Rock physical parameter transient electromagnetic detection and analysis method based on deep in-situ environment fidelity reconstruction
Patent Information
- Application Number
- CN202610980499.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-07-02
- Publication Date
- 2026-09-15
Smart Images
Figure CN122755104A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a method for testing and analyzing rock physical parameters, specifically a transient electromagnetic detection and analysis method for rock physical parameters based on faithful reconstruction of deep in-situ environment, belonging to the field of rock physical and mechanical parameter testing technology. Background Technology
[0002] As the development of energy resources such as coal, oil, and natural gas continues to advance into deeper areas, deep rock masses are subjected to high temperature, high pressure, and high geostress environments for extended periods. Their pore structure, fluid occurrence, and electrical properties differ significantly from those under normal temperature and pressure conditions. Porosity, water saturation, and other physical properties are crucial indicators characterizing the features and resource occurrence of deep reservoirs. The accuracy of their testing and inversion directly impacts the evaluation, development, utilization, and engineering safety of deep resources.
[0003] Traditional core testing methods typically involve transferring the core sample from deep depths to surface conditions. Because the temperature and pressure change rapidly after the core is removed from its in-situ environment, it can lead to stress release, microfracture propagation, pore structure reconstruction, and fluid redistribution. This causes the test results to deviate from the true in-situ conditions and fail to accurately reflect the actual physical properties of the rock mass. Therefore, it is necessary to reconstruct the in-situ temperature and pressure environment at depth under surface experimental conditions and conduct rock testing under faithful simulation.
[0004] Rock physical properties such as porosity and water saturation are closely related to their electrical properties such as resistivity, and can be obtained through inversion analysis using electrical tests. Transient electromagnetic methods (TEM), as a non-contact electrical detection technique, offer advantages such as no electrode contact required, suitability for sealed pressurized environments, and no damage to rock samples, making them suitable for testing rock electrical properties under complex conditions. However, existing TEM techniques are primarily geared towards large-scale detection or infinitely homogeneous media conditions, making them difficult to directly apply to the small-scale, confined space environment of deep core laboratories. On one hand, the fidelity chamber and internal medium introduce additional electromagnetic responses; on the other hand, the boundary effects of finite-sized rock samples affect the diffusion process of the transient electromagnetic field, leading to errors in resistivity calculations. Furthermore, existing methods primarily focus on resistivity acquisition, lacking inversion analysis of physical properties such as porosity and water saturation, and do not fully consider the influence of temperature, pressure, and their coupling effects on the test results, making it difficult to meet the needs of deep resource development. Therefore, there is an urgent need for a transient electromagnetic detection and analysis method for rock physical parameters based on in-situ environment fidelity reconstruction that can achieve resistivity solution and physical parameter inversion, and obtain test results that are closer to the true state of deep in-situ conditions. Summary of the Invention
[0005] To address the problems existing in the prior art, this invention provides a transient electromagnetic detection and analysis method for rock physical parameters based on the faithful reconstruction of deep in-situ environment. This method can achieve resistivity calculation and inversion of physical parameters such as porosity and water saturation in the reconstructed deep in-situ faithful environment, thereby obtaining test results that are closer to the true state of deep in-situ conditions. This method can provide data support for deep resource development and engineering safety.
[0006] To achieve the above objectives, the testing system used in this method for transient electromagnetic detection and analysis of rock physical parameters based on fidelity reconstruction of deep in-situ environment includes a fidelity chamber, a transient electromagnetic testing unit, a temperature and pressure control unit, and a data acquisition and processing unit.
[0007] The fidelity chamber is an integrated pressure-bearing shell with a sample testing chamber that is coaxially arranged and axially connected inside. At both ends of the fidelity chamber in the axial direction, there are also coaxially sealed conversion flanges.
[0008] The transient electromagnetic testing unit includes a transmitting coil and a receiving coil. The transmitting coil is coaxially arranged with the sample testing cavity, and the two transmitting coils are respectively positioned at both ends of the sample testing cavity in the axial direction. Multiple receiving coils are evenly distributed along the circumferential direction of the sample testing cavity and positioned between the two transmitting coils, with the axial direction of the receiving coils along the circumferential direction of the sample testing cavity.
[0009] The temperature and pressure control unit includes a loading device, a heating device, a cooling device, a temperature sensor, and a pressure sensor;
[0010] The data acquisition and processing unit includes a central controller and an acquisition control loop. The central controller is electrically connected to the transmitting coil, the receiving coil, and the temperature and pressure control unit, respectively.
[0011] The method for transient electromagnetic detection and analysis of rock physical parameters based on faithful reconstruction of deep in-situ environment includes the following steps:
[0012] S1, Data Acquisition and Preprocessing: The test system is used to acquire raw induced electromotive force (EMF) signal data. The acquired raw EMF signals are preprocessed by performing zero drift correction, noise filtering, superposition averaging, and outlier removal on each channel signal in sequence. The preprocessed raw EMF signals are then subtracted from the background signal without rock samples under the corresponding working conditions to obtain the effective signal of the true transient electromagnetic response of the rock sample. Based on the system calibration parameters and the equivalent parameters of the transmitting and receiving coils, the apparent resistivity of each channel is calculated according to different time channels. The results of multiple channels are then weighted and fused to obtain the equivalent apparent resistivity corresponding to the working conditions.
[0013] S2, Boundary effect correction: Boundary correction parameters are constructed based on the geometric dimensions and response characteristics of the core sample to correct the apparent resistivity and obtain the corrected resistivity that reflects the true electrical characteristics of the core sample.
[0014] S3, Construct a joint inversion model: Based on corrected resistivity, porosity Water saturation As parameters to be inverted, a joint inversion model is constructed by correcting resistivity data through multiple time windows;
[0015] S4, joint constraint inversion under multiple temperature, multiple pressure, and temperature-pressure coupling conditions: under different temperature and pressure conditions, the corrected resistivity is obtained and the corresponding porosity is inverted. and water saturation Multiple sets of parameter samples are formed. A temperature-pressure coupled physical property parameter model suitable for the target rock sample was established, and joint constraint inversion was performed to achieve comparable output under multiple working conditions.
