Pipeline Discretisation – Why? How!? (10-minute read)

…, not the most enthralling subject. However, it is a very important subject especially, when designing pipelines (for transport) and reception facilities (for processing) of multiphase fluids.--Note, article has not been updated, though OLGA has ;-) --

From the title, this is surely…, not the most enthralling subject. However, it is a very important subject especially, when designing pipelines (for transport) and reception facilities (for processing) of multiphase fluids. This represents a “summation of my thoughts” on progress so far relating to pipeline discretisation.

I’m referring to Pipeline discretisation as actions taken on existing bathymetric/as-laid pipeline or other profiles to produce a more realistic (and optimised) pipeline model for simulation purposes.

As a flow assurance engineer, you’d typically have access to topographical/bathymetric data, pipeline alignment sheets, on-bottom stability analysis data or actual as-laid pipeline data, to create a pipeline profile ready for simulation. Some data from actual surveys may also have some associated (maybe instrumentation related) noise. These may need to be modified before use in a simulation programme like OLGA, either to reduce the number of pipe sections (in order to improve simulation speed), reduce/eliminate noise, or to make the pipeline profile more realistic, for accurate (especially for multiphase fluids) predictions.

Several studies show the impact of pipe inclination on predicted liquid holdup at turndown, consequently, the elevation profile of a pipeline has a large effect on predicted liquid holdup and flow regime within the pipeline (as well as the liquid handling at the reception).

I found there was a paucity of relevant and actionable information on pipeline discretisation within the public domain. Below are some interesting documents I came across and you are encouraged to read them to get the complete story (available from Onepetro, ASME and OGJ).

One of the earliest documents (published 2000) I found that assists in characterising certain pipeline profiles, based on their propensity to induce liquid holdup (and potentially create operational issues) is by B. Barrau [1]. He introduced a dimensionless mathematical indicator called Profile Indicator (PI). This allows you to quickly compare profiles of different pipelines (for likely liquid holdup issues) without carrying out a detailed simulation. It’s ingeniously simple and quite well explained within the publication. However, I have to put in this proviso, “DO NOT” use the equation to calculate the actual liquid holdup in your line – it is only an indicator!

I’ve created an excel spreadsheet that shows the basic equations required to accomplish this.

The PI was developed based on research that lead to:

• A relevant set of reference fluid (GLR of 0.028 vol/vol) and flow conditions (superficial gas velocity of 2 m/s) for a pipeline were identified and the impact of inclination on the liquid holdup at these conditions was quantified (see paper for basis);
• A mathematical correlation between slope and liquid holdup was developed at these conditions and used to quantify liquid holdup in a pipeline (characterized as a sequence of pipe sections/segments of different slope) at these reference conditions.

The fluid and flow reference conditions ensure that the calculation is independent of fluid, operating conditions and pipe diameter.

The estimation of PI involves:

1. Estimation of the liquid holdup per pipe section;
2. Summation of the PI values per pipe section;
3. Multiplication by 1000 to give a more reasonable value as shown in below formula:

We can also get an idea of the likely fluid behaviour within pipelines dependent on the PI value. PI values of 20 or less, are most likely to be horizontal pipelines or may have possibly been oversimplified (eg. when taken directly from bathymetric maps), whilst high PI values (>= 80) are likely to have serious liquid issues.   

The PI could also be used to make profiles taken from bathymetric maps more realistic for simulation purposes. This is done by calculating PI of a similar pipeline within the vicinity (if available), comparing it with the PI from the bathymetric map (which would likely be lower) and systematically adding random angular sections (more on this further down) in order to increase the PI value to match. It is a better idea to use this in concert with other tools such as TC (Total Climb).

In 2005, Havard Eidsmoen et al [2], published a paper relating to modelling gas condensate lines. Four pipeline models were compared based on a 77km (48mile) pipeline. The original model (Mod-1) used actual survey data taken every 1m (3.3ft), Mod-2 was modified to contain 40m (131ft) pipe sections, Mod-3 was modified to contain 500m (1640ft) pipe sections and in Mod-4, the pipeline was divided into 4 sections (of varying lengths) based on significant seabed features. 

There were significant differences in the pipeline angle distributions between Mod-1 and Mod-2, which is expected as the very detailed 1m (3.3ft) survey may have included the effect of rocks or other seabed debris which may give significant inclinations. Mod-2 and Mod-3 produced more similar angle distributions. Offshore pipelines are typically made from 12.2m (40ft) long individual pipes and its unlikely there will be extensive differences on a per meter basis except due to damage.

The use of PI is not covered in any real depth. It shows that using unrefined and noisy detailed seabed surveys directly in simulations without modifications to make it more realistic, may lead to over-prediction of liquid holdup.

Donald Jackson in a 2008 paper [3] discussed using an “anchored filtering” methodology that leads to dramatic time and computer memory usage improvements without “significantly” impacting the integrity of results. Initially an arbitrary maximum change in angle, amax is selected. Then the values from the 2nd pipe segment (i.e. angle, elevation) are deleted, if the positive difference in angle between the 1st and 3rd pipe segments exceed amax then keep the 3rd pipe segment and compare the 3rd and 4th pipe segment angles. Otherwise, if the positive difference in angle between the 1st and 3rd pipe segments are less than amax then delete the 3rd pipe segment and compare the 1st and 4th pipe segment angles and so on. There is some deviation between the initial and the modified pipeline length. Once you get around the different filtering methodologies used, it seems disarmingly easy to use. However, only 2 sets of data were used in the study and it is uncertain how well liquid holdup is distributed along the pipeline or if the overall shape of the original pipeline is maintained.

