Soil column porosity dynamic inversion system and method and sensor array structure

Abstract

The invention discloses a soil column porosity dynamic inversion system and method and a sensor array structure, and belongs to the technical field of environmental soil tests. The system comprises a test soil column system; the acoustic monitoring module is used for acquiring ultrasonic travel time and amplitude information in the soil column; the resistivity monitoring module is used for acquiring resistivity information in the soil column; and the data processing host receives data of the acoustic monitoring module and the resistivity monitoring module, executes a joint inversion algorithm based on a rock physical coupling model, and dynamically inverts spatial distribution and time evolution of the three-dimensional porosity in the soil column by constructing a target function containing ultrasonic travel time / amplitude data and resistivity data at the same time. According to the invention, real-time, three-dimensional, high-resolution and high-adaptability soil column internal structure monitoring can be realized, and solid data support is provided for environmental rock and soil pollution migration mechanism research and restoration effect evaluation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of environmental geotechnical test, and particularly relates to a soil column porosity dynamic inversion system, method and sensor arrangement structure. BACKGROUND

[0002] In the research fields of environmental geotechnical engineering, soil physics and underground pollution migration, the spatial distribution and evolution process of porosity are key factors to determine the seepage behavior and solute migration characteristics of soil. Especially in the presence of reaction-type solute precipitation and soil fine particle migration-induced pore clogging, the dynamic change of porosity is a key indicator for analyzing these mechanisms. Soil column test, as a common test method, has the advantages of controllable structure, clear boundary and strong repeatability, and is widely used in the research of complex processes such as pollutant migration and particle deposition.

[0003] At present, common porosity detection methods include weighing method, CT scanning, gas permeation method and nuclear magnetic resonance (NMR) technology. Although these methods have certain detection capabilities under static conditions, they still face multiple limitations in dynamic monitoring:

[0004] First, the limitations of traditional static detection methods: weighing method, gas permeation method and other destructive or contact measurement methods cannot achieve in-situ continuous observation. Although CT scanning can obtain high-resolution three-dimensional structure, its time resolution is low, and the scanning process takes a long time, making it difficult to capture the dynamic changes of porosity on the scale of minutes or even seconds. In addition, high-precision CT usually requires millimeter-scale samples, and the data obtained from millimeter-scale structures cannot represent the pollutant migration behavior in larger-scale soil columns. The macroscopic applicability of the data in engineering scale is significantly reduced, limiting its applicability in macroscopic seepage analysis.

[0005] Second, the development and shortcomings of dynamic imaging technology: In recent years, geophysical methods such as electrical resistivity tomography (ERT) and electromagnetic induction imaging (EMI) have been gradually introduced into soil structure dynamic monitoring due to their non-invasive, low cost, and visual monitoring advantages. However, single physical field monitoring methods have inherent limitations: ERT is sensitive to saturation changes, but has limited resolution of pore structure; acoustic monitoring is sensitive to medium stiffness and structure changes, but is greatly affected by fluid in saturated porous media. Using any method alone is prone to multiple solutions in inversion, and is limited by sensor arrangement, often having detection blind areas, strong boundary effects, and insufficient spatial resolution.

[0006] The constraint of sensor arrangement mode: more importantly, the current most monitoring system adopts uniform point arrangement mode, and there are problems such as uneven signal coverage of low-density measuring point arrangement, obvious blind area, poor repeatability of high-density measuring point arrangement and high system cost. These problems significantly affect the inversion quality, also increase the test cost, and limit the application of this method in the process of high-frequency test.

[0007] Therefore, developing a soil column internal porosity dynamic inversion system capable of realizing real-time, three-dimensional, high-resolution and strong adaptability has become a technical problem to be solved urgently in the field of environmental geotechnical engineering and soil physics. SUMMARY

[0008] In view of the shortcomings of the existing soil column porosity dynamic monitoring technology, the present application provides a soil column porosity dynamic inversion system, which aims to realize real-time, three-dimensional, high-resolution and strong adaptability of soil column internal structure monitoring, and provides solid data support for environmental geotechnical pollution migration mechanism research and repair effect evaluation.

[0009] In order to realize the above technical purpose, the present application realizes the following technical scheme:

[0010] A soil column porosity dynamic inversion system comprises:

[0011] A rigid cylindrical sleeve for filling soil samples;

[0012] An acoustic monitoring module comprising a plurality of ultrasonic probes arranged on the wall of the rigid cylindrical sleeve according to a Fibonacci array, and an ultrasonic signal generating device and a collecting device connected with the ultrasonic probes, for acquiring ultrasonic travel time and amplitude information inside the test soil column;

[0013] A resistivity monitoring module comprising a plurality of resistivity probes arranged on the wall of the rigid cylindrical sleeve according to a Fibonacci array, and a resistivity test host connected with the resistivity probes, for acquiring resistivity information inside the test soil column;

[0014] A data processing host receives data of the acoustic monitoring module and the resistivity monitoring module, and executes a joint inversion algorithm based on a rock physics coupling model, dynamically inverts the spatial distribution and time evolution of three-dimensional porosity inside the test soil column by constructing a joint inversion objective function containing ultrasonic travel time / amplitude data and resistivity data at the same time; the Fibonacci array refers to that the ultrasonic probes and the resistivity probes are arranged in a cylindrical coordinate system according to golden angle rotation and equiaxial step length, so that the ultrasonic probes and the resistivity probes realize approximate equal-area coverage on the surface of the rigid cylindrical sleeve.

