PINN-based displacement efficiency analysis method for eccentric annulus multiphase flow field

Abstract

The invention discloses a PINN-based displacement efficiency analysis method for an eccentric annulus multiphase flow field, and relates to the technical field of oil-gas exploration and development, and the method comprises the following steps: S1, constructing an eccentric annulus model in a well cementation process, and determining the speed of a fluid in an eccentric annulus; s2, determining the upper boundary of the eccentric annulus model; s3, determining boundary conditions of the first fluid and boundary conditions of the second fluid; s4, obtaining the latest boundary condition of the first fluid and the latest boundary condition of the second fluid; s5, determining a kinematics formula of a material interface; s6, training the PINN network; and S7, determining the flow field distribution and displacement efficiency of the fluid in the eccentric annulus. According to the method, all physical constraints are ensured to be fully supervised, the detailed data sampling strategy enables the PINN model to comprehensively capture physical information in each region in the training process, and the robustness of overall solution is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of oil and gas exploration and development, and particularly relates to a method for analyzing the displacement efficiency of the flow field of eccentric annulus multiphase flow based on PINN. Background Art

[0002] In the field of oil exploration and development, the study of the flow law of multiphase fluids in porous media is of great significance for improving drilling efficiency, optimizing oil and gas recovery rate, and ensuring environmental safety. Taking the cementing operation as an example, during the cement injection process in a directional well, due to the continuous change of the well inclination angle and azimuth angle with the well depth, although centralizers are installed on the casing, with the change of the wellbore trajectory, it is difficult for the casing to be centered in the wellbore under its own weight, thus forming a wide side and a narrow side in the annulus gap, resulting in a large difference in the fluid flow velocities between the wide side and the narrow side, and causing the displacement fluid and the displaced fluid to mix in the eccentric annulus during the cement injection process, and the displacement interface becomes unstable. For this flow process, when traditional numerical simulation methods (such as Fluent) are used to handle such complex geometric structures, fine grid division is required to capture the details of the flow field, but the calculation cost is high and time-consuming.

[0003] Physics-informed neural network (PINN) provides an innovative approach to solve the problem of eccentric annulus multiphase flow. Aiming at the problem of solving relevant partial differential equations in an asymmetric annular domain, PINN directly maps the nonlinear relationship between the flow field variables and geometric parameters through a global approximation function, and can efficiently simulate the flow characteristics of non-Newtonian fluids in the eccentric annulus without grid division. Combining the advantage of GPU-accelerated training, it can shorten the single-well simulation period, which takes several weeks in the traditional method, to the hour level. At the same time, by integrating well logging data and physical conservation laws, it can automatically learn the anisotropy of formation permeability and the uncertainty of drilling fluid rheological parameters, and improve the adaptability to dynamic boundary conditions (such as drill string rotation and mud pump displacement changes). Summary of the Invention

[0004] In order to solve the above problems, the present invention proposes a method for analyzing the displacement efficiency of the flow field of eccentric annulus multiphase flow based on PINN.

[0005] The technical solution of the present invention is: a method for analyzing the displacement efficiency of the flow field of eccentric annulus multiphase flow based on PINN includes the following steps:

[0006] S1. Construct an eccentric annulus model for the cementing process and determine the velocity of the fluid in the eccentric annulus;

[0007] S2. Determine the upper boundary of the eccentric annulus model based on the velocity of the fluid in the eccentric annulus;

[0008] S3. Determine the boundary conditions of the first fluid, and determine the boundary conditions of the second fluid according to the upper boundary of the eccentric annulus model;

[0009] S4. Transforming the boundary conditions of the first fluid and the boundary conditions of the second fluid to obtain the latest boundary conditions of the first fluid and the latest boundary conditions of the second fluid;

[0010] S5. Determine the kinematic formula of the material interface;

[0011] S6. Training the PINN network based on the latest boundary conditions of the first fluid, the latest boundary conditions of the second fluid, and the kinematic formula of the material interface;

[0012] S7. Use the trained PINN network to determine the flow field distribution and displacement efficiency of the fluid in the eccentric annulus.

