A Stochastic Inversion Method for Heat Transfer Data Based on Fracture Network

Abstract

The present invention relates to the technical field of fracture network research, and discloses a stochastic inversion method for heat transfer data based on a fracture network, which includes the following steps: Step 1, obtain fracture network data; Step 2, input the fracture network data into a heat transfer numerical simulation model to simulate the temperature breakthrough curves (BTCs) between injection and production wells; Step 3, use an efficient curve fitting algorithm to compare the simulated BTCs with the measurement data of the actual site to quantify the adaptation degree of different fracture network models; Step 4, sort the generated fracture network data according to the fitting results, and select the fracture network configuration that best matches the actual data as the inversion result. Compared with traditional methods that often rely on repeatedly running numerical models with high computational costs and are difficult to quickly explore the optimal solution in complex fracture fields, the present invention has high efficiency and accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of fracture network research, and particularly to a stochastic inversion method for heat transfer data based on a fracture network. Background Art

[0002] The geometric morphology and connectivity of fracture networks in enhanced geothermal systems (EGS) have a crucial impact on heat transfer efficiency and fluid flow. Characterizing fracture networks through heat transfer data inversion has become an important research method. Heat transfer data are usually recorded in the form of temperature breakthrough curves (BTCs) between injection and production wells. These data can reflect the heat transfer behavior of fluids passing through fracture networks and provide important bases for inverting fracture network characteristics. However, due to the high nonlinearity, heterogeneity, and complex geometric topology of fracture networks, accurate characterization still faces many technical challenges.

[0003] There are significant deficiencies in existing technologies for fracture network inversion. First, fracture network inversion is a non-linear and ill-posed problem. Single temperature data are not sufficient to fully constrain the geometric parameters of fractures, easily leading to non-unique solutions or uncertainties in inversion results. Second, in the characterization of fracture geometric features, existing methods often neglect key factors such as fracture directionality, aperture, length, and connectivity, and the generated models lack physical authenticity. In addition, the computational cost of numerical simulation is high. Especially in complex fracture networks, the process of solving transient fluid flow and heat transfer equations is time-consuming and laborious. Thousands of simulation models need to be run in inversion, and the efficiency is extremely low. Finally, current inversion methods are difficult to adapt to the geological characteristics of different geothermal fields, such as the main direction, distribution density, and connectivity of fractures.

[0004] To address the above deficiencies, this study develops a data-driven inversion method to explore a more efficient and accurate fracture network characterization scheme. This method can not only reduce the computational cost but also enhance the adaptability to different geological characteristics, thus providing new theoretical support and practical paths for geothermal energy development. Summary of the Invention

[0005] To solve the technical problems raised in the background art, the present invention provides an efficient fracture network characterization method based on heat transfer data inversion.

[0006] The present invention is implemented by the following technical solutions: A stochastic inversion method for heat transfer data based on a fracture network, comprising the following steps:

[0007] Step 1: Obtain fracture network data;

[0008] Step 2: Input the fracture network data into a heat transfer numerical simulation model to simulate the temperature breakthrough curve (BTCs) between injection and production wells;

[0009] Step 3: Use an efficient curve fitting algorithm to compare the simulated BTCs with the measurement data of the actual site and quantify the adaptation degree of different fracture network models;

[0010] Step 4: Sort the generated fracture network data according to the fitting results and select the fracture network configuration that best matches the actual data as the inversion result.

[0011] Construct a reference data set

[0012] Establish a number of reference fracture networks and conduct numerical simulations of the fluid-heat transfer process on them to obtain high-resolution temperature breakthrough curves (BTCs) as the benchmark data for subsequent inversion analysis. These reference data sets are sourced from actual measurement data or highly reliable synthetic simulation data to ensure representativeness for the target site.

[0013] The specific steps of Step 3 are as follows: Match the simulated curve with the reference data

[0014] Compare the simulated BTCs corresponding to each generated fracture network with the reference BTCs, and use the root mean square error (RMSE) as the metric for the matching error to quantify the difference between the two sets of data at key monitoring points. The calculation of RMSE covers the overall shape of the temperature curve and the change trend at key nodes to ensure the comprehensiveness and accuracy of the evaluation results.

