Method and device for determining transient state of oil-gas two-phase flow in fluctuating pipeline by considering multiple flow patterns

Abstract

The invention relates to the technical field of multiphase flow mass transfer simulation, and provides a fluctuating pipeline oil-gas two-phase flow transient determination method and device considering multiple flow patterns. The corresponding method comprises the following steps: generating respective momentum equations of the oil phase and the gas phase in the fluctuating pipeline according to respective phase density, volume phase volume fraction, phase velocity, mass exchange rate, acting force between the oil phase and the gas phase and interface relative pressure of the oil phase and the gas phase; according to the respective phase density, the phase velocity and the friction factor of the oil phase and the gas phase, determining the relationship between the inter-phase pressure difference generated by the surface tension in the fluctuating pipeline and the relationship between the stable slug flow and the respective phase friction force of the oil phase and the gas phase; determining a flow pattern type according to the hydraulic parameters of the fluctuating pipeline; and determining the oil-gas two-phase flow transient state of the fluctuating pipeline according to the momentum equation, the inter-phase pressure difference, the relationship and the flow pattern type. According to the oil-gas two-phase flow transient state determined by the method, the dynamic change of the flow process can be better reflected, and the time-varying characteristic and spatial distribution of the oil-gas two-phase flow transient state can be more accurately represented.

Description

Technical Field

[0001] This application relates to the field of multiphase flow mass simulation technology, particularly the field of transient simulation technology of oil and gas multiphase flow, specifically to a method and apparatus for determining transient flow of oil and gas two-phase flow in undulating pipelines that considers multiple flow patterns. Background Technology

[0002] As a critical infrastructure component in oilfield development, multiphase flow pipelines play an indispensable role. Ensuring the safe operation and management of such systems is crucial for maintaining efficient, environmentally friendly, and sustainable resource extraction practices. Transient simulation of flow pattern transitions in undulating pipelines is of paramount importance for ensuring the safety and efficiency of oil and gas transportation systems. In these pipelines, the coexistence of liquid and gas phases under varying terrain conditions generates complex flow patterns (including stratified flow, annular flow, bubbly flow, and slug flow), each exhibiting unique dynamic behavior and interphase interaction mechanisms. These flow patterns are governed by the interaction of gravity, inertia, and viscous forces, and further complicated by transient thermal and pressure effects. Slug flow presents particular challenges due to its intermittent nature; the alternating liquid plugs and bubbles can induce severe flow instabilities and impose significant mechanical loads on pipeline infrastructure. However, establishing a comprehensive transient multiphase flow model remains challenging with current technologies. While commercial software demonstrates reasonable effectiveness in describing transient multiphase flow patterns, its closed-source commercial nature and often incomplete descriptions in the literature hinder other researchers from effectively reproducing its work. Furthermore, due to the inherent conflict between the computational stability requirements of the underlying thermal-hydraulic model upon which transient algorithms rely and the accuracy requirements of empirical correlations, a complete fundamental model and related algorithms for transient multiphase flow patterns have not yet been fully proposed. Therefore, researchers often focus on steady-state flow pattern classification studies or use simplified laminar flow assumptions to handle multiphase flow problems. Such methods are insufficient for simulating multiphase flow in fluctuating pipes.

[0003] Traditional steady-state models widely used in the industry often fail to capture the dynamic changes in flow processes. These models are based on steady-state assumptions and ignore the spatiotemporal variations that are crucial for a comprehensive understanding of flow behavior. Summary of the Invention

[0004] The present application provides a method and apparatus for determining the transient state of two-phase oil and gas flow in undulating pipelines that considers multiple flow patterns, with the aim of solving at least some of the aforementioned technical problems existing in the prior art.

[0005] To achieve the above objectives, firstly, this invention provides a method for determining the transient state of two-phase oil-gas flow in undulating pipelines, considering multiple flow patterns, including: Based on the phase density, volumetric phase content, phase velocity, mass exchange rate of the oil and gas phases, the interaction force between the oil and gas phases, and the relative interfacial pressure, the momentum equations for the oil and gas phases in the undulating pipeline are generated. The relationship between the interphase pressure difference generated by surface tension in the undulating pipe and the phase friction force between the stable slug flow and the respective phase friction force of the oil and gas phases is determined based on the phase density, phase velocity and friction factor of the oil and gas phases. The flow pattern type is determined based on the hydraulic parameters of the undulating pipe. The transient state of the oil-gas two-phase flow in the undulating pipeline is determined based on the momentum equation, the interphase pressure difference, the relationship, and the flow pattern type.

[0006] In some embodiments of this application, the step of generating momentum equations for the oil and gas phases in the fluctuating pipeline based on their respective phase densities, volumetric phase content, phase velocities, mass exchange rates, interactions between the oil and gas phases, and relative interfacial pressures includes: The mass conservation equations for the oil and gas phases are generated based on their respective phase densities, volumetric phase content, phase velocities, and mass exchange rates. The momentum conservation equations for the oil and gas phases are generated based on their respective phase densities, volumetric phase content, phase velocities, the forces between the oil and gas phases, and the relative interfacial pressures. Based on the mass conservation equation and the momentum conservation equation, the momentum equations for the oil and gas phases in the fluctuating pipeline are generated respectively.

[0007] In some embodiments of this application, the relationship between the interphase pressure difference generated by surface tension in the undulating pipeline and the phase friction force between the stable slug flow and the respective phases of the oil and gas phases is determined based on the phase density, phase velocity, and friction factor of the oil and gas phases, including: The wall shear stress and interface shear stress of the oil and gas phases are determined based on their respective phase density, phase velocity and friction factor. The relationship is determined based on the wall shear stress and the interface shear stress. The interphase pressure difference is determined based on the phase density and phase velocity of the oil and gas phases, respectively. In some embodiments of this application, the forces between the oil and gas phases include: the frictional resistance of each of the oil and gas phases, the force generated by mass transfer between the gas and liquid phases caused by phase change, and the interphase pressure induced by surface tension.

