Method and device for determining unsteady model for commissioning of pipeline in permafrost zone

Abstract

The embodiment of the application provides a method and device for determining a non-steady-state model of pipeline commissioning in a frozen soil area. The method comprises: obtaining a BN model of a multi-medium fluid, the BN model comprising a plurality of relaxation processes, the plurality of relaxation processes comprising at least a chemical potential relaxation process, a velocity relaxation process, a pressure relaxation process, a temperature relaxation process and an energy relaxation process; obtaining a multiphase flow control body for multiphase frozen soil area pipeline flow; determining a control equation for the multiphase frozen soil area pipeline flow based on the control body parameters of the multiphase flow control body, the multiphase flow control body and the BN model; and determining a non-steady-state model of frozen soil area pipeline commissioning based on the control equation in the case that the time step and the space step of the multiphase flow control body meet a first preset condition and the velocity relaxation process meets a second preset condition. The application introduces the BN model, introduces a corresponding term corresponding to heat exchange on the basis of the BN model, thereby effectively improving the accuracy of pipeline area pressure calculation.

Description

Technical Field

[0001] This application relates to the field of pipeline transportation technology, specifically to a method, apparatus, system, and storage medium for determining an unsteady-state model for pipeline commissioning in permafrost regions. Background Technology

[0002] Permafrost regions are widely distributed in my country, containing abundant oil and natural gas resources. Due to their advantages such as low cost, large capacity, small land occupation, and short construction period, laying buried pipelines in permafrost regions is currently and will remain the primary route for transporting oil and gas resources. Buried oil pipelines in permafrost regions are generally put into operation using a water-water combined transport method, a process involving a gas-liquid two-phase unsteady flow. The complex environment of buried pipelines, coupled with the low temperatures of the permafrost region and significant elevation differences, further complicates their commissioning.

[0003] Currently, the most widely used model for unsteady gas-liquid two-phase flow in pipelines is the Wiggert model. This model is designed for gas cavitation in pipelines, neglects gas momentum, employs isothermal assumptions, and does not include energy equations. Therefore, it cannot simulate the heat exchange between the fluid inside the pipeline and the surrounding frozen soil. Discrete vapor model (DVCM) and discrete cavitation model (DGCM) are relatively simple and can be directly combined with the traditional method of characteristics (MOC). However, the pressure calculation error is large in the cavitation region, and for long-distance oil pipelines, the accumulation of errors can lead to a large deviation in the final calculation. In addition, there is a numerical model in the literature that combines the DGCM model with the shock wave capture method, which can significantly improve the accuracy and stability of numerical calculations. All of these models employ isothermal assumptions, and therefore are not applicable to the thermodynamic coupling problem between frozen soil and the two-phase flow inside the pipeline. Summary of the Invention

[0004] The purpose of this application is to provide a method, apparatus, system, and storage medium for determining the unsteady-state model for pipeline commissioning in permafrost areas, in order to solve the technical defect in the prior art where the two-phase flow model does not consider the heat exchange phenomenon inside and outside the pipeline, resulting in a large deviation in the pressure calculation of the pipeline area.

[0005] To achieve the above objectives, the first aspect of this application provides a method for determining an unsteady-state model for pipeline commissioning in permafrost regions, the method comprising:

[0006] Obtain a BN model for multi-medium fluids. The BN model includes multiple relaxation processes, which include at least chemical potential relaxation, velocity relaxation, pressure relaxation, temperature relaxation, and energy relaxation.

[0007] Obtain a multiphase flow control volume for pipeline flow in multiphase frozen soil regions;

[0008] Based on the control volume parameters of the multiphase flow control volume, the multiphase flow control volume, and the BN model, the control equations for pipeline flow in multiphase frozen soil regions are determined.

[0009] Under the condition that the time step and spatial step of the multiphase flow control volume meet the first preset condition and the velocity relaxation process meets the second preset condition, the unsteady-state model for pipeline commissioning in the frozen soil area is determined based on the control equation.

