Inclined pipe low-liquid-volume gas-liquid-foam multiphase flow characteristic prediction method

Abstract

The invention provides a method for predicting low-liquid-volume gas-liquid-foam multiphase flow characteristics of an inclined pipe. The method comprises the steps that firstly, according to basic gas-liquid physical property parameters, gas-liquid phase apparent velocity, a pipeline inclination angle and the diameter, the flow pattern of the gas-liquid-foam multiphase flow of the inclined pipe is judged by adopting the minimum interfacial shear stress and a mechanical dynamic equilibrium rule; 2, judging the flow pattern of gas-liquid-foam multiphase flow of the inclined pipe, and calculating the closed relation of section phase volume fraction, wetted wall fraction, foam density and viscosity; 3, calculating the wetted perimeter, area and interface length of each phase, and deducing the actual flow velocity or flow velocity distribution relational expression of each phase; 4, improving and correcting the classical correlation formula of each phase-wall surface friction factor and each phase interface friction factor, and calculating the shear stress of each phase-wall surface and each phase interface according to the actual flow velocity; 5, performing pressure gradient solution or iterative calculation according to the corresponding flow pattern control model; the prediction precision can be improved, and the stability and efficiency of the foam drainage technology are effectively improved.

Description

Technical Field

[0001] The present invention relates to the field of oil and gas storage and transportation engineering, and in particular to a method for predicting the characteristics of low-liquid-volume gas-liquid-foam multiphase flow in inclined pipes, which is suitable for flow characteristic analysis and design optimization of foam drainage technology in gathering and transportation pipelines. Background Art

[0002] Natural gas gathering and transportation pipelines are susceptible to low-liquid accumulation due to the operating environment and terrain, which impacts pipeline transportation efficiency and increases the risk of pipeline corrosion and damage to downstream equipment. Currently, commonly used drainage pigs are prone to blockage in complex gathering and transportation networks, disrupting normal production processes and limiting their adaptability. Foam drainage technology transforms accumulated liquid into low-density foam through the injection of surfactants, relying on the natural gas's inherent energy to carry the liquid. This technology offers the advantages of no production impact, low investment costs, and ease of operation.

[0003] Accumulated liquid forms a variety of complex gas-liquid two-phase flow patterns within the pipeline, and the surfactant foam system causes the intermittent flow patterns to dissipate, resulting in a gas-liquid-foam separation flow state. Foam is a multiphase thermodynamically unstable dispersion system formed by gas as the dispersed phase and a liquid film as the dispersion medium. The gas-liquid-foam multiphase flow formed within the gathering and transportation pipeline is significantly different from conventional gas-liquid two-phase flow in terms of flow pattern type, phase distribution, and flow characteristics. As a result, the classic gas-liquid two-phase flow prediction method is no longer applicable. Therefore, achieving accurate prediction of gas-liquid-foam multiphase flow characteristics is of great engineering significance to the design, management, and application of foam drainage technology for gathering and transportation pipelines.

[0004] Currently, most domestic and international researchers have focused on pure gas-liquid two-phase flow and established relatively mature and systematic empirical or semi-theoretical flow prediction models. Some researchers have also conducted research on the characteristics and prediction methods of gas-liquid two-phase flows containing foam under surfactant action, but these studies primarily focus on vertical gas well production scenarios, lacking sufficient understanding of the conditions of inclined natural gas gathering and transmission pipelines with undulating terrain. Using existing pure gas-liquid two-phase models to predict multiphase flows containing foam can lead to flow pattern and pressure gradient predictions that deviate significantly from actual conditions. Existing gas-liquid two-phase flow models containing foam also distort phase holdup and pressure gradient predictions because they fail to account for liquid film formation during foam drainage and the uneven phase distribution across the inclined pipe due to gravity. Therefore, with the future expansion of foam drainage technology in oil and gas field development and surface gathering and transmission projects, it is crucial to develop a stable and effective method for predicting gas-liquid-foam multiphase flow characteristics.

[0005] However, at present, no corresponding inclined pipe gas-liquid-foam multiphase flow characteristics prediction method has been established for low-liquid natural gas gathering and transportation pipeline scenarios at home and abroad, making it difficult to predict the effect of foam drainage technology. Summary of the Invention

[0006] The present invention proposes a method for predicting the gas-liquid-foam multiphase flow characteristics of low-liquid-volume inclined pipelines, which can improve the prediction accuracy and effectively improve the stability and efficiency of the foam drainage technology. It is of great significance to the realization and application of foam drainage technology for low-liquid-volume inclined pipelines containing foam multiphase flow.

[0007] The present invention adopts the following technical solutions.

[0008] A method for predicting the characteristics of gas-liquid-foam multiphase flow in an inclined pipe with low liquid volume, the method being used to obtain graphic data of gas-liquid-foam multiphase flow patterns in an inclined pipe with low liquid volume, including foam liquid film stratified flow, foam stratified flow, and foam annular flow, comprising the following steps:

[0009] Step 1: Based on the given basic gas-liquid physical parameters, gas-liquid phase apparent flow velocity, pipe inclination angle and diameter, the minimum interfacial shear stress and mechanical dynamic equilibrium law are used to determine the flow pattern of the gas-liquid-foam multiphase flow in the inclined pipe;

[0010] Step 2: Determine the flow pattern of the gas-liquid-foam multiphase flow in the inclined pipe and calculate the cross-sectional phase holdup, wetted wall fraction, foam density, and viscosity closure relationship;

[0011] Step 3: By constructing the foam liquid film and foam stratified flow elliptical annular interface control model, as well as the foam annular flow circular annular interface control model, the wetted perimeter, area, and interface length of each phase are calculated based on the cross-sectional phase holdup and wetted wall fraction, and the actual flow velocity or flow velocity distribution relationship of each phase is derived;

[0012] Step 4: Improve and modify the classical correlation formula of each phase-wall friction factor and phase interface friction factor, and calculate the shear stress of each phase-wall and phase interface according to the actual flow rate;

[0013] Step 5: Based on the cross-sectional distribution and shear stress calculation results of each phase, combined with the given basic gas-liquid physical properties and pipeline inclination, the pressure gradient is solved or iteratively calculated according to the corresponding flow pattern control model.

[0014] In step 1, the basic gas-liquid physical parameters include density, viscosity, and interfacial tension. In step 1, by calculating the minimum interfacial shear stress and incorporating the dynamic equilibrium law of mechanics, the first and second critical gas velocities of the inclined pipeline are obtained as follows:

[0015] f gf =(2×τ gf ) / [ρ g (U g -U m )×|U g -U m |]

[0016]

[0017] By calculating Δf gf With ΔU SG Is the ratio of 0? Get the first critical gas velocity CU SG1 ;

[0018] The second critical gas velocity CU is obtained by the dynamic equilibrium law of mechanics SG2 ;

[0019] Where: f gf is the air-foam interface friction factor; τ gf is the air-foam interface shear stress, Pa; ρ g , ρ m are the gas phase and mixed phase densities, kg / m 3 ;U m 、U g are the mixed flow rate and gas phase flow rate, m / s; U SG is the gas phase apparent velocity, m / s; g is the acceleration due to gravity, m / s 2 ; d is the inner diameter of the pipe, m; K is an empirical constant, calibrated by specific experimental data.

