Vertical barrier wall leakage detection and inversion method based on tracer agent and analytical model

Abstract

The invention belongs to the technical field of vertical barrier wall leakage detection, and particularly relates to a vertical barrier wall leakage detection and inversion method based on a tracer and an analytical model. A tracer agent is injected around the vertical barrier wall or in a wall body, the diffusion path and concentration distribution of the tracer agent are detected by utilizing the characteristic that the tracer agent diffuses at a leakage point or is carried by water flow, and the size of a leakage channel is obtained through inversion, so that the leakage condition of the vertical barrier wall is efficiently judged, and the size of a leakage crack of the vertical barrier wall is quantified. The detection efficiency and accuracy of the leakage condition of the vertical barrier wall are remarkably improved, and the defects of a traditional method for detecting the leakage condition of the vertical barrier wall are overcome. Through the technical scheme provided by the invention, the service characteristics of vertical barrier walls made of different materials can be better evaluated, and reliable technical support is provided for field pollutant control and field repair.

Description

Technical Field

[0001] The present invention belongs to the technical field of vertical barrier wall leakage detection, and more specifically relates to a vertical barrier wall leakage detection and inversion method based on tracers and analytical models. Background Art

[0002] Vertical barrier walls are currently the most effective technology for limiting the migration of pollutants. Depending on the materials used for the wall, commonly used flexible anti-fouling vertical barrier wall materials include soil-bentonite, cement-bentonite, geocomposite bentonite waterproof blanket (GCL), geomembrane (GMB) composite barrier wall, etc. However, in actual applications, vertical barrier walls often have leakage problems due to improper construction, pollutant corrosion, geomembrane damage, seepage erosion, poor interface contact, etc., which not only directly weakens its ability to block pollutants, but also seriously shortens its expected service life, which may lead to further diffusion of pollutants in the soil, aggravate the risk of environmental pollution, increase subsequent remediation costs, and pose a dual threat to the social economy and ecological environment. Therefore, accurately detecting the leakage status of vertical barrier walls and quantitatively evaluating the size of leakage channels have become core problems that need to be urgently solved in the management and prevention of contaminated sites.

[0003] Traditional vertical barrier wall leakage detection technology has limitations such as low sensitivity and inaccurate leakage point positioning. The detection depth of the commonly used dual-electrode method at home and abroad does not exceed 3m. However, the insertion depth of the vertical barrier wall can reach more than 30m, and the existing detection methods cannot directly identify the leakage. Furthermore, the accuracy of the existing high-density electrical method and geological radar detection decreases significantly with the increase of burial depth, which cannot meet the requirements of accurate detection of leakage channels. In recent years, the tracer-based leakage channel identification method has begun to attract attention and has been successfully applied to deep leakage detection of dams and identification of advantageous channels in oil fields. The tracer method refers to injecting tracers into the injection wells in the study area, and then obtaining the tracer output curve through the monitoring wells. Combined with the tracer migration model, the characteristics of the leakage channel are deduced. However, if the tracer method is applied to the leakage detection of vertical barrier walls, there will be a series of defects and problems. First, the structure of the vertical barrier wall is usually more complex, and the wall materials are diverse, which easily leads to deviations between the migration behavior of the tracer in the wall and the expected model, thereby affecting the accuracy of leakage channel identification. Secondly, since vertical barrier walls are often buried deep underground, their environmental conditions (such as temperature, pressure, humidity, etc.) are significantly different from those on the surface or shallow structures, which may affect the stability and reactivity of the tracer, thereby interfering with the accurate judgment of the leakage channel. In addition, the injection and monitoring process of the tracer requires high-precision equipment and technical support, which is relatively expensive, and in some cases, the tracer may cause secondary pollution to the environment and needs to be handled with caution. Summary of the invention

[0004] In view of the above technical problems, the present invention provides a method for detecting and inverting the leakage of a vertical barrier wall based on a tracer and an analytical model. By injecting a tracer around or into the vertical barrier wall, using the characteristics of the tracer diffusing at the leakage point or being carried by the water flow, detecting the diffusion path and concentration distribution of the tracer, and inversely obtaining the size of the leakage channel, so as to efficiently determine the leakage situation of the vertical barrier wall and quantify the size of the leakage fissures or holes in the vertical barrier wall, achieving the purpose of significantly improving the detection efficiency and accuracy of the leakage situation of the vertical barrier wall and making up for the deficiencies of traditional methods for detecting the leakage of vertical barrier walls.

[0005] To achieve the above object, the present invention provides a method for detecting and inverting the leakage of a vertical barrier wall based on a tracer and an analytical model, including the following steps:

[0006] Step S1: Arrange injection wells and monitoring wells, and respectively collect, detect and record the background values of the water sample tracers in the injection wells and monitoring wells;

[0007] Step S2: Add the tracer to the injection well, and at a certain time interval frequency, collect, detect and record the concentration values of the tracer in several monitoring wells, and draw the tracer concentration-time output curve of the monitoring wells;

[0008] Step S3: According to the tracer concentration-time output curve of the monitoring wells, combined with the analytical model, inversely obtain the tracer concentration field distribution from the injection well to the monitoring wells, and calculate the geometric characteristics of the leakage channel of the vertical barrier wall.

[0009] According to some embodiments of the present invention, the geometric characteristics of the leakage channel of the vertical barrier wall in step S3 are the size parameters of the leakage channel of the vertical barrier wall, which are calculated by using the cubic law of fissures or the empirical formula of leakage flow through holes.

[0010] In some more preferred embodiments, the types of leakage channels corresponding to different types of barrier walls are different. For example, for a vertical barrier wall including but not limited to soil-bentonite material, the potential leakage channel type is a fissure. When the leakage channel type is a fissure, the cubic law of fissures shown in formula (1) is used for calculation:

[0011]

[0012] Among them, b is the fissure width; ρ is the density of water; g is the acceleration of gravity; μ is the dynamic viscosity of water.