[0015] Beneficial effects: Traditional soil column monitoring usually adopts equidistant annular or regular grid point distribution mode, which will produce local over-dense and sparse areas on the cylindrical surface, resulting in uneven sensitivity distribution and significant observation blind area. The present application adopts Fibonacci array, that is, the sensor and voxel center point are arranged in the cylindrical coordinate system in the way of near golden angle rotation and equal axial step, so that the point is approximately equal-area distributed in the statistical sense. Its advantages are: ①maximize the curved surface coverage efficiency under the limited number of sensors, and significantly reduce the blind area; ②make the ultrasonic wave propagation path and resistivity measurement line form rich intersection angles and length combinations in three-dimensional space, improve the independence of Jacobian matrix vector, and improve the inversion condition number; ③compared with the same number of equidistant annular point distribution, higher spatial resolution can be obtained or the number of sensors is reduced under the same resolution, thereby reducing the hardware cost and wiring complexity.

[0016] At the same time, the present application utilizes the sensitive complementarity of acoustic and electric data to different physical parameters, fundamentally reduces the multi-solution of inversion, and for the first time realizes the high-resolution, dynamic and three-dimensional visualization monitoring of the pore structure in the soil column.

[0017] As a further preferred embodiment of the above-mentioned dynamic inversion system technical scheme of the present application, the joint inversion objective function at least includes: a weighted residual term based on ultrasonic observation data and theoretical data, a weighted residual term based on resistivity observation data and theoretical data, a spatial regularization term for constraining the smoothness of the spatial distribution of porosity, and a time regularization term for constraining the smoothness of the time evolution of porosity.

[0018] Beneficial effects: By constructing an objective function containing acoustic and electric data residuals, and weighting with measured variance, high signal-to-noise ratio data is dominant in inversion, effectively suppressing noise interference. Spatial regularization (such as total variation constraint) can suppress noise amplification and ensure solution stability while maintaining the clarity of structure boundaries such as pore clogging zone; time regularization forces the smooth evolution of porosity field at adjacent time, so that the inversion result conforms to the continuity of physical process, and a reliable time evolution sequence is output.

[0019] As a further preferred embodiment of the above-mentioned dynamic inversion system technical scheme of the present application, the ultrasonic probe and the resistivity probe are respectively detachably connected with the barrel wall of the rigid cylindrical sleeve.

[0020] As a further preferred embodiment of the above-mentioned dynamic inversion system technical scheme of the present application, the data processing host computer discretizes the three-dimensional space inside the test soil column into a plurality of voxels, and the number of voxel divisions matches the sensor spatial distribution of the Fibonacci array and the amount of data for joint inversion.

[0021] Beneficial effects: The application divides the three-dimensional region of the soil column into 675 voxels, matches the parameter scale with the order of magnitude of the observation data, and introduces spatial smoothing / full variation regularity and time regularity. The spatial regularity can inhibit local noise amplification and excessive oscillation, and the time regularity ensures that the evolution of the porosity with time is smooth and consistent with the physical process. The "parameter scale-data scale-regularity form" collaborative design enables the inversion to have good stability and computability while maintaining sufficient structural resolution.

[0022] As a further preferred embodiment of the above-mentioned dynamic inversion system of the application, the system further comprises a seepage control module for injecting a test solution into the test soil column system and controlling the seepage process, comprising a double-acting push-pull syringe pump, an electromagnetic valve and a flow guide pipe, the test solution passes through the double-acting push-pull syringe pump and the electromagnetic valve to control the solution injection flow rate, the waste liquid is discharged into a waste liquid collection tank, and they are connected to each other through the flow guide pipe, the upper end of the rigid cylindrical sleeve is provided with an upper end cover, and the upper end cover is provided with a liquid discharge port; the lower end of the rigid cylindrical sleeve is provided with a lower end cover, and the lower end cover is provided with a liquid inlet.

[0023] Beneficial effects: The use of a double-acting push-pull syringe pump in combination with a multi-way electromagnetic valve can accurately control the seepage rate, flow direction and residence time, and facilitate the reproduction of various boundary conditions and pollution infiltration conditions in the same device. By coupling with the acoustic-electric joint inversion system, the application can realize online inversion of the porosity field in situ seepage test without frequent disassembly of the test specimen or interruption of the test, greatly improving the experimental efficiency and engineering usability of the results.