[0013] Furthermore, in S2, the calculation formula for the upper boundary H(z) of the eccentric annulus model is:

[0014]

[0015] Where ε represents the eccentricity, R1 represents the radius of the first wellbore, R2 represents the radius of the second wellbore, and θ represents the angular position of a point in the polar coordinate system.

[0016] Furthermore, in S3, the boundary condition of the first fluid is expressed as:

[0017] u1(y,0)=g 11 (y), u1(y,l)=g 21 (y), u1(0,z)=0, τ1(h,z)=τ2(h,z);

[0018]

[0019] Where u1(y,0) represents the velocity boundary condition of the first fluid at z=0, g 11 (y) represents the velocity value of the first fluid at z = 0, u1(y, l) represents the velocity boundary condition of the first fluid at z = l, g 21 (y) represents the velocity of the first fluid at z = l, u1(0,z) represents the velocity of the first fluid at y = 0, τ1(h,z) represents the shear stress of the first fluid at y = h, τ2(h,z) represents the shear stress of the second fluid at y = h, y represents the ordinate of the expanded graph, z represents the abscissa of the expanded graph, l represents the length along the z direction, h represents the position of the fluid from the interface, H S Indicates the H value at z = L, H LThe value of H at z = 0, μ1 represents the viscosity of the first fluid, L represents the subscript of H at z = 0, S represents the subscript of H at z = L, H represents the upper boundary height, ρ1 represents the density of the first fluid, and θ represents the angular position of a point in the polar coordinate system;

[0020] The expression for the boundary conditions of the second fluid is:

[0021]

[0022] In the formula, u2(y, 0) represents the velocity boundary condition of the second fluid at z = 0, g 12 (y) represents the velocity value of the second fluid at z = 0, u2(y, l) represents the velocity boundary condition of the second fluid at z = l, g 22 (y) represents the velocity value of the second fluid at z = l, u2 represents the velocity of the second fluid, u1(h, z) represents the velocity of the first fluid at y = h, u2(h, z) represents the velocity of the second fluid at y = h, H(z) represents the upper boundary of the eccentric annular control model, μ2 represents the viscosity of the second fluid, and ρ2 represents the density of the second fluid.

[0023] Furthermore, in S4, the expression for the latest boundary conditions of the first fluid is:

[0024]

[0025] In the formula, U1(y, 0) represents the corrected velocity of the first fluid at z = 0, U1(y, l) represents the corrected velocity of the first fluid at z = l, U1(0, z) represents the corrected velocity of the first fluid at y = 0, μ1 represents the viscosity of the first fluid, μ2 represents the viscosity of the second fluid, U1 represents the corrected velocity of the first fluid, U2 represents the corrected velocity of the second fluid, y represents the ordinate of the developed diagram, z represents the abscissa of the developed diagram, l represents the length along the z direction, and h represents the position of the fluid from the interface;

[0026] In S4, the expression for the latest boundary conditions of the second fluid is:

[0027]

[0028] U1(h, z) = U2(h, z);

[0029] In the formula, U2(y, 0) represents the corrected velocity of the second fluid at z = 0, U2(y, l) represents the corrected velocity of the second fluid at z = l, U2 represents the corrected velocity of the second fluid, represents the shear rate of the second fluid at z = 0, represents the shear rate of the second fluid at z = l, U1(h, z) represents the corrected velocity of the first fluid at the interface, U2(h, z) represents the corrected velocity of the second fluid at the interface, and H(z) represents the upper boundary of the eccentric annular control model.

[0030] Furthermore, in S5, the kinematic formula of the material interface is:

[0031]

[0032] where h represents the position of the fluid from the interface, t represents time, and x represents the axial coordinate of the wellbore.