[0013] In some other preferred embodiments, for example, a barrier wall of the geomembrane type is adopted, including but not limited to a composite barrier wall of a geosynthetic clay liner (GCL) and a geomembrane (GMB). Its potential leakage channels are holes. When the type of such leakage channels is holes, the empirical formula for calculating the leakage flow rate of the holes as shown in Equation (2) is used:

[0014] v·S = 0.2769kHD 0.0462 b 0.0971ln D+0.8235 (2)

[0015] Wherein, D is the thickness of the vertical barrier wall or the waterproof blanket, with the unit of m; b is the radius size of the hole, with the unit of m; S is the cross-sectional area, with the unit of m 2 , and the calculation method is πb 2 ; k is the permeability coefficient of the vertical barrier wall, with the unit of m / s; H is the water head difference on both sides of the vertical barrier wall, with the unit of m.

[0016] Preferably, before arranging the injection wells and monitoring wells, it further includes:

[0017] Step S01: Obtain the hydrogeological data of the site according to the analysis of the hydrogeological characteristics of the test site, specifically including data such as geological maps, cross-sectional views, existing wells, and groundwater levels; and

[0018] Step S02: According to the above hydrogeological data, preliminarily judge the groundwater flow field information around the test site, obtain the maximum groundwater depth data, permeability coefficient, and water flow line direction data, which provide a reference for the depths of the injection wells and monitoring wells. Of course, the above groundwater flow field information around the test site, such as the maximum groundwater depth data, permeability coefficient, and water flow line direction data, can also be directly adopted from existing ready-made data. In this way, in some specific embodiments of the present invention, the steps of obtaining the hydrogeological data of the site and preliminarily judging the surrounding groundwater flow field information can be omitted, and the positions and depths of the injection wells and monitoring wells can be determined more quickly.

[0019] According to the hydrogeological data obtained from the above analysis of the hydrogeological characteristics, reasonably determine the positions and depths of the injection wells and monitoring wells. The injection wells should be set in the core area of the test site to ensure uniform injection of the tracer and coverage of the potential leakage area; the monitoring wells should be arranged downstream of the groundwater flow direction and perpendicular to the main water flow line to effectively monitor the diffusion of the tracer and the leakage path in the water. The layout of the wells is designed with reference to the specification of HJT-2020 "Technical Specification for Groundwater Environment Monitoring".

[0020] Preferably, when detecting the background values of the water level and tracer concentration, a water level survey, water quality survey, and sampling are carried out for all injection wells and monitoring wells to detect the tracer concentration, and the background value of the tracer concentration is determined.

[0021] Preferably, when adding the tracer into the injection well in step S2, the tracer input amount model shown in formula (3) is used to add the tracer:

[0022]

[0023] where M is the added amount of the effective substance of the tracer; λ is the safety factor, and the recommended value in general contaminated sites is 1×10 -4 -5×10 -3 ; MDL is the minimum detectable limit of the tracer equipment, with the unit of g / m 3 ; r is the average well spacing between the injection well and the monitoring well, with the unit of m; h is the average effective aquifer thickness of the test site, with the unit of m; is the porosity. According to the M value calculated by the above tracer input amount model, the total amount of the injected tracer is determined. In the present invention, tracers including but not limited to, for example, fluorobenzoic acid, sulfur hexafluoride, and sodium chloride are used. Among them, fluorobenzoic acid is preferred because it has almost no pollution to the environment and a low detection limit, and can be detected at only 1 μg / L. The tracer is configured into a solution with a concentration of 500 - 1000 mg / L, stirred evenly, and injected into the injection well at a constant speed and normal pressure.

[0024] Preferably, in step S2, the certain time interval is to collect water samples once every quarter, and the interval between every two collections is more than 2 months and no more than 5 months, and a total of 4 times are collected every year.

[0025] More preferably, if no tracer is detected in the sample, it indicates that the leakage in the test area is not obvious, and the collection and detection frequency of "collecting water samples once every quarter, and the interval between every two collections is more than 2 months and no more than 5 months" can be continued; while if a tracer is detected in the collected water sample, several collection and detection times are increased, and the collection and detection time interval is shortened to 1 - 2 months, and the tracer concentration - time production curves at each point are obtained according to the concentration values of the tracer at each point and at each time.

[0026] Preferably, step S3 includes:

[0027] Step S31, constructing a control equation for one - dimensional dispersion - convection migration under the control of the hydraulic head;

[0028] Step S32, according to the control equation, inversely calculating the tracer concentration field distribution and migration - related parameters from the injection well to the monitoring well, and then selecting to use the cubic law of fractures or the empirical formula for leakage flow of holes according to the type of the vertical cut - off wall as described above to determine the size parameters of the permeation channels of the vertical cut - off wall.

[0029] Preferably, in the test site, in order to avoid wasting leakage detection time in full-precision simulation, the tracer seepage path between the injection well and the monitoring well can be appropriately simplified in the analytical model. The characteristics of the analytical model proposed by the present invention are as follows: First, it is assumed that the tracer is transported in a porous medium divided into m layers, and the porous medium is divided into 0 < l0 < l1 < … < l m-1 <l m = L layers. Let c i (x, t) represent the tracer concentration in the i-th layer, where x ∈ (l i-1 , l i ) represents the distance from the inlet x = 0, and t > 0 represents time. Then, the control equation for one-dimensional dispersion-convection transport in the i-th layer is shown in Equation (4):

[0030]

[0031] Among them, R i > 0 is the retardation coefficient; D i > 0 is the effective hydrodynamic coefficient; v i is the seepage velocity; c i is the tracer concentration.