[0008] In some embodiments of this application, determining the transient state of the oil-gas two-phase flow in the undulating pipeline based on the momentum equation, the interphase pressure difference, the relationship, and the flow pattern type includes: A one-dimensional two-fluid model of the oil-gas two-phase flow is generated based on the momentum equation, the interphase pressure difference, the relationship, and the flow pattern type. Solve the one-dimensional two-fluid model to determine the transient state of the oil-gas two-phase flow.

[0009] In some embodiments of this application, a method for determining the transient state of two-phase oil-gas flow in undulating pipelines considering multiple flow patterns further includes: The dynamic pressure term of the momentum equation is determined based on the difference between the average phase pressure of the oil and gas phases and the relative interfacial pressure. The steps for determining the difference between the phase average pressure and the interfacial relative pressure include:

[0010] P q For phase average pressure, P qk For relative pressure on the interface, These are empirical parameters. For reference density, For liquid phase velocity, The velocity between the gas and liquid phases.

[0011] Secondly, this application provides a transient determination device for oil and gas two-phase flow in undulating pipelines that considers multiple flow patterns. The device includes: The momentum equation generation module is used to generate the momentum equations for the oil and gas phases in the undulating pipeline based on their respective phase densities, volumetric phase content, phase velocities, mass exchange rates, the forces between the oil and gas phases, and the relative interfacial pressure. The relationship determination module is used to determine the relationship between the interphase pressure difference generated by surface tension in the undulating pipeline and the phase friction force between the stable slug flow and the respective phase friction force of the oil and gas phases based on the phase density, phase velocity and friction factor of the oil and gas phases. A flow pattern type determination module is used to determine the flow pattern type based on the hydraulic parameters of the undulating pipe. The transient determination module is used to determine the transient state of the oil and gas two-phase flow in the undulating pipeline based on the momentum equation, the interphase pressure difference, the relationship, and the flow pattern type.

[0012] In some embodiments of this application, the momentum equation generation module includes: The mass conservation equation generation unit is used to generate the mass conservation equations for the oil and gas phases based on their respective phase densities, volumetric phase content, phase velocities, and mass exchange rates. The momentum conservation equation generation unit is used to generate the momentum conservation equations for the oil and gas phases based on their respective phase densities, volumetric phase content, phase velocities, interactions between the oil and gas phases, and relative interfacial pressures. The momentum equation generation unit is used to generate the respective momentum equations for the oil and gas phases in the fluctuating pipeline based on the mass conservation equation and the momentum conservation equation.

[0013] In some embodiments of this application, the relationship determination module includes: The shear stress determination unit is used to determine the wall shear stress and interface shear stress of the oil and gas phases respectively based on their respective phase density, phase velocity and friction factor. A relationship determination unit is used to determine the relationship based on the wall shear stress and the interface shear stress. The interphase pressure difference determination unit is used to determine the interphase pressure difference based on the phase density and phase velocity of the oil and gas phases.

[0014] In some embodiments of this application, the transient determination module includes: A one-dimensional two-fluid model generation unit is used to generate a one-dimensional two-fluid model of the oil-gas two-phase flow based on the momentum equation, the interphase pressure difference, the relationship, and the flow pattern type. A one-dimensional two-fluid model solving unit is used to solve the one-dimensional two-fluid model and determine the transient state of the oil and gas two-phase flow.

[0015] In some embodiments of this application, a transient determination device for undulating pipeline oil and gas two-phase flow considering multiple flow patterns further includes: The dynamic pressure term determination module is used to determine the dynamic pressure term of the momentum equation based on the difference between the average phase pressure of the oil and gas phases and the relative pressure at the interface. The interphase pressure difference determination unit is executed by the following formula:

[0016] P q For phase average pressure, P qk For relative pressure on the interface, These are empirical parameters. For reference density, For liquid phase velocity, The velocity between the gas and liquid phases.

[0017] Thirdly, this application provides a computer program product, including a computer program / instruction that, when executed by a processor, implements the steps of a transient determination method for fluctuating pipeline oil and gas two-phase flow considering multiple flow patterns.

[0018] Fourthly, this application provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps of a transient determination method for undulating pipeline oil and gas two-phase flow considering multiple flow patterns.

[0019] Fifthly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of a transient determination method for undulating pipeline oil and gas two-phase flow considering multiple flow patterns.

[0020] As described above, this application provides a method and apparatus for determining the transient state of oil-gas two-phase flow in an undulating pipeline, considering multiple flow patterns. The method includes: first, generating momentum equations for each of the oil and gas phases in the undulating pipeline based on their respective phase densities, volumetric phase fill, phase velocities, mass exchange rates, inter-phase forces, and interfacial relative pressures; next, determining the relationship between the interphase pressure difference generated by surface tension and the phase friction forces between the stable slug flow and the oil and gas phases in the undulating pipeline based on their respective phase densities, phase velocities, and friction factors; determining the flow pattern type based on the hydraulic parameters of the undulating pipeline; and finally, determining the transient state of the oil-gas two-phase flow in the undulating pipeline based on the momentum equations, interphase pressure difference, relationships, and flow pattern type.