[0016] Furthermore, in S1, the effective signal of the true transient electromagnetic response of the rock sample is obtained, as follows:
[0017] Background signals without samples were collected under the same temperature and pressure conditions. Acquired raw signals from sample testing And perform background calibration on the multi-channel transient response data to obtain the first... The effective transient electromagnetic signal of the channel is represented as follows:
[0018]
[0019] In the formula: For the first Time series of effective transient electromagnetic induction electromotive force after background subtraction at the same temperature and pressure without samples; This is the original signal from the sample test; This refers to the background signal without samples under the same operating conditions. Number the receiving channel; The sampling time.
[0020] Furthermore, in S1, the determination of the track at different times is as follows:
[0021] The acquired transient electromagnetic signals were filtered and divided into time domains. First, data before the emission current was turned off and early distortion data with significant turn-off tail effects were removed, and only the late time period that met the signal-to-noise ratio requirements was retained. Then, the time channels were divided in a logarithmic manner.
[0022] Furthermore, in S1, when calculating the apparent resistivity of each channel based on different time measurements, the specific steps are as follows:
[0023] Let the first The start and end times of each measurement track are: and The average electromotive force corresponding to this track is expressed as follows:
[0024]
[0025] In the formula: For the first The average induced electromotive force of each track; For the first Time width of each measurement track; To effectively respond to the electromotive force amplitude;
[0026] After the transmitting current of the transmitting coil is turned off, the magnetic field diffusion equation is expressed as follows:
[0027]
[0028] In the formula: The magnetic field strength; The dielectric permeability; Resistivity; for The Laplace operator is used to characterize the spatial diffusion term of the magnetic field;
[0029] The response of the receiving coil is expressed as follows:
[0030]
[0031] In the formula: Represents the second magnetic induction intensity, where For position vector, Sampling time; The effective area of the receiving coil; The effective area of the receiving coil The unit normal vector;
[0032] The basic analytical response is represented as follows:
[0033]
[0034] In the formula: This represents the theoretical response value of the induced electromotive force under ideal infinite homogeneous medium conditions; It is a step turn-off function; For system comprehensive coefficients, ,in This is a comprehensive coefficient that includes the transmit current amplitude, coil turns, coupling geometry, system gain, and calibration parameters. The permeability of free space, The effective area of the transmitting coil, The effective area of the receiving coil;
[0035] The diffusion scale of the eddy current after the emitter current is turned off is defined as follows:
[0036]
[0037] In the formula: for The eddy current diffusion scale at the sampling time characterizes the diffusion range of the transient electromagnetic response in the core sample. The resistivity of the rock sample; The vacuum permeability;
[0038] Define the radial and axial dimensionless parameters respectively, as follows:
[0039]
[0040] In the formula: The radius of the core sample is denoted as . This represents the axial length of the core sample. The eddy current diffusion scale; , These represent the relative relationships between the diffusion scale and the radius and axial dimension of the core sample, respectively.
[0041] Define the normalization quantity as follows:
[0042]
[0043] In the formula: This is the normalized induced electromotive force function; The kernel function is cylindrical;
[0044] Then the first The underlying apparent resistivity corresponding to each measurement channel is expressed as follows:
[0045]
[0046] In the formula: Based on apparent resistivity.
[0047] Furthermore, S2 is detailed below.
[0048] Define the boundary correction coefficients as follows:
[0049]
[0050] In the formula: Indicates the boundary correction factor; For an ideal infinite medium kernel function; For cylindrical rock core samples;
[0051] Introducing comprehensive boundary parameters As shown below:
[0052]
[0053] The boundary correction coefficients are then approximated as follows:
[0054]
[0055] In the formula: and The first boundary correction calibration parameters and the second boundary correction calibration parameters are respectively determined through numerical forward modeling, standard sample testing, or rock sample experiments of the same size.
[0056] The resistivity expression after correction for finite size boundaries is as follows:
[0057]
[0058] In the formula: express Corrected resistivity at that moment; express The resistivity at time t.
[0059] Furthermore, the corrected resistivity is solved iteratively, as follows:
[0060] First, we take the basic apparent resistivity as the initial value, as shown below:
[0061]
[0062] In the formula: This represents the initial resistivity obtained through iterative solution;
[0063] Then, the diffusion scale is calculated based on the current iteration value, as shown below:
[0064]
[0065] In the formula: This refers to the iteration step number; Indicates the first During the next iteration The calculated eddy diffusion scale; For the first Next iteration resistivity;
[0066] The dimensionless parameters for radial and axial directions are as follows:
[0067]
[0068] Therefore, the correction coefficient for the current iteration step can be obtained. And update the resistivity, as shown below:
[0069]
[0070] The iteration is considered to have converged when the following convergence condition is met:
[0071]
[0072] In the formula: This is the convergence threshold;
[0073] at this time That is, as the survey track Corrected resistivity at time 1 .
[0074] Furthermore, in S3, the Archie relation is used to establish the relationship between the corrected resistivity and porosity and water saturation, as shown below:
[0075]
[0076] In the formula: The resistivity of the core sample after finite size boundary correction; Let the pore fluid resistivity under the current temperature and pressure conditions be denoted as . ; Porosity; Water saturation; The cementation index; Archie saturation index;
[0077] Taking the logarithm of the above expression, we get:
[0078]
[0079] porosity Water saturation Using resistivity data corrected by multiple time windows as the parameters to be inverted, a joint inversion model is constructed to uniformly solve for porosity and water saturation, and the objective function is established as shown below. :
[0080]
[0081] In the formula: The number of effective time windows for participating in the inversion;
[0082] By minimizing the objective function To achieve porosity With water saturation The joint solution.
[0083] Furthermore, in S4, a temperature-pressure coupling model is established based on the regression method of multi-condition experimental data, as detailed below:
[0084] By gradually changing the temperature With pressure We acquired transient electromagnetic response data under different temperature and pressure conditions, established a model relating resistivity to temperature and pressure using statistical regression, and created a temperature-pressure coupled resistivity model in logarithmic form, as shown below:
[0085]
[0086] In the formula: For reference constant terms; Temperature coefficient; Pressure coefficient; This is the temperature-pressure coupling coefficient;
[0087] Establish the least squares objective function as shown below:
[0088]
[0089] In the formula: This represents the total number of experimental conditions.
