Numerical simulation of unsteady flow multiphase flow in oil and gas pipelines and control strategy of section plug flow

Energy reform in today’s society is constantly developing, and China has become the world’s largest energy supply system. In order to promote China’s social and economic development faster and stronger, the state has established a new energy supply industry chain mainly based on coal and electricity, focusing on the vigorous development of oil, natural gas and renewable energy. Multi-phase mixed transmission technology can reduce the construction cost of oil and gas sub-transmission pipelines, so it is one of the more common transmission methods at present. However, due to the process of oil and gas field extraction and transportation, there are factors such as flow rate changes, terrain undulation, and changes in the water to gas ratio, liquid plugging, gas-liquid layered flow alternately repeated segment plugging phenomenon will occur in the multiphase movement [1-2]. Segmental plugging phenomenon generated by multiphase flow is commonly found in oil and gas field development, gas-liquid pipeline mixing and transportation, as well as petrochemical and other categories. The instability and intermittency of the plugged flow can lead to strong periodic fluctuations in the pressure, holding rate, and gas-liquid phase flow rate in the pipeline, and the resulting fluid stress impacts can threaten the safe transportation of the pipeline and the stable operation of the equipment on the downstream processing platform [3-5]. In addition, there is a high probability of severe segmental plugging flow formation during transportation in marine riser systems, and the frequency of segmental plugging is greatly increased, which exacerbates the hazardous level of system operation [6-8]. Therefore, the blockage phenomenon in multiphase flow has become a key research object, which puts forward higher requirements for the accurate prediction of blockage flow and precise calculation results. In order to accurately predict the motion state of gas-liquid phase fluids in pipelines, the development of software for numerical simulation of unsteady flow multiphase flow has become a research hotspot, which is of great significance for the stable operation of multiphase transport pipelines and the guarantee of safe flow.

Scholars at home and abroad have done a lot of research on multiphase flow and pipeline corrosion respectively, which is mainly manifested in the flow change mechanism division basis, such as temperature, pressure, fluid medium and other aspects of the influence on pipeline corrosion, and the design of relevant prediction models to predict the multiphase flow corrosion rate. Zhang, H. et al. showed that corrosion is a complex hydrodynamic process, and from the factors related to the water to explain the multiphase flow corrosion mechanism and correlation with corrosion behavior, and also predicted pipeline corrosion damage by establishing an empirical and mechanical based prevention model [9]. Jin, H. et al. detected and simulated the damage events of a carbon steel tee pipe under the action of a multiphase flow field by using Scanning Electron Microscopy (SEM) and Computational Fluid Dynamics (CFD), and the results of their study showed that there were large velocity gradients in some regions of the pipe. Corrosive media in water with chaotic flow conditions aggravate the flow corrosion phenomenon inside the pipe [10]. Obaseki, M. et al. developed a multiphase flow simulation model, taking into account both carbon dioxide (CO2) and hydrogen sulfide (H2S) corrosion inside the pipeline, as well as the effect of chloride concentration, which significantly increased the accuracy of predicting corrosion rates inside oil and gas pipelines [11]. Peng, S. et al. used principal component analysis (PCA) algorithm to reduce the data dimensionality in order to extract the main corrosion influencing factors, and combined with Chaotic Particle Swarm Optimization (CPSO) algorithm to optimize the hyperfine parameters in Support Vector Regression (SVR), and the proposed hybrid intelligent algorithm of PCA-CPSO-SVR has a better performance for the prediction of corrosion rate in multiphase flow pipelines [12]. Redondo, C. et al. proposed a computational fluid dynamics (CFD)-based approach to simulate erosion and corrosion in oil and gas pipelines, which utilizes the high-order discontinuous Galerkin spectral element method to accurately model the flow state, phase distribution, and contact surfaces inside the pipeline, increasing the accuracy of erosion and corrosion rates inside oil and gas pipelines [13]. da Silva, C. A. et al. assembled a test loop in the laboratory to simulate the conditions of 80% water-containing wells, and used multiple regression and Box-Cox transform methods to test the effects of different pipeline material qualities and the nature of the multiphase flow in the pipe on the corrosion rate of the pipe, which provides the possibility of damage prediction and matrix parameter optimization for multiphase loop tests [14].

