Two-phase flow induced vibrations in a marine riser conveying a fluid with rectangular pulse train mass

Highlights

• Influence of two-phase flow induced vibration (2-FIV) on structural limit states for a marine riser.

• The governing equations of motion are solved by Runge-Kutta-finite difference numerical analysis.

• Large amplitude motions are observed at the bottom end of a steel lazy wave riser.

• 2-FIV can consume substantial percentage of the ULS usage factor, and cause serious fatigue damage.

Abstract

A riser conveys fluids from a subsea system to a host floater; however, oil and gas phases may alternate, increasing pipe's stress and damaging downstream facilities. This paper studies the nonlinear planar vibrations of a steel lazy wave riser excited by slug flow. The employed formulations comprise the Euler-Bernoulli beam model and the steady plug-flow model with a time-space-varying mass per unit length in the form of a rectangular pulse train. The equations are solved by a Runge-Kutta finite difference scheme and frequency-response curves are constructed for effective tension, curvature, usage factor and fatigue damage. The results offer a useful insight of the slugging frequencies and slug lengths that may receive attention during the design of risers.

Introduction

A riser is an important interface between a subsea system and its host platform in the exploration and production of offshore hydrocarbons. A type of riser, the steel lazy wave riser (SLWR) has been proven over the past few years as a cost effective solution for the production of fields in ultra-deep water and harsh environment (Hoffman et al., 2010; Moore et al., 2017). Buoyancy modules are distributed at its middle length in order to keep its compliant configuration, isolating floater motions from the touch down zone, and hence, improving the fatigue life (Felisita et al., 2017). Furthermore, it is made of steel pipe, which is a suitable material for the exploitation of high pressure and high temperature reservoirs (Cheng and Cao, 2013).

It has been recognised that the slug flow regime inside SLWRs could be an issue, especially at the sag section where liquids could be accumulated (Kim and Kim, 2015). Accordingly, two-phase flow-induced vibration (2-FIV) or slug-induced vibration can occur, diminishing the riser's fatigue life (Cheng and Cao, 2013).

Slug flow is a phenomenon in which liquid “slugs” and gas “bubbles” of a two-phase flow alternate in the pipe. This may result in parametric vibrations due to the time-varying mass in the form of a square wave (Paidoussis, 2014) which could resonate with the structural system (Chatjigeorgiou, 2017). In the oil and gas industry, the slug flow pattern hinders the operations of downstream facilities (Kadri et al., 2011; Li et al., 2017) and the induced vibrations increase the fatigue damage of piping systems (van der Heijden et al., 2014). Hence, methods to mitigate the slugging, such as using a wavy pipe (Xing et al., 2013) or a self-lifting arrangement (Adefemi et al., 2017), have been proposed. Furthermore, 2-FIV occurs in other hydraulic systems, such as spiral pipes conveying boiling liquid in heat exchangers (Gulyayev and Tolbatov, 2004; Yan et al., 2013), at the outlet of steam generators in piping of nuclear power plants (Fujita, 1990; Ortiz-Vidal et al., 2017), in parallel pipes for direct steam generation by solar heating (Tshuva et al., 1999) and in aspirating pipes with density pulsations due to shallow immersion (Paidoussis, 2014).

Several papers have focused on the slug flow characterisation. Numerical and experimental methods have been applied to study inclined pipeline-riser systems (Han and Guo, 2015), vertical risers (Abdulkadir et al., 2014; Fokin et al., 2006) and hybrid risers (Gong et al., 2014). The experiments on an s-shaped riser are of particular interest for this paper; they have been conducted inside a stainless steel pipeline-riser system with a gas-liquid mixer, and the observations have helped to develop of a stability criteria for the flow (Li et al., 2017).

