A method and apparatus for determining proppant settling path within a fracture

Abstract

This specification provides a method and apparatus for determining the settling path of proppant within a fracture. Based on spatial scale parameters and settling time parameters, the corresponding target fracture parameters are determined. Using a first module of a pre-defined proppant settling prediction model, the fluid response parameters of the target fracture at different spatiotemporal locations are determined based on the target fracture parameters. The proppant settling prediction model is a neural network model constructed with a composite loss function, which includes residual terms of the governing equations and multi-physical boundary constraint terms. Using a second module of the pre-defined proppant settling prediction model, the settling velocity and positional changes of proppant particles within the target fracture are determined based on the fluid response parameters. Based on the settling velocity and positional changes, the settling path of the proppant particles within the target fracture is determined over the entire prediction time range. This overcomes the shortcomings of existing technologies that struggle to comprehensively reveal the particle-scale settling process.

Description

Technical Field

[0001] This manual belongs to the field of oil and gas field reservoir stimulation technology, and in particular relates to a method and device for determining the settling path of proppant in fractures. Background Technology

[0002] Currently, research on the settlement and migration patterns of proppant within cracks mainly relies on numerical simulations and physical experiments, which makes it difficult to efficiently and comprehensively reveal the settlement patterns of proppant.

[0003] There is currently no effective solution to the above problems. Summary of the Invention

[0004] This specification provides a method and apparatus for determining the settlement path of proppant within cracks, which solves the problems of long calculation time, scale limitation, and difficulty in accurately reflecting the actual migration law in the prediction of proppant settlement in large-scale cracks by traditional numerical simulation methods.

[0005] This specification provides a method for determining the settlement path of proppant within a crack, including: The spatial scale parameters and settlement time parameters of the target crack in the target area are obtained, and the corresponding target crack parameters are determined based on the spatial scale parameters and the settlement time parameters; wherein, the target crack parameters include spatial dimension information and temporal dimension information; Using the first module of a pre-defined proppant settling prediction model, the fluid response parameters of the target crack at different spatiotemporal locations are determined based on the target crack parameters; wherein, the proppant settling prediction model is a neural network model trained based on a composite loss function, the composite loss function including residual terms of the control equation related to proppant migration within the crack and multi-physical boundary constraint terms reflecting the coupled boundary behavior of the proppant; The second module of the preset proppant settling prediction model determines the settling velocity and position change information of the proppant particles in the target crack based on the fluid response parameters. Based on the settlement velocity and location change information, the settlement path of the proppant particles within the target fracture is determined over the entire predicted time range; wherein, the settlement path is used for a structured representation of the proppant settlement behavior and an assessment of the fracture's conductivity.

[0006] In one embodiment, the fluid response parameters include: horizontal velocity components, vertical velocity components, pressure values, and polymer stress tensors at different spatiotemporal locations within the target crack; the residual terms of the governing equation are fluid control residuals constructed based on a preset momentum equation; the multi-physical boundary constraint terms include: wall slip loss term, inlet boundary loss term, pressure drop loss term, vortex loss term, and pressure anchor point loss term.

[0007] In one embodiment, the process of determining the pressure anchor point loss term includes: Based on the spatial scale parameters of the target crack, determine the reference position coordinates for pressure calibration; Based on the reference position coordinates, determine the predicted pressure value at the corresponding position; The squares of the predicted pressure values ​​are summed and the mean is taken to construct the pressure anchor point loss term; wherein, the pressure anchor point loss term is used to introduce physical constraints on the pressure field of key areas inside the target crack.

[0008] In one embodiment, the process of determining the vortex loss term includes: Based on the horizontal and vertical velocity components of the target crack at different spatiotemporal locations, determine the velocity field distribution information at the corresponding locations; Based on the velocity field distribution information, calculate the partial derivatives of the horizontal velocity component with respect to the vertical direction and the partial derivatives of the vertical velocity component with respect to the horizontal direction to determine the predicted vorticity value at the corresponding location. Based on the predicted vorticity value and the preset target vortex value, the deviation at multiple spatial sampling points is determined; Based on the deviation, a corresponding vortex loss term is constructed; wherein, the vortex loss term is used to physically constrain the vortex characteristics in the velocity field.

[0009] In one embodiment, the vortex loss term is determined according to the following formula:

[0010] in, For the vortex loss term, To predict vorticity values, For the target vortex value, The horizontal velocity component is... The vertical velocity component is... Let be the partial derivative of the horizontal velocity with respect to the vertical direction. This is the partial derivative of the vertical velocity with respect to the horizontal direction.

[0011] In one embodiment, determining the corresponding target crack parameters based on the spatial scale parameter and the settlement time parameter includes: Based on the spatial scale parameters of the target crack, determine the spatial distribution information used to characterize the crack region; Based on the target crack settlement time parameters, determine the time evolution interval and time deviation length suitable for the settlement process, and determine the corresponding time sampling information based on the time evolution interval and time deviation length; The spatial distribution information is combined with the temporal sampling information to determine the target crack parameters that match the spatial scale parameters of the target crack.

[0012] In one embodiment, determining the settlement path of the proppant particles within the target fracture over the entire predicted time range based on the settlement velocity and location change information includes: Based on the position change information, the spatial position of each proppant particle at the initial moment is determined; Based on the settling velocity information and the preset time step, the displacement increment of each proppant particle between adjacent time steps is determined; Based on the spatial location and the displacement increment, determine the updated position of each proppant particle at the current time step; Based on the continuity between the updated position and the previous time step position, the motion trajectory of each proppant particle at multiple time steps is determined. Based on the continuous distribution of the motion trajectory within the predicted time range, the settling path of the proppant particles within the target crack is determined throughout the entire predicted time range.

[0013] In one embodiment, the method further includes: Based on the sedimentation path, the spatial coverage parameter of proppant particles inside the target fracture is determined; wherein, the spatial coverage parameter is used to characterize the deposition density of proppant particles at different spatiotemporal locations within the target fracture; Based on the spatial coverage parameter, the equivalent conductivity index of the target fracture is determined; wherein, the equivalent conductivity index is used to quantitatively evaluate the target fracture's ability to maintain fracturing fluid flow after proppant settling.

[0014] This specification provides a device for determining the settlement path of proppant within a crack, comprising: The first determining module is used to acquire the spatial scale parameters and settlement time parameters of the target crack in the target area, and determine the corresponding target crack parameters based on the spatial scale parameters and the settlement time parameters; wherein, the target crack parameters include spatial dimension information and time dimension information; The second determining module is used to determine the fluid response parameters of the target crack at different spatiotemporal locations based on the target crack parameters using the first module of the preset proppant settlement prediction model; wherein, the proppant settlement prediction model is a neural network model trained based on a composite loss function, the composite loss function including the residual term of the control equation related to proppant migration within the crack and the multi-physical boundary constraint term reflecting the coupled boundary behavior of the proppant; The third determining module is used to determine the settling velocity and position change information of the proppant particles in the target crack based on the fluid response parameters, using the second module of the preset proppant settling prediction model. The path determination module is used to determine the settling path of the proppant particles within the target fracture over the entire predicted time range based on the settling velocity and position change information; wherein, the settling path is used for the structured representation of proppant settling behavior and the assessment of fracture conductivity.

[0015] This specification also provides an electronic device, including a processor and a memory for storing processor-executable instructions, wherein the processor, when executing the instructions, implements a method for determining the settling path of proppant within a crack.

[0016] This specification also provides a computer-readable storage medium having computer instructions stored thereon, which, when executed, implement a method for determining the settling path of proppant within a fracture.