Oil and gas transportation pipelines can be divided into upright and curved pipes, due to the high cost and difficult maintenance of subsea measurements, a large number of scholars tend to design feedback control systems with efficient segmental plugging control performance to reduce or eliminate segmental plugging flow by regulating the air pressure and flow rate. Nnabuife, S. G., et al. pointed out that the feedback control is an effective method for preventing the segmental plugging flow in the transportation of offshore oil and gas production and that its avoiding liquid blockage at the bottom of the pipeline by controlling the flow rate or pressure in the pipeline, but the difficulty in measuring the flow rate of multiphase flow is a serious problem that prevents the segmented plug control technique from obtaining robustness [15]. Jahanshahi, E. et al. found that variations in inflow conditions, nonlinearities in the process, and modeling errors are the main reasons for the lack of robustness of the segmented plug resistance feedback controllers, and so four different controllers were designed based on the nonlinear and linear analyses and evaluated for their robustness. Four different controllers were designed based on nonlinear and linear analyses and evaluated for their robustness to time delay, operating point variations, and inflow perturbations, and the experimental results were consistent with the observability theory [16]. Nnabuife, S. G. et al. investigated a Doppler ultrasound-based segmental plug flow control scheme for offshore multiphase pipeline and riser systems, which achieves larger valve openings than the open-loop unsteady system, realizes stability at lower valve openings, and is well suited for manual valve opening It is very suitable for manual throttling [17]. Guo, W. et al. proposed an oil, gas and water three-phase flow measurement method based on the basic temperature and differential pressure signals. By analyzing the temperature fluctuation of the heated pipe wall caused by Taylor bubbles and liquid plugs, they successfully measured the fluid flow and the differential pressure inside the pipe, and then obtained the oil content of the liquid-phase flow, and the theoretical model established to correlate the flow characteristics of the multiphase flow and the flow rate had the The theoretical model established to correlate the flow characteristics of multiphase flow with the flow rate has validity and accuracy [18]. Shi, S. et al. constructed a transient segment plug flow model applicable to curved transportation pipelines, and by comparing the results of model calculations and experimental measurements under the same conditions, it was found that the errors of both transient pressures and liquid content in the middle of the curved pipe were within reasonable limits, which proved that the prediction performance of the proposed model was good [19]. Jahanshahi, E. et al. introduced a segment plug flow control method that relies on the opening of a throttle valve on the deck platform to regulate the pressure or flow rate of the pipe, and proposed an anti-segment plug control scheme based on virtual flow measurement, which combined with a cascade structure to realize a more stable control [20].

This paper realizes the numerical simulation of unsteady flow multiphase flow in oil and gas pipelines based on computational fluid dynamics and fluid volume modeling, as well as the design of the PID control strategy for the segment plug flow. The proposed numerical simulation model is used to analyze the pressure characteristics of the severe segment plug flow, so as to design a PID system for the control of the segment plug flow in the oil and gas pipeline, and verify the controllability of the PID system and the effectiveness of the proposed strategy from the aspects of the pressure control at the bottom of the riser, the pressure control at the top of the riser, the mixing density control at the top of the riser, and the mass flow control at the top of the riser, respectively. The validity of the PID system and the strategy proposed in this paper has been verified.

2

Numerical simulation model for unsteady flow multiphase flow in oil and gas pipelines

Numerical simulation is widely used in multiphase flow studies of oil and gas pipelines as an effective means to study complex fluid dynamics problems. Commonly used numerical simulation methods include the computational fluid dynamics (CFD) method, finite volume method (FVM), and Lagrangian-Eulerian method. These methods are capable of simulating the unsteady flow process of fluids in pipelines by solving basic physical equations such as conservation of mass, conservation of momentum, and conservation of energy.

2.1

Numerical simulation process based on CFD software

In this paper, numerical simulation of multiphase flow in unsteady flow of oil and gas pipeline is carried out by CFD software [21]. CFD software is mainly a numerical simulation application software developed on modern CFD technology to simulate fluid flow in real situations and collect relevant data for application development. Computational fluid dynamics is mainly based on discrete numerical computation methods, using electronic computers to collect the internal and external numerical changes of fluid flow through different solid boundaries, which are used to analyze, experiment and simulate the test, so as to solve the problems that may arise in the process of practice.

CFD software is a product of the combination of modern fluid mechanics, numerical computation and computer science and technology, and fluid mechanics is a key problem to be solved in the process of oil and gas pipeline storage and transportation, mainly due to the fluid has mobility and variability, the theory has the nature and universality, and it is not possible to use the invariant theory to solve the problem of changing fluid mechanics.

CFD software is adaptable, widely used, easy and fast to operate, all CFD software components are similar, mainly by the pre-processing, solver, post-processing three parts, which corresponds to the pre-processing, solver, post-processing three parts of the processing module. The primary function of the pre-processor is to perform geometric modeling and mesh generation. The solver is used to determine the CFD processing method, select the discretization method for discretization, select the numerical calculation method, and input the relevant parameters. Post-processing is mainly used to visualize and animate the velocity field, temperature field, pressure field, and other different field data. The calculation flow of the CFD software is shown in Figure 1.

2.2

Control equations

In this paper, we mainly study the relationship between the multiphase flow characteristics of oil-gas-water mixtures and the flow parameters, and there is little change in temperature and pressure over a short distance, the growth and decomposition process of natural gas (the main component of which is methane) hydrate particles is not obvious, and at the same time, methane gas has a very low solubility in water, so that the generation and decomposition of hydrate, the gas-phase dissolution and desorption, and the temperature changes are not taken into account in the modeling process. Since there is no heat and mass transfer process between gas-liquid hydrate, its transient control equations can be expressed as Eqs. (1) and (2).