[0020] In step 2, according to the calculated CU SG1 , CU SG2 Determine the flow type as follows:

[0021] When U SG Less than CU SG1 When U SG Greater than CU SG1 and smaller than CU SG2 When U SG Greater than CU SG2 When , the multiphase flow pattern is foam annular flow;

[0022] In step 2, based on the flow pattern, the cross-sectional phase holdup, wetted wall fraction, foam density, and viscosity closure relationship are calculated. The specific method is as follows: When the flow pattern is foam liquid film and foam stratified flow:

[0023] Liquid cross-section holdup H l The piecewise function is:

[0024]

[0025] Mixed phase cross-sectional content H m The fitting formula is:

[0026]

[0027] Foam air content Fg The expression is:

[0028] F g =(ρ l -ρ f ) / (ρ l -ρ g )

[0029] Foam density ρ f The correlation is:

[0030]

[0031] Re SL =ρ l U SL d / μ l

[0032] The relationship between the wetted wall fraction Θ is:

[0033]

[0034] Where U t is the Turner velocity, m / s; γ is the surface tension of the surfactant solution; C D is the resistance coefficient; U SL is the liquid phase apparent velocity, m / s; ρ l is the liquid density, kg / m 3 ;Re SL is the apparent liquid phase Reynolds number; μ l is the liquid phase dynamic viscosity, Pa·s;

[0035] When the flow pattern is foam annular flow:

[0036] Considering the influence of gas-liquid flow rate on liquid film thickness δ l Perform fitting and obtain the following relationship:

[0037]

[0038] Foam density ρ f expression:

[0039]

[0040] According to the experimental data, the foam gas content F g The associated formula is as follows:

[0041]

[0042] Where c eff is the actual surfactant concentration, ppm; μ f is the dynamic viscosity of the foam phase, Pa·s.

[0043] In step 3, an elliptical annular interface control model for foam film and foam stratified flow is constructed, as well as a circular annular interface control model for foam annular flow. Based on the cross-sectional phase holdup and wetted wall fraction, the wetted perimeter, area, and interface length of each phase are calculated. The specific method is as follows:

[0044] Method A1: When the manifold is foam liquid film and foam stratified flow, the foam fluid density is low, the interface curvature changes significantly when driven by the airflow, and the high viscosity characteristics cause its wetted perimeter to be continuously large, so the following is constructed: Figure 4 The elliptical ring interface model shown in the figure is used, and the following formula is obtained through the geometric relationship of the ellipse:

[0045] S g =(1-Θ)·πd

[0046] S m =S f +S l =Θ·πd

[0047] S gf =π|b|+2(a-|b|)

[0048] A m =A f +A l =H m A

[0049] A g =(1-H m )A

[0050] Where S g 、S m 、S l 、S f The wetted perimeters of the gas phase, mixed phase, liquid phase and foam phase pipe sections, m; S gf is the length of the air-foam interface, m; a and b are the major and minor axes of the elliptical gas phase channel, respectively; A is the cross-sectional area of ​​the channel, m 2 ; A g 、A f 、A l 、A m are the cross-sectional areas of the gas phase, foam phase, liquid phase and mixed phase, m 2 ;

[0051] Method A2: When the manifold is a foam annular flow, the geometric relationship between the phase circles and the annular structure of the annular interface control model is obtained:

[0052] A g =0.25π(d-2δ) 2

[0053] Sgf =π·(d-2δ)

[0054] A f =0.25π[(d-2δ l ) 2 -(d-2δ) 2 ]

[0055] S fl =π(d-2δ l )

[0056] Where δ is the total film thickness of the foam phase and liquid phase, m; S fl is the foam phase-liquid phase interface length, m.

[0057] In step 3, the actual flow rate or flow rate distribution relationship of each phase is derived as follows:

[0058] Actual flow rate conversion between foam liquid film and foam stratified flow:

[0059] U g =[U SG -U SL ·(F ga / (1-F ga ))] / (1-H m )

[0060] U mf =U SL / (H l +(H m -H l )·(1-F g ))

[0061] F ga =1-[H l +(H m -H l )·(1-F g )] / H m

[0062] Where, F ga is the mixed phase gas content; U mf is the mixed phase velocity, m / s;

[0063] Actual flow velocity conversion for foamy annular flow:

[0064] U g =U SG ·d 2 / (d-2δ) 2

[0065] In the case of foam annular flow, the velocity distribution expression is as follows:

[0066]

[0067] Where r is the radial coordinate, m; U is the average velocity of the mainstream, m / s; μ is the fluid dynamic viscosity, Pa·s; ρ is the fluid density, kg / m 3 When the flow is a foam annular flow, the velocity of the liquid layer and the foam layer is obtained by integrating the boundary conditions, specifically:

[0068] U l | r＝R =0

[0069]

[0070] A c =A g / (A g +A f )

[0071]

[0072]

[0073] Where A c is the area ratio coefficient of gas phase and foam phase; U SL,c is the liquid phase apparent velocity; Q L,c is the liquid phase flow rate; Q l , Q f are the liquid layer flow rate and foam layer flow rate, m 3 / h.

[0074] In step 4, the classical correlations between the phase-wall friction factor and the phase interface friction factor are improved and modified. The specific method is as follows:

[0075] Method B1, gas-wall friction factor f g The standard Blasius relationship is used for characterization:

[0076]

[0077] Re g =ρ g U g d g / μ g

[0078] d g =4A g / (S g +S gf )

[0079] Method B2, mixed phase-wall friction factor f mThe Deshpand foam flow friction factor is used to characterize and correct it, and its specific form is as follows:

[0080]

[0081] d m =4A m / S m

[0082]

[0083] Where, Re g is the gas phase Reynolds number; d g is the gas phase hydraulic diameter, m; μ g 、μ m are the dynamic viscosities of the gas phase and the mixed phase, Pa·s; d m is the hydraulic diameter of the mixed phase, m; coefficient C m 、n m and n are constants.

[0084] In step 4, based on the improved correction of the classical correlation of friction factor and the actual flow rate, the shear stress of each phase-wall and phase interface is calculated. The specific method is as follows:

[0085] When the manifold is foam liquid film and foam stratified flow:

[0086]

[0087] τ gf =f gf [ρ g (U g -U m )|U g -U m |] / 2

[0088] ρ m =F ga ρ g +(1-F ga )ρ l

[0089] When the manifold is foam annular flow:

[0090] τ gf =f gf [ρ g (U g -U f )|U g -U f |] / 2≈f gf [ρ g U g |U g |] / 2

[0091]

[0092] Where, τ g , τ m are the gas-wall and mixed-phase-wall shear stresses, respectively; U f is the foam phase flow rate, m / s.

[0093] In step 5, the pressure gradient calculation formula is derived using the interface control equations of the elliptical ring and the circular ring, as follows:

[0094] When the manifold is foam liquid film and foam stratified flow:

[0095]

[0096] Where, dP g / dL is the gas phase pressure gradient, Pa / m; θ is the angle between the pipeline and the horizontal direction,

[0097] When the manifold is foam annular flow:

[0098]

[0099] Where dP / dL is the annular flow pressure gradient, Pa / m.

