Michael A. Adewumi

Simulation of transients in natural gas pipelines using hybrid TVD schemes

The mathematical model describing transients in natural gas pipelines constitutes a non-homogeneous system of non-linear hyperbolic conservation laws. The time splitting approach is adopted to solve this non-homogeneous hyperbolic model. At each time step, the non-homogeneous hyperbolic model is split into a homogeneous hyperbolic model and an ODE operator. An explicit 5-point, second-order-accurate total variation diminishing (TVD) scheme is formulated to solve the homogeneous system of non-linear hyperbolic conservation laws. Special attention is given to the treatment of boundary conditions at the inlet and the outlet of the pipeline. Hybrid methods involving the Godunov scheme (TVD/Godunov scheme) or the Roe scheme (TVD/Roe scheme) or the Lax–Wendroff scheme (TVD/LW scheme) are used to achieve appropriate boundary handling strategy. A severe condition involving instantaneous closure of a downstream valve is used to test the efficacy of the new schemes. The results produced by the TVD/Roe and TVD/Godunov schemes are excellent and comparable with each other, while the TVD/LW scheme performs reasonably well. The TVD/Roe scheme is applied to simulate the transport of a fast transient in a short pipe and the propagation of a slow transient in a long transmission pipeline. For the first example, the scheme produces excellent results, which capture and maintain the integrity of the wave fronts even after a long time. For the second example, comparisons of computational results are made using different discretizing parameters. Copyright

Possible Detection of Multiple Blockages Using Transients

This work explores the possibility of utilizing the interaction between a pressure pulse propagating in a pipe with the blockages therein, as a means of blockage detection and characterization. Whereas an earlier work focused on a single blockage, the present work attempts to extend the strategy to multiple blockages. A one-dimensional isothermal non-compositional single-phase Eulerian model was used to describe the propagation of a pressure pulse through a pipe with multiple blockages. Pressure variations at the inlet caused by reflections of the propagating transient are monitored and analyzed. This analysis is used to make deductions about the internal configuration of the pipe. The results demonstrate that the technique is feasible and that accurate characterization of multiple blockages is possible.

Low-Liquid Loading Multiphase Flow in Natural Gas Pipelines

Pressure and temperature variations of natural gas flows in a pipeline may cause partial gas condensation. Fluid phase behavior and prevailing conditions often make liquid appearance inevitable, which subjects the pipe flow to a higher pressure loss. This study focuses on the hydrodynamic behavior of the common scenarios that may occur in natural gas pipelines. For this purpose, a two-fluid model is used. The expected flow patterns as well as their transitions are modeled with emphasis on the low-liquid loading character of such systems. In addition, the work re-examines previous implementations of two-flow model for gas-condensate flow.

Pressure Transients Across Constrictions

The modeling of pressure transient across constrictions is achieved by using a one-dimensional, isothermal, noncompositional, single-phase representation of the Eulerian model. A TVD scheme was used to solve the ensuing nonhomogeneous hyperbolic set of first-order quasi-linear partial differential equations. Three types of constrictions were modeled and in each case the behavior of the transient was analyzed, This analysis was used to interpret the pressure response at the inlet resulting from the reflection of the transient at the constrictions. The comparisons between the predicted and inputted data are very good, suggesting that the technique has much promise.

Particle deposition from turbulent flow in a pipe

Abstract Diffusive particle deposition rates are predicted on the walls of a straight, smooth circular tube in which fully developed turbulent flow exist. As a pre-requisite to calculating particle wall flux, the particle mass balance equation (convective diffusion) is solved, using the method of separation of variables. A sub-layer model is used, in which a thin laminar sub-layer is considered to be imbedded within the turbulent boundary layer. In the region outside the laminar sub-layer, the time-averaged transport of particles to the wall is enhanced because of the turbulence induced eddy-diffusivity of the particles. Inside the laminar sub-layer close to the wall, the effect of turbulence is considered negligible and transport of particles to the surface is dominated by particle Brownian diffusivity. Using method of separation of variables, the problem is reduced to one of solving an ordinary differential equation which belongs to the Sturm-Liouville class of equations. We compute and report the first ten eigenvalues and associated eigenfunctions of the reduced equation along with the relevant constants needed to estimate the evolving particle number density profile and time-averaged particle wall deposition rates. Particle deposition rates have been estimated for Reynolds numbers and particle Schmidt numbers ranges of greatest practical interest. Asymptotic eigenvalues are reported and are seen to be in good agreement with the computed values. Application of the results to estimate the inertial contribution to the particle deposition rates in the eddy diffusion-impaction regime is also illustrated and generalizations of our methods have been discussed.