[0032] The control equation (4) for one-dimensional dispersion-convection transport needs to be used in conjunction with the initial conditions, interface conditions, and boundary conditions. The concentration is initially assumed to be constant in each layer, that is:

[0033] c i (x, 0) = f i (5)

[0034] Among them: f i is the concentration-time function.

[0035] At the interface between adjacent layers, it is assumed that the concentration and the dispersion flux are continuous.

[0036] c i (l i , t) = c i+1 (l i , t) (6)

[0037]

[0038] In the formula: θ i is the volumetric water content.

[0039] At the inlet (x = 0) and the outlet (x = L), the generalized third boundary condition is considered:

[0040]

[0041]

[0042] where: a0, b0, a L , b L are constants; g0(t), g L (t) are arbitrarily specified time functions; in particular, b0 and b L are both non - negative numbers; at least one of a0 or b0 is not zero, and at least one of a L or b L is not zero.

[0043] In the current test site, we consider the injection boundary condition to be the Dirichlet boundary condition, that is, the boundary condition in the form of concentration:

[0044] c1(0,t) = c0(t) (10)

[0045] Therefore, the relevant parameters in equations (8) and (9) can be determined as: a0 = 1, b0 = 0, g0(t) = c0(t), a L = 0, b L = 1, g L (t) = 0.

[0046] To solve the multi - layer transport model equations (4)–(9), we reformulate the model into m independent single - layer problems, introducing the time - varying unknown function g i (t) to represent the following scalar factor of the (negative) dispersion flux at the layer interface.

[0047]

[0048] The following equivalent form of the multi - layer transport model equations (4)–(9) is obtained:

[0049] The first layer (i = 1):

[0050]

[0051] c1(x,0) = f1 (13)

[0052]

[0053] For the intermediate soil layers (i = 2,…,m - 1):

[0054]

[0055] c i (x,0) = f i (17)

[0056]

[0057] The last layer (i = m):

[0058]

[0059] c m (x, 0) = f m (21)

[0060]

[0061] For each soil layer in each case, perform the Laplace transform to obtain the concentration calculation equations for different soil layers:

[0062] C1(x, s) = A1(x, s)G0(s) + B1(x, s)G1(s) + P1(x, s) (24)

[0063] C i (x, s) = A i (x, s)G i-i (s) + B i (x, s)G i (s) + P i (x, s), i = 2, …, m - 1 (25)

[0064] C m (x, s) = A m (x, s)G m-1 (s) + B m (x, s)G m (s) + P m (x, s) (26)

[0065] The definitions of the functions Pi, Ai, and Bi (i = 1, …, m) in the above three equations are as follows:

[0066] For the first layer (i = 1):

[0067]

[0068] Where:

[0069] β1(s) = [a0 - b0λ 1,1 (s)]λ 1,2 (s) exp(-[λ 1,1 (s) - λ 1,2 (s)] l1) - [a0 - b0λ 1,2 (s)]λ 1,1 (s) (28)

[0070] For the intermediate layers (i = 2, …, m - 1):

[0071]

[0072] Wherein:

[0073] β i (s) = λ i,1 (s)λ i,2 (s){exp(-[λ i,1 (s)-λ i,2 (s)](l i -l i-1 )) - 1} (30)

[0074] For the last layer of soil (i = m):

[0075]

[0076] Wherein:

[0077] β m (s) = [a L +b L λ m,2 (s)]λ m,1 (s)exp(-[λ m,1 (s)-λ m,2 (s)](l m -l m-1 )) - [a L +b L λ m,1 (s)]λ m,2 (s) (32)

[0079] For all soil layers:

[0080]

[0081] When all variables in expressions (24)-(26) are defined, in order to determine the Laplace transforms G1(s), …, G m-1 (t) of the unknown interface functions g1(t), …, g m-1 (s), it is necessary to impose the continuity condition of concentration on each interface in the Laplace domain, that is:

[0082] C i (l i , s) = C i+1 (l i , s), i = 1, …, m - 1. (34)

[0083] Substitute expressions (24)-(26) into equation (34) to obtain a linear system of x = [G1(s), …, G m-1 (s)] T which is solved in the following matrix form:

[0084] Ax = b (35)

[0085] Where: is a diagonal matrix, is a vector. Among them, represents the complex number field.

[0086] Substitute G1(s), …, G m-1 (s) after matrix solution into expressions (24)-(26), and the concentration values at any position and time in the Laplace domain can be obtained.

[0087] Compare the concentration values obtained by analytical calculation with the production curve in the monitoring well to obtain the migration velocity v after analytical inversion.

[0088] Substitute the inverted v into the cubic law of equations (1) and (2) to obtain the crack size in the case of leakage of the geomembrane.

[0089] For different types of barrier walls, the corresponding leakage channel types are different. For soil-bentonite vertical barrier walls, the potential seepage channel type is cracks, and the calculation equation used is the crack law, which is introduced as follows:

[0090]

[0091] Where: b is the crack size, with the unit of m; ρ is the density of water, with the unit of kg / m 3 ; g is the acceleration due to gravity, m 2 / s; μ is the hydrodynamic viscosity coefficient, with the unit of Pa·s.

[0092] For barrier walls of the geomembrane type, such as geocomposite bentonite waterproof blankets (GCL), geomembrane (GMB) composite barrier walls, their potential leakage channels are holes, and the empirical formula for the leakage flow rate of holes is used:

[0093] v·S = 0.2769kHD 0.0462 b 0.0971lnD+0.8235 (2)

[0094] Where: D is the thickness of the waterproof blanket, with the unit of m, b is the radius size of the hole, with the unit of m, S is the cross-sectional area, with the unit of m 2 , and the calculation method is πb 2 , k is the permeability coefficient of the vertical barrier wall, with the unit of m / s, and H is the head difference on both sides of the vertical barrier wall, with the unit of m.