[0090] By minimizing the objective function The coefficients of the temperature-pressure coupled resistivity model were obtained. , , and .
[0091] Furthermore, the corrected resistivity under different temperature and pressure conditions is uniformly converted to the same reference condition, as follows:
[0092] Let the reference temperature and reference pressure be respectively and The equivalent corrected resistivity under the corresponding reference operating condition is ,but:
[0093]
[0094] In the formula: This is the equivalent resistivity after conversion to the reference operating condition; For actual temperature and pressure conditions The corrected resistivity is as follows.
[0095] Furthermore, after obtaining the resistivity under a unified reference condition, the porosity is analyzed using the resistivity-rock property parameter inversion model of S3. and water saturation A joint solution is performed to establish the response relationship between rock physical parameters and temperature and pressure, as shown below:
[0096]
[0097]
[0098] In the formula: Porosity function representing the effects of temperature, pressure, and thermo-pressure coupling; This represents the water saturation function under the corresponding operating conditions;
[0099] The parameter relationship can be approximated as follows:
[0100]
[0101]
[0102] In the formula: and These represent the porosity and water saturation under reference operating conditions, respectively. , , These are the response coefficients of porosity to temperature, pressure, and temperature-pressure coupling, respectively. , , These are the response coefficients of water saturation to temperature, pressure, and temperature-pressure coupling, respectively.
[0103] Under different temperature and pressure conditions, the corrected resistivity was obtained and the corresponding porosity was inverted. and water saturation Multiple sets of parameter samples are formed. By using regression methods to determine each response coefficient, a temperature-pressure coupled physical property parameter model suitable for the target rock sample is established.
[0104] Compared with existing technologies, this transient electromagnetic detection and analysis method for rock physical parameters based on the faithful reconstruction of deep in-situ environment adopts the technical route of "faithful environment reconstruction - multi-channel transient electromagnetic non-contact acquisition - precise signal processing - apparent resistivity correction - physical parameter inversion". By reconstructing the high-temperature and high-pressure environment of deep in-situ rocks within a test chamber, and using non-contact multi-channel transient electromagnetic testing under faithful conditions, it accurately acquires effective transient response data of in-situ rock samples. An apparent resistivity correction method is established to obtain the equivalent resistivity of the rock samples. Based on the corrected resistivity, porosity, water saturation, and other physical parameters are inverted. Furthermore, a model is established to demonstrate the influence of temperature, pressure, and their coupling on resistivity and inversion results, achieving comparable output under multiple working conditions. This enables non-contact, non-destructive, and precise detection of the physical and mechanical parameters of deep in-situ rocks, providing key technical support for theoretical research and engineering practice in the field of deep rock mechanics. Specifically, it has the following beneficial effects:
[0105] 1. This invention enables non-contact multi-channel transient electromagnetic (TEM) testing of rock samples under in-situ fidelity environment reconstruction conditions in deep environments, obtaining transient electromagnetic response data that more closely approximates the actual deep environment.
[0106] 2. This invention can establish a resistivity correction and solution method to address the apparent resistivity system deviation caused by the finite size and geometric boundary conditions of rock samples, obtain the equivalent resistivity of rock samples for subsequent inversion, and improve the accuracy and consistency of resistivity parameters.
[0107] 3. This invention can construct inversion models of physical property parameters such as porosity and water saturation based on the corrected resistivity, realize the quantitative inversion and output of rock sample physical property parameters, and provide key basis for the evaluation of deep rock mass structure and fluid occurrence.
[0108] 4. This invention can establish a calibration and normalization mechanism for resistivity changes under temperature, pressure and their coupling conditions, and quantify their impact on the inversion results of physical property parameters, so as to achieve comparable output of inversion results under multiple working conditions and extraction of deep patterns. Attached Figure Description
[0109] Figure 1 This is a schematic diagram of the fidelity chamber structure of the testing system used in this invention;
[0110] Figure 2 yes Figure 1 Top view.
[0111] In the figure: 1. Fidelity chamber; 2. Transmitting coil; 3. Receiving coil; 4. Rock core sample. Detailed Implementation
[0112] This method for transient electromagnetic detection and analysis of rock physical parameters based on the faithful reconstruction of deep in-situ environment firstly reconstructs the high-temperature and high-pressure environment of deep in-situ rocks within a test chamber. Under faithful conditions, it uses non-contact multi-channel transient electromagnetic methods to accurately acquire effective transient response data of in-situ rock samples. Then, it establishes an apparent resistivity correction method to address the influence of the geometric boundaries of rock samples in small, confined spaces on the transient electromagnetic response, thereby obtaining the equivalent resistivity of the rock samples. Finally, based on the corrected resistivity, it inverts physical parameters such as porosity and water saturation, and establishes a model of the influence of temperature, pressure, and their coupling on resistivity and inversion results, realizing the quantitative inversion and output of rock sample physical parameters.
[0113] like Figure 1 As shown, the testing system used in this method for transient electromagnetic detection and analysis of rock physical parameters based on fidelity reconstruction of deep in-situ environment includes a fidelity chamber 1, a transient electromagnetic testing unit, a temperature and pressure control unit, and a data acquisition and processing unit.
[0114] The fidelity chamber 1 is an integral pressure-bearing shell, with an axially through sample testing chamber inside for accommodating the cylindrical rock core sample 4 and reconstructing the high-temperature and high-pressure boundary conditions. The fidelity chamber 1 is equipped with insulating supports and positioning components for fixing the rock sample and reducing the impact of the chamber structure on the stability of the test signal. At both ends of the fidelity chamber 1 in the axial direction, there are also coaxially sealed conversion flanges for standardized connection and force transmission with external temperature and pressure pipelines. The conversion flanges can reliably connect the coil inside the chamber to the external acquisition and control system under high-temperature and high-pressure conditions, ensuring stable transmission of excitation current and induced voltage signals, while preventing leakage of the medium along the lead-out channel.