Continuity equation: (1) $\frac{\partial (α_{φ} ρ_{φ})}{\partial_{i}} + \nabla \cdot (α_{φ} ρ_{φ} {\vec{u}}_{φ}) = 0$

Momentum equation: (2) $\frac{\partial (α_{φ} ρ_{φ} {\vec{u}}_{φ})}{\partial_{ι}} + \nabla \cdot (α_{φ} ρ_{φ} {\vec{u}}_{φ} {\vec{u}}_{φ}) = - α_{φ} \nabla p + \nabla \cdot (α_{φ} τ_{φ}) + α_{φ} ρ_{φ} \vec{g} + {\vec{F}}_{φ}$ (3) $τ_{g / 1} = μ (\nabla {\vec{u}}_{g / 1} + \nabla {\vec{u}}_{g / 1}^{T}) - \frac{2}{3} μ (\nabla \cdot {\vec{u}}_{g / 1}) I$ (4) $τ_{s} = (- p_{s} + λ_{s} \nabla \cdot {\vec{u}}_{s}) I + μ_{s} (\nabla {\vec{u}}_{s} + \nabla {\vec{u}}_{s}^{T}) - \frac{2}{3} μ_{s} (\nabla \cdot {\vec{u}}_{s}) I$

Where: α denotes phase volume fraction. ρ denotes the phase density, kg/m³. The subscript φ denotes the different phases, φ = d denotes the dispersed phase (g is the gas phase, s is the aqueous phase), φ = c denotes the continuous phase (1 is the oil phase). $\vec{u}$ denotes the instantaneous velocity of motion of the corresponding phase, m/s. p is the local pressure, Pa. μ is the dynamic viscosity, Pa·s. I is the unit tensor. $\vec{g}$ is the gravitational acceleration, m/s². $\vec{F}$ is the interphase force N/m³, denotes the momentum transfer between the two phases. τ for viscous stress tensor, Pa. p_s for solid phase pressure. λ_s is the solid phase bulk viscosity. The above control equations can characterize the flow field within the multiphase system and can provide the flow parameters of multiphase flow for the solution of the population equilibrium model.

2.3

Turbulence modeling

In computational fluid dynamics, numerical computation methods for turbulence are roughly divided into three categories: direct simulation, large eddy simulation, and Reynolds time-averaged equations. Direct simulation is the use of three-dimensional unsteady Navier-Stokes equations, the turbulence of the direct numerical calculation method, the requirements must use a small time and space step, so the memory space and computational speed requirements are very high, and can not be used for engineering numerical calculations. Large eddy simulation is to use three-dimensional unsteady Navier-Stokes equations to directly simulate large-scale eddies, and the effect of small-scale eddies on the flow is taken into account through an approximate model, this method still has a high demand on memory space and computational speed, but with the development of computer technology, it has gained a certain degree of application. The Reynolds time-averaged method is to average the unsteady Navier-Stokes equations over time to obtain the control equations about the time-averaged physical quantities, which contain unknown quantities such as the product of pulsation quantities to be modeled. Currently, the k – ε two-equation model in the Reynolds time-averaged equations is more commonly used in engineering.

The specific expression of the k – ε model included in OpenFOAM is shown below: (5) $\frac{\partial (α ρ k)}{\partial t} + \nabla \cdot (α ρ k \vec{u}) - \nabla \cdot (α ρ D_{k} \nabla k) = α ρ G - \frac{2}{3} α ρ (\nabla \cdot \vec{u}) k - α ρ ε + S_{k}$ (6) $\begin{array}{l} \frac{\partial (α ρ ε)}{\partial t} + \nabla \cdot (α ρ ε \bar{u}) - \nabla \cdot (α ρ D_{ε} \nabla ε) \\ = C_{1} α ρ G \frac{ε}{k} - ((\frac{2}{3} C_{1} - C_{3}) α ρ (\nabla \cdot \bar{u}) ε) - C_{2} α ρ \frac{ε}{k} + S_{ε} \end{array}$

This model is used for all three phases of oil, gas and water mixtures in this paper. Among them: (7) $G = ν_{t} (\nabla \vec{u} + \nabla {\vec{u}}^{T} - \frac{2}{3} (\nabla \cdot \vec{u}) I) : \nabla \vec{u}$ (8) $D_{k} = \frac{ν_{i}}{σ_{k}} + ν$ (9) $D_{ε} = \frac{ν_{i}}{σ_{ε}} + ν$ (10) $ν_{i} = C_{μ} \frac{k^{2}}{ε}$

Where: k is the turbulent kinetic energy, m²/s². ε is the turbulent kinetic energy dissipation rate, m²/s³. The constant takes the value C_μ = 0.09,C₁ = 1.44,C₂ = 1.92,C₃ = 0,σ_k = 1.0,σ_ε = 1.3.

2.4

Multiphase flow modeling

In FLUENT software application, there are three types of multiphase flow models to choose from: mixed model, fluid volume model and Eulerian model.

The mixing model is mainly used in the case where the coupling between phases is weak, the Stokes is less than 1 and the particle and base phase velocities are roughly in the same direction. This is because when dealing with multiphase flow problems, each component is treated as a continuous medium that runs through each other. The main applied flow regimes of the mixing model are droplet flow, bubble flow and slurry flow, and the main applications are gas injection, hydrocyclone, solid suspension, and bubble column reactor.

Volume of fluid (VOF) models are generally used primarily to solve problems where one or more fluid interfaces exist in a fluid that are not intermixed with each other [22]. When using the fluid volume model in FLUENT software, the phases share a common set of momentum equations, and when the cell is completely occupied by one phase, standard interpolation methods are used to obtain the surface fluxes. The main applied flow regimes of the fluid volume model are stratified flow, free surface flow, and free surface flow. The main applications of the model are boiling, coating, grouting, and floating of near-shore isolates.

