Viscoelastic Pipeline Research Articles

Determination of creep function coefficients of viscoelastic pipes using a transient-guided machine learning model

ABSTRACT This study introduces a novel framework for the estimation of creep function coefficients in viscoelastic pipelines, employing a combination of machine learning (ML) and transient hydraulics. Specifically, the efficacy of eXtreme Gradient Boosting (XGBoost) as an advanced regression method is evaluated within this framework. A transient simulation model, utilizing the method of characteristics, is formulated to create the reservoir-pipe-valve (RPV) scenarios under diverse boundary conditions. After conducting model calibration, the model is used to generate datasets with the transient hydraulic responses at the measurement points. The fast Fourier transform (FFT) is then applied to transform the generated samples into the frequency domain. Feature selection is accomplished through principal component analysis (PCA) to identify optimal input variables for XGBoost. In estimating the creep function, six coefficients are employed, with the feature selection analysis indicating that each coefficient is associated with a specific signal. Importantly, it is demonstrated that attempting to estimate all six coefficients using a single set of signals is unfeasible. The results affirm the accuracy of the proposed ML-based framework in determining creep function coefficients.

Transient wave-leak interaction analysis for improved leak detection in viscoelastic pipelines

Transient wave reflection methods (TWRMs) have exhibited favorable capability in leak detection for elastic pipelines, but applications have demonstrated their relatively low accuracy for viscoelastic pipelines. This paper investigates the transient wave behaviour, the principal tenet for leak detection by TWRMs, in a leaky viscoelastic pipeline to understand the mechanism of wave modification by leaks and viscoelasticity. Based on the correspondence principle, this research derives analytical formulations of the leak-induced wave reflection and phase difference at any measurement point in a viscoelastic pipe. According to the measured reflection coefficient, an optimization algorithm is further developed to detect the leak. The methodologies are then assessed and discussed through sinusoidal and sigmoid perturbations in numerical and laboratory tests. The extensive analyses indicate that measurement distance and leak ratio affect the magnitude of the reflected wave, yet, the wave phase shift is relatively independent of the leak ratio for practical applications.

Effect of non-stationary external forces on vibrations of composite pipelines conveying fluid

The effect of non-stationary external forces on the vibration of pipelines made of composite materials is investigated in the paper. A mathematical model of composite pipeline vibration is developed, considering the viscosity properties of the structure and pipeline base material, axial forces, internal pressure, resistance forces, and external disturbances. A mathematical model of viscoelastic pipelines conveying fluid under vibrations is constructed based on the Boltzmann-Volterra integral model. The mathematical model to study a pipeline is based on the Euler-Bernoulli beam theory. Considering the physicomechanical properties of the pipeline material, the mathematical model of the problems under consideration presents a system of integro-differential equations (IDE) in partial derivatives with corresponding initial and boundary conditions. The nonlinear partial differential equations, obtained using the Bubnov-Galerkin method under considered boundary conditions, are reduced to solving the system of ordinary integro-differential equations. A computational algorithm is developed based on eliminating features of integro-differential equations with weakly singular kernels, followed by using quadrature formulas.

Numerical simulation of a viscoelastic pipeline vibration under pulsating fluid flow

PurposeThe purpose of this study is to create a mathematical model, a numerical algorithm and a computer program for studying the vibration of composite pipelines based on the theory of beams used in the oil and gas industry, agriculture and water management, housing and communal services and other areas.Design/methodology/approachA mathematical model of vibration of a viscoelastic pipeline based on the theory of beams with a pulsating fluid flowing through it was developed. Using the Bubnov-Galerkin method, based on the polynomial approximation of deflections, the problem is reduced to the study of systems of ordinary integro-differential equations, the solution of which is found by a numerical method. A computational algorithm was developed for solving problems of vibrations of composite pipelines conveying pulsating liquid.FindingsThe stability and amplitude-time characteristics of vibration of composite pipelines with a pulsating fluid flowing in it are studied for wide range of changes in the parameters of deformable systems and fluid flow. The critical velocities of fluid flow at which the viscoelastic pipe loses its rectilinear equilibrium shape are found. The effect of singularity in the kernels of heredity on the vibrations of structures with viscoelastic properties was numerically studied. It is shown that with an increase in the viscosity parameter of the pipeline material, the critical flow velocity decreases. It was determined that an increase in the value of the fluid pulsation frequency and the excitation coefficient leads to a decrease in the critical velocity of the fluid flow. It was established that an increase in the parameters of the Winkler foundation and the rigidity parameter of the continuous layer leads to an increase in the critical flow velocity.Originality/valueThe study of the vibration of pipelines made of composite materials is of great theoretical and applied interest. The solution to this problem is an effective application of the theory of viscoelasticity to real processes. Therefore, the methods and problems of pipeline vibrations attract much attention from researchers. This study is devoted to solving the above problems and therefore its subject is relevant. The paper considers the results of numerical simulation of the processes of vibration of a composite pipeline based on the theory of shells during the flow of a pulsating liquid through it. A mathematical model of vibration of a composite pipeline was developed. A computational algorithm was developed for solving problems of vibrations of composite pipelines conveying pulsating liquid.