[0095] Different from the prior art, the above technical solution can more accurately determine the geometric characteristics of the leakage channels of the vertical barrier wall, including size parameters of the leakage channels, etc., by arranging injection wells and monitoring wells, collecting, detecting and recording the concentration values of tracers, making tracer concentration-time curves, and performing inversion in combination with an analytical model. The technical solution of the present invention is applicable not only to fissure-type leakage channels but also to hole-type leakage channels, and can more comprehensively cover different types of leakage situations by using different calculation formulas (cubic law of fissures and empirical formula for leakage flow of holes). By constructing the control equation of one-dimensional dispersion-convection transport and inversely demonstrating the distribution of the tracer concentration field and related transport parameters based on this, the accuracy and scientificity of the inversion are improved. Through the technical solution provided by the present invention, the service characteristics of vertical barrier walls made of different materials can be better evaluated, providing reliable technical support for site pollutant prevention and site remediation.

[0096] The above relevant descriptions of the invention content are only an overview of the technical solution of this application. In order to enable those of ordinary skill in the art to more clearly understand the technical solution of this application, and thus can be implemented according to the content recorded in the description and the drawings, and in order to make the above objects, other objects, features and advantages of this application more easily understood, the following is described in conjunction with the specific embodiments of this application and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0097] The drawings are only used to illustrate the principles, implementation methods, applications, features, effects, etc. of the specific embodiments of this application and other related contents, and should not be considered as a limitation to this application.

[0098] In the drawings of the specification:

[0099] Figure 1 is a schematic diagram of the steps of the method for detecting and inversing the leakage of a vertical barrier wall based on tracers and an analytical model proposed by the present invention;

[0100] Figure 2 is a schematic flowchart of the method for detecting and inversing the leakage of a vertical barrier wall based on tracers and an analytical model proposed by the present invention;

[0101] Figure 3 is a schematic diagram of the layout of injection wells and monitoring wells of a geomembrane (GMB) composite barrier wall and a soil-bentonite vertical barrier wall shown in a specific embodiment of the present invention;

[0102] Figure 4 is a comparison between the analytical algorithm for the leakage of a geomembrane (GMB) composite barrier wall in the present invention and field test data;

[0103] Figure 5 is a comparison between the analytical algorithm for the leakage of a soil-bentonite vertical barrier wall in the present invention and field test data. Detailed Implementation Modes

[0104] To illustrate in detail the possible application scenarios, technical principles, specific implementable solutions, achievable objectives and effects of this application, the following will be described in detail with reference to the specific examples listed and in conjunction with the accompanying drawings. The embodiments described herein are only used to more clearly illustrate the technical solutions of this application, so they are only examples and cannot be used to limit the protection scope of this application.

[0105] Referring to "embodiments" herein means that the specific features, structures or characteristics described in connection with the embodiments can be included in at least one embodiment of this application. The term "embodiment" appearing in various positions in the specification does not necessarily refer to the same embodiment, nor does it particularly limit its independence or relevance to other embodiments. In principle, in this application, as long as there is no technical contradiction or conflict, the technical features mentioned in each embodiment can be combined in any way to form corresponding implementable technical solutions.

[0106] Unless otherwise defined, the meanings of the technical terms used herein are the same as those generally understood by those skilled in the technical field to which this application belongs; the use of the relevant terms herein is only for describing specific embodiments and is not intended to limit this application.

[0107] In the description of this application, the term "and / or" is an expression used to describe the logical relationship between objects, indicating that three relationships can exist. For example, A and / or B means: there is A, there is B, and there is both A and B at the same time. In addition, the character " / " herein generally represents an "or" logical relationship between the associated objects before and after.

[0108] In this application, terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual quantity, primary-secondary or order relationship between these entities or operations.

[0109] Without more limitations, in this application, the expressions such as "including", "comprising", "having" or other similar expressions used in the statements are intended to cover non-exclusive inclusion. These expressions do not exclude that there may be other elements in the process, method or product including the said elements, so that the process, method or product including a series of elements may not only include those defined elements, but also include other elements not explicitly listed, or also include elements inherent to this process, method or product.

[0110] Similar to the understanding in the "Examination Guidelines", in this application, expressions such as "greater than", "less than", "exceeding", etc. are understood not to include the base number; expressions such as "above", "below", "within", etc. are understood to include the base number. In addition, in the description of the embodiments of this application, the meaning of "a plurality of" is two or more (including two), and similar expressions related to "many" are also understood in this way, such as "multiple groups", "multiple times", etc., unless otherwise specifically defined.

[0111] In the description of the embodiments of this application, the spatially related expressions used, such as "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "perpendicular", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", "axial", "radial", "circumferential", etc., the indicated orientation or positional relationship is based on the orientation or positional relationship shown in the specific embodiment or the drawing, and is only for the convenience of describing the specific embodiment of this application or facilitating the reader's understanding, rather than indicating or implying that the device or component referred to must have a specific position, a specific orientation, or be constructed or operated in a specific orientation. Therefore, it should not be understood as a limitation to the embodiments of this application.

[0112] Unless otherwise clearly specified or limited, in the description of the embodiments of this application, the terms such as "installed", "connected", "coupled", "fixed", "arranged", etc. should be understood in a broad sense. For example, the "connection" can be a fixed connection, a detachable connection, or an integral arrangement; it can be a mechanical connection, an electrical connection, or a communication connection; it can be directly connected, or indirectly connected through an intermediate medium; it can be the internal communication of two elements or the interaction relationship between two elements. For those skilled in the art to which this application pertains, the specific meanings of the above terms in the embodiments of this application can be understood according to specific circumstances.

