A method for predicting the migration of DNA tracers and characterizing the flow field of a site

Abstract

The present invention discloses a method for predicting the migration of DNA tracers and characterizing the flow field of a site, belonging to the field of environmental geotechnics. This method obtains the expressions of the concentrations of DNA tracers in the fast zone and the slow zone through the use of Laplace transform, Fourier transform, and numerical inversion. On this basis, the necessary parameters of the model, such as the molecular diffusion coefficient of the tracer, the thickness of the aquifer, the dispersion degree, and the injection attenuation rate of the tracer, are determined according to the hydrogeological conditions revealed by the strata and the monitoring results of the tracer concentration in the injection well of the in-situ tracer experiment. The genetic algorithm is coupled with the proposed analytical solution, and the fitting degree between the tracer production curve of the monitoring well and the prediction result is used as the control quantity to determine the average linear velocity and porosity of the fast zone and the slow zone of the site soil, so as to achieve the fine characterization of the flow field in the heterogeneous soil of the site. This method combines an analytical model, a genetic algorithm, and an in-situ tracer experiment. The obtained prediction results are accurate and objective, and the calculation is convenient without relying on software, which is suitable for engineering applications.

Description

Technical Field

[0001] The present invention relates to the field of environmental geotechnics, and particularly to a method for predicting the migration of DNA tracers and characterizing the flow field of a site. Background Art

[0002] The tracer method is used to characterize the hydrogeological conditions of a site by injecting a tracer into groundwater and detecting its migration. Compared with traditional physical sampling methods, the tracer method can reduce the direct interference with groundwater bodies and has little environmental impact. In addition, due to the high sensitivity and strong stability of tracers, the movement of water flow can be accurately characterized in complex and heterogeneous geological environments. Therefore, the tracer method is widely used in hydrogeological surveys, engineering construction, and groundwater pollution site surveys. At present, a large number of natural or synthetic chemical substances have been used as tracers and widely applied to different sites. Traditional tracers include silica, stable isotopes, artificial bromides, chlorides, fluorescent agents, etc. However, natural groundwater bodies are very likely to contain traditional tracers, resulting in the emergence of environmental background values, which in turn affect the tracer output curve. In addition, although the environmental background values of some artificial tracers are very low, due to the powerful dilution function of groundwater bodies, the injected tracers are often difficult to identify because of their too low concentration. The cost of using and analyzing some tracers (such as fluorobenzoic acid) is very high. The new DNA tracer can effectively overcome the above defects. Compared with existing tracers, DNA tracers have the advantages of strong specificity, high sensitivity, good stability, controllable degradation characteristics, and environmental friendliness. Even in a complex environment, they can still maintain their integrity, facilitating long-term storage and use.

[0003] Existing indoor and field experiments have found that the output curve of DNA tracers is very likely to show a double-peak phenomenon, and existing models cannot describe the double-peak phenomenon. In addition, currently commonly used prediction models often need to rely on finite element or finite volume software such as COMSOL and MODFLOW, and the modeling process is complex and time-consuming, which is extremely inconvenient for engineering applications. Therefore, it is necessary to propose a DNA tracer migration prediction method with convenient application and accurate results to achieve fine characterization of the site flow field. Summary of the Invention

[0004] In view of the above problems, the present application provides a method for predicting the migration of DNA tracers and characterizing the flow field of a site.

[0005] To achieve the above object, the present invention provides a method for predicting the migration of DNA tracers and characterizing the flow field of a site, including the following steps:

[0006] Construct a DNA tracer migration model, which is configured to be constructed according to the migration behavior of DNA tracers in the underground soil and water environment;

[0007] Obtain the condition information of the DNA tracer migration model, which is configured to be generated through background value investigation and the working conditions of the experimental site. The condition information includes initial conditions and boundary conditions;

[0008] Input the dimensionless parameters into the tracer migration mathematical model, and with the help of Laplace transform and Fourier transform, obtain the analytical solution in the Laplace domain of the DNA tracer migration in the underground soil and water environment;

[0009] Obtain the fast-region concentration expression and slow-region concentration expression of the DNA tracer in heterogeneous soil by operating the analytical solution through a numerical inversion algorithm;

[0010] Obtain the type information of the DNA tracer, the formation information where the DNA tracer is injected, and the well information where the DNA tracer is injected, and generate the necessary parameter information of the DNA tracer migration model. The well information includes the tracer monitoring concentration of the injection well and the spatial position information of the monitoring well;

[0011] Output the tracer production curve by the genetic algorithm with the necessary parameter information, the fast-region concentration expression, and the slow-region concentration expression, and generate the site flow field characterization information according to the tracer production curve.