[0010] In the embodiments of this application, the BN model is as shown in formula (1):

[0011]

[0012]

[0013]

[0014]

[0015] In the BN model, from top to bottom, the equations are the mass balance equation, momentum balance equation, energy balance equation, and volume fraction evolution equation for medium k. k ,ρ k ,u k ,p k , E k qk represent volume fraction, density, velocity, pressure, viscous stress tensor, total energy, and heat flux, respectively.

[0016] In the embodiments of this application, multiple relaxation processes are as shown in formula (2):

[0017]

[0018]

[0019]

[0020]

[0021]

[0022] From top to bottom, these are the chemical potential relaxation process, velocity relaxation process, pressure relaxation process, temperature relaxation process, and energy relaxation process, v kl , η kl , These represent the corresponding relaxation rates.

[0023] In the embodiments of this application, determining the control equations for pipeline flow in multiphase frozen soil regions based on the control volume parameters of the multiphase flow control volume, the multiphase flow control volume, and the BN model includes: integrating the BN model over the control volume using a preset method to determine the control equations for pipeline flow in multiphase frozen soil regions based on the control volume parameters and the BN model.

[0024] In the embodiments of this application, the governing equation is determined according to formula (3):

[0025]

[0026] Where U is a conserved variable, H(U) is the interaction between phases at each system surface of the control volume, and C i (t) represents the volume of the control volume, and v represents the movement speed of the control volume interface.

[0027] In the embodiments of this application, the unsteady-state model is determined according to formula (4):

[0028]

[0029]

[0030]

[0031]

[0032] Where ρ is the density of the mixture, p is the pressure of the mixture, and πdτ w,k To control the wall friction of the body, To control the elastic deformation of the pipe, α k πdK(T0-T) represents the heat exchange between the control volume and the soil, where A is the cross-sectional area of ​​the control volume pipe, g is the gravitational acceleration, d is the inner diameter of the control volume pipe, and K is the overall heat transfer coefficient of the control volume.

[0033] In the embodiments of this application, the governing equations satisfy volume conservation and area conservation, which are determined according to formulas (5) and (6), respectively:

[0034]

[0035]

[0036] Where U is a conserved variable, H(U) is the interaction between phases at each system surface of the control volume, and C i (t) represents the volume of the control volume, and v represents the movement speed of the control volume interface.

[0037] A second aspect of this application provides an apparatus for determining an unsteady-state model, comprising:

[0038] The memory is configured to store instructions; and

[0039] The processor is configured to retrieve the instructions from the memory and, when executing the instructions, to implement the method for determining a non-steady-state model for pipeline commissioning in permafrost regions according to any of the preceding embodiments.

[0040] A third aspect of this application provides a system for determining a nonsteady-state model, including the apparatus described above for determining a nonsteady-state model.

[0041] A fourth aspect of this application provides a machine-readable storage medium storing instructions that, when executed by a processor, configure the processor to perform the aforementioned method for determining an unsteady-state model for pipeline commissioning in permafrost regions.

[0042] The above technical solution proposes a method for determining the unsteady-state model for pipeline commissioning in permafrost regions. This method includes obtaining a multi-medium fluid BN model, which comprises multiple relaxation processes, including at least chemical potential relaxation, velocity relaxation, pressure relaxation, temperature relaxation, and energy relaxation. It also involves obtaining a multiphase flow control volume for pipeline flow in multiphase permafrost regions; determining the control equations for pipeline flow in multiphase permafrost regions based on the control volume parameters, the multiphase flow control volume, and the BN model; and determining the unsteady-state model for pipeline commissioning in permafrost regions based on the control equations, provided that the time and space steps of the multiphase flow control volume meet a first preset condition and the velocity relaxation process meets a second preset condition. This technical solution considers the heat exchange between the pipeline and the external environment during actual production. By introducing an interaction BN model that can simulate pressure waves, and by introducing terms corresponding to heat exchange on the BN model, the accuracy of pressure calculations in the pipeline area is effectively improved.