[0021] The transient state of the oil and gas two-phase flow determined by the method provided in this application can better reflect the dynamic changes of the flow process and more accurately characterize its time-varying properties and spatial distribution. This is more conducive to understanding the flow mechanism, optimizing system design, and improving operational efficiency. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 A flowchart illustrating a transient determination method for oil and gas two-phase flow in undulating pipelines considering multiple flow patterns, provided in this application embodiment. Figure 1 ; Figure 2 This is a schematic diagram of the flow pattern determination process provided in the embodiments of this application; Figure 3 A flowchart illustrating step 100 provided in an embodiment of this application; Figure 4 A flowchart illustrating step 200 provided in an embodiment of this application; Figure 5 A flowchart illustrating a transient determination method for oil and gas two-phase flow in undulating pipelines considering multiple flow patterns, provided in this application embodiment. Figure 2 ; Figure 6 A flowchart illustrating step 400 provided in an embodiment of this application; Figure 7 A schematic diagram illustrating the principle of solving a one-dimensional two-fluid model as provided in the embodiments of this application; Figure 8 A flowchart illustrating a transient determination method for oil and gas two-phase flow in undulating pipelines that considers multiple flow patterns, provided as a specific application example of this application; Figure 9 A schematic diagram of the physical representation of several slug models provided for specific application examples of this application; Figure 10 A schematic diagram of the improved SIMPLE algorithm provided for a specific application example of this application; Figure 11 A topographical diagram of the undulating pipeline L1 provided as a specific application example of this application; Figure 12 A schematic diagram of the pressure output of the undulating pipeline L1 provided as a specific application example of this application; Figure 13 A schematic diagram of the velocity output of the undulating pipe L1 provided as a specific application example of this application; Figure 14 A schematic diagram of the liquid holdup output of the undulating pipeline L1 provided as a specific application example of this application; Figure 15 A schematic diagram of the temperature output of the undulating pipe L1 provided as a specific application example of this application; Figure 16 A schematic diagram illustrating the change in inlet flow velocity for a specific application example of this application; Figure 17 A schematic diagram illustrating the change in inlet liquid holdup rate for a specific application example of this application; Figure 18 A schematic diagram of inlet pressure fluctuation provided for a specific application example of this application; Figure 19 A schematic diagram illustrating the fluctuation of the exit phase velocity for a specific application example of this application; Figure 20 This is a schematic diagram of a transient determination device for oil and gas two-phase flow in an undulating pipeline that considers multiple flow patterns, provided in an embodiment of this application. Figure 21 This is a schematic diagram of the structure of the electronic device in the embodiments of this application. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0025] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0026] It should be noted that the terms "comprising" and "having" and any variations thereof in the specification, claims and accompanying drawings of this application are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such process, method, product or device.

[0027] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0028] Currently, transient simulation of multiphase flow in oil and gas pipelines remains a persistent challenge, as existing models fail to effectively integrate empirical correlations into the transient framework. The core difficulty lies in numerical instability—originating from the discretized Navier-Stokes equations—which amplifies local biases caused by empirical correlations during time stepping, leading to solution divergence. To address the aforementioned issues and at least some of the technical problems described in the background section of this application, see [link to relevant documentation]. Figure 1 In some embodiments of this application, a method for transient determination of oil and gas two-phase flow in undulating pipelines considering multiple flow patterns includes the following: Step 100: Generate the momentum equations for the oil and gas phases in the undulating pipeline based on their respective phase densities, volumetric phase content, phase velocities, mass exchange rates, the interaction forces between the oil and gas phases, and the relative interfacial pressure. Step 200: Determine the relationship between the interphase pressure difference generated by surface tension in the undulating pipeline and the phase friction force between the stable slug flow and the oil and gas phases based on the phase density, phase velocity and friction factor of the oil and gas phases respectively. Step 300: Determine the flow pattern type based on the hydraulic parameters of the undulating pipe; Step 400: Determine the transient state of the oil-gas two-phase flow in the undulating pipeline based on the momentum equation, the interphase pressure difference, the relationship, and the flow pattern type.

[0029] As described above, this application provides a method for determining the transient state of oil-gas two-phase flow in an undulating pipeline considering multiple flow patterns. The method includes: first, generating momentum equations for each of the oil and gas phases in the undulating pipeline based on their respective phase densities, volumetric phase fill, phase velocities, mass exchange rates, inter-phase forces, and interfacial relative pressures; next, determining the relationship between the interphase pressure difference generated by surface tension and the phase friction forces between the steady slug flow and the oil and gas phases based on their respective phase densities, phase velocities, and friction factors; determining the flow pattern type based on the hydraulic parameters of the undulating pipeline; and finally, determining the transient state of the oil-gas two-phase flow in the undulating pipeline based on the momentum equations, interphase pressure difference, relationships, and flow pattern type.

[0030] The transient state of the oil and gas two-phase flow determined by the method provided in this application can better reflect the dynamic changes of the flow process and more accurately characterize its time-varying properties and spatial distribution. This is more conducive to understanding the flow mechanism, optimizing system design, and improving operational efficiency.

[0031] Step 100 can be implemented using a two-fluid model, which captures the fundamental characteristics of multiphase flow in each phase while selectively simplifying flow details to highlight the underlying physical mechanisms. This model is established using cross-sectional average variables that treat both phases as continuous media, deriving a set of governing equations that independently describe the mass, momentum, and energy properties of each phase.

[0032] For step 200, in addition to the governing equations in step 100, appropriate closure relationships are also needed to complete the numerical calculation. This application not only provides the necessary friction parameters and the interphase pressure difference caused by surface tension, but also considers the influence of stable slug flow on friction characteristics.

[0033] For step 300, see Figure 2 This application adopts an improved version of the Barnea flow pattern conversion criterion, which is applicable to the entire pipe inclination condition, and integrates auxiliary techniques such as the N. Petalas method. This comprehensive framework integrates key physical factors including the KH instability threshold, the influence mechanism of pipe inclination on flow pattern conversion, and interface wave height characteristics, thereby achieving robust flow pattern determination. Figure 2The algorithm systematically combines multi-scale physical factors with hierarchical criteria evaluation to ensure accurate identification of various pipe flow patterns, while maintaining computational efficiency under steady-state and transient flow conditions.

[0034] In some embodiments of this application, see Figure 3 Step 100 includes: Step 101: Generate the mass conservation equations for the oil and gas phases based on their respective phase densities, volumetric phase content, phase velocities, and mass exchange rates. This application provides a rigorous system of equations that maintains the independence of the laws of conservation of mass, momentum, and energy for each phase, while explicitly considering interphase transfer mechanisms (including interphase pressure differences). The resulting closed set of governing equations fully characterizes the thermodynamic non-equilibrium states and hydrodynamic interactions between phases.

