Pipe Inclination Research Articles

Pressure drops and flow patterns in sand-mixture pipes

The paper discusses a relation between the flow friction and the flow pattern in a pipe transporting a sand–water mixture. The study is based on the laboratory experiments that were carried out in a 150-mm pipe for flows of various sand fractions and different flow patterns. Three pipe inclinations (horizontal, vertical and −35° descending pipes) were used to establish different flow patterns. During the tests the flow patterns varied from fully stratified to fully suspended. In the fully stratified flow all particles were transported in a granular bed sliding over the bottom of a pipe or in a shear layer linked to the granular bed (all particles were transported as the contact load). In the fully suspended flow no bed was present in a pipe and all particles were dispersed within a carrying liquid (all particles were transported as the suspended load). In many cases the flow was partially stratified, i.e. a proportion of solid particles occupied a granular bed at the bottom of a pipe and the rest of the particles were dispersed within a carrying liquid above the bed. The tested solids were three narrowly graded fractions of sand ( d 50=0.12, 0.37 and 1.85 mm) and two sorts of mixed sand (blended from two narrowly graded fractions: the 0.37-mm sand+the 0.12-mm sand or the 1.85-mm sand+the 0.12-mm sand). The distribution of solids across the pipe cross-section was measured to identify the flow pattern. Integral flow parameters (mean mixture velocity, delivered concentration of solids, differential pressure) were measured to determine the flow friction for various flow conditions. The paper presents a survey of selected results from a large database collected during a long measuring campaign. It shows the way the measured solids distributions across a pipe cross-section were analyzed to distinguish between the contact load and the suspended load and compares the frictional pressure drops in mixtures of different flow patterns. The measurements confirmed that flows with a higher degree of flow stratification exhibit considerably higher friction than flows with a lower degree of stratification. For the horizontal flow of the mixture of the volumetric concentration 0.12–0.13 at velocities slightly above the deposition-limit threshold (around 3 m/s) the frictional pressure drop in the 0.12-mm sand mixture was approximately two thirds of that in the 0.38-mm sand mixture and less than one half of that in the 1.85-mm sand mixture. The addition of the 0.12-mm sand (the solids concentration 0.13–0.15) to the mixture of the concentration 0.12–0.13 of either the 0.37-mm sand or the 1.85-mm sand reduced the solids effect on the total frictional pressure drop to approximately one half at velocities slightly above the deposition-limit threshold. The vertical flows exhibit slightly less solids friction than the horizontal non-stratified flows. For the mixtures of concentration 0.26 of both the 0.37-mm sand and the mixed sand blended of the 0.37-mm sand and the 0.12-mm sand, the solids effect on the total frictional pressure drop in vertical flow was approximately two thirds of that in a non-stratified horizontal flow. A comparison of the experimental data with the predictive models for the frictional pressure drop suggests that more reliable models are available for stratified flows than for non-stratified flows.

Translational velocities of elongated bubbles in continuous slug flow

The translational velocities of elongated bubbles in continuous slug flow were measured for various flow rates, pipe inclinations and pipe diameters. Measurements were carried out by cross-correlating the output signals of consecutive optical fiber probes and by image processing technique. In addition, the velocities of single elongated bubbles in a stagnant and in a flowing liquid were measured by the same techniques. For all cases the measured velocities were compared to appropriate correlations. The measured velocities of single elongated bubbles were in all cases predicted quite well by the correlations while the velocities in continuous slug flow, for certain cases, were considerably underpredicted. This discrepancy is ascribed to the influence of the dispersed bubbles in the liquid slug region. A simplified model is proposed to calculate the translational velocity in continuous slug flow. The results of the model compare well with the measured translational velocities of elongated bubbles in continuous slug flow.

SOLUTION NONUNIQUENESS FOR SEPARATED GAS–LIQUID FLOW IN PIPES AND WELLS. I. OCCURRENCE

ABSTRACT The occurrence of multiple solutions has been investigated and discussed in this paper. Multiple solution regions are displayed by either a U SL–U SG map or a X–Y map. It is found that many parameters impose influence on the multiple solution regions, including fluid properties, pipe ID, pipe inclination angle, wall inflow or outflow, empirical correlations for wall friction and interfacial friction factors, and so on. For example, the multiple solution region could change significantly if different interfacial friction factor correlations are applied. Multiple solutions are only possible for upward flow for separated flow in a pipe without wall mass transfer. However, for wellbore flow case, depending on wall inflow or outflow of fluids and their flow rates, multiple solutions may also exist for horizontal and downward flow. More specifically, for wall inflow case (production well), multiple solutions only exist for upward flow for the gas inflow-dominant case, whereas they may exist for upward, horizontal and downward flow for liquid inflow-dominant situations. The opposite is expected for wall outflow (injection well) case.