[0115] The transient electromagnetic test unit includes a transmitting coil 2 and a receiving coil 3, such as... Figure 2 As shown, the transmitting coil 2 is coaxially arranged with the sample testing cavity, and the two transmitting coils 2 are respectively positioned at both ends of the sample testing cavity in the axial direction. Multiple receiving coils 3 are evenly distributed along the circumferential direction of the sample testing cavity and positioned between the two transmitting coils 2. The axial direction of the receiving coils 3 is along the circumferential direction of the sample testing cavity. The transmitting coil 2 is used for main excitation and radial response acquisition, and the multiple receiving coils 3 are used to form multiple sets of transverse response acquisition channels, thereby realizing the joint acquisition of transverse and radial transient electromagnetic responses of the core sample 4.
[0116] The temperature and pressure control unit includes a loading device, a heating device, a cooling device, a temperature sensor, and a pressure sensor. It can load, stabilize, and control the confining pressure and pore pressure along a path. The temperature and pressure control unit can perform closed-loop regulation based on real-time temperature and pressure signals to ensure that the sample test chamber smoothly reaches and maintains the target working condition. It also supports changes in effective pressure along a set path to simulate different burial depth conditions. The temperature and pressure control unit is equipped with necessary over-limit interlocks and pressure relief protection to meet stable operation and safety requirements.
[0117] The data acquisition and processing unit includes a central controller, an acquisition control loop, and supporting software. The central controller is electrically connected to transmitting coil 2, receiving coil 3, and the temperature and pressure control unit. Through the host computer software interface, it can perform fully automated operation of the entire process, including chamber sealing, temperature and pressure regulation, ultrasonic test initiation, data acquisition, and analysis. It can also achieve channel switching control, raw signal acquisition, and storage. A remote control module can be used to achieve centralized monitoring and protection linkage of the temperature and pressure loading, electrical test initiation, and acquisition process via industrial communication, ensuring the safety, stability, and data consistency of the experimental process.
[0118] When using the above testing system to conduct tests in a deep in-situ environment, the specific workflow is as follows:
[0119] First, initial state calibration is performed, including checking the chamber sealing and temperature and pressure control, confirming the installation and channel mapping relationship of the transient electromagnetic test unit, detecting coil connectivity and insulation status, and acquiring baseline signals and background signals without rock samples; abnormal channels are marked or corrected to ensure the stability of test results.
[0120] Then, core loading is performed: the core sample 4 extracted from the deep chamber is placed inside the test chamber and axially and radially positioned to ensure a stable relative position between the outer wall of the core sample 4 and the transmitting coil 2 and receiving coil 3. After completing the sealed connection of the fidelity chamber 1, the medium is injected into the test chamber through the conversion flange, and venting and sealing checks are performed to ensure the stability and reliability of the test environment.
[0121] Then, the temperature and pressure environment is reconstructed: the temperature and pressure control unit is activated, and the target temperature is applied to the test chamber. and target pressure Closed-loop regulation ensures that the temperature and pressure parameters within the test chamber smoothly reach the set operating conditions and remain stable. After reaching the target temperature and pressure, a steady-state holding period is maintained to reduce the impact of transient fluctuations on subsequent transient electromagnetic tests, thereby achieving accurate reconstruction of the deep in-situ temperature and pressure environment.
[0122] Finally, transient electromagnetic response signal acquisition was performed: After the temperature and pressure conditions stabilized, the transient electromagnetic testing unit was activated, and a pulsed magnetic field or periodic pulsed current excitation was applied to the core sample 4 through the transmitting coil 2. After the transmitting current was turned off, the receiving coils 3 synchronously acquired the timing signal of the induced electromotive force corresponding to the secondary field of the core sample 4, obtaining multi-channel raw induced electromotive force signal data in the transverse and radial directions. During the test, the transmitting current waveform, the working status of each channel, the sampling frequency, the number of superpositions, the signal gain, and operating parameters such as temperature and pressure were recorded simultaneously. At the same time, background signals without rock samples were acquired under the same operating conditions for subsequent correction.
[0123] This method for transient electromagnetic detection and analysis of rock physical parameters based on faithful reconstruction of deep in-situ environment includes the following steps:
[0124] S1, Data Acquisition and Preprocessing: After acquiring the raw induced electromotive force (EMF) signal data using the testing system, the acquired raw EMF signal is preprocessed. The signals of each channel are sequentially subjected to zero drift correction, noise filtering, superposition averaging, and outlier removal. The preprocessed raw EMF signal is then subtracted from the background signal without rock sample under the corresponding working condition to obtain the effective signal of the true transient electromagnetic response of the rock sample. Based on the system calibration parameters and the equivalent parameters of transmitting coil 2 and receiving coil 3, the apparent resistivity of each channel is calculated according to different time channels, and the results of multiple channels are weighted and fused to obtain the equivalent apparent resistivity corresponding to the working condition.
[0125] Channels exhibiting saturation, waveform distortion, or significant deviations from consistency requirements are marked and their weights are reduced or removed in subsequent calculations to improve the usability and reliability of the original data. Specifically:
[0126] S1-1, to eliminate the influence of the fidelity chamber and background medium on the transient electromagnetic response in the deep in-situ environment, background signals without samples were collected under the same temperature and pressure conditions. Acquired raw signals from sample testing And perform background calibration on the multi-channel transient response data to obtain the first... The effective transient electromagnetic signal of the channel is represented by the following equation (1):
[0127]
[0128] In the formula: For the first Time series of effective transient electromagnetic induction electromotive force after background subtraction at the same temperature and pressure without samples; This is the original signal from the sample test; This refers to the background signal without samples under the same operating conditions. Number the receiving channel; The sampling time.
[0129] S1-2, the acquired transient electromagnetic signals are filtered and divided into time domains. First, the data before the emission current is turned off and the early distortion data with obvious turn-off tail effects are removed, and only the late time period that meets the signal-to-noise ratio requirements is retained. Then, the time channels are divided in a logarithmic manner.
