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.

Design and Experimental Analyses of Small-flow High-head Centrifugal-vortex Pump for Gas-Liquid Two-phase Mixture

The design method of small-flow high-head centrifugal-vortex pump was presented. This pump, configured with inducer, complex-centrifugal impeller and open-vortex impeller, was put forward to deliver gas-liquid two-phase mixture. An HTB-5/60 type sample pump was developed and tested on a closed-loop test rig. Experimental studies on performance and cavitation tests for gas-liquid two-phase mixture were carried out compared with pure-water experimental results. Also the effect of gas phase on pump was analyzed and discussed. The experimental results show that performance and cavitation characteristics of the sample purnp deteriorates progressively with increasing volume fraction of gas. When the total capacity Qm is between 4.5 m^3·h^-1 and 6 m^3·h^-1 and the gas flow rate qg below 0.66 m^3·h^-1, or qg/Qm is lower than 15%, the characteristic curves are approximately parallel to those in pure water test, but the performance deteriorates sharply until an abrupt flow-cutting at a critical volume fraction of gas. This pump is found suitable for transporting gas-liquid two-phase mixture when working around rated capacity of 5 m^3·h^-1 with qglQm below 15%.

Flow Regime Identification of Gas-liquid Two-phase Flow Based on HHT

A new method to identify flow regime in two-phase flow was presented, based on signal processing of differential pressure using Hilbert Huang transform （HHT）. Signals obtained from a Venturi meter were decomposed into different intrinsic mode functions （IMFs） with HHT, then the energy fraction of each intrinsic mode and the mean value of residual function were calculated, from which the rules of flow regime identification were summarized. Experiments were carried out on two-phase flow in the horizontal tubes with 50mm and 40mm inner diameter, while water flowrate was in the range of 1.3m^3.h^-1 to 10.5m^3.h^-1, oil flowrate was from 4.2m^3.h^-1 to 7.0m^3.h^-1 and gas flowrate from 0 to 15m^3.h^-1. The results show that the proposed rules have high precision for single phase, bubbly, and slug, plug flow regirne identification, which are independent of not only properties of two-phase fluid. In addition, the method can meet the need of industrial application because of its simple calculation.

Simulation and Analysis on the Two-Phase Flow Fields in a Rotating-Stream-Tray Absorber by Using Computational Fluid Dynamics

The flow field of gas and liquid in a φ150mm rotating-stream-tray (RST) scrubber is simulated by using computational fluid dynamic (CFD) method. The sismulation is based on the two-equation RNG κ-ε turbulence model, Eulerian multiphase model, and a real-shape 3D model with a huge number of meshes. The simulation results include detailed information about velocity, pressure, volume fraction and so on. Some features of the flow field are obtained: liquid is atomized in a thin annular zone; a high velocity air zone prevents water drops at the bottom from flying towards the wall; the pressure varies sharply at the end of blades and so on. The results will be helpful for structure optimization and engineering design.

Identification Method of Gas-Liquid Two-phase Flow Regime Based on Image Multi-feature Fusion and Support Vector Machine

The knowledge of flow regime is very important for quantifying the pressure drop, the stability and safety of two-phase flow systems. Based on image multi-feature fusion and support vector machine, a new method to identify flow regime in two-phase flow was presented. Firstly, gas-liquid two-phase flow images including bub- bly flow, plug flow, slug flow, stratified flow, wavy flow, annular flow and mist flow were captured by digital high speed video systems in the horizontal tube. The image moment invariants and gray level co-occurrence matrix texture features were extracted using image processing techniques. To improve the performance of a multiple classifier system, the rough sets theory was used for reducing the inessential factors. Furthermore, the support vector machine was trained by using these eigenvectors to reduce the dimension as flow regime samples, and the flow regime intelligent identification was realized. The test results showed that image features which were reduced with the rough sets theory could excellently reflect the difference between seven typical flow regimes, and successful training the support vector machine could quickly and accurately identify seven typical flow regimes of gas-liquid two-phase flow in the horizontal tube. Image multi-feature fusion method provided a new way to identify the gas-liquid two-phase flow, and achieved higher identification ability than that of single characteristic. The overall identification accuracy was 100%, and an estimate of the image processing time was 8 ms for online flow regime identification.

