Numerical Solutions of the Classical and Modified Buckley-Leverett Equations Applied to Two-Phase Fluid Flow

Climate change is a reality. The burning of fossil fuels from oil, natural gas and coal is responsible for much of the pollution and the increase in the planet’s average temperature, which has raised discussions on the subject, given the emergencies related to climate. An energy transition to clean and renewable sources is necessary and urgent, but it will not be quick. In this sense, increasing the efficiency of oil extraction from existing sources is crucial, to avoid waste and the drilling of new wells. The purpose of this work was to add diffusive and dispersive terms to the Buckley-Leverett equation in order to incorporate extra phenomena in the temporal evolution between the water-oil and oil-water transitions in the pipeline. For this, the modified Buckley-Leverett equation was discretized via essentially weighted non-oscillatory schemes, coupled with a three-stage Runge-Kutta and a fourth-order centered finite difference methods. Then, computational simulations were performed and the results showed that new features emerge in the transitions, when compared to classical simulations. For instance, the dispersive term inhibits the diffusive term, adding oscillations, which indicates that the absorption of the fluid by the porous medium occurs in a non-homogeneous manner. Therefore, based on research such as this, decisions can be made regarding the replacement of the porous medium or the insertion of new components to delay the replacement.

An Improved Coupled Level Set and Continuous Moment-of-Fluid Method for Simulating Multiphase Flows with Phase Change

An improved algorithm for computing multiphase flows is presented in which the multimaterial Moment-of-Fluid(MOF)algorithm for multiphase flows,initially described by Li et al.(2015),is enhanced addressing existing MOF difficulties in computing solutions to problems in which surface tension forces are crucial for understanding salient flow mechanisms.The Continuous MOF(CMOF)method is motivated in this article.The CMOF reconstruction method inherently removes the"checkerboard instability"that persists when using the MOF method on surface tension driven multiphase(multimaterial)flows.The CMOF reconstruction algorithm is accelerated by coupling the CMOF method to the level set method and coupling the CMOF method to a decision tree machine learning(ML)algorithm.Multiphase flow examples are shown in the two-dimensional(2D),three-dimensional(3D)axisymmetric"RZ",and 3D coordinate systems.Examples include two material and three material multiphase flows:bubble formation,the impingement of a liquid jet on a gas bubble in a cryogenic fuel tank,freezing,and liquid lens dynamics.

Review of gas-solid two phase flow rate-concentration detection technology

The indirect detection method basic principle of rate and concentration,application range and research results on gassolid two phase flow were discussed.The present development situation and the existing problems of rate and concentration detection technology were analyzed and summarized.Emphatically analyzed the existing problems in the industrial application and research status of electrostatic method in measuring phase concentration.Design criterion of electrostatic phase concentration sensor is given,the superiority and wide industrial application prospect of the sensor used for phase concentration measurement are clarified.

Gas Condensate Two Phase Flow Performance in Porous Media Considering Capillary Number and Non-Darcy Effects

Retrograde condensation frequently occurs during the development of gas condensate reservoirs. The loss of productivity is often observed due to the reduced relative permeability to gas as condensate accumulates near the well bore region. How to describe the condensate blockage effect exactly has been a continuous research topic. However, up to now, the present methods usually over-estimate or underestimate the productivity reduction due to an incorrect understanding of the mechanism of flow in porous medium, which inevitably results in an inaccurate prediction of production performance. It has been found in recent numerous theoretical and experimental studies that capillary number and non-Darcy flow have significant influence on relative permeability in regions near the well bore. The two effects impose opposite impacts on production performance, thus leading to gas condensate flow showing characteristics different from general understanding. It is significant for prediction of performance in gas condensate wells to understand the two effects exactly. The aim of the paper is to describe and analyze the flow dynamics in porous media accurately during the production of gas condensate reservoirs. Based on the description of three-zone flow mechanism, capillary number and non-Darcy effect are incorporated in the analysis of relative permeability, making it possible to describe the effect of condensate blockage. The effect of capillary number and inertial flow on gas and condensate relative permeability is analyzed in detail. Novel Inflow Performance Relation (IPR) models considering high velocity effects are formulated and the contrast analysis of different IPR models is conducted. The result shows that the proposed method can help predict the production performance and productivity more accurately than conventional methods.

THE FRICTIONAL RESISTANCE CHARACTERISTICS OF GAS LIQUID TWO PHASE FLOW IN HELICAL COILED TUBES

This paper deal with the frictional resistance characteristics of gas liquid two phase flow in vertical upward helical coiled tubes under the system pressure 0.1 0.6MPa. By means of dimension analysis and π theorem, the correlation formulas were obtained for calculating the frictional resistance coefficients of gas liquid two phase flow in helical coiled tubes. The calculated results agree well with the experimental results.