[0113] The vertical barrier wall mainly establishes a barrier with very low permeability underground. Through this barrier, the flow direction of contaminated groundwater is changed to prevent pollutants from spreading to sensitive areas such as drinking water wells, wetlands, or rivers. By using underground barriers to seal pollutants or change the direction of underground water flow, the purpose of controlling the horizontal migration of pollution levels is achieved, which is currently the most effective technology for restricting the migration of pollutants. Traditional vertical barrier wall leakage detection technologies, such as the dual-electrode method commonly used at home and abroad, have a detection depth of no more than 3m. However, the insertion depth of the vertical barrier wall can reach more than 30m, and existing detection methods cannot directly identify the leakage situation. Further, the accuracy of existing high-density electrical methods and ground-penetrating radar detection decreases significantly with the increase of burial depth, and cannot meet the requirements for accurate detection of leakage channels. In addition, existing vertical barrier wall leakage detection technologies have limitations such as low sensitivity and inaccurate leakage point positioning. In contrast, the tracer-based leakage detection method, by utilizing the characteristics of tracer diffusion at the leakage point and transport with water flow, combined with an analytical mathematical model to reverse the transport law and concentration field distribution of the tracer, can not only efficiently determine the leakage situation of the vertical barrier wall, but also quantitatively determine the size of the leakage fissures of the vertical barrier wall, significantly improving the detection efficiency and accuracy, and making up for the deficiencies of traditional methods. In the leakage detection of vertical barrier walls in contaminated sites, tracers can be injected around or into the vertical barrier wall, and by using their characteristics of diffusion at the leakage point or being carried by water flow, the diffusion path and concentration distribution of the tracers are detected, and the size of the leakage channel is inversely obtained.

[0114] The present invention mainly selects injection wells and monitoring wells according to the actual situation of the test site, injects tracers into the injection wells, monitors the tracers in the monitoring wells to obtain the production curve, obtains its leakage rate according to analytical inversion, and combines the cubic law to judge the size of the barrier wall fissures.

[0115] Please refer to Figure 1 and Figure 2 , the tracer-based landfill leakage channel detection method proposed by the present invention mainly includes the following steps:

[0116] First, organize background information and prepare for experiments. The specific steps are as follows:

[0117] Step S01, summarize and organize on-site data

[0118] Obtain hydrogeological data related to the landfill according to the analysis of the hydrogeological characteristics of the test site, including geological maps, cross-sections, and parameters of existing water wells;

[0119] Step S02, based on the hydrogeological data, preliminarily judge the information of the underground water flow field around the landfill, obtain the maximum groundwater depth data, permeability coefficient, and water flow line direction data, providing a reference for determining the depths of the injection wells and monitoring wells.

[0120] The hydrogeological conditions of this site are relatively complex, mainly including two types: phreatic water and slightly confined water. Among them, the phreatic water is replenished by atmospheric precipitation and surface runoff, with a seasonal fluctuation range of 0.5 - 1.0 m, the historical highest water level is 4.50 m, and the highest water level in the recent 3 - 5 years is 4.20 m; the slightly confined water is mainly stored in the silt layer, with strong water permeability, the water level elevation is about -0.50 m, and the confined water level elevation is about -24.0 m. The maximum buried depth of groundwater is 45.0 m. The permeability coefficient of the soil layer at this site ranges from 1×10 -6 -5×10 -6 m / s. According to the monitoring results, the groundwater flow direction is from north to south.

[0121] In some other specific embodiments, if the information on the groundwater flow field around the above test site, such as the maximum buried depth data of groundwater, the permeability coefficient, and the water streamline direction data, is already available data, it can also be directly adopted, that is, steps S01 and S02 are omitted.

[0122] Step S1: Arrange injection wells and monitoring wells, and collect, detect, and record the background values of the water sample tracers in the injection wells and monitoring wells respectively.

[0123] According to the specific geological and hydrogeological conditions of the test site, reasonably determine the positions and depths of the injection wells and monitoring wells. In specific embodiments, for the geosynthetic clay liner (GMB) composite cutoff wall, injection well 1 and monitoring wells 1 and 2 are selected; for the soil - bentonite vertical cutoff wall, injection well 2 and monitoring well 3 are selected. To ensure uniform injection of the tracer and coverage of potential leakage areas; the monitoring wells should be arranged downstream of the groundwater flow direction and distributed perpendicular to the main water streamline to effectively monitor the diffusion of the tracer in the water and the leakage path. The layout of the wells is designed with reference to the "Technical Specification for Groundwater Environment Monitoring" HJT - 2020. Conduct water level surveys, water quality surveys on all injection wells and monitoring wells, and sample and detect the tracer concentration to determine the background value of the tracer concentration.

[0124] Step S2: On - site injection tracer monitoring, with a certain time interval as the frequency, collect, detect, and record the concentration values of the tracer in several of the monitoring wells, and draw the tracer concentration - time output curve of the monitoring wells.

[0125] Specifically, please refer to Figure 3 the cross - sectional view between the injection well and the monitoring well as shown, and it can be seen that the injection well and the monitoring well adopted in this embodiment have a geosynthetic clay liner (GMB) composite cutoff wall or a soil - bentonite vertical cutoff wall between them.

[0126] When adding the tracer to the injection well in step S2, determine the tracer dosage according to the established tracer input amount model shown in formula (3) of the tracer input amount model.

[0127]

[0128] where M is the amount of tracer active substance added; λ is the safety factor, and the recommended value in general contaminated sites is 1×10 -4 -5×10 -3 ; MDL is the minimum detectable limit of the tracer equipment, with the unit of g / m 3 ; r is the average well spacing between the injection well and the monitoring well, with the unit of m; h is the average effective aquifer thickness of the test site, with the unit of m; is the porosity.