The Eulerian model is the most widely used model among the three models, which can calculate arbitrary particles and continuous-phase substances, coexisting in each phase and solving the conservation equations for each phase, and the conservation equations for each phase include single-phase terms and interface terms. The main applications of the Eulerian model are droplet flow, bubble flow, particle flow, slurry flow, and fluidized bed. These applications include hydraulic transport, sedimentation, high-concentration particle flow, reactors, and so on.

The internal flow field of the oil and gas pipeline studied in this paper involves fluid dynamics challenges such as unsteady, multiphase, and turbulent flows, and it is necessary to track the free-surface flow of the pipeline, thus, the volume of fluid model (VOF model) among the three multiphase flow models is selected.

The basic idea of the VOF method is to define the relative ratio between the volume of fluid in the desired calculation range and the volume of the calculation range as a descriptive function F = f(x,y,z,t). For any cell in the range, the descriptive function is defined as follows: when F = 1, it means that the cell is occupied. When F = 0, it is an empty cell. When 0 < F < 1, it means that the fluid only partially occupies the cell, and the cell in this case is defined as a free surface cell, and the VOF method is used to represent the fluid occupying the cell and the shape of the free surface.

The region occupied by the fluid and the shape of the free surface expressed by the VOF method are shown in Fig. 2, from which it can be seen that the free surface exists only in the free surface cells and not in the empty or volume-filled cells. Normally when dealing with the free surface problem, there is usually no need to consider the interpenetration between the two phases, so it is usually possible to use function F to capture the surface of the free cell, so that the free flow can be simulated numerically. From the definition of function f, it is not difficult to conclude that the direction of the maximum gradient of f is the normal direction of the free surface, therefore, according to the F-value analysis method of the free surface cell and the neighboring cells, under the linear approximation of the free surface, we can obtain the direction and position of the free surface in the free surface cell. Then the kinematic boundary conditions of the complex free surface can be satisfied by the direction and position of the free surface.

When solving multiphase flow problems analytically by the VOF method, it is necessary to control each volume cell in the fluid so that the volume fractions of all phases satisfy the sum of 1. If a_q denotes the volume fraction of q phases in the cell, then in the control volume cell, the value of α_q can be classified into three kinds: α_q = 0,α_q = 1 or 0 < α_q < 1, which corresponds to the absence of q phases, the presence of q phases or the presence of q phases and other phases, in that case. phase and other phases, and since the sum of all phase volume fractions is 1, α_q satisfies the equation: (11) $\sum_{q = 1}^{n} α_{q} = 1$

Where: n is the total number of phases.

Solving for each phase separation is shown in Eq. (12): (12) $\frac{\partial α_{q}}{\partial t} + \vec{ν} \cdot \nabla α_{q} = \frac{S_{a_{q}}}{ρ_{q}}$

When using the finite volume method, in each free surface cell, the density and viscosity in the free surface cell are affected by the volume fraction of each phase because the properties of each phase are different. So when considering the property parameters appearing in the control equation, the volume fraction of each phase needs to be taken into account, and the selection of the density and viscosity in the VOF method is the average value of each property, such as the volume fraction average density is: (13) $\frac{\partial}{\partial t} (ρ \vec{ν}) + \nabla \cdot (ρ \vec{ν ν}) = - \nabla p + \nabla \cdot [μ (\nabla \vec{ν} + \nabla {\vec{ν}}^{T})] + ρ \vec{g} + \bar{F}$

3

Design of plug flow control strategies for oil and gas pipeline sections

3.1

Segmental plug flow and the need to control it

In the oil and gas industry, oil and gas multi-phase mixed transmission technology has a very wide range of applications in the field of pre-exploitation and post-transmission. At present, the main battlefield of oil and gas development has been gradually transferred to the ocean, polar and other natural environments of the more adverse areas, for environmental and economic considerations, it is usually inappropriate to lay two pipelines to transport oil and natural gas alone, which gives rise to the use of a pipeline to transport multi-phase transmission technology can reduce the oil and gas field mining costs by 10% to 40%, bringing significant economic benefits, with a single-phase transport pipeline The advantages of single-phase pipeline are incomparable. In recent years, mixing pipelines have been widely used in the offshore oil industry, where flat pipes laid on the seabed and risers connected to offshore platforms connect offshore oil and gas fields, onshore terminals or storage facilities into an organic whole, ensuring that all aspects of offshore oil and gas extraction can be coordinated with each other. The offshore oil and gas mixing pipeline is shown in Figure 3.

In the process of oil and gas mixing, multiphase flow occurs in the pipeline. Oil, gas and water multiphase mixtures will form different flow patterns in the pipeline due to factors such as oil/gas ratio, flow rate and topography, etc. Segmental plug flow is a frequently occurring harmful flow pattern, and the pressure and flow rate fluctuations caused by the alternating flow of gas and liquid phases will have a negative impact on the production process. The serious blockage flow is the most harmful type of blockage flow, which usually occurs in the connecting pipeline of the two ocean platforms, and the length of the liquid blockage is much larger than the height of the riser, which leads to a wide range of periodic fluctuations of the pressure in the pipeline and the instantaneous flow rate of gas and liquid at the outlet of the pipeline, and it brings a lot of problems and hazards to the design and production: 1)

The high pressure generated at the valves or bends of the mixing pipeline will cause violent vibration of the pipeline, which will cause cracks or even breakage of the pipeline in serious cases.