[0035] Specifically, the mass conservation equation in step 100 is:

[0036] Step 102: Generate the momentum conservation equations for the oil and gas phases based on their respective phase densities, volumetric phase content, phase velocities, interactions between the oil and gas phases, and relative interfacial pressures. Mutually q The momentum conservation equation is stated as follows:

[0037] In equations (1) and (2), q represents the corresponding phase (gas phase or liquid phase). The volumetric phase content, Density, kg / m³ 3 u is the phase velocity. The mass exchange rate is expressed in kg / (m³). 3 ·s), P qk The interfacial relative pressure (Pa) F q This refers to the interaction force between the oil and gas phases (interphase force). The pipe inclination angle is the angle between the pipe and the horizontal direction.

[0038] Step 103: Generate the momentum equations for the oil and gas phases in the fluctuating pipeline based on the mass conservation equation and the momentum conservation equation.

[0039] In equation (2), the interphase forces F q Includes the action on qFrictional resistance on the phase fluid, the force generated by mass transfer between the gas and liquid phases caused by phase change, and the interphase pressure difference induced by surface tension; among them, the interphase pressure difference induced by surface tension can effectively suppress small-scale disturbances below the cutoff wavelength.

[0040]

[0041] In equation (3), P q Indicates the average pressure of the phase. P qk Represents the relative pressure at the interface (Pa); τ qw This indicates the wall shear stress between the phase and the pipe wall. τ k Corresponding to the interfacial shear stress (Pa) between the gas and liquid phases; S k It is the wetting perimeter length (m) of the gas-liquid interface; u qi Defines the velocity (m / s) of the fluid undergoing a phase change before the phase change. Parameters The slug factor represents the proportionate volume fraction of the separated flow within a discrete pipe segment. In transient multiphase flow simulations, temperature variations during the flow process must also be considered; preferably, this application employs a single-temperature model.

[0042] By deriving formulas (1) to (3), the final form of the momentum equation in step 103, namely equation (4), can be obtained.

[0043]

[0044] In some embodiments of this application, see Figure 4 Step 200 includes: Step 201: Determine the wall shear stress and interface shear stress of the oil and gas phases respectively based on their respective phase density, phase velocity and friction factor. For steps 201 to 203, in addition to the basic governing equations, appropriate closure relationships are also required to complete the numerical calculations. Therefore, this application not only provides the necessary friction parameters and the interphase pressure difference caused by surface tension, but also considers the influence of stable slug flow on frictional characteristics.

[0045] Specifically, regarding step 201, the wall shear stress and interfacial shear stress Through Fanning friction factor f To express.

[0046]

[0047] In this application, the subscripts of the parameters have the following meanings: g represents the gas phase, l represents the liquid phase, and K represents the gas-liquid phase transition.

[0048] Step 202: Determine the relationship based on the wall shear stress and the interface shear stress; Step 203: Determine the interphase pressure difference based on the phase density and phase velocity of the oil and gas phases.

[0049] In some embodiments of this application, the forces between the oil and gas phases include: the frictional resistance of each of the oil and gas phases, the force generated by mass transfer between the gas and liquid phases caused by phase change, and the interphase pressure induced by surface tension.

[0050] In some embodiments of this application, see Figure 5 A method for determining the transient state of two-phase oil-gas flow in undulating pipelines, considering multiple flow patterns, further includes: Step 500: Determine the dynamic pressure term of the momentum equation based on the difference between the average phase pressure of the oil and gas phases and the relative interfacial pressure. In the source term of the momentum equation (3), this application models the pressure difference between the average phase pressure and its interfacial pressure as a dynamic pressure term, the expression of which is:

[0051] In the formula, P q For phase average pressure, P qk For relative pressure on the interface, These are empirical parameters. For reference density, For liquid phase velocity, The velocity of the gas-liquid phase is the velocity of the wave at the interface, as shown in equation (8).

[0052]

[0053] In the formula, Where S is the Reynolds number, ST is the surface tension coefficient, and S is the surface tension coefficient. g Let m be the wetted perimeter of the gas phase.

[0054] The interfacial pressure term in the momentum equation characterizes the capillary pressure discontinuity on both sides of the gas-liquid interface, governed by the Young-Laplace equation:

[0055] In some embodiments of this application, see Figure 6 Step 400 includes: Step 401: Generate a one-dimensional two-fluid model of the oil-gas two-phase flow based on the momentum equation, the interphase pressure difference, the relationship, and the flow pattern type; Step 402: Solve the one-dimensional two-fluid model to determine the transient state of the oil-gas two-phase flow.

[0056] Regarding step 402, this application employs the finite volume method to numerically solve the one-dimensional two-fluid model. This method integrates the transport equations over a discrete control volume to form algebraic equations and uses an interleaved grid system: scalar variables (including pressure, temperature, volume fraction, and density) are stored at the center of the fully indexed grid (…). i , i ± 1), while vector variables (such as velocity) are stored in a semi-indexed grid interface ( i ± 1 / 2). For example... Figure 7 As shown, this design can effectively suppress pressure field oscillations and prevent pressure-velocity decoupling.

[0057] Other physical properties, such as viscosity, heat capacity, and surface tension, are also defined at the center of the grid. If a specific variable is needed at a given location but is not explicitly stored, a first-order upwind interpolation scheme will be used for calculation. However, for thermophysical properties that require lookup from a property table, a central difference scheme will be used for calculation.

[0058] To further illustrate this solution, this application also provides a specific implementation of a method for determining the transient state of two-phase oil-gas flow in undulating pipelines that considers multiple flow patterns. See [link to implementation details]. Figure 8 Specifically, it includes the following:

[0059] S1: Establish the governing equations to characterize the thermodynamic non-equilibrium state and hydrodynamic interaction between phases.