[0033] Furthermore, S6 includes the following sub-steps:

[0034] S61. Determine the first PDE residual and the second PDE residual;

[0035] S62. Determine the boundary residual of the first fluid according to the latest boundary conditions of the first fluid, and determine the boundary residual of the second fluid according to the latest boundary conditions of the second fluid;

[0036] S63. Determine the residual of the interface between the first fluid and the second fluid;

[0037] S64. Take the sum of the first PDE residual, the second PDE residual, the boundary residual of the first fluid, the boundary residual of the second fluid, and the residual of the interface between the first fluid and the second fluid as the total loss function of the PINN network;

[0038] S65. Use the total loss function to update the parameters of the PINN network and complete the training of the PINN network.

[0039] Furthermore, in S61, the first PDE residual is expressed as:

[0040]

[0041] where represents the Laplace operator, U1(y, z) represents the corrected velocity field distribution of the first fluid, y represents the ordinate of the developed diagram, z represents the abscissa of the developed diagram, and Ω1 represents the first subdomain;

[0042] In S61, the second PDE residual is expressed as:

[0043]

[0044] where U2(y, z) represents the corrected velocity field distribution of the second fluid, and Ω2 represents the second subdomain.

[0045] Furthermore, in S62, the boundary residual of the first fluid The expression is:

[0046]

[0047] Where U1(y,0) represents the corrected velocity of the first fluid at z=0, U1(y,l) represents the corrected velocity of the first fluid at z=l, U1(0,z) represents the corrected velocity of the first fluid at y=0, y represents the ordinate of the expanded graph, z represents the abscissa of the expanded graph, and l represents the length along the z direction;

[0048] In S62, the boundary residual of the second fluid The expression is:

[0049]

[0050] Where, U2(y,0) represents the corrected velocity of the second fluid at z=0, U2(y,l) represents the corrected velocity of the second fluid at z=l, and U2 represents the corrected velocity of the second fluid. represents the shear rate of the second fluid at z = 0, represents the shear rate of the second fluid at z = l, U1(h,z) represents the corrected velocity of the first fluid at the interface, U2(h,z) represents the corrected velocity of the second fluid at the interface, y represents the ordinate of the expanded diagram, z represents the abscissa of the expanded diagram, l represents the length along the z direction, and H(z) represents the upper boundary of the eccentric environmental control model.

[0051] Furthermore, in S63, the residual of the interface between the first fluid and the second fluid The expression is:

[0052]

[0053] Where U1(h,z) represents the corrected velocity of the first fluid at the interface, U2(h,z) represents the corrected velocity of the second fluid at the interface, v1 represents the viscosity of the first fluid, μ2 represents the viscosity of the second fluid, y represents the ordinate of the expanded graph, z represents the abscissa of the expanded graph, and h represents the position of the fluid from the interface.

[0054] The beneficial effects of the present invention are:

[0055] (1) The present invention constructs independent neural networks for the first fluid region, the second fluid region, and the interface position, respectively. Each network focuses on fitting the modified velocity field of its region, overcoming the problem that a traditional single network is difficult to simultaneously capture the physical characteristics and complex boundary conditions of different regions, thereby significantly improving the overall solution accuracy and stability.

[0056] (2) The present invention introduces multiple physical constraints such as PDE residuals, boundary conditions, and interface continuity, and uses a joint loss function for optimization during the training process to achieve an end-to-end solution for complex flow problems; this loss construction based on physical information enables the model to not only perform excellently in data fitting but also have high interpretability and consistency in physical meaning;

[0057] (3) The present invention ensures that all physical constraints are fully supervised. This meticulous data sampling strategy enables the PINN model to comprehensively capture physical information in each region during the training process, improving the robustness of the overall solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 is a flowchart of the displacement efficiency analysis method for the eccentric annulus multiphase flow field based on PINN;

[0059] Figure 2 is a physical model diagram;

[0060] Figure 3 is a simplified diagram of the mathematical model;

[0061] Figure 4 is the displacement effect diagram of two fluids. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0062] The embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0063] As Figure 1 shown, the present invention provides a displacement efficiency analysis method for the eccentric annulus multiphase flow field based on PINN, including the following steps:

[0064] S1. Construct an eccentric annulus model for the cementing process and determine the velocity of the fluid in the eccentric annulus;

