Wax deposition modeling in oil-water stratified pipe flow

Wax deposition in oil-water stratified flow is commonly encountered onshore and offshore oil production pipe systems,and typically reduces transportation capacity of oil.The accurate predicted model of wax deposition has becomes an indispensable approach to design effective remediation strategies.However,a reliable mechanistic model for wax deposition prediction in oil-water two-phase stratified pipe flow is lacking to validate the deposition process.In this work,a three-dimensional(axial,radial,and angular)robust wax deposit model for oil-water stratified circular pipe flow was developed.The model of formation of a gel deposit based on the first principles of rheology was developed,associated with the results obtained from hydrodynamics and heat/mass transfer simulations.The predictions for wax deposition are found to compare satisfactorily with experimental data with two different oils for single phase and four different water cuts for oil-water stratified pipe flow.It can be seen from the wax gelation mechanism that an increase in water cut can help to reduce the wall/oil-deposit interface shear stress,thereby leading to an increase in the degree of gelation as well as the deposit rate.Furthermore,a local deposit analysis in the circumferential direction was conducted,for water cut 75%and total flow rate 5 m3/h,which provided insights to understand that the thickness on pipe wall was roughly uniformly distributed locates near the top of the pipe and the nearer the position gets close to two points,where the oil-water interface contacts the inner wall,the deposition thickness quickly dropped to 0.It was attributed to the fact that a roughly uniformly thickness far away from the oil-water interface contact the inner wall resulted in the slowly changes temperature along the circumferential pipe wall wetted by oil.

Non-symmetric distributions of solids deposition for solid-water stratified flow in deviated tubing strings

Dynamic performance on solids flow with water in deviated tubing is essential for the reliability of pump and normal operation of horizontal and directional wells.Compared with coal-water flow in vertical tubing and sand-oil flow with high production in deviated tubing,solids deposition with water shows obvious non-symmetric distributions in deviated tubing from simulations and experiments.The mathematical model of two phase flow was developed under coupling conditions of deviated tubing,low flow rate and viscosity based on the kinetic theory of granular flow and first-order discrete scheme.The results show that solid-water stratified flow in deviated tubing can be divided into two zones of suspension bed and the moving bed throughout the flow field.The solid flowing velocity with water is negative and particles slide down at the bottom of moving bed zone.The process of solids flow with water in deviated tubing will produce pressure loss and consume the kinetic energy.The thickness of deposited layer and the flowing velocity of solids flow downward with water at the moving bed zone enhance with the decreased inlet flow rate and the increased particle size,tubing inside diameter(ID)and inclination angle.Solids are easier into suspension from the upper part of moving bed zone to suspension bed zone and more solid particles flow with water towards the tubing outlet with the increase of inlet flowing velocity.The decision is made to reduce the screen width,tubing ID and inclination angle to maintain to be greater than critical deposition velocity in order to prevent solids settling.And it provides the theoretical basis and technical reserves for solid control and offers an effective approach to enhance tubing cleaning in deviated strings.

Gas-water stratified flow patterns from electromagnetic tomography

Because of gravitational differentiation of multi-phase fluids, gas-water flow is usually stratified in highly inclined or horizontal gas wells. By using electrode arrays to scan flowing fluids, electromagnetic tomography can identify the flow patterns of mixed fluid from the different electrical properties of gas and water. The responses for different gas-water interface locations were calculated and then physical measurements were undertaken. We compared the results of the numerical simulation with the experimental data, and found that the response characteristics were consistent in the circumstances of uniform physical fields and stratified flows. By analyzing the signal characteristics, it is found that, with the change of the interface location, the response curves showed ＂steps＂ whose position and width were decided by the location of fluid interface. The measurement accuracy of this method depended on the vertical distance between adjacent electrodes. The results showed that computer simulation can simulate the measurement of the electromagnetic tomography accurately, so the physical experiment can be replaced.

Stability of Stratified Gas-Liquid Flow in Horizontal and Near Horizontal Pipes

A viscous Kelvin-Helmholtz criterion of the interfacial wave instability is proposed in this paper based on the linear stability analysis of a transient one-dimensional two-fluid model. In thismodel, the pressure is evaluated using the local momentum balance rather than the hydrostatic approximation. The criterion predicts well the stability limit of stratified flow in horizontal and nearly horizontal pipes. The experimental and theoretical investigation on the effect of pipe inclination on the interfacial instability are carded out. It is found that the critical liquid height at the onset of interfacial wave instability is insensitive to the pipe inclination. However, the pipe inclination significantly affects critical superficial liquid velocity and wave velocity especially lor low gas velocities.