[0017] Based on the method for determining the settling path of proppant within a fracture provided in this specification, the spatial scale parameters and settling time parameters of the target fracture in the target area are obtained, and the corresponding target fracture parameters are determined according to the spatial scale parameters and the settling time parameters; wherein, the target fracture parameters include spatial dimension information and temporal dimension information; using the first module of a preset proppant settling prediction model, the fluid response parameters of the target fracture at different spatiotemporal locations are determined according to the target fracture parameters; wherein, the proppant settling prediction model is a neural network model trained based on a composite loss function, the composite loss function including residual terms of the governing equations related to proppant migration within the fracture and multi-physical boundary constraint terms reflecting the coupled boundary behavior of the proppant; using the second module of the preset proppant settling prediction model, the settling velocity and position change information of the proppant particles within the target fracture are determined according to the fluid response parameters; and the settling path of the proppant particles within the target fracture is determined according to the settling velocity and position change information over the entire prediction time range; wherein, the settling path is used for the structured expression of proppant settling behavior and the evaluation of fracture conductivity. Thus, by introducing a neural network model with residual terms of the governing equations and multiple physical boundary constraints, the coupling behavior of fluid and proppant in large-scale fractures can be learned and predicted under physical constraints, significantly improving simulation efficiency and computational accuracy. This method does not rely on costly physical experiments or complex discrete element numerical calculations, enabling dynamic simulation and structured representation of proppant sedimentation patterns in large-scale fractures in a short time. This overcomes the shortcomings of existing technologies in comprehensively revealing particle-scale sedimentation processes, providing efficient and reliable data support for fracture conductivity assessment and fracturing construction optimization. Attached Figure Description

[0018] To more clearly illustrate the embodiments of this specification, the accompanying drawings used in the embodiments will be briefly introduced below. The drawings described below are only some embodiments recorded in this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a flowchart illustrating a method for determining the settlement path of proppant within a crack, as provided in one embodiment of this specification. Figure 2 This is a schematic diagram of the electronic device structure provided in one embodiment of this specification; Figure 3 This is a schematic diagram of the structural composition of a device for determining the settling path of proppant in a crack, provided in one embodiment of this specification. Figure 4 This is a schematic diagram of a PINN training flow rate result provided in one embodiment of this specification; Figure 5 This is a schematic diagram of a loss function result provided in one embodiment of this specification; Figure 6 This is a schematic diagram of a particle motion trajectory provided in one embodiment of this specification; Figure 7 This is a schematic diagram of a streamline provided in one embodiment of this specification; Figure 8 This is a schematic diagram of particle settling velocity provided in one embodiment of this specification. Detailed Implementation

[0020] To enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this specification, and not all embodiments. Based on the embodiments in this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this specification.

[0021] See Figure 1 As shown in the embodiments of this specification, a method for determining the settlement path of proppant within a crack is provided, wherein the method is specifically applied to the server side. In specific implementation, the method may include the following: S101: Obtain the spatial scale parameters and settlement time parameters of the target crack in the target area, and determine the corresponding target crack parameters based on the spatial scale parameters and the settlement time parameters; wherein, the target crack parameters include spatial dimension information and time dimension information; S102: Using the first module of the preset proppant settlement prediction model, the fluid response parameters of the target crack at different spatiotemporal locations are determined according to the target crack parameters; wherein, the proppant settlement prediction model is a neural network model trained based on a composite loss function, the composite loss function including the residual terms of the control equation related to proppant migration within the crack and the multi-physical boundary constraint terms reflecting the coupled boundary behavior of the proppant; S103: Using the second module of the preset proppant settling prediction model, the settling velocity and position change information of the proppant particles in the target crack are determined according to the fluid response parameters; S104: Based on the settlement velocity and position change information, determine the settlement path of the proppant particles within the target fracture over the entire predicted time range; wherein, the settlement path is used for the structured representation of proppant settlement behavior and the assessment of fracture conductivity.

[0022] Among them, the aforementioned spatial scale parameters can be the geometric structure and size characteristics of the target crack in three-dimensional space, usually including indicators such as crack length, height, width, and propagation direction, which are the basic parameters for determining the crack spatial boundary and discretization accuracy.

[0023] The aforementioned settlement time parameters can indicate the time range and time resolution used to simulate proppant settlement behavior, typically including the total predicted time length and time step, used to construct the time evolution interval of the settlement process inside the crack.

[0024] The aforementioned target crack parameters can be constructed based on spatial scale parameters and settlement time parameters, combining spatial dimension information describing the spatial distribution of cracks and temporal dimension information describing the temporal evolution of the settlement process, and are used to define the computational region and time range required for the simulation of the entire crack system.

[0025] The aforementioned fluid response parameters can be used to characterize the fluid state characteristics inside the crack at different times and spatial locations, specifically including the horizontal velocity component, the vertical velocity component, the pressure value, and the polymer stress tensor, reflecting the coupling behavior between the fluid field and the proppant.

[0026] The aforementioned settling velocity and position change information can be calculated based on the aforementioned fluid response parameters, and is used to describe the instantaneous velocity and position change trend of proppant particles after being subjected to fluid action inside the crack.

[0027] The aforementioned settling path can be a set of proppant particle movement trajectories tracked based on particle position change information over the entire prediction time range. It can structurally express the spatial distribution evolution process of proppant within the fracture and is a key basis for evaluating fracture conductivity and optimizing fracturing design.

[0028] In some embodiments, the first module utilizing a preset proppant settlement prediction model determines the fluid response parameters of the target crack at different spatiotemporal locations based on the target crack parameters. Specifically, this may include: First, the spatial scale parameters and settlement time parameters of the target crack in the target area are obtained. The spatial scale parameters include the length, width, and height of the target crack, and the settlement time parameters include the start time, end time, and time step of the settlement analysis. Based on the above parameters, target crack parameters are constructed. The target crack parameters include at least: spatial dimension information characterizing the spatial structure of the crack, including the three-dimensional geometric range and resolution scale of the crack; and temporal dimension information characterizing the evolution cycle of the settlement process, including the time range and discrete time interval involved in the prediction.

[0029] Then, a spatiotemporal sampling coordinate system for the crack region is constructed using the aforementioned target crack parameters, and an input data set is generated accordingly. Specifically, the target crack region is first discretized into a three-dimensional space to obtain a series of sampling units with definite spatial coordinates. Next, combined with time dimension information, each time step within the prediction time range is set to form a combined sample of spatial location and time point, which serves as the input to the model.

[0030] Next, the constructed target crack parameters and their corresponding spatiotemporal sampling points are input into the first module of the proppant settling prediction model. This first module is constructed using a Physical-Informed Neural Network (PINN) structure. By embedding physical constraints of the fluid control equations within the crack into the neural network, the model learns both data distribution characteristics and physical laws during training. This module employs a multilayer perceptron network structure. By receiving each set of spatiotemporal coordinate information, it outputs the fluid response parameters corresponding to that point. These fluid response parameters include the horizontal velocity, vertical velocity, local pressure, and stress state information of the polymer fluid at that point.

[0031] During model training, the first module optimizes the model by constructing a composite loss function, which consists of residual terms from the governing equations and multi-physics boundary constraint terms. The residual terms constrain the model predictions to adhere to the laws of fluid momentum and mass conservation, ensuring physical consistency. The multi-physics boundary constraint terms ensure that the predictions meet real physical boundary conditions such as no-slip, constant pressure, or constant velocity at the crack boundary. In this way, the neural network not only relies on limited labeled data for training but also automatically learns the flow field distribution characteristics inside the crack through the constraints of the physical equations. The training data can be derived from partial samples of numerical simulations or physical experiments, providing an initial reference for the network.

[0032] Through the above steps, the first module can quickly and stably predict the fluid response state of the target crack at different spatiotemporal locations based on the target crack parameters without relying on full experimental or simulation data, providing highly physically reliable flow field background data for subsequent proppant settling velocity and path deduction.

[0033] In some embodiments, the second module utilizing a preset proppant settling prediction model determines the settling velocity and positional changes of the proppant particles within the target fracture based on the fluid response parameters. Specifically, this may include: By inputting the target crack parameters and their corresponding fluid response parameters at different spatiotemporal locations, including horizontal velocity components, vertical velocity components, pressure values, and polymer stress tensors, the second module of the proppant settling prediction model is driven to perform prediction calculations. This second module is constructed using a deep learning structure based on a Physics-Informed Neural Network (PINN). This structure, in addition to having a supervised learning path, introduces residual terms and multi-physical boundary constraint terms from the momentum conservation equation, mass conservation equation, and boundary interaction rules describing the proppant's motion behavior. These are used to form a composite loss function with physical constraints, thereby training the network parameters.