[0130] Let the first The start and end times of each measurement track are: and Then the average electromotive force corresponding to the track can be expressed as shown in the following equation (2):
[0131]
[0132] In the formula: For the first The average induced electromotive force of each track; For the first Time width of each measurement track; To effectively respond to the electromotive force amplitude, subsequent apparent resistivity calculations will use... Replacing continuous time domain representation .
[0133] After the transmitting current of transmitting coil 2 is turned off, induced eddy currents are generated inside core sample 4 under the condition of primary field removal and a secondary field is formed. Under quasi-static conditions, the electromagnetic response of this process satisfies the Maxwell equations, and the magnetic field diffusion equation shown in equation (3) can be further derived as follows:
[0134]
[0135] In the formula: The magnetic field strength; The dielectric permeability; Resistivity; for The Laplace operator is used to characterize the spatial diffusion term of the magnetic field.
[0136] Equation (3) shows that the transient electromagnetic response is essentially a diffusion and decay process of the secondary field in the conductive medium after the emission current is turned off.
[0137] The receiving coil 3 actually records the rate of change of the secondary magnetic flux with respect to time, and its response can be expressed as shown in the following equation (4):
[0138]
[0139] In the formula: Represents the second magnetic induction intensity, where For position vector, Sampling time; The effective area of receiving coil 3; The effective area of receiving coil 3 The unit normal vector;
[0140] Under the conditions of a homogeneous reference medium and a large-scale approximation, the transient electromagnetic response within the late time window can be approximated as a power-law decay form, from which the basic analytical response expression shown in equation (5) can be obtained:
[0141]
[0142] In the formula: This represents the theoretical response value of the induced electromotive force under ideal infinite homogeneous medium conditions; It is a step turn-off function; For system comprehensive coefficients, ,in This is a comprehensive coefficient that includes the transmit current amplitude, coil turns, coupling geometry, system gain, and calibration parameters. The permeability of free space, The effective area of transmitting coil 2, This represents the effective area of receiving coil 3.
[0143] Equation (5) describes the basic transient electromagnetic response characteristics under uniform reference medium conditions. Based on the diffusion relationship shown in Equation (5), the diffusion scale of the eddy current after the emitter current is turned off can be defined as shown in Equation (6) below:
[0144]
[0145] In the formula: for The eddy current diffusion scale at the sampling time characterizes the diffusion range of the transient electromagnetic response in core sample 4. The resistivity of the rock sample; is the vacuum permeability.
[0146] Since the application object is a cylindrical rock core sample of finite size, which has both radial sidewall boundaries and axial end face boundaries, it is necessary to define the radial and axial dimensionless parameters separately, as shown in the following equation (7):
[0147]
[0148] In the formula: The radius of core sample 4 is given. y is the axial length of core sample 4; The eddy current diffusion scale; , This indicates the relative relationship between the diffusion scale and the radius and axial dimension of the core sample 4, used to characterize the degree of approximation of the radius and length of the influence of the geometric boundary on the electromagnetic diffusion process.
[0149] To facilitate the inverse calculation of resistivity from the observed voltage, equation (5) is normalized. A reverse normalization method is preferred, where the device parameters and the basic time decay term are uniformly moved to the left side. The normalization quantity can be defined according to equation (5), as shown in equation (8) below:
[0150]
[0151] In the formula: This is the normalized induced electromotive force function; It is a cylindrical kernel function.
[0152] The purpose of this normalization process is to eliminate the system's overall coefficients. and explicit time power-law terms The influence of this. For an ideal homogeneous reference medium, the kernel function can be denoted as: , and have .
[0153] Without considering the boundary effects of finite-sized cylindrical core samples, then the first... The apparent resistivity of the base corresponding to each test track is expressed by the following equation (9):
[0154]
[0155] In the formula: Based on apparent resistivity.
[0156] Equation (9) is the inversion result obtained under the premise of a homogeneous reference medium, and does not yet take into account the influence of the sidewall and end face boundaries of the finite cylindrical rock sample on the secondary field attenuation curve.
[0157] S2, Calculation of resistivity corrected for boundary effects in finite cylindrical core samples:
[0158] Since the rock sample is not an ideal infinitely homogeneous medium, when the eddy diffusion scale... Gradually approaching or When the eddy current loop is constrained by geometric boundaries, the induced electromotive force decay law deviates from the response characteristics under homogeneous conditions. Based on the kernel function deviation, a boundary correction coefficient can be defined as shown in equation (10):
[0159]
[0160] In the formula: Indicates the boundary correction factor; For an ideal infinite medium kernel function; is the kernel function for a cylindrical rock core sample.
[0161] Equation (10) shows that the boundary correction is essentially derived from the deviation of the actual kernel function from the ideal kernel function.
[0162] Under the condition of finite-size cylindrical rock core samples, the kernel function Simple closed-form solutions are generally difficult to obtain, therefore an engineering calibration expression is used. To facilitate calculation, synthetic boundary parameters can be introduced. As shown in equation (11):
[0163]
[0164] Equation (10) can be further approximated as shown in equation (12):
[0165]
[0166] In the formula: and These are the first boundary correction calibration parameters and the second boundary correction calibration parameters, respectively, which can be determined through numerical forward modeling, standard sample testing, or rock sample experiments of the same size.
[0167] when When the eddy current diffusion scale is much smaller than the core sample size, the boundary effect can be ignored. ;when When the value increases, it indicates that the eddy current diffusion scale gradually approaches the boundary of the core sample, and the boundary effect is enhanced, corresponding to the correction factor. It also increases accordingly.
[0168] Therefore, combining equations (9) and (12), we can obtain the resistivity expression after correction for finite size boundaries, as shown in equation (13) below:
[0169]
[0170] In the formula: express Corrected resistivity at that moment; express The resistivity at time t.
[0171] Due to the correction factor As the diffusion scale changes, and the diffusion scale is determined by the current iterative resistivity, an iterative method is used to solve the problem in actual calculations.
[0172] First, the apparent resistivity is taken as the initial value, as shown in equation (14):
[0173]
[0174] In the formula: This represents the initial resistivity obtained through iterative solution.
[0175] Then, the diffusion scale is calculated based on the current iteration value, as shown in equation (15):
[0176]
[0177] In the formula: This refers to the iteration step number; Indicates the first During the next iteration The calculated eddy diffusion scale; For the first Next iteration resistivity.