[0012] In some embodiments, the DNA tracer migration model is represented by formula (1), and formula (1) is as follows:

[0013]

[0014] In formula (1), C f is the concentration of the DNA tracer in the fast region, C s is the concentration of the DNA tracer in the slow region, R df is the retardation factor of the DNA tracer in the fast region, R ds is the retardation factor of the DNA tracer in the slow region, r is the radial distance between the DNA tracer and the edge of the injection well when the DNA tracer is vertically injected into the well, z is the axial distance between the DNA tracer and the top of the aquifer, t is the migration time of the DNA tracer, D fr is the hydrodynamic dispersion coefficient of the DNA tracer in the fast region along the radial direction, D fz is the hydrodynamic dispersion coefficient of the DNA tracer in the fast region along the axial direction, D sr is the hydrodynamic dispersion coefficient of the DNA tracer in the slow region along the radial direction, D sz is the hydrodynamic dispersion coefficient of the DNA tracer in the slow region along the axial direction, v f is the average linear velocity of the fast region, v s is the average linear velocity of the slow region, θ f is the porosity of the fast region, θ s is the porosity of the slow region, and α is the mass transfer coefficient applicable to both the fast region and the slow region.

[0015] In some embodiments, the dimensionless parameters are represented by Formulas (2) to (4), and Formula (2) is as follows:

[0016]

[0017] Formula (3) is as follows:

[0018]

[0019] Formula (4) is as follows:

[0020]

[0021] In Formulas (2) to (4), C fD is the first dimensionless parameter, C sD is the second dimensionless parameter, t D is the third dimensionless parameter, r D is the fourth dimensionless parameter, z D is the fifth dimensionless parameter, χ is the sixth dimensionless parameter, k is the seventh dimensionless parameter, R s is the eighth dimensionless parameter, R f is the ninth dimensionless parameter, θ f is the tenth dimensionless parameter, θ s is the eleventh dimensionless parameter, C0 is the peak concentration of the tracer in the injection well, β is the injection coefficient, α r is the longitudinal dispersivity of the aquifer, α z is the transverse dispersivity of the aquifer, ω f is the proportion of fast zone pores, which is the ratio of the fast zone porosity to the total soil porosity (ω f =λ f / (λ f +θ s ), and B is the aquifer thickness.

[0022] In some embodiments, the analytical solution is represented by Formulas (5) to (8), and Formula (5) is as follows:

[0023]

[0024] Formula (6) is as follows:

[0025]

[0026] Formula (7) is as follows:

[0027]

[0028] Formula (8) is as follows:

[0029]

[0030] In Formulas (5) to (8), is the dimensionless fast-region concentration of the DNA tracer in the Laplace domain, is the dimensionless slow-region concentration of the DNA tracer in the Laplace domain, and are two first eigenvectors of matrix A, and are two second eigenvectors of matrix A, Y q is the concentration calculation parameter in region q, where q = 1 represents the fast region and q = 2 represents the slow region, is Y q is the parameter after Fourier transform of Y, n is the Fourier operator, m is the Laplace operator, N1 is the first intermediate calculation parameter, N3 is the second intermediate calculation parameter, Ai A [ξ 1n (r D )] is the Airy function in the operation, Ai A [ξ 2n (r D )] is the Airy function in the operation, ξ 1n is the third intermediate calculation parameter, ξ 2n is the fourth intermediate calculation parameter, and M1 is the fifth intermediate calculation parameter.

[0031] In some embodiments, the fast-region concentration expression is represented by Formula (9), and Formula (9) is as follows:

[0032]

[0033] Among them, the first Laplace inversion parameter is represented by Formula (10), and the said Formula (10) is as follows:

[0034]

[0035] In Formulas (9) and (10), C q (t) is the concentration of the DNA tracer in region q, 0 < k < M, M is a fixed constant, γ k is the first Laplace inversion parameter, is the dimensionless concentration of the DNA tracer in region q in the Laplace domain, δ k is the second Laplace inversion parameter. When k = 0, When k ≠ 0, i is the imaginary unit.

