Multiphase flow pump flow performance modeling method fusing process knowledge and graph convolutional networks

Abstract

The application discloses a multiphase flow pump flow characteristic modeling method fusing process knowledge and a graph convolution network, and comprises the following steps: 1) collecting input and output training samples under different multiphase conveying conditions, and establishing a global TGCN model of the reciprocating multiphase flow pump flow characteristic; 2) based on the process knowledge of the reciprocating multiphase flow pump and the prediction result of the GTGCN, identifying three stages of the multiphase flow pump flow characteristic under a new condition; 3) intercepting training data of all mutation stages, establishing a local TGCN model of the mutation stage, and optimizing the prediction result of the mutation stage in step 2); 4) using the process knowledge, optimizing the prediction result of the opening hysteresis and the sine stage obtained in step 2); 5) combining the optimization results of steps 3) and 4), and completing online prediction of the input sample set flow characteristic under the new condition; and the application can realize modeling and prediction of the reciprocating multiphase flow pump flow characteristic under time-varying multiphase conveying conditions.

Description

Technical Field

[0001] This invention relates to the technical field of modeling and predicting important parameters in the design phase of multiphase flow pumps, specifically to a method for modeling the flow characteristics of reciprocating multiphase flow pumps that is suitable for time-varying operating conditions of mixed oil and gas transportation and integrates process knowledge and time-series graph convolutional networks. Background Technology

[0002] Oil and gas co-transport technology can effectively improve oil extraction efficiency and reduce extraction costs. Because oil well products are a mixture of oil, gas, water, and other media in varying proportions, the heterogeneous phase interactions generated during actual co-transport will force irregular movements of the inlet and outlet valves of the reciprocating multiphase flow pump, leading to delayed valve opening and closing, and thus... Figure 1 The diagram illustrates the flow characteristics of a reciprocating multiphase flow pump. Due to the compressibility of gases, the discharge valve fails to open immediately at its designed opening point of crank angle θ = 180°, resulting in a lag phase where the flow rate Q is approximately zero. As the pressure within the pump chamber gradually increases, the discharge valve opens; at the moment of opening, the high-pressure gas generated during the pump compression process carries the transported medium and rapidly surges out, reaching its maximum flow rate. As the mixed transported medium is discharged from the pump chamber, the pump chamber pressure drops rapidly, and the flow rate also fluctuates rapidly and gradually decreases, forming a sudden change phase. Finally, the pump chamber pressure approaches the pump outlet pressure, the gas is no longer compressed, and the flow rate of the multiphase flow pump approaches the theoretical value for a reciprocating pump transporting a pure liquid phase, i.e., the flow characteristics exhibit a sinusoidal phase. These flow pulsations generated during the discharge process of the reciprocating multiphase flow pump, accompanied by pressure fluctuations, cause noise and vibration in transport equipment, including the multiphase flow pump, reducing transport efficiency and potentially leading to equipment failure. Therefore, it is necessary to optimize the pump's structural parameters based on actual mixed transport conditions to expand the pump's applicability and reduce the impact of flow pulsations. Since flow rate is a key parameter in the engineering design of multiphase flow pumps, establishing a mathematical model between the flow characteristics of multiphase flow pumps and the parameters of complex oil and gas mixed transportation is of great significance for optimizing the engineering design of multiphase flow pumps and ensuring their stable operation under design conditions.

[0003] Mechanistic models and computational fluid dynamics (CFD) simulation models are the two main methods for studying the flow characteristics of multiphase flow pumps. Due to the lack of effective methods for identifying characteristic parameters such as multiphase flow patterns and phase content, most mechanistic models assume that the multiphase flow exhibits stable homogeneous flow with conserved mass and energy during transport. These models fail to realistically reflect the complex characteristics of multiphase flow, such as the velocity differences and dispersion of each phase, interphase interactions, leakage, and energy losses. Therefore, the calculation results obtained based on mechanistic models have a very limited scope of application.

[0004] Given the complexity and limitations of mechanistic models in describing multiphase flow phenomena, Computational Fluid Dynamics (CFD), with its advantages in handling complex flow calculations, has been widely used to solve multiphase flow engineering problems, leading to the development of CFD models for the flow characteristics of multiphase pumps such as twin-screw, vortex, and reciprocating pumps. However, most of these CFD models employ single multiphase and turbulence models, which are unsuitable for describing the entire process of multiphase flow influenced by numerous complex coupling factors, resulting in multiple flow patterns. Therefore, the research results of CFD on multiphase flow are rarely directly applied to engineering practice.