2)

During the liquid release stage, the liquid stream will erupt into the downstream separator in a very short period of time, resulting in a rapid rise in the separator level, generating the separator overflow phenomenon and affecting normal production.

3)

In the gas release stage, it leads to the generation of natural gas hydrate and wax deposition phenomenon, and even blocks the pipeline in serious cases.

4)

At the end of oil and gas field production, especially when the oil and gas production is low, severe section plugging flow is most likely to occur, which leads to higher back pressure that can easily cause dead wells and bring very unfavorable effects to the reservoir. Therefore, from the protection of equipment, reduce operating costs, improve production and other considerations, research on the inhibition and control of severe blockage flow is particularly important, not only for the development of oil and gas resources to provide a strong theoretical support and technical support, but also to protect the oil and gas pipeline and the downstream equipment of the operation of the safety of a very important significance.

3.2

Segment plug flow control strategies for oil and gas pipelines

Based on the research of domestic and foreign literature, this paper develops the design of plug flow control strategy for oil and gas pipeline segments from the following aspects: 1)

According to the actual pipeline conditions in an oilfield, the multiphase flow transient simulation software OLGA is used to build a simulation model of oil and gas mixing and transmission process, and the serious segment plugging flow phenomenon generated in the mixing and transmission process is suppressed and controlled by using the PID control module of the software [23].

2)

Aiming at the difficulty of adjusting parameters due to the absence of process model in the traditional PID scheme for suppressing segmental plugging flow, the system identification method is proposed to establish the mathematical model of the controlled process, and the oil and gas mixing and transmission process is modeled by two methods, namely, nonparametric model identification and parametric model identification. The input signals generated by MATLAB for identification are converted in OLGA to obtain the output data of the process, on the basis of which the system identification toolbox is used to identify the controlled process, and then obtain the mathematical model of the oil and gas mixing and transportation process.

3)

Aiming at the characteristics of the oil and gas mixing and transmission process that there are big differences in the working points and characteristics under different initial valve openings, a robust control scheme is proposed to consider the controlled process as a family of models, and an optimal H∞ robust controller is designed through the selection of the uptake weighting function, the tracking weighting function, and the control action weighting function.

4)

Based on the OPC communication, the dynamic data of the oil and gas mixing and transmission process is uploaded to the OLGA OPC server in real time, and the OPC client built within MATLAB connects with the server to realize the function of real-time interaction of the data, and the effect of the H∞ robust controller is verified in terms of tracking performance and anti-interference performance.

4

Analysis of the effect of PID control of segmental plug flow based on numerical simulation

This paper firstly analyzes the pressure characteristics of severe blockage flow through numerical simulation model, and then adjusts the improved PID automatic controller according to the numerical simulation results to realize the blockage flow control in the case of unsteady flow multiphase flow in the oil and gas pipeline.

4.1

Pressure Characterization of Severe Segment Plug Flow

4.1.1

Segment plug flow pressure change under different operating conditions

In this paper, the experiments under specific working conditions (64 experimental conditions: gas converted velocity ranging from 0.0149 m/s to 1.1 m/s, and liquid converted velocity ranging from 0.006 m/s to 1.1 m/s) accomplished in the simulation system of severe section plugging in horizontal-downward-dipping-vertical-vertical riser pipeline will be studied. Study, in-depth analysis of the pressure characteristic parameters of the severe section plug flow.

The pressure of severe section plugging flow shows strong cyclic characteristics in the flow process, and the range of pressure fluctuation is also broad. In order to investigate the pressure fluctuation law in the horizontal-downturned-vertical riser oil-gas mixing pipeline with severe segmental plug flow, the pressure data at three target locations, namely, the inlet of downturned pipe, the bottom of riser and the middle of riser, are collected and analyzed in the multiphase flow experiments, and are expressed as P1, P2, and P3, respectively.

The pressure trend along the oil and gas mixing pipeline simulation system with time is shown in Fig. 4. Among them, the converted gas velocity is 0.041 m/s and the converted liquid velocity is 0.0604 m/s.

As can be seen from Fig. 4, this flow pattern is a typical severe segment plug flow, and the pressure in the mixing pipeline system in which it is located shows a strong cyclic cyclic characteristic, with four cyclic stages of liquid plug formation, liquid plug outflow, gas-liquid eruption and liquid reflux in Figs. X1, X2, X3 and X4, respectively, with a large overall range of fluctuations. The value of the inlet pressure P1 of the downturned pipe is obviously larger than the pressure values of the other two target positions. The reason for this is that when the converted flow rate of both phases of the medium is low, a severe segmental plug flow occurs in the mixing pipeline system. In the liquid plug outflow stage, the gas and liquid phase flow rates in the mixing piping system are basically stable, so there is little difference in the potential energy of the liquid at the target location. In addition, because the inclination angle of the downturned pipe is only -5°, from a macroscopic point of view, the positional potential energy at the location of P1 is slightly larger than that at the bottom of the riser, however, due to the large friction loss in the pipeline, its value even exceeds the difference in the positional potential energy of the two. From Bernoulli’s equation, it can be seen that the pressure potential energy of the inlet of the downturned pipe will be greater than that of the bottom of the riser, i.e., P1>P2.

