim 22, wherein the first method is performed using acceleration data captured over substantially the same period of time as that in which the measurement(s) of the at least one property of the fluid used in the second method are made.

24. The method of claim 22 or 23, further comprising comparing the respective stress at the one or more locations within the subsea pipe structure calculated by the first method with the respective stress at the one or more locations within the subsea pipe structure calculated by the second method.

25. The method of claim 22, wherein one of either the first method or the second method is used to calculate the respective stress at the one or more locations on the subsea pipe structure based on previously recorded historic data and the other of either the first method or the second method is used to calculate the respective stress at the one or more locations on the subsea pipe structure based on substantially real time data.

26. The method of any of claims 9, 19 or 20 or any of claims 22 to 25 when dependent upon claims9, 19, or 20, further comprising: for each repetition, recording the respective stress of the one or more locations on the structure in association with a timestamp, so as to generate time-series stress data for the one or more locations on the structure.

27. The method of claim 26, further comprising: determining a stress cycle count or frequency from the time-series stress data.

28. The method of claim 27, further comprising: comparing the stress cycle count or frequency to a predetermined threshold and taking a predetermined action if the stress cycle count or frequency is above the predetermined threshold.

29. The method of claim 28, wherein the predetermined action comprises triggering an alarm.

30. The method of any one of claims 26 to 29, further comprising: determining a remaining fatigue life of the structure based at least in part on the time-series stress data.

31. The method of claim 30, wherein determining the remaining fatigue life of the structure comprises comparing the stress cycle count or frequency to a predetermined maximum stress cycle count or frequency for the structure.

32. The method of claim 30 or 31, further comprising: outputting an indication of the remaining fatigue life of the structure.

33. The method of claim 32, wherein the indication is a qualitative indication.

34. The method of claim 32, wherein the indication is a quantitative indication.

35. The method of any one of the preceding claims wherein the virtual model of the structure is a calibrated virtual model representing the characteristics of the structure when the structure is under operating conditions.

36. The method of claim 35, further comprising: calibrating the virtual model to generate the calibrated virtual model by: receiving vibration data for the structure captured while the structure is under operating conditions; determining modal properties of the structure while the structure is under operating conditions based on the vibration data; and modifying the virtual model so that the modal properties of the virtual model substantially match those of the structure while the structure is under operating conditions, wherein modifying the virtual model comprises one or more of: modifying one or more boundary conditions of the virtual model; and modifying one or more values representing a mass of a respective one or more elements of the virtual model.

37. The method of claim 36 when dependent upon any one of claims 1 to 7, wherein the vibration data is received from the one or more accelerometers.

38. The method of any one of the preceding claims, wherein the structure is a pipeline.

39. The method of any one of claims 12 to 38, wherein the fluid contained within the structure comprises oil, gas, water or any combination thereof.

40. An apparatus adapted to carry out a method according to any one of claims 1 to 39.

41. A computer program which, when executed by a processor, causes the processor to carry out a method according to any one of claims 1 to 39.

42. A computer-readable medium storing a computer program according to claim 41.