[0100] In step 5, based on the cross-sectional distribution and shear stress calculation results of each phase, combined with the given basic physical properties and pipeline inclination, and according to the flow pattern prediction results, the corresponding pressure gradient solution or iterative calculation is performed as follows:

[0101] After inputting the fluid physical parameters, pipe diameter, inclination angle and gas-liquid superficial velocity, the foam liquid film and foam stratified flow are directly solved by calculating the phase fraction distribution, gas / mixed phase flow structure parameters and wall friction factor, and substituting them into the control equation to solve the pressure gradient; the foam annular flow requires setting the initial value of the liquid film thickness. By calculating the closed relationship such as the liquid film thickness, the gas / mixed phase flow structure parameters, and the wall friction factor, the pressure gradient is calculated by substituting them into the control equation. After verification by integral operation, if it does not converge, it is re-iterated until the accuracy requirements are met, and finally the pressure gradient and related flow parameters are output synchronously.

[0102] The prediction method is used to predict the working condition of an inclined pipeline in a foam drainage operation of a natural gas undulating gathering and transportation pipeline; the inclined pipeline is an upward-inclined pipe section, and a measuring pipe section made of a transparent material is provided at the upward-inclined pipe section, and the measuring pipe section is used for visual observation.

[0103] The present invention conducts predictive modeling of low-liquid-volume gas-liquid-foam multiphase flow in inclined pipes. Based on the minimum interfacial shear stress and the law of mechanical dynamic equilibrium, it determines the critical transition conditions for foam film stratified flow, foam stratified flow, and foam annular flow, and judges the flow pattern of gas-liquid-foam multiphase flow in inclined pipes. It also establishes and compares pressure gradient prediction models for foam film stratified flow, foam stratified flow, and foam annular flow, and improves prediction accuracy through iterative optimization. This effectively improves the stability and efficiency of foam drainage technology, which is of great significance to the implementation and application of foam drainage technology for low-liquid-volume inclined pipelines containing foam multiphase flow.

[0104] Compared with the prior art, the present invention has at least the following beneficial effects:

[0105] 1. This paper establishes a foamy multiphase flow model suitable for inclined pipelines, focusing on identifying gas-liquid-foam separation flow patterns and predicting phase holdup and pressure gradients. An elliptical ring interface model is proposed to more accurately describe the geometric characteristics of the interface in foamy stratified flows. The wetted wall fraction is introduced to describe the degree of foam adhesion to the pipe wall. The effect of foam diffusion on flow resistance is quantified by combining mixed phase holdup and the Reynolds number. Based on experimental observations of foam drainage, a piecewise function of liquid holdup as a function of gas-liquid flow velocity is proposed, which outperforms traditional models that assume a fixed liquid holdup or ignore the liquid phase.

[0106] 2. This invention dynamically characterizes foam density through gas velocity and Reynolds number, and improves foam viscosity calculation, more closely matching the actual foam formation and collapse process. Using minimum interfacial shear stress and the principle of dynamic mechanical equilibrium, it determines the critical transition conditions between foam film, foam stratified flow, and foam annular flow, and determines the flow pattern of gas-liquid-foam multiphase flow in an inclined tube, thus solving the problem of insensitivity to changes in interfacial shear stress.

[0107] 3. This invention achieves high-precision prediction of foam multiphase flow in inclined pipelines through innovative geometric models, dynamic closure relationships, and flow pattern conversion criteria, and has clear engineering application value in the field of foam drainage technology in natural gas gathering and transportation pipelines. BRIEF DESCRIPTION OF THE DRAWINGS

[0108] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0109] Attachment Figure 1 This is a schematic diagram of the flow pattern conversion boundary prediction;

[0110] Attachment Figure 2 This is a schematic diagram of the calculation process of the pressure gradient and critical gas velocity prediction model;

[0111] Attachment Figure 3 Schematic diagram comparing the experimental measured interface and the predicted interface of the gas-foam phase;

[0112] Attachment Figure 4 Schematic diagram of the elliptical ring interface control model in the embodiment. DETAILED DESCRIPTION

[0113] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without creative work are within the scope of protection of the present invention.

[0114] The present invention establishes a method for predicting the characteristics of low-liquid-volume gas-liquid-foam multiphase flow in an inclined tube, which can determine the critical transition conditions of foam liquid film stratified flow, foam stratified flow, and foam annular flow, thereby predicting the flow pattern of the multiphase flow. A pressure gradient prediction model for foam liquid film stratified flow, foam stratified flow, and foam annular flow was established, and the interface structure and phase distribution were determined. The accuracy of the model was verified by laboratory measured data. The following example uses an up-sloping section of a natural gas gathering and transportation pipeline. The annular channel consists of a pipeline with an inner diameter of 50 mm and a length of 36 m. The measuring section is made of transparent organic glass for easy visual observation, and the other sections are made of stainless steel.

[0115] As shown in the figure, a method for predicting the characteristics of gas-liquid-foam multiphase flow in an inclined pipe with low liquid volume is provided. The method is used to obtain graphic data of gas-liquid-foam multiphase flow patterns in an inclined pipe with low liquid volume, including foam liquid film stratified flow, foam stratified flow, and foam annular flow, and includes the following steps:

[0116] Step 1: Based on the given basic gas-liquid physical parameters, gas-liquid phase apparent flow velocity, pipe inclination angle and diameter, the minimum interfacial shear stress and mechanical dynamic equilibrium law are used to determine the flow pattern of the gas-liquid-foam multiphase flow in the inclined pipe;

[0117] Step 2: Determine the flow pattern of the gas-liquid-foam multiphase flow in the inclined pipe and calculate the cross-sectional phase holdup, wetted wall fraction, foam density, and viscosity closure relationship;

[0118] Step 3: By constructing the foam liquid film and foam stratified flow elliptical annular interface control model, as well as the foam annular flow circular annular interface control model, the wetted perimeter, area, and interface length of each phase are calculated based on the cross-sectional phase holdup and wetted wall fraction, and the actual flow velocity or flow velocity distribution relationship of each phase is derived;

[0119] Step 4: Improve and modify the classical correlation formula of each phase-wall friction factor and phase interface friction factor, and calculate the shear stress of each phase-wall and phase interface according to the actual flow rate;

[0120] Step 5: Based on the cross-sectional distribution and shear stress calculation results of each phase, combined with the given basic gas-liquid physical properties and pipeline inclination, the pressure gradient is solved or iteratively calculated according to the corresponding flow pattern control model.