[0060] The specific establishment process is as described in formulas (1) to (4).

[0061] S2: Establish a closed relationship to perform numerical calculations on the governing equations.

[0062] The specific establishment process is as described in formulas (5) to (9).

[0063] S3: Determine the flow pattern type based on the hydraulic parameters of the undulating pipe.

[0064] See Figure 2 Preliminary manifold characterization involves a multi-formula system containing numerous empirical equations. The flowchart for basic manifold identification is shown below. Figure 2 As shown. The prediction criteria include complex non-binary decision parameters (rather than simple yes / no conditions). This application has specifically developed an additional flow pattern identification criterion for fluctuating pipeline conditions.

[0065] For pipe sections with an absolute inclination angle of less than 15°, an additional evaluation criterion using apparent gas velocity as a secondary discrimination parameter is introduced. When inequality (10) is satisfied, a secondary judgment is made on the initially identified stratified flow: excessively high gas velocities will trigger reclassification into slug flow due to interfacial instability, while subcritical gas velocities will maintain the stratified flow judgment. This refinement is specifically designed for flow pattern conversion conditions in near-horizontal pipe configurations (when gravity and interfacial shear forces are close to equilibrium).

[0066]

[0067] For pipe sections with an absolute inclination angle exceeding 60°, there is a tendency to misclassify slug flow as stratified flow. To correct this problem, a dimensionless parameter is introduced. L vs and N vg The stratified flow in the steeply inclined pipe is re-evaluated. When inequality (12) is satisfied and the absolute inclination angle exceeds 60°, the flow pattern is reclassified as slug flow; otherwise, the original stratified flow determination is maintained. Similarly, for the downsloping pipe with an inclination angle exceeding 60°, if equation (12) is satisfied, the initially determined annular flow will be reclassified as slug flow; if the condition is not satisfied, the annular flow determination is retained. The volumetric flow rates of the liquid phase and the gas phase are denoted as follows: Q l and Q g .

[0068]

[0069] For pipe sections with an inclination angle below -60° or above 30°, if the initially determined annular flow simultaneously satisfies inequality (12), it is reclassified as slug flow; otherwise, the annular flow determination is maintained. This conditional conversion criterion takes into account the dominant role of gravity on phase distribution in pipe configurations with large inclination angles (where gravity significantly affects phase distribution).

[0070] Next, the governing equations for the dispersed flow model are established. Specifically, this application introduces a multi-flow-type analysis method by considering the influence of separated flows on the discretized Navier-Stokes equations. To prevent violations of conservation principles, this method strictly adheres to the basic momentum equation and continuity equation in transient simulations while selectively applying steady-state empirical slug flow correlations, used only to determine key parameters, including the slug element length. L Gas velocity in the liquid film region v gf Bubble velocity in the slug zone v g and liquid holdup in the blockage area H .

[0071] like Figure 9 As shown, multiple slug elements may exist within a single spatial step. Δx A dispersed flow region forms within the liquid film region, while a sufficiently stable separated flow region may also exist. Furthermore, the figure also depicts the phase retention rate of the liquid film region. H lf , H gf ) and speed ( v lf , v gf ), and the stalemate rate of the dispersed flow region ( H ls , H gs ) and speed ( v ls , v gs ).

[0072] We assume that all slug elements have identical hydrodynamic properties. Under sufficiently short time discretization conditions, the nucleation and subsequent migration of bubbles within each liquid film region exhibit uniform periodicity. Furthermore, the model is constrained by the assumption that bubbles in the liquid film region undergo only one migration event per time step. The feature length is... Δx The pipe section is partially occupied by slug units, and the model considers the void region. These basic assumptions lead to the following equations:

[0073] In equation (15), Ω represents the slug frequency. Based on the slug flow parameters calculated above, the frictional forces acting on the two phases within each slug unit can be determined.

[0074]

[0075] The frictional forces between the gas phase, liquid phase, and pipe wall within a single-stage plug unit, as well as the interfacial frictional forces, can be calculated using equation (18). The frictional resistance parameters of the liquid film region... τ gf and τ lf See equation (19).

[0076]

[0077] v ls The value of can be calculated using equation (20).

[0078]

[0079] The interface parameters in equation (18) are given by equation (21).

[0080]

[0081] In equation (21), β Representative by Figure 9 The central angle formed by the gas-liquid interface and the center point of the pipe is shown. It can be deduced that for each slug element, the following force balance relationship exists:

[0082] Furthermore, for equation (22), the following numerical relationship exists:

[0083] The meanings of the parameters in the above formula are shown in Table 1.

[0084] Table 1

[0085] S4: Solve the one-dimensional two-fluid model to determine the transient state of the oil and gas two-phase flow.

[0086] See Figure 10 This application provides an improved SIMPLE algorithm within the current framework, specifically designed for multiphase flow pattern analysis. The computation process begins with a comprehensive flow pattern characterization workflow: the system sequentially evaluates two key hydrodynamic parameters—the length of the slug flow element. L and liquid phase content H ls These parameters serve as the core criteria for distinguishing between stratified and dispersed flows. Given... L and H ls The algorithm employs empirical characteristics of correlation to perform rigorous validity checks to eliminate numerical artifacts and explicitly excludes... L Exceeding the feature mesh size ( L s > Δx )or H ls Non-physical solutions with values ​​below the 0.8 threshold are excluded. Furthermore, the method employs a minimum slip criterion for verification, thereby ensuring the numerical stability and physical consistency of the manifold identification process.

[0087] For dispersed flows confirmed by this diagnosis, the algorithm employs a modified momentum conservation equation to account for interphase interactions. The core SIMPLE process is then executed: through an iterative pressure-velocity correction loop (with a convergence threshold set to | p' / p | max ≤10 ³) Solve for the corrected pressure field, velocity field, and density field, where p qk = p qk + p qk , u q = u q + u q ', ρ q = ρ q + ρ q ' After the pressure field converges, the algorithm continues to calculate the temperature at the next time step (t = t + Δt). T and volume fraction of each phase α q .