Laminar stratified pipe flow

The Boundary Element Method (BEM) has been used to evaluate the integral and local flow properties of two-phase laminar–laminar stratified flow in a pipe for interface shapes determined by exact solution of the Young–Laplace equation. Results are presented for the volumetric flow rates, the interface and wall shear stresses and the velocity profiles on the interface and through the cross-section of the pipe. For the case of a flat planar interface, the results obtained from the BEM were compared against those from the analytical solution for a 50% holdup (i.e. with a flat interface passing through the horizontal axis) and with previous numerical solutions obtained using the bipolar coordinate system. Comparisons for the case of a circular interface were made with the Fourier integral method described by others. The solutions from the boundary integral method agree very well with these published results for special cases. Solutions are presented for a range of parameter values. The interface shape is determined by the Bond number, holdup or contact angle. The flow is controlled by these parameters, as well as the viscosity ratio, and the pipe inclination, which determines the relative driving forces on the two fluids. It is concluded that the BEM offers great flexibility and accuracy in addressing this class of flows.

Direct-contact condensation heat transfer model in RELAP5/MOD3.2 with/without noncondensable gases for horizontally stratified flow

Direct-contact condensation experiments on atmospheric steam and steam/air mixture on subcooled water flowing co-currently in nearly-horizontal channels are carried out and the local heat transfer coefficients are obtained. Inlet air mass fraction in the mixture is varied by up to 50%. Based on previous and present experimental data, a direct-contact condensation database is constructed. The horizontally stratified condensation model of RELAP5/MOD3.2 overpredicts both co-current and counter-current experimental data. The correlation proposed by Kim predicts the database relatively well compared with that of RELAP5/MOD3.2. In the presence of noncondensable gases, RELAP5/MOD3.2 overpredicts the database with percentage errors of 55.1 and 61.1% for pipe inclination angles of θ=2.1° and θ=5.0°, respectively. The UCB correction factor is modified to consider the effects of noncondensable gases on heat transfer coefficients. When Kim's correlation is substituted with the Dittus–Boelter type correlation in RELAP5/MOD3.2 and a modified correction factor is used, the prediction errors are greatly reduced to 20.7 and 28.8% for inclination angles of θ=2.1° and θ=5.0°, respectively.

The transport of particles at low loading in near-horizontal pipes by intermittent flow

The transport of sand particles at low concentration in horizontal and near horizontal pipes in air/water slug flow has been studied. Low concentration means less than 1 in 1000 by volume, a level of concentration of interest in the transport of sand by oil and gas in subsea flowlines (Stevenson & Thorpe, Proceedings of the Ninth International Conference on Multiphase Flow, Cannes, France, 1999) but much lower than the range of interest in all previous work on hydraulic conveying which may be thought to be a related field of study. The velocity of sands of sieving diameter of 1.1 and 0.51 mm have been measured for various gas and liquid flowrates and in liquids of viscosity in the range 1.0– 7.1 mPa s in two 12 m long pipes of internal diameter 40 and 70 mm . Video recordings have been analysed to determine the mechanisms involved in transport of particles in slug flow and are used to explain the observed decrease in particle propagation velocity with increased liquid viscosity. There being no totally satisfactory mechanistic model for intermittent flow in the literature, a semi-theoretical model for sand transport is not currently facilitated. Therefore the approach taken is that of dimensional analysis. Particle velocity, V P , is successfully correlated using dimensionless groups which include liquid viscosity, particle size and liquid and gas flow rates. The preferred correlation for sand in liquids of viscosity less than about 5 mPa s is V P j f =0.95 1+ j g j f − 1.38 j g j f +0.88 Fr f Re f Fr f d D 1.5 −0.180. All the parameters, except gravitational acceleration, have been varied in the experimental programme. It is found that particle velocity, V P is independent of pipe inclination in slug flow for pipe inclinations of up to three degrees. The above correlation is used to produce an equation that predicts the point of incipient-sand deposition. This equation can be used to estimate the maximum turndown of two-phase offshore oil production from satellite wells before sand will begin to deposit at the bottom of the pipe.

Stability Analysis of Stratified Oil/Water Flow in Inclined Pipelines

Summary A theoretical study was conducted to investigate flow-pattern transitions in slightly inclined pipelines carrying oil/water mixtures. Two criteria obtained in the linear-stability theory of stratified oil/water flow were used to predict the transition from a stratified-to nonstratified-flow pattern. A comparison of theoretical transition boundaries with published experimental data for horizontal and inclined pipes (±1° and ±5°) was performed. The study revealed that pipe inclination has a significant effect on the stratified-flow region. The results obtained can be useful for the design and operation of crude-oil flowlines and directional wells.