[0015] Optionally, the specific steps of Step 4 are as follows: The operation of optimizing the fracture network is as follows:

[0016] Based on the matching results, select the fracture network with the minimum error as the inversion result. Specifically, select the top 100 fracture networks with the lowest RMSE values, representing the set of fracture geometric features that best match the reference thermal behavior; this method can not only reduce the uncertainty of a single solution but also further explore the equivalence and possible geometric variability of the fracture network through statistical analysis.

[0017] Optionally, it further includes Step 5, which conducts diversity analysis and parameter optimization

[0018] Conduct further analysis on the selected set of fracture networks to explore the variation range of geometric parameters such as fracture length, azimuth angle, and position and their impact on the BTCs matching. Through the diversity statistics of different fracture geometric characteristics, the control mechanism of the fracture network on the heat transfer process can be deeply understood, providing a theoretical basis for subsequent parameter optimization.

[0019] Optionally, the fracture network data can be obtained through a fracture network generation method, which specifically includes the following steps:

[0020] Step 1.1: Parameter setting and initialization in matlab;

[0021] Step 1.2: Generate a fracture network;

[0022] Step 1.3, read the fracture network data generated in Step 1.2, store the data in a three-dimensional matrix DataDFN_CNN, and save it as a data in the format of DataDFN_CNN.mat;

[0023] The operation of Step 1.2 is as follows:

[0024] Step a: Generate fracture lengths;

[0025] Step b: Generate fracture angles;

[0026] Step c: Randomly generate fracture positions;

[0027] Step d: Detect and remove shadow areas;

[0028] Step e: Fracture intersection requirements;

[0029] Step f: Judge the connectivity of the fracture network;

[0030] Step g: Save the finally generated fracture network data as a matrix format with a size of Nfrac*4, where: Nfrac: represents the number of generated fractures, and each row represents a fracture; 4: represents the four key attributes of each fracture.

[0031] Optionally, the numerical model simulation is constructed by the following method;

[0032] Establish a physical model; Fluid flow is based on Darcy's law, cubic law, and considering the hydraulic coupling between fractures and matrix, ensuring the dynamic balance between different regions before establishment; Heat transfer is based on the convection-conduction coupling equation and the heat exchange model between fractures and matrix;

[0033] Numerical discretization and solution method; The discretization method includes using the finite element method (FEM) to discretize the fluid and heat transfer equations and using a time stepping scheme; The solution process solves the transient flow and heat transfer equation sets by configuring stable iterative algorithms, such as the successive iteration method or nonlinear solver, and optimizes the computational efficiency of large-scale numerical models through parallel computing and appropriate convergence criteria;

[0034] Set model parameters and boundary conditions;

[0035] Establish a two-dimensional geothermal reservoir model to simulate the fracture network and matrix regions in the geothermal system. The typical size of the domain is 200m×200m, and set the wellbore regions on both sides, which are injection wells and production wells respectively, and the wellbore regions are given high permeability and high porosity;

[0036] Boundary conditions:

[0037] The left injection well is set under constant hydraulic head and low temperature (20 °C) conditions to simulate the cold water injection process.

[0038] The right production well is set under constant hydraulic head and heat outflow conditions to simulate the hot water collection.

[0039] The upper and lower boundaries are set as adiabatic boundaries to avoid heat exchange with the external environment.

[0040] The initial condition is set as a uniform temperature distribution of 100 °C for both the matrix and the fracture network.

[0041] Material properties:

[0042] Fracture area: high conductivity, low porosity, emphasizing that fractures are the main channels for fluids.

[0043] Matrix area: low conductivity, high porosity, ensuring that heat conduction is the main heat transfer mode;

[0044] Thermophysical parameters such as thermal conductivity, specific heat capacity, and density are set according to typical geothermal reservoir lithology parameters.

[0045] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0046] The fracture network generation algorithm of the present invention generates a large number of fracture networks that satisfy geometric constraints. Subsequently, based on the fluid - heat transfer model coupling porous media and fractures, the heat transfer process of each fracture network is numerically simulated to generate the temperature breakthrough curves (BTCs) between injection and production wells. Then, by fitting the simulated BTCs with the actual observed data, the fitness of each fracture network is quantitatively evaluated, and finally the fracture configuration that best matches the actual site is selected.