[0005] In recent years, some data-driven empirical models, which do not require a substantial understanding of the complex internal mechanisms of multiphase flow, have gradually been used to solve some problems related to multiphase flow. However, given the time-varying operating conditions such as well gas cut and bottom hole pressure, as well as the limitations of multiphase flow testing technology, conveniently, quickly, and accurately obtaining multiphase flow parameters within pumps remains a challenge for industries such as petrochemicals, and cannot provide a large amount of reliable modeling data for subsequent conventional data-driven modeling methods.

[0006] To address the aforementioned issues, a method for modeling the flow characteristics of reciprocating multiphase flow pumps by integrating process knowledge and temporal graph convolutional networks (PKTGCN) has been proposed. TGCN can effectively learn the topological structure and process temporal information between variables, capturing the coupling relationships between input variables and between input and output variables. Simultaneously, process knowledge of multiphase flow can assist TGCN modeling, reducing its dependence on large amounts of modeling data and improving the model's generalization ability. A literature search revealed no reports on multiphase flow pump flow characteristic modeling methods that integrate process knowledge and temporal graph convolutional networks. Summary of the Invention

[0007] This invention aims to overcome the aforementioned shortcomings of existing technologies by providing a method for modeling the flow characteristics of reciprocating multiphase flow pumps that integrates process knowledge and graph convolutional networks. This method can learn the topological structure and temporal information between input process variables based on a limited sample, capturing the relationship between the flow characteristics of multiphase flow pumps and complex oil and gas mixed-transport conditions. This assists engineers in better understanding the internal mechanisms of multiphase flow, thereby optimizing the engineering design of multiphase flow pumps.

[0008] A method for modeling the flow characteristics of multiphase flow pumps by fusing process knowledge and graph convolutional networks includes the following steps:

[0009] 1) Collect input and output training samples under different mixed transport conditions and establish a global TGCN (GTGCN) model of the flow characteristics of reciprocating multiphase flow pump;

[0010] First, we analyze the factors affecting the flow characteristics of the reciprocating multiphase flow pump and determine the variables of the input matrix X, i.e., the nodes of the GTGCN model.

[0011] Secondly, input-output training samples were collected for the pump crank angle range of θ = 180° to 360° under different mixed-transport conditions. Where x m For the m-th input sample, y m Let f(X,A) be the m-th output sample, where M is the total number of samples. Taking the GTGCN model with two hidden layers as an example, the predicted output f(X,A) of GTGCN can be obtained as follows:

[0012]

[0013] In the formula, σ(·) is the activation function and ReLU is the linear rectification function. In this matrix, A is the adjacency matrix, and I is the identity matrix. Let A be the degree matrix of A. n,m I n,m Let A and W0 represent the nth row and mth column elements of A and I, respectively, and N be the number of nodes. W0 represents the weight matrix between the input layer and the hidden layer, and W1 represents the weight matrix between the hidden layer and the output layer. During the GTGCN training process, A, W0, and W1 are usually initialized arbitrarily first, and then the root mean square error shown in formula (2) is used to optimize A, W0, and W1.

[0014]

[0015] in, It is y m The predicted values. When the loss reaches its minimum, the values ​​of A, W0, and W1 are confirmed, and the GTGCN model shown in formula (1) completes the training process.

[0016] 2) Based on the process knowledge of reciprocating multiphase flow pumps and the prediction results of GTGCN, three stages of the flow characteristics of multiphase flow pumps under new operating conditions are identified;

[0017] First, using the GTGCN model trained in step (1), the input sample sequence of the new working condition is processed. The flow characteristics are used to predict, where L is the number of input samples.