A Mechanistic Model for Multiphase Flow in Pipes

Abstract Mechanistic models for multiphase flow calculations can improve our ability to predict pressure drop and holdup in pipes, especially in situations that cannot easily be modeled in a laboratory and for which reliable empirical correlations are not available. In this paper, a new mechanistic model, applicable to all pipe geometries and fluid properties, is presented. New empirical correlations are proposed for liquid/wall and liquid/gas interfacial friction in stratified flow, for the liquid fraction entrained and the interfacial friction in annular-mist flow, and for the distribution coefficient used in the determination of holdup in intermittent flow. Introduction Empirical models often prove inadequate in that they are limited by the range of data on which they were based and, generally, cannot be used with confidence in all types of fluids and conditions encountered in oil and gas fields. Furthermore, many such models exhibit large discontinuities(1) at the flow pattern transitions and this can lead to convergence problems when these models are used for the simultaneous simulation of petroleum reservoirs and associated production facilities. Mechanistic models, on the other hand, are based on fundamental laws and thus can offer more accurate modeling of the geometric and fluid property variations. All of the models presented in the literature are either incomplete(2,3), in that they only consider flow pattern determination, or are limited in their applicability to only some pipe inclinations(4,5). A preliminary version(6)of the model proposed here that overcomes these limitations was presented in 1996. For most of the flow patterns observed, one or more empirical closure relationships are required even when a mechanistic approach is used. Where correlations available in the literature are inadequate for use in such models, new correlations must be developed. In order to be able to achieve this, access to reliable experimental data is important. A large amount of experimental data has been collected through the use of a Multiphase Flow Database(7) developed at Stanford University. The database presently contains over 20,000 laboratory measurements and approximately 1,800 measurements from actual wells. Based on subsets of these data, the previously proposed model(6) included a detailed investigation of the annular mist flow regime and new correlations for the liquid fraction entrained and for interfacial friction. This model has since been refined based on additional investigations of the stratified and intermittent flow regimes, and is the subject of this paper. Flow Pattern Determination The procedure for flow pattern determination begins with the assumption that a particular flow pattern exists and is followed by an examination of various criteria that establish the stability of the flow regime. If the regime is shown to be unstable, a new flow pattern is assumed and the procedure is repeated. Figure 1 shows flow pattern transitions based on the superficial velocities of the phases where the stability criteria (transition boundaries S1, S2, etc.) considered in this model are sketched. The procedure for flow pattern determination is illustrated in Figure 3, where it is seen that the examination of the dispersed bubble flow regime is the first to be considered.

Pressure Loss/Gain Boundary of Gas-Liquid Downward Flow in Inclined and Vertical Pipes

Gas-liquid downward flow is frequently encountered in hilly-terrain pipelines, downcomer pipes extending from offshore production platforms to sea floors, and steam injection wells in thermal enhanced recovery operations. Since the gravitational and frictional terms in the total pressure gradient equation for downward flow have opposite signs, gas-liquid downward flow in inclined and vertical pipes may experience either pressure loss or pressure gain, depending on flow rates, pipe geometry, and fluid properties. A mechanistic model for the pressure loss/gain boundary of gas-liquid downward flow in inclined and vertical pipes is developed in this work and is verified with available experimental results. The effects of pipe inclination angle, inside diameter, wall roughness, and fluid physical properties on the pressure loss/gain boundary are presented. [S0195-0738(00)00302-2]

Investigation of Transition From Annular to Intermittent Flow in Pipes

A new unified model is proposed for the transition from annular to intermittent flow patterns for the entire range of pipe inclination angles. Experimentally, it has been observed that the transition from annular flow takes place at a critical void fraction. To obtain a transition boundary equation, conservation of momentum equations for gas and the liquid film are combined and solved with the critical void fraction. The new model captures the correct transition characteristics, agrees favorably with experimental flow pattern data, and performs the best when compared with previous transition models. [S0195-0738(00)00601-4]

Liquid wall friction in two‐phase turbulent gas laminar liquid stratified pipe flow