[0024] The application further discloses a dynamic inversion method for soil column porosity, which adopts the system and comprises the following steps:

[0025] S1, a data synchronous acquisition step: synchronously acquiring ultrasonic travel time / amplitude data obtained by an ultrasonic probe and resistivity data obtained by a resistivity probe; S2, a dynamic joint inversion step: based on a rock physics coupling model, a joint inversion objective function containing the ultrasonic travel time / amplitude data and the resistivity data is constructed and solved, and the spatial distribution of the three-dimensional porosity inside the soil column at the current time is inverted; S3, a time evolution monitoring step: steps S1 and S2 are repeatedly executed at a preset time interval to obtain the three-dimensional porosity distribution inside the soil column at different times, and then the time evolution process of the porosity is obtained.

[0026] Beneficial effects: The method flows the optimized hardware arrangement, data acquisition and advanced inversion algorithm, clearly defines the standardized operation and calculation path from the original data to the final three-dimensional porosity spatio-temporal evolution result, and ensures the repeatability and comparability of the monitoring results, laying a foundation for the method to become a standard test method.

[0027] Further, in step S2, the joint inversion objective function is:

[0028] ,

[0029] where, is the porosity of the voxel;

[0030] is the forward calculation function of the ultrasonic wave, which is used to calculate the data vector composed of the theoretical travel time and the theoretical log amplitude of each ultrasonic wave propagation path when the porosity field is given;

[0031] is the resistivity forward calculation function under the complete electrode model framework, which is used to calculate the theoretical apparent resistivity data vector of each electrode combination when the porosity field is given;

[0032] and are the ultrasonic observation data vector and the resistivity observation data vector, respectively;

[0033] and are the weight matrices of the ultrasonic data and the resistivity data, respectively, and each observation data is weighted according to the variance estimation results of repeated measurements and reciprocal measurements;

[0034] is the spatial regularization matrix, which is used to realize the spatial second-order smoothing or the spatial constraint in the form of total variation (TV);

[0035] is the time regularization matrix, which is used to describe the difference between the porosity fields of adjacent monitoring time points;

[0036] and are the spatial regularization parameter and the time regularization parameter, respectively;

[0037] represents the Euclidean two-norm.

[0038] Beneficial effects: Single electrical or single acoustic imaging tends to have strong coupling with porosity, water saturation and medium composition changes, and is prone to multi-solution. The application unifies the voxel resistivity and the voxel longitudinal wave velocity as functions of medium parameters such as voxel porosity and water saturation by improving the Archie formula and the wave velocity relationship formula based on the effective medium theory, and simultaneously introduces the electrical residual term and the acoustic residual term in the joint objective function. In this way, on the one hand, the high sensitivity of electricity to the properties and connectivity of pore water and the high sensitivity of acoustics to the stiffness and density changes can be utilized to form complementary constraints in the parameter space of the two physical fields, significantly reducing the imaging non-uniqueness; on the other hand, by setting the weight matrix and the spatial and temporal regularization operator for the two types of observation data, the high signal-to-noise ratio data can be dominant in the inversion, the interference of the low signal-to-noise ratio data can be suppressed, and the clarity of the structure boundary such as the plugging zone can be maintained, so that the porosity field obtained by the inversion is more stable in spatial structure, more smooth in time evolution and more reasonable in physical meaning.

[0039] Further, in step S2, a joint inversion objective function is constructed based on a rock physics coupling model, and the rock physics coupling model jointly expresses the resistivity characteristics and the acoustic wave velocity characteristics of the soil as functions of the porosity, wherein,

[0040] The resistivity characteristics adopt an improved Archie formula:

[0041] ,

[0042] In the formula, is the voxel resistivity, is the resistivity of the pore fluid, is the water saturation of the soil, is an empirical coefficient related to the pore structure, m is a pore structure index, and n is a saturation index; is the voxel porosity.

[0043] The acoustic wave velocity characteristics adopt a formula based on the effective medium theory or an empirical relationship:

[0044] , ,

[0045] In the formula, is the voxel longitudinal wave velocity; is the solid phase longitudinal wave velocity, is an empirical parameter, is the voxel ultrasonic wave amplitude attenuation coefficient, indicating the energy attenuation intensity of the ultrasonic wave per unit propagation distance.

[0046] Beneficial effects: the improved Archie formula is used to describe the resistivity characteristics, and the wave velocity relationship based on effective medium theory or empirical calibration is used to describe the acoustic characteristics, so that the voxel resistivity , voxel P-wave velocity and attenuation coefficient are uniformly expressed as functions of a few physical parameters such as voxel porosity and water saturation . Compared with direct empirical fitting of the resistivity field and wave velocity field, the advantages of this approach are: first, the model form is mature, the physical meaning is clear, and the parameters , , , , etc. can be determined by using existing core experiments or laboratory calibration tests, which is convenient for promotion and reproduction; second, the electrical response and acoustic response are constrained in the same pore structure and water saturation framework, the electrical and acoustic parameters are no longer independent of each other, and the coupling between porosity, saturation and composition is significantly weakened; third, the , , obtained under different test conditions have good comparability and scalability, providing a reliable foundation for subsequent numerical simulation and engineering interpretation based on these physical parameters.