Local Flow Regime Transition Criteria of Gas-Liquid Two-phase Flow in Vertical Upward Tube with a Horizontal Rod

The upward multiphase cross flow and heat transfer in the vertical tube may occur in oil production and chemical facilities. In this study, the local flow patterns of an upward gas-water two phase cross flow in a vertical tube with a horizontal rod have been investigated with an optical probe and the digital high speed video system. The local flow patterns are defined as the bubble, slug, churn and annular flow patterns. Optical probe signals are ana- lyzed in terms of probability density function, and it is proved that the local flow patterns can be recognized by this method. The transition mechanisms between the different flow patterns have been analyzed and the corresponding transitional models are proposed. Finally, local flow pattern maps of the upward gas-water two-phase flow in the vertical tube with a horizontal rod are constructed.

Numerical Simulation and Experimental Analysis of the Influence of Asymmetric Pressure Conditions on the Splitting of a Gas-Liquid Two-Phase Flow at a T-Junction

Dedicated experiments and numerical simulations have been conducted to investigate the splitting characteristics of a gas-liquid two phase flow at a T junction.The experiments were carried out for different gas-liquid velocities.The flow rates in the two branches were measured accurately to determine how the two considered phases distribute in the two outlets.The experimental results have shown that when the two outlet pressures are asymmetric,the two-phase flow always tends to flow into the outlet which has a lower pressure.As the inlet liquid velocity increases,however,the two-phase flow gradually tends to split evenly.Compared with the experiment results,the pressure difference between the two outlets can be determined more accurately by means of numerical simulation.The trends of experimental results and simulations are in very good agreement.

Multi-scale Chaotic Analysis of the Characteristics of Gas-Liquid Two-phase Flow Patterns

Using the high-speed camera the time sequences of the classical flow patterns of horizontal gas-liquid pipe flow are recorded, from which the average gray-scale values of single-frame images are extracted. Thus obtained gray-scale time series is decomposed by the Empirical Mode Decomposition (EMD) method, the various scales of the signals are processed by Hurst exponent method, and then the dual-fractal characteristics are obtained. The scattered bubble and the bubble cluster theories are applied to the evolution analysis of two-phase flow patterns. At the same time the various signals are checked in the chaotic recursion chart by which the two typical characteristics (diagonal average length and Shannon entropy) are obtained. Resulting term of these properties, the dynamic characteristics of gas-liquid two-phase flow patterns are quantitatively analyzed. The results show that the evolution paths of gas-liquid two-phase flow patterns can be well characterized by the integrated analysis on the basis of the gray-scale time series of flowing images from EMD, Hurst exponents and Recurrence Plot (RP). In the middle frequency section (2nd, 3rd, 4th scales), three flow patterns decomposed by the EMD exhibit dual fractal characteristics which represent the dynamic features of bubble cluster, single bubble, slug bubble and scattered bubble. According to the change of diagonal average lengths and recursive Shannon entropy characteristic value, the structure deterministic of the slug flow is better than the other two patterns. After the decomposition by EMD the slug flow and the mist flow in the high frequency section have obvious peaks. Anyway, it is an effective way to understand and characterize the dynamic characteristics of two-phase flow patterns using the multi-scale non-linear analysis method based on image gray-scale fluctuation signals.

Evaluation of frictional pressure drop correlations for air-water and air-oil two-phase flow in pipeline-riser system

Accurate prediction of the frictional pressure drop is important for the design and operation of subsea oil and gas transporting system considering the length of the pipeline. The applicability of the correlations to pipeline-riser flow needs evaluation since the flow condition in pipeline-riser is quite different from the original data where they were derived from. In the present study, a comprehensive evaluation of 24prevailing correlation in predicting frictional pressure drop is carried out based on experimentally measured data of air-water and air-oil two-phase flows in pipeline-riser. Experiments are performed in a system having different configuration of pipeline-riser with the inclination of the downcomer varied from-2°to-5°to investigated the effect of the elbow on the frictional pressure drop in the riser. The inlet gas velocity ranges from 0.03 to 6.2 m/s, and liquid velocity varies from 0.02 to 1.3 m/s. A total of885 experimental data points including 782 on air-water flows and 103 on air-oil flows are obtained and used to access the prediction ability of the correlations. Comparison of the predicted results with the measured data indicate that a majority of the investigated correlations under-predict the pressure drop on severe slugging. The result of this study highlights the requirement of new method considering the effect of pipe layout on the frictional pressure drop.