[0034] Specifically, during model training, the proppant settling velocity and position change sequence from historical simulation data or physical experimental data are used as supervision signals. At the same time, spatial and temporal dimension information constructed using parameters such as the spatial scale of the target crack and the settling time interval are used together with the aforementioned fluid response parameters as network inputs. The composite loss function guides the model output to satisfy the proppant movement path that meets the physical environment constraints of the crack.

[0035] The neural network model trained as described above can quickly output the settling velocity field and location distribution sequence of proppant particles at different time periods and spatial locations within the crack, given only the geometric dimensions and spatiotemporal response information of the target crack, thereby obtaining complete settling path data.

[0036] Based on the above embodiments, by introducing a neural network model with residual terms of the governing equations and multiple physical boundary constraints, the coupling behavior of fluid and proppant in large-scale fractures can be learned and predicted under physical constraints, significantly improving simulation efficiency and computational accuracy. This method does not rely on costly physical experiments or complex discrete element numerical calculations, and can achieve dynamic simulation and structured representation of proppant sedimentation patterns in large-scale fractures in a short time. This overcomes the shortcomings of existing technologies in comprehensively revealing particle-scale sedimentation processes, providing efficient and reliable data support for fracture conductivity assessment and fracturing construction optimization.

[0037] In some embodiments, the fluid response parameters include: horizontal velocity components, vertical velocity components, pressure values, and polymer stress tensors at different spatiotemporal locations within the target crack; the residual terms of the governing equation are fluid control residuals constructed based on a preset momentum equation; the multi-physical boundary constraint terms include: wall slip loss term, inlet boundary loss term, average velocity loss term, pressure drop loss term, vortex loss term, and pressure anchor point loss term.

[0038] The aforementioned horizontal velocity component refers to the instantaneous velocity of the fluid in the transverse direction (such as the X-axis or Y-axis) of the fracture during proppant settling. This velocity affects the migration trend of the proppant in the horizontal plane and is of great significance for analyzing whether the proppant is prone to deviating from the main fracture channel and whether there is transverse offset and aggregation. It is a key parameter for predicting the transverse propagation path.

[0039] The aforementioned vertical velocity component refers to the velocity component of the fluid along the direction of gravity (usually the Z-axis), and is one of the main driving forces that directly determines whether the proppant settles and the rate of settling. In the fracture space, this parameter is used to determine the settling trend of particles under gravity and is an indispensable input variable for simulating the settling path.

[0040] The pressure values ​​mentioned above represent the instantaneous fluid pressure at any point in the fracture and are important parameters controlling the flow behavior within the fracture. The existence of a pressure gradient drives the fluid to flow from the high-pressure zone to the low-pressure zone and also affects the direction and velocity of proppant particles as they move with the fluid. Therefore, it plays a central role in simulating flow field evolution and particle motion.

[0041] The polymer stress tensor described above describes the internal stress state of a polymer fluid at a specific location and is typically used to reflect its non-Newtonian rheological behavior. It can reveal the viscoelastic effects of the fluid, such as shear thickening and flow hysteresis, thus influencing the settling trajectory and stability of particles in viscoelastic fluids. This parameter is particularly suitable for simulating real-world flow scenarios under cross-linked polymer fracturing fluid conditions.

[0042] The residual terms of the aforementioned governing equations can be considered a key part of the PINN neural network used to ensure that the network output conforms to physical laws; specifically, in this case, they are the residual terms of the momentum equation. They measure the difference between the neural network's prediction and the fluid momentum conservation equation; the smaller the residual, the more closely the prediction conforms to physical laws. This term ensures that the model can still capture the physical essence of fracture fluid dynamics even when driven by unsupervised data.

[0043] The aforementioned wall-no-slip loss term can be used to constrain the velocity boundary conditions of the model at the crack wall, ensuring that the fluid velocity at the wall is zero (i.e., no-slip condition), which conforms to the real physical boundary behavior. This loss term plays an important role in constructing accurate near-wall flow states and boundary layer thicknesses, and is particularly suitable for modeling the state of particles moving or accumulating near the crack wall.

[0044] The aforementioned inlet boundary loss term can be used to force the velocity or pressure at the inlet to satisfy known input boundary conditions, such as constant injection velocity or constant pressure injection. It ensures the physical consistency of the fluid entering the system from the crack inlet in the simulation environment, prevents boundary disturbances from affecting the internal solution, and is a prerequisite for constructing a stable initial flow field.

[0045] The pressure drop loss term described above reflects the pressure attenuation characteristics along the flow direction of the fracture and is often used to constrain the reasonable variation trend of pressure from the inlet to the outlet in simulations. A reasonable pressure drop characteristic can reflect the flow resistance distribution of the fracture, thereby indirectly affecting the flow velocity, shear stress, and proppant settling trend.

[0046] The aforementioned vortex loss term can be used to limit unreasonable vortex structures in model predictions, ensuring that non-physical or violently oscillating velocity vortices do not appear in the flow field. This has a suppressive effect on the prediction of proppant motion in local backflow and swirling regions, helping to improve the numerical stability and physical interpretability of the model.

[0047] The aforementioned pressure anchor loss term sets the pressure value at a specific location in the model as the reference anchor, which is used to improve the overall stability and convergence speed of pressure field prediction in the neural network. By constraining the model output with known pressure values ​​at certain key points, pressure drift or non-convergence can be effectively prevented, which is beneficial to improving the accuracy of the global solution.

[0048] In some embodiments, the residual term of the governing equation is a fluid control residual constructed based on a preset momentum equation, which may include: First, for any target spatiotemporal sampling point in the crack region, the fluid state parameters at that point are obtained, including the velocity components in the horizontal and vertical directions, pressure, and the anisotropic stress components of the polymer fluid.

[0049] Then, based on the calculation logic of momentum conservation, the rate of change of velocity, pressure gradient, and stress derivative at that point are calculated in the horizontal and vertical directions, respectively. Combined with the fluid density, momentum control residual terms in both directions are constructed. Each residual term reflects the degree of deviation of the flow state at that point from the preset physical conservation relationship.

[0050] Furthermore, to achieve physical consistency of the overall flow field, the control residuals in the horizontal and vertical directions were calculated for multiple spatiotemporal sampling points within the crack region, and the sum of their squares was used to construct the average loss function of the control equation residuals. This loss function was used as one of the optimization objectives during the neural network training phase to guide the model output to better satisfy the momentum conservation law in the spatiotemporal dimension.

[0051] The above methods can improve the numerical stability and physical reliability of fluid response prediction models under the background of proppant settling.

[0052] Specifically, the residual terms of the momentum conservation governing equations along the horizontal direction are determined according to the following formula:

[0053] in, This represents the momentum conservation residual in the horizontal direction. Represents the velocity component along the horizontal direction. Represents the velocity component along the vertical direction. Indicates local fluid pressure. Indicates fluid density, This represents the polymer stress tensor component in the x-direction. This represents the shear stress component in the xz direction.

[0054] Determine the residual terms of the momentum conservation governing equations along the vertical direction using the following formula:

[0055] in, This represents the momentum conservation residual in the vertical direction. Represents the velocity component along the vertical direction. The normal stress component in the z-direction.

[0056] Determine the residual terms of the governing equations using the following formula:

[0057] in, For the residual terms of the governing equation, and Let represent the spatial location and time of the i-th training sampling point.

[0058] In some embodiments, determining the wall slip loss term may include, in specific implementations, the following: First, the boundary regions corresponding to the upper and lower walls of the crack are identified, i.e., the positions of the upper and lower surfaces in the vertical direction. Then, at the spatiotemporal sampling points at these boundary locations, the corresponding horizontal and vertical velocity components are extracted, and the average loss value of the sum of squares of the velocity components is constructed. This loss value serves as the wall no-slip loss term, penalizing cases where non-physical slip velocities occur at the boundary locations.