[0047] The application further discloses a sensor arrangement structure for soil column monitoring, a plurality of sensors are arranged on the surface of a rigid cylindrical sleeve in a Fibonacci array mode, the sensors comprise ultrasonic probes and / or resistivity probes, and are used for synchronously collecting physical field information inside the soil column.

[0048] Beneficial effects: the arrangement structure itself constitutes an independent innovation, and has the advantages of high space coverage efficiency and strong wiring regularity, which is not only suitable for the acoustic-electric combined system of the application, but also can provide an optimal sensor arrangement scheme for other multi-physical field monitoring (such as temperature field and strain field) based on cylindrical samples, and has wide applicability and promotion value. BRIEF DESCRIPTION OF DRAWINGS

[0049] Figure 1 FIG. 1 is a structural schematic diagram of a soil column porosity dynamic inversion system according to the application;

[0050] Figure 2 FIG. 3 is a connection structure schematic diagram of an ultrasonic probe and a resistivity probe and a rigid cylindrical sleeve according to the application;

[0051] Figure 3 FIG. 4 is a combined monitoring inversion principle and implementation method schematic diagram according to the application.

[0052] Figure 4 FIG. 5 is a comparison result of normalized permeability under different constant injection flow rates.

[0053] Wherein, 1-test solution, 2-bidirectional push-pull injection pump, 3-solenoid valve, 4-waste liquid collection tank, 5-flow guide pipe, 6-fixing frame, 7-rigid cylindrical sleeve, 8-resistivity test host, 9-ultrasonic signal generating device, 10-ultrasonic signal converter, 11-oscilloscope, 12-signal amplifier, 13-data processing host; 7-1-ultrasonic probe, 7-2-resistivity probe, 7-3-ultrasonic data transmission wiring, 7-4 high-density resistivity test main cable, 7-5 soil column test system cylinder wall; 7-1-1-ultrasonic emission / receiving sensor, 7-1-2-first mounting nut, 7-1-3-first screw thread, 7-1-4-ultrasonic transducer, 7-2-1-second mounting nut, 7-2-2-second screw thread, 7-2-3-copper electrode. DETAILED DESCRIPTION

[0054] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present application.

[0055] In the present application, the terms "comprising", "containing" or any other variant thereof are intended to cover non-exclusive inclusion, so that the process, method, article or equipment including a series of elements not only includes those elements, but also includes other elements not explicitly listed or inherent to such process, method, article or equipment. Without more limitation, the element defined by the statement "including a" does not exclude the presence of other identical elements in the process, method, article or equipment including the element.

[0056] As shown in Figure 1 The soil column porosity dynamic inversion system of the present application includes test solution 1, bidirectional push-pull injection pump 2, solenoid valve 3, waste liquid collection tank 4, flow guide pipe 5, fixing frame 6, test soil column system, resistivity test host 8, ultrasonic signal generating device 9, ultrasonic signal converter 10, oscilloscope 11, signal amplifier 12 and data processing host 13.

[0057] The test soil column system includes rigid cylindrical sleeve 7 arranged on fixing frame 6, and rigid cylindrical sleeve 7 is a two-half structure, which is detachably cleaned through threaded connection.

[0058] Test solution 1 is connected to solenoid valve 3 through bidirectional push-pull injection pump 2 to control the solution injection flow rate, and the waste liquid is discharged into waste liquid collection tank 4, which are connected to each other through flow guide pipe 5.

[0059] The ultrasonic probe 7-1 and resistivity probe 7-2 are placed on the surface of the rigid cylindrical sleeve 7. The Fibonacci array refers to the ultrasonic probe 7-1 and resistivity probe 7-2 being arranged in a cylindrical coordinate system according to the golden angle rotation and equal axial step size, so that the ultrasonic probe 7-1 and resistivity probe 7-2 achieve approximately equal area coverage on the surface of the rigid cylindrical sleeve 7 and are sealed by threads. The ultrasonic acquisition data is transmitted to the data processing host 13 through the ultrasonic data transmission cable 7-3 via the oscilloscope 11 and signal amplifier 12. The ultrasonic waves are generated by the ultrasonic signal generator 9 and the ultrasonic signal converter adjusts the transmission / reception type of each ultrasonic probe. The resistivity acquisition signal is connected to the resistivity testing host 8 through the high-density resistivity testing main cable 7-4 and transmitted to the data processing host 13 to complete the inversion and visualization processing of the monitoring data.

[0060] The method for inverting soil column porosity using the dynamic inversion system of this invention includes the following steps:

[0061] Step 1: Install the soil column testing system and turn on the power to the acoustic-electric combined monitoring device to form a closed circuit. The specific steps are as follows:

[0062] A rigid cylindrical sleeve 7 with an inner diameter of 150mm, an outer diameter of 180mm, and a height of 300mm is fixed to a fixed frame 6. In this embodiment, the rigid cylindrical sleeve 7 is made of non-conductive and high-strength machine glass cylinder. It connects the inlet and outlet ports of the upper and lower end caps with the guide pipe, solenoid valve, and bidirectional push-pull injection pump to complete the seepage circuit.