[0129] Then, inject the tracer. Determine the total amount of the injected tracer according to the M value calculated by the above total dilution model of the tracer. In this embodiment, fluorobenzoic acid tracer is used, and in other embodiments, other tracers commonly used in the art can also be used. Fluorobenzoic acid has almost no pollution to the environment and has a low detection limit. It can be detected at only 1 μg / L; configure the tracer into a solution with a concentration of 500 - 1000 mg / L, stir evenly, and inject it into the injection well at a constant speed under normal pressure.

[0130] After injecting the tracer, start sampling and monitoring the monitoring wells. The sampling frequency is: collect once every quarter, with a time interval of more than 2 months and no more than 5 months between two samplings, and collect 4 times a year; if no tracer is detected in the sample, it means that the leakage in the test area is not obvious, and continue to maintain the established collection frequency; if the tracer is detected, several additional collection and detection times can be increased, and the tracer concentration-time output curves at each point can be obtained according to the tracer concentrations at each point and at each time.

[0131] Step S3: According to the concentration-time curves of the tracer in each monitoring well, combined with the analytical model, invert the distribution of the tracer concentration field from the injection well to the monitoring well, calculate the geometric characteristics of the leakage channel using the cubic law of fractures, and finally determine the width of the fractures of the cutoff wall and whether leakage occurs; or calculate the geometric characteristics of the leakage channel using the empirical formula for the leakage flow rate of holes, and finally determine the size of the holes in the cutoff wall and whether leakage occurs.

[0132] In the test site, in order to avoid wasting leakage detection time in full-precision simulation, the seepage path of the tracer between the injection well and the monitoring well can be appropriately simplified in the analytical model. The characteristics of the analytical model proposed by the present invention are that it considers the transport of the tracer in a migration medium divided into m layers (as Figure 3 shown. In this cross-sectional view, a specific "layer" refers to the block obtained by longitudinally dividing the test site from the injection well to the monitoring well direction), and the layering of the medium is 0 < l0 < l1 < … < l m-1 < l m = L. Let c i (x, t) represent the tracer concentration in the i-th layer, where x ∈ (li-1 , l i ), representing the distance from the inlet at x = 0, t > 0 represents time, and the one-dimensional diffusion and migration equation for the i-th layer is:

[0133]

[0134] In the formula: R i > 0 is the retardation coefficient, D i > 0 is the effective hydrodynamic coefficient, v i is the seepage velocity, c i is the tracer concentration.

[0135] The control equation (4) needs to be used in conjunction with the initial conditions, interface conditions, and boundary conditions. The concentration is initially assumed to be constant in each layer, i.e.:

[0136] c i (x, 0) = f i (5)

[0137] Where: f i is the concentration-time function.

[0138] At the interface between adjacent layers, it is assumed that the concentration and the dispersion flux are continuous.

[0139] c i (l i , t) = c i+1 (l i , t) (6)

[0140]

[0141] In the formula: θ i is the volumetric water content.

[0142] At the inlet (x = 0) and the outlet (x = L), the generalized third boundary condition is considered:

[0143]

[0144] In the formula: a0, b0, a L , b L are constants; g0(t), g L (t) are arbitrarily specified time functions; in particular, b0 and b L are both non-negative; at least one of a0 or b0 is not zero, and at least one of a L or b L is not zero.

[0145] In this test site, we consider the injection boundary condition as the Dirichlet boundary condition, that is, the boundary condition in the form of concentration:

[0146] c1(0,t) = c0(t) (10)

[0147] Therefore, the relevant parameters in equations (8) and (9) can be determined as: a0 = 1, b0 = 0, g0(t) = c0(t), a L = 0, b L = 1, g L (t) = 0.

[0148] To solve the multi - layer transport model equations (4)–(9), we reformulate the model into m independent single - layer problems, introducing the time - varying unknown function g i (t), which is used to represent the following scalar factor of the (negative) dispersion flux at the layer interface.

[0149]

[0150] The following equivalent form of the multi - layer transport model (4)–(9) is obtained:

[0151] The first layer (i = 1)

[0152]

[0153] c1(x,0) = f1 (13)

[0154]

[0155] For the intermediate soil layers (i = 2,…,m - 1)

[0156]

[0157] c i (x,0) = f i (17)

[0158]

[0159] The last layer (i = m)

[0160]

[0161] c m (x,0) = f m (21)

[0162]

[0163] For each case of the soil layer, performing the Laplace transform, the concentration calculation equations for different soil layers can be obtained:

[0164] C1(x, s) = A1(x, s)G0(s) + B1(x, s)G1(s) + P1(x, s) (24)

[0165] C i (x, s) = A i (x, s)G i-i (s) + B i (x, s)G i (s) + P i (x, s), i = 2, …, m - 1 (25)

[0166] C m (x, s) = A m (x, s)G m-1 (s) + B m (x, s)G m (s) + P m (x, s) (26)

[0167] The functions P i , A i , B i (i = 1, …, m) are defined as follows:

[0168] For the first layer (i = 1):

[0169]

[0170] Where:

[0171] β1(s) = [a0 - b0λ 1,1 (s)]λ 1,2 (s)exp(-[λ 1,1 (s) - λ 1,2 (s)]l1) - [a0 - b0λ 1,2 (s)]λ 1,1 (s)(28)

[0172] For the middle layers (i = 2, …, m - 1):

[0173]

[0174] Where:

[0175] β i (s) = λ i,1 (s)λ i,2 (s){exp(-[λ i,1 (s) - λ i,2 (s)](l i - l i-1 )) - 1} (30)