[0178] From the aforementioned equation (7), we can obtain the following equation (16):
[0179]
[0180] Therefore, the correction coefficient for the current iteration step can be obtained. And update the resistivity, as shown in equation (17):
[0181]
[0182] The iteration is considered to be convergent when the convergence condition shown in equation (18) is met:
[0183]
[0184] In the formula: This is the convergence threshold.
[0185] at this time That is, as the survey track Corrected resistivity at time 1 .
[0186] S3, Rock property parameter inversion based on corrected resistivity:
[0187] Resistivity, while a comprehensive response parameter of rock to external electromagnetic excitation, characterizes the strength of a rock's electrical conductivity. However, it cannot directly correspond to the more engineering-significant pore structure, fluid occurrence state, and seepage capacity in deep reservoirs or engineering rock masses. Therefore, obtaining the corrected resistivity based on transient electromagnetic testing and boundary correction of finite-size core samples is only an intermediate step in characterizing the physical properties of deep rocks. The corrected resistivity serves as a bridge to further invert key physical properties such as rock porosity and water saturation, thereby achieving a quantitative characterization of deep storage characteristics and fluid occurrence conditions.
[0188] After obtaining the corrected resistivity, for core samples containing conductive fluid, it is preferable to use the Archie relation to establish the relationship between the corrected resistivity and porosity and water saturation, as shown in the following equation (19):
[0189]
[0190] In the formula: The resistivity of the core sample after finite size boundary correction; Let the pore fluid resistivity under the current temperature and pressure conditions be denoted as . ; Porosity; Water saturation; The cementation index; This is the Archie saturation index.
[0191] Taking the logarithm of equation (19) above, we get equation (20) below:
[0192]
[0193] As can be seen from equation (20) above, when the saturation condition is unknown, it is difficult to simultaneously and uniquely determine the resistivity based solely on resistivity data under a single measurement condition. and Therefore, porosity Water saturation As parameters to be inverted, a joint inversion model is constructed by correcting resistivity data through multiple time windows. The porosity and water saturation are solved uniformly, and the objective function shown in equation (21) can be established. :
[0194]
[0195] In the formula: The effective time window for participating in the inversion.
[0196] By minimizing the objective function Porosity can be achieved With water saturation The joint solution.
[0197] S4, Constructing a response model for resistivity and rock physical property parameters under temperature-pressure coupled conditions:
[0198] Under the conditions of faithful reconstruction of deep in-situ environments, temperature, pressure, and temperature-pressure coupling not only alter the resistivity obtained from transient electromagnetic tests, but also further affect pore structure compression, fracture opening and closing, changes in fluid conductivity, and the distribution of pore fluids, thus systematically influencing porosity, water saturation, and other properties. If temperature, pressure, and their coupling effects are not incorporated into the interpretation chain, even after the aforementioned boundary corrections are completed, the obtained corrected resistivity and its inverted physical property parameters can only reflect the results under certain local experimental conditions, making it difficult to truly characterize the actual response characteristics of rocks under deep in-situ environments.
[0199] Increased temperature can cause changes in pore fluid ion mobility, fluid resistivity, and mineral surface electrochemical activity; increased pressure can lead to pore compression, microcrack closure, and changes in fluid channel geometry; and temperature and pressure are not independent of each other, their coupling effect can also change the deformation characteristics of rock skeleton and fluid distribution.
[0200] The temperature-pressure coupling model was established based on a regression method using multi-condition experimental data. Specifically, in the deep in-situ environment fidelity chamber 1, the temperature was gradually changed... With pressure A set of transient electromagnetic response data under different temperature and pressure conditions was obtained. For each set of data, the aforementioned steps were completed sequentially. After obtaining multiple sets of temperature and pressure data, a model of the relationship between resistivity and temperature and pressure was established by statistical regression. Considering that the rock resistivity usually exhibits an exponential change with temperature and pressure, a temperature-pressure coupled resistivity model was established in logarithmic form, as shown in the following equation (22):
[0201]
[0202] In the formula: For reference constant terms; Temperature coefficient; Pressure coefficient; This is the temperature-pressure coupling coefficient.
[0203] The above coefficients were determined through regression analysis using multi-condition experimental data. Specifically, the least squares objective function can be established as shown in equation (23):
[0204]
[0205] In the formula: This represents the total number of experimental conditions.
[0206] By minimizing the objective function The coefficients of the temperature-pressure coupled resistivity model can then be obtained. , , and .
[0207] After obtaining the above model coefficients, the corrected resistivity under different temperature and pressure conditions can be further converted to the same reference condition. Let the reference temperature and reference pressure be respectively... and The equivalent corrected resistivity under the corresponding reference operating condition is Based on the above equation (22), we can further obtain the following equation (24):
[0208]
[0209] In the formula: This is the equivalent resistivity after conversion to the reference operating condition; For actual temperature and pressure conditions The corrected resistivity is as follows.
[0210] Equation (24) above can be used to unify the corrected resistivity measured under different temperature and pressure conditions to the same interpretation standard.
[0211] After obtaining the resistivity under a unified reference condition, the aforementioned resistivity-rock property parameter inversion model can be further used to determine the porosity. and water saturation A joint solution is performed, and the response relationship between rock physical parameters and temperature and pressure is further established, as shown in equations (25) and (26) below:
[0212]
[0213]
[0214] In the formula: Porosity function representing the effects of temperature, pressure, and thermo-pressure coupling; The water saturation function represents the water content under the corresponding working conditions. The above parameter relationship can be further approximated as shown in the following equations (27) and (28):
[0215]
[0216]
[0217] In the formula: and These represent the porosity and water saturation under reference operating conditions, respectively. , , These are the response coefficients of porosity to temperature, pressure, and temperature-pressure coupling, respectively. , , These are the response coefficients of water saturation to temperature, pressure, and temperature-pressure coupling, respectively.