[0059] This loss term, together with other control loss terms, constructs the total loss function during neural network training, thereby enabling the model to further approximate the zero-velocity constraint condition of the actual crack boundary while satisfying global momentum conservation.

[0060] Specifically, the no-slip loss term of the wall surface can be determined using the following formula:

[0061] in, This is the loss term for wall slip-free loss. This indicates the number of sampling points selected within the wall boundary region. This represents the velocity component along the horizontal direction at the sampling point. This represents the velocity component along the vertical direction at the sampling point. Sampling area representing the wall boundary

[0062] In some embodiments, determining the inlet boundary loss term may include, in specific implementations, the following: First, a target velocity distribution function is preset to define the desired velocity values ​​at different vertical positions in the inlet region. Typically, a parabolic distribution function is used to construct the horizontal target velocity component, while the vertical velocity is set to zero to simulate a typical inlet velocity profile. Then, multiple spatiotemporal sampling points are selected within the inlet boundary region, and the differences between the model-predicted velocity and the target velocity are extracted to construct the corresponding velocity residuals. An average loss value is then generated based on the sum of squared residuals. This loss value is the inlet boundary loss term, which can be used as a supervisory signal during neural network training to improve prediction accuracy at the inlet boundary.

[0063] Specifically, the inlet boundary loss term can be determined using the following formula:

[0064] in, This represents the horizontal velocity value of the target at time z, where the vertical position is z. This represents the maximum or characteristic value of the target velocity distribution at the inlet boundary. This represents the target's vertical velocity. Represents the loss term at the entry boundary. This indicates the number of training samples selected within the entrance boundary region. This indicates the spatial region where the entrance boundary is located.

[0065] In some embodiments, determining the average velocity loss term may include, in specific implementations, the following: Multiple spatiotemporal sampling points are selected within the core region (such as the main channel or the center of the computational domain). The average value of the horizontal velocity component within this region is calculated, and this average value is compared with a set minimum reference velocity to construct a velocity loss function based on the maximum value. If the average speed predicted by the model is lower than a set threshold (e.g., 0.05), a non-zero loss term is generated, prompting the model to adjust its results during training to meet the minimum speed requirement. Conversely, if the predicted speed already meets the requirement, this loss term is zero and does not affect the optimization process of other loss function terms.

[0066] Specifically, the average velocity loss term can be determined using the following formula:

[0067] in, This represents the average velocity loss term. This represents the set of spatial-temporal sampling points in the core region.

[0068] In some embodiments, determining the pressure drop loss term may include, in specific implementations, the following: Multiple pressure sampling points can be selected at the inlet and outlet boundaries, respectively. Based on the predicted pressure values ​​at these boundary points, the difference between the average inlet pressure and the average outlet pressure is calculated as the average pressure drop. Subsequently, this average pressure drop is compared with the set target pressure drop, and the squared difference between the two is calculated as the pressure drop loss term. This loss term reflects the deviation between the current model's predicted pressure drop and the target pressure drop; the larger the deviation, the higher the loss, thus guiding the model to further optimize prediction accuracy.

[0069] Specifically, the pressure drop loss term can be determined using the following formula:

[0070] in, This represents the average pressure drop value predicted by the model. This represents the local pressure value predicted by the model. The set of sampling points representing the entrance boundary. The set of sampling points representing the exit boundary. This indicates the preset target pressure drop value. This represents the pressure drop loss item.

[0071] In some embodiments, the process of determining the pressure anchor point loss term, when the method is specifically implemented, may further include the following: S1: Determine the reference position coordinates for pressure calibration based on the spatial scale parameters of the target crack; S2: Determine the predicted pressure value at the corresponding location based on the reference location coordinates; S3: Sum the squares of the predicted pressure values ​​and take the mean to construct a pressure anchor point loss term; wherein, the pressure anchor point loss term is used to introduce physical constraints on the pressure field of key areas inside the target crack.

[0072] Specifically, the pressure anchor point loss term can be determined using the following formula:

[0073] in, For the pressure anchor point loss term, This is the normalized pressure value. This represents the number of sampling points.

[0074] In some embodiments, the process of determining the vortex loss term, when the method is specifically implemented, may further include the following: S1: Determine the velocity field distribution information at the corresponding location based on the horizontal and vertical velocity components of the target crack at different spatiotemporal locations; S2: Based on the velocity field distribution information, calculate the partial derivatives of the horizontal velocity component with respect to the vertical direction and the partial derivatives of the vertical velocity component with respect to the horizontal direction to determine the predicted vorticity value at the corresponding location. S3: Determine the deviation at multiple spatial sampling points based on the predicted vorticity value and the preset target vortex value; S4: Based on the deviation, construct the corresponding vortex loss term; wherein, the vortex loss term is used to physically constrain the vortex characteristics in the velocity field.

[0075] In some embodiments, the vortex loss term is determined according to the following formula:

[0076] in, For the vortex loss term, To predict vorticity values, For the target vortex value, The horizontal velocity component is... The vertical velocity component is... Let be the partial derivative of the horizontal velocity with respect to the vertical direction. This is the partial derivative of the vertical velocity with respect to the horizontal direction.

[0077] In some embodiments, the method for determining the corresponding target crack parameters based on the spatial scale parameter and the settlement time parameter may further include the following: S1: Determine the spatial distribution information used to characterize the crack region based on the spatial scale parameters of the target crack; S2: Based on the target crack settlement time parameters, determine the time evolution interval and time deviation length that are suitable for the settlement process, and determine the corresponding time sampling information based on the time evolution interval and time deviation length; S3: Combine the spatial distribution information with the temporal sampling information to determine the target crack parameters that match the spatial scale parameters of the target crack.

[0078] Specifically, firstly, the spatial scale parameters and settlement time parameters of the target crack to be analyzed are collected. The spatial scale parameters include the length, width, and height of the crack, which reflect the three-dimensional spatial extent of the crack; the settlement time parameters include the time start point, time end point, and time step involved in the proppant settlement analysis, which are used to characterize the temporal evolution of the settlement process.

[0079] Then, based on spatial scale parameters, the crack region is spatially meshed. Specifically, a three-dimensional uniform or non-uniform mesh can be used to discretize the crack region, constructing a coordinate set characterizing the spatial distribution of the crack, thus obtaining the spatial distribution information of the crack region. This spatial distribution information can provide spatial support for subsequent fluid response parameter prediction and particle trajectory evolution analysis.

[0080] Next, based on the settlement time parameter, a time evolution interval adapted to the crack settlement process is constructed. Specifically, the total evolution time interval can be set according to the settlement start and end points, and the entire interval can be discretized into several time sampling points according to the preset time step, thereby forming time sampling information used to characterize the dynamic features of the settlement process.

[0081] Finally, the spatial distribution information and temporal sampling information obtained above are combined to construct a spatiotemporally coupled target crack parameter set. This parameter set can be used to drive the PINN proppant settling prediction model to predict the fluid field response and simulate particle trajectories within the target crack, ensuring that the prediction process maintains a high degree of consistency with the actual crack scenario in both spatial and temporal dimensions.

[0082] The above implementation method enables unified modeling of crack geometry and the temporal characteristics of the settlement process, providing structured input information for subsequent proppant settlement trajectory calculation based on physical guided neural networks, which helps improve prediction accuracy and model stability.

[0083] In some embodiments, the method for determining the settlement path of the proppant particles within the target fracture over the entire predicted time range based on the settlement velocity and location change information may further include the following: S1: Determine the spatial position of each proppant particle at the initial moment based on the position change information; S2: Based on the settling velocity information and the preset time step, determine the displacement increment of each proppant particle between adjacent time steps; S3: Determine the updated position of each proppant particle in the current time step based on the spatial position and the displacement increment; S4: Based on the continuity between the updated position and the previous time step position, determine the motion trajectory of each proppant particle at multiple time steps; S5: Based on the continuous distribution of the motion trajectory within the predicted time range, determine the settling path of the proppant particles within the target crack throughout the entire predicted time range.