[0088] The simulation progresses through time-step updates of dynamic parameters, with physical properties continuously refreshed through interpolation from pre-calculated thermodynamic data tables—a crucial characteristic for maintaining compositional invariance when dealing with multiphase flow systems. Notably, this implementation integrates a bidirectional coupling between the flow pattern module and the core solver: the velocity field... u q Parameters related to flow patterns F q All updates are based on the identified flow pattern. This framework supports the simultaneous calculation of thermodynamic properties such as viscosity and surface tension with flow pattern transitions, and the calculation terminates upon reaching a preset termination time. By integrating flow pattern-specific momentum equations with the standard SIMPLE framework, this method provides a robust solution for capturing complex multiphase flow dynamics while maintaining computational efficiency (based on tabulated attribute updates).

[0089] Simulation Results: In the simulation of undulating multiphase flow pipelines, two types of boundary conditions typically exist: Constant Boundary Conditions (CBC) and Virtual Boundary Conditions (VBC). Under CBC conditions, both the inlet mass flow rate and outlet pressure remain constant over time; conversely, when either parameter exhibits time-varying characteristics, it is classified as VBC. To evaluate the computational performance of this work during flow pattern transitions, the simulation focuses on analyzing the changes in hydraulic parameters at the accumulation point and topographic peak point under VBC conditions.

[0090] This undulating pipe (L1) multiphase flow case study has a total length of 12.225 km, a maximum elevation change of 50 m, and includes multiple upward and downward sloping sections. The pipe's inner diameter is 259 mm, and the wall roughness is 8 × 10⁻⁶. m, thermal conductivity of the pipe wall For more detailed parameters, please refer to Table 2. The terrain of pipeline L1 is as follows: Figure 11 As shown.

[0091] Table 2 Field data and input boundary conditions for pipeline L1

[0092] The fluid composition used in this application is shown in Table 3. The basic thermodynamic properties were calculated using the PR equation of state. The model used in this application for calculating basic properties using the PR equation has been verified to fully meet the requirements of transient simulation. The composition data shown in Table 3 indicate that the fluid system used in this application is mainly composed of heavy oil and exhibits a significantly high liquid holdup.

[0093] Table 3 Fluid composition

[0094] CBC Case Study: For pipeline L1, the inlet mass flow rate is 22.266 kg / s, the outlet pressure is 8.8 MPa, the inlet fluid temperature is 329.15 K, and the ambient temperature is 288.15 K. This case study uses the method described in this application and OLGA software for simulation, and the simulation results are compared and analyzed. Figures 12 to 15 As shown, the calculation results of this application and OLGA are in high agreement on key hydraulic parameters, including pressure, gas-liquid mixing velocity, and liquid volume fraction, with deviations remaining within an acceptable range of 5%. However, the liquid volume fraction predicted in this application is slightly higher than that of OLGA. This slight difference may stem from OLGA's consideration of the droplet phase in its momentum equation, enabling it to achieve the required pressure drop with a lower liquid volumetric flow rate. However, for high liquid holdup conditions, the impact of the droplet phase on the calculation is negligible.

[0095] VBC Case Study: To further evaluate the robustness and transient performance of the model, this application introduces a continuous flow rate fluctuation at the inlet, with an amplitude of 30 kg / s, occurring every 100 seconds, starting at 5700 seconds. The change in the two-phase fluid velocity at the inlet is as follows: Figure 16 as well as Figure 17 As shown.

[0096] Obviously, Figure 16 as well as Figure 17This indicates that the adjusted inlet liquid flow rate values ​​show almost no error between OLGA and this application. However, there is a numerical deviation of approximately 10% for the gas flow rate. This difference may stem from the different thermophysical property models used in the two calculation methods. Regarding the fluctuation in inlet phase holdup, the maximum deviation occurs at 6600 seconds. At this point, the calculated HOL value in this application is 0.49, while the value obtained from OLGA is 0.52, a difference of less than 0.02. For multiphase flow engineering applications, this magnitude of deviation is negligible.

[0097] This numerical simulation employs constant inlet flow rate and constant outlet pressure as boundary conditions. Therefore, studying the pressure fluctuations at the inlet and the flow rate changes at the outlet will provide valuable insights for evaluating the model's behavior. Figure 18 As shown, the peak inlet pressure of the two models is almost the same, but there is a slight deviation in the valley region. Figure 17 The results show that the HOL in this application is located at a low valley position, resulting in a reduced contribution of liquid phase pressure to the pressure equation derived from the continuity equation. However, quantitative analysis shows that the maximum deviation occurs at 6636 seconds, with an absolute difference of 0.13 MPa and a corresponding relative deviation of only 5%, which is negligible for engineering calculations.

[0098] Figure 19 The study reveals a significant difference in phase velocity fluctuations at the outlet between the two models, primarily attributed to the impact of algorithmic differences on wave propagation characteristics. Despite the different transient behaviors, both models converge to highly similar steady-state values. Specifically, the liquid phase velocities are almost identical, while the gas phase velocities exhibit minor differences due to the use of different empirical correlations in the phase separation modeling. However, the maximum deviation of the steady-state values ​​observed after 12,000 seconds is only 1.07 m / s, a negligible deviation from an engineering calculation perspective.

[0099] also, Figure 19 This demonstrates that the numerical model provided in this application can achieve computational stability more quickly. This characteristic, combined with its excellent transient behavior characterization ability, indicates that the proposed model is particularly suitable for engineering analyses requiring robust and stable numerical performance. From an industrial application perspective, these results confirm that the accuracy provided in this application is sufficient to meet practical engineering requirements.