NUMERICAL SIMULATION OF CHARGED GAS-LIQUID TWO PHASE JET FLOW IN ELECTROSTATIC SPRAYING

Multi-fluid k-e-kp, two phase turbulence model is used to simulate charged gas-liquid two phase coaxial jet, which is the transorting flow field in electrostatic spraying. Compared with the results of experiment, charged gas-liquid two-phase turbulence can be well predicted by this model.

Computational Analysis of Centrifugal Pump Delivering Solid-liquid Two-phase Flow during Startup Period

The transient behavior of centrifugal pumps during transient operating periods, such as startup and stopping, has drawn more and more attention recently because of urgent needs in engineering. Up to now, almost all the existing studies on this behavior are limited to using water as working fluid. The study on the transient behavior related to solid-liquid two-phase flow has not been seen yet. In order to explore the transient characteristics of a high specific-speed centrifugal pump during startup period delivering the pure water and solid-liquid two-phase flow, the transient flows inside the pump are numerically simulated using the dynamic mesh method. The variable rotational speed and flow rate with time obtained from experiment are best fitted as the function of time, and are written into computational fluid dynamics （CFD） code-FLUENT by using a user defined function. The predicted heads are compared with experimental results when pumping pure water. The results show that the difference in the transient performance during startup period is very obvious between water and solid-liquid two-phase flow during the later stage of startup process. Moreover, the time for the solid-liquid two-phase flow to achieve a stable condition is longer than that for water. The solid-liquid two-phase flow results in a higher impeller shaft power, a larger dynamic reaction force, a more violent fluctuation in pressure and a reduced stable pressure rise comparing with water. The research may be useful to tmderstanding on the transient behavior of a centrifugal pump under a solid-liquid two-phase flow during startup period.

Measurement of Two Phase Flow in Porous Medium Using High-resolution Magnetic Resonance Imaging

Measurement of two phase flow in porous medium for sequestration was carried out using high-resolution magnetic resonance imaging (MRI) technique. The porous medium was a packed bed of glass beads. Spin echo multi sequence was used to measure the distribution of CO2 and water in the porous medium. The intensity images show that the fluid distribution is non-uniform due to its viscosity and pore structure of porous medium. The velocity distribution of fluids is calculated from the saturation of water and porosity of porous medium. The experimental results show that fluid velocities vary with time and position. The capillary dispersion rate donated the effects of capillary, which was largest at water saturations of 0.45. The displacement process is different between in BZ-02 and BZ-2. The final water residual saturation depends on permeability and porosity.

A USM-Θ two-phase turbulence model for simulating dense gas-particle flows

A second-order moment two-phase turbulence model for simulating dense gas-particle flows （USM-Θ model）, combining the unified second-order moment twophase turbulence model for dilute gas-particle flows with the kinetic theory of particle collision, is proposed. The interaction between gas and particle turbulence is simulated using the transport equation of two-phase velocity correlation with a two-time-scale dissipation closure. The proposed model is applied to simulate dense gas-particle flows in a horizontal channel and a downer. Simulation results and their comparison with experimental results show that the model accounting for both anisotropic particle turbulence and particle-particle collision is obviously better than models accounting for only particle turbulence or only particle-particle collision. The USM-Θ model is also better than the k-ε-kp-Θ model and the k-ε-kp-εp-Θ model in that the first model can simulate the redistribution of anisotropic particle Reynolds stress components due to inter-particle collision, whereas the second and third models cannot.

NUMERICAL SIMULATION OF 3-D DENSE SOLID-LIQUID TWO-PHASE TURBULENT FLOW IN A NON-CLOGGING MUD PUMP

A mathematical model is set to evaluate the 3-D dense solid-liquid two-phaseturbulent flow in a non-clogging mud pump, the flow feature in the impeller channel is simulatedwith the tool of IPSA. Meanwhile, resort to TECPLOT as the post-processor, the simulation results isvisualized. The results show the main flow characteristics: There exists backflow and aberrantvelocities at inlet area and a relative velocity slip between two phases; A jet-wake flow pattern isdiscerned around the shroud-suction side area; The relative velocity vector of solid phase iscloser to the pressure surface than that of liquid phase and the trend is more obvious with theincrease of diameter; The kinetic energy of turbulence k and the dissipation rate e reach theirpeaks at the corner of pressure and suction surface. The simulation results show a good agreementwith the experimental flow features in the impeller channel, which prove the turbulent model used isvalid and provide a theoretical design basis to non-clogging pumps.