[0065] S2. Determine the upper boundary of the eccentric annulus model based on the velocity of the fluid in the eccentric annulus;

[0066] S3. Determine the boundary conditions of the first fluid and determine the boundary conditions of the second fluid according to the upper boundary of the eccentric annulus model;

[0067] S4. Transform the boundary conditions of the first fluid and the boundary conditions of the second fluid to obtain the updated boundary conditions of the first fluid and the updated boundary conditions of the second fluid;

[0068] S5. Determine the kinematic formula of the material interface;

[0069] S6. Train the PINN network based on the updated boundary conditions of the first fluid, the updated boundary conditions of the second fluid, and the kinematic formula of the material interface;

[0070] S7. Determine the flow field distribution and displacement efficiency of the fluid in the eccentric annulus using the trained PINN network.

[0071] The present invention breaks through the bottleneck of traditional numerical simulation through the PINN (Physics-Informed Neural Network) method, providing an efficient solution for eccentric annulus flow simulation. Specifically, it can predict the velocity field of multiple fluids and the displacement interface distribution under eccentric annuli in real time; at the same time, it constructs a prediction model for eccentric annulus multiphase flow, providing theoretical support for the evaluation of the sand-carrying efficiency of slickwater in staged fracturing of shale gas horizontal wells. At the theoretical level, this research explores the PINN modeling method for multi-physical field coupling problems in asymmetric geometric domains, promotes the development of a special solution framework in the field of petroleum engineering, and provides key technical support for the development of intelligent drilling technology.

[0072] Based on the concentric annulus narrow slit theory, the present invention further constructs an unfolded structure model of the eccentric annulus and conducts an analytical solution for the flow problem between two irregularly shaped plates. Its unfolded structure characteristics are as Figure 2 shown.

[0073] Due to symmetry, solving for the velocity of the fluid in the eccentric annulus is similar to solving for the velocity of the fluid between two plates, as Figure 3 shown.

[0074] In the embodiment of the present invention, in S2, the calculation formula for the upper boundary H(z) of the eccentric annulus model is:

[0075]

[0076] In the formula, ε represents the eccentricity, R1 represents the radius of the first wellbore, R2 represents the radius of the second wellbore, and θ represents the angular position of a point in the polar coordinate system.

[0077] In the embodiment of the present invention, in S3, the expression for the boundary condition of the first fluid is:

[0078] u1(y,0) = g 11 (y), u1(y,l) = g 21 (y), u1(0,z) = 0, τ1(h,z) = τ2(h,z);

[0079]

[0080] In the formula, u1(y,0) represents the velocity boundary condition of the first fluid at z = 0, and g 11 (y) represents the velocity value of the first fluid at z = 0, u1(y,l) represents the velocity boundary condition of the first fluid at z = l, and g 21(y) represents the velocity value of the first fluid at z = l, u1(0,z) represents the velocity of the first fluid at y = 0, τ1(h,z) represents the shear stress of the first fluid at y = h, τ2(h,z) represents the shear stress of the second fluid at y = h, y represents the ordinate of the developed diagram, z represents the abscissa of the developed diagram, l represents the length in the z direction, h represents the position of the fluid from the interface, H S represents the value of H at z = L, H L represents the value of H at z = 0, μ1 represents the viscosity of the first fluid, L represents the subscript of H at z = 0, S represents the subscript of H at z = L, H represents the upper boundary height, ρ1 represents the density of the first fluid, θ represents the angular position of a point in the polar coordinate system;

[0081] The expression for the boundary condition of the second fluid is:

[0082]

[0083] In the formula, u2(y,0) represents the velocity boundary condition of the second fluid at z = 0, g 12 (y) represents the velocity value of the second fluid at z = 0, u2(y,l) represents the velocity boundary condition of the second fluid at z = l, g 22 (y) represents the velocity value of the second fluid at z = l, u2 represents the velocity of the second fluid, u1(h,z) represents the velocity of the first fluid at y = h, u2(h,z) represents the velocity of the second fluid at y = h, H(z) represents the upper boundary of the eccentric annular control model, μ2 represents the viscosity of the second fluid, ρ2 represents the density of the second fluid.