[0047] The core of the present invention lies in its high efficiency and accuracy. Compared with traditional methods that often rely on repeatedly running numerically expensive models and are difficult to quickly explore the optimal solution in complex fracture fields, the present invention has the following improvements:

[0048] 1. Greatly improve the inversion efficiency: enabling rapid simulation and inversion of large - scale fracture networks, providing feasibility for the design and optimization of enhanced geothermal systems.

[0049] 2. Support multi - scenario applications: applicable to the fracture network characterization and design optimization of actual geothermal sites, and can also be extended to the analysis of fluid and heat transfer processes in other energy systems.

[0050] 3. Reduce the computational cost: reducing the dependence on high - performance computing equipment and significantly reducing the computational time, providing support for economic analysis in geothermal development.

[0051] Therefore, the present invention not only breaks through the efficiency bottleneck of fracture network characterization, but also provides a new idea for the performance improvement and optimal design of geothermal systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a sample diagram of fracture network data produced by the present invention;

[0053] Figure 2 It is a dynamic distribution diagram of the temperature field output by the numerical simulation of the present invention;

[0054] Figure 3 It is a temperature breakthrough curve graph of each monitoring point;

[0055] Figure 4 It is a comparison diagram of fracture network inversion using the characterization method proposed by the present invention;

[0056] Figure 5 It is a flow chart of the inversion method proposed by the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0057] Next, in combination with the accompanying drawings and specific embodiments, the present invention will be further described. It should be noted that, on the premise of no conflict, the following described embodiments or technical features can be arbitrarily combined to form new embodiments.

[0058] Embodiment 1:

[0059] Referring to Figures 1 - 5 , a stochastic inversion method for heat transfer data based on a fracture network proposed in this solution includes the following steps:

[0060] Step 1. Obtain fracture network data;

[0061] Step 2. Input the fracture network data into the heat transfer numerical simulation model to simulate the temperature breakthrough curves (BTCs) between injection and production wells;

[0062] Step 3. Adopt an efficient curve fitting algorithm to compare the simulated BTCs with the measurement data of the actual site, and quantify the adaptation degree of different fracture network models;

[0063] Step 4. Sort the generated fracture network data according to the fitting results, and select the fracture network configuration that best matches the actual data as the inversion result.

[0064] Construct a reference data set

[0065] A number of reference fracture networks are established, and numerical simulations of the fluid-heat transfer process are carried out on them to obtain high-resolution temperature breakthrough curves (BTCs) as benchmark data for subsequent inversion analysis. These reference data sets are derived from actual measurement data or highly reliable synthetic simulation data to ensure representativeness of the target site.

[0066] The specific steps of Step 3 are as follows: Matching the simulated curve with the reference data

[0067] Compare the simulated BTCs corresponding to each generated fracture network with the reference BTCs. Use the root mean square error (RMSE) as a metric for the matching error to quantify the differences between the two sets of data at key monitoring points. The calculation of RMSE covers the overall shape of the temperature curve and the change trends at key nodes, ensuring the comprehensiveness and accuracy of the evaluation results.

[0068] Optionally, the specific steps of Step 4 are as follows: The operation of optimizing the fracture network is as follows:

[0069] Based on the matching results, select the fracture network with the minimum error as the inversion result. Specifically, select the top 100 fracture networks with the lowest RMSE values, representing the set of fracture geometric features that best match the reference thermal behavior. This method can not only reduce the uncertainty of a single solution but also further explore the equivalence and possible geometric variability of the fracture network through statistical analysis.

[0070] Optionally, it further includes Step 5 for diversity analysis and parameter optimization

[0071] Conduct further analysis on the optimized set of fracture networks to explore the variation ranges of geometric parameters such as fracture length, azimuth angle, and position and their impacts on the BTCs matching. Through the diversity statistics of different fracture geometric characteristics, the control mechanism of the fracture network on the heat transfer process can be deeply understood, providing a theoretical basis for subsequent parameter optimization.