[0121] In step 1, the basic gas-liquid physical parameters include density, viscosity, and interfacial tension. In step 1, by calculating the minimum interfacial shear stress and incorporating the dynamic equilibrium law of mechanics, the first and second critical gas velocities of the inclined pipeline are obtained as follows:

[0122] f gf =(2×τ gf ) / [ρ g (U g -U m )×|U g -U m |]

[0123]

[0124] By calculating Δf gf With ΔU SG Is the ratio of 0? Get the first critical gas velocity CU SG1 ;

[0125] The second critical gas velocity CU is obtained by the dynamic equilibrium law of mechanics SG2 ;

[0126] Where: f gf is the air-foam interface friction factor; τ gf is the air-foam interface shear stress, Pa; ρ g , ρ m are the gas phase and mixed phase densities, kg / m 3 ;U m 、U g are the mixed flow rate and gas phase flow rate, m / s; U SG is the gas phase apparent velocity, m / s; g is the acceleration due to gravity, m / s 2 ; d is the inner diameter of the pipe, m; K is an empirical constant, calibrated by specific experimental data.

[0127] In step 2, according to the calculated CU SG1 , CU SG2 Determine the flow type as follows:

[0128] When U SG Less than CU SG1 When U SG Greater than CU SG1 and smaller than CU SG2 When U SG Greater than CUSG2 When , the multiphase flow pattern is foam annular flow;

[0129] In step 2, based on the flow pattern, the cross-sectional phase holdup, wetted wall fraction, foam density, and viscosity closure relationship are calculated. The specific method is as follows: When the flow pattern is foam liquid film and foam stratified flow:

[0130] Liquid cross-section holdup H l The piecewise function is:

[0131]

[0132] Mixed phase cross-sectional content H m The fitting formula is:

[0133]

[0134] Foam air content F g The expression is:

[0135] F g =(ρ l -ρ f ) / (ρ l -ρ g )

[0136] Foam density ρ f The correlation is:

[0137]

[0138] Re SL =ρ l U SL d / μ l

[0139] The relationship between the wetted wall fraction Θ is:

[0140]

[0141] Where U t is the Turner velocity, m / s; γ is the surface tension of the surfactant solution; C D is the resistance coefficient; U SL is the liquid phase apparent velocity, m / s; ρ l is the liquid density, kg / m 3 ;Re SL is the apparent liquid phase Reynolds number; μ l is the liquid phase dynamic viscosity, Pa·s;

[0142] When the flow pattern is foam annular flow:

[0143] Considering the influence of gas-liquid flow rate on liquid film thickness δ lPerform fitting and obtain the following relationship:

[0144]

[0145] Foam density ρ f expression:

[0146]

[0147] According to the experimental data, the foam gas content F g The associated formula is as follows:

[0148]

[0149] Where c eff is the actual surfactant concentration, ppm; μ f is the dynamic viscosity of the foam phase, Pa·s.

[0150] In step 3, an elliptical annular interface control model for foam film and foam stratified flow is constructed, as well as a circular annular interface control model for foam annular flow. Based on the cross-sectional phase holdup and wetted wall fraction, the wetted perimeter, area, and interface length of each phase are calculated. The specific method is as follows:

[0151] Method A1: When the manifold is foam liquid film and foam stratified flow, the foam fluid density is low, the interface curvature changes significantly when driven by the airflow, and the high viscosity characteristics cause its wetted perimeter to be continuously large, so the following is constructed: Figure 4 The elliptical ring interface model shown in the figure is used, and the following formula is obtained through the geometric relationship of the ellipse:

[0152] S g =(1-Θ)·πd

[0153] S m =S f +S l =Θ·πd

[0154] S gf =π|b|+2(a-|b|)

[0155] A m =A f +A l =H m A

[0156] A g =(1-H m )A

[0157] Where S g 、S m 、S l 、S f The wetted perimeters of the gas phase, mixed phase, liquid phase and foam phase pipe sections, m; Sgf is the length of the air-foam interface, m; a and b are the major and minor axes of the elliptical gas phase channel, respectively; A is the cross-sectional area of ​​the channel, m 2 ; A g 、A f 、A l 、A m are the cross-sectional areas of the gas phase, foam phase, liquid phase and mixed phase, m 2 ;

[0158] Method A2: When the manifold is a foam annular flow, the geometric relationship between the phase circles and the annular structure of the annular interface control model is obtained:

[0159] A g =0.25π(d-2δ) 2

[0160] S gf =π·(d-2δ)

[0161] A f =0.25π[(d-2δ l ) 2 -(d-2δ) 2 ]

[0162] S fl =π(d-2δ l )

[0163] Where δ is the total film thickness of the foam phase and liquid phase, m; S fl is the foam phase-liquid phase interface length, m.

[0164] In step 3, the actual flow rate or flow rate distribution relationship of each phase is derived as follows:

[0165] Actual flow rate conversion between foam liquid film and foam stratified flow:

[0166] U g =[U SG -U SL ·(F ga / (1-F ga ))] / (1-H m )

[0167] U mf =U SL / (H l +(H m -H l )·(1-F g ))

[0168] F ga =1-[H l +(H m-H l )·(1-F g )] / H m

[0169] Where, F ga is the mixed phase gas content; U mf is the mixed phase velocity, m / s;

[0170] Actual flow velocity conversion for foamy annular flow:

[0171] U g =U SG ·d 2 / (d-2δ) 2

[0172] In the case of foam annular flow, the velocity distribution expression is as follows:

[0173]

[0174] Where r is the radial coordinate, m; U is the average velocity of the mainstream, m / s; μ is the fluid dynamic viscosity, Pa·s; ρ is the fluid density, kg / m 3 When the flow is a foam annular flow, the velocity of the liquid layer and the foam layer is obtained by integrating the boundary conditions, specifically:

[0175] U l | r＝R =0

[0176]

[0177] A c =A g / (A g +A f )

[0178]

[0179] Where A c is the area ratio coefficient of gas phase and foam phase; U SL,c is the liquid phase apparent velocity; Q L,c is the liquid phase flow rate; Q l , Q f are the liquid layer flow rate and foam layer flow rate, m 3 / h.

[0180] In step 4, the classical correlations between the phase-wall friction factor and the phase interface friction factor are improved and modified. The specific method is as follows:

[0181] Method B1, gas-wall friction factor f g The standard Blasius relationship is used for characterization:

[0182]

[0183] Re g =ρ g U g d g / μ g

[0184] d g =4A g / (S g +S gf )

[0185] Method B2, mixed phase-wall friction factor f m The Deshpand foam flow friction factor is used to characterize and correct it, and its specific form is as follows:

[0186]

[0187] d m =4A m / S m

[0188]

[0189] Where, Re g is the gas phase Reynolds number; d g is the gas phase hydraulic diameter, m; μ g 、μ m are the dynamic viscosities of the gas phase and the mixed phase, Pa·s; d m is the hydraulic diameter of the mixed phase, m; coefficient C m 、n m and n are constants.

[0190] In step 4, based on the improved correction of the classical correlation of friction factor and the actual flow rate, the shear stress of each phase-wall and phase interface is calculated. The specific method is as follows:

[0191] When the manifold is foam liquid film and foam stratified flow:

[0192]

[0193] τ gf =f gf [ρ g (U g -U m )|U g -U m |] / 2

[0194] ρ m =F ga ρ g+(1-F ga )ρ l

[0195] When the manifold is foam annular flow:

[0196] τ gf =f gf [ρ g (U g -U f )|U g -U f |] / 2≈f gf [ρ g U g |U g |] / 2

[0197]

[0198] Where, τ g , τ m are the gas-wall and mixed-phase-wall shear stresses, respectively; U f is the foam phase flow rate, m / s.