[0084] In the embodiment of the present invention, in S4, the expression for the latest boundary condition of the first fluid is:

[0085]

[0086] In the formula, U1(y,0) represents the corrected velocity of the first fluid at z = 0, U1(y,l) represents the corrected velocity of the first fluid at z = l, U1(0,z) represents the corrected velocity of the first fluid at Y = 0, μ1 represents the viscosity of the first fluid, μ2 represents the viscosity of the second fluid, U1 represents the corrected velocity of the first fluid, U2 represents the corrected velocity of the second fluid, y represents the ordinate of the developed diagram, z represents the abscissa of the developed diagram, l represents the length in the z direction, h represents the position of the fluid from the interface;

[0087] In S4, the expression for the latest boundary condition of the second fluid is:

[0088]

[0089] U1(h,z) = U2(h,z);

[0090] Wherein, U2(y,0) represents the corrected velocity of the second fluid at z = 0, U2(y,l) represents the corrected velocity of the second fluid at z = l, and U2 represents the corrected velocity of the second fluid. represents the shear rate of the second fluid at z = 0. represents the shear rate of the second fluid at z = l, U1(h,z) represents the corrected velocity of the first fluid at the interface, U2(h,z) represents the corrected velocity of the second fluid at the interface, and H(z) represents the upper boundary of the eccentric annulus control model.

[0091] In the embodiment of the present invention, in S5, the kinematic formula of the material interface is:

[0092]

[0093] Wherein, h represents the position of the fluid from the interface, t represents time, and x represents the wellbore axial coordinate.

[0094] In the embodiment of the present invention, S6 includes the following sub-steps: [[ID=2I]]

[0095] S61. Determine the first PDE residual and the second PDE residual;

[0096] S62. Determine the boundary residual of the first fluid according to the latest boundary condition of the first fluid, and determine the boundary residual of the second fluid according to the latest boundary condition of the second fluid;

[0097] S63. Determine the residual of the interface between the first fluid and the second fluid;

[0098] S64. Take the sum of the first PDE residual, the second PDE residual, the boundary residual of the first fluid, the boundary residual of the second fluid, and the residual of the interface between the first fluid and the second fluid as the total loss function of the PINN network;

[0099] S65. Use the total loss function to update the parameters of the PINN network to complete the training of the PINN network.

[0100] PDE refers to partial differential equation.

[0101] In the embodiment of the present invention, in S61, the first PDE residual has the following expression:

[0102]

[0103] Wherein, denotes the Laplace operator, U1(y,z) represents the velocity field distribution of the first fluid after correction, y represents the ordinate of the developed diagram, z represents the abscissa of the developed diagram, and Ω1 represents the first subdomain;

[0104] In S61, the second PDE residual has the following expression:

[0105]

[0106] In the formula, U2(y,z) represents the velocity field distribution of the second fluid after correction, and Ω2 represents the second subdomain.

[0107] In the embodiment of the present invention, in S62, the boundary residual of the first fluid has the following expression:

[0108]

[0109] In the formula, U1(y,0) represents the velocity of the first fluid after correction at z = 0, U1(y,l) represents the velocity of the first fluid after correction at z = l, U1(0,z) represents the velocity of the first fluid after correction at y = 0, y represents the ordinate of the developed diagram, z represents the abscissa of the developed diagram, and l represents the length in the z direction;

[0110] In S62, the boundary residual of the second fluid has the following expression:

[0111]

[0112] In the formula, U2(y,0) represents the velocity of the second fluid after correction at z = 0, U2(y,l) represents the velocity of the second fluid after correction at z = l, U2 represents the velocity of the second fluid after correction, represents the shear rate of the second fluid at z = 0, represents the shear rate of the second fluid at z = l, U1(h,z) represents the velocity of the first fluid after correction at the interface, U2(h,z) represents the velocity of the second fluid after correction at the interface, y represents the ordinate of the developed diagram, z represents the abscissa of the developed diagram, l represents the length in the z direction, and H(z) represents the upper boundary of the eccentric annular control model.