[0063] according to Figure 1 As shown, an ultrasonic probe and a resistivity probe are installed on the outer surface of the rigid cylindrical sleeve 7: the ultrasonic probe has a mounting hole diameter of 16 mm, is fitted with a metal sleeve and an O-ring and tightened with a back nut, and the transducer can be integrated as a transmitter / receiver.

[0064] The electrode holes are 2mm in diameter, lined with PTFE / PEEK tubing, with 0.5–1.0 mm of the copper electrode end face exposed and coated with conductive paste. Adhere to construction tolerances: the center-to-center distance between any two holes must be ≥ the sum of the two hole radii + 3 mm; the distance from the hole center to the upper and lower end faces of the cylinder must be ≥ the hole radius + 3 mm. The ultrasonic coaxial cable and high-density multi-core cable should be laid in layers, shielded, and grounded, maintaining an insulation clearance of at least 10mm to avoid acoustic-electrical crosstalk.

[0065] Then, the resistivity testing host, ultrasonic pulse / receiver link, oscilloscope and data processing host are turned on in sequence to perform channel self-test, continuity, open / short circuit, contact impedance, ultrasonic coupling and low voltage holding leak detection to confirm that the electro-acoustic acquisition link is closed and usable.

[0066] Step 2: Enable dynamic monitoring and set the ultrasonic frequency / velocity prior, ERT sampling cycle, and joint inversion refresh period. The recommended ultrasonic center frequency is 100–400kHz, selected based on the soil sample and geometry. The oscilloscope sampling rate should be ≥10MS / s. The ERT constant current should be 1–10mA, and voltage sampling should be performed at the host's built-in rate. The output time interval for the joint inversion should be set to 60s.

[0067] according to Figure 1 The process shown triggers ultrasonic wave transmission. The pulse, via a matching network, excites a piezoelectric transducer to enter the soil column. After propagating in the medium, it is collected by a receiving transducer. The conversion / switching module configures the same transducer as a "transmitter / receiver" and records the waveform. Each pair of monitoring points (T...) x →R x This forms a penetration path and returns the travel time and amplitude information of that path;

[0068] Taking 48 ultrasonic monitoring points on the surface as an example, the number of unique paths that form pairs is: = 1128, therefore 1128 ultrasound messages can be obtained.

[0069] The electrical resistivity method employs a four-electrode Wenner-α arrangement. Taking 47 electrical resistivity monitoring points on the surface as an example, the step size... Total number of feasible windows Therefore, 345 sets of resistivity information were obtained. The regular cycle completes 28–36 sets of resistivity and 60–120 ultrasonic paths within 60 seconds; every 10–15 minutes, a cycle of about 60 sets of "calibration sequences" is inserted for reciprocity / repeatability testing and online updates of weights, contact impedance, and coupling compensation.

[0070] Step 3: Joint inversion of voxel porosity. The specific steps are as follows: The cylindrical information is generalized and stored at the center point of the internal voxels using a local averaging method. The center coordinates of the voxel points are determined according to the Fibonacci array, and the golden angle spiral is uniformly determined according to cylindrical coordinates.

[0071] The cylindrical radius of this device is R = 75 mm. The circumferential average arc length spacing of the 47 resistivity measurement points is approximately 2πR / 47≈10 mm. After the axial stepping of the superimposed spiral, the three-dimensional "equivalent base distance" is on the order of more than ten millimeters. The bulk diffusion of resistivity means that the characteristic scale of the resolvable structure is usually greater than 1–2 times the base distance. Based on this, the radial grid is taken as Δr ≈ 25 mm, which can span a typical kernel width with 2–3 voxels. This avoids being too fine and causing ill-conditioning, and also avoids being too coarse and losing details.

[0072] For ultrasound, the effective propagation of center frequencies of 100–400 kHz corresponds to millimeter- to centimeter-level wavelengths on an experimental scale. Travel time is an integral observation along a path, controlled by geometric intersections and path coverage. An axial grid of Δz≈20 mm and a circumferential grid of Δθ≈24° can obtain enough non-collinear crossings within one pass to ensure the recoverability of the slow-speed field at this scale. Ultimately, the three-dimensional region of the soil column was voxelized to 3 (radial) × 15 (circumferential) × 15 (axial) = 675 voxels, which matches both the data volume and the physical resolution.

[0073] The joint inversion criterion for ultrasonic information, resistivity information, and voxel porosity is as follows: using voxel porosity... Using the main parameters, resistivity and acoustic wave velocity characteristics are assimilated into the same objective function through a rock physics coupling model. The resistivity characteristics are expressed using a modified Archie formula:

[0074] (1);

[0075] In the formula, Voxel resistivity The resistivity of the pore fluid. For water phase saturation, These are empirical coefficients related to pore structure, where m is the pore structure index and n is the saturation index; Voxel porosity.

[0076] The acoustic wave velocity characteristics are expressed using formulas based on effective medium theory or empirical relationships:

[0077] , (2);

[0078] In the formula, Voxel longitudinal wave velocity; For solid-phase longitudinal wave velocity, These are empirical parameters. is the attenuation coefficient of the voxel ultrasound amplitude, which represents the intensity of energy attenuation of ultrasound per unit propagation distance. , , , The parameters are determined based on existing core experiments or laboratory calibration.