Near Wake of a Horizontal Circular Cylinder in Stably Stratified Flows

The near wake of a circular cylinder in linearly stratified flows of finite depth was experimentally investigated by means of flow visualization and measurements of vortex shedding frequencies, at Reynolds numbers 3.5 × 103-1.2 × 104 and stratification parameters kd 0-2.0. The non-dimensional parameter kd is defined as kd = Nd/U, where N is the Brunt-Vaisala frequency, d, the diameter of the cylinder, and U, the approaching flow velocity. The study demonstrates that as kd increases from zero, the vortex shedding from a circular cylinder progressively strengthens, while the Strouhal number gradually becomes lower than that for homogeneous flow. This phenomenon can be explained by the effect of the increasingly stable stratification which enhances the two-dimensionality of the near-wake flow of the circular cylinder;the enhanced two-dimensionality of the flow strengthens the roll-up of the separated shear layer. Above a certain value of kd, however, vortex formation and shedding are strongly suppressed and the Strouhal number rises sharply. This observation is attributable to the development of stationary lee waves downstream of the circular cylinder because the lee waves strongly suppress vertical fluid motions.

Computational Analysis of the Oscillatory Mixed Convection Flow along a Horizontal Circular Cylinder in Thermally Stratified Medium

The present work emphasizes the significance of oscillatory mixed convection stratified fluid and heat transfer characteristics at different stations of non-conducting horizontally circular cylinder in the presence of thermally stratified medium.To remove the difficulties in illustrating the coupled PDE’s,the finite-difference scheme with efficient primitive-variable formulation is proposed to transform dimensionless equations.The numerical simulations of coupled non-dimensional equations are computed in terms velocity of fluid,temperature and magnetic field which are computed to examine the fluctuating components of skin friction,heat transfer and current density for various emerging parameters.The governing parameters namely,thermally stratification parameter𝑆𝑆𝑡𝑡,mixed-convection parameter𝜆𝜆,Prandtl number Pr,magnetic force parameter𝜉𝜉and magnetic-Prandtl number𝛾𝛾are displayed graphically at selected values for velocity and heat transfer mechanism.It is computed that heat transfer attains maximum amplitude and good variations in the presence of thermally stratified parameter at each position𝛼𝛼=𝜋𝜋6⁄,𝛼𝛼=𝜋𝜋3⁄and𝛼𝛼=𝜋𝜋around the surface of non-conducting horizontally cylinder.The velocity of fluid attains certain height at station𝛼𝛼=𝜋𝜋6⁄for higher value of stratification parameter.It is also found that the temperature gradient decreases with stratification parameter𝑆𝑆𝑡𝑡,but it increases after a certain distance𝑌𝑌from the cylinder.The novelty of the current work is that due to non-conducting phenomena the magnetic effects are strongly observed far from the surface but exact at the surface are zero for each position.

Interfacial Shear Stress of Stratified Flow in a Horizontal Pipe

Experimental data are presented for the void fraction and the shear stresses of stratified gas-liquid flow in a pipe. A new technique was used to measure the interface shear stress. The interfacial shear stress was determined by using two methods: a momentum balance of gas and an extrapolation of the Reynolds shear stress profile at the gas-liquid interface. A new formula , relating to the interfacial friction factor with the void fraction and superficial gas Reynold number, was developed to predict the interface shear stress . The predicted values are in good agreement with experimental data.

Partial phase flow rate measurements for stratified oil-water flow in horizontal wells

To accurately measure and evaluate the oil-water production profile of horizontal wells, a dynamic measurement experiment of oil-water two-phase flow in horizontal wells and numerical simulation were combined to establish a method for measuring the partial phase flow rate of oil-water two-phase stratified flow in horizontal wells. An experimental work was performed in horizontal oil-water two-phase flow simulation well using combination production logging tool including mini-capacitance sensor and mini-spinner. The combination tool provides a recording of holdup and velocity profiles at five different heights of the borehole cross-section. The effect of total flow rate and water-cut on the response of spinner and capacitive sensor at five measured positions were investigated. The capacitance water holdup interpolation imaging algorithm was used to determine the local fluid property and oil-water interface height, and the measured local fluid speed was combined with the numerical simulation result to establish an optimal calculation model for obtaining the partial phase flow rate of the oil-water two-phase stratified flow in the horizontal well. The calculated flow rates of five measured points are basically consistent with the experimental data, the total flow rate and water holdup from calculation are in agreement with the set values in the experiment too, suggesting that the method has high accuracy.