[0072] Optionally, the numerical model simulation is constructed by the following method;

[0073] Physical model establishment; Fluid flow is established based on Darcy's law, cubic law, and considering the hydraulic coupling between fractures and matrix to ensure the dynamic balance of fluid between different regions; Heat transfer is established based on the convection-conduction coupling equation and the heat exchange model between fractures and matrix;

[0074] Numerical discretization and solution method; The discretization method includes using the finite element method (FEM) to discretize the fluid and heat transfer equations and using a time stepping scheme; The solution process solves the transient flow and heat transfer equations through a stable iterative algorithm such as the successive iterative method or a nonlinear solver, and optimizes the computational efficiency of large-scale numerical models through parallel computing and appropriate convergence criteria;

[0075] Set model parameters and boundary conditions;

[0076] Establish a two-dimensional geothermal reservoir model to simulate the fracture network and matrix region in the geothermal system. The typical size of the domain is 200m×200m. Set the wellbore regions on both sides, namely the injection well and the production well respectively. The wellbore regions are given high permeability and high porosity;

[0077] Boundary conditions:

[0078] Set a constant hydraulic head and low temperature (20°C) condition for the left injection well to simulate the cold water injection process.

[0079] Set a constant hydraulic head and heat outflow condition for the right production well to simulate the hot water extraction.

[0080] Set the upper and lower boundaries as adiabatic boundaries to avoid heat exchange with the external environment.

[0081] Set the initial condition as a uniform temperature distribution of 100°C for both the matrix and the fracture network.

[0082] Material properties:

[0083] Fracture region: High conductivity, low porosity, emphasizing that fractures are the main channels for fluids.

[0084] Matrix region: Low conductivity, high porosity, ensuring that heat conduction is the main heat transfer mode;

[0085] Set the thermophysical parameters such as thermal conductivity, specific heat capacity, and density according to the typical geothermal reservoir lithology parameters.

[0086] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0087] The fracture network generation algorithm of the present invention generates a large number of fracture networks that meet geometric constraints. Subsequently, based on the fluid - heat transfer model coupling porous media and fractures, the heat transfer process of each fracture network is numerically simulated to generate the temperature breakthrough curves (BTCs) between the injection and production wells. Then, by fitting the simulated BTCs with the actual observed data, the fitness of each fracture network is quantitatively evaluated, and finally the fracture configuration that best matches the actual site is selected.

[0088] Example 2: In this solution, the fracture network data can be obtained through the fracture network generation method, which specifically includes the following steps:

[0089] Step 1.1: Parameter setting and initialization in matlab.

[0090] Step 1.2: Generate the fracture network;

[0091] Step 1.3: Read the fracture network data generated in Step 1.2, store the data in the three-dimensional matrix DataDFN_CNN, and save it as a data in the format of DataDFN_CNN.mat;

[0092] The operations in Step 1.2 are as follows:

[0093] Step a: Fracture length generation;

[0094] Step b: Fracture angle generation;

[0095] Step c: Random generation of fracture positions;

[0096] Step d: Shadow area detection and removal;

[0097] Step e: Fracture intersection requirements;

[0098] Step f: Judgment of fracture network connectivity;

[0099] Step g: Save the finally generated fracture network data as a matrix format with a size of Nfrac * 4, where: Nfrac: represents the number of generated fractures, and each row represents a fracture; 4: represents the four key attributes of each fracture.

[0100] Specifically, the parameter settings and initialization operations are as follows:

[0101] Number of fractures: The number of fractures in each fracture network is randomly generated, and the range of the number of fractures is set according to requirements, such as between [14, 20].

[0102] Fracture angle: Set the fracture direction parameters angle1 = -10 and angle2 = 65, representing two main fracture directions. std = 2 is the standard deviation of the fracture angle.

[0103] Spatial size: Define the spatial size of the fracture network, xL = 200, yL = 200, and set the minimum value lmin = 50 and the maximum value lbig = 140 of the fracture length.

[0104] The operations to generate the fracture network include the following steps.

[0105] Fracture length generation

[0106] The fracture length is generated according to the statistical model of fractal geometry, and the specific steps are as follows:

[0107] Parameter setting: Set the range between the minimum value lminl and the maximum value lbig of the fracture length. The length of each fracture is randomly generated within this range.

[0108] Distribution generation: Use the fractional dimension D and the power a to control the distribution of fracture lengths. Calculate the probability distribution of fracture lengths through the following formula.