Concerning the 2-FIV, early experiments with air-water flow may be attributed to Hara (1977), and Hara and Yamashita (1978), where parametric vibrations were found owing to density fluctuations. Miwa et al. (2015) have written a comprehensive review on the 2-FIV, mainly with references earlier than 2014. While the Euler-Bernoulli is often adopted to study the 2-FIV (An and Su, 2015; Bai et al., 2018a; Ortiz-Vidal et al., 2017; van der Heijden et al., 2014; Wang et al., 2018c), using the Timoshenko beam model yields in the prediction of higher response amplitude when the system is about to lose stability (Ma et al., 2017). In other studies, experiments have been often used to validate the predictions by the beam models (Ortiz-Vidal et al., 2017; Wang et al., 2018c). Furthermore, with the advent of high performance computing, computational fluid dynamics (CFD) coupled with finite element method (FEM) codes have been used to solve fluid-structure interaction (FSI) problems in subsea pipeline systems (Jia, 2012; Li et al., 2016; Lu et al., 2016; Onuoha et al., 2018, 2016).

Limiting the discussion to 2-FIV in marine compliant risers, Ortega et al. (2012) used a Lagrangian tracking model two-phase flow code coupled with an FEM code in order to solve planar motions of a flexible lazy wave riser, and they found that the irregular characteristics of the slug flow generate irregular loads and responses of the structure. Later, Ortega et al. (2017) included wave loads into their model, and the riser's response got amplified. Chatjigeorgiou (2017) analysed the linearised in-plane motions of a catenary riser conveying a steady slug-flow and subjected to forced top excitation. It was concluded that the said flow amplifies the dynamic components of the riser's response. Recently, Zhu et al. (2018) performed experiments in an air-water test loop, where the in-plane vibrations, out-of-plane vibrations and the flow structure were observed inside a transparent silica gel tube in catenary configuration by means of high speed cameras. Results showed that the lateral vibrations are negligible, and hence, the idea of using planar motion models seems to be a plausible approximation. Furthermore, a number of useful contributions to the analysis and design of marine risers or pipelines are available in the literature published in recent years (Ai et al., 2018; Lou et al., 2016; Park et al., 2015, 2018; Yuan et al., 2017; Khan and Ahmad, 2017; Li and Low, 2012; Guo et al., 2013; Gao et al., 2014, 2016; Xu et al., 2017; Bai et al., 2017, 2018b; Zhang et al., 2015; Ye et al., 2014; Dong et al., 2012; Wang et al., 2018a, Wang et al., 2018b; Katifeoglou and Chatjigeorgiou, 2016; Vendhan, 2014; Gu et al., 2017).

The aim of this paper is to understand how the riser behaves before the time-varying mass of the slug flow, and whether the response is high enough to be considered in the structural design. To that end, a phenomenological model of the slug flow is used, namely a plug-flow model with time-space-varying mass in the form of rectangular pulse train, whereas the structure is modelled as an Euler-Bernoulli beam. In our application of interest, no floater motions are included, and the surrounding seawater is quiescent, providing only added mass and drag damping. By conducting a numerical study, we detect the slugging frequencies that may lead the riser to attain the ultimate limit state (ULS) or cause major damage for the fatigue limit state (FLS).

Scholars of the International Ship and Offshore Structures Congress (ISSC) have identified that the research of loads on risers should focus on the development of simplified methods for use in practical design applications (Hirdaris et al., 2014), and this paper is aligned towards that objective. The rectangular pulse train mass model here used assumes a known varying mass across the riser, and therefore, it is considerably simpler than the aforementioned methods which require solving the fluid equations. Moreover, the said rectangular pulse train mass model has been used successfully in the past in the analysis of jumpers for subsea piping systems, where vibrations were predicted in a realistic way (van der Heijden et al., 2014). Accordingly, this article offers two main contributions: (1) a mathematical model which can be used to benchmark more complex solutions that consider rigorous FSI models, and (2) an assessment on the relevance of 2-FIV for the limit state design of risers.

Although the present work focuses on SLWRs, the governing equations are general for elastic extensible pipes conveying fluid, and thus, the present approach can be applied to analyse other types of hydraulic systems by selecting the appropriate boundary conditions, tube properties and internal flow parameters.

Regarding the organisation of the paper, Section 2 introduces the governing system of equations and the numerical methods used to investigate the problem. Section 3 presents the numerical results of riser's response as function of slugging frequency and slug length. In section 4, we analyse the time histories of the said responses to assess the ULS and FLS. Conclusions are given in Section 5.