[0199] In step 5, the pressure gradient calculation formula is derived using the interface control equations of the elliptical ring and the circular ring, as follows:

[0200] When the manifold is foam liquid film and foam stratified flow:

[0201]

[0202] Where, dP g / dL is the gas phase pressure gradient, Pa / m; θ is the angle between the pipeline and the horizontal direction,

[0203] When the manifold is foam annular flow:

[0204]

[0205] Where dP / dL is the annular flow pressure gradient, Pa / m.

[0206] In step 5, based on the cross-sectional distribution and shear stress calculation results of each phase, combined with the given basic physical properties and pipeline inclination, and according to the flow pattern prediction results, the corresponding pressure gradient solution or iterative calculation is performed as follows:

[0207] After inputting the fluid physical parameters, pipe diameter, inclination angle and gas-liquid superficial velocity, the foam liquid film and foam stratified flow are directly solved by calculating the phase fraction distribution, gas / mixed phase flow structure parameters and wall friction factor, and substituting them into the control equation to solve the pressure gradient; the foam annular flow requires setting the initial value of the liquid film thickness. By calculating the closed relationship such as the liquid film thickness, the gas / mixed phase flow structure parameters, and the wall friction factor, the pressure gradient is calculated by substituting them into the control equation. After verification by integral operation, if it does not converge, it is re-iterated until the accuracy requirements are met, and finally the pressure gradient and related flow parameters are output synchronously.

[0208] The prediction method is used to predict the working condition of an inclined pipeline in a foam drainage operation of a natural gas undulating gathering and transportation pipeline; the inclined pipeline is an upward-inclined pipe section, and a measuring pipe section made of a transparent material is provided at the upward-inclined pipe section, and the measuring pipe section is used for visual observation.

[0209] Example:

[0210] This example takes the up-dip section of a natural gas gathering and transportation pipeline as an example. The loop consists of a pipeline with an inner diameter of 50 mm and a length of 36 m. The measuring section is made of transparent organic glass for easy visual observation, and the other sections are made of stainless steel.

[0211] This example provides a method for predicting the characteristics of gas-liquid-foam multiphase flow in an inclined tube with low liquid volume. A gas-liquid-foam multiphase flow pattern diagram for an inclined tube with low liquid volume is proposed, including foam film stratified flow, foam stratified flow, and foam annular flow. Based on given basic gas-liquid physical parameters (density, viscosity, interfacial tension), gas-liquid phase apparent velocity, pipe inclination angle, and pipe diameter, the minimum interfacial shear stress and mechanical dynamic equilibrium laws are used to determine the flow pattern of the gas-liquid-foam multiphase flow in the inclined tube. An elliptical annular interface control model is constructed for the foam film and foam stratified flows, while a circular annular interface control model is constructed for the foam annular flow. Each model calculates the closed relationship between cross-sectional phase holdup, wetted wall fraction, foam density, and viscosity based on empirical experimental data. Based on the cross-sectional phase holdup and wetted wall fraction, the wetted perimeter, area, and interface length of each phase are calculated, and the actual flow velocity or velocity distribution relationship for each phase is derived. Classical correlations for phase-wall friction factors and interfacial friction factors are modified to calculate the shear stresses at each phase-wall and interfacial surfaces based on the actual flow velocity. Based on the calculated cross-sectional distribution and shear stress results for each phase, combined with given basic physical properties and pipeline inclination, the pressure gradient is solved or iteratively calculated according to the corresponding flow pattern control model. This prediction method can provide theoretical and technical guidance for the development and control application of foam drainage technology for fluctuating natural gas gathering and transmission pipelines.

[0212] refer to Figure 1 and Figure 2 , the method described in this example includes the following steps:

[0213] (1) Based on the given basic gas-liquid physical parameters (density, viscosity, interfacial tension), gas-liquid phase apparent velocity, pipe inclination and diameter, the minimum interfacial shear stress and mechanical dynamic equilibrium law are used to obtain the first and second critical gas velocities:

[0214] f gf =(2×τ gf ) / [ρ g (U g -U m )×|U g -U m |]

[0215]

[0216] By calculating Δf gf With ΔU SG Is the ratio of 0? Get the first critical gas velocity CU SG1 .

[0217] The second critical gas velocity CU is obtained by the dynamic equilibrium law of mechanics SG2 .

[0218] Where: f gf is the air-foam interface friction factor; τ gf is the air-foam interface shear stress, Pa; ρ g , ρ m are the gas phase and mixed phase densities, kg / m 3 ;U m 、U g is the mixed flow rate and gas phase flow rate, m / s; U SG is the gas phase apparent velocity, m / s; g is the acceleration due to gravity, m / s 2 ; d is the inner diameter of the pipe, m; K is an empirical constant, calibrated by specific experimental data.

[0219] (2) According to the calculated CU SG1 , CU SG2 Determine the flow type and get Figure 1 Flow pattern conversion boundary prediction map:

[0220] When U SG Less than CU SG1 When U SG Greater than CU SG1 and smaller than CU SG2 When U SG Greater than CU SG2 When , the multiphase flow pattern is foam annular flow;

[0221] refer to Figure 2The method for calculating the pressure gradient of each flow pattern of the present invention comprises the following steps:

[0222] 1. When the flow pattern is foam liquid film and foam stratified flow:

[0223] (1) Given an initial U SG , calculate the cross-sectional content, wetted wall fraction, and foam density of each phase under given physical property parameters through closed-formula equations:

[0224] Liquid cross-section holdup H l The piecewise function is:

[0225]

[0226] Formula 1;

[0227]

[0228] Mixed phase cross-sectional content H m The fitting formula is:

[0229]

[0230] Foam air content F g The expression is:

[0231] F g =(ρ l -ρ f ) / (ρ l -ρ g ) Formula 4;

[0232] Foam density ρ f The correlation is:

[0233]

[0234] Re SL =ρ l U SL d / μ l Formula 6;

[0235] The relationship between the wetted wall fraction Θ is:

[0236]

[0237] Where U t is the Turner velocity, m / s; γ is the surface tension of the surfactant solution; C D is the resistance coefficient; U SG 、U SL are the superficial velocity of gas phase and liquid phase, m / s; ρ l , ρ g Respectively, the density of liquid phase and gas phase, kg / m3 ;Re SL is the apparent liquid phase Reynolds number; μ l is the liquid phase dynamic viscosity, Pa·s; g is the acceleration due to gravity, m / s 2 ; d is the inner diameter of the pipe, m.