[0079] The resistivity of the j-th voxel is obtained. longitudinal wave velocity of the j-th voxel and the ultrasonic amplitude attenuation coefficient of the j-th voxel Subsequently, the present invention employs the following forward calculation method to construct the resistivity forward calculation function. With the forward calculation function of ultrasound For the resistivity forward calculation function With the resistivity of the j-th voxel Characterize the electrical properties of each voxel, and through relationships Obtain the spatially distributed electric coefficient field Within the framework of the complete electrode model (CEM), the governing equations are solved for a set of electrode combinations numbered A, M, N, and B:

[0080] (3);

[0081] In the formula, This is a spatial position vector in the Cartesian coordinate system, used to represent the position of any point inside the soil column; The internal potential field of the soil column is obtained by applying corresponding current injection and potential boundary conditions; then, based on the potential difference and injection current of each measuring line, the theoretical apparent resistivity data of the l-th measuring line is calculated. The value of l ranges from 1 to... , This represents the total number of resistivity measurement lines. Arranging the theoretical apparent resistivity of all measurement lines in order yields a vector:

[0082] (4);

[0083] Due to the resistivity of the j-th voxel Voxel porosity is obtained through equation (1). and water phase saturation Decision, therefore Essentially, it is voxel porosity. The function.

[0084] For the ultrasonic forward calculation function The theoretical travel time and theoretical logarithmic amplitude attenuation of the i-th ultrasonic wave propagation path can be written as:

[0085] , (5);

[0086] In the formula, This is the reference amplitude for the transmitting end; Let be the theoretical received amplitude for the i-th path; The slowness of the j-th voxel is defined as follows: =1 / v j v j Let the longitudinal wave velocity be the velocity of the j-th voxel. Let be the ultrasonic amplitude attenuation coefficient of the j-th voxel; Let be the equivalent traversal length of the i-th path within the j-th voxel; The weight of the i-th path in the j-th voxel used for calculating ultrasonic amplitude attenuation; i ranges from 1 to... , This represents the total number of ultrasonic wave propagation paths; j ranges from 1 to... , The total number of voxels obtained by discretizing the interior of the soil column.

[0087] The theoretical travel time and theoretical logarithmic amplitude attenuation of all paths are combined sequentially to form the ultrasonic forward calculation function:

[0088] (6);

[0089] Due to the slowness of the j-th voxel and the ultrasonic amplitude attenuation coefficient of the j-th voxel Dependence on the porosity of the j-th voxel Therefore, the forward calculation function of ultrasound Similarly, voxel porosity The function.

[0090] After obtaining the resistivity forward calculation function With the forward calculation function of ultrasound Subsequently, this invention employs a weighted least squares approach to construct the joint inversion objective function:

[0091] (7);

[0092] In the formula, The aforementioned ultrasonic forward calculation function is used to map voxel porosity to the theoretical travel time and theoretical logarithmic amplitude of each ultrasonic propagation path, where the theoretical travel time of the i-th path is... Theoretical logarithmic magnitude A i The theoretical received amplitude for the i-th path, The aforementioned resistivity forward calculation function is used to map voxel porosity to the theoretical apparent resistivity of each electrode combination, using the Jacobian kernel. The Jacobian kernel describes the influence of the j-th voxel on the l-th apparent resistivity observation, satisfying the following: , The potential field distribution at any location inside the soil column when a current is injected into a given electrode combination AB. To determine the accompanying potential field of the corresponding electrode pair MN under the same current injection conditions, It is a volume infinitesimal element;

[0093] and These are the ultrasonic observation data vector and the resistivity observation data vector, respectively.

[0094] and The weight matrices are for ultrasonic data and resistivity data, respectively, and the variance estimates obtained from repeated measurements and reciprocal measurements are used to weight each observation data.

[0095] This is a spatial regularization matrix used to implement spatial constraints in the form of second-order smoothness or total variation (TV).

[0096] This is the time regularization matrix, used to describe the difference in porosity field between adjacent monitoring times;

[0097] and These are the spatial regularization parameter and the temporal regularization parameter, respectively.

[0098] This represents the Euclidean second norm.

[0099] The parameters are solved using the Gauss-Newton iterative method. In the k-th iteration, based on the objective function... Calculate porosity with respect to voxels Solve for the voxel porosity increment using the first-order gradient and approximate second-order derivative. , and according to Update, among which This is the estimated voxel porosity value at the k-th iteration. This represents the estimated voxel porosity at the (k+1)th iteration. This is the step size factor, which can be determined through methods such as line search.

[0100] To ensure physical feasibility, this invention selects voxel porosity as the variable to be determined. And apply box constraints to each component. j=1,2……, , This represents the total number of voxels obtained by discretizing the interior of the soil column. In practical implementation, two equivalent methods can be used:

[0101] First, after each iteration update, the porosity of voxel numbered j is... Perform a truncation projection to forcibly truncate values ​​outside the interval to [0,1].