[0043] Other features and advantages of the embodiments of this application will be described in detail in the following detailed description section. Attached Figure Description

[0044] The accompanying drawings are provided to further illustrate the embodiments of this application and form part of the specification. They are used together with the following detailed description to explain the embodiments of this application, but do not constitute a limitation on the embodiments of this application. In the drawings:

[0045] Figure 1 The illustration shows a flowchart of a method for determining an unsteady-state model for pipeline commissioning in permafrost regions according to an embodiment of this application.

[0046] Figure 2 This schematic diagram illustrates a control body for single-phase and multiphase flow according to an embodiment of this application;

[0047] Figure 3 The diagram illustrates the internal structure of a computer device according to an embodiment of this application. Detailed Implementation

[0048] 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. It should be understood that the specific embodiments described herein are only for illustration and explanation of the embodiments of this application and are not intended to limit the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0049] It should be noted that if the embodiments of this application involve directional indicators (such as up, down, left, right, front, back, etc.), the directional indicators are only used to explain the relative positional relationship and movement of the components in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indicators will also change accordingly.

[0050] Furthermore, if the embodiments of this application involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. If the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed in this application.

[0051] Figure 1 The illustration schematically shows a flowchart of a method for determining a non-steady-state model for pipeline commissioning in permafrost regions, according to an embodiment of this application. Figure 1 As shown in the embodiment of this application, a method for determining the unsteady-state model for pipeline commissioning in frozen soil areas is provided. The method may include the following steps.

[0052] Step 101: Obtain the BN model of the multi-medium fluid. The BN model includes multiple relaxation processes, which include at least chemical potential relaxation process, velocity relaxation process, pressure relaxation process, temperature relaxation process and energy relaxation process.

[0053] In this application's embodiments, the BN model refers to the Baer-Nuziato model. It should be noted that before constructing the model, this application thoroughly investigated various multiphase transient flow models describing pipelines, including the DVCM model, DGCM model, Wiggert model, and other similar models. These models are mostly based on strong assumptions, such as the single-temperature assumption (i.e., the temperature between all phases remains the same), the single-velocity assumption, and the concentration of gas phase volume at grid points. Furthermore, most of these models neglect the energy equation, which is crucial for simulating pipeline commissioning, and do not comprehensively consider the compressibility of each phase fluid. Therefore, the modeling approach of this application starts from the most complete Baer-Nuziato model and derives an unsteady multiphase flow model for the pipeline commissioning process. The BN model includes multiple relaxation processes, including chemical potential relaxation, velocity relaxation, pressure relaxation, temperature relaxation, and energy relaxation. A relaxation process refers to the process by which a system in equilibrium, after being subjected to a transient external disturbance, will inevitably recover to its original equilibrium state after a certain period of time. The time it takes for the system to gradually recover from a non-equilibrium state to an equilibrium state is called the relaxation time.

[0054] In this embodiment of the application, the BN model is as shown in formula (1):

[0055]

[0056]

[0057]

[0058]

[0059] In the BN model, from top to bottom, the equations are the mass balance equation, momentum balance equation, energy balance equation, and volume fraction evolution equation for medium k. k ,ρ k ,u k ,p k , E k qk represent volume fraction, density, velocity, pressure, viscous stress tensor, total energy, and heat flux, respectively.

[0060] Among them, the total energy E k Including internal energy e k and kinetic energy Internal energy e k The density and pressure can be related through the equation of state, specifically as shown in equation (1-1):

[0061]

[0062]

[0063] e k =e k (ρ k ,p k (1-1)

[0064] In this embodiment, multiple relaxation processes are shown in formula (2):

[0065]

[0066]

[0067]

[0068]

[0069]

[0070] From top to bottom, these are the chemical potential relaxation process, velocity relaxation process, pressure relaxation process, temperature relaxation process, and energy relaxation process, v kl ,θ kl η kl , These represent the corresponding relaxation rates.

[0071] It should be noted that these relaxation processes correspond to phase transition, interphase friction, interphase compression, and heat exchange, respectively. The expression for the energy relaxation process represents the energy exchange caused by the phase transition. Each medium has its own state parameters, equations of state, constitutive relations, and governing equations. The media are coupled through equations relating to volume fractions.