[0113] In the embodiment of the present invention, in S63, the residual of the interface between the first fluid and the second fluid has the following expression:

[0114]

[0115] Wherein, U1(h,z) represents the corrected velocity of the first fluid at the interface, U2(h,z) represents the corrected velocity of the second fluid at the interface, μ1 represents the viscosity of the first fluid, μ2 represents the viscosity of the second fluid, y represents the ordinate of the developed diagram, z represents the abscissa of the developed diagram, and h represents the position of the fluid from the interface.

[0116] In the embodiment of the present invention, three independent neural networks are designed to fit different physical quantities respectively. The neural network NN1(y,z;θ1) is constructed to realize the fitting of the corrected velocity field U1(y,z) in the first fluid region to capture its complex flow characteristics; the neural network NN2(y,z;θ2) is constructed to realize the fitting of the corrected velocity field U2(y,z) in the second fluid region to ensure that the fluid behavior in this region can be accurately reflected; the network NN h (x,t;θ h ) approximately fits the interface h(x,t), so as to accurately describe the dynamic change of the two-phase fluid interface.

[0117] The present invention adopts a fully connected feedforward neural network, the input is (z, y), and the input data is preprocessed by normalization to ensure that the numerical range is suitable for the activation function; the number of hidden layers is set to 8, and the number of neurons in each layer is 50, and tanh is used as the activation function. The output formula of each layer is: h (l) =tanh(W (l) h (l-1) +b (l) ). Where l = 1, 2, 3...8, W (l) is the weight matrix, and b (l) is the bias matrix. The output layer directly outputs U i (y,z) without using the activation function. The optimizer adopts the Adam optimizer for global search in the initial stage and uses L-BFGS for fine-tuning later.

[0118] In S64, starting from the loss function, the gradient of the loss function with respect to each parameter in the network is calculated reversely according to the chain rule. Specifically, first calculate the direct gradient of the loss function with respect to the output layer of the network, and then backpropagate this gradient to the middle layer and input layer of the network, and calculate the contribution gradient of each layer parameter to the loss function layer by layer. The network parameters are updated using the joint optimization algorithm (Adam and L-BFGS). Taking gradient descent as an example, the parameter update formula is: Where η represents the learning rate, represents the gradient of the loss function with respect to the parameter θ, and θ old represents the parameter value before update. A relatively low learning rate (0.001) should be set initially.

[0119] Repeat the above steps of forward propagation, loss calculation, gradient calculation, and parameter update until the convergence condition is met. Common convergence conditions include the loss function value being lower than a certain threshold, the loss function value not decreasing significantly within several iterations, or reaching the preset maximum number of iterations.

[0120] The present invention draws a trend graph of the change in the loss function to show the change trends of the total loss function and each sub-loss term (such as PDE residual, boundary condition loss, and interface continuity loss) with the number of iterations or training epochs. By observing the decline of these curves, it can be judged whether the model gradually converges to a stable state. A velocity field distribution map is drawn to visually present the velocity field distribution within a two-dimensional region in a visual way. This helps to understand the prediction results of the model for the physical field and analyze the variation law of velocity in different regions and the overall flow pattern.

[0121] Figure 4 It is the displacement effect diagram of two fluids. During the displacement process, the fluid interface is advancing, and fluid 2 (displacing fluid) gradually replaces fluid 1 (displaced fluid).

[0122] Those of ordinary skill in the art will realize that the embodiments described herein are for helping readers understand the principles of the present invention, and it should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific deformations and combinations without departing from the essence of the present invention according to the technical revelations disclosed in the present invention, and these deformations and combinations are still within the protection scope of the present invention.