[0102] Secondly, introduce unconstrained variables. The relationship is parameterized through the Sigmoid parameter. The optimization problem is transformed into problems involving unconstrained variables. The unconstrained solution automatically satisfies the voxel porosity throughout the entire iteration process. Physical constraints ∈ [0,1].

[0103] Furthermore, a structural coupling method is used for cross-validation. First, the voxel resistivity is considered as a spatially distributed resistivity field. The longitudinal wave velocity of voxels is considered as a spatially distributed wave velocity field. Both are solved simultaneously as two-parameter fields to be inverted; a cross-gradient constraint term is added to the joint objective function. To ensure that the principal gradient directions of the resistivity field and the wave velocity field are as consistent as possible, thus guaranteeing the consistency of the interface position of the two physical properties in space, the voxel porosity is then obtained through empirical mapping. .

[0104] Inversion results and effect verification:

[0105] To verify the reliability of the voxel porosity inversion results, ① a fine particle injection and migration test was conducted in a soil column with an initial porosity of approximately 0.35. The inlet pressure at different times under constant injection flow rate (velocity) was recorded, and Darcy's law Q=-KA was applied. s (dp / dL) yields the change in the normalized permeability K / K0 of the soil column, where Q is the inlet injection flow rate, and A... s Let L be the inlet cross-sectional area, L be the height of the soil column, and K0 be the initial permeability coefficient. ② Voxel porosity was obtained at different times. After determining the three-dimensional spatial distribution, a numerical seepage model consistent with the geometric dimensions and boundary conditions of the test soil column was established based on this distribution. The equivalent permeability performance of the soil column at different times was calculated and the results were compared. The seepage process was characterized using the volume-averaged Naiver-Stokes equation. Under saturation conditions, the fluid mass conservation equation is:

[0106] (8);

[0107] In the formula, For fluid density, Let be the fluid velocity vector. The momentum conservation equation for the fluid is:

[0108] (9);

[0109] In the formula, For fluid pressure, The dynamic viscosity of the fluid. This is the volumetric resistance term experienced by the fluid when it flows in a porous medium (including the resistance of the solid skeleton to the fluid). This is the gravitational acceleration vector.

[0110] Figure 4The results of normalized permeability comparison under different constant injection flow rates are presented. The solid line represents the permeability decay curve recorded in the experiment, and the broken line represents the numerical simulation results calculated based on the inverted porosity field. It can be found that with the continuous injection of fine particles, the pressure loss of the porous medium increases continuously, and the normalized permeability K / K0 gradually decreases. Moreover, the lower the injection flow rate, the greater the decrease in normalized permeability K / K0.

[0111] Although the experimentally recorded curves are affected by factors such as flow rate fluctuations and temperature changes, resulting in some high-frequency noise, the overall trend of their envelopes and the normalized permeability K / K0 variation curves obtained from the inversion simulation are highly consistent with the experimental curves. The deviation between the inversion simulation results and the experimental data in the range of 0–6 PV is basically controlled within 0.05. Based on the comparison of the evolution law of the comprehensive equivalent permeability, it can be concluded that the porosity inversion results based on Fibonacci acoustic and electrical joint monitoring in this invention can realistically reflect the pore structure evolution process of the soil column test, thus verifying the effectiveness of the method of this invention.

[0112] Step 4: Dynamic information collection at the next moment.

[0113] This disclosure also provides a sensor array structure for soil column monitoring, wherein multiple sensors are arranged in a Fibonacci array pattern on the surface of a rigid cylindrical sleeve, and the sensors include ultrasonic probes and / or resistivity probes for synchronously acquiring physical field information inside the soil column.

[0114] The above description of the embodiments is intended to enable those skilled in the art to understand and use the present invention. It will be apparent to those skilled in the art that various modifications can be made to these embodiments, and the general principles described herein can be applied to other embodiments without inventive effort. Therefore, the present invention is not limited to the above embodiments. Improvements and modifications made by those skilled in the art based on the principles of the present invention, without departing from the scope of the invention, should be within the protection scope of the present invention.

Claims

1. A dynamic inversion system for soil column porosity, characterized in that, include: Rigid cylindrical sleeve (7) is used to fill soil samples; The acoustic monitoring module includes multiple ultrasonic probes (7-1) arranged on the wall of the rigid cylindrical sleeve (7) according to the Fibonacci array, as well as an ultrasonic signal generator (9) and a data acquisition device connected to the ultrasonic probes, for acquiring ultrasonic travel time and amplitude information inside the test soil column. The resistivity monitoring module includes multiple resistivity probes (7-2) arranged on the wall of the rigid cylindrical sleeve (7) according to the Fibonacci array, and a resistivity testing host (8) connected to the resistivity probes, for obtaining resistivity information inside the test soil column; The data processing host (13) receives the data from the acoustic monitoring module and the resistivity monitoring module, and executes the joint inversion algorithm based on the rock physics coupling model. By constructing a joint inversion objective function that simultaneously includes ultrasonic travel time / amplitude data and resistivity data, the spatial distribution and temporal evolution of the three-dimensional porosity inside the test soil column are dynamically inverted. The Fibonacci array refers to the ultrasonic probe (7-1) and the resistivity probe (7-2) being arranged in the cylindrical coordinate system according to the golden angle rotation and the equiaxial step size, so that the ultrasonic probe (7-1) and the resistivity probe (7-2) achieve approximately equal area coverage on the surface of the rigid cylindrical sleeve (7).