[0109] N fra (L) = c·L -a

[0110] where L is the length of the fracture, a is the power controlling the fracture length distribution, and c is the normalization constant. The lengths generated in this way follow a power-law distribution and can simulate the distribution of fractures of different lengths in nature.

[0111] Random length generation: Generate the length of each fracture through the cumulative distribution function (CDF). The fracture lengths are obtained by random number sampling to ensure the diversity of the fracture network.

[0112] Fracture angle generation; The angles of the fractures are generated based on a normal distribution and randomly deviate from two main directions:

[0113] Main angles: Set two main directions, namely θ1 = -10° and θ2 = 65°.

[0114] Random deviation: Use a normal distribution with a standard deviation σ = 2° to generate the actual angle of each fracture. Some fractures will randomly deviate from the main direction to simulate the direction changes in the fracture network.

[0115] Angle normalization: Ensure that the generated angles are between 0° and 180° to avoid overly large or small angles.

[0116] Random generation of fracture positions;

[0117] Random center point generation: Randomly generate the center point positions of each fracture within the set domain [0, xL] × [0, yL]. This position follows a uniform distribution.

[0118] Specific area generation: For the first few fractures, a specific y-direction distribution can be set so that their centers are located in a specific area (such as near the center of the domain) to simulate a more ordered fracture distribution.

[0119] Shadow area detection and removal;

[0120] After generating the fractures, it is necessary to detect whether the newly generated fractures invade the shadow areas of the existing fractures:

[0121] Shadow area generation: Generate a shadow area for each fracture, usually a certain width (w, 2 unit lengths) around the fracture, and this area represents the influence range of the fracture.

[0122] Shadow area detection: Through the geometric intersection algorithm, detect whether the newly generated crack overlaps with the existing crack shadow area. If there is an overlap, it means that the generation position of the new crack is inappropriate, and the center position or angle needs to be regenerated.

[0123] Crack intersection requirements;

[0124] The connectivity of the crack network is achieved by forcing the new crack to intersect with the existing cracks:

[0125] Forced intersection: For each newly generated crack, require it to intersect with at least 1 existing crack. This process is achieved by detecting the geometric intersection points of the two cracks.

[0126] Geometric intersection detection: Use the geometric intersection algorithm to detect whether two cracks intersect. If the intersection requirement is not met, the algorithm will regenerate the center or angle of the crack until the intersection condition is satisfied.

[0127] Judgment of crack network penetrability;

[0128] The finally generated crack network needs to ensure that it penetrates from the left side to the right side of the domain:

[0129] Left - right penetration detection: After the crack network is generated, the algorithm will check whether there is a connected path from x = 0 at the left side of the domain to x = xL at the right side. Only when the crack network meets this connectivity will it be considered a qualified crack network.

[0130] Penetrability determination: If the crack network does not meet the penetrability requirement, the generation process will start over until a penetrating crack network is generated.

[0131] The generated crack network data will finally be saved in a matrix format of size Nfrac * 4. Among them:

[0132] Nfrac: Represents the number of generated cracks (fractures), and each row represents a crack. 4: Represents the four key attributes of each crack, specifically: x1: The x - coordinate of the starting point of the crack. y1: The y - coordinate of the starting point of the crack. x2: The x - coordinate of the ending point of the crack. y2: The y - coordinate of the ending point of the crack. A total of 9000 such crack network samples are generated as training data.

[0133] An example is as shown in the following table, specifically as Figure 1 shown.

[0134]

[0135]

[0136] The above embodiments are only the preferred embodiments of the present invention, and cannot be used to limit the scope of protection of the present invention. Any non-substantive changes and substitutions made by those skilled in the art based on the present invention fall within the scope of protection required by the present invention.

