1165This paper deals with dynamic analysis of Pipeline Inspection Gauge (PIG) flow control in natural gas pipelines. The dynamic behaviour of PIG depends on the pressure differential generated by injected gas flow behind the tail of the PIG and expelled gas flow in front of its nose. To analyze dynamic behaviour characteristics (e.g. gas flow, the PIG position and velocity) mathematical models are derived. Two types of nonlinear hyperbolic partial differential equations are developed for unsteady flow analysis of the PIG driving and expelled gas. Also, a non-homogeneous differential equation for dynamic analysis of the PIG is given. The nonlinear equations are solved by method of characteristics (MaC) with a regular rectangular grid under appropriate initial and boundary conditions. Runge-Kutta method is used for solving the steady flow equations to get the initial flow values and for solving the dynamic equation of the PIG. The upstream and downstream regions are divided into a number of elements of equal length. The sampling time and distance are chosen under Courant -Friedrich-Lewy (CFL) restriction. Simulation is performed with a pipeline segment in the Korea gas corporation (KOGAS) low pressure system, Ueijungboo-Sangye line. The simulation results show that the derived mathematical models and the proposed computational scheme are effective for estimating the position and velocity of the PIG with a given operational condition of pipeline. A: Pipe cross section area [m 2 ] c : Wave speed [m/s] C : Linear damping coefficient of PIG [Ns/m] C c : Convection heat transfer coefficient [W/m 2 K] C; : Specific heat at constant volume [J/kgK] d : Internal diameter of pipe [rn] e : Internal energy per unit mass [J/kg] • Corresponding Author, FfPsta FfPdYn r, g h f k K I L PI G m M : Darcy friction coefficient : Braking force [N] : Friction force per unit pipe length [N/m] : Friction force between PIG and pipe wall' including [N] : Static friction force : Dynamic friction force : PIG driving force [N] : Gravity acceleration [m/S2] : Pipe head loss [m] : Pipe wall roughness [m] : Wear factor per distance travel [N/m] : Length of pipeline [m] : Length of PIG [m] : Hydraulic mean radius of pipe [m] : Weight of PIG [kg] P : Flow pressure [N/m 2 ] q : Compound rate of heat inflow per unit area of pipe wall [W'/m 2 ] R : Gas constant [J/kgK] S : Perimeter of pipe [m] T : Flow temperature [K] Text : Seabed temperature [K] u : Flow velocity [m/s] x : Distance from pipe inlet [m] XPiC : Position of PIG [m] VPlC : Velocity of PIG [rn/s] Greeks r : The ratio of specific heat !.I : Kinetic viscosity of flow [m 2/s] p : Fluid density [kg/m 3 ] SubscriptsL, R, M, N, S, 0, P: The grid points, and 0, I : The points at inlet and outlet of pipeline
In this paper, a control scheme that combines a kinematic controller and a sliding mode dynamic controller with external disturbances is proposed for an automatic guided vehicle to track a desired trajectory with a specified constant velocity. It provides a method of taking into account specific mobile robot dynamics to convert desired velocity control inputs into torques for the actual mobile robot. First, velocity control inputs are designed for the kinematic controller to make the tracking error vector asymptotically stable. Then, a sliding mode dynamic controller is designed such that the mobile robot's velocities converge to the velocity control inputs. The control law is obtained based on the backstepping technique. System stability is proved using the Lyapunov stability theory. In addition, a scheme for measuring the errors using a USB camera is described. The simulation and experimental results are presented to illustrate the effectiveness of the proposed controller.
This paper introduces modeling and simulation results for pipeline inspection gauge (PIG) with bypass flow control in natural gas pipeline. The dynamic behaviour of the PIG depends on the different pressure across its body and the bypass flow through it. The system dynamics includes: dynamics of driving gas flow behind the PIG, dynamics of expelled gas in front of the PIG, dynamics of bypass flow, and dynamics of the PIG. The bypass flow across the PIG is treated as incompressible flow with the assumption of its Mach number smaller than 0.45. The governing nonlinear hyperbolic partial differential equations for unsteady gas flows are solved by method of characteristics (MOC) with the regular rectangular grid under appropriate initial and boundary conditions. The Runge-Kuta method is used for solving the steady flow equations to get initial flow values and the dynamic equation of the PIG. The sampling time and distance are chosen under Courant-Friedrich-Lewy (CFL) restriction. The simulation is performed with a pipeline segment in the Korea Gas Corporation (KOGAS) low pressure system, Ueijungboo -Sangye line. Simulation results show us that the derived mathematical model and the proposed computational scheme are effective for estimating the position and velocity of the PIG with bypass flow under given operational conditions of pipeline.A : Pipe cross section [m 2 ] c : Wave speed [m/s] C : Linear damping coefficient of the PIG [Ns/m] C c : Convection heat transfer coefficient [W/m 2 K] d : Internal diameter of pipe Em] dvalve : Bypass valve diameter Em] r, : Braking force [N]
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.