AbstractThe main result of the present work is an analytic expression for the mean liquid wall shear stress in two‐phase turbulent gas/laminar liquid stratified pipe flow. The Navier‐Stokes equations are solved assuming a flat fluid‐fluid interface subject to a constant interfacial shear — approximating the interfacial drag exerted by the gas. The effect of a pipe inclination is accounted for, thereby retaining the interesting two‐phase phenomenon of backflow in upwardly inclined pipes. The corresponding expression for the wall shear stress distribution is obtained by formal differentiation. Its limiting behaviour in the triple points, where the fluid‐fluid interface meets the pipe wall, is determined by residue calculus. The expression for the mean wall shear stress is given by integration. It is found to be a linear combination of two terms. The first term accounts for the free surface liquid flow in the absence of the gas. The corresponding approximate hydraulic diameter model is found to be in surprisingly good agreement with this term. The second term represents the shear flow associated with the interfacial drag exerted by the gas (not accounted for by the hydraulic diameter approximation). The shear flow increases the flow rate near the interface on behalf of the flow rate near the pipe wall, thus reducing the wall shear stress below the free surface flow value. Expedient evaluation of the expression for the mean wall shear stress, suitable for use in a 1‐D multiphase pipe flow simulator, is facilitated by replacing certain one‐parameter integrals with highly accurate rational approximations.

Neural-Net Identification of Flow Regime With Band Spectra of Flow-Generated Sound

Summary Multiphase production log interpretation requires that the flow regime along hole in the wellbore is known. Flow regime is the cased-hole analog of lithology. Knowledge of the flow regime will help to interpret tool signals, will help to evaluate the flow rate on a per phase basis, and will reduce post-processing load. The flow regime can be classified correctly by a neural net in up to 87% of all cases using 1/3 octave band spectra of flow-generated sound plus the pipe inclination angle. Without the inclination an 88% correct classification can be achieved. A neural net trained on commercially available tool data (noise cuts) appears to be too sensitive to the wellbore inclination. Hence, application of automated neural net interpretation of noise logs requires a new generation of noise logging tools.

Two-phase flow in inclined parallel pipes

Two-phase flow in parallel pipes is associated with the application of Direct Steam Generation by solar heating. In this process boiling water is fed into many parallel pipes from a common manifold. Instability and non-uniformity of the flow in this case can be a major operational problem. In this work the gas and liquid distribution in two parallel pipes is mapped experimentally. It is found that the flow distribution can be either symmetric or asymmetric depending on the flow conditions and pipe inclination. A model that explains the observed phenomena is proposed.

Preventing buoyancy-driven flows of two Bingham fluids in a closed pipe - Fluid rheology design for oilfield plug cementing

The mechanically unstable situation of a heavy Bingham fluid resting on top of a light Bingham fluid in an inclined closed-ended pipe can be stabilised if the fluids have sufficiently large yield stresses. This paper focuses on determining the yield stresses that are sufficient to keep the fluids statically stable for a given fluid density difference, pipe diameter and pipe inclination. The results are applicable to a broad class of practically observable flows. This situation provides an idealised model for the oilfield process of plug cementing.

Gas-Liquid Interfacial Characteristics in an Inclined Upward Annular Flow.

This paper presents experimental data of the effects of pipe inclination on the circumferential variation of characteristics of annular liquid film and on the interfacial shear stress. In this experiment, film thickness was measured using the needle contact method and disturbance wave frequency and wave velocity were calculated from the output signals of time varying liquid film thickness by the constant current method. The inclination angles examined were 0°, 15°, 30°, 45°, 60° and 75° from the horizontal. Superficial velocities of air and water ranged from 20 m/s to 40 m/s and from 0.06 m/s and 0.20 m/s, respectively. The following results were obtained : i) The increase in pipe inclination makes the circumferential distribution of disturbance wave height uniform, while the wave velocity, frequency and length are not affected by the inclination. ii) A new correlation for the interfacial friction factor in an inclined upward pipe is obtained by modification of Fukano's correlation. iii) Simple charts were obtained to represent the relationship among interfacial shear stress, film thickness and flow rates of both phases.

A comparison of analytical and numerical models with experimental data for gas-solid flow through a straight pipe at different inclinations

An analytical model for gas-solid suspension flow through an inclined section of pipe was developed. This model predicts the ratio of the total pressure drop in an inclined pipe to that of a horizontal pipe. The model has been used to predict the critical pipe angle, which is defined as the angle at which the maximum pressure drop for a given solids flow rate is achieved. This angle differs from 90° (found in a single-phase flow) and is directly proportional to the ratio between the gas superficial velocity and the particle terminal velocity. The three-dimensional conservation equations for steady-state two-phase flow in an inclined pipe were solved numerically for constant solids and gas flow rates at different pipe inclinations. This model was based on the continuum theory for describing the mass and momentum balance equations for the fluid and solid phases. A packing model, describing the shear stress of the solid phase as a function of its volume fraction, is suggested in order to limit the maximum value of the solid volume fraction. A new model for particle-wall interaction was developed taking into account the angle of inclination of the pipe. The prediction of the numerical model was compared with experimental data obtained in a specially designed test rig. In general, the agreement between the experimental data and the models was satisfactory. The results of the numerical simulation also confirmed that the critical pipe angle for gas-solid flow is lower than 90°. The assumptions made during the development of the models were assessed in order to explain the differences between the predicted and measured values of the flow parameters for different flow regimes.