Claims

1. A displacement efficiency analysis method for the flow field of eccentric annulus multiphase flow based on PINN, characterized in that, It includes the following steps: S1. Construct an eccentric annulus model for the cementing process and determine the velocity of the fluid in the eccentric annulus; S2. Based on the velocity of the fluid in the eccentric annulus, determine the upper boundary of the eccentric annulus model; S3. Determine the boundary conditions of the first fluid and, according to the upper boundary of the eccentric annulus model, determine the boundary conditions of the second fluid; S4. Transform the boundary conditions of the first fluid and the second fluid to obtain the updated boundary conditions of the first fluid and the updated boundary conditions of the second fluid; S5. Determine the kinematic formula of the material interface; S6. Based on the updated boundary conditions of the first fluid, the updated boundary conditions of the second fluid, and the kinematic formula of the material interface, train the PINN network; S7. Use the trained PINN network to determine the flow field distribution and displacement efficiency of the fluid in the eccentric annulus.

2. The displacement efficiency analysis method of the eccentric annulus multiphase flow field based on PINN according to claim 1, characterized in that, In the above S2, the calculation formula for the upper boundary H(z) of the eccentric annulus model is: In the formula, ε represents the eccentricity, R1 represents the radius of the first wellbore, R2 represents the radius of the second wellbore, and θ represents the angular position of a point in the polar coordinate system.

3. The displacement efficiency analysis method of the eccentric annulus multiphase flow field based on PINN according to claim 1, wherein In the above S3, the expression for the boundary conditions of the first fluid is: u1(y, 0) = g 11 (y), u1(y, l) = g 21 (y), u1(0, z) = 0, τ1(h, z) = τ2(h, z); Where, u1(y, 0) represents the velocity boundary condition of the first fluid at z = 0, g 11 (y) represents the velocity value of the first fluid at z = 0, u1(y, l) represents the velocity boundary condition of the first fluid at z = l, g 21 (y) represents the velocity value of the first fluid at z = l, u1(0, z) represents the velocity of the first fluid at y = 0, τ1(h, z) represents the shear stress of the first fluid at y = h, τ2(h, z) represents the shear stress of the second fluid at y = h, y represents the ordinate of the developed diagram, z represents the abscissa of the developed diagram, l represents the length in the z direction, h represents the position of the fluid from the interface, H S represents the value of H at z = L, H L represents the value of H at z = 0, μ1 represents the viscosity of the first fluid, L represents the subscript of H at z = 0, S represents the subscript of H at z = L, H represents the upper boundary height, ρ1 represents the density of the first fluid, θ represents the angular position of a point in the polar coordinate system; The expression for the boundary conditions of the second fluid is: where \(u_2(y, 0)\) represents the velocity boundary condition of the second fluid at \(z = 0\), and \(g\) 12 (y) represents the velocity value of the second fluid at \(z = 0\), \(u_2(y, l)\) represents the velocity boundary condition of the second fluid at \(z = l\), and \(g\) 22 (y) represents the velocity value of the second fluid at \(z = l\), \(u_2\) represents the velocity of the second fluid, \(u_1(h, z)\) represents the velocity of the first fluid at \(y = h\), \(u_2(h, z)\) represents the velocity of the second fluid at \(y = h\), \(H(z)\) represents the upper boundary of the eccentric annulus control model, \(\mu_2\) represents the viscosity of the second fluid, and \(\rho_2\) represents the density of the second fluid.

4. The displacement efficiency analysis method of the eccentric annulus multiphase flow field based on PINN according to claim 1, characterized in that, In the above S4, the expression for the updated boundary conditions of the first fluid is: U1(y, 0) = 0, U1(y, l) = 0, U1(0, z) = 0, In the formula, U1(y, 0) represents the corrected velocity of the first fluid at z = 0, U1(y, l) represents the corrected velocity of the first fluid at z = l, U1(0, z) represents the corrected velocity of the first fluid at y = 0, μ1 represents the viscosity of the first fluid, μ2 represents the viscosity of the second fluid, U1 represents the corrected velocity of the first fluid, U2 represents the corrected velocity of the second fluid, y represents the ordinate of the developed diagram, z represents the abscissa of the developed diagram, l represents the length along the z direction, and h represents the position of the fluid from the interface; In the above S4, the expression for the updated boundary conditions of the second fluid is: U2(y, 0) = 0, U2(y, l) = 0, U1(h, z) = U2(h, z); Wherein, U2(y, 0) represents the corrected velocity of the second fluid at z = 0, U2(y, l) represents the corrected velocity of the second fluid at z = l, and U2 represents the corrected velocity of the second fluid. represents the shear rate of the second fluid at z = 0. represents the shear rate of the second fluid at z = l, U1(h, z) represents the corrected velocity of the first fluid at the interface, U2(h, z) represents the corrected velocity of the second fluid at the interface, and H(z) represents the upper boundary of the eccentric annular control model.