Erich Zakarian et al (2009)[5] introduced the first real rigorous pipeline discretisation methodology using PI (Profile Indicator), TC (Total Climb), angle distribution and laying down a set of requirements to be fulfilled. It was initially developed as a solution for modelling ultra long pipeline profiles with a very large number of pipe sections. The requirements for a successful pipeline discretisation exercise also entail what could be described as common sense measures:

• Ensuring pipeline length is preserved;
• Making sure the final geometry is broadly similar to the original one;
• Preserving PI, TC and angle distribution.

It also dovetailed with the previous work by B. Barrau[2] on PI, giving further detail on the process of systematically adding random angular sections within the pipeline profile, via physical adjustment of the complexification coefficient.

Erich Zakarian et al (2013)[6] in continuation of the work started in the previous 2009 paper, introduced the concepts of Terrain Indicator (TI), Rough Profile Indicator (RPI) and Smooth Profile Indicator (SPI) which can be used to quantify the roughness of an elevation profile. This is in addition to the PI and TC which can be used to quantify the propensity to accumulate liquids. TI and RPI can be used in this respect to increase the roughness of a preliminary pipeline profile taken from a bathymetric map.

Erich Zakarian et al (2014)[7] published a paper that ties-in with the previous 2 papers and introduces a method of smoothing out noise in bathymetric or other data that was created and popularised by Savitzky and Golay (1964)[8]. Savitzky and Golay wrote one of the 10 seminal papers that ever been published in the Analytical Chemistry Journal. Savitzky and Golay smoothing via least squares method avoids unduly degrading the underlying data, maintains the smoothing of data and preserves features of the distribution such as relative maxima, minima and width. The value used for the moving average varies from 1 pipe (12.2m) for noise reduction to 2 pipes for conversion of bathymetric profile to bottom of pipe profiles

Benjamin Kitt et al. (2016)[9] published a paper detailing their creation of software that iterates through a number of possible pipeline routes by taking into consideration, the potential pipeline profile versus a choice of either the pressure drop, or liquid holdup (at steady state conditions) in order to arrive at the “Least Cost Path”. The algorithm employed to determine the “optimal” paths is based on a variant of an algorithm first postulated by Dijkstra (1956). The software allows the optimisation of the pipeline route either for minimum pressure loss or minimum liquid holdup. It utilises a fluid composition inputted by the user.

The underlying multiphase flow model uses a unified model (unlike PI) encompassing the full range of inclination angles a pipeline traverses using Xiao (1990), and correlations for predicting the flow conditions in a pipeline for multiphase flow by Gomez et al. (2000) and Shoham (2006) as a basis.

Two adjustment factors (FHYD - Hydraulic Performance Adjustment Factor and FCS - Cost Surface Adjustment Factor) are provided to mathematically adjust the hydraulic or pressure parameters.

The model was mainly tested on short pipelines and a manual estimation of PI (not automatically included in model) was carried out for comparison. It was mentioned that using this could speed up the model especially for longer pipeline lengths

OLGA, which is the go-to flow assurance tool includes a tool (profile generator) for filtering and simplifying profiles prior to use in simulations. However, it hasn’t really been designed for filtering noise from detailed seabed/land surveys and shouldn’t really be used for this purpose.

An adjustable box filter allows longer pipe section lengths to be selected, whilst trying to follow the main contours of the pipeline. In the next stage, angle distribution filters with minimum specified pipe lengths can be run, to reduce the remaining number of pipe sections whilst trying to maintain the angle distribution. This is especially important for multiphase fluids.

What I found

I have found that the methodology expatiated on within the 3 papers by Erich Zakarian et al., give sufficient tools to discretise profiles from a detailed seabed survey, a rough profile from bathymetric charts, an as-laid pipe survey or otherwise, into a form suitable for modelling.

I found it more flexible than the profile indicator available within past versions of OLGA, as it includes a rudimentary means of noise reduction/removal, and it can be created within an Excel spreadsheet. Please comment if there’re any similar or better tools available.

Share the article if you find it useful!

References:

[1.]     Profile Indicator helps predict pipeline liquid holdup slugging – Bertrand Barrau, Oil and Gas Journal Volume 98, Issue 8, page 58 – 62 Feb. 2000.

[2.]     Issues relating to proper modelling of the profile of long gas condensate pipelines – Havard Eidsmoen, Ian Roberts, PSIG 0501, Nov. 2005.

[3.]     Filtering Elevation Profile Data to Improve Performance of Multiphase Pipeline Simulations.

[4]      Pipeline Modeling: Getting the right data and getting the data right.

[5]      Discretization Methods for Multiphase Flow Simulation of Ultra-Long Gas-Condensate Pipelines – E. Zakarian, H Holm, D. Larrey BHR Conf. 2009

[6]      Discretisation, Characterisation and Complexification of Multiphase Pipeline Elevation Profiles – E. Zakarian, J Morgan, H Holm, D. Larrey BHR Conf. 2013

[7.]     Flow Assurance Indicators for the Design of Long Subsea Tiebacks – E. Zakarian, J Morgan, OTC 2014

[8.]     Smoothing and Differentiation of Data by Simplified Least Squares Procedures – Analytical Chemistry, 36, 1964 pg. 1627 - 1639

[9]      Pipeline Route Planning for Multiphase Pipelines – Benjamin Kitt, Aaron Licker, Joshua Cull, IPC2016-64198, Sept. 2016