[0084] Specifically, firstly, based on the proppant particle position change information obtained in the previous steps, the initial spatial position of each proppant particle within the target fracture at the start of settling is determined. This initial spatial position can be derived from experimentally acquired data, fracture simulation initialization data, or the output of a training model, representing the original distribution state of each particle in the spatial region of the target fracture.

[0085] Subsequently, combining the settling velocity information and the set time step, a time-step motion simulation is performed on each particle. Within each time step, based on the settling velocity value at the current particle location, the displacement change within the current time period is estimated. The displacement change includes both horizontal and vertical displacement, which comprehensively reflects the actual migration trend of the particle in the crack space.

[0086] Based on the aforementioned displacement changes, the spatial position of the particle at the current time step is updated, and this update result is associated with the position at the previous time step, thus obtaining the spatial trajectory segment at the current time step. This trajectory record can be stored using a sequence data structure to ensure the continuity of the trajectory in time and the accuracy of the position coordinates.

[0087] Repeat the above steps, iterating through each time step within the entire prediction time range, to gradually construct the complete motion trajectory of each particle within the prediction period. Finally, by summarizing the motion trajectory sequences of all particles, a dataset of the sedimentation paths of proppant particles within the target crack throughout the entire prediction time range is formed.

[0088] This settlement path dataset can be used for further visualization, settlement efficiency analysis, fracture conductivity assessment, or as input data for other modules, providing a basis for determining proppant placement effectiveness and optimizing fracturing construction parameters.

[0089] In some embodiments, the particle settling velocity can also be calculated using the following semi-implicit formula:

[0090] in, This represents the velocity of the particles in the horizontal direction (x-direction) at the current time step, i.e., the updated settling velocity. The velocity of the particle in the horizontal direction (x direction) at the previous time step. This represents the equivalent drag coefficient experienced by the particle in the x-direction. Indicates the mass of the particles. This represents the velocity of the surrounding fluid in the x-direction. Indicates the time step. This represents the discontinuous force term experienced by the particle in the x-direction.

[0091] Specifically, by introducing influencing factors such as fluid viscous resistance, discontinuous forces, and relative velocity experienced by particles, the particle velocity is dynamically updated on a time step scale, thereby more realistically reflecting the settling path and dynamic response of particles in complex fracture environments.

[0092] In some embodiments, the method may further include the following: S1: Based on the sedimentation path, determine the spatial coverage parameter of proppant particles inside the target fracture; wherein, the spatial coverage parameter is used to characterize the deposition density of proppant particles at different spatiotemporal locations within the target fracture; S2: Determine the equivalent conductivity index of the target fracture based on the spatial coverage parameter; wherein the equivalent conductivity index is used to quantitatively evaluate the target fracture's ability to maintain fracturing fluid flow after proppant settling.

[0093] Specifically, firstly, based on the sedimentation path, the spatial coverage parameter of proppant particles inside the target fracture is determined. Specifically, based on the spatial grid division results of the fracture, statistical analysis is performed on the proppant sedimentation path of each grid cell throughout the entire prediction time range to determine the coverage of proppant particle deposition within that grid cell, and the spatial coverage parameter of that grid cell is obtained accordingly. The spatial coverage parameter characterizes the deposition density of proppant particles at different spatiotemporal locations within the target fracture, reflecting the spatial uniformity and enrichment of proppant distribution at each location.

[0094] Then, based on the spatial coverage parameter, the equivalent conductivity index of the target fracture is determined. Specifically, based on the coverage distribution at various spatial locations within the fracture and combined with a preset conductivity evaluation standard, an overall conductivity index reflecting the target fracture's ability to maintain fracturing fluid flow after proppant settling is extracted. This equivalent conductivity index can serve as a quantitative parameter for measuring the proppant settling effect and fracture support integrity.

[0095] Through the above process, the key parameters for assessing the proppant flow capacity can be transformed from the sedimentation path without introducing additional formulas and calculation details, ensuring the engineering practicality and data interpretability of the proppant sedimentation simulation process.

[0096] As can be seen from the above, the embodiment of this specification provides a method for determining the settling path of proppant within a fracture. This method acquires the spatial scale parameters and settling time parameters of a target fracture in a target area, and determines the corresponding target fracture parameters based on the spatial scale parameters and the settling time parameters. The target fracture parameters include spatial dimension information and temporal dimension information. Using a first module of a preset proppant settling prediction model, the fluid response parameters of the target fracture at different spatiotemporal locations are determined based on the target fracture parameters. The proppant settling prediction model is a neural network model trained based on a composite loss function, which includes residual terms of the control equations related to proppant migration within the fracture and multi-physical boundary constraint terms reflecting the coupled boundary behavior of the proppant. Using a second module of the preset proppant settling prediction model, the settling velocity and position change information of the proppant particles within the target fracture are determined based on the fluid response parameters. Based on the settling velocity and position change information, the settling path of the proppant particles within the target fracture is determined over the entire prediction time range. The settling path is used for the structured expression of proppant settling behavior and the evaluation of fracture conductivity. Thus, by introducing a neural network model with residual terms of the governing equations and multiple physical boundary constraints, the coupling behavior of fluid and proppant in large-scale fractures can be learned and predicted under physical constraints, significantly improving simulation efficiency and computational accuracy. This method does not rely on costly physical experiments or complex discrete element numerical calculations, enabling dynamic simulation and structured representation of proppant sedimentation patterns in large-scale fractures in a short time. This overcomes the shortcomings of existing technologies in comprehensively revealing particle-scale sedimentation processes, providing efficient and reliable data support for fracture conductivity assessment and fracturing construction optimization.

[0097] See Figure 2 As shown in the embodiments of this specification, a specific electronic device is also provided, wherein the electronic device includes a network communication port 201, a processor 202 and a memory 203, and the above structures are connected by internal cables so that the various structures can perform specific data interaction.

[0098] Specifically, the network communication port 201 can be used to acquire the spatial scale parameters and settlement time parameters of the target crack in the target area, and determine the corresponding target crack parameters based on the spatial scale parameters and the settlement time parameters; wherein, the target crack parameters include spatial dimension information and time dimension information.

[0099] The processor 202 can specifically be used to determine the fluid response parameters of the target fracture at different spatiotemporal locations based on the target fracture parameters using a first module of a preset proppant settling prediction model; wherein the proppant settling prediction model is a neural network model trained based on a composite loss function, the composite loss function including residual terms of the control equations related to proppant migration within the fracture and multi-physical boundary constraint terms reflecting the coupled boundary behavior of the proppant; and using a second module of the preset proppant settling prediction model, determine the settling velocity and position change information of the proppant particles within the target fracture based on the fluid response parameters; and determine the settling path of the proppant particles within the target fracture over the entire prediction time range based on the settling velocity and position change information; wherein the settling path is used for the structured expression of proppant settling behavior and the evaluation of fracture conductivity.

[0100] The memory 203 can be used to store the corresponding instruction program.

[0101] Based on the above method, the relevant structural performance of electronic equipment can be effectively utilized to improve the data processing speed of electronic equipment and efficiently realize a method for determining the settling path of proppant in cracks.

[0102] In this embodiment, the network communication port 201 can be a virtual port bound to different communication protocols, thereby enabling the sending or receiving of different data. For example, the network communication port can be a port responsible for web data communication, a port responsible for FTP data communication, or a port responsible for email data communication. Furthermore, the network communication port can also be a physical communication interface or communication chip. For example, it can be a wireless mobile network communication chip, such as GSM or CDMA; it can also be a Wi-Fi chip; or it can be a Bluetooth chip.

[0103] In this embodiment, the processor 202 can be implemented in any suitable manner. For example, the processor can take the form of a microprocessor or processor and a computer-readable medium storing computer-readable program code (e.g., software or firmware) executable by the (micro)processor, logic gates, switches, application-specific integrated circuits (ASICs), programmable logic controllers, and embedded microcontrollers, etc. This specification is not limiting.