[0218] All the above coefficients can be determined through regression analysis of multi-condition experimental data. Under different temperature and pressure conditions, the corrected resistivity was obtained and the corresponding porosity was inverted. and water saturation Multiple sets of parameter samples are formed. By further using least squares fitting or other regression methods, the response coefficients in equations (27) to (28) can be determined, thereby establishing a temperature-pressure coupled physical property parameter model suitable for the target rock sample.
[0219] This method for transient electromagnetic detection and analysis of rock physical parameters based on the faithful reconstruction of deep in-situ environment adopts a technical route of "faithful environment reconstruction - multi-channel transient electromagnetic non-contact acquisition - precise signal processing - apparent resistivity correction - physical parameter inversion". By reconstructing the high temperature and high pressure environment of deep in-situ rocks in the test chamber, and using non-contact multi-channel transient electromagnetic testing under faithful conditions, it accurately obtains the effective transient response data of in-situ rock samples. An apparent resistivity correction method is established to obtain the equivalent resistivity of the rock samples. Based on the corrected resistivity, physical parameters such as porosity and water saturation are inverted. A model of the influence of temperature, pressure and their coupling on resistivity and inversion results is established to achieve comparable output under multiple working conditions. This method enables non-contact, non-destructive, and precise detection of the physical and mechanical parameters of deep in-situ rocks, and can provide key technical support for theoretical research and engineering practice in the field of deep rock mechanics.
Claims
1. A method for transient electromagnetic detection and analysis of rock physical parameters based on faithful reconstruction of deep in-situ environment, characterized in that, The testing system used includes a fidelity chamber (1), a transient electromagnetic testing unit, a temperature and pressure control unit, and a data acquisition and processing unit; The fidelity chamber (1) is an integral pressure-bearing shell with a sample testing chamber that is coaxially arranged and axially connected inside. The two ends of the fidelity chamber (1) in the axial direction are also coaxially sealed with conversion flanges. The transient electromagnetic test unit includes a transmitting coil (2) and a receiving coil (3). The transmitting coil (2) is coaxially arranged with the sample test cavity, and the two transmitting coils (2) are respectively positioned at both ends of the axial direction of the sample test cavity. Multiple receiving coils (3) are evenly distributed along the circumferential direction of the sample test cavity and positioned between the two transmitting coils (2), and the axial direction of the receiving coils (3) is along the circumferential direction of the sample test cavity. The temperature and pressure control unit includes a loading device, a heating device, a cooling device, a temperature sensor, and a pressure sensor; The data acquisition and processing unit includes a central controller and an acquisition control loop. The central controller is electrically connected to the transmitting coil (2), the receiving coil (3), and the temperature and pressure control unit, respectively. The method for transient electromagnetic detection and analysis of rock physical parameters based on faithful reconstruction of deep in-situ environment includes the following steps: S1, Data Acquisition and Preprocessing: The test system is used to collect raw induced electromotive force signal data, and the collected raw induced electromotive force signal is preprocessed. The signals of each channel are sequentially subjected to zero drift correction, noise filtering, superposition averaging and outlier removal. The raw induced electromotive force signal after preprocessing is deducted from the background signal without rock sample under the corresponding working condition to obtain the effective signal of the real transient electromagnetic response of the rock sample. According to the system calibration parameters and the equivalent parameters of the transmitting coil (2) and receiving coil (3), the apparent resistivity of each channel is calculated according to different time channels, and the results of multiple channels are weighted and fused to obtain the equivalent apparent resistivity corresponding to the working condition. S2, Boundary effect correction: Boundary correction parameters are constructed based on the geometric dimensions and response characteristics of the core sample to correct the apparent resistivity and obtain the corrected resistivity that reflects the true electrical characteristics of the core sample. S3, Construct a joint inversion model: Based on corrected resistivity, porosity Water saturation As parameters to be inverted, a joint inversion model is constructed by correcting resistivity data through multiple time windows; S4, Joint constraint inversion under multiple temperature, multiple pressure, and temperature-pressure coupling conditions: Under different temperature and pressure conditions, the corrected resistivity is obtained and the corresponding porosity is inverted. and water saturation Multiple sets of parameter samples are formed. A temperature-pressure coupled physical property parameter model suitable for the target rock sample was established, and joint constraint inversion was performed to achieve comparable output under multiple working conditions.
2. The method for transient electromagnetic detection and analysis of rock physical parameters based on faithful reconstruction of deep in-situ environment according to claim 1, characterized in that, In S1, the effective signal of the true transient electromagnetic response of the rock sample is obtained, as follows: Background signals without samples were collected under the same temperature and pressure conditions. Acquired raw signals from sample testing And perform background calibration on the multi-channel transient response data to obtain the first... The effective transient electromagnetic signal of the channel is represented as follows: In the formula: For the first Time series of effective transient electromagnetic induction electromotive force after background subtraction at the same temperature and pressure without samples; This is the original signal from the sample test; This refers to the background signal without samples under the same operating conditions. Number the receiving channel; The sampling time.
3. The method for transient electromagnetic detection and analysis of rock physical parameters based on fidelity reconstruction of deep in-situ environment according to claim 2, characterized in that, In S1, the determination of the track at different times is as follows: The acquired transient electromagnetic signals were filtered and divided into time domains. First, data before the emission current was turned off and early distortion data with significant turn-off tail effects were removed, and only the late time period that met the signal-to-noise ratio requirements was retained. Then, the time channels were divided in a logarithmic manner.