Experimental study on pressure characteristics of direct water hammer in the viscoelastic pipeline

Abstract With the increasing popularity of long-distance water supply projects and the development of materials technology, the variation of water hammer characteristics in the viscoelastic pipeline has become the focus of researchers. To find out the mechanism of water hammer in the viscoelastic pipe of both elastic and viscous properties, an experiment was set up to study the direct water hammer generated by rapid closure of the downstream valve in the polymethyl methacrylate (PMMA) pipe, with six flow velocities in nearly 70 tests. The experimental results showed that the maximum water hammer pressure generated in the viscoelastic pipe in all flow velocities was (20% at most) greater than the traditional value of Joukowsky's formula. A faster closing time of the valve caused a higher water hammer pressure. The difference in water hammer pressure generated between the fastest and the slowest closing time of the valve was 14–17% at each flow velocity. Based on the relationship between the stress and strain of the pipe wall in the viscoelastic pipe, the reason that the water hammer characteristic in the viscoelastic pipeline was different from the traditional value was explained. The study provides a reference for the mechanism of transient flow in viscoelastic pipelines.

On the Spectrum Localization of an Operator-Function Arising at Studying Oscillations of a Viscoelastic Pipeline with Kelvin–Voigt Friction

On the Spectrum Localization of an Operator-Function Arising at Studying Oscillations of a Viscoelastic Pipeline with Kelvin–Voigt Friction

A novel leak localization method using forward and backward transient characteristics

A novel leak localization method is presented based on the forward and backward transient analysis. The approach applies discrepancies between results from the forward and backward transient simulations by the Method of Characteristics (MOC) to locate potential leaks along a pipeline. This method is supposed to provide high localization efficiency because it does not need to perform any inverse calibration procedure, as demonstrated in leak exercises in both elastic and viscoelastic pipelines. The performance of the developed method is then validated through a simulated oil conveyance pipeline system in a noisy environment. The extensive applications and analyses reveal that the noise in the viscoelastic pipe is amplified gradually in the forward and backward MOC due to the numerical computation of the convolution integral terms, which thus could affect to a certain extent the accuracy of the developed method in practical applications.

Illegal connection detection in a viscoelastic pipeline using inverse transient analysis in the time domain

Abstract Illegal connection (IC) in water supply systems and water network wastes water as well as energy and reduces water quality, which has negative technical and economic effects on water management. Transient-based defect detection is a powerful method applied in water pipelines. This paper investigates the efficiency of the transient-based inverse transient analysis (ITA) method in estimating the characteristics of ICs in the viscoelastic water supply system in the time domain. To better evaluate this method, an experimental transient model was developed using polyethylene pipelines (with a length of 158 meters and a nominal diameter of 2 inches). In the first step, the hydraulic transient solver was calibrated in the calibration approach of dynamic parameters of pressure wave speed and pipe wall viscoelasticity. Then, the sensitivity of the ITA method to the spatial step of the method of characteristics and signal sample size was assessed. Finally, the efficiency of the ITA method was evaluated for several experiments with different transient intensities and a noisy signal. The results indicated that the accuracy for locating the IC was higher than the accuracy for the IC's length.

Hydraulic Transients in Viscoelastic Pipeline System with Sudden Cross-Section Changes

It is well known that the water hammer phenomenon can lead to pipeline system failures. For this reason, there is an increased need for simulation of hydraulic transients. High-density polyethylene (HDPE) pipes are commonly used in various pressurised pipeline systems. Most studies have only focused on water hammer events in a single pipe. However, typical fluid distribution networks are composed of serially connected pipes with various inner diameters. The present paper aims to investigate the influence of sudden cross-section changes in an HDPE pipeline system on pressure oscillations during the water hammer phenomenon. Numerical and experimental studies have been conducted. In order to include the viscoelastic behaviour of the HDPE pipe wall, the generalised Kelvin–Voigt model was introduced into the continuity equation. Transient equations were numerically solved using the explicit MacCormack method. A numerical model that involves assigning two values of flow velocity to the connection node was used. The aim of the conducted experiments was to record pressure changes downstream of the pipeline system during valve-induced water hammer. In order to validate the numerical model, the simulation results were compared with experimental data. A satisfactory compliance between the results of the numerical calculations and laboratory data was obtained.