[0018] Secondly, based on the process knowledge of multiphase flow pumps, the flow characteristics predicted by the GTGCN model are divided into three stages: start-up hysteresis, abrupt change, and sinusoidal flow. Because the GTGCN model has a strong ability to capture the topological structure and timing information between process variables, the characteristic of the flow rate rapidly increasing from zero to its peak value at the instant the discharge valve opens can be identified. That is, the GTGCN model can identify the connection point x in the start-up hysteresis and abrupt change stages. q , q∈L. Furthermore, based on the theoretical formula for reciprocating pumps delivering pure liquid phase, for x... q The traffic corresponding to the following samples Perform calculations

[0019]

[0020] In the formula, D is the inner diameter of the pump cylinder, ω is the angular velocity of the pump, r is the crank radius, λ is the ratio of r to the connecting rod length, and θ is the angular velocity of the pump. l It is x l The corresponding crank angle.

[0021] Furthermore, Compared with GTGCN's predictions Comparison, i.e.

[0022]

[0023] Here, η is a positive coefficient. Typically, for the same multiphase flow pump, since its sinusoidal flow characteristics can be approximately described by theoretical formulas, the GTGCN model applies to all input samples. The flow characteristics in the sinusoidal phase have good predictive performance. Therefore, when δ l When equation (3) is satisfied, x l Input samples that fall into the mutation phase are considered input samples; otherwise, they fall into the sinusoidal phase. Furthermore, the larger the η value, the fewer input samples will be classified as belonging to the mutation phase. When the first point x of the sinusoidal phase is identified... i When i∈L, the input samples for the start-up lag stage of the multiphase flow pump flow characteristics under the new operating condition can be obtained as {x1,…,x q-1 The input sample for the mutation phase is {x}. q ,…,x i-1 The input sample for the sinusoidal phase is {x}. i ,…,x L}

[0024] 3) Extract training data from all mutation stages, establish a local TGCN (LTGCN) model for the mutation stage, and optimize the prediction results of the mutation stage in step (2).

[0025] Given the rapid nonlinear characteristics of the mutation stage, it is difficult for a limited number of modeling samples to accurately describe the characteristics of this stage. Therefore, a new local TGCN model is established to optimize the prediction results of the mutation stage in step (2).

[0026] First, from The training data for all mutation stages is extracted from the data.

[0027] Secondly, given Figure 1 The characteristics of the abrupt change phase are highly correlated with the opening point of the discharge valve. Therefore, the angle of the abrupt change phase under each operating condition is replaced by the difference between the angle and the opening point angle under the same operating condition. The training data S contains samples x of the abrupt change phase under a certain operating condition.j For example, its crank angle θ j Using θ j The starting point θ under the same working conditions o The difference Δθ j To replace, that is

[0028] Δθ j =θ j -θ o (5)

[0029] Thus, using formula (5) from The training data obtained from all mutation stages under different working conditions were transformed to obtain training samples for building the LTGCN model. J∈M is the number of training data in the mutation phase. The LTGCN model is constructed using formulas (1) and (2).

[0030] Finally, using formula (5), the input sample {x} of the mutation stage under the new working condition obtained in step (2) is transformed into the input sample {x}. q ,…,x i-1 The turning angle in} is replaced by the difference between the turning angle θq of the starting point xq, and the flow characteristics are re-predicted using the trained LTGCN model to replace the prediction results of the GTGCN model for the flow characteristics during the sudden change phase in step (2).

[0031] 4) Optimize the prediction results of the start-up lag and sinusoidal phase obtained in step (2) using process knowledge;

[0032] based on Figure 1 The provided process knowledge of the multiphase flow pump is used to analyze the input samples {x1,…,x} of the start-up hysteresis phase obtained in step (2). q-1 The predicted flow characteristics of} are set to 0 to replace the predicted flow characteristics of the GTGCN model in step (2) for the start-lag stage. The theoretical formula (3) is used to evaluate the input sample {x} for the sinusoidal stage. i ,…,x L The calculation is performed to replace the prediction results of the GTGCN model for the sinusoidal stage flow characteristics in step (2).

[0033] 5) Combine the optimization results of steps (3) and (4) to complete the input sample set under the new working condition. Online prediction of traffic characteristics.