[0072] Step 102: Obtain the multiphase flow control volume for pipeline flow in multiphase frozen soil areas.

[0073] In this application, permafrost refers to various rocks and soils containing ice at temperatures below zero degrees Celsius. It can generally be divided into short-term permafrost (a few hours / days to half a month), seasonal permafrost (half a month to several months), and perennial permafrost. Perennial permafrost, also known as permanent permafrost, refers to soil layers that remain frozen for two years or more. Permafrost exhibits rheological properties, and its long-term strength is far lower than its instantaneous strength. Due to these characteristics, constructing engineering structures in permafrost regions faces two major dangers: frost heave and thaw settlement. In this application, the permafrost region can refer to a perennial permafrost area. It should be noted that the control volume is a concept in fluid mechanics and thermodynamics, referring to a fixed, unchanging spatial volume enclosed by control surfaces within a specific space. The boundary of this space is called the control surface, which can be the wall of a real object or an imaginary interface. The control volume can be geometrically closed and fixed relative to a selected coordinate system. Within the control body, the exchange of matter and energy can occur, but this exchange is limited; that is, there is an exchange of mass and energy between the control body and the external environment, but it is not frictionless. For example... Figure 2 The diagram illustrates a control module for both single-phase and multiphase flow. Figure 2 In the image, from left to right, are a single-phase flow control volume and a multiphase flow control volume. The multiphase flow case is clearly much more complex than the single-phase flow case. In a multiphase flow control volume, each phase has corresponding parameters such as density, velocity, pressure, temperature, equation of state, and constitutive relations. Interphase interactions exist in a multiphase flow control volume, such as the interphase viscous stress tensor. Interphase heat flow q I And the interactions between each phase and the external environment, such as the frictional force τ between each phase and the wall. kwx The heat flow q between each phase and the external environment w,k .

[0074] Step 103: Determine the control equations for pipeline flow in multiphase frozen soil regions based on the control volume parameters, multiphase flow control volume, and BN model.

[0075] In this embodiment of the application, after obtaining the BN model and the multiphase flow control volume, according to as follows Figure 2 The control volume parameters of the multiphase flow control volume shown can be obtained. Therefore, the control equations for pipeline flow in multiphase frozen soil areas can be further determined based on the control volume parameters of the multiphase flow control volume, the multiphase flow control volume, and the BN model.

[0076] In this embodiment of the application, determining the control equations for pipeline flow in multiphase frozen soil regions based on the control volume parameters of the multiphase flow control volume, the multiphase flow control volume, and the BN model includes: integrating the BN model over the control volume using a preset method to determine the control equations for pipeline flow in multiphase frozen soil regions based on the control volume parameters and the BN model.

[0077] It should be noted that the traditional single-phase pipe fluid dynamics equations are relatively mature. However, in the control volume of traditional single-phase pipe flow, the interaction between the fluid and the pipe and the external environment includes the frictional force of the pipe wall. The heat flow q of the fluid through the pipe wall and the outside environment w In addition, internal friction exists in the fluid. The original single-phase flow control volume model equations do not include heat exchange between the fluid and the external environment, i.e., the heat flow q from the external environment. w Therefore, the corresponding term Kπd(T) is introduced in this application. env -T) represents the heat flow q between the pipe wall and the outside environment. w The governing equations for a single-phase flow control system can be expressed as shown in equation (2-1):

[0078]

[0079] Where θ is the pipe inclination angle of the single-phase flow control volume, A is the pipe cross-sectional area of ​​the single-phase flow control volume, g is the gravitational acceleration, d is the pipe inner diameter of the single-phase flow control volume, and K is the overall heat transfer coefficient.

[0080] To obtain the representation of the BN model in pipeline commissioning, this technical solution simplifies it within the multiphase flow control volume using the ALE (Arbitrary Lagrangian–Eulerian) method. The ALE method is used to integrate the BN model within the control volume to obtain the vector form, thus deriving the corresponding control equations for pipeline flow in multiphase frozen soil regions. The ALE method is a numerical method for solving fluid mechanics problems, combining the advantages of Lagrangian and Eulerian methods, and is suitable for handling problems with large deformations and moving meshes.