A Hydrodynamic Modei for Slug Frequency in Horizontal Gas-Liquid Two-Phase Flow

The prediction of slug frequency has important significance on gas-liquid two-phase flow. A hydrody-namic modei was put forward to evaluate slug frequency for horizontal two-phase flow, based on the dependence of slug frequency on the frequency of unstable interfacial wave. Using air and water, experimental verification of the modei was carried out in a large range of flow parameters. Six electrical probes were installed at different positions of a horizontal plexiglass pipe to detect slug frequency development. The pipe is 30m long and its inner diameter is 24 mm. It is observed experimentally that the interfacial wave frequency at the inlet is about l to 3 times the frequency of stable slug. The slug frequencies predicted by the modei fit well with Tronconi (1990) modei and the experimental data. The combination of the hydrodynamic modei and the experimental data results in a conclusion that the frequency of equilibrium liquid slug is approximately half the miniraum frequency of interfacial wave.

Experimental Research on Gas-Liquid Two-Phase Spiral Flow in Horizontal Pipe

In view of the importance of gas-liquid two-phase spiral flow and the few research reports at home and abroad,the gas-liquid two-phase spiral flow patterns have been researched in a horizontal pipe with different parameters investigated by means of observation and a high-speed camera.Since the appearance of spiral flow makes the distribution of twophase flow more complicated,the flow patterns appearing in the experiments were divided into the Spiral Wavy Stratified Flow(SWS),the Spiral Bubble Flow(SB),the Spiral Slug Flow(SS),the Spiral Linear Flow(SL),the Spiral Axial Flow(SA),and the Spiral Dispersed Flow(SD) by the observations and with reference to the predecessors' research achievements.A flow pattern map has been drawn up.The influence of velocity,vane angle and vane area on flow pattern conversion boundary and pressure drop has been studied,with a solid foundation laid for the future research work.

Three-dimensional Computational Fluid Dynamics Modeling of Two-phase Flow in a Structured Packing Column

Characterizing the complex two-phase hydrodynamics in structured packed columns requires a power- ful modeling tool. The traditional two-dimensional model exhibits limitations when one attempts to model the de- tailed two-phase flow inside the columns. The present paper presents a three-dimensional computational fluid dy- namics （CFD） model to simulate the two-phase flow in a representative unit of the column. The unit consists of an CFD calculations on column packed with Flexipak 1Y were implemented within the volume of fluid （VOF） mathe- matical framework. The CFD model was validated by comparing the calculated thickness of liquid film with the available experimental data. Special attention was given to quantitative analysis of the effects of gravity on the hy- drodynamics. Fluctuations in the liquid mass flow rate and the calculated pressure drop loss were found to be quali- tatively in agreement with the experimental observations.

Reconstructing bubble profiles from gas-liquid two-phase flow data using agglomerative hierarchical clustering method

The knowledge of bubble profiles in gas-liquid two-phase flows is crucial for analyzing the kinetic processes such as heat and mass transfer, and this knowledge is contained in field data obtained by surface-resolved computational fluid dynamics (CFD) simulations. To obtain this information, an efficient bubble profile reconstruction method based on an improved agglomerative hierarchical clustering (AHC) algorithm is proposed in this paper. The reconstruction method is featured by the implementations of a binary space division preprocessing, which aims to reduce the computational complexity, an adaptive linkage criterion, which guarantees the applicability of the AHC algorithm when dealing with datasets involving either non-uniform or distorted grids, and a stepwise execution strategy, which enables the separation of attached bubbles. To illustrate and verify this method, it was applied to dealing with 3 datasets, 2 of them with pre-specified spherical bubbles and the other obtained by a surface-resolved CFD simulation. Application results indicate that the proposed method is effective even when the data include some non-uniform and distortion.