[0238] (2) The geometric parameters of each phase of the foam multiphase flow are calculated by using the geometric relationship of the elliptical ring interface control model:

[0239] S g =(1-Θ)·πd Formula 8;

[0240] S m =S f +S l =Θ·πd Formula 9

[0241] S gf =π|b|+2(a-|b|) Formula 10;

[0242] A m =A f +A l =H m A formula 11;

[0243] A g =(1-H m )A formula 12;

[0244] Where S g 、S m 、S l 、S f The wetted perimeters of the gas phase, mixed phase, liquid phase and foam phase pipe sections, m; S gf is the length of the air-foam interface, m; a and b are the major and minor axes of the elliptical gas phase channel, respectively; A is the cross-sectional area of ​​the channel, m 2 ; A g 、A f 、A l 、A m are the cross-sectional areas of the gas phase, foam phase, liquid phase and mixed phase, m 2 ;

[0245] (3) Calculate the flow rate of each phase of the foam multiphase flow using the results of the closed-loop relationship:

[0246] U g =[U SG -U SL ·(F ga / (1-F ga ))] / (1-H m ) Formula 13;

[0247] U mf =U SL / (H l +(H m -H l )·(1-F g )) Formula 14;

[0248] F ga =1-[H l +(H m -H l )·(1-F g )] / H m Formula 15;

[0249] Where, F ga is the mixed phase gas content; U mf 、U g are the mixed phase and gas phase velocities, m / s, respectively.

[0250] (4) Improve and modify the classical correlation between each phase-wall friction factor and phase interface friction factor:

[0251] 1) Gas-wall friction factor f g The standard Blasius relationship is used for characterization:

[0252]

[0253] Re g =ρ g U g d g / μ g Formula 17;

[0254] d g =4A g / (S g +S gf ) Formula 18;

[0255] 2) Mixed phase-wall friction factor f m The foam flow friction factor proposed by Deshpand is used for characterization and is modified as follows:

[0256]

[0257] d m =4A m / S m Formula 20;

[0258]

[0259] Where, Re gis the gas phase Reynolds number; d g is the gas phase hydraulic diameter, m; μ g 、μ m are the dynamic viscosities of the gas phase and the mixed phase, Pa·s; d m is the hydraulic diameter of the mixed phase, m; coefficient C m 、n m and n are constants; U m is the mixing flow velocity, m / s; ρ m is the density of the mixed phase, kg / m 3 .

[0260] (5) Based on the improved correction of the classical correlation formula of friction factor, the shear stress of each phase-wall and phase interface is calculated in combination with the actual flow rate:

[0261]

[0262] ρ m =F ga ρ g +(1-F ga )ρ l Formula 25;

[0263] Where, τ g , τ m are the gas-wall and mixed-phase-wall shear stresses, respectively; τ gf is the shear stress at the air-foam interface, Pa; θ is the angle between the pipeline and the horizontal direction, °.

[0264] (6) Using the above results, solve the pressure gradient:

[0265]

[0266] Where, dP g / dL is the gas phase pressure gradient, Pa / m.

[0267] 2. When the flow pattern is foam annular flow:

[0268] (1) Given the initial gas-liquid apparent velocity and initial film thickness, the liquid film thickness δ is calculated by the closed relationship l , foam density ρ f , foam viscosity μ f :

[0269]

[0270] Where c eff is the actual surfactant concentration, ppm; U t is the Turner velocity, m / s; γ is the surface tension of the surfactant solution; C D is the resistance coefficient; USL 、U SG are the superficial velocity of liquid and gas phase, m / s; ρ l , ρ g Respectively, the density of liquid phase and gas phase, kg / m 3 ;Re SL is the apparent liquid phase Reynolds number; F g is the foam air content; g is the acceleration of gravity, m / s 2 ;μ l is the liquid phase dynamic viscosity, Pa·s.

[0271] (2) According to the geometric relationship between the circular and annular structures of each phase, calculate the area of ​​each phase and the interface length:

[0272] A g =0.25π(d-2δ) 2 Formula a5;

[0273] S gf =π·(d-2δ) Formula a6;

[0274] A f =0.25π[(d-2δ l ) 2 -(d-2δ) 2 Formula a7;

[0275] S fl =π(d-2δ l ) Formula a8;

[0276] Where δ is the total film thickness of the foam phase and liquid phase, m; S fl is the length of the foam phase-liquid phase interface, m; A g 、A f are the cross-sectional areas of the gas phase and foam phase pipes, m 2 ; d is the inner diameter of the pipe, m.

[0277] (3) Calculate the shear stress and friction factor of each phase-wall and phase interface based on the actual flow rate:

[0278] τ gf =f gf [ρ g (U g -U f )|U g -U f |] / 2≈f gf [ρ g U g |U g |] / 2 formula a9;

[0279]

[0280] Where, τ g , τ m are the gas-wall and mixed phase-wall shear stresses, respectively; U f 、U g are the foam phase and gas phase flow rates, m / s; f gf is the air-foam interface friction factor.

[0281] (4) Calculate the pressure gradient using the ring interface governing equation:

[0282]

[0283] Where dP / dL is the annular flow pressure gradient, Pa / m; θ is the angle between the pipeline and the horizontal direction, degrees.

[0284] (5) Calculate the velocity gradient dU of the liquid layer and foam layer l / dr、dU f / dr:

[0285] U l | r＝R =0 formula a12;

[0286]

[0287] A c =A g / (A g +A f )Formula a14;

[0288]

[0289] Where r is the radial coordinate, m; U is the average velocity of the mainstream, m / s; μ is the fluid dynamic viscosity, Pa·s; ρ is the fluid density, kg / m 3 ; τ gf is the air-foam interface shear stress, Pa; A c is the area ratio coefficient of gas phase and foam phase.

[0290] (6) Calculate the liquid phase apparent velocity U by integrating the velocity distribution of each phase in space SL,c :

[0291]

[0292] Where Q l , Q f are the liquid layer flow rate and foam layer flow rate, m 3 / h; U SL,c is the liquid phase apparent velocity; Q L,c is the liquid phase flow rate; A is the cross-sectional area of ​​the pipe, m2 .

[0293] (7) Finally, if U SL,c with U SL When the difference reaches the convergence condition, the correct pressure gradient prediction value is obtained; otherwise, the total film thickness value is adjusted and the iteration is continued until the termination condition is met.

[0294] Refer to Table 1, Table 2, Figure 3 , comparison between the model described in this patent and the experimental results:

[0295] Table 1 compares the actual experimentally measured values ​​with the pressure gradient changes predicted by the present invention for each flow pattern. It can be seen that the pressure gradient changes predicted by the present invention for each flow pattern are close to the actual measured values, verifying the accuracy of the present model. Compared with previous models, the present model performs better. For example, the van Nimwegen model generally predicts values ​​higher than the measured values, while the Ajani model generally predicts values ​​lower than the measured values, indicating that the performance of both models is not ideal.

[0296] Table 1 Pressure gradient calculation error table

[0297]

[0298] (1) The present invention measures the instantaneous phase holdup by the wire mesh sensor method and the volume phase holdup by the quick-closing valve method, and uses MATLAB software post-processing to obtain experimental values ​​of parameters such as liquid and foam phase holdups, foam density, and wetted wall fraction as shown in Table 2.

[0299] It can be seen from Table 2 that the prediction errors of the parameters related to the phase distribution of each flow pattern in the present invention are very small, and the prediction effect is good.

[0300] Table 2 Phase distribution calculation error table

[0301]

[0302] (2) From Figure 3 As can be seen, the model proposed in this paper can effectively predict the location of phase interfaces in multiphase flows, demonstrating high prediction accuracy through in-depth analysis of gas-liquid flow characteristics. Comparison of experimentally observed flow interfaces with the model's predicted geometric interfaces verifies the model's accuracy in reflecting actual flow interface characteristics. This intuitively demonstrates the model's ability to replicate actual flow phenomena, enhancing its practical application in foam drainage technology.