[0034] The beneficial effects of this invention are as follows:

[0035] The proposed method for modeling the flow characteristics of multiphase flow pumps, which integrates process knowledge and graph convolutional networks, enables the modeling and prediction of the flow characteristics of reciprocating multiphase flow pumps under time-varying mixed-transport conditions. Compared to mechanistic models and CFD simulation models, this method utilizes a piecewise modeling approach, providing an engineering-friendly implementation method. Compared to conventional data-driven empirical modeling, this method integrates process knowledge, offering a modeling approach based on small samples. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of the flow characteristics of the reciprocating multiphase flow pump of the present invention;

[0037] Figure 2 This is a flowchart of the method of the present invention;

[0038] Figure 3 This is a comparison chart of the stage identification results of the GTGCN model and the GPR model;

[0039] Figure 4 This is a comparison chart of the prediction results of the LTGCN, GTGCN, and GPR models for the mutation stage;

[0040] Figure 5 This is a comparison chart showing the results of optimizing the traffic characteristics predicted by the GTGCN model using the PKTGCN model. Detailed Implementation

[0041] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0042] like Figure 2 As shown, the method for modeling the flow characteristics of a multiphase flow pump by fusing process knowledge and graph convolutional networks includes the following steps:

[0043] 1) Collect input and output training samples under different mixed transport conditions and establish a global TGCN (GTGCN) model of the flow characteristics of reciprocating multiphase flow pump;

[0044] Based on engineering experience with reciprocating multiphase flow pumps, the pump inlet pressure p is determined. s Pump outlet pressure p d Pump chamber pressure p c The gas content β at the pump inlet under standard atmospheric pressure o Gas content β in the pump chamber c =P o β o / (P c (1-β o )+P o β oPump chamber temperature T and pump angular velocity ω are both measurable factors affecting the flow rate of a reciprocating multiphase flow pump. Furthermore, given that the flow characteristics of a reciprocating multiphase flow pump are typically described by a curve with the crank angle (θ = ωt = 180°~360°, t being time) on the x-axis and the flow rate on the y-axis, the nodes of the GTGCN model, i.e., the variables in the input matrix X, are defined as follows: The corresponding flow rate is the output variable. M is the total number of samples.

[0045] The structural parameters of the experimental reciprocating multiphase flow pump prototype are: D = 0.115 m, r = 0.045 m, λ = 0.125, and the design parameters are: ω = 8π rad / s, P s =0.2~0.4MPa, P d =1.0~3.0MPa, β o =0~0.8, room temperature around 300K. The experiment collected 706 samples in 12 groups from 12 different mixed transport conditions, of which 9 groups (S1,…,S9) were used for training, and 3 groups (S……S9 ...S9…S9…S9…S 10 ,S 11 ,S 12 () is used for testing. The GTGCN model is trained using formulas (1) and (2).

[0046] 2) Based on process knowledge of reciprocating multiphase flow pumps and prediction results from GTGCN, three stages of the flow characteristics of multiphase flow pumps under new operating conditions are identified; Figure 3-5 (This is a comparison of the prediction results and experimental results of one of the test sets of this invention)

[0047] With S 10 For example, the prediction results of the GTGCN model are as follows: Figure 3 As shown. It can be seen that GTGCN captures the abrupt change in flow rate at the moment the discharge valve opens, accurately identifying point 1 of the abrupt change phase, namely x4. Furthermore, given that the GTGCN model has a good understanding of S... 10 The predictive performance of the sinusoidal phase is good, so in this implementation process, η = 1 is set, and the first point of the sinusoidal phase, i.e., x, is identified using formulas (3) and (4). 16 Therefore, S 10 The three phases of the flow characteristics were identified: the input sample for the start-up lag phase was {x1, x2, x3}, the input sample for the mutation phase was {x4, ..., x...}. 15 The input sample for the sinusoidal phase is {x}. 16 ,…,x 58}

[0048] 3) Extract training data from all mutation stages, establish a local TGCN (LTGCN) model for the mutation stage, and optimize the prediction results of the mutation stage in step (2).

[0049] 119 mutation stage samples were extracted from 706 training samples, and their crank angle θ was transformed using formula (5). Subsequently, the LTGCN model was trained based on formulas (1) and (2), and the input samples {x4,…,x} from the mutation stage in step (2) were processed. 15 Re-predicting was performed, and the prediction results are shown below. Figure 4 As shown.

[0050] 4) Optimize the prediction results of the start-up lag and sinusoidal phase obtained in step (2) using process knowledge;

[0051] Set the output flow of the input sample {x1,x2,x3} in the hysteresis phase to zero, and use formula (3) to adjust the output flow of the input sample {x1,x2,x3} in the sine phase. 16 ,…,x 58 The output flow rate is calculated.