Efficient leak detection in single and branched polymeric pipeline systems by transient wave analysis

The widespread use of plastic pipes in different fluid conveyance systems has greatly driven the recent development and application of transient-based methods (TBMs) for leak detection in viscoelastic/polymeric pipelines. Current TBMs for viscoelastic pipe leak detection are usually achieved by a two-step procedure, namely viscoelastic parameters identification and leak detection, which requires the pre-knowledge of intact system states (i.e., non-leak) for comparative analysis. This paper presents an efficient single-step frequency domain inverse transient analysis (FDITA) method for simultaneous identifications of viscoelastic parameters and leaks in plastic pipes, so as to enhance the applicability and accuracy of TBMs. Both the single and branched polymeric pipe systems are applied for the method development and application. To this end, analytical solutions of single and branched systems from the transfer matrix method are firstly derived to represent the transient frequency responses of viscoelastic pipelines with leaks. A global optimized nonlinear curve fitting method is then employed to identify both viscoelastic parameters and potential leaks by knowing/measuring other system and flow conditions. Extensive experimental validations and numerical applications of both single and branched pipe systems demonstrate the very good efficiency and accuracy of the developed method for leak detection in different viscoelastic pipe systems. Furthermore, the mechanism of transient wave-leak-viscoelasticity is analysed based on these application results and theoretical evidence. Finally, a sensitivity analysis is performed to quantify and discuss the advantages and potential limitations of the developed method in the paper.

Mathematical modeling parametric vibrations of the pipeline with pulsating fluid flow

A mathematical model of the dynamics of a straight viscoelastic pipe conveying pulsating fluid has been developed in the paper. Using the Bubnov-Galerkin method, a mathematical model of the problem is reduced to solving a system of ordinary integro-differential equations, where time is an independent variable. Solution of integro-differential equations is determined by a numerical method based on the elimination of a singularity in the relaxation kernel of an integral operator. A system of algebraic equations is obtained according to the numerical method for unknowns. To solve the system of algebraic equations, the Gauss method is used. A computational algorithm is developed for solving the problems of the dynamics of viscoelastic pipelines conveying fluid.

Numerical study of the effect of viscoelastic properties of the material and bases on vibration fatigue of pipelines conveying pulsating fluid flow

The article presents the results of mathematical and computer modeling of the oscillatory processes of viscoelastic pipelines considering stationary external loads. A mathematical model of viscoelastic pipeline vibrations based on the theory of beams was developed when a pulsating fluid flows through it. Using the Bubnov-Galerkin method, based on a polynomial approximation of deflections, the problem was reduced to the study of a system of ordinary integro-differential equations, the solution of which was found numerically. A computational algorithm has been developed to solve vibration problems of composite pipelines conveying pulsating fluid. Stability and amplitude-time characteristics of vibrations of composite pipelines conveying pulsating fluid were studied at wide range of parameters variation of deformable systems and fluid flow. Critical fluid flow rates were found at which a viscoelastic pipe lost its rectilinear equilibrium shape. A singularity effect in hereditary kernels on vibrations of structures with viscoelastic properties was numerically studied. It was shown that with an increase in viscosity parameter of the pipeline material, the critical flow rate decreases. It was revealed that an increase in fluid pulsation frequency and excitation coefficient led to a decrease in the fluid flow critical rate. It was stated that an increase in Winkler bases parameters and the rigidity parameter of a continuous layer led to an increase in the critical flow rate.

Numerical modeling of vibration fatigue of viscoelastic pipelines conveying pulsating fluid flow

The effect of investigation results on viscoelastic properties of the material and bases on vibration fatigue of a pipeline conveying pulsating fluid flow is given in the paper. A mathematical model of viscoelastic pipeline vibrations based on the theory of beams was developed when a pulsating fluid flows through it. A computational algorithm has been developed to solve vibration problems of composite pipelines conveying pulsating fluid. Stability and amplitude-time characteristics of vibrations of composite pipelines conveying pulsating fluid were studied at wide range of parameters variation of deformable systems and fluid flow.

