Dynamic Modeling of Non-Isothermal Gas Pipeline Systems

2004 ◽  
Author(s):  
Mohammad Abbaspour ◽  
Kirby S. Chapman ◽  
Ali Keshavarz
Keyword(s):  
Natural Gas ◽  
Finite Difference ◽  
Mathematical Models ◽  
Gas Pipeline ◽  
Pipeline System ◽  
Time Step ◽  
Inertia Term ◽  
Fully Implicit ◽  
Pipeline Systems ◽  
Implicit Finite Difference

Natural gas systems are becoming more and more complex as the usage of this energy source increase. Mathematical models are used to design, optimize, and operate increasingly complex natural gas pipeline systems. Researchers continue to develop unsteady mathematical models that focus on the unsteady nature of these systems. Many related design problems, however, could be solved using steady-state modeling. Several investigators have studied the problem of compressible fluid flow through pipelines and have developed various numerical schemes, which include the method of characteristics, finite element methods, and explicit and implicit finite difference methods. The choice partly depends on the individual requirements of the system under investigation. In this work, the fully implicit finite difference method was used to solve the continuity, momentum, energy, and equations of state for flow within a gas pipeline system. The particular solution method described in this paper does not neglect the inertia term in the conservation of momentum equation. It also considered the compressibility factor as a function of temperature and pressure, and the friction factor as a function of the Reynolds number. the fully implicit method representation of the equations offer the advantage of guaranteed stability for a large time step, which is very useful for the gas industry. The results show that the effect of treating the gas in a non-isothermal manner is extremely necessary for pipeline flow calculation accuracies, especially for rapid transient processes. The results indicate that the inertia term plays an important role in the gas flow analysis and cannot be neglected from the calculation.

Seismic Vulnerability Assessment and Retrofit of a Major Natural Gas Pipeline System: A Case History

2005 ◽  
Vol 21 (2) ◽  
pp. 539-567 ◽  
Author(s):  
Dharma Wijewickreme ◽  
Douglas Honegger ◽  
Allen Mitchell ◽  
Trevor Fitzell
Keyword(s):  
Natural Gas ◽  
Vulnerability Assessment ◽  
Seismic Vulnerability ◽  
Ground Improvement ◽  
Lateral Spreading ◽  
Gas Pipeline ◽  
Pipeline System ◽  
Seismic Vulnerability Assessment ◽  
Natural Gas Pipeline ◽  
Pipeline Systems

The performance of pipeline systems during earthquakes is a critical consideration in seismically active areas. Unique approaches to quantitative estimation of regional seismic vulnerability were developed for a seismic vulnerability assessment and upgrading program of a 500-km-long natural gas pipeline system in British Columbia, Canada. Liquefaction-induced lateral spreading was characterized in a probabilistic manner and generic pipeline configurations were modeled using finite elements. These approaches, developed during the early part of this 10-year program, are more robust than typical approaches currently used to assess energy pipeline systems. The methodology deployed within a GIS environment provided rational means of distinguishing between seismically vulnerable sites, and facilitated the prioritization of remedial works. While ground improvement or pipeline retrofit measures were appropriate for upgrading most of the vulnerable sites, replacement of pipeline segments using horizontal directional drilling to avoid liquefiable zones were required for others.

Dynamic Simulation of Gas-Liquid Homogeneous Flow in Natural Gas Pipeline Using Two-Fluid Conservation Equations

2005 ◽  
Author(s):  
Mohammad Abbaspour ◽  
Kirby S. Chapman ◽  
Larry A. Glasgow ◽  
Zhongquan C. Zheng
Keyword(s):  
Natural Gas ◽  
Large Time ◽  
Gas Pipeline ◽  
Phase Flow ◽  
Time Step ◽  
Two Phase ◽  
Natural Gas Pipeline ◽  
Fully Implicit ◽  
Large Time Step ◽  
Two Fluid

Homogeneous two-phase flows are frequently encountered in a variety processes in the petroleum and gas industries. In natural gas pipelines, liquid condensation occurs due to the thermodynamic and hydrodynamic imperatives. During horizontal, concurrent gas-liquid flow in pipes, a variety of flow patterns can exist. Each pattern results from the particular manner by which the liquid and gas distribute in the pipe. The objective of this study is to simulate the non-isothermal, one-dimensional, transient homogenous two-phase flow gas pipeline system using two-fluid conservation equations. The modified Peng-Robinson equation of state is used to calculate the vapor-liquid equilibrium in multi-component natural gas to find the vapor and liquid compressibility factors. Mass transfer between the gas and the liquid phases is treated rigorously through flash calculation, making the algorithm capable of handling retrograde condensation. The liquid droplets are assumed to be spheres of uniform size, evenly dispersed throughout the gas phase. The method of solution is the fully implicit finite difference method. This method is stable for gas pipeline simulations when using a large time step and therefore minimizes the computation time. The algorithm used to solve the nonlinear finite-difference thermo-fluid equations for two phase flow through a pipe is based on the Newton-Raphson method. The results show that the liquid condensate holdup is a strong function of temperature, pressure, mass flow rate, and mixture composition. Also, the fully implicit method has advantages, such as the guaranteed stability for large time step, which is very useful for simulating long-term transients in natural gas pipeline systems.

