A method for calculating three-dimensional permeability tensor of fractured aquifer controlled by faulted structure

Abstract

This invention discloses a method for calculating the three-dimensional permeability coefficient tensor of fractured aquifers controlled by fracture structures, relating to the field of hydrogeological exploration technology. The method includes: collecting borehole core samples for X-ray CT scanning and three-dimensional reconstruction; establishing a digital core fracture network model; simulating and calculating the permeability coefficient of the core in the x, y, and z directions using the creep flow equation, thereby determining the anisotropy of the core sample; conducting single-well pumping tests, recording the pumping volume and water level depth, and plotting the time-lapse curves; based on this, constructing a three-dimensional unsteady flow numerical model of groundwater, and setting incomplete well units according to the actual well depth and filter length; using the core anisotropy as a constraint, iteratively inverting the principal permeability coefficient tensor of the aquifer. By closely linking the microscopic fracture morphology characterization with the macroscopic hydraulic response through well units, high-precision parameter inversion can be achieved with only a single-well pumping test, offering advantages such as low cost and high reliability.

Description

Technical Field

[0001] This invention relates to the field of hydrogeological exploration technology, and in particular to a method for calculating the three-dimensional permeability coefficient tensor of fractured aquifers controlled by fracture structures. Background Technology

[0002] Fault zones, as an important component of geological structures, often control the occurrence and migration of fissure water, forming aquifers. The permeability of fissure aquifers is significantly anisotropic, influenced by factors such as the strike, dip angle, spacing, aperture, and connectivity of fissures within the fault zone. Typically, the main permeability direction is parallel to the strike of the main fracture, while permeability is weaker in directions perpendicular to the fault surface. This anisotropic permeability directly affects the distribution of groundwater flow fields, recharge and discharge paths, and water-bearing capacity assessment. Determining the permeability tensor is of great significance in fields such as deep underground engineering.

[0003] Traditional hydrogeological exploration methods involve deploying a main pumping well and multiple observation wells to conduct a pumping test with multiple wells. This allows for simultaneous monitoring of drawdown-time curves at different directions and distances, followed by solving for the principal value of the permeability tensor using unsteady flow theory or numerical inversion methods. However, for deep underground engineering projects, the cost of constructing observation wells is extremely high, making it difficult to meet the requirements of determining the aquifer permeability tensor through pumping tests with multiple wells in practical engineering. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating the three-dimensional permeability coefficient tensor of fractured aquifers controlled by fracture structures, aiming to solve or improve at least one of the above-mentioned technical problems.

[0005] To achieve the above objectives, the present invention provides the following solution: A method for calculating the three-dimensional permeability tensor of fractured aquifers controlled by fracture structures includes: Core samples were collected from the borehole. After preprocessing the core samples, X-ray CT scans were performed to obtain grayscale images. The grayscale image is reconstructed and modeled to establish a three-dimensional digital core model. The reconstructed model is then filtered and denoised to construct a core fracture network. Based on the fracture network, a creeping flow equation was established to simulate the flow velocity under different pressure gradients in the x, y, and z directions of the core. The core permeability tensor was calculated to determine the anisotropy of the core. Conduct single-well pumping tests, record the pumping volume and water level depth, and plot the duration curve of the single-well pumping test. Based on the duration curve of single-well pumping test, a three-dimensional unsteady flow numerical model of groundwater is constructed, and well units are set according to the actual well structure. Using the anisotropy of the core samples as a constraint, the principal permeability coefficient tensor of the aquifer was iteratively inverted using a trial-and-error method.

[0006] Further preprocessing includes: The core samples were pieced together to form a complete core with internal fissures. The surface of the pieced core was cleaned and vacuum dried to remove moisture and eliminate its influence on imaging.

[0007] Furthermore, the grayscale image is reconstructed and modeled to establish a three-dimensional digital core model. The reconstructed model is then filtered and denoised to construct a core fracture network, including: Anisotropic diffusion filtering is used to process grayscale images to eliminate noise and improve the signal-to-noise ratio of grayscale images; The fracture network of the core sample was reconstructed by using the threshold method to identify the fractures and rock matrix.

