Remerciez-le!

Remerciez @Admin pour avoir partagé cet document gratuitement, de la manière la plus simple, en partageant sur les réseaux sociaux.

Speed Control of Pipeline Pig Using the QFT Method M. Mirshamsi and M. Rafeeyan

Speed Control of Pipeline Pig Using the QFT Method M. Mirshamsi and M. Rafeeyan Department of Mechanical Eng., Faculty of Engineering, Yazd University - Islamic Republic of Iran e-mail: mirshamsi_malihe@yahoo.com - rafeeyan@yazduni.ac.ir Résumé — Contrôle de la vitesse d’un racleur grâce à la méthode de synthèse QFT — Pour qu’une inspection de pipeline soit efficace, l’opération de raclage doit être réalisée à vitesse constante. Cet article présente une méthode simple et efficace fondée sur la théorie QFT (Quantitative Feedback Theory), système de régulation robuste bien connu, permettant de contrôler la vitesse d’un racleur avec bypass dans un oléoduc. Ce régulateur classique commande l’ouverture ou la fermeture d’une soupape installée sur le racleur. Le racleur est ensuite contrôlé grâce au volume de fluide qui le traverse. Pour cela, l’équation dynamique non linéaire du mouvement du racleur est convertie en un ensemble de structures linéaires instables équivalentes via la méthode Sobhani-Rafeeyan (méthode SR). Puis, un régulateur de type QFT est synthétisé. La méthode présentée est conçue pour des pipelines bidimensionnels dans deux situations différentes. Le régulateur créé est simulé numériquement grâce à la boîte à outils Simulink du logiciel MATLAB. Les résultats de la simulation montrent que le régulateur peut être utilisé pour contrôler efficacement la vitesse du racleur lorsque celui-ci passe dans des oléoducs. Abstract — Speed Control of Pipeline Pig Using the QFT Method — To provide an efficient inspection of pipeline, pigging operations must be executed at a constant speed. This paper presents an efficient and simple method based on Quantitative Feedback Theory (QFT), which is a well-known robust controller scheme, for speed control of a pig with bypass flow in a liquid pipeline. This classical-type controller commands the valve installed in the body of the pig to open or close. Then, the pig is controlled using the amount of bypass flow across its body. For this purpose, the nonlinear dynamic equation of motion of the pig is converted to a family of linear uncertain equivalent plants using Sobhani-Rafeeyan’s method (SR method). Then, for this family of uncertain equivalent plants, a QFT-type controller is synthesized. The presented method is developed for two-dimensional pipelines in two cases. The designed controllers are simulated numerically using the Simulink toolbox of the MATLAB software. The simulation results show that the designed controller can be used for speed control of the pig with good performance when it runs in the liquid pipelines. Oil & Gas Science and Technology – Rev. IFP Energies nouvelles, Vol. 67 (2012), No. 4, pp. 693-701 Copyright © 2012, IFP Energies nouvelles DOI: 10.2516/ogst/2012008 Oil & Gas Science and Technology – Rev. IFP Energies nouvelles, Vol. 67 (2012), No. 4 694 LIST OF SYMBOLS Ah Area cross-section of the valve D Pipeline diameter g Acceleration of gravity lpig Length of the pig ptail Pressure in the tail of the pig pnose Pressure in the nose of the pig Vpig Velocity of the pig z(x) Height of the selected position d Internal diameter of pipeline dvalve Bypass valve diameter Greek symbols ρ Density of fluid μ Coefficient of friction INTRODUCTION Pigging operations are common and frequently used in the oil and gas transportation industries since it is the only way to monitor the conditions of the inside walls of the buried pipelines for inspection purposes. There are several types of pigs and each type is designed for a desired purpose. All of the pigs act better if they run at a near constant speed. Most pigging operations such as batching, cleaning and liquid removal in gas pipelines are done at normal operating velocities with the regular flow of the product. This velocity is generally in the range of 1-5 m/s in liquid pipelines and 2-7 m/s in gas pipelines [1]. The smart pigs (pipeline inspection gauges) are usually equipped with a number of transducers which are installed on it circumferentially for detection of surface defects such as cracks, corrosion, etc. Frequency response limitations of these transducers, which are often MFL (Magnetic Flux Leakage) type, lead to keeping their speeds nearly constant during data acquisition. The more accurate