[0176] For the last layer of soil (i = m):

[0177]

[0179] Wherein:

[0180] β m (s) = [a L +b L λ m,2 (s)]λ m,1 (s)exp(-[λ m,1 (s)-λ m,2 (s)](l m -l m-1 )) - [a L +b L λ m,1 (s)]λ m,2 (s) (32)

[0182] For all soil layers:

[0183]

[0184] With all variables in expressions (24)-(26) defined, to determine the Laplace transforms G1(s),...,G m-1 (t) of the unknown interface functions g1(t),...,g m-1 (t), it is necessary to impose the continuity condition of concentration on each interface in the Laplace domain, i.e.:

[0185] C i (l i ,s) = C i+1 (l i ,s), i = 1,...,m - 1. (34)

[0186] Substituting expressions (24)-(26) into equation (34), a linear system of x = [G1(s),...,G m-1 (s)] T is obtained and solved in the following matrix form:

[0187] Ax = b (35)

[0188] Wherein: is a diagonal matrix,

[0189] is a vector. Among them, represents the complex number field.

[0190] After solving the matrix for G1(s), …, G m-1 (s), substituting them into expressions (24)-(26), the Laplace transform of the concentration at any position and time in the Laplace domain can be obtained.

[0191] Figure 4 The accuracy of the analytical and monitoring well production curves was verified. The relevant tracer migration parameters between the injection well and the monitoring well obtained by analytical inversion are as follows.

[0192] Please refer to Figure 3 , the analytical model of the geomembrane (GMB) composite barrier wall contains five layers of media, from left to right are the aquifer, bentonite layer, GMB geomembrane layer, bentonite layer, and aquifer. Among them, for the aquifer from injection well 1 to monitoring well 1, the widths on both sides are 41.1 m; for the aquifer from injection well 1 to monitoring well 2, the width near the injection well is 41.1 m, and the width of the aquifer near the monitoring well is 108.3 m; the relevant parameters of the vertical barrier wall are: the thickness of the GMB geomembrane is 1 mm; the thickness of the bentonite on both sides is 0.3 m;

[0193] In the analytical model of monitoring well 1, the tracer migration parameters corresponding to the aquifer are diffusion coefficient D1 = 1.5×10 - 6 m / s 2 , velocity v1 = 5×10 -6 m / s, the tracer migration parameters corresponding to the bentonite are diffusion coefficient D2 = 1×10 -9 m / s 2 , velocity v2 = 1×10 -7 m / s, the tracer migration parameters corresponding to the GMB geomembrane are diffusion coefficient and velocity respectively: D3 = 3×10 -8 m / s 2 , velocity v3 = 3×10 -6 m / s.

[0194] In the analytical model of monitoring well 2, the tracer migration parameters corresponding to the aquifer are diffusion coefficient D1 = 6×10 -6 m / s 2 , velocity v1 = 2.4×10 -6 m / s, the tracer migration parameters corresponding to the bentonite are diffusion coefficient D2 = 1×10 -9 m / s 2 , velocity v2 = 1×10 -7 m / s, the tracer migration parameters corresponding to the GMB geomembrane are diffusion coefficient and velocity respectively: D3 = 3×10 -8 m / s 2 , velocity v3 = 3×10 -6 m / s.

[0195] Please refer to Figure 4 , from which it can be found that the seepage velocity of the GMB geomembrane obtained by analytical inversion matches well with the experimental data, proving that the seepage velocity v of the GMB geomembrane after seepage occurs can be substituted into the empirical formula for pore leakage flow rate to calculate its hole size.

[0196] According to the calculation formula for hole leakage flow rate:

[0197] v·S = 0.2769kHD 0.0462 b 0.0971lnD+0.8235 (2)

[0198] where D is the thickness of the waterproof blanket, in units of (m), b is the radius size of the hole, in units of (m), S is the cross-sectional area, in units of (m 2 ), and the calculation method is πb 2 , k is the permeability coefficient of the vertical barrier wall, in units of (m / s), and H is the water head difference on both sides of the vertical barrier wall, in units of (m).

[0199] According to the seepage velocity v = 3×10 -6 m / s of the soil-bentonite vertical barrier wall obtained by the above analytical inversion, the size of the hole b is calculated to be 2.8 mm.

[0200] Please refer to again Figure 3 , in another research area, there is a leakage situation in the soil-bentonite vertical barrier wall. The analytical model of the soil-bentonite vertical barrier wall constructed includes three layers of media. The thickness of the soil-bentonite vertical barrier wall is 1 m, and the distances between the soil-bentonite vertical barrier wall and the injection well and the monitoring well are both 30 m.

[0201] In the analytical model of the soil-bentonite vertical barrier wall, the tracer migration parameters corresponding to the aquifers on both sides are diffusion coefficient D1 = 1.8×10 -6 m / s 2 , velocity v1 = 3.24×10 -6 m / s, and the tracer migration parameters corresponding to the soil-bentonite vertical barrier wall are diffusion coefficient D2 = 3.27×10 -5 m / s 2 , velocity v2 = 3.27×10 -3 m / s.

[0202] Please refer to Figure 5 , from Figure 5 it can be seen that the seepage velocity of the soil-bentonite vertical barrier wall obtained by analytical inversion matches well with the experimental data, proving that the seepage velocity v of the soil-bentonite vertical barrier wall after leakage occurs can be substituted into the fracture law formula to calculate its fracture width size.