[0008] Furthermore, a creeping flow equation was established based on the fracture network to simulate the flow velocity under different pressure gradients in the x, y, and z directions of the core. The core permeability tensor was calculated to determine the anisotropy of the core, including: Assuming the core matrix is ​​non-conductive, and water flows through the fractures within the core, the Stokes equation is established for the fracture network, expressed as: In the formula, To calculate the dynamic viscosity of the fluid; The velocity vector of the fluid; For pressure; Apply pressure differences to the boundaries in the x, y, and z directions respectively, and calculate the flow velocities in the x, y, and z directions at steady time. Calculate the permeability tensor using Darcy's law, with the expression: In the formula, Let be the permeability coefficient tensor matrix.

[0009] Furthermore, based on the duration curves of single-well pumping tests, a three-dimensional unsteady flow numerical model of groundwater is constructed, and well units are set according to the actual well structure, including: The governing equations for a three-dimensional numerical model of groundwater seepage are constructed, and their expressions are as follows: In the formula, , , These are the principal permeability coefficients in the x, y, and z directions of the core sample, respectively. Groundwater level; For source and sink terms, it represents the amount of water replenished or discharged per unit volume of aquifer per unit time. Specific Storage of an aquifer represents the volume of water that a unit volume of aquifer can release when the water head drops by one unit. It is a time variable; The boundary value conditions for the three-dimensional groundwater seepage numerical model are defined as follows: In the formula, This is the initial water level; The known groundwater level on the first type of boundary; This represents the three-dimensional seepage region under study. These are first-type boundary conditions; The well unit is configured as an incomplete well based on the actual well depth and filter length.

[0010] Furthermore, based on the anisotropy of the core samples as a constraint, the principal permeability tensor of the aquifer is iteratively inverted using a trial-and-error method, including: Initialize the principal permeability coefficient tensor and use the numerical model to calculate the water level of the well unit; Compare the difference between the calculated water level and the measured water level in the stable section; the calculation error is expressed as: In the formula, For error; The water level in the stable section of the pumping well is calculated using a numerical model. The water level in the stable section of the pumping well is obtained from the actual measurement during the pumping test; The principal permeability coefficient tensor matrix is ​​calculated iteratively, and its expression is: In the formula, Let ii be the principal permeability coefficients calculated in the nth iteration, and let ii be xx, yy, and zz respectively. The solution is iterated until the error is less than the error threshold. After convergence, the principal permeability coefficient tensor is obtained.

[0011] Furthermore, by utilizing the inverted permeability coefficient tensor and taking the fault zone strike as the main permeability direction, a numerical model of the equivalent medium of the fault zone is established to simulate the water level changes caused by pumping water from deep geothermal wells.

[0012] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects: This invention discloses a method for calculating the three-dimensional permeability tensor of fractured aquifers controlled by fracture structures. The method uses borehole cores to extract fracture morphology to characterize the anisotropy of the aquifer. Using the anisotropy as a constraint, the permeability tensor is inverted using a single-hole pumping test. This method does not require multiple boreholes to measure the water level and has the advantages of low cost and high reliability. Attached Figure Description

[0013] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0014] Figure 1 This is a schematic flowchart of the method of the present invention; Figure 2 This is a schematic diagram of the three-dimensional digital core model reconstructed from a two-dimensional grayscale image in this embodiment; Figure 3 This is a schematic diagram of the core fracture network in this embodiment; Figure 4 This is a schematic diagram of the pumping test duration curve in this embodiment; Figure 5 This is an isostatic map of deep geothermal well pumping in this embodiment. Detailed Implementation

[0015] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0016] The purpose of this invention is to provide a method for calculating the three-dimensional permeability coefficient tensor of fractured aquifers controlled by fracture structures, aiming to solve or improve at least one of the above-mentioned technical problems.

[0017] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0018] like Figure 1 As shown, this invention provides a method for calculating the three-dimensional permeability tensor of fractured aquifers controlled by fracture structures, comprising: Step 1: Collect core samples from the borehole. After preprocessing the core samples, perform X-ray CT scanning to obtain grayscale images, including: Pre-processing includes: piecing together the cores to form a complete core, which contains internal fractures, due to the fractures caused by the fractures; cleaning the surface of the pieced cores and vacuum drying them to remove moisture and eliminate the influence of moisture on imaging.