Flow patterns and critical criteria of thermally stratified shear flow in braided rivers

Flow characteristics of thermally stratified shear flow in braided rivers are particularly complicated and poorly understood. In this study, a series of typical flow patterns was examined and their critical criteria were determined. Four flow patterns were identified: mixed, locally unstable, continuously stratified, and two-layer flow. Temperature distributions of the four types of flow patterns were analyzed and compared.The critical Froude numbers for unstable flow, FDcr1, and stable flow, FDcr2, were determined to be 6 and 1, respectively, and comparison of FDcr1 and FDcr2 to the peak Froude numbers, FD1 at the outer bank and FD2 at the inner bank along the anabranch, allowed the flow patterns to be assessed. Then, a discriminant based on initial Jeffreys-Keulegan stability parameters was established to distinguish the flow stages from twolayer flow to completely mixed flow. It is indicated that the three critical Jeffreys-Keulegan parameters increased with the diversion angle of braided rivers. Results also show that, compared to the stratified flow in straight and curved channels, it was more difficult for braided stratified flow to maintain as two-layer flow, and it more easily became mixed flow. Consequently, empirical expressions for stability criteria of the thermally stratified shear flow in braided rivers are presented.

THE SOLITARY WAVES IN STRATIFIED SHEAR FLOW

In this paper,the basic equation of internal long waves in stratified shear flow is derived un- der Boussinesq assumption,the first order approximation solution is given for solitary waves with the effects of slowly varying topograph at the sea bottom,weak stratification and basic shear flow.

A Model of Turbulent-Laminar Gas-Liquid Stratified Flow

The time-dependent liquid film thickness and pressure drop are measured by using parallel-wire conduc tance probes and capacitance differential-pressure transducer. A mathematical model with iterative procedure to calculate holdup and pressure drop in horizontal and inclined gas-liquid stratified flow is developed. The predictions agree well with over a hundred experimental data in 0.024 and 0.04 m diameter pipelines.

Numerical simulation of stratified turbulent two-phase flow in aquatic environment

The two fluid model of stratified turbulent two phase flow in aquatic environment is developed in this paper. The motion of each phase is described by a unified multi fluid model in an Eulerian coordinate system. The laws of turbulent transportation for each phase, and the restriction of each other between the two phases are completely simulated. The complex two phase turbulence with strong buoyancy effects is selected to examine numerically. The extensive experimental data obtained in stratified flow are used here. Comparison of the results of numerical simulation with the experimental data is conducted. It has shown that the results of numerical simulation are satisfactory.

A Model for Predicting Holdup and Pressure Drop in Gas- Liquid Stratified Flow

The time-dependent liquid film thickness and pressure drop were measured by using parallel-wire conductance probes and capacitance differential-pressure transducers. Applying the eddy viscosity theory and an appropriate correlation of interfacial sear stress,a new two-dimensional separated model of holdup and pressure drop of turbulent/turbulent gas-liquid stratified flow was presented. Prediction results agreed well with experimental data.

Lie Point Symmetry Algebras and Finite Transformation Groups of Baroclinic Mode for Rotating Stratified Flows

The transformation groups and symmetries of the baroclinic mode for rotating stratified flow can be obtained via the standard approach. Applying the symmetry group on some special solutions, the newly obtained results disprove a known conjecture.

Three-Dimensional Numerical Simulation of Stably Stratified Flows over a Two-Dimensional Hill

Stably stratified flows over a two-dimensional hill are investigated in a channel of finite depth using a three-dimensional direct numerical simulation (DNS). The present study follows onto our previous two-dimensional DNS studies of stably stratified flows over a hill in a channel of finite depth and provides a more realistic simulation of atmospheric flows than our previous studies. A hill with a constant cross-section in the spanwise (y) direction is placed in a 3-D computational domain. As in the previous 2-D simulations, to avoid the effect of the ground boundary layer that develops upstream of the hill, no-slip conditions are imposed only on the hill surface and the surface downstream of the hill;slip conditions are imposed on the surface upstream of the hill. The simulated 3-D flows are discussed by comparing them to the simulated 2-D flows with a focus on the effect of the stable stratification on the non-periodic separation and reattachment of the flow behind the hill. In neutral (K = 0, where K is a non-dimensional stability parameter) and weakly stable (K = 0.8) conditions, 3-D flows over a hill differ clearly from 2-D flows over a hill mainly because of the three-dimensionality of the flow, that is the development of a spanwise flow component in the 3-D flows. In highly stable conditions (K = 1, 1.3), long-wavelength lee waves develop downstream of the hill in both 2-D and 3-D flows, and the behaviors of the 2-D and 3-D flows are similar in the vicinity of the hill. In other words, the spanwise component of the 3-D flows is strongly suppressed in highly stable conditions, and the flow in the vicinity of the hill becomes approximately two-dimensional in the x and z directions.