[0081] In this embodiment, the governing equation is determined according to formula (3):

[0082]

[0083] Where U is a conserved variable, H(U) is the interaction between phases at each system surface of the control volume, and C i (t) represents the volume of the control volume, and v represents the movement speed of the control volume interface.

[0084] In the formula, the conserved variable H(U) represents the interaction between phases at each surface of the control volume. The conserved variable H(U) includes volume fraction, mass, momentum, and energy, and can be in vector form as shown in formula (3-1):

[0085]

[0086] Where, α k , ρ k,u k ,p k , Let represent the volume fraction, density, velocity vector, pressure, and specific total energy of the k-th phase, respectively.

[0087] In the formula, the corresponding flux can include a vector form as shown in formula (3-2):

[0088]

[0089] To further determine the expression of the BN model in pipeline commissioning, the control equations of the multiphase flow control system can be discretized. Therefore, equation (3) can be further expanded into the discretized form shown in equation (3-3):

[0090]

[0091] The last two terms include the interaction terms between the multiphase flow control volume and the external environment, where n is the outward normal vector at the wall of the multiphase flow control volume.

[0092] In this embodiment, the governing equations satisfy volume conservation and area conservation, which are determined according to formulas (5) and (6), respectively:

[0093]

[0094]

[0095] Where U is a conserved variable, H(U) is the interaction between phases at each system surface of the control volume, and C i (t) represents the volume of the control volume, and v represents the movement speed of the control volume interface.

[0096] It should be noted that during the discretization of the control equations, the control equations of the multiphase flow control volume need to satisfy the volume conservation relationship and area conservation relationship as shown in formulas (5) and (6).

[0097] Step 104: Under the condition that the time step and spatial step of the multiphase flow control volume meet the first preset condition and the velocity relaxation process meets the second preset condition, determine the unsteady-state model for pipeline commissioning in the frozen soil area based on the control equation.

[0098] In the embodiments of this application, it should be noted that the first preset condition may refer to the time step and spatial step approaching zero, and the second preset condition may refer to the time of the velocity relaxation process approaching zero, i.e., when the interphase friction is large. Therefore, when the time step and spatial step of the multiphase flow control volume approach zero and the time of the velocity relaxation process approaches zero, the unsteady-state model for pipeline commissioning in frozen soil areas can be determined based on the control equations of the multiphase flow control volume.

[0099] In this embodiment, the unsteady-state model is determined according to formula (4):

[0100]

[0101]

[0102]

[0103]

[0104] Where ρ is the density of the mixture, p is the pressure of the mixture, and πdτ w,k To control the wall friction of the body, To control the elastic deformation of the pipe, α k πdK(T0-T) represents the heat exchange between the control volume and the soil, where A is the cross-sectional area of ​​the control volume pipe, g is the gravitational acceleration, d is the inner diameter of the control volume pipe, and K is the overall heat transfer coefficient of the control volume.

[0105] In this technical solution, by incorporating interaction with the external environment into formula (3-3), and with the time step and spatial step approaching zero, we can obtain the pipeline commissioning unsteady multiphase flow model one as shown in formula (4-1):

[0106]

[0107]

[0108]

[0109]

[0110] In actual testing, it was found that the wave structure was complex, the computational load was large, and the problem being solved was a rigid system with a limited time step. Therefore, in order to improve computational efficiency, the model needs to be simplified appropriately. The multiphase flow BN model (relaxed system) is simplified by asymptotic analysis. That is, when the velocity relaxation time approaches zero (the interphase friction is large), the asymptotic analysis is performed with the relaxation time as a small quantity (retained to the zero order). Formula (4-1) can be further simplified to obtain the unsteady-state model for pipeline commissioning in frozen soil areas as shown in Formula (4). Compared with the model shown in Formula (4-1), the model shown in Formula (4) has a greater advantage in computational efficiency. Moreover, the Riemann solution of the simplified unsteady-state model is simplified from a seven-wave structure to a three-wave structure. The three-wave structure Riemann solver has higher computational efficiency and is more robust.