[0303] In summary, this example provides a method for predicting the characteristics of low-liquid-volume gas-liquid-foam multiphase flow in an inclined tube, including proposing a low-liquid-volume gas-liquid-foam multiphase flow pattern diagram in an inclined tube, including foam liquid film stratified flow, foam stratified flow, and foam annular flow; according to given basic gas-liquid physical parameters (density, viscosity, interfacial tension), gas-liquid phase apparent velocity, pipe inclination angle and diameter, the minimum interfacial shear stress and mechanical dynamic equilibrium law are used to determine the flow pattern of gas-liquid-foam multiphase flow in an inclined tube; by constructing an elliptical ring interface control model for foam liquid film and foam stratified flow, as well as foam annular flow The annular interface control model is used to calculate the closed relationship between the cross-sectional phase content, wet wall fraction, foam density and viscosity; based on the cross-sectional phase content and wet wall fraction, the wet perimeter, area and interface length of each phase are calculated, and the actual flow velocity or flow velocity distribution relationship of each phase is derived; the classical correlation formula of each phase-wall friction factor and phase interface friction factor is improved and modified, and the shear stress of each phase-wall and phase interface is calculated according to the actual flow velocity; based on the cross-sectional distribution and shear stress calculation results of each phase, combined with the given basic physical properties and pipeline inclination, according to the flow type prediction results, the pressure gradient is solved or iteratively calculated accordingly. The present invention establishes a foam-containing multiphase flow model suitable for inclined pipelines, focusing on solving the pressure gradient prediction problem of foam liquid film, foam stratified flow and foam annular flow. An elliptical annular interface model is proposed to more accurately describe the geometric characteristics of the stratified interface of multiphase flow, introduce the wet wall fraction to describe the degree of foam adhesion to the pipe wall, and combine the mixed phase content and Reynolds number to quantify the effect of foam diffusion on flow resistance. Combined with the segmented change trend of experimental observations, a segmented function of liquid phase content with gas-liquid flow rate is proposed, which is better than the assumption of fixed liquid content or neglect of liquid phase in traditional models. The foam density is dynamically characterized by gas velocity and Reynolds number, and the foam viscosity calculation is improved to better fit the actual foam generation and bursting process. The minimum interface shear stress and mechanical dynamic equilibrium law are used to determine the critical conversion conditions of foam liquid film stratified flow, foam stratified flow and foam annular flow, and the flow pattern of gas-liquid-foam multiphase flow in the inclined pipe is judged, which solves the problem of insensitivity to changes in interface shear stress. The present invention realizes high-precision prediction of foam multiphase flow in inclined pipes through innovative geometric models, dynamic closure relations and flow pattern conversion criteria, and has clear engineering application value.

Claims

1. A method for predicting the characteristics of low-liquid-volume gas-liquid-foam multiphase flow in an inclined pipe, characterized by: The prediction method is used to obtain graphic data of inclined tube low liquid volume gas-liquid-foam multiphase flow patterns including foam liquid film stratified flow, foam stratified flow, and foam annular flow, and comprises the following steps: Step 1: Based on the given basic gas-liquid physical parameters, gas-liquid phase apparent flow velocity, pipe inclination angle and diameter, the minimum interfacial shear stress and mechanical dynamic equilibrium law are used to determine the flow pattern of the gas-liquid-foam multiphase flow in the inclined pipe; Step 2: Determine the flow pattern of the gas-liquid-foam multiphase flow in the inclined pipe and calculate the cross-sectional phase holdup, wetted wall fraction, foam density, and viscosity closure relationship; Step 3: By constructing the foam liquid film and foam stratified flow elliptical annular interface control model, as well as the foam annular flow circular annular interface control model, the wetted perimeter, area, and interface length of each phase are calculated based on the cross-sectional phase holdup and wetted wall fraction, and the actual flow velocity or flow velocity distribution relationship of each phase is derived; Step 4: Improve and modify the classical correlation formula of each phase-wall friction factor and phase interface friction factor, and calculate the shear stress of each phase-wall and phase interface according to the actual flow rate; Step 5: Based on the cross-sectional distribution and shear stress calculation results of each phase, combined with the given basic gas-liquid physical properties and pipeline inclination, the pressure gradient is solved or iteratively calculated according to the corresponding flow pattern control model.

2. The method for predicting gas-liquid-foam multiphase flow characteristics in an inclined tube with low liquid volume according to claim 1, characterized in that: In step 1, the basic gas-liquid physical parameters include density, viscosity, and interfacial tension. In step 1, by calculating the minimum interfacial shear stress and incorporating the dynamic equilibrium law of mechanics, the first and second critical gas velocities of the inclined pipeline are obtained as follows: f gf =(2×τ gf ) / [ρ g (IN g -IN m )×|U g -IN m |] By calculating Δf gf With ΔU SG Is the ratio of 0? Get the first critical gas velocity CU SG1 ; The second critical gas velocity CU is obtained by the dynamic equilibrium law of mechanics SG2 ; Where: f gf is the air-foam interface friction factor; τ gf is the air-foam interface shear stress, Pa; ρ g , ρ m are the gas phase and mixed phase densities, kg / m 3 ;U m 、U g are the mixed flow rate and gas phase flow rate, m / s; U SG is the gas phase apparent velocity, m / s; g is the acceleration due to gravity, m / s 2 ; d is the inner diameter of the pipe, m; K is an empirical constant, calibrated by specific experimental data.

3. The method for predicting the characteristics of gas-liquid-foam multiphase flow in an inclined tube with low liquid volume according to claim 2, characterized in that: In step 2, according to the calculated CU SG1 , CU SG2 Determine the flow type as follows: When U SG Less than CU SG1 When , the multiphase flow pattern is foam liquid film stratified flow; When U SG Greater than CU SG1 and smaller than CU SG2 When , the multiphase flow pattern is foam stratified flow; When U SG Greater than CU SG2 When , the multiphase flow pattern is foam annular flow; In step 2, based on the flow pattern, the cross-sectional phase holdup, wetted wall fraction, foam density, and viscosity closure relationship are calculated. The specific method is as follows: When the flow pattern is foam liquid film and foam stratified flow: Liquid cross-section holdup H l The piecewise function is: Mixed phase cross-sectional content H m The fitting formula is: Foam air content F g The expression is: F g =(ρ l -r f ) / (ρ l -r g ) Foam density ρ f The correlation is: Bid SL Zρ l U SL d / µ l The relationship between the wetted wall fraction Θ is: Where U t is the Turner velocity, m / s; γ is the surface tension of the surfactant solution; C D is the resistance coefficient; U SL is the liquid phase apparent velocity, m / s; ρ l is the liquid density, kg / m 3 ;Re SL is the apparent liquid phase Reynolds number; μ l is the liquid phase dynamic viscosity, Pa·s; When the flow pattern is foam annular flow: Considering the influence of gas-liquid flow rate on liquid film thickness δ l Perform fitting and obtain the following relationship: Foam density ρ f expression: According to the experimental data, the foam gas content F g The associated formula is as follows: Where c eff is the actual surfactant concentration, ppm; μ f is the dynamic viscosity of the foam phase, Pa·s.