[0052] 5) Combine the optimization results of steps 3) and 4) to complete the input sample set under the new working condition. Online prediction of traffic characteristics.

[0053] The optimization results obtained in steps 3) and 4) are used to replace the prediction results of the GTGCN model in step (2), thus obtaining the prediction results of the PKTGCN model proposed in this invention. See [link to relevant documentation]. Figure 5 As shown.

[0054] Repeat steps 2 through 5 to obtain prediction results for two more test samples.

[0055] The results of stage identification of the flow characteristics of the three test samples by the GTGCN model proposed in this method are compared with the stage identification results and experimental results of the GPR model, as shown in Table 1.

[0056] Table 1 shows the stage identification results of the flow characteristics of the test sample set using the method of the present invention (the numbers in parentheses represent the actual number of sample points).

[0057]

[0058] As shown in Table 1, the stage identification results of the flow characteristics of the three sample sets obtained by the method of this invention are basically consistent with the actual results. This indicates that the proposed time-series graph convolutional network, with its powerful ability to capture the topological structure and temporal information between process variables and aided by knowledge of multiphase flow pump processes, accurately identified the three stages of the predicted flow characteristics curve of multiphase flow pumps under new operating conditions based on a limited number of modeling samples.

[0059] The prediction results of the LTGCN model proposed in this method on the flow characteristics of the abrupt change phase of three test samples were compared with the prediction results of the GTGCN and GPR models and the experimental results. The maximum absolute value of error (ME) and mean squared error (RMSE), two commonly used indicators, were selected as evaluation criteria. The definitions of the two evaluation criteria are as follows:

[0060]

[0061]

[0062] For both ME and RMSE, lower values ​​are better. The comparison results are shown in Table 2.

[0063] Table 2. Predictive performance of the method of the present invention during the abrupt change phase of flow characteristics in the test sample set (minimum value marked in bold).

[0064]

[0065] As shown in Table 2, the local model LTGCN proposed in this invention can better capture the flow characteristics of each test sample during the abrupt change phase. Compared with the global model GTGCN used for phase identification, the LTGCN model considers the correlation between the characteristics of the abrupt change phase and the opening point of the discharge valve, and can more accurately describe the rapid nonlinear characteristics of the abrupt change phase. Compared with the global GPR model, the LTGCN model utilizes a graph network structure to more effectively establish the topological relationships between input variables.

[0066] The prediction results of the PKTGCN model proposed in this method for all stages of flow characteristics of three test samples were compared with the prediction results of GTGCN and experimental results. The corresponding ME and RMSE indices are shown in Table 3.

[0067] Table 3. Predictive performance of the method of the present invention on the flow characteristics of the test sample set (minimum value marked in bold).

[0068]

[0069] As shown in Table 3, by utilizing the process knowledge of reciprocating multiphase flow pumps, assigning a value of 0 to the predicted flow rate after start-up lag, and replacing the predicted flow rate of the sinusoidal part with the calculation results of the theoretical formula, the prediction performance of the three test samples was further improved.

[0070] Therefore, the modeling method proposed in this invention, which integrates process knowledge and graph convolutional networks, is universal and versatile, capable of accurately predicting the flow characteristics of reciprocating multiphase flow pumps based on limited modeling samples. Furthermore, its simple and reliable segmented implementation method reduces design complexity, lowers design costs, and saves modeling time, providing an effective auxiliary means for current reciprocating multiphase flow pump design.

[0071] The embodiments described in this specification are merely examples of implementations of the inventive concept. The scope of protection of this invention should not be considered as limited to the specific forms stated in the embodiments. The scope of protection of this invention also extends to equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.