An improved large eddy simulation of two-phase flows in a pump impeller

An improved large eddy simulation using a dynamic second-order sub-grid-scale （SGS） stress model has been developed to model the governing equations of dense turbulent particle-liquid two-phase flows in a rotating coordinate system, and continuity is conserved by a mass-weighted method to solve the filtered governing equations. In the cur- rent second-order SGS model, the SGS stress is a function of both the resolved strain-rate and rotation-rate tensors, and the model parameters are obtained from the dimensional consistency and the invariants of the strain-rate and the rotation-rate tensors. In the numerical calculation, the finite volume method is used to discretize the governing equations with a staggered grid system. The SIMPLEC algorithm is applied for the solution of the discretized governing equations. Body- fitted coordinates are used to simulate the two-phase flows in complex geometries. Finally the second-order dynamic SGS model is successfully applied to simulate the dense turbu-lent particle-liquid two-phase flows in a centrifugal impeller. The predicted pressure and velocity distributions are in good agreement with experimental results.

Numerical simulation of two-phase flow in fractured porous media using streamline simulation and IMPES methods and comparing results with a commercial software

Streamline simulation is developed to simulate waterflooding in fractured reservoirs. Conventional reservoir simulation methods for fluid flow simulation in large and complex reservoirs are very costly and time consuming. In streamline method, transport equations are solved on one-dimensional streamlines to reduce the computation time with less memory for simulation. First, pressure equation is solved on an Eulerian grid and streamlines are traced. Defining the "time of flight", saturation equations are mapped and solved on streamlines. Finally, the results are mapped back on Eulerian grid and the process is repeated until the simulation end time. The waterflooding process is considered in a fractured reservoir using the dual porosity model. Afterwards, a computational code is developed to solve the same problem by the IMPES method and the results of streamline simulation are compared to those of the IMPES and a commercial software. Finally, the accuracy and efficiency of streamline simulator for simulation of two-phase flow in fractured reservoirs has been proved.

Gamma-ray attenuation technique for measuring void fraction in horizontal gas-liquid two-phase flow

The measurement of void fraction is of importance to the oil industry and chemical industry. In this article, the principle and mathematical method of determining the void fraction of horizontal gas-liquid flow by using a sin- gle-energy γ-ray system is described. The γ-ray source is the radioactive isotope of 241Am with γ-ray energy of 59.5 keV. The time-averaged value of the void fraction in a 50.0-mm i.d. transparent horizontal pipeline is measured under various combinations of the liquid flow and gas flow. It is found that increasing the gas flow rate at a fixed liquid flow rate would increase the void fraction. Test data are compared with the predictions of the correlations and a good agreement is found. The result shows that the designed γ-ray system can be used for measuring the void fraction in a horizontal gas-liquid two-phase flow with high accuracy.

MICROGRAVITY EXPERIMENTS OF TWO-PHASE FLOW PATTERNS ABOARD MIR SPACE STATION

A first experimental study on two-phase how patterns at a long-term, steady microgravity condition was conducted on board the Russian Space Station 'MIR' in August 1999. Carbogal and air are used as the liquid and the gas phase, respectively. Bubble, slug, slug-annular transitional, and annular hows are observed. A new region of annular how with lower liquid superficial velocity is discovered, and the region of the slug-annular transitional flow is wider than that observed by experiments on board the parabolic aircraft. The main patterns are bubble, slug-annular transitional and annular flows based on the experiments on board MIR space station. Some influences on the two-phase how patterns in the present experiments are discussed.

A control volume based finite element method for simulating incompressible two-phase flow in heterogeneous porous media and its application to reservoir engineering

Applying the standard Galerkin finite element method for solving flow problems in porous media encounters some difficulties such as numerical oscillation at the shock front and discontinuity of the velocity field on element faces.Discontinuity of velocity field leads this method not to conserve mass locally.Moreover,the accuracy and stability of a solution is highly affected by a non-conservative method.In this paper,a three dimensional control volume finite element method is developed for twophase fluid flow simulation which overcomes the deficiency of the standard finite element method,and attains high-orders of accuracy at a reasonable computational cost.Moreover,this method is capable of handling heterogeneity in a very rational way.A fully implicit scheme is applied to temporal discretization of the governing equations to achieve an unconditionally stable solution.The accuracy and efficiency of the method are verified by simulating some waterflooding experiments.Some representative examples are presented to illustrate the capability of the method to simulate two-phase fluid flow in heterogeneous porous media.