the data acquisition, the greater the decrease in cost and time of the maintenance and future dangerous accidents. To keep the velocity of the pig constant, a bypass flow pig type can be used. The speed of this pig is controlled using the amount of bypass flow across its body. The amount of bypass flow is regulated by a valve installed on it. This pig is driven by injected fluid flow behind its tail and expelled fluid flow in front of its nose. Few studies have been done on the motion of pigs, especially concerning their speed control in pipelines. Some of these studies are experimental research or have a commercial basis. Dynamic modeling of various pigs is one of the current subjects that several interesting investigations have been conducted on. It seems that the first one was introduced by [2]. This modeling was modified and improved by removing some limitations in [3]. The first pigging model based on full two- phase transient flow formulation was proposed by [4]. This model is composed of correlations for pressure drop across the pig, slug holdup, pigging efficiency, a pig velocity model and a gas and liquid mass flow boundary condition applied to the slug front. Some other complementary research was also reported for pigging simulation in two-phase flow straight pipelines [5-8]. Transient pig motion through gas and liquid pipelines was presented by [9]. Modeling and simulation for pig flow control in a natural gas pipeline was studied by [10]. This paper solved the governing partial differential equa- tions of the pig using the method of characteristics. Another modeling with a similar solution method but with more accurate equations was studied by [11]. It seems that the first investigation which deals with the speed control of a bypass flow pig in a natural gas pipeline was [1]. In this research, a simple nonlinear controller was proposed for controlling the pig velocity when it moves in a natural gas straight pipeline. Also, to provide an efficient tool to assist in the control and design of pig operations through pipelines, a numerical code has been developed by [12]. The results obtained with the code in this research were compared with experimental results and a good agreement between the two was obtained. In all these studies mentioned, researchers assumed that the pig moves in a straight line in the plane. Simulation of a small pig in space pipeline was studied first by [13]. In this research, the effect of the flow field on the pig’s trajectory was ignored. This effect was considered in [14] for a bypass flow pig in space pipeline. The objective of the present work is to synthesize a linear classical feedback controller for speed control of the bypass flow pig to keep its velocity near a constant value. To do this, the nonlinear equation of motion of the pig is converted to a family of linear uncertain equivalent plants using the SR method [15]. Then, for two different case studies, QFT-type robust controllers are synthesized for the family of linear uncertain plants. The designed controllers are simulated on the main system (nonlinear system). The simulation results show that these controllers can control the speed of the pig perfectly. 1 GOVERNING EQUATION OF THE PIG MOTION Figure 1 shows a typical small pig moving inside a two- dimensional pipeline and its free body diagram. The weight of the pig, mg, dry friction, Fμ = μN, normal force by the pipe wall, N, upstream acting force of the fluid, F 1 and downstream acting force of the fluid, F 2, are the forces acting on the pig. The dynamic equations of the pig, derived from Newton’s second law along the tangential and normal directions, are as follows: N – mg cosθ = man (1) F 1 – F 2 – mg sinθ – sgn(x ·)Fμ = mat (2) where θ is the angle of the tangent to the centerline curve of the pipeline with respect to the x-axis at any point; i.e. if f(x) M Mirshamsi and M Rafeeyan / Speed Control of Pipeline Pig Using the QFT Method 695 is assumed to be the function of the centerline of the pig, thus we can write: (3) If s measures along the pig’s path and the radius of curvature of the path is R, then we can derive both accelerations of the pig as follows: (4) (5) (6) The term F 1 – F 2 on the left side of Equation (2) can be derived as follows [13]: see Equation (7). a d s dt f x f x f x x x f x t = = ′′ ′ + ′ + + ′ 2 2 2 2 2 1 1 ( ) ( ) ( ) ( )2 a V R f x f x x n pig = = ′′ + ′ 2 2 2 1 ( ) ( ) V s uploads/Management/ speed-control-of-pipeline-pig-using-the-qft-method.pdf