Pressure transient characteristics of non-uniform conductivity fractured wells in viscoelasticity polymer flooding based on oil-water two-phase flow

Polymer flooding in fractured wells has been extensively applied in oilfields to enhance oil recovery.In contrast to water,polymer solution exhibits non-Newtonian and nonlinear behavior such as effects of shear thinning and shear thickening,polymer convection,diffusion,adsorption retention,inaccessible pore volume and reduced effective permeability.Meanwhile,the flux density and fracture conductivity along the hydraulic fracture are generally non-uniform due to the effects of pressure distribution,formation damage,and proppant breakage.In this paper,we present an oil-water two-phase flow model that captures these complex non-Newtonian and nonlinear behavior,and non-uniform fracture characteristics in fractured polymer flooding.The hydraulic fracture is firstly divided into two parts:high-conductivity fracture near the wellbore and low-conductivity fracture in the far-wellbore section.A hybrid grid system,including perpendicular bisection(PEBI)and Cartesian grid,is applied to discrete the partial differential flow equations,and the local grid refinement method is applied in the near-wellbore region to accurately calculate the pressure distribution and shear rate of polymer solution.The combination of polymer behavior characterizations and numerical flow simulations are applied,resulting in the calculation for the distribution of water saturation,polymer concentration and reservoir pressure.Compared with the polymer flooding well with uniform fracture conductivity,this non-uniform fracture conductivity model exhibits the larger pressure difference,and the shorter bilinear flow period due to the decrease of fracture flow ability in the far-wellbore section.The field case of the fall-off test demonstrates that the proposed method characterizes fracture characteristics more accurately,and yields fracture half-lengths that better match engineering reality,enabling a quantitative segmented characterization of the near-wellbore section with high fracture conductivity and the far-wellbore section with low fracture conductivity.The novelty of this paper is the analysis of pressure performances caused by the fracture dynamics and polymer rheology,as well as an analysis method that derives formation and fracture parameters based on the pressure and its derivative curves.

Fluid−Structure Interaction of Two-Phase Flow Passing Through 90° Pipe Bend Under Slug Pattern Conditions

Numerical simulations of evolution characteristics of slug flow across a 90°pipe bend have been carried out to study the fluid−structure interaction response induced by internal slug flow.The two-phase flow patterns and turbulence were modelled by using the volume of fluid(VOF)model and the Realizable k−εturbulence model respectively.Firstly,validation of the CFD model was carried out and the desirable results were obtained.The different flow patterns and the time-average mean void fraction was coincident with the reported experimental data.Simulations of different cases of slug flow have been carried out to show the effects of superficial gas and liquid velocity on the evolution characteristics of slug flow.Then,a one-way coupled fluid-structure interaction framework was established to investigate the slug flow interaction with a 90°pipe bend under various superficial liquid and gas velocities.It was found that the maximum total deformation and equivalent stress increased with the increasing superficial gas velocity,while decreased with the increasing superficial liquid velocity.In addition,the total deformation and equivalent stress has obvious periodic fluctuation.Furthermore,the distribution position of maximum deformation and stress was related to the evolution of slug flow.With the increasing superficial gas velocity,the maximum total deformation was mainly located at the 90°pipe bend.But as the superficial liquid velocity increases,the maximum total deformation was mainly located in the horizontal pipe section.Consequently,the slug flow with higher superficial gas velocity will induce more serious cyclical impact on the 90°pipe bend.

A two-phase type-curve method with multiscale fluid transport mechanisms in hydraulically fractured shale reservoirs

The quantitative understanding of hydraulic fracture(HF)properties guides accurate production forecasts and reserve estimation.Type curve is a powerful technique to characterize HF and reservoir properties from flowback and long-term production data.However,two-phase flow of water and hydrocarbon after an HF stimulation together with the complex transport mechanisms in shale nanopores exacerbate the nonlinearity of the transport equation,causing errors in type-curve analysis.Accordingly,we propose a new two-phase type-curve method to estimate HF properties,such as HF volume and permeability of fracture,through the analysis of flowback data of multi-fractured shale wells.The proposed type curve is based on a semianalytical solution that couples the two-phase flow from the matrix with the flow in HF by incorporating matrix influx,slippage effect,stress dependence,and the spatial variation of fluid properties in inorganic and organic pores.For the first time,multiple fluid transport mechanisms are considered into two-phase type-curve analysis for shale reservoirs.We analyze the flowback data from a multi-fractured horizontal well in a shale gas reservoir to verify the field application of the proposed method.The results show that the fracture properties calculated by the type-curve method are in good agreement with the long-time production data.