Numerical simulation of predicting and reducing solid particle erosion of solid-liquid two-phase flow in a choke

Chokes are one of the most important components of downhole flow-control equipment. The particle erosion mathematical model, which considers particle-particle interaction, was established and used to simulate solid particle movement as well as particle erosion characteristics of the solid-liquid two-phase flow in a choke. The corresponding erosion reduction approach by setting ribs on the inner wall of the choke was advanced. This mathematical model includes three parts： the flow field simulation of the continuous carrier fluid by an Eulerian approach, the particle interaction simulation using the discrete particle hard sphere model by a Lagrangian approach and calculation of erosion rate using semiempirical correlations. The results show that particles accumulated in a narrow region from inlet to outlet of the choke and the dominating factor affecting particle motion is the fluid drag force. As a result, the optimization of rib geometrical parameters indicates that good anti-erosion performance can be achieved by four ribs, each of them with a height （H） of 3 mm and a width （B） of 5 mm equaling the interval between ribs （L）.

TWO-PHASE FLOW PATTERNS IN A 90° BEND AT MICROGRAVITY

Bends are widely used in pipelines carrying single-and two-phase fluids in both ground and space applications.In particular,they play more important role in space applications due to the extreme spatial constraints.In the present study,a set of experimental data of two-phase flow patterns and their transitions in a 90°bend with inner diameter of 12.7 mm and curvature radius of 76.5 mm at microgravity conditions are reported.Gas and liquid superficial velocities are found to range from (1.0～23.6)m/s for gas and(0.09～0.5)m/s for liquid,respectively.Three major flow patterns, namely slug,slug-annular transitional,and annular flows,are observed in this study.Focusing on the differences between flow patterns in bends and their counterparts in straight pipes,detailed analyses of their characteristics are made.The transitions between adjoining flow patterns are found to be more or less the same as those in straight pipes,and can be predicted using Weber number models satisfactorily. The reasons for such agreement are carefully examined.

A consistent projection-based SUPG/PSPG XFEM for incompressible two-phase flows

In this paper, a consistent projection-based streamline upwind/pressure stabilizing Petrov-Galerkin （SUPG/PSPG） extended finite element method （XFEM） is presented to model incompressible immiscible two-phase flows. As the application of linear elements in SUPG/PSPG schemes gives rise to inconsistency in stabilization terms due to the inability to regenerate the diffusive term from viscous stresses, the numerical accuracy would deteriorate dramatically. To address this issue, projections of convection and pressure gradient terms are constructed and incorporated into the stabilization formulation in our method. This would substantially recover the consistency and free the practitioner from burdensome computations of most items in the residual. Moreover, the XFEM is employed to consider in a convenient way the fluid properties that have interfacial jumps leading to discontinuities in the velocity and pressure fields as well as the projections. A number of numerical examples are analyzed to demonstrate the complete recovery of consistency, the reproduction of interfacial discontinuities and the ability of the proposed projection-based SUPG/PSPG XFEM to model two-phase flows with open and closed interfaces.

High-order fully implicit SIMPLE-based model for fully implicit simulation of upward two-phase flow

The drift-flux model has a practical importance in two-phase flow analysis.In this study,a finite volume solution is developed for a transient four-equation drift-flux model through the staggered mesh,leading to the development of a fully implicit discretization method.The main advantage of the fully implicit method is its unconditional stability.Newton's scheme is a popular method of choice for the solution of a nonlinear system of equations arising from fully implicit discretization of field equations.However,the lack of convergence robustness and the construction of Jacobian matrix have created several difficulties for the researchers.In this paper,a fully implicit model is developed based on the SIMPLE algorithm for two-phase flow simulations.The drawbacks of Newton's method are avoided in the developed model.Different limiter functions are considered,and the stabilized method is developed under steady and transient conditions.The results obtained by the numerical modeling are in good agreement with the experimental data.As expected,the results prove that the developed model is not restricted by any stability limit.

Simulation Experiments in Electromagnetic Tomography Well Logging in Two-phase Flow

Electromagnetic Computer Tomography （ECT） is a method to probe the interior of an inhomogeneous medium via surface measurement in a non-linear way. Due to the great differences in conductivity and permittivity between oil and water in the well, Electromagnetic Tomography Well Logging （ETWL）, a new flow imaging measurement system, is proposed to describe the distribution and movement of oil/water two-phase flow in the well by scanning the detected region and applying a suitable data processing algorithm. The results of the numerical simulation and physical modeling show that the system could provide a clear image of the flow profile.