Nonisothermal Transient Flow in Natural Gas Pipeline

2008 ◽  
Vol 75 (3) ◽  
Author(s):  
M. Abbaspour ◽  
K. S. Chapman
Keyword(s):  
Gas Flow ◽  
Transient Flow ◽  
Flow Analysis ◽  
Compressibility Factor ◽  
Momentum Equation ◽  
Gas Pipeline ◽  
Time Step ◽  
Inertia Term ◽  
Fully Implicit ◽  
Energy Equations

The fully implicit finite-difference method is used to solve the continuity, momentum, and energy equations for flow within a gas pipeline. This methodology (1) incorporates the convective inertia term in the conservation of momentum equation, (2) treats the compressibility factor as a function of temperature and pressure, and (3) considers the friction factor as a function of the Reynolds number and pipe roughness. The fully implicit method representation of the equations offers the advantage of guaranteed stability for a large time step, which is very useful for gas pipeline industry. The results show that the effect of treating the gas in a nonisothermal manner is extremely necessary for pipeline flow calculation accuracies, especially for rapid transient process. It also indicates that the convective inertia term plays an important role in the gas flow analysis and cannot be neglected from the calculation.

Tests of the Stability and Time-Step Sensitivity of Semi-Implicit Reservoir Stimulation Techniques

1972 ◽  
Vol 12 (03) ◽  
pp. 253-266 ◽  
Author(s):  
James S. Nolen ◽  
D.W. Berry
Keyword(s):  
Finite Difference ◽  
Difference Equations ◽  
Implicit Method ◽  
Significant Advance ◽  
Relative Permeabilities ◽  
Time Step ◽  
Finite Difference Equations ◽  
Nonlinear Form ◽  
Implicit Finite Difference ◽  
Excellent Stability

Abstract A reservoir simulation technique that employs semi-implicit approximations to relative permeabilities exhibits excellent stability and permeabilities exhibits excellent stability and convergence characteristics when applied to water- or gas-coning problems. Recent workers in this area have made a simplifying assumption in order to linearize the flow terms of the semi-implicit finite-difference equations. This paper describes a method of solving efficiently paper describes a method of solving efficiently the nonlinear form of the equations and demonstrates that time-step sensitivity is reduced by iterating on the nonlinear terms. In addition, it addresses the problem of allocating a well's production among multiple grid blocks. Example problems include both water-coning and gas-percolation applications. Introduction Multiphase reservoir simulators traditionally have employed finite-difference approximations in which relative permeabilities are evaluated explicitly at the beginning of each time step. Simulators of this type are capable of handling many reservoir studies in a perfectly satisfactory fashion, but they are incapable of solving economically problems characterized by high flow velocities. Included in this category are the studies of such phenomena as well coning and gas percolation. The difficulty in such problems is a stability limitation imposed by the use of explicit relative permeabilities. In an attempt to overcome this permeabilities. In an attempt to overcome this limitation, Blair and Weinaug developed a simulator that employed implicitly evaluated relative permeabilities. The increased stability of their permeabilities. The increased stability of their equations allowed the use of time steps much larger than previously possible, but this was counteracted by an increase in the computational work per time step and an increased difficulty in the iterative solution of the difference equations. While the net result was a significant advance in the solution of coning problems, improvements still were needed to increase the dependability and decrease the cost of obtaining solutions for such problems. More recently, two papers were published describing a method that employs semi-implicit relative permeabilities. This method is greatly superior to the fully implicit method, both in computational effort and maximum time-step size. In developing this method, the previous workers made a simplifying assumption to obtain linear finite-difference equations. We have developed a reservoir simulator based on the nonlinear form of the semi-implicit finite-difference equations. This paper describes the techniques used in the simulator and presents the results of some tests conducted with it. These include time-step sensitivity studies and tests of alternate production allocation methods. Some of these tests compare the nonlinear form of the semi-implicit method with the linear form. SPEJ P. 253

Mathematical Model of Energy Storage in Gas Hydrate and its Flow in Pipeline Systems

2016 ◽  
Author(s):  
Oluwatoyin Akinsete ◽  
Sunday Isehunwa
Keyword(s):  
Mathematical Model ◽  
Natural Gas ◽  
Gas Hydrate ◽  
Storage Capacity ◽  
Hydrate Formation ◽  
Momentum Conservation ◽  
Gas Pipeline ◽  
Energy Needs ◽  
Pipeline Systems ◽  
And Storage

ABSTRACT Natural gas, one of the major sources of energy for the 21st century, provides more than one-fifth of the worldwide energy needs. Storing this energy in gas hydrate form presents an alternative to its storage and smart solution to its flow with the rest of the fluid without creating a difficulty in gas pipeline systems due to pressure build-up. This study was design to achieve this situation in a controlled manner using a simple mathematical model, by applying mass and momentum conservation principles in canonical form to non-isothermal multiphase flow, for predicting the onset conditions of hydrate formation and storage capacity growth of the gas hydrate in pipeline systems. Results from this developed model shows that the increase in hydrate growth, the more the hydrate storage capacity of gas within and along the gas pipeline. The developed model is therefore recommended for management of hydrate formation for natural gas storage and transportation in gas pipeline systems.

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