Dynamic analysis of the suspended composite pipelines conveying pulsating fluid

The problems of oscillations of a viscoelastic pipeline conveying fluid flow are considered in the paper. Mathematical models of these problems are constructed in a one-dimensional statement. The motion of a pipeline completely filled with a flowing fluid is studied. The transverse oscillations of a pipeline interact with the pipe walls, changing the nature of system oscillations. It is assumed that a pulsating fluid flows in the pipeline. Though the effect of flowing fluid on the pipe motion is considered in the paper, the effect of the pipe on fluid flow is not taken into account here. The mathematical model of the problem is described by the systems of partial integro-differential equations (IDE) with corresponding initial and boundary conditions. Partial IDE obtained using the Bubnov-Galerkin method under considered boundary conditions are reduced to solving ordinary IDE systems with constant coefficients relative to time function. The integration of systems of equations obtained on the basis of a polynomial approximation of deflections was carried out numerically. Based on this method, the algorithms are developed for numerically solving one-dimensional problems of oscillation and stability of viscoelastic pipes conveying fluid flow. It was found that an increase in internal pressure parameter leads to a decrease in critical flow rate. It was shown that an increase in the singularity parameter and the rigidity parameter of continuous layer of a base leads to an increase in critical flow rate. It was revealed that an increase in transverse stationary external load leads to an increase in the amplitude of pipe oscillations.

Numerical simulation of vibration of composite pipelines conveying fluids with account for lumped masses

Vibration problems of pipelines made of composite materials with account for lumped masses are considered in the paper. A mathematical model of motion of pipelines conveying fluid flow is developed based on the Winkler base with account for viscosity properties of the material of structures and pipeline bases, axial forces, internal pressure, resistance forces and lumped masses. To describe the strain processes in viscoelastic materials, the Boltzmann-Volterra integral model with weakly singular hereditary kernels is used. Using the Bubnov-Galerkin method, the problem is reduced to the study of a system of ordinary integro-differential equations. A computational algorithm is developed based on the elimination of the features of integro-differential equations with weakly singular kernels, followed by the use of quadrature formulas. The effect of rheological parameters of the pipeline material, lumped masses, internal pressure, Reynolds numbers and base parameters on the vibration of a viscoelastic pipeline conveying fluid flow is analyzed. It is revealed that the viscosity parameters of the material and the pipeline base lead to a significant change in critical flow rate. It was found that an increase in the viscosity parameter, the parameters of lumped masses and internal pressure leads to a decrease in critical flow rate. It is shown that when the lumped masses are moved away from the center along the pipeline length the vibration frequency increases.

Dynamic Analysis of the Viscoelastic Pipeline Conveying Fluid with an Improved Variable Fractional Order Model Based on Shifted Legendre Polynomials

Viscoelastic pipeline conveying fluid is analyzed with an improved variable fractional order model for researching its dynamic properties accurately in this study. After introducing the improved model, an involuted variable fractional order, which is an unknown piecewise nonlinear function for analytical solution, an equation is established as the governing equation for the dynamic displacement of the viscoelastic pipeline. In order to solve this class of equations, a numerical method based on shifted Legendre polynomials is presented for the first time. The method is effective and accurate after the numerical example verifying. Numerical results show that how dynamic properties are influenced by internal fluid velocity, force excitation, and variable fractional order through the proposed method. More importantly, the numerical method has shown great potentials for dynamic problems with the high precision model.

Numerical Simulation of Vibration of Composite Pipelines Conveying Pulsating Fluid

Vibration problems of pipelines made of composite materials conveying pulsating flow of gas and fluid are investigated in the paper. A dynamic model of motion of pipelines conveying pulsating fluid flow supported by a Hetenyi’s base is developed taking into account the viscosity properties of the structure material, axial forces, internal pressure and Winkler’s viscoelastic base. To describe the processes of viscoelastic material strain, the Boltzmann–Volterra integral model with weakly singular hereditary kernels is used. Using the Bubnov–Galerkin method, the problem is reduced to the study of a system of ordinary integro-differential equations (IDE). A computational algorithm is developed based on the elimination of the features of IDE with weakly singular kernels, followed by the use of quadrature formulas. The effect of rheological parameters of the pipeline material, flow rate and base parameters on the vibration of a viscoelastic pipeline conveying pulsating fluid is analyzed. The convergence analysis of the approximate solution of the Bubnov–Galerkin method is carried out. It was revealed that the viscosity parameters of the material and the pipeline base lead to a significant change in the critical flow rate. It was stated that an increase in excitation coefficient of pulsating flow and the parameter of internal pressure leads to a decrease in the critical flow rate. It is shown that an increase in the singularity parameter, the Winkler base parameter, the rigidity parameter of the continuous base layer and the Reynolds number increases the critical flow rate.