[0111] This technical solution takes into account the heat exchange between pipelines and the external environment during actual production. By introducing the BN model, which can simulate the interaction of pressure waves, and by introducing terms corresponding to heat exchange on the basis of the BN model, the accuracy of pressure calculation in the pipeline area is effectively improved.

[0112] Compared to previous models, this technical solution derives a multiphase flow unsteady-state model suitable for pipeline commissioning based on the BN multiphase flow model. This model includes equations for heat exchange with the external environment that were not considered in the original model, introduces corresponding terms, and simplifies the model into a set of equations that are more conducive to solving, providing a solid foundation for subsequent numerical solutions and establishing a multiphase flow model for pipeline commissioning that conforms to the physical process.

[0113] This application provides a storage medium storing a program that, when executed by a processor, implements the above-described method for determining the unsteady-state model for pipeline commissioning in permafrost regions.

[0114] This application provides a processor for running a program, wherein the program executes the above-described method for determining the unsteady-state model for pipeline commissioning in permafrost regions.

[0115] In one embodiment, a computer device is provided, which may be a server, and its internal structure diagram may be as follows: Figure 3 As shown. The computer device includes a processor A01, a network interface A02, a memory (not shown), and a database (not shown) connected via a system bus. The processor A01 provides computing and control capabilities. The memory includes internal memory A03 and a non-volatile storage medium A04. The non-volatile storage medium A04 stores an operating system B01, a computer program B02, and a database (not shown). The internal memory A03 provides an environment for the operation of the operating system B01 and the computer program B02 in the non-volatile storage medium A04. The database stores data for determining a non-steady-state model for pipeline commissioning in permafrost regions. The network interface A02 communicates with external terminals via a network connection. When the processor A01 executes the computer program B02, it implements a method for determining a non-steady-state model for pipeline commissioning in permafrost regions.

[0116] Those skilled in the art will understand that Figure 3 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0117] This application provides an apparatus including a processor, a memory, and a program stored in the memory and executable on the processor. When the processor executes the program, it performs the following steps: acquiring a BN model of a multi-medium fluid, the BN model including multiple relaxation processes, the multiple relaxation processes including at least a chemical potential relaxation process, a velocity relaxation process, a pressure relaxation process, a temperature relaxation process, and an energy relaxation process; acquiring a multiphase flow control volume for pipeline flow in a multiphase frozen soil region; determining the control equations for pipeline flow in a multiphase frozen soil region based on the control volume parameters of the multiphase flow control volume, the multiphase flow control volume, and the BN model; and determining the unsteady-state model for pipeline commissioning in the frozen soil region based on the control equations, provided that the time step and spatial step of the multiphase flow control volume meet a first preset condition and the velocity relaxation process meets a second preset condition.

[0118] In one embodiment, the BN model is as shown in Equation (1):

[0119]

[0120]

[0121]

[0122]

[0123] In the BN model, from top to bottom, the equations are the mass balance equation, momentum balance equation, energy balance equation, and volume fraction evolution equation for medium k. k ,ρ k ,u k ,p k , E k qk represent volume fraction, density, velocity, pressure, viscous stress tensor, total energy, and heat flux, respectively.

[0124] In one embodiment, multiple relaxation processes are as shown in Equation (2):

[0125]

[0126]

[0127]

[0128]

[0129]

[0130] From top to bottom, these are the chemical potential relaxation process, velocity relaxation process, pressure relaxation process, temperature relaxation process, and energy relaxation process, v kl , η kl , These represent the corresponding relaxation rates.

[0131] In one embodiment, determining the control equations for pipeline flow in a multiphase frozen soil region based on the control volume parameters of the multiphase flow control volume, the multiphase flow control volume, and the BN model includes: integrating the BN model over the control volume using a preset method to determine the control equations for pipeline flow in a multiphase frozen soil region based on the control volume parameters and the BN model.