4. The method for transient electromagnetic detection and analysis of rock physical parameters based on fidelity reconstruction of deep in-situ environment according to claim 3, characterized in that, In S1, when calculating the apparent resistivity of each channel based on different time measurements, the details are as follows: Let the first The start and end times of each measurement track are: and The average electromotive force corresponding to this track is expressed as follows: In the formula: For the first The average induced electromotive force of each track; For the first Time width of each measurement track; To effectively respond to the electromotive force amplitude; After the transmitting current of the transmitting coil (2) is turned off, the magnetic field diffusion equation is expressed as follows: In the formula: The magnetic field strength; The dielectric permeability; Resistivity; for The Laplace operator is used to characterize the spatial diffusion term of the magnetic field; The response of the receiving coil (3) is expressed as follows: In the formula: Represents the second magnetic induction intensity, where For position vector, Sampling time; The effective area of the receiving coil (3); The effective area of the receiving coil (3) The unit normal vector; The basic analytical response is then expressed as follows: In the formula: This represents the theoretical response value of the induced electromotive force under ideal infinite homogeneous medium conditions; It is a step turn-off function; For system comprehensive coefficients, ,in This is a comprehensive coefficient that includes the transmit current amplitude, coil turns, coupling geometry, system gain, and calibration parameters. The permeability of free space, The effective area of the transmitting coil (2) is The effective area of the receiving coil (3); The diffusion scale of the eddy current after the emitter current is turned off is defined as follows: In the formula: for The eddy current diffusion scale at the sampling time characterizes the diffusion range of the transient electromagnetic response in the core sample. The resistivity of the rock sample; The vacuum permeability; Define the radial and axial dimensionless parameters respectively, as follows: In the formula: The radius of the core sample is denoted as . This represents the axial length of the core sample. The eddy current diffusion scale; , These represent the relative relationships between the diffusion scale and the radius and axial dimension of the core sample, respectively. Define the normalization quantity as follows: In the formula: This is the normalized induced electromotive force function; The kernel function is cylindrical; Then the first The underlying apparent resistivity corresponding to each measurement channel is expressed as follows: In the formula: Based on apparent resistivity.
5. The method for transient electromagnetic detection and analysis of rock physical parameters based on fidelity reconstruction of deep in-situ environment according to claim 4, characterized in that, S2 is as follows. Define the boundary correction coefficients as follows: In the formula: Indicates the boundary correction factor; For an ideal infinite medium kernel function; For cylindrical rock core samples; Introducing comprehensive boundary parameters As shown below: The boundary correction coefficients are then approximated as follows: In the formula: and The first boundary correction calibration parameters and the second boundary correction calibration parameters are respectively determined through numerical forward modeling, standard sample testing, or rock sample experiments of the same size. The resistivity expression after correction for finite size boundaries is as follows: In the formula: express Corrected resistivity at that moment; express The resistivity at time t.
6. The method for transient electromagnetic detection and analysis of rock physical parameters based on fidelity reconstruction of deep in-situ environment according to claim 5, characterized in that, The corrected resistivity is solved iteratively, as follows: First, we take the basic apparent resistivity as the initial value, as shown below: In the formula: This represents the initial resistivity obtained through iterative solution; Then, the diffusion scale is calculated based on the current iteration value, as shown below: In the formula: This refers to the iteration step number; Indicates the first During the next iteration The calculated eddy diffusion scale; For the first Next iteration resistivity; The dimensionless parameters for radial and axial directions are as follows: Therefore, the correction coefficient for the current iteration step can be obtained. And update the resistivity, as shown below: The iteration is considered to have converged when the following convergence condition is met: In the formula: This is the convergence threshold; at this time That is, as the survey track Corrected resistivity at time 1 .
7. The method for transient electromagnetic detection and analysis of rock physical parameters based on fidelity reconstruction of deep in-situ environment according to claim 6, characterized in that, In S3, the Archie relation is used to establish the relationship between the corrected resistivity, porosity, and water saturation, as shown below: In the formula: The resistivity of the core sample after finite size boundary correction; Let the pore fluid resistivity under the current temperature and pressure conditions be denoted as . ; Porosity; Water saturation; The cementation index; Archie saturation index; Taking the logarithm of the above expression, we get: porosity Water saturation Using resistivity data corrected by multiple time windows as the parameters to be inverted, a joint inversion model is constructed to uniformly solve for porosity and water saturation, and the objective function is established as shown below. : In the formula: The number of effective time windows for participating in the inversion; By minimizing the objective function To achieve porosity With water saturation The joint solution.
8. The method for transient electromagnetic detection and analysis of rock physical parameters based on fidelity reconstruction of deep in-situ environment according to claim 7, characterized in that, In S4, a temperature-pressure coupling model is established based on regression methods using multi-condition experimental data, as detailed below: By gradually changing the temperature With pressure We acquired transient electromagnetic response data under different temperature and pressure conditions, established a model relating resistivity to temperature and pressure using statistical regression, and created a temperature-pressure coupled resistivity model in logarithmic form, as shown below: In the formula: For reference constant terms; Temperature coefficient; Pressure coefficient; This is the temperature-pressure coupling coefficient; Establish the least squares objective function as shown below: In the formula: This represents the total number of experimental conditions. By minimizing the objective function The coefficients of the temperature-pressure coupled resistivity model were obtained. , , and .
9. The method for transient electromagnetic detection and analysis of rock physical parameters based on fidelity reconstruction of deep in-situ environment according to claim 8, characterized in that, The corrected resistivity under different temperature and pressure conditions is uniformly converted to the same reference condition, as follows: Let the reference temperature and reference pressure be respectively and The equivalent corrected resistivity under the corresponding reference operating condition is ,but: In the formula: This is the equivalent resistivity after conversion to the reference operating condition; For actual temperature and pressure conditions The corrected resistivity is as follows.
10. The method for transient electromagnetic detection and analysis of rock physical parameters based on fidelity reconstruction of deep in-situ environment according to claim 9, characterized in that, After obtaining the resistivity under a unified reference condition, the porosity was analyzed using the resistivity-rock property parameter inversion model of S3. and water saturation A joint solution is performed to establish the response relationship between rock physical parameters and temperature and pressure, as shown below: In the formula: Porosity function representing the effects of temperature, pressure, and thermo-pressure coupling; This represents the water saturation function under the corresponding operating conditions; The parameter relationship can be approximated as follows: In the formula: and These represent the porosity and water saturation under reference operating conditions, respectively. , , These are the response coefficients of porosity to temperature, pressure, and temperature-pressure coupling, respectively. , , These are the response coefficients of water saturation to temperature, pressure, and temperature-pressure coupling, respectively. Under different temperature and pressure conditions, the corrected resistivity was obtained and the corresponding porosity was inverted. and water saturation Multiple sets of parameter samples are formed. By using regression methods to determine each response coefficient, a temperature-pressure coupled physical property parameter model suitable for the target rock sample is established.