ANALYTICAL SOLUTION OF FLOW IN INFINITE STRATIFIED OIL RESERVOIR AND ITS APPLICATION

This paper presents an analytical solution for the production function and pressure distribution function of flow in infinite stratified oil reservoir with crosflow under the condition of constant wellbore pressure (CWP condition) by Weber's integral transformation. The calculation results are shown in the form of curves and these results can be used to analyse unsteady flow test of production with CWP condition.

Analysis of current induced by long internal solitary waves in stratified ocean

An approximate theoretical expression for the current induced by long internal solitary waves is presented when the ocean is continuously or two-layer stratified. Particular attention is paid to characterizing velocity fields in terms of magnitude, flow components, and their temporal evolution/spatial distribution. For the two-layer case, the effects of the upper/lower layer depths and the relative layer density difference upon the induced current are further studied. The results show that the horizontal components are basically uniform in each layer with a shear at the interface. In contrast, the vertical counterparts vary monotonically in the direction of the water depth in each layer while they change sign across the interface or when the wave peak passes through. In addition, though the vertical components are generally one order of magnitude smaller than the horizontal ones, they can never be neglected in predicting the heave response of floating platforms in gravitationally neutral balance. Comparisons are made between the partial theoretical results and the observational field data. Future research directions regarding the internal wave induced flow field are also indicated.

Numerical Simulation of Jet Issuing Diagonally Upward into Density-Stratified Fluid in Cylindrical Tank

This study simulates the behavior of a jet issuing into a two-layer density-stratified fluid in a cylindrical tank and the resulting mixing phenomena. The upper and lower fluids are water and an aqueous solution of sodium chloride (NaCl), respectively, with the lower fluid issuing diagonally upward from a nozzle on the bottom of the tank. The angle between the centerline of the jet and the tank bottom is 60°. The phenomena when the Reynolds number Re of the jet is 475, 1426, and 2614 are simulated. The mass concentration of the aqueous solution of NaCl is 0.02. The simulation successfully grasps the jet behavior and the resulting mixing, which agree with the authors’ experimental results at the corresponding Re value. The secondary flows that appear in the horizontal cross-sections consist of a pair of vortices and flows along the tank wall. The secondary flow at the density interface represents the intrusion of an internal density current, which gives rise to mixing along the interface.

Behavior of a Jet Issuing Diagonally Upward into Two-Layer Density-Stratified Fluid in a Cylindrical Tank

This study is concerned with the experimental investigation of a jet issuing diagonally upward into a two-layer density-stratified fluid in a cylindrical tank and the resulting mixing phenomena. The upper and lower fluids are water and an aqueous solution of sodium chloride (NaCl), respectively, and the lower fluid issues from a nozzle on the bottom of the tank. The angle between the centerline of the jet and the bottom of the tank is 60o, and the mass concentration of the NaCl solution is 0.02. The investigation reveals that secondary flow is caused by the jet in the horizontal cross-sections of the tank and that it is composed of a pair of vortices. It confirms that the secondary flow at the density interface corresponds to an internal density current. The investigation also clarifies the effect of the Reynolds number of the jet on mixing between the lower and upper fluids.

VISIOMETRICS OF 2D SHOCK-PLANAR S/F/S CURTAIN INTERACTIONS: VORTEX DOUBLE LAYERS, VORTEX PROJECTILES AND DECAYING STRATIFIED TURBULENCE

Vortex double layers (VDLs) and vortex projectiles (VPs) are the essential coherent structures which emerge in the shock excited (s/f/s) planar parallel "curtain" simulations of a 2D shock tube with PPM. These opposite signed layers, formed by shock induced baroclinic deposition of vorticity, "ind" and are strongly affected by secondary reflected shocks and vortex interactions. In our visiometric mode of working, we quantify several of these processes and introduce time epochs to discuss the emerging phenomena and normalizations to scale (collapse) the data at M =1.5 and 2.0. This versatile configuration, easily obtained in the laboratory, allows us to study the formation, evolution and reacceleration of VPs and stratified turbulence and mixing.