[0100] As described above, in order to address the ongoing challenge of transient simulation of multi-flow-mode flows in undulating pipes, the method proposed in this application has the following beneficial effects: First, it integrates the interface pressure difference term to enhance the calculation accuracy of transient flows in undulating pipes; second, it couples the SIMPLE algorithm to handle multi-flow-mode flows; and finally, it establishes a basic multiphase flow model that integrates drift-flux theory and the SIMPLE method, effectively overcoming the long-standing limitations of applying empirical correlations to transient modeling.

[0101] The method proposed in this application achieves engineering-acceptable accuracy across the entire flow domain of undulating pipelines. Key parameters such as pressure, liquid holdup, and velocity typically exhibit deviations of less than 5-10% at topographic peaks and low points, and often remain below 3% under equilibrium conditions. The model demonstrates robustness in handling transient flow conditions caused by complex topographic changes, and converges faster during elevation transitions compared to commercial benchmarks. Minor deviations arise from differences in numerical format and thermodynamic modeling compared to existing commercial tools, particularly concerning undisclosed discretization methods for inclined pipe sections in commercial software. However, the model maintains reliable predictive power, with maximum pressure deviations below 9.8% at severe low points and liquid holdup errors below 3% across all elevation changes. These performance metrics meet industrial requirements for undulating pipeline systems.

[0102] Based on the same inventive concept, this application also provides a transient determination device for undulating pipeline oil-gas two-phase flow considering multiple flow patterns, which can be used to implement the method described in the above embodiments, as shown in the following embodiments. Since the principle of solving the problem in the transient determination device for undulating pipeline oil-gas two-phase flow considering multiple flow patterns is similar to that of the transient determination method for undulating pipeline oil-gas two-phase flow considering multiple flow patterns, the implementation of the transient determination device for undulating pipeline oil-gas two-phase flow considering multiple flow patterns can refer to the implementation of the transient determination method for undulating pipeline oil-gas two-phase flow considering multiple flow patterns, and repeated details will not be elaborated further. As used below, the terms "unit" or "module" can refer to a combination of software and / or hardware that performs a predetermined function. Although the system described in the following embodiments is preferably implemented in software, hardware implementation, or a combination of software and hardware, is also possible and contemplated.

[0103] This application provides a specific implementation of a device for determining the transient state of oil-gas two-phase flow in undulating pipelines that considers multiple flow patterns, capable of realizing a method for determining the transient state of oil-gas two-phase flow in undulating pipelines considering multiple flow patterns. See [link to relevant documentation]. Figure 20 A transient determination device for oil and gas two-phase flow in undulating pipelines that considers multiple flow patterns specifically includes the following components: The momentum equation generation module 10 is used to generate the momentum equations of the oil and gas phases in the undulating pipeline based on the phase density, volumetric phase content, phase velocity, mass exchange rate, interaction force between the oil and gas phases, and relative interfacial pressure of each phase. The relationship determination module 20 is used to determine the relationship between the interphase pressure difference generated by surface tension in the undulating pipeline and the phase friction force between the stable slug flow and the respective phase friction force of the oil and gas phases based on the phase density, phase velocity and friction factor of the oil and gas phases. The flow pattern type determination module 30 is used to determine the flow pattern type based on the hydraulic parameters of the undulating pipe. The transient determination module 40 is used to determine the transient state of the oil and gas two-phase flow in the undulating pipeline based on the momentum equation, the interphase pressure difference, the relationship, and the flow pattern type.

[0104] This application also provides a specific implementation of an electronic device capable of implementing all steps in the transient determination method for undulating pipeline oil and gas two-phase flow considering multiple flow patterns in the above embodiments. See [link to implementation details]. Figure 21 The electronic devices specifically include the following: Processor 1201, memory 1202, communications interface 1203, and bus 1204; The processor 1201, memory 1202, and communication interface 1203 communicate with each other via bus 1204; the communication interface 1203 is used to realize information transmission between server-side devices, power measurement devices, and user-side devices.

[0105] The processor 1201 is used to call the computer program in the memory 1202. When the processor executes the computer program, it implements all the steps in the transient determination method for fluctuating pipeline oil and gas two-phase flow considering multiple flow patterns in the above embodiment. For example, when the processor executes the computer program, it implements the following steps: Based on the phase density, volumetric phase content, phase velocity, mass exchange rate of the oil and gas phases, the interaction force between the oil and gas phases, and the relative interfacial pressure, the momentum equations for the oil and gas phases in the undulating pipeline are generated. The relationship between the interphase pressure difference generated by surface tension in the undulating pipe and the phase friction force between the stable slug flow and the respective phase friction force of the oil and gas phases is determined based on the phase density, phase velocity and friction factor of the oil and gas phases. The flow pattern type is determined based on the hydraulic parameters of the undulating pipe. The transient state of the oil-gas two-phase flow in the undulating pipeline is determined based on the momentum equation, the interphase pressure difference, the relationship, and the flow pattern type.

[0106] Embodiments of this application also provide a computer-readable storage medium capable of implementing all steps of the transient determination method for undulating pipeline oil-gas two-phase flow considering multiple flow patterns in the above embodiments. The computer-readable storage medium stores a computer program that, when executed by a processor, implements all steps of the transient determination method for undulating pipeline oil-gas two-phase flow considering multiple flow patterns in the above embodiments. For example, when the processor executes the computer program, it implements the following steps: Based on the phase density, volumetric phase content, phase velocity, mass exchange rate of the oil and gas phases, the interaction force between the oil and gas phases, and the relative interfacial pressure, the momentum equations for the oil and gas phases in the undulating pipeline are generated. The relationship between the interphase pressure difference generated by surface tension in the undulating pipe and the phase friction force between the stable slug flow and the respective phase friction force of the oil and gas phases is determined based on the phase density, phase velocity and friction factor of the oil and gas phases. The flow pattern type is determined based on the hydraulic parameters of the undulating pipe. The transient state of the oil-gas two-phase flow in the undulating pipeline is determined based on the momentum equation, the interphase pressure difference, the relationship, and the flow pattern type.