[0019] A high-resolution X-ray core imaging system was used to perform CT scans on the core samples to obtain two-dimensional grayscale images of different sections of the core samples.

[0020] Step 2 involves reconstructing and modeling the grayscale image to establish a 3D digital core model. The reconstructed model is then filtered and denoised to construct a core fracture network, including: like Figure 2 As shown, a three-dimensional grayscale model is reconstructed using two-dimensional grayscale images with different cross-sections, and the three-dimensional grayscale model is cut and processed into a regular cylindrical digital core. Anisotropic diffusion filtering is used to process grayscale images to eliminate noise and improve the signal-to-noise ratio of grayscale images; like Figure 3 As shown, the fracture network of the core sample was reconstructed by using the threshold method to identify the fractures and rock matrix.

[0021] Step 3: Establish the creep flow equation based on the fracture network, simulate the flow velocity under different pressure gradients in the x, y, and z directions of the core, calculate the core permeability tensor, and determine the anisotropy of the core, including: Assuming the core matrix is ​​non-conductive, and water flows through the fractures within the core, the Stokes equation is established for the fracture network, expressed as: In the formula, To calculate the dynamic viscosity of the fluid; The velocity vector of the fluid; For pressure; Apply pressure differences to the boundaries in the x, y, and z directions respectively, and calculate the flow velocities in the x, y, and z directions at steady time. Calculate the permeability tensor using Darcy's law, with the expression: In the formula, Let be the permeability coefficient tensor matrix (unit: cm / s).

[0022] In this embodiment, the principal permeability coefficients in the x, y, and z directions of the core are 1.356 × 10⁻⁶, respectively. -4 cm / s, 2.66×10 -6 cm / s, 1.715×10 -5 cm / s. Anisotropy K xx :Kyy :K zz =50.98:1:6.45.

[0023] like Figure 4 As shown, in step 4, a single-well pumping test is conducted, and the pumping volume and water level depth are recorded. The duration curve of the single-well pumping test is plotted. Step 5: Based on the duration curve of the single-well pumping test, construct a three-dimensional unsteady flow numerical model of groundwater, and set up well units according to the actual well structure, including: The governing equations for a three-dimensional numerical model of groundwater seepage are constructed, and their expressions are as follows: In the formula, , , These are the principal permeability coefficients in the x, y, and z directions of the core sample, respectively. Groundwater level; For source and sink terms, it represents the amount of water replenished or discharged per unit volume of aquifer per unit time. Specific Storage of an aquifer represents the volume of water that a unit volume of aquifer can release when the water head drops by one unit. It is a time variable; The boundary value conditions for the three-dimensional groundwater seepage numerical model are defined as follows: In the formula, This is the initial water level; The known groundwater level on the first type of boundary; This represents the three-dimensional seepage region under study. These are first-type boundary conditions; The well unit is configured as an incomplete well based on the actual well depth and filter length.

[0024] Step 6: Using the anisotropy of the core sample as a constraint, the principal permeability tensor of the aquifer is inverted using an iterative method, including: Initialize the principal permeability coefficient tensor. In this embodiment, K xx0 =5.098 m / d, K yy0 =0.1 m / d, K zz0 =0.645m / d, the water level of the well unit was calculated using a numerical model; Compare the difference between the calculated water level and the measured water level in the stable section; the calculation error is expressed as: In the formula, For error; The water level in the stable section of the pumping well is calculated using a numerical model. The water level in the stable section of the pumping well is obtained from the actual measurement during the pumping test; The principal permeability coefficient tensor matrix is ​​calculated iteratively, and its expression is: In the formula, Let ii be the principal permeability coefficients calculated in the nth iteration, and let ii be xx, yy, and zz respectively. The solution is iterated until the error is less than the error threshold. In this embodiment, the error threshold is 0.01. After convergence, the principal permeability coefficient tensor is obtained.

[0025] like Figure 5 As shown, in step 7, using the inverted permeability tensor, a numerical model of the equivalent medium of the fault zone is established with the fault zone strike as the main permeability direction to simulate the water level changes caused by deep geothermal well pumping. In this embodiment, the simulated pumping volume is 30m³. 3 Groundwater level contour map under / h working conditions.