5. The displacement efficiency analysis method of the eccentric annulus multiphase flow field based on PINN according to claim 1, wherein In the above S5, the kinematic formula of the material interface is: In the formula, h represents the position of the fluid from the interface, t represents time, and x represents the axial coordinate of the wellbore.

6. The displacement efficiency analysis method of the eccentric annulus multiphase flow field based on PINN according to claim 1, characterized in that, The above S6 includes the following sub-steps: S61. Determine the first PDE residual and the second PDE residual; S62. According to the updated boundary conditions of the first fluid, determine the boundary residual of the first fluid, and according to the updated boundary conditions of the second fluid, determine the boundary residual of the second fluid; S63. Determine the residual of the interface between the first fluid and the second fluid; S64. Take the sum of the first fluid PDE residual, the second fluid PDE residual, the boundary residual of the first fluid, the boundary residual of the second fluid, and the residual of the interface between the first fluid and the second fluid as the total loss function of the PINN network; S65. Use the total loss function to update the parameters of the PINN network and complete the training of the PINN network.

7. The displacement efficiency analysis method of the eccentric annulus multiphase flow field based on PINN according to claim 6, characterized in that, In S61, the first PDE residual has the following expression: In the formula, represents the Laplace operator, U1(y,z) represents the velocity field distribution of the first fluid after correction, y represents the ordinate of the developed view, z represents the abscissa of the developed view, and Ω1 represents the first subdomain; In S61, the second PDE residual has the following expression: In the formula, U2(y, z) represents the corrected velocity field distribution of the second fluid, and Ω2 represents the second sub-domain.

8. The displacement efficiency analysis method of the eccentric annulus multiphase flow field based on PINN according to claim 6, wherein In S62, the boundary residual of the first fluid has the following expression: Where, U1(y, 0) represents the corrected velocity of the first fluid at z = 0, U1(y, l) represents the corrected velocity of the first fluid at z = l, U1(0, z) represents the corrected velocity of the first fluid at y = 0, y represents the ordinate of the developed diagram, z represents the abscissa of the developed diagram, and l represents the length in the z direction; In S62, the boundary residual of the second fluid has the following expression: In the formula, U2(y, 0) represents the corrected velocity of the second fluid at z = 0, U2(y, l) represents the corrected velocity of the second fluid at z = l, and U2 represents the corrected velocity of the second fluid. represents the shear rate of the second fluid at z = 0. represents the shear rate of the second fluid at z = l, U1(h, z) represents the corrected velocity of the first fluid at the interface, U2(h, z) represents the corrected velocity of the second fluid at the interface, y represents the ordinate of the developed diagram, z represents the abscissa of the developed diagram, l represents the length in the z direction, and H(z) represents the upper boundary of the eccentric annular control model.

9. The displacement efficiency analysis method for the eccentric annulus multiphase flow field based on PINN according to claim 6, wherein, In S63, the residual of the interface between the first fluid and the second fluid is expressed as: Where, U1(h, z) represents the corrected velocity of the first fluid at the interface, U2(h, z) represents the corrected velocity of the second fluid at the interface, μ1 represents the viscosity of the first fluid, μ2 represents the viscosity of the second fluid, y represents the ordinate of the developed diagram, z represents the abscissa of the developed diagram, and h represents the position of the fluid from the interface.

Images