Circumferential Distribution of Film Thicknes and Film Flow Rate in an Inclined Upward Annular Flow.

This paper presents the circumferential distribution of film thickness and the relation between film flow rate and film thickness in an inclined upward annular flow. In this experiment, film thickness was measured by the needle contact method, and axial film flow rate was calculated assuming Karman's universal velocity profile. As a result, it was clarified that the circumferential distribution of film thickness is affected by gravity, the effects of pipe inclination on the distribution can be seen clearly at the top and bottom of the tube, an increase in inclination makes the distribution uniform, the effect of pipe inclination on the relation between film flow rate and film thickness increases as film flow rate increases, and film thickness increases with the inclination in the case of constant interfacial shear force and film flow rate.

An Experimental Study on Downward Slug Flow in Inclined Pipes

Summary The downward simultaneous flow of gas and liquid is often encountered in hilly terrain pipelines and injection wells. Most of the methods for predicting pressure drop in gas/liquid, two-phase flow in pipes have been developed for either upward vertical or upward inclined pipes. This study experimentally investigates downward co-current slug flow in inclined pipes. A new test facility was designed and built to acquire data for the entire range of pipe inclination angles. A series of slug flow experiments was conducted in a 2-in. diameter, 65-ft long clear PVC pipe installed on an inclinable structure. Liquid holdup and pressure drop measurements were obtained for downward inclination angles from 0° to −30° at different flow conditions. Translational velocity and liquid-slug holdup correlations were investigated based on the acquired data for different inclination angles.

Effect of Inclination on Distribution of Entrainment Flow Rate in an Inclined Upward Annular Flow.

The droplet entrainment in an annular flow plays an important role in heat and mass transfer. owever the fundamental experimental data such as film thickness, entrainment flow rate and disturbance wave velocity in the case of an inclined upward annular flow are very few compared with similar data in the case of two-phase flow in vertical and horizontal pipelines. In this paper, experimental data on the distribution of entrainment flow rate and the onset of liquid entrainment in an inclined upward annular flow are presented and the effects of the inclination angle are examined. In this experiment, the isokinetic sampling probe technique was used for the measurement of the entrained droplet flow rate and the ranges of inclination angle examined were 0, 30, 45, 60°and 75°from horizontal. As a result, it was clarified that the difference in droplet mass flux between the upper and lower tubes becomes small as pipe inclination increases, the entrainment fraction increases as both the flow rate and the inclination increase and the critical gas velocity for the onset of entrainment becomes small as the liquid film Reynolds number and the inclination increase. Furthermore, Ishii & Mishima's correlation for the entrainment fraction was modified for application to the inclined upward annular flow.

Experimental studies of flooding in nearly horizontal pipes

To investigate the flooding phenomenon in nearly horizontal pipes, experimental studies are performed for air and water countercurrent flow in a test section with a length of 2160 mm, with three different inner diameters of 40, 60 and 70 mm, with different types of end geometry, and with various inclination angles. The effects of the pipe diameter, end geometry and inclination angle on flooding are examined. Two mechanisms governing the transition to flooding are proposed: inner flooding and entrance flooding. The inner flooding is initiated by unstable wave growth, i.e. slugging, at the inner location of the pipe. The entrance flooding is always observed to take place at the entrance of the water flow without slugging. The effect of the inclination angle on flooding is predominant within quite a narrow range of inclination (0° < θ < 1°). A small deviation of the inclination angle from the horizontal plane causes a large deviation of the required air flow rates for flooding. Two local void fractions are measured by parallel wire probes and a scale marked rule in two regions (sub- and super-critical regions). The local effects of the void fraction on slug formation models are investigated. It is found that the differences in the exponents of the void fraction terms of the existing slug formation models mainly result from the definition of the void fraction used. When the void fraction measured in the sub-critical region is used in the slug formation model, Mishima et al.'s model well predicts the trend of the present data. However, if the void fraction measured in the super-critical region is used, Taitel et al.'s model better predicts the present data.