[0107] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on its differences from other embodiments. In particular, hardware + program embodiments are relatively simple in description because they are fundamentally similar to method embodiments; relevant parts can be referred to the descriptions in the method embodiments.

[0108] The foregoing has described specific embodiments of this specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired result. In some embodiments, multitasking and parallel processing are possible or may be advantageous.

[0109] While this application provides method operation steps as shown in the embodiments or flowcharts, more or fewer operation steps may be included based on conventional or non-inventive labor. The order of steps listed in the embodiments is merely one possible execution order among many and does not represent the only execution order. In actual device or client product execution, the method can be executed in the order shown in the embodiments or drawings or in parallel (e.g., in a parallel processor or multi-threaded processing environment).

[0110] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0111] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0112] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0113] This application uses specific embodiments to illustrate the principles and implementation methods of this application. The description of the above embodiments is only for the purpose of helping to understand the method and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for transient determination of two-phase oil-gas flow in undulating pipelines considering multiple flow patterns, characterized in that, include: Based on the phase density, volumetric phase content, phase velocity, mass exchange rate of the oil and gas phases, the interaction force between the oil and gas phases, and the relative interfacial pressure, the momentum equations for the oil and gas phases in the undulating pipeline are generated. The relationship between the interphase pressure difference generated by surface tension in the undulating pipe and the phase friction force between the stable slug flow and the respective phase friction force of the oil and gas phases is determined based on the phase density, phase velocity and friction factor of the oil and gas phases. The flow pattern type is determined based on the hydraulic parameters of the undulating pipe. The transient state of the oil-gas two-phase flow in the undulating pipeline is determined based on the momentum equation, the interphase pressure difference, the relationship, and the flow pattern type.

2. The method for determining the transient state of two-phase oil-gas flow in undulating pipelines according to claim 1, characterized in that, The process of generating momentum equations for the oil and gas phases in the fluctuating pipeline based on their respective phase densities, volumetric phase content, phase velocities, mass exchange rates, the forces between the oil and gas phases, and the relative interfacial pressure includes: The mass conservation equations for the oil and gas phases are generated based on their respective phase densities, volumetric phase content, phase velocities, and mass exchange rates. The momentum conservation equations for the oil and gas phases are generated based on their respective phase densities, volumetric phase content, phase velocities, the forces between the oil and gas phases, and the relative interfacial pressures. Based on the mass conservation equation and the momentum conservation equation, the momentum equations for the oil and gas phases in the fluctuating pipeline are generated respectively.

3. The transient determination method for two-phase flow of oil and gas in undulating pipelines according to claim 1, characterized in that, The relationship between the interphase pressure difference generated by surface tension in the undulating pipeline and the phase friction force between the stable slug flow and the respective phases of the oil and gas phases is determined based on the phase density, phase velocity, and friction factor of the oil and gas phases, including: The wall shear stress and interface shear stress of the oil and gas phases are determined based on their respective phase density, phase velocity and friction factor. The relationship is determined based on the wall shear stress and the interface shear stress. The interphase pressure difference is determined based on the phase density and phase velocity of the oil and gas phases.

4. The method for determining the transient state of two-phase oil-gas flow in undulating pipelines according to claim 1, characterized in that, The forces between the oil and gas phases include: the frictional resistance of each phase, the force generated by mass transfer between the gas and liquid phases due to phase change, and the interphase pressure induced by surface tension.

5. The method for determining the transient state of two-phase flow in undulating pipelines according to claim 1, characterized in that, Determining the transient state of the oil-gas two-phase flow in the undulating pipeline based on the momentum equation, the interphase pressure difference, the relationship, and the flow pattern type includes: A one-dimensional two-fluid model of the oil-gas two-phase flow is generated based on the momentum equation, the interphase pressure difference, the relationship, and the flow pattern type. Solve the one-dimensional two-fluid model to determine the transient state of the oil-gas two-phase flow.

6. The method for determining transient two-phase flow of oil and gas in undulating pipelines according to any one of claims 1 to 5, characterized in that, Also includes: The dynamic pressure term of the momentum equation is determined based on the difference between the average phase pressure of the oil and gas phases and the relative interfacial pressure. Determining the interphase pressure difference based on the respective phase densities and phase velocities of the oil and gas phases includes: P q For phase average pressure, P qk For relative pressure on the interface, These are empirical parameters. For reference density, For liquid phase velocity, The velocity between the gas and liquid phases.

7. A device for determining the transient state of two-phase oil-gas flow in undulating pipelines considering multiple flow patterns, characterized in that, include: The momentum equation generation module is used to generate the momentum equations for the oil and gas phases in the undulating pipeline based on their respective phase densities, volumetric phase content, phase velocities, mass exchange rates, the forces between the oil and gas phases, and the relative interfacial pressure. The relationship determination module is used to determine the relationship between the interphase pressure difference generated by surface tension in the undulating pipeline and the phase friction force between the stable slug flow and the respective phase friction force of the oil and gas phases, based on the phase density, phase velocity and friction factor of the oil and gas phases. A flow pattern type determination module is used to determine the flow pattern type based on the hydraulic parameters of the undulating pipe. The transient determination module is used to determine the transient state of the oil and gas two-phase flow in the undulating pipeline based on the momentum equation, the interphase pressure difference, the relationship, and the flow pattern type.

8. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instruction is executed by the processor, it implements the steps of the transient determination method for fluctuating pipeline oil and gas two-phase flow considering multiple flow patterns as described in any one of claims 1 to 6.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the transient determination method for undulating pipeline oil and gas two-phase flow considering multiple flow patterns as described in any one of claims 1 to 6.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the steps of the transient determination method for undulating pipeline oil and gas two-phase flow considering multiple flow patterns as described in any one of claims 1 to 6.

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