[0132] In one embodiment, the governing equation is determined according to formula (3):

[0133]

[0134] Where U is a conserved variable, H(U) is the interaction between phases at each system surface of the control volume, and C i (t) represents the volume of the control volume, and v represents the movement speed of the control volume interface.

[0135] In one embodiment, the unsteady model is determined according to formula (4):

[0136]

[0137]

[0138]

[0139]

[0140] Where ρ is the density of the mixture, p is the pressure of the mixture, and πdτ w,k To control the wall friction of the body, To control the elastic deformation of the pipe, α k πdK(T0-T) represents the heat exchange between the control volume and the soil, where A is the cross-sectional area of ​​the control volume pipe, g is the gravitational acceleration, d is the inner diameter of the control volume pipe, and K is the overall heat transfer coefficient of the control volume.

[0141] In one embodiment, the governing equations satisfy volume conservation and area conservation, which are determined according to formulas (5) and (6), respectively:

[0142]

[0143]

[0144] Where U is a conserved variable, H(U) is the interaction between phases at each interface of the control volume, Ci(t) is the volume of the control volume, and v is the velocity of the interface of the control volume.

[0145] This application also provides a computer program product, which, when executed on a data processing device, is suitable for executing an initialization program with the following method steps: acquiring a BN model of a multi-medium fluid, the BN model including multiple relaxation processes, the multiple relaxation processes including at least a chemical potential relaxation process, a velocity relaxation process, a pressure relaxation process, a temperature relaxation process, and an energy relaxation process; acquiring a multiphase flow control volume for pipeline flow in a multiphase frozen soil region; determining the control equations for pipeline flow in a multiphase frozen soil region based on the control volume parameters of the multiphase flow control volume, the multiphase flow control volume, and the BN model; and determining the unsteady-state model for pipeline commissioning in the frozen soil region based on the control equations, provided that the time step and spatial step of the multiphase flow control volume meet a first preset condition and the velocity relaxation process meets a second preset condition.

[0146] In one embodiment, the BN model is as shown in Equation (1):

[0147]

[0148]

[0149]

[0150]

[0151]

[0152] In the BN model, from top to bottom, the equations are the mass balance equation, momentum balance equation, energy balance equation, and volume fraction evolution equation for medium k. k ,ρ k ,u k ,p k , E k qk represent volume fraction, density, velocity, pressure, viscous stress tensor, total energy, and heat flux, respectively.

[0153] In one embodiment, multiple relaxation processes are as shown in Equation (2):

[0154]

[0155]

[0156]

[0157]

[0158]

[0159] From top to bottom, these are the chemical potential relaxation process, velocity relaxation process, pressure relaxation process, temperature relaxation process, and energy relaxation process, v kl , η kl , These represent the corresponding relaxation rates.

[0160] In one embodiment, determining the control equations for pipeline flow in a multiphase frozen soil region based on the control volume parameters of the multiphase flow control volume, the multiphase flow control volume, and the BN model includes: integrating the BN model over the control volume using a preset method to determine the control equations for pipeline flow in a multiphase frozen soil region based on the control volume parameters and the BN model.

[0161] In one embodiment, the governing equation is determined according to formula (3):

[0162]

[0163] Where U is a conserved variable, H(U) is the interaction between phases at each system surface of the control volume, and C i (t) represents the volume of the control volume, and v represents the movement speed of the control volume interface.

[0164] In one embodiment, the unsteady model is determined according to formula (4):

[0165]

[0166]

[0167]

[0168]

[0169] Where ρ is the density of the mixture, p is the pressure of the mixture, and πdτ w,k To control the wall friction of the body, To control the elastic deformation of the pipe, α k πdK(T0-T) represents the heat exchange between the control volume and the soil, where A is the cross-sectional area of ​​the control volume pipe, g is the gravitational acceleration, d is the inner diameter of the control volume pipe, and K is the overall heat transfer coefficient of the control volume.