[0104] In this embodiment, the memory 203 may include a hierarchy. In a digital system, anything that can store binary data can be a memory. In an integrated circuit, a circuit with storage function but no physical form is also called a memory, such as RAM, FIFO, etc. In a system, a storage device with a physical form is also called a memory, such as a memory stick, TF card, etc.

[0105] This specification also provides a computer-readable storage medium based on the above-described method for determining the settling path of proppant within a fracture. The method acquires spatial scale parameters and settling time parameters of a target fracture in a target region, and determines corresponding target fracture parameters based on the spatial scale parameters and the settling time parameters. The target fracture parameters include spatial dimension information and temporal dimension information. Using a first module of a pre-set proppant settling prediction model, the fluid response parameters of the target fracture at different spatiotemporal locations are determined based on the target fracture parameters. The proppant settling prediction model is a neural network model trained based on a composite loss function, which includes residual terms of the governing equations related to proppant migration within the fracture and multi-physical boundary constraint terms reflecting the coupled boundary behavior of the proppant. Using a second module of the pre-set proppant settling prediction model, the settling velocity and position change information of proppant particles within the target fracture are determined based on the fluid response parameters. Based on the settling velocity and position change information, the settling path of the proppant particles within the target fracture is determined over the entire prediction time range. The settling path is used for a structured representation of proppant settling behavior and for evaluating the fracture's conductivity.

[0106] In this embodiment, the storage medium includes, but is not limited to, Random Access Memory (RAM), Read-Only Memory (ROM), Cache, Hard Disk Drive (HDD), or Memory Card. The memory can be used to store computer program instructions. The network communication unit can be an interface configured according to standards specified in the communication protocol for network connection communication.

[0107] In this embodiment, the specific functions and effects implemented by the program instructions stored in the computer-readable storage medium can be explained in comparison with other embodiments, and will not be repeated here.

[0108] See Figure 3 At the software level, this specification also provides a device for determining the settling path of proppant within a crack, which may specifically include the following structural modules: The first determining module 301 is used to acquire the spatial scale parameters and settlement time parameters of the target crack in the target area, and determine the corresponding target crack parameters based on the spatial scale parameters and the settlement time parameters; wherein, the target crack parameters include spatial dimension information and time dimension information; The second determining module 302 is used to determine the fluid response parameters of the target crack at different spatiotemporal locations based on the target crack parameters using the first module of the preset proppant settlement prediction model; wherein, the proppant settlement prediction model is a neural network model trained based on a composite loss function, the composite loss function including the residual term of the control equation related to proppant migration within the crack and the multi-physical boundary constraint term reflecting the coupled boundary behavior of the proppant; The third determining module 303 is used to determine the settling velocity and position change information of the proppant particles in the target crack based on the fluid response parameters using the second module of the preset proppant settling prediction model. The path determination module 304 is used to determine the settling path of the proppant particles in the target fracture over the entire predicted time range based on the settling velocity and position change information; wherein the settling path is used for the structured representation of proppant settling behavior and the assessment of fracture conductivity.

[0109] In some embodiments, the first determining module 301 described above, in its specific implementation, includes the following fluid response parameters: horizontal velocity components, vertical velocity components, pressure values, and polymer stress tensors at different spatiotemporal locations within the target crack; the residual terms of the control equation are fluid control residuals constructed based on a preset momentum equation; and the multi-physical boundary constraint terms include: wall slip loss term, inlet boundary loss term, average velocity loss term, pressure drop loss term, vortex loss term, and pressure anchor point loss term.

[0110] In some embodiments, the process of determining the pressure anchor point loss term involves, in specific implementation, determining the reference position coordinates for pressure calibration based on the spatial scale parameters of the target crack; determining the predicted pressure value at the corresponding position based on the reference position coordinates; summing the squares of the predicted pressure values ​​and taking the mean to construct the pressure anchor point loss term; wherein, the pressure anchor point loss term is used to introduce physical constraints on the pressure field of key areas inside the target crack.

[0111] In some embodiments, the process of determining the vortex loss term involves, in specific implementation, determining the velocity field distribution information at the corresponding location based on the horizontal and vertical velocity components of the target crack at different spatiotemporal locations; calculating the partial derivatives of the horizontal velocity component with respect to the vertical direction and the partial derivatives of the vertical velocity component with respect to the horizontal direction based on the velocity field distribution information to determine the predicted vorticity value at the corresponding location; determining the deviation at multiple spatial sampling points based on the predicted vorticity value and the preset target vortex value; and constructing the corresponding vortex loss term based on the deviation. The vortex loss term is used to physically constrain the vortex characteristics in the velocity field.

[0112] In some embodiments, the above-mentioned vortex loss term is determined according to the following formula:

[0113] in, For the vortex loss term, To predict vorticity values, For the target vortex value, The horizontal velocity component is... The vertical velocity component is... Let be the partial derivative of the horizontal velocity with respect to the vertical direction. This is the partial derivative of the vertical velocity with respect to the horizontal direction.

[0114] In some embodiments, the first determining module 301, in specific implementation, determines spatial distribution information for characterizing the crack region based on the spatial scale parameters of the target crack; determines the time evolution interval and time aberration length adapted to the settlement process based on the settlement time parameters of the target crack, and determines the corresponding time sampling information based on the time evolution interval and time aberration length; combines the spatial distribution information and the time sampling information to determine target crack parameters that match the spatial scale parameters of the target crack.

[0115] In some embodiments, the path determination module 304, in specific implementation, determines the spatial position of each proppant particle at the initial moment based on the position change information; determines the displacement increment of each proppant particle between adjacent time steps based on the settling velocity information and a preset time step; determines the updated position of each proppant particle at the current time step based on the spatial position and the displacement increment; determines the motion trajectory of each proppant particle on multiple time steps based on the continuity relationship between the updated position and the position of the previous time step; and determines the settling path of the proppant particles in the target crack throughout the entire predicted time range based on the continuous distribution of the motion trajectory within the predicted time range.

[0116] In some embodiments, the device further includes: determining a spatial coverage parameter of proppant particles inside the target fracture based on the sedimentation path; wherein the spatial coverage parameter is used to characterize the deposition density of the proppant particles at different spatiotemporal locations within the target fracture; and determining an equivalent conductivity index of the target fracture based on the spatial coverage parameter; wherein the equivalent conductivity index is used to quantitatively evaluate the target fracture's ability to maintain fracturing fluid flow after proppant sedimentation.

[0117] It should be noted that the units, devices, or modules described in the above embodiments can be implemented by computer chips or physical entities, or by products with certain functions. For ease of description, the above devices are described by dividing them into various modules according to their functions. Of course, in implementing this specification, the functions of each module can be implemented in the same software and / or hardware, or modules that implement the same function can be implemented by a combination of sub-modules or sub-units, etc. The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and there may be other division methods in actual implementation. For example, units or components can be combined or integrated into another system, or some features can be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection between the devices or units shown or discussed can be through some interfaces, and the indirect coupling or communication connection between devices or units can be electrical, mechanical, or other forms.

[0118] As can be seen from the above, based on the proppant settling path determination device provided in the embodiments of this specification, the spatial scale parameters and settling time parameters of the target crack in the target area are obtained, and the corresponding target crack parameters are determined according to the spatial scale parameters and the settling time parameters; wherein, the target crack parameters include spatial dimension information and temporal dimension information; using the first module of the preset proppant settling prediction model, the fluid response parameters of the target crack at different spatiotemporal locations are determined according to the target crack parameters; wherein, the proppant settling prediction model is a neural network model trained based on a composite loss function, the composite loss function including the residual term of the control equation related to proppant migration in the crack and the multi-physical boundary constraint term reflecting the coupled boundary behavior of the proppant; using the second module of the preset proppant settling prediction model, the settling velocity and position change information of the proppant particles in the target crack are determined according to the fluid response parameters; and the settling path of the proppant particles in the target crack is determined according to the settling velocity and position change information over the entire prediction time range; wherein, the settling path is used for the structured expression of proppant settling behavior and the evaluation of crack conduction capacity.