Two-dimensional steady state hydrodynamic analysis of gas—solids flow in vertical pneumatic conveying systems

Abstract Pneumatic conveying, as a mode of solid particles transportation, is widely used in the petroleum, chemical, petrochemical, gas processing and food processing industries. Within the last decade, there has been increasing demand for an optimized utilization of this technology, particularly in the energy conversion processes. Such optimized utilization of this technology requires good understanding of the hydrodynamic behavior of gas-solids mixture flow in pipes and the capability to predict such behavior. Empirical correlations have been developed in the literature for predicting some of the more commonly sought design variables such as pressure drop. Most of such correlations were developed using one-dimensionally based experimental data. Apart from being limited to the data-base used in developing them, they ignore the effect of radial non-uniformity of the basic variables such as solid velocity, void fraction, etc. More recent experimentations confirm this non-radial uniformity of such important design variables as solid velocity and solid concentration. We present a two-dimensional steady state two-phase hydrodynamic model to describe upward co-current pneumatic conveying of solid particles in vertical pipe. The model incorporates viscous dissipation terms in both the gas phase and the particulate phase. Numerical solution was obtained using the numerical method of lines. The predicted system variables and their distributions under different operating conditions agree with the observed behavior of the system reported in the literature. The predicted solid velocity profiles using this model agree reasonably well with available experimental data.

Study of Gas Condensation in Transmission Pipelines With a Hydrodynamic Model

A nonisothermal, ID, compositional, two-fluid, multiphase hydrodynamic model is used to describe the incipient formation and dynamic behavior of condensate in a natural-gas pipeline with undulating topology. The 26-in. (66-cm)-diameter case-study transmission pipeline traverses 180 elevation changes in its 30.72-mile (49.4-km) span. Results demonstrate the predictive and descriptive potential of the model in field applications and the significant effect of inclination and inclination changes on the hydrodynamics of gas/condensate flow in transmission pipelines. The model presented can serve both predictive and design purposes.

Compositional Multiphase Hydrodynamic Modeling of Gas/Gas-Condensate Dispersed Flow in Gas Pipelines

A nonisothermal ID steady-state compositional two-phase hydrodynamic model describes the formation and flow dynamics of gas condensate in horizontal natural gas pipelines. The two major constituents of the model, hydrodynamics and phase behavior, are coupled through the phase-generation/disappearance-related terms in the continuity and momentum equations. The model is demonstrably capable of predicting the amount, quantity, and distribution of condensate in the pipeline, in addition to the other commonly sought engineering design variables. Parametric studies show that the model is capable of predicting the phenomena associated with gas condensation in pipelines.

Multiphase hydrodynamic analysis of pneumatic transportation ofdrill cuttings in air drilling

Abstract Analysis of wellbore hydraulics is motivated by the need for improved understanding of this system so as to enhance air drilling operation. A viable wellbore hydraulics model is utilized as the basis for this study. Several important parameters that influence air drilling operations are analyzed, such as drill cutting size and size distribution, hole size changes, attrition, and particle shape. This work defines several areas that need special investigation and sheds light on several previously unanswered questions. The most salient findings are that hole size changes, cuttings size and size distribution and particle shape affect the wellbore hydraulics very significantly. The analysis leads to the evolution of a clear explanation for choking in air drilling.

A Unified Two-Fluid Model for Multiphase Flow in Natural Gas Pipelines

A unified two-fluid model for multiphase natural gas and condensate flow in pipelines is presented. The hydrodynamic model consists of steady-state one-dimensional mass and continuity balances for each phase and a combined energy equation to give a system of five first-order ordinary differential equations. The hydrodynamic model is coupled with a phase behavior model based on the Peng-Robinson equation of state to handle the vapor-/liquid equilibrium calculations and thermodynamic property predictions. The model handles single and two-phase flow conditions and is able to predict the transition between them. It also generates profiles for pressure, temperature, and the fluid velocities in both phases as well as their holdups. The expected flow patterns as well as their transitions are modeled with emphasis on the low liquid loading character of such systems. The expected flow regimes for this system are dispersed liquid, annular-mist, stratified smooth as well as stratified wavy.Copyright