An Experimental Study on the Void Fraction for Gas-Liquid Two-Phase Flows in a Horizontal Pipe

The flow patterns and the void fraction related to a gas-liquid two-phase flow in a small channel are experimentally studied.The test channel is a transparent quartz glass circular channel with an inner diameter of 6.68 mm.The working fluids are air and water and their superficial velocities range from 0.014 to 8.127 m/s and from 0.0238 to 0.556 m/s,respectively.The void fraction is determined using the flow pattern images captured by a high-speed camera,while quick closing valves are used for verification.Four flow patterns are analyzed in experiments:slug flow,bubbly flow,annular flow and stratified flow.For intermittent flows(bubbly flow and slug flow),the cross-sectional void fraction is in a borderline condition while its probability distribution function(PDF)image displays a bimodal structure.For continuous flows(annular flow and stratified flow)the cross-sectional void fraction behaves as a fluctuating continuous curve while the(PDF)image displays a single peak structure.The volumetric void fraction data are also compared with available predictive formulas,and the results show that the agreement is very good.An effort is also provided to improve the so-called Gregory and Scott model using the available data.

Local Flow Regime Transition Criteria of Gas-Liquid Two-phase Flow in Vertical Upward Tube with a Horizontal Rod

The upward multiphase cross flow and heat transfer in the vertical tube may occur in oil production and chemical facilities. In this study, the local flow patterns of an upward gas-water two phase cross flow in a vertical tube with a horizontal rod have been investigated with an optical probe and the digital high speed video system. The local flow patterns are defined as the bubble, slug, churn and annular flow patterns. Optical probe signals are ana- lyzed in terms of probability density function, and it is proved that the local flow patterns can be recognized by this method. The transition mechanisms between the different flow patterns have been analyzed and the corresponding transitional models are proposed. Finally, local flow pattern maps of the upward gas-water two-phase flow in the vertical tube with a horizontal rod are constructed.

Gas-Liquid Two-Phase Axial Backmixing Through Structured Packing at Elevated Pressure

An experimental study of the extent of axial backmixing in both gas and liquid phases was conducted in a 150 mm ID column packed with Mellapak 250Y corrugated structured packing. The column was operated at pressures ranging from 0.3 MPa to 2.0MPa with nitrogen and water flowing countercurrently through the packing. The amount of axial backmixing was experimentally evaluated by the pulse response techniques using hydrogen in gas phase and an aqueous solution of NaCl in liquid phase as inert tracers. The response of the tracer was monitored by means of thermal conductivity in the gas phase and electrical conductance in the liquid phase. The experimentally determined residence time distribution (RTD) curves were interpreted in terms of the diffusion-type modei. The results indicated that the axial backmixing in the gas increased notably with gas flowrate and slightly with operating pressure and liquid flowrate. The liquid-phase axial backmixing was an increasing function of both gas and liquid flowrates and insensitive to pressure. Various correlations were developed for reproducing the experimental mixing data. The agreement between experimental and correlated data appeared to be acceptable and within ±20% of difference.

Branch Quality Control of Gas-Liquid Two-Phase Flow Using a Novel T-Junction Type Distributor

In order to eliminate mal-distribution and ensure the side arm to produce desirable gas quality a special distributor is proposed. The experimental distributor mainly consists of a straight through section,a gas extraction line,a liquid extraction line and a side arm branch. A gas orifice and a liquid orifice are mounted at the gas and liquid extraction line respectively to control the outlet gas quality. The diameter of the liquid orifice was set to 2. 50 mm and three gas orifices with different size( dG= 2. 65,5. 00,10. 00 mm) were tested. The experiments were carried out at an air-water two-phase flow loop. The gas superficial velocity ranged from 6. 0 to 20. 0 m /s and the liquid superficial velocity was in the range of 0. 02- 0. 18 m /s. Flow patterns such as wave flow,slug flow and annular flow were observed. The gas quality of the side arm branch was found mainly determined by the flow area ratio of the gas orifice to the liquid orifice and independent of gas and liquid superficial velocity,flow patterns and extraction flux.