[0026] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0027] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for calculating a three-dimensional permeability tensor of a fractured aquifer controlled by a fault, comprising: include: Core samples were collected from the borehole. After preprocessing the core samples, X-ray CT scans were performed to obtain grayscale images. The grayscale image is reconstructed and modeled to establish a three-dimensional digital core model. The reconstructed model is then filtered and denoised to construct a core fracture network. Based on the fracture network, a creeping flow equation was established to simulate the flow velocity under different pressure gradients in the x, y, and z directions of the core. The core permeability tensor was calculated to determine the anisotropy of the core. Conduct single-well pumping tests, record the pumping volume and water level depth, and plot the duration curve of the single-well pumping test. Based on the duration curve of single-well pumping test, a three-dimensional unsteady flow numerical model of groundwater is constructed, and well units are set according to the actual well structure. Using the anisotropy of the core samples as a constraint, the principal permeability coefficient tensor of the aquifer was iteratively inverted using a trial-and-error method.

2. The method of claim 1, wherein, The preprocessing includes: The core samples were pieced together to form a complete core with internal fissures. The surface of the pieced core was cleaned and vacuum dried to remove moisture and eliminate its influence on imaging.

3. The method of claim 1, wherein, The process of reconstructing and modeling grayscale images, establishing a three-dimensional digital core model, filtering and denoising the reconstructed model, and constructing a core fracture network includes: Anisotropic diffusion filtering is used to process grayscale images to eliminate noise and improve the signal-to-noise ratio of grayscale images; The fracture network of the core sample was reconstructed by using the threshold method to identify the fractures and rock matrix.

4. The method of claim 1, wherein, The process of establishing a creeping flow equation based on a fracture network, simulating flow velocities under different pressure gradients in the x, y, and z directions of the core, calculating the core permeability tensor, and determining the anisotropy of the core includes: Assuming the core matrix is ​​non-conductive, and water flows through the fractures within the core, the Stokes equation is established for the fracture network, expressed as: In the formula, To calculate the dynamic viscosity of the fluid; The velocity vector of the fluid; For pressure; Apply pressure differences to the boundaries in the x, y, and z directions respectively, and calculate the flow velocities in the x, y, and z directions at steady time. Calculate the permeability tensor using Darcy's law, with the expression: In the formula, is the permeability tensor matrix.

5. The method of claim 1, wherein, The process involves constructing a three-dimensional unsteady flow numerical model of groundwater based on the duration curve of a single-well pumping test, and setting well units according to the actual well structure, including: The governing equations for a three-dimensional numerical model of groundwater seepage are constructed, and their expressions are as follows: In the formula, , , These are the principal permeability coefficients in the x, y, and z directions of the core sample, respectively. Groundwater level; For source and sink terms, it represents the amount of water replenished or discharged per unit volume of aquifer per unit time. Specific Storage of an aquifer represents the volume of water that a unit volume of aquifer can release when the water head drops by one unit. It is a time variable; The boundary value conditions for the three-dimensional groundwater seepage numerical model are defined as follows: In the formula, This is the initial water level; The known groundwater level on the first type of boundary; This represents the three-dimensional seepage region under study. These are first-type boundary conditions; The well unit is configured as an incomplete well based on the actual well depth and filter length.

6. The method of claim 1, wherein, The method of using the anisotropy of core samples as a constraint to invert the principal permeability tensor of the aquifer using an iterative method includes: Initialize the principal permeability coefficient tensor and use the numerical model to calculate the water level of the well unit; Compare the difference between the calculated water level and the measured water level in the stable section; the calculation error is expressed as: wherein is the error; is the water level in the stable section of the pumping well calculated by the numerical model; is the water level in the stable section of the pumping well measured by the pumping test; The principal permeability coefficient tensor matrix is ​​calculated iteratively, and its expression is: In the formula, Let ii be the principal permeability coefficients calculated in the nth iteration, and let ii be xx, yy, and zz respectively. The solution is iterated until the error is less than the error threshold. After convergence, the principal permeability coefficient tensor is obtained.

7. The method of claim 1, wherein: It also includes: using the inverted permeability coefficient tensor, with the fault zone orientation as the main permeability direction, to establish a numerical model of the equivalent medium of the fault zone, and to simulate the water level changes caused by pumping water from deep geothermal wells.

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