2. The dynamic inversion system for soil column porosity according to claim 1, characterized in that, The joint inversion objective function includes at least: a weighted residual term based on ultrasonic observation data and theoretical data, a weighted residual term based on resistivity observation data and theoretical data, a spatial regularization term for constraining the smoothness of the spatial distribution of porosity, and a temporal regularization term for constraining the smoothness of the temporal evolution of porosity.

3. The dynamic inversion system for soil column porosity according to claim 1, characterized in that, The ultrasonic probe (7-1) and resistivity probe (7-2) are respectively connected to the wall of the rigid cylindrical sleeve (7) in a detachable sealed manner.

4. The dynamic inversion system for soil column porosity according to claim 1, characterized in that, The data processing host (13) discretizes the three-dimensional space inside the test soil column into multiple voxels, and the number of voxels is matched with the sensor spatial distribution of the Fibonacci array and the amount of data retrieved by joint inversion.

5. The dynamic inversion system for soil column porosity according to claim 1, characterized in that, It also includes a seepage control module, which includes a bidirectional push-pull injection pump (2) and a solenoid valve (3); the outlet of the bidirectional push-pull injection pump (2) is sequentially connected to the solenoid valve (3) and the inlet of the lower end cap of the rigid cylindrical sleeve (7) through a first guide pipe, and the outlet of the upper end cap of the rigid cylindrical sleeve (7) is connected to the waste liquid collection tank device (4) or the inlet of the bidirectional push-pull injection pump (2) through a second guide pipe, so as to realize the injection, flow direction and flow rate control of the test solution (1).

6. A dynamic inversion method for the porosity of a soil column, characterized in that, The dynamic inversion system for soil column porosity as described in any one of claims 1 to 5 includes the following steps: S1. Data Synchronization Acquisition Step: Synchronously acquire ultrasonic travel time / amplitude data obtained by the ultrasonic probe and resistivity data obtained by the resistivity probe; S2. Dynamic Joint Inversion Step: Based on the rock physics coupling model, construct and solve the joint inversion objective function that simultaneously includes the ultrasonic travel time / amplitude data and resistivity data to invert the spatial distribution of three-dimensional porosity inside the soil column at the current moment; S3. Temporal Evolution Monitoring Step: Repeat steps S1 and S2 at preset time intervals to obtain the three-dimensional porosity distribution inside the soil column at different times, thereby obtaining the temporal evolution process of porosity.

7. The dynamic inversion method for soil column porosity according to claim 6, characterized in that, In step S2, the joint inversion objective function is: ， in, Voxel porosity; This is the ultrasonic forward calculation function, used to calculate a data vector consisting of the theoretical travel time and theoretical logarithmic amplitude of each ultrasonic propagation path given a porosity field. This is a resistivity forward calculation function within the framework of the complete electrode model (CEM), used to calculate the theoretical apparent resistivity data vector for each electrode combination given a porosity field. and These are the ultrasonic observation data vector and the resistivity observation data vector, respectively. and The weight matrices are for ultrasonic data and resistivity data, respectively, and the variance estimates obtained from repeated measurements and reciprocal measurements are used to weight each observation data. This is a spatial regularization matrix used to implement spatial constraints in the form of second-order smoothness or total variation (TV). This is the time regularization matrix, used to describe the difference in porosity field between adjacent monitoring times; and These are the spatial regularization parameter and the temporal regularization parameter, respectively. This represents the Euclidean second norm.

8. The dynamic inversion method for soil column porosity according to claim 7, characterized in that, In step S2, the rock physics coupling model expresses the resistivity and acoustic velocity characteristics of the soil as a function of porosity, wherein... The resistivity characteristics are expressed using a modified Archie formula: ， In the formula, Voxel resistivity The resistivity of the pore fluid. The water saturation of the soil. These are empirical coefficients related to pore structure, where m is the pore structure index and n is the saturation index; Voxel porosity; The acoustic wave velocity characteristics are expressed using formulas based on effective medium theory or empirical relationships: ， ， In the formula, Voxel longitudinal wave velocity; For solid-phase longitudinal wave velocity, These are empirical parameters. is the attenuation coefficient of the voxel ultrasound amplitude, which represents the intensity of energy attenuation of ultrasound per unit propagation distance.

9. A sensor array structure for a soil column porosity dynamic inversion system as described in any one of claims 1 to 5, characterized in that, Multiple sensors are arranged in a Fibonacci array pattern on the surface of a rigid cylindrical sleeve. The sensors include ultrasonic probes and / or resistivity probes for synchronously acquiring physical field information inside the soil column.

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