[0119] In a specific scenario example, the method and apparatus for determining the settlement path of proppant within a crack, provided in this specification, can be applied. This solves the problems of long calculation times, scale limitations, and difficulty in accurately reflecting the actual migration patterns in predicting proppant settlement within large-scale cracks using traditional numerical simulation methods. The specific implementation process may include the following:

[0120] In some embodiments, the target fracture is set with a length of 1 m, a width of 6 mm, and a height of 0.3 m to simulate the settling process of proppant particles inside the fracture. In this implementation, a constant flow velocity of 0.4 m / s is set along the fracture axial direction, and the total simulation time is 2 s; the direction of gravitational acceleration is set vertically downwards, with a magnitude of -9.81 m / s². The fracturing fluid carrying the proppant is a shear-thinning fluid with the following physical parameters: fluid density of 1000 kg / m³, consistency coefficient k of 0.145 Pa·s⁻¹. The fluid has a flow index of 0.5, a solvent zero-shear viscosity of 0.05 Pa·s, and a shear thinning coefficient α of 0.2. The viscoelastic characteristics of the fracturing fluid are characterized by the elastic modulus G = 200 Pa and the relaxation time λ = 12 s. The proppant particles are particulate materials with a density of 2650 kg / m³.

[0121] Under the aforementioned conditions, a dynamic model characterizing the particle settling process is constructed based on the fracture geometric boundary and fluid properties. Combining this model with the particle-fluid interaction mechanism, the settling path of the particles at different time steps is determined. Furthermore, based on the particle trajectories, the coverage distribution of particles at various locations within the target fracture space is calculated, yielding the corresponding spatial coverage parameters. Subsequently, based on the spatial deposition characteristics of the particles, the equivalent conductivity index of the fracture after proppant settling is determined, characterizing the changing trend of the fracture's ability to maintain fracturing fluid flow.

[0122] In some embodiments, see Figure 4 As shown in the figure, the average inlet velocity during training changes with the number of training epochs, which is used to characterize the degree to which the boundary constraints of the physical-guided neural network model are satisfied. Figure 4 The ordinate (Avg Inlet ux (m / s)) represents the average value (in m / s) of the lateral velocity component of the inlet region predicted by the model after each training round, while the abscissa represents the number of training rounds.

[0123] from Figure 4It can be seen that the average entry speed rises rapidly in the early stage of training, reaching a peak (greater than 2 m / s) around the 50th round. Subsequently, as the boundary terms in the loss function gradually take effect on the model's inverse constraints, the model's output entry speed drops rapidly and tends to stabilize. After 100 rounds, the average speed stabilizes at around 0.4 m / s, and then maintains small fluctuations in larger training rounds. This indicates that the constructed neural network has effectively learned the entry boundary conditions and gradually optimized to a stable state that satisfies the target entry speed constraint during training.

[0124] The results validate the effectiveness of introducing an inlet boundary loss term during training. This constraint allows the model to adaptively adjust network parameters to approximate the set inlet velocity target distribution, thereby improving overall physical consistency and prediction accuracy. This training process can be combined with other boundary condition loss terms and physical conservation equation residual terms to construct a composite loss function, forming a multi-source constraint hybrid optimization mechanism to enhance the generalization ability of neural networks under complex flow conditions.

[0125] In some embodiments, see Figure 5 As shown in the figure, the changing trends of various loss terms during the training of the Physical Information Neural Network (PINN) are illustrated. These are the PINN loss components, with the horizontal axis representing the training epoch and the vertical axis representing the loss value. Specifically, Figure 5 Using the training epoch as the x-axis and the logarithm of different loss terms as the y-axis, we plotted the evolution curves of the momentum conservation residual, the continuity residual, the initial condition, the wall boundary, the inlet boundary, the outlet boundary, and the total loss term as they evolved during the training process.

[0126] from Figure 5 As can be seen, all loss terms are at a relatively high level in the early stages of training. With iterative updates to the network parameters, the losses gradually decrease and tend to stabilize. Among them, the momentum and continuity terms show the largest decreases in the first 100 rounds, indicating that the neural network has learned the physical constraints of the governing equations well in the early stages. The initial condition terms and boundary condition terms (including entrance, wall, and exit) continue to decrease slowly after 200 rounds, reflecting the long-term impact of boundary information on network learning. The total loss term curve shows the overall trend of the sum of multiple losses, and its fluctuations in the later stages of training are mainly caused by perturbations of individual boundary terms.

[0127] The results demonstrate that the composite loss function mechanism, constructed using multiple loss terms, can guide the neural network to simultaneously satisfy multiple physical constraints. During training, the decay rate and stable value of different loss terms reflect the contribution intensity of each physical constraint to the network optimization process, thus providing a quantitative basis for the subsequent dynamic adjustment of weight factors and loss term design. This method is suitable for handling complex flow problems with multiple boundaries and constraints, exhibiting high training stability and physical consistency.

[0128] In some embodiments, see Figure 6 As shown in the figure, the flow field and particle trajectory generated based on the solution results of the Physical Information Neural Network (PINN) are illustrated. The crack region is constructed using two-dimensional coordinates (X, Z), with a gray background representing the velocity distribution of the fluid in the horizontal direction (x-direction). Colors from dark to light represent the velocity distribution from low to high. It can be seen that the flow velocity is higher near the center of the crack, while the velocity near the upper and lower boundaries approaches zero, consistent with the flow characteristics of viscous fluids satisfying no-slip conditions in the wall region.

[0129] The figure overlays the particle paths, representing the actual settling trajectories of specific particles under the influence of the flow field. As shown, after entering from the initial position at the inlet, the particles travel primarily along a horizontal path, indicating that under conditions where flow velocity dominates and particle gravity has a relatively small effect, the particle settling depth is limited. This result verifies the accuracy of the aforementioned particle settling velocity calculation module and reflects that under specific crack structures and flow field boundary conditions, particles tend to migrate horizontally rather than settle vertically.

[0130] The visualization of this figure verifies that the particle-fluid coupling field based on PINN simulation has good physical consistency and flow trend capture ability, which can provide data support for subsequent assessment of fracturing proppant deposition distribution and proppant carrying capacity.

[0131] In some embodiments, see Figure 7 As shown in the figure, the streamline diagram within the two-dimensional crack region generated by the trained PINN neural network is used to reveal the flow field structure and local anomalous flow behaviors such as backflow / vortices. In the figure, the x-axis and z-axis represent the length and height directions of the crack, respectively. The streamlines are indicated by arrows representing the instantaneous flow direction of the fluid. The arrow density and color represent the flow velocity magnitude, and their value distribution is shown in the grayscale bar of velocity magnitude on the right side of the figure.

[0132] As can be observed from the figure, the overall flow trend proceeds along the x-direction, conforming to the preset inlet velocity boundary conditions. However, near the upper and lower boundaries of the crack and around x=0.5 m in the middle, significant streamline bending and aggregation phenomena occur, forming local backflow zones and even weak vortex structures. The existence of these local backflow and disturbance zones will affect the migration and deposition behavior of sand-carrying particles, especially near the boundary where particle accumulation zones are prone to form.

[0133] The results shown in the figure verify that the velocity vector field generated based on PINN simulation has good physical consistency and resolution, and can accurately identify the abnormal flow regions inside the fracture, thus providing a basis for the analysis of the flow field structure inside the fracture, the prediction of proppant settlement, and the evaluation of fracturing effect.

[0134] In some embodiments, see Figure 8 As shown in the figure, the graph illustrates the change in proppant settling speed versus time, generated under the PINN prediction results, to analyze the settling behavior of particles under non-Newtonian fluid conditions. The horizontal axis (Time (s)) represents the simulation time (in seconds), and the vertical axis (Settling speed (m / s)) represents the vertical settling speed (in meters per second). A negative settling speed indicates that the particles are moving along the direction of gravity.