[0170] In one embodiment, the governing equations satisfy volume conservation and area conservation, which are determined according to formulas (5) and (6), respectively:

[0171]

[0172]

[0173] Where U is a conserved variable, H(U) is the interaction between phases at each interface of the control volume, Ci(t) is the volume of the control volume, and v is the velocity of the interface of the control volume.

[0174] 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.

[0175] 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.

[0176] 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.

[0177] 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.

[0178] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0179] Memory may include non-persistent memory in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0180] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0181] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0182] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A method for determining a non-steady state model for commissioning of a pipeline in permafrost regions, characterized in that, The determination method comprises: obtaining a BN model of the multi-medium fluid, the BN model comprising a plurality of relaxation processes, the plurality of relaxation processes at least comprising a chemical potential relaxation process, a velocity relaxation process, a pressure relaxation process, a temperature relaxation process, and an energy relaxation process; obtaining a multiphase flow control body for the multiphase permafrost region pipeline flow; determining a control equation for the multiphase permafrost region pipeline flow based on control body parameters of the multiphase flow control body, the multiphase flow control body, and the BN model; in a case where a time step and a space step of the multiphase flow control body satisfy a first preset condition and the velocity relaxation process satisfies a second preset condition, determining a non-steady-state model of the permafrost region pipeline production based on the control equation; wherein the control equation is determined according to formula (3): （3） wherein, is a conserved variable, H(U) is the interaction between the phases at each system surface of the control volume, is the volume of the control volume, v is the velocity of the control volume interface; wherein the non-steady-state model is determined according to formula (4): （4） wherein, is the density of the mixture, is the pressure of the mixture, is the wall friction of the control body, is the elastic deformation of the pipe of the control body, is the heat exchange with the soil, A is the pipe cross-sectional area of the control body, g is the acceleration of gravity, d is the pipe inner diameter of the control body, and K is the total heat transfer coefficient of the control body. wherein the control equation satisfies volume conservation and area conservation, the volume conservation and the area conservation being determined according to formulas (5) and (6), respectively: （5） （6） wherein, is a conserved variable, H(U) is the interaction between the phases at each system surface of the control volume, C i ( t ) is the volume of the control volume, v is the velocity of the interface of the control volume.

2. The method for determining the unsteady model of the frozen ground region pipeline commissioning according to claim 1, characterized in that, the BN model is shown in formula (1): （1） In the BN model, from top to bottom are, in sequence, a medium k mass balance equation, a momentum balance equation, an energy balance equation, and an evolution equation of volume fraction, qk are volume fraction, density, velocity, pressure, viscous stress tensor, total energy, and heat flow, respectively.

3. The method for determining the unsteady model of the frozen ground region pipeline commissioning according to claim 2, characterized in that, the plurality of relaxation processes are shown in formula (2): （2） wherein the chemical potential relaxation process, the velocity relaxation process, the pressure relaxation process, the temperature relaxation process and the energy relaxation process are arranged from top to bottom in the order given, respectively, denote the respective relaxation rates.

4. The method for determining the unsteady model of the commissioning of a pipeline in permafrost zones according to claim 1, characterized in that, the determination of the control equation for the multiphase permafrost region pipeline flow based on the control body parameters of the multiphase flow control body, the multiphase flow control body, and the BN model comprises: integrating the BN model with respect to the control body based on a preset method to determine the control equation of the multiphase permafrost region pipeline flow based on parameters of the control body and the BN model.

5. An apparatus for determining a non-steady state model, characterized by comprise: a memory configured to store instructions; and a processor configured to call the instructions from the memory and enable the determination method of the non-steady-state model of the permafrost region pipeline production according to any one of claims 1 to 4 when the instructions are executed.

6. A system for determining a non-steady state model, characterized by, comprise the apparatus according to claim 5.

7. A machine-readable storage medium having stored thereon instructions, the instructions being executable by a machine to cause the machine to perform operations comprising: The instructions, when executed by the processor, cause the processor to be configured to perform the determination method of the non-steady-state model of the permafrost region pipeline production according to any one of claims 1 to 4.

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