[0203] According to the fracture law, its formula is:

[0204]

[0205] Where: b is the size of the fracture width to be determined, with the unit of m; ρ is the density of water, with the unit of kg / m 3 , in this embodiment, it is taken as 1000 kg / m 3 , g is the acceleration of gravity m 2 / s, in this embodiment, the simplified value is 9.8 m 2 / s, μ is the hydrodynamic viscosity coefficient, with the unit of Pa·s, and in this embodiment, the value is 1×10 -3 Pa·s

[0206] According to the seepage velocity v = 3.6×10 -6 m / s obtained by the above analytical inversion, the calculated size of the fracture width is 1 mm.

[0207] In summary, the above technical solution provided by the present invention fully considers the problem of pollutant leakage caused by the formation of dominant leakage channels due to tiny fractures in the structure or damage to the geomembrane during the service period of the vertical barrier wall, and proposes a systematic analytical calculation method for leakage channels and a judgment process for the size of leakage channels. This method can effectively improve the accuracy of leakage detection and leakage channel identification of the vertical barrier wall, and is applicable to the leakage analysis of different types of vertical barrier walls under complex polluted site conditions. Through the technical solution provided by the present invention, the service characteristics of the vertical barrier wall can be better evaluated, providing reliable technical support for site pollutant prevention and site remediation.

[0208] Finally, it should be noted that although the above embodiments have been described in the text of the specification and drawings of the present application, the patent protection scope of the present application cannot be limited thereby. Any technical solutions obtained by equivalent structure or equivalent process substitution or modification using the content recorded in the text of the specification and drawings of the present application based on the essential concept of the present application, as well as the direct or indirect implementation of the technical solutions of the above embodiments in other related technical fields, etc., are all included in the patent protection scope of the present application.

Claims

1. A vertical barrier wall leakage detection and inversion method based on tracers and analytical models, characterized in that: The following steps are involved: Step S1: Arrange injection wells and monitoring wells, and collect, detect and record the background value of the tracer in the water samples of the injection wells and monitoring wells respectively; Step S2: adding the tracer to the injection well, collecting, detecting and recording the concentration values ​​of the tracer in a number of the monitoring wells at a certain time interval, and drawing a tracer concentration-time output curve of the monitoring wells; Step S3: According to the tracer concentration-time output curve of the monitoring well, combined with the analytical model, the tracer concentration field distribution from the injection well to the monitoring well is inverted, and the geometric characteristics of the vertical barrier wall leakage channel are calculated.

2. The vertical barrier wall leakage detection and inversion method according to claim 1 is characterized in that: The geometrical characteristics of the vertical barrier wall leakage channel in step S3 are the size parameters of the vertical barrier wall leakage channel, which are calculated using the crack cubic law or the empirical formula of the hole leakage flow.

3. The vertical barrier wall leakage detection and inversion method according to claim 2 is characterized in that: When the leakage channel type is a crack, the crack cubic law shown in formula (1) is used for calculation: Where b is the crack width; ρ is the density of water; g is the acceleration due to gravity; and μ is the hydrodynamic viscosity coefficient.

4. The vertical barrier wall leakage detection and inversion method according to claim 2 is characterized in that: When the leakage channel type is a hole, the hole leakage flow rate empirical formula shown in formula (2) is used for calculation: v·S=0.2769kHD 0.0462 b 0.0971ln D+0.8235 (2) Where D is the thickness of the vertical barrier wall, in m; b is the radius of the hole, in m; S is the cross-sectional area, in m 2 , calculated as πb 2 ; k is the permeability coefficient of the vertical barrier wall, in m / s; H is the water head difference on both sides of the vertical barrier wall, in m.

5. The vertical barrier wall leakage detection and inversion method according to claim 1 is characterized in that: Before the injection wells and monitoring wells are arranged, the method further includes: Step S01: first obtain the hydrogeological data of the test site, the hydrogeological data including geological maps, cross-sections, existing wells and groundwater levels; and Step S02: Based on the hydrogeological data, preliminarily determine the groundwater flow field information around the test site, and obtain the maximum groundwater depth data, permeability coefficient and water flow line direction data.

6. The vertical barrier wall leakage detection and inversion method according to claim 1 is characterized in that: When adding the tracer to the injection well in step S2, the tracer is added according to the tracer input amount model shown in formula (3): Where M is the amount of effective substance added to the tracer; λ is the security factor, and the recommended value in general contaminated sites is 1×10 -4 -5×10 -3 ; MDL is the minimum detection limit of the tracer equipment, in g / m 3 ; r is the average well distance between the injection well and the monitoring well, in m; h is the average effective aquifer thickness of the test site, in m; is the porosity.

7. The vertical barrier wall leakage detection and inversion method according to claim 1 is characterized in that: The certain time interval is to collect water samples once every quarter, and the interval between each two collections is more than 2 months and no more than 5 months.

8. The vertical barrier wall leakage detection and inversion method according to claim 7 is characterized in that: If tracers are detected in the collected water samples, the number of collection and testing times will be increased and the time interval between collection and testing will be shortened.

9. The vertical barrier wall leakage detection and inversion method according to claim 1, characterized in that: The step S3 comprises: Step S31, constructing a control equation for one-dimensional diffusion-convective transport; Step S32: Invert the tracer concentration field distribution and migration-related parameters from the injection well to the monitoring well according to the control equation.

10. The vertical barrier wall leakage detection and inversion method according to claim 9, characterized in that: Assume that the tracer is transported in a porous medium divided into m layers, and the porous medium is divided into 0 <l0<l1<…<l m-1 <l m = L layers, let c i (x,t) represents the tracer concentration of the i-th layer, where x∈(l i-1 ,l i ) represents the distance from the inlet x=0, t>0 represents the time, then the governing equation of the one-dimensional diffusion-convective transport of the i-th layer is as shown in formula (4): Among them, R i >0 is the blocking coefficient; D i >0 is the effective hydrodynamic coefficient; v i is the seepage velocity; c i is the tracer concentration.

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