Claims

1. A random inversion method for heat transfer data based on a fracture network, characterized in that It includes the following steps: Step 1: Obtain fracture network data; Step 2: Input the fracture network data into a heat transfer numerical simulation model to simulate the temperature breakthrough curve between injection and production wells; Step 3: Use an efficient curve fitting algorithm to compare the simulated temperature breakthrough curve with the measurement data of the actual site, and quantify the adaptation degree of different fracture network models; Step 4: Sort the generated fracture network data according to the fitting results, and select the fracture network configuration that best matches the actual data as the inversion result; The numerical model simulation is constructed by the following method; Physical model establishment; Fluid flow is based on Darcy's law, cubic law and considering the hydraulic coupling between fractures and matrix to ensure the dynamic balance between different regions before establishment; Heat transfer is based on the convection-conduction coupling equation and the heat exchange model between fractures and matrix; Numerical discretization and solution method; The discretization method includes using the finite element method to discretize the fluid and heat transfer equations and using a time stepping scheme; The solution process solves the transient flow and heat transfer equations through a stable iterative algorithm, and the iterative algorithm is a step-by-step iterative method or a non-linear solver. Through parallel computing and appropriate convergence criteria, the computational efficiency of large-scale numerical models is optimized; Set model parameters and boundary conditions; Establish a two-dimensional geothermal reservoir model to simulate the fracture network and matrix regions in the geothermal system. The typical size of the domain is 200m×200m. Set the wellbore regions on both sides, which are the injection well and production well respectively. The wellbore regions are given high permeability and high porosity; Boundary conditions: Set a constant hydraulic head and low temperature condition for the left injection well to simulate the cold water injection process; Set a constant hydraulic head and heat outflow condition for the right production well to simulate the hot water collection; Set the upper and lower boundaries as adiabatic boundaries to avoid heat exchange with the external environment; Set the initial condition as a uniform temperature distribution of 100°C for both the matrix and fracture network; Material properties: Fracture region: High conductivity, low porosity, emphasizing that fractures are the main channels for fluids; Matrix region: Low conductivity, high porosity, ensuring that heat conduction is the main heat transfer method; The thermophysical parameters of thermal conductivity, specific heat capacity and density are set according to typical geothermal reservoir lithology parameters.

2. The stochastic inversion method of heat transfer data based on a fracture network according to claim 1, wherein The specific content of Step 3 is as follows: Match the simulated curve with the reference data Compare the simulated temperature breakthrough curve corresponding to each generated fracture network with the reference temperature breakthrough curve, and use the root mean square error as a metric for the matching error to quantify the difference between the two sets of data at key monitoring points. The calculation of the root mean square error covers the overall shape of the temperature curve and the change trend at key nodes, ensuring the comprehensiveness and accuracy of the evaluation results.

3. The stochastic inversion method of heat transfer data based on a fracture network according to claim 1, wherein The specific content of Step 4 is as follows: The operation of the fracture network is as follows: Based on the matching results, select the fracture network with the minimum error as the inversion result, and select the top 100 fracture networks with the lowest root mean square error values, representing the set of fracture geometric features that best match the reference thermal behavior; This method can not only reduce the uncertainty of a single solution, but also further explore the equivalence and possible geometric variability of the fracture network through statistical analysis.

4. A random inversion method for heat transfer data based on a fracture network as described in claim 1, characterized in that It also includes Step 5, which is to conduct diversity analysis and parameter optimization; Further analyze the fracture network set, explore the variation ranges of fracture length, azimuth angle, and position and their effects on the matching of the temperature breakthrough curve. Through the diversity statistics of different fracture geometric characteristics, deeply understand the control mechanism of the fracture network on the heat transfer process, and provide a theoretical basis for subsequent parameter optimization.

5. A random inversion method for heat transfer data based on a fracture network as described in claim 1, characterized in that, The fracture network data is obtained through the fracture network generation method, which specifically includes the following steps: Step 1.1: Parameter setting and initialization in Matlab; Step 1.2: Generate the fracture network; Step 1.3: Read the fracture network data generated in Step 1.2, store the data in the three-dimensional matrix DataDFN_CNN, and save it as the data in the format of DataDFN_CNN.mat; The operation of Step 1.2 is as follows: Step a: Generate fracture length; Step b: Generate fracture angle; Step c: Randomly generate fracture positions; Step d: Detect and remove the shadow area; Step e: Fracture intersection requirements; Step f: Judge the connectivity of the fracture network; Step g: Save the finally generated fracture network data in a matrix format with a size of Nfrac*4, where: Nfrac represents the number of generated fractures, and each row represents a fracture; 4 represents the four key attributes of each fracture.

Images