A LARGE TIME STEP ROE SCHEME APPLIED TO TWO-PHASE FLOW

2016 ◽  
Author(s):  
Sofia Lindqvist ◽  
Halvor Lund
Keyword(s):  
Large Time ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Time Step ◽  
Two Phase ◽  
Large Time Step

scholarly journals Numerical Fractional-Calculus Model for Two-Phase Flow in Fractured Media

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Wenwen Zhong ◽  
Changpin Li ◽  
Jisheng Kou
Keyword(s):  
Porous Media ◽  
Large Time ◽  
Two Phase Flow ◽  
Time Derivative ◽  
Fractured Porous Media ◽  
Phase Flow ◽  
Petroleum Reservoir ◽  
Time Step ◽  
Two Phase ◽  
Large Time Step

Numerical simulation of two-phase flow in fractured porous media is an important topic in the subsurface flow, environmental problems, and petroleum reservoir engineering. The conventional model does not work well in many cases since it lacks the memory property of fracture media. In this paper, we develop a new numerical formulation with fractional time derivative for two-phase flow in fractured porous media. In the proposed formulation, the different fractional time derivatives are applied to fracture and matrix regions since they have different memory properties. We further develop a two-level time discrete method, which uses a large time step for the pressure and a small time step size for the saturation. The pressure equation is solved implicitly in each large time step, while the saturation is updated by an explicit fractional time scheme in each time substep. Finally, the numerical tests are carried out to demonstrate the effectiveness of the proposed numerical model.

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.

scholarly journals Diffuse-interface two-phase flow models with different densities: A new quasi-incompressible form and a linear energy-stable method

2018 ◽  
Vol 28 (04) ◽  
pp. 733-770 ◽  
Author(s):  
M. Shokrpour Roudbari ◽  
G. Şimşek ◽  
E. H. van Brummelen ◽  
K. G. van der Zee
Keyword(s):  
Two Phase Flow ◽  
Linear Method ◽  
Diffuse Interface ◽  
Integration Scheme ◽  
Phase Flow ◽  
Time Step ◽  
Two Phase ◽  
Time Step Size ◽  
Mixture Density ◽  
Energy Stable

While various phase-field models have recently appeared for two-phase fluids with different densities, only some are known to be thermodynamically consistent, and practical stable schemes for their numerical simulation are lacking. In this paper, we derive a new form of thermodynamically-consistent quasi-incompressible diffuse-interface Navier–Stokes–Cahn–Hilliard model for a two-phase flow of incompressible fluids with different densities. The derivation is based on mixture theory by invoking the second law of thermodynamics and Coleman–Noll procedure. We also demonstrate that our model and some of the existing models are equivalent and we provide a unification between them. In addition, we develop a linear and energy-stable time-integration scheme for the derived model. Such a linearly-implicit scheme is nontrivial, because it has to suitably deal with all nonlinear terms, in particular those involving the density. Our proposed scheme is the first linear method for quasi-incompressible two-phase flows with non-solenoidal velocity that satisfies discrete energy dissipation independent of the time-step size, provided that the mixture density remains positive. The scheme also preserves mass. Numerical experiments verify the suitability of the scheme for two-phase flow applications with high density ratios using large time steps by considering the coalescence and breakup dynamics of droplets including pinching due to gravity.

Accuracy Study of the Flux-Corrected Transport Numerical Method Applied to Transient Two-Phase Flow Simulations in Gas Pipelines

2012 ◽  
Author(s):  
Aline B. Figueiredo ◽  
David E. G. P. Bueno ◽  
Renan M. Baptista ◽  
Felipe B. F. Rachid ◽  
Gustavo C. R. Bodstein
Keyword(s):  
Numerical Method ◽  
Flow Pattern ◽  
Two Phase Flow ◽  
Second Order ◽  
Phase Flow ◽  
Specific Class ◽  
Gas Pipelines ◽  
Time Step ◽  
Two Phase ◽  
Flux Corrected Transport

The ability to produce accurate numerical simulations of transient two-phase flows in gas pipelines has long been an important issue in the oil industry. A reliable prediction of such flows is a difficult task to accomplish due to the numerous sources of uncertainties, such as the basic two-phase flow model, the flow-pattern models, the initial condition and the numerical method used to solve the system of partial differential equations. Several numerical methods, conservative or not, of first- and second-order accuracies may be used to discretize the problem. In this paper we use the flux-corrected transport (FCT) finite-difference method to solve a one-dimensional single-pressure four-equation two-fluid model for the two-phase flow that occurs in a nearly horizontal pipeline characterized by the stratified-flow pattern. Because the FCT algorithm is of indeterminate order, we use a test case to assess the spatial and time accuracies for the specific class of hyperbolic problem that we obtain with the modeling employed here. The results show that the method is first order in time and second order in space, which have important consequences on the choice of mesh spacing and time step for a desired accuracy.