[0135] like Figure 8 As shown, the sand-carrying particles rapidly acquire settling velocity under the influence of gravity at the initial moment. Subsequently, the settling velocity slightly decreases, exhibiting an overall approximately linear decreasing trend. This indicates that under low Reynolds number conditions, the particles are subjected to the combined effects of fluid resistance and changes in shear rate, resulting in typical deceleration settling characteristics. This result verifies that the Physical Information Neural Network (PINN) constructed in this application can accurately capture the dynamic evolution of force balance and rheological coupling during particle settling, considering non-Newtonian shear thinning characteristics and elastic response.

[0136] While this specification provides the steps of operation for the methods described in the embodiments or flowcharts, more or fewer steps may be included based on conventional or non-inventive means. The order of steps listed in the embodiments is merely one possible order of execution among many steps and does not represent the only possible order. In actual device or client product execution, the methods shown in the embodiments or drawings may be executed sequentially or in parallel (e.g., in a parallel processor or multi-threaded processing environment, or even a distributed data processing environment). The terms "comprising," "including," or any other variations thereof are intended to cover a non-exclusive inclusion, such that a process, method, product, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, product, or apparatus. Without further limitations, the presence of other identical or equivalent elements in a process, method, product, or apparatus that includes said elements is not excluded. The terms "first," "second," etc., are used to denote names and do not indicate any particular order.

[0137] Those skilled in the art will also know that, besides implementing the controller using purely computer-readable program code, the same functions can be achieved by logically programming the method steps, making the controller function as logic gates, switches, application-specific integrated circuits (ASICs), programmable logic controllers (PLCs), and embedded microcontrollers. Therefore, such a controller can be considered a hardware component, and the devices within it used to implement various functions can also be considered structures within that hardware component. Alternatively, the devices used to implement various functions can be considered as both software modules implementing the method and structures within a hardware component.

[0138] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that this specification can be implemented by means of software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solutions of this specification can essentially be embodied in the form of a software product. This computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, mobile terminal, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments of this specification.

[0139] Although this specification has been described by way of examples, those skilled in the art will recognize that many variations and modifications are possible without departing from the spirit of this specification, and it is intended that the appended claims cover such variations and modifications without departing from the spirit of this specification.

Claims

1. A method for determining the settlement path of proppant within a crack, characterized in that, include: The spatial scale parameters and settlement time parameters of the target crack in the target area are obtained, and the corresponding target crack parameters are determined based on the spatial scale parameters and the settlement time parameters; wherein, the target crack parameters include spatial dimension information and temporal dimension information; Using the first module of a pre-defined proppant settling prediction model, the fluid response parameters of the target crack at different spatiotemporal locations are determined based on the target crack parameters; wherein, the proppant settling prediction model is a neural network model trained based on a composite loss function, the composite loss function including residual terms of the control equation related to proppant migration within the crack and multi-physical boundary constraint terms reflecting the coupled boundary behavior of the proppant; The second module of the preset proppant settling prediction model determines the settling velocity and position change information of the proppant particles in the target crack based on the fluid response parameters. Based on the settlement velocity and location change information, the settlement path of the proppant particles within the target fracture is determined over the entire predicted time range; wherein, the settlement path is used for a structured representation of the proppant settlement behavior and an assessment of the fracture's conductivity.

2. The method according to claim 1, characterized in that, The fluid response parameters include: horizontal velocity components, vertical velocity components, pressure values, and polymer stress tensors at different spatiotemporal locations within the target crack; the residual terms of the governing equations are fluid control residuals constructed based on a preset momentum equation; the multi-physical boundary constraint terms include: wall slip loss term, inlet boundary loss term, average velocity loss term, pressure drop loss term, vortex loss term, and pressure anchor point loss term.

3. The method according to claim 2, characterized in that, The process of determining the pressure anchor point loss term includes: Based on the spatial scale parameters of the target crack, determine the reference position coordinates for pressure calibration; Based on the reference position coordinates, determine the predicted pressure value at the corresponding position; The squares of the predicted pressure values ​​are summed and the mean is taken to construct the pressure anchor point loss term; wherein, the pressure anchor point loss term is used to introduce physical constraints on the pressure field of key areas inside the target crack.

4. The method according to claim 2, characterized in that, The process of determining the vortex loss term includes: Based on the horizontal and vertical velocity components of the target crack at different spatiotemporal locations, determine the velocity field distribution information at the corresponding locations; Based on the velocity field distribution information, calculate the partial derivatives of the horizontal velocity component with respect to the vertical direction and the partial derivatives of the vertical velocity component with respect to the horizontal direction to determine the predicted vorticity value at the corresponding location. Based on the predicted vorticity value and the preset target vortex value, the deviation at multiple spatial sampling points is determined; Based on the deviation, a corresponding vortex loss term is constructed; wherein, the vortex loss term is used to physically constrain the vortex characteristics in the velocity field.

5. The method according to claim 4, characterized in that, The vortex loss term is determined according to the following formula: in, For the vortex loss term, To predict vorticity values, For the target vortex value, The horizontal velocity component is... The vertical velocity component is... Let be the partial derivative of the horizontal velocity with respect to the vertical direction. This is the partial derivative of the vertical velocity with respect to the horizontal direction.

6. The method according to claim 1, characterized in that, Determining the corresponding target crack parameters based on the spatial scale parameters and the settlement time parameters includes: Based on the spatial scale parameters of the target crack, determine the spatial distribution information used to characterize the crack region; Based on the target crack settlement time parameters, determine the time evolution interval and time deviation length suitable for the settlement process, and determine the corresponding time sampling information based on the time evolution interval and time deviation length; The spatial distribution information is combined with the temporal sampling information to determine the target crack parameters that match the spatial scale parameters of the target crack.

7. The method according to claim 1, characterized in that, The step of determining the settlement path of the proppant particles within the target fracture over the entire predicted time range based on the settlement velocity and location change information includes: Based on the position change information, the spatial position of each proppant particle at the initial moment is determined; Based on the settling velocity information and the preset time step, the displacement increment of each proppant particle between adjacent time steps is determined; Based on the spatial location and the displacement increment, determine the updated position of each proppant particle at the current time step; Based on the continuity between the updated position and the previous time step position, the motion trajectory of each proppant particle at multiple time steps is determined. Based on the continuous distribution of the motion trajectory within the predicted time range, the settling path of the proppant particles within the target crack is determined throughout the entire predicted time range.

8. The method according to claim 1, characterized in that, The method further includes: Based on the sedimentation path, the spatial coverage parameter of proppant particles inside the target fracture is determined; wherein, the spatial coverage parameter is used to characterize the deposition density of proppant particles at different spatiotemporal locations within the target fracture; Based on the spatial coverage parameter, the equivalent conductivity index of the target fracture is determined; wherein, the equivalent conductivity index is used to quantitatively evaluate the target fracture's ability to maintain fracturing fluid flow after proppant settling.

9. A device for determining the settling path of proppant within a crack, characterized in that, include: The first determining module is used to acquire the spatial scale parameters and settlement time parameters of the target crack in the target area, and determine the corresponding target crack parameters based on the spatial scale parameters and the settlement time parameters; wherein, the target crack parameters include spatial dimension information and time dimension information; The second determining module is used to determine the fluid response parameters of the target crack at different spatiotemporal locations based on the target crack parameters using the first module of the preset proppant settlement prediction model; wherein, the proppant settlement prediction model is a neural network model trained based on a composite loss function, the composite loss function including the residual term of the control equation related to proppant migration within the crack and the multi-physical boundary constraint term reflecting the coupled boundary behavior of the proppant; The third determining module is used to determine the settling velocity and position change information of the proppant particles in the target crack based on the fluid response parameters, using the second module of the preset proppant settling prediction model. The path determination module is used to determine the settling path of the proppant particles within the target fracture over the entire predicted time range based on the settling velocity and position change information; wherein, the settling path is used for the structured representation of proppant settling behavior and the assessment of fracture conductivity.

10. An electronic device, characterized in that, It includes a processor and a memory for storing processor-executable instructions, wherein the processor, when executing the instructions, implements the steps of the method for determining the proppant settling path within a fracture as described in any one of claims 1 to 8.

Images