Claims

1. A method for modeling the flow characteristics of multiphase flow pumps by integrating process knowledge and graph convolutional networks, characterized in that, Includes the following steps: Step 1) Collect input and output training samples under different mixed transport conditions and establish a GTGCN model of the flow characteristics of a reciprocating multiphase flow pump; Step 2) Based on the process knowledge of reciprocating multiphase flow pumps and the prediction results of GTGCN, identify the three stages of the flow characteristics of multiphase flow pumps under the new operating conditions; The specific process of step 2) is as follows: Using the GTGCN model trained in step 1), the input sample sequence for the new working condition is processed. The traffic characteristics are used to predict, where L is the number of input samples; Based on the process knowledge of multiphase flow pumps, the flow characteristics predicted by the GTGCN model are divided into three stages: start-up hysteresis, abrupt change, and sinusoidal flow. The GTGCN model can identify join points that initiate hysteresis and abrupt transition phases. ; Based on the theoretical formula for reciprocating pumps delivering pure liquid phase, The traffic corresponding to the following samples Perform the calculation: ； In the formula, D is the inner diameter of the pump cylinder, ω is the angular velocity of the pump, r is the crank radius, and λ is the ratio of r to the connecting rod length. yes The corresponding crank angle; Will Compared with GTGCN's predictions Comparison, i.e. ； Where η is a positive coefficient; when When formula (3) is satisfied, Input samples belonging to the mutation phase are considered input samples; otherwise, they belong to the sinusoidal phase. Furthermore, the larger the η value, the fewer input samples fall into the mutation phase. When the first point of the sinusoidal phase is identified... At that time, the input sample for the start-up lag stage of the multiphase flow pump flow characteristics under the new operating condition can be obtained as follows: The input sample for the mutation phase is The input sample for the sinusoidal phase is ; Step 3) Extract training data for all mutation stages, build an LTGCN model for the mutation stages, and optimize the prediction results for the mutation stages in Step 2); The specific process of step 3) is as follows: Rebuild an LTGCN model and optimize the prediction results for the mutation stage in step 2); from The training data for all mutation stages are extracted from the data; the rotation angle of each mutation stage under each working condition is replaced by the difference between the rotation angle and the starting point rotation angle under the same working condition. Using training data S as samples of the mutation stage under a certain working condition For example, its crank angle θ j use Opening point under the same working conditions difference To replace, that is ； Using formula (5) from The training data obtained from all mutation stages under different working conditions were transformed to obtain training samples for building the LTGCN model. , This is the number of training data points during the mutation phase; Using formula (5), the input samples of the mutation stage under the new working condition obtained in step 2) are processed. The corner in the middle is also used in relation to the opening point. The corner The difference is replaced, and the trained LTGCN model is used to re-predict its flow characteristics, replacing the prediction results of the GTGCN model for the flow characteristics during the abrupt change phase in step 2). Step 4) Optimize the prediction results of the start-up lag and sinusoidal phase obtained in Step 2) using process knowledge; Step 5) Combine the optimization results of steps 3) and 4) to complete the input sample set under the new working condition. Online prediction of traffic characteristics.

2. The method for modeling the flow characteristics of a multiphase flow pump by fusing process knowledge and graph convolutional networks according to claim 1, characterized in that, The specific process of step 1) is as follows: Analyze the factors affecting the flow characteristics of a reciprocating multiphase flow pump and determine the variables of the input matrix X, i.e., the nodes of the GTGCN model; Collect pump crank angle under different mixed transportation conditions Interval input / output training samples ,in For the m-th input sample, Let M be the m-th output sample, where M is the total number of samples; Taking the GTGCN model with two hidden layers as an example, the predicted output of GTGCN can be obtained. for: ； In the formula, It is an activation function, ReLU is a linear rectified function. A is the adjacency matrix, and I is the identity matrix. Let A be the degree matrix. , Let A and I represent the nth row and mth column elements respectively, and N be the number of nodes. This represents the weight matrix between the input layer and the hidden layer. A represents the weight matrix between the hidden layer and the output layer; during GTGCN training, A, and First, initialize arbitrarily, then use the root mean square error shown in formula (2) to evaluate A. and Optimize; ； in, yes The predicted value, when the loss reaches its minimum, A, and The value of is confirmed, and the GTGCN model shown in formula (1) completes the training process.

3. The method for modeling the flow characteristics of a multiphase flow pump by fusing process knowledge and graph convolutional networks according to claim 1, characterized in that, The specific process of step 4) is as follows: Based on the process knowledge of multiphase flow pumps, the input samples of the start-up hysteresis stage obtained in step 2) are analyzed. The predicted flow characteristics are set to 0 to replace the predicted flow characteristics of the GTGCN model in step 2) for the start-up lag stage; the input samples for the sinusoidal stage are processed using formula (3). Perform calculations to replace the GTGCN model's prediction of the sinusoidal phase flow characteristics in step 2).

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