The maximum pressure of the severe section plug flow is the highest limit that the pressure measurement P2 at the bottom of the riser can reach in a complete cycle, and this value generally occurs in the liquid plug outflow stage. The experimental curve of the maximum pressure of the severe section plug flow with the change of the converted gas velocity is shown in Fig. 5.

From Fig. 5, it can be seen that P_max will decrease with the increase of the discounted air velocity. When the V_SL reaches 0.1512m/s, 0.2103m/s and 0.2541m/s respectively, the three folding lines are approximately horizontal in the interval of 0.03m/s~0.17m/s, which means that under the above experimental conditions, even if the discounted air velocity increases, the P_max is still basically stable. While performing actual experimental measurements, a typical severe segmental plug flow was observed.

Under the condition that the converted liquid velocity is a constant value, increasing the inlet gas-phase flow rate, the flow pattern in the mixing piping system changes from the typical severe blockage flow to a transitional flow pattern. If the inlet gas-phase flow rate is increased again, the liquid plug can not be generated in the mixing piping system, and the severe plug flow disappears. The size of P_max is determined by the combined effect of the liquid column height in the vertical riser and the friction loss, in which the hydrostatic pressure plays a major role. When the typical severe blockage flow in a mixing piping system is in the stage of liquid plug outflow, the liquid plug in the vertical riser reaches the top and its length reaches the limit, and will remain stable thereafter, and the pressure measurement at the target position also reaches the limit and remains stable. The maximum pressure in this flow pattern is less than the P_max of typical severe segmental plug flow because there is no obvious plug outflow, i.e., the liquid column in the vertical riser does not reach the top, and when the flow pattern in the system is transitional, the plug length (i.e., hydrostatic pressure) will slowly become smaller as the inlet gas-phase flow rate increases. As a result, P_max shows a stable and then decreasing trend with the increase of the horizontal coordinate (converted gas velocity).

The experimentally obtained maximum pressure variation curve of severe section plug flow with the converted liquid velocity is shown in Fig. 6. As can be seen from Fig. 6, when the converted gas velocity is 0.0568 m/s, the flow pattern in the mixing pipeline system is typical severe segmental plugging flow in the interval of 0.04 m/s to 0.43 m/s in the horizontal coordinate (converted liquid velocity), and the magnitude of P_max is kept at about 77.60 kPa. When the converted gas velocity is increased to 0.1524m/s, the flow pattern in the system is transitional flow pattern, because of the increase of the inlet liquid phase flow rate, the height of the liquid column formed in the vertical riser grows, so the P_max shows a rising trend. By increasing the inlet liquid-phase flow rate again, the liquid column in the vertical riser will be able to reach the top, and the flow pattern is thus transformed into a typical severe segmental plugging flow, and the P_max is maintained at about 77.30 kPa. As a result, Pmax shows an increasing and then stabilizing trend with the increase of the horizontal coordinate (converted liquid velocity).

4.1.2

Changes in the magnitude of pressure fluctuations in the segment plug flow

In order to quantitatively analyze the relative magnitude of the hazard of severe section plugging, this paper further investigates the change in its pressure fluctuation amplitude. Pressure fluctuation amplitude P_amp, i.e.: riser bottom pressure measurement P2 in a complete cycle, the difference between its great value and the smallest value.

The experimentally obtained curves of the amplitude of pressure fluctuations of the severe section plug flow with the converted gas velocity are shown in Fig. 7.

From Fig. 7, it can be seen that the pressure fluctuation amplitude decreases with the increase of the horizontal coordinate when the converted liquid velocity is 0.0524m/s, 0.0635m/s and 0.0937m/s, respectively. In addition, the amplitude of pressure fluctuation increases and then decreases with the increase of the horizontal coordinate when the converted liquid velocity is 0.1512m/s, 0.2103m/s and 0.2541m/s, respectively.

Combined with the observation of the two-phase flow in the experiment, the two-phase flow in the mixing pipeline system is a typical severe segmental plugging flow in the experimental conditions covered by the left side of the turning point of each folding line in the figure, while the right side shows a transitional flow pattern. Thus, it can be obtained that when it is a typical severe section plug flow, P_amp increases with the increase of the horizontal coordinate. When it is a transitional flow type, P_amp decreases with the increase of the horizontal coordinate. Under the condition that the converted liquid velocity is a constant value, increasing the inlet gas-phase flow rate, the flow pattern in the mixing pipeline system will change from the typical severe segment plugging flow to the transitional flow pattern.