Mathematical simulation of nonlinear oscillations of viscoelastic pipelines conveying fluid

• A mathematical model of the problem of nonlinear oscillations of a viscoelastic pipeline conveying fluid is developed. • A computational algorithm is developed to solve the problems of the dynamics of viscoelastic pipelines. • Numerically investigated the influence of singularity in the heredity kernels on vibrations of the pipeline. A mathematical model of the problem of nonlinear oscillations of a viscoelastic pipeline conveying fluid is developed in the paper. The Boltzmann–Volterra integral model with weakly singular kernels of heredity is used to describe the processes of pipeline strain. Using the Bubnov–Galerkin method, the mathematical model of the problem is reduced to the study of a system of ordinary integro-differential equations, where time is an independent variable. The solution of integro-differential equations is determined by a numerical method based on the elimination of the singularity in the relaxation kernel of the integral operator. Using the numerical method for unknowns, a system of algebraic equations is obtained. To solve a system of algebraic equations, the Gauss method is used. A computational algorithm is developed to solve the problems of the dynamics of viscoelastic pipelines with a flowing fluid. The algorithm of the proposed method makes it possible to investigate in detail the effect of rheological parameters on the character of vibrational strength of viscoelastic pipelines with a fluid flow, in particular, in the study of free oscillations of pipelines based on the theory of ideally elastic shells. On the basis of the computational algorithm developed, a set of applied computer programs has been created, which makes it possible to carry out numerical studies of pipeline oscillations. The influence of singularity in the heredity kernels and the geometric parameters of the pipeline on the vibrations of structures possessing viscoelastic properties is numerically investigated. It is shown that an account of viscoelastic properties of pipeline material leads decrease in the amplitude and frequency of oscillation. It is established that to reveal the influence of viscoelastic properties of structure material on the pipeline oscillations, it is necessary to use the Abel-type weakly singular kernels of heredity. The obtained results of numerical simulation can be used in the enterprises of oil and gas industries, as well as in design organizations.

Extended Bubble Cavitation Model to predict water hammer in viscoelastic pipelines

The equation of continuity describing the two-phase bubble flow was modified to take into account the influence of the viscoelasticity of the pipe walls. The modified equation of continuity together with the equation of motion was solved using the method of characteristics. Simulations carried out using in-house written program in Matlab indicate a high correspondence between simulated and experimental runs. The modified Shu model is characterized by simple construction, thanks to which it is easy to quickly implement this solution in commercial computer programs used to model transient states in pipes. It takes into account three basic phenomena accompanying these flows, namely: frequency-dependent hydraulic resistance, cavitation and viscoelastic effect off the pipe wall. Further work on its extension is underway.

Analogy of a Linear Chain and Seismic Vibrations of Segmental and Viscoelastic Pipelines

In the problem of seismic vibrations of a segmental pipeline with damping joints, deformed by the law of linear viscoelasticity, an original analogy with a linear chain of concentrated masses was put forward. The constructed discrete system generalizes the monatomic lattice model in the sense that the viscoelastic interaction between the masses of the chain is considered and, moreover, the forced (and not own) oscillations of such a system are investigated. By the transition from a discrete system to a continuous one, the integro-differential oscillation equation of a segmented pipeline with viscoelastic joints in an elastically resisting medium is obtained. This equation is a generalization of the well-known Klein–Gordon differential equation describing the “constrained” vibrations of an elastic rod or string in a medium with elastic resistance. In addition, the equation gives the problem of seismic vibrations of a continuous pipeline from a polymer (viscoelastic) material. Joint stationary seismic vibrations of a viscoelastic pipeline and soil were studied in an exact formulation and maximum stresses in the pipeline were found by solving the resulting integro-differential equation. The same stresses were found using the “hard pinch” engineering approach, according to which displacements and deformations in the seismic wave and pipeline are the same. By analyzing the stresses found under the viscoelasticity law in the form of the Kelvin–Voigt model relationship, it is established that the generally accepted position that the engineering approach gives an upper estimate for the stresses in the pipeline is valid only in the subsonic case (when the seismic wave velocity is lower than the wave velocity in the pipeline) and is not valid in the supersonic mode, when the exact theory can lead to stresses exceeding those calculated on the basis of the engineering approach.