scholarly journals Multiscale Time-Splitting Strategy for Multiscale Multiphysics Processes of Two-Phase Flow in Fractured Media

2011 ◽  
Vol 2011 ◽  
pp. 1-24 ◽  
Author(s):  
Jisheng Kou ◽  
Shuyu Sun ◽  
Bo Yu
Keyword(s):  
Porous Media ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Step Size ◽  
Time Step ◽  
Two Phase ◽  
Time Step Size ◽  
Multi Scale ◽  
Rapid Changes ◽  
Time Splitting

The temporal discretization scheme is one important ingredient of efficient simulator for two-phase flow in the fractured porous media. The application of single-scale temporal scheme is restricted by the rapid changes of the pressure and saturation in the fractured system with capillarity. In this paper, we propose a multi-scale time splitting strategy to simulate multi-scale multi-physics processes of two-phase flow in fractured porous media. We use the multi-scale time schemes for both the pressure and saturation equations; that is, a large time-step size is employed for the matrix domain, along with a small time-step size being applied in the fractures. The total time interval is partitioned into four temporal levels: the first level is used for the pressure in the entire domain, the second level matching rapid changes of the pressure in the fractures, the third level treating the response gap between the pressure and the saturation, and the fourth level applied for the saturation in the fractures. This method can reduce the computational cost arisen from the implicit solution of the pressure equation. Numerical examples are provided to demonstrate the efficiency of the proposed method.

Modified Verlet Method Involving Second-Order Mid-Point Rule Applied to Balls Falling in One-Dimensional Potentials

2011 ◽  
Vol 1 (1) ◽  
pp. 1-19
Author(s):  
Hidenori Yasuda
Keyword(s):  
Phase Separation ◽  
Liquid Film ◽  
Two Phase Flow ◽  
Interface Region ◽  
New Method ◽  
Phase Flow ◽  
Time Step ◽  
Two Phase ◽  
One Dimensional ◽  
Ball Motion

AbstractA modified Verlet method which involves a kind of mid-point rule is constructed and applied to the one-dimensional motion of elastic balls of finite size, falling under constant gravity in space and then under the chemical potential in the interface region of phase separation within a two-liquid film. When applied to the simulation of two balls falling under constant gravity in space, the new method is found to be computationally superior to the usual Verlet method and to Runge–Kutta methods, as it allows a larger time step for comparable accuracy. The main purpose of this paper is to develop an efficient numerical method to simulate balls in the interface region of phase separation within the two-liquid film, where the ball motion is coupled with two-phase flow. The two-phase flow in the film is described via shallow water equations, using an invariant finite difference scheme that accurately resolves the interface region. A larger time step in computing the ball motion, more comparable with the time step in computing the two-phase flow, is a significant advantage. The computational efficiency of the new method in the coupled problem is demonstrated for the case of four elastic balls in the two-liquid film.

Solving a mixture model of two-phase flow with velocity non-equilibrium using WENO wavelet methods

2018 ◽  
Vol 28 (9) ◽  
pp. 2052-2071 ◽  
Author(s):  
Alice de Jesus Kozakevicius ◽  
Dia Zeidan ◽  
Alex A. Schmidt ◽  
Stefan Jakobsson
Keyword(s):  
Two Phase Flow ◽  
Weno Scheme ◽  
Phase Flow ◽  
Two Phase Flows ◽  
Time Step ◽  
Two Phase ◽  
Content Type ◽  
Conservative Form ◽  
Wavelet Methods ◽  
Non Equilibrium

Purpose The purpose of this work is to present the implementation of weighted essentially non-oscillatory (WENO) wavelet methods for solving multiphase flow problems. The particular interest is gas–liquid two-phase mixture with velocity non-equilibrium. Numerical simulations are carried out on different scenarios of one-dimensional Riemann problems for gas–liquid flows. Results are validated and qualitatively compared with solutions provided by other standard numerical methods. Design/methodology/approach This paper extends the framework of WENO wavelet adaptive method to a fully hyperbolic two-phase flow model in a conservative form. The grid adaptivity in each time step is provided by the application of a thresholded interpolating wavelet transform. This facilitates the construction of a small yet effective sparse point representation of the solution. The method of Lax–Friedrich flux splitting is used to resolve the spatial operator in which the flux derivatives are approximated by the WENO scheme. Findings Hyperbolic models of two-phase flow in conservative form are efficiently solved, as shocks and rarefaction waves are precisely captured by the chosen methodology. Substantial computational gains are obtained through the grid reduction feature while maintaining the quality of the solutions. The results indicate that WENO wavelet methods are robust and sufficient to accurately simulate gas–liquid mixtures. Originality/value Resolution of two-phase flows is rarely studied using WENO wavelet methods. It is the first time such a study on the relative velocity is reported in two-phase flows using such methods.

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