The experimentally obtained pressure fluctuation amplitude with converted liquid velocity for the severe section plug flow is shown in Fig. 8. From Fig. 8, it can be seen that when the V_SG is 0.0438 m/s, the pressure fluctuation amplitude decreases with the increase of the horizontal coordinate. When V_SG is 0.1365m/s, the pressure fluctuation amplitude increases and then decreases with the increase of the horizontal coordinate. The other four folds show an increasing trend with the increase of the transverse coordinate. Combined with the observation of the two-phase flow in the experiment, under the experimental conditions covered by the left side of the maximum value of each folded line in the figure, the flow pattern in the mixing pipeline system is a transitional flow pattern, and the right side is a typical severe segmental plug flow. Therefore, it can be concluded that P_amp decreases with the increase of the horizontal coordinate when it is a typical severe segmental plug flow. When it is a transitional flow type, P_amp increases with the increase of the horizontal coordinate. Under the condition that the converted gas velocity is a constant value, increasing the inlet liquid-phase flow rate, the flow pattern in the mixing pipeline system will be changed from a transitional flow pattern to a typical severe blockage flow.

4.2

PID system controllability analysis

In this paper, a PID control system is designed based on the oil and gas pipeline segment plug flow control strategy, and its controllability is analyzed.

4.2.1

PID control of riser bottom pressure

The control effect of the PID controller on the pressure P₁ at the bottom of the riser is shown in Figure 9.

As can be seen from Figure 9, the control and follow-up effects of the PID controller on the pressure at the bottom of the riser meet the requirements. Before 1350s, the change of the pressure at the bottom of the riser conforms to the characteristics of the pressure change at the bottom of the riser under severe slug flow conditions, showing the characteristics of periodicity and fluctuation, after 1350s, the PID controller starts to act, and the peak value of the pressure P₁ at the bottom of the riser gradually decreases and then follows the set value of 71.8bara. Then, at 2650s, the system setpoint changes in steps, and the PID controller controls the pressure value to follow the setpoint. At 4400s, the system setpoint changes step again, and the PID controller can still follow the setpoint of 71.8bara well, which indicates that the PID controller has achieved a good control effect and following effect in the control of the pressure at the bottom of the riser with severe slug flow.

At this time, the variation of the operating variable valve opening z is shown in Fig. 10. From Fig. 10, it can be seen that the valve opening of the PID controller controlling the severe segmental plug flow of the riser shows a staged trend, and it has been maintained at the initial throttle valve opening of 0.228 before 1350s, and after 1350s, in order to inhibit the severe segmental plug flow condition of the riser, the valve opening decreases to 0.079, and then rises to 0.626, and then the segmental plug flow is controlled and the valve opening gradually The valve opening gradually stabilized. Then 2650s due to the change of the reference value of the valve opening also changed, in order to make each characteristic parameter can be converged to the reference value to make it become stable, the valve opening also changed, firstly, it rose to 0.474 and then fell to 0.164, and then tended to level off. Then in 4400s after another step change, the valve opening and first fell to 0.082 and then rose to 0.476, after the reference value is no longer changed, the valve opening gradually converge to 0.228. From the changes in the valve opening can be seen, the PID controller effectively inhibit the riser serious section of the plugging flow, while the system’s better responsiveness to track the set value very quickly, so that the system is stable. Stabilization.

4.2.2

PID control of pressure at the top of the standpipe

The control effect of the PID controller controlling the pressure at the top of the riser is shown in Figure 11.

As can be seen from Figure 11, the PID controller can also achieve a better control effect by controlling the pressure P₂ at the top of the riser. After the 1350s controller starts to function, it can be clearly seen that the peak value of the fluctuation becomes smaller, the maximum and minimum values are 52.21bara and 51.29bara respectively, the first 2650s step change, the reference value is set to 51.9bara step to 51.1bara, in 4400s it is the opposite, the simulation process of the two reference value step changes can well show the better control effect and following effect of the PID controller, indicating that the system can be stably controlled.

4.2.3

PID control of flow mixing density at the top of the standpipe

The control effect of the PID controller controlling the logistics mixing density rho _T at the top of the riser is shown in Fig. 12. From Figure 12, it can be seen that the PID controller to control the top of the riser logistics mixing density rho _T can also achieve better control results. It is known that the average density of the liquid phase is 967.288kg/m³, the average density of the gas phase is 1.0124kg/m³, and the average gas content of the logistics is 40.37%, then when the material flow rate is mixed at the top of the standpipe and is controlled to be smooth, the mixing density of the material flow rate is: (14) $r h o_T = 967.288 \times (1 - 40.37 %) + 1.0124 \times 40.37 % = 577.203 k g / m^{3}$

Then when the final PID controller controls the mixing density of the logistics at the top of the riser, the stabilization value is stabilized at 577.2 kg/m³.

As can be seen from Fig. 12, before 1350s, the mixing density is also in the severe section plugging flow condition, and the great periodic fluctuation occurs, when the PID controller starts to act, rho _T firstly decreases to 176.4kg/m³ from 1350s, and then after 215s, rho _T rises to 661.5kg/m³, and after that, it gradually tends to the reference value of 577.2kg/m³. At 2650s, due to the step change of the system, the valve opening changes with it, at this time rho _T also changes, but because the system has been stabilized before 2650s, the tendency of instability is smaller. 2650s, due to the step change of the system, the valve opening is changed, at this time 33 also changes, but because the system has been stabilized before 2650s, the trend of instability is smaller, so after the step change in 2650s, the system can be stabilized faster, in 66s from the maximum value of 597.3kg/m³ to 348.5kg/m³, and then converge to the reference value soon after. Similarly, in the step change of 4400s, the PID controller also stabilizes the system very quickly, and finally the system converges to the reference value of 577.2kg/m³. For the inhibitory control of rho _T, the simulation of the two step changes of the reference value can well show the good control effect and the following effect of the PID controller, which indicates that the system can be stabilized and stabilized very quickly.