4. The method for predicting gas-liquid-foam multiphase flow characteristics in an inclined tube with low liquid volume according to claim 3, characterized in that: In step 3, an elliptical annular interface control model for foam film and foam stratified flow is constructed, as well as a circular annular interface control model for foam annular flow. Based on the cross-sectional phase holdup and wetted wall fraction, the wetted perimeter, area, and interface length of each phase are calculated. The specific method is as follows: Method A1: When the manifold is a foam liquid film or foam stratified flow, the foam fluid has a low density. When driven by the airflow, the interface curvature changes significantly. The high viscosity characteristic causes the wetted perimeter to be continuously large. Therefore, an elliptical ring interface model is constructed as shown in Figure 1, and the following formula is obtained through the geometric relationship of the ellipse: S g =(1-Θ)·πd S m =S f +S l =Θ·πd S gf =π|b|+2(a-|b|) A m =A f +A l =H m A A g =(1-H m )A Where S g 、S m 、S l 、S f are the wetted perimeters of the pipe sections for gas phase, mixed phase, liquid phase and foam phase, m; S gf is the air-foam interface length, m; a and b are the major and minor axes of the elliptical gas phase channel, respectively; A is the cross-sectional area of ​​the channel, m 2 ; A g 、A f 、A l 、A m are the cross-sectional areas of the gas phase, foam phase, liquid phase and mixed phase, m 2 ; Method A2: When the manifold is a foam annular flow, the geometric relationship between the phase circles and the annular structure of the annular interface control model is obtained: A g =0.25π(d-2δ) 2 S gf =π·(d-2d) A f =0.25π[(d-2δ l ) 2 -(d-2d) 2 ] S fl =π(d-2δ l ) Where δ is the total film thickness of the foam phase and liquid phase, m; S fl is the foam phase-liquid phase interface length, m.

5. The method for predicting the characteristics of gas-liquid-foam multiphase flow in an inclined tube with low liquid volume according to claim 4, characterized in that: In step 3, the actual flow rate or flow rate distribution relationship of each phase is derived as follows: Actual flow rate conversion between foam liquid film and foam stratified flow: IN g =[U SG -IN SL ·(F ga / (1-F ga ))] / (1-H m ) U mf =U SL / (H l +(H m -H l )·(1-F g )) F ga =1-[H l +(H m -H l )·(1-F g )] / H m Where, F ga is the mixed phase gas content; U mf is the mixed phase velocity, m / s; Actual flow velocity conversion for foamy annular flow: U g =U SG ·d 2 / (d-2δ) 2 In the case of foam annular flow, the velocity distribution expression is as follows: Where r is the radial coordinate, m; U is the average velocity of the mainstream, m / s; μ is the fluid dynamic viscosity, Pa·s; ρ is the fluid density, kg / m 3 When the flow is a foam annular flow, the velocity of the liquid layer and the foam layer is obtained by integrating the boundary conditions, specifically: U l | r＝R ＝0 A c =A g / (A g +A f ) Where A c is the area ratio coefficient of gas phase and foam phase; U SL,c is the liquid phase apparent velocity; Q L,c is the liquid phase flow rate; Q l , Q f are the liquid layer flow rate and foam layer flow rate, m 3 / h.

6. The method for predicting the characteristics of low-liquid-volume gas-liquid-foam multiphase flow in an inclined tube according to claim 5, characterized in that: In step 4, the classical correlations between the phase-wall friction factor and the phase interface friction factor are improved and modified. The specific method is as follows: Method B1, gas-wall friction factor f g The standard Blasius relationship is used for characterization: Bid g Zρ g U g d g / µ g d g =4A g / (S g +S gf ) Method B2, mixed phase-wall friction factor f m The Deshpand foam flow friction factor is used to characterize and correct it, and its specific form is as follows: d m =4A m / S m Where, Re g is the gas phase Reynolds number; d g is the gas phase hydraulic diameter, m; μ g 、μ m are the dynamic viscosities of the gas phase and the mixed phase, Pa·s; d m is the hydraulic diameter of the mixed phase, m; coefficient C m 、n m and n are constants.

7. The method for predicting characteristics of gas-liquid-foam multiphase flow in an inclined tube with low liquid volume according to claim 6, characterized in that: In step 4, based on the improved correction of the classical correlation of friction factor and the actual flow rate, the shear stress of each phase-wall and phase interface is calculated. The specific method is as follows: When the manifold is foam liquid film and foam stratified flow: τ gf =f gf [ρ g (IN g -IN m )|U g -IN m |] / 2 r m =F ga r g +(1-F ga )r l When the manifold is foam annular flow: τ gf =f gf [ρ g (IN g -IN f )|U g -IN f |] / 2≈f gf [ρ g IN g |In g |] / 2 Where, τ g , τ m are the gas-wall and mixed-phase-wall shear stresses, respectively; U f is the foam phase flow rate, m / s.

8. The method for predicting the characteristics of gas-liquid-foam multiphase flow in an inclined tube with low liquid volume according to claim 7, characterized in that: In step 5, the pressure gradient calculation formula is derived using the interface control equations of the elliptical ring and the circular ring, as follows: When the manifold is foam liquid film and foam stratified flow: Where, dP g / dL is the gas phase pressure gradient, Pa / m; θ is the angle between the pipeline and the horizontal direction, When the manifold is foam annular flow: Where dP / dL is the annular flow pressure gradient, Pa / m.

9. The method for predicting gas-liquid-foam multiphase flow characteristics in an inclined tube with low liquid volume according to claim 8, characterized in that: In step 5, based on the cross-sectional distribution and shear stress calculation results of each phase, combined with the given basic physical properties and pipeline inclination, and according to the flow pattern prediction results, the corresponding pressure gradient solution or iterative calculation is performed as follows: After inputting the fluid physical parameters, pipe diameter, inclination angle and gas-liquid superficial velocity, the foam liquid film and foam stratified flow are directly solved by calculating the phase fraction distribution, gas / mixed phase flow structure parameters and wall friction factor, and substituting them into the control equation to solve the pressure gradient; the foam annular flow requires setting the initial value of the liquid film thickness. By calculating the closed relationship such as the liquid film thickness, the gas / mixed phase flow structure parameters, and the wall friction factor, the pressure gradient is calculated by substituting them into the control equation. After verification by integral operation, if it does not converge, it is re-iterated until the accuracy requirements are met, and finally the pressure gradient and related flow parameters are output synchronously.

10. The method for predicting gas-liquid-foam multiphase flow characteristics in an inclined tube with low liquid volume according to claim 1, characterized in that: The prediction method is used to predict the working condition of an inclined pipeline in a foam drainage operation of a natural gas undulating gathering and transportation pipeline; the inclined pipeline is an upward-inclined pipe section, and a measuring pipe section made of a transparent material is provided at the upward-inclined pipe section, and the measuring pipe section is used for visual observation.

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