4.2.4

PID control of logistics mass flow at the top of the riser

The control effect of the PID controller controlling the logistics mass flow rate W at the top of the riser is shown in Fig. 13.

As can be seen from Fig. 13, the PID controller controlling the logistics mass flow rate W at the top of the riser can also achieve a better control effect. For the logistics mass flow rate W, it is known that the liquid-phase mass flow rate is 9.85 kg/s, the gas-phase mass flow rate is 0.641 kg/s, and the total logistics mass flow rate is 10.491 kg/s. Therefore, when the material flow rate is mixed at the top of the riser and controlled to a smooth state, the So when the material flow is mixed at the top of the riser and controlled to be smooth, the mass flow rate of the stream can reach the reference value of 10.491kg/s.

As can be seen from Figure 13, before 1350s, the mass flow rate of the logistics in the pipeline is also in a serious section of the plug flow condition, a huge fluctuation occurred periodically, when the PID controller began to play a role in the W from 1350s began to decline and then rise to 16.95kg/s, from the highest point to stabilize the value of only 148s, and then gradually converge to the reference value of 10.491kg/s. At 2650s, as the system undergoes a step change, the valve opening changes with it, at this time, W also changed. 2650s, due to the step change of the system, the valve opening is changed, at this time, W also changed, at this time, due to the sudden change of the system, the mass flow rate of the logistics for the change of the pressure at the bottom of the standpipe will react strongly, so at this time, W firstly rises to 17.29kg/s and then falls to 7.04kg/s, the whole process only took 32s, and then quickly recovered to the reference value of the neighborhood. The whole process took only 32s, after which it quickly recovered to the vicinity of the reference value. Similarly, in the step change of 4400s, because the bottom pressure of the pipe is a small to large step, the bottom pressure of the pipe is increasing, the mass flow rate of the logistics at the top of the pipe riser firstly decreases and then rises, but the range of fluctuation is small, in the range of 7.04kg/s~13.85kg/s, and then it quickly converges to the reference value of 10.491kg/s. For the inhibitory control of W, the two times of For W suppression control, the simulation of the step change of the reference value can well show the better control effect and following effect of the PID controller, indicating that the system can be stabilized and stabilized quickly.

In summary, it can be seen that the segment plug flow control strategy combining the numerical simulation method and the improved PID control system in this paper is effective in controlling the segment plug flow in oil and gas pipelines.

5

Conclusion

In this paper, a numerical simulation model of unsteady flow multiphase flow in oil and gas pipeline is constructed by combining computational fluid dynamics and fluid volume model, and a PID control strategy for segment plugging flow is designed and the effectiveness of the strategy is analyzed.

Through the experiments on the pressure characteristics of severe blockage flow in oil and gas pipelines, it is found that the maximum pressure is stable and then decreases with the increase of the converted gas velocity, and increases and then stabilizes with the increase of the converted liquid velocity. The magnitude of pressure fluctuation under the typical severe sectional flow pattern increases with the increase of gas velocity and decreases with the increase of liquid velocity. The amplitude of pressure fluctuation under the transition flow type decreases with the increase of gas velocity and increases with the increase of liquid velocity.

Meanwhile, the results of the PID automatic control study of severe section plugging show that the PID system designed based on the strategy of this paper is able to control the pressure in the middle of the vertical riser in the oil and gas mixing pipeline system to fluctuate within the expected range, thus successfully suppressing the severe section plugging. Under the influence of the throttle valve PID automatic control, the bottom pressure of the riser, the top pressure of the riser, the mixing density of the logistics at the top of the riser, and the mass flow rate of the logistics at the top of the riser are controlled at the reference stable values of 71.8 bara, 51.1 bara/51.7 bara, 577.2 kg/m³, and 10.491 kg/s, respectively, which indicates that the PID system can help realize the effective control of section plugging flow in oil and gas pipelines. It shows that the PID system can help to realize the effective control of the section plug flow in the natural gas pipeline, which verifies the effectiveness of the section plug flow control strategy proposed in this paper.

Langue:: Anglais

Périodicité:: 1 fois par an
Sujets de la revue:: Sciences de la vie, Sciences de la vie, autres, Mathématiques, Mathématiques appliquées, Mathématiques générales, Physique, Physique, autres

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Numerical simulation of unsteady flow multiphase flow in oil and gas pipelines and control strategy of section plug flow

Xin Tian

Xin Liu

Guoying Lu

Jian Cui

Publié en ligne: 19 mars 2025

Reçu: 23 oct. 2024

Accepté: 09 févr. 2025

DOI: https://doi.org/10.2478/amns-2025-0373

Mots clésComputational fluid dynamics, Fluid volume modeling, PID control, Numerical simulation, Segmental plug flow control

© 2025 Xin Tian et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Mots clés
Computational fluid dynamics, Fluid volume modeling, PID control, Numerical simulation, Segmental plug flow control