[0036] In some embodiments, the background value investigation is the investigation of the initial concentration of the DNA tracer in the site soil before the injection experiment, and the initial condition is configured as the initial concentration of the DNA tracer;

[0037] The experimental site conditions include the DNA tracer injection method and the site aquifer structure. The boundary conditions are configured as the DNA tracer concentration function at the injection well, the top tracer concentration of the DNA tracer transport model, the bottom tracer concentration of the DNA tracer transport model, and the tracer concentration at infinity of the DNA tracer transport model. Alternatively, the boundary conditions are configured as the DNA tracer concentration function at the injection well, the top tracer concentration gradient of the DNA tracer transport model, the bottom tracer concentration gradient of the DNA tracer transport model, and the tracer concentration gradient at infinity of the DNA tracer transport model.

[0038] In some embodiments, the necessary parameter information includes the molecular diffusion coefficient of the DNA tracer, the aquifer thickness, the dispersivity in the radial direction of the aquifer, the dispersivity in the axial direction of the aquifer, the decay rate of the DNA tracer, the position parameter where the concentration peak of the DNA tracer appears, and the standard deviation of the DNA tracer concentration distribution along the axial direction;

[0039] Obtaining the type information of the DNA tracer, the formation information where the DNA tracer is placed, and the well information where the DNA tracer is placed, and generating the necessary parameter information of the DNA tracer transport model includes:

[0040] After injecting the DNA tracer, monitor the concentration of the DNA tracer in the injection well;

[0041] Use the boundary conditions to fit the DNA tracer concentration to obtain the decay rate of the DNA tracer, the position information where the concentration peak appears, and the standard deviation of the concentration distribution along the axial direction.

[0042] In some embodiments, output the tracer production curve through the genetic algorithm with the necessary parameter information, the fast zone concentration expression, and the slow zone concentration expression, and generate the site flow field characterization information based on the tracer production curve, including:

[0043] Monitor the concentration of the DNA tracer in the monitoring well for a preset time period and plot the tracer production curve;

[0044] Generate curve error information based on the tracer production curve;

[0045] Input the curve error information into the genetic algorithm coupling model to obtain the prediction results, which include the fast zone average linear velocity, fast zone porosity, slow zone average linear velocity, and slow zone porosity of the soil where the site is located;

[0046] Generate the site flow field characterization information based on the prediction results.

[0047] Different from the prior art, the above technical solution divides the fast zone (preferential pathway) and slow zone (matrix flow) of the soil, and uses Laplace transform, Fourier transform and numerical inversion to obtain a prediction method for the migration of DNA tracers in heterogeneous soil that does not rely on simulation software, has accurate calculation results and is convenient to use, overcoming the defect that traditional models cannot describe the double-peak phenomenon; in addition, based on the site conditions, formation exploration data and tracer experiment results, with the fitting degree between the prediction result and the monitoring value as the control variable, the genetic algorithm is used to run the analytical model to search for the average linear velocity and porosity of the fast zone and slow zone of the soil, realizing low-cost and fine characterization of the site flow field.

[0048] The above description of the invention content is 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 then 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 and drawings of this application. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The drawings are only used to illustrate the principles, implementation methods, applications, features and effects of the specific embodiments of the present invention and other related contents, and should not be considered as a limitation to this application.

[0050] In the drawings of the specification:

[0051] Figure 1 is the flow chart of the prediction of the migration of DNA tracers in the site and the characterization of the flow field according to the present invention;

[0052] Figure 2 is the comparison diagram of the analytical solution of the migration of DNA tracers and the experimental results in the embodiment;

[0053] Figure 3 is the fitting result diagram of the tracer concentration at the injection well boundary in a certain industrial legacy site case in the embodiment;

[0054] Figure 4 Comparison diagram of the search results and monitoring results of the genetic algorithm coupled with the analytical solution in a certain industrial legacy site case in the embodiment;

[0055] Figure 5 is the fitting result diagram of the tracer concentration at the injection well boundary in a certain pesticide-contaminated site case in the embodiment;

[0056] Figure 6 Comparison diagram of the search results and monitoring results of the genetic algorithm coupled with the analytical solution in a certain pesticide-contaminated site case in the embodiment. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0057] To describe in detail the possible application scenarios, technical principles, specific implementable solutions, achievable objectives and effects of this application, etc., 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.

[0058] Referring to "embodiment" in this article means that the specific features, structures or characteristics described in connection with the embodiment may be included in at least one embodiment of this application. The term "embodiment" that appears 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.

[0059] Unless otherwise defined, the meanings of the technical terms used in this article are the same as those generally understood by those skilled in the technical field to which this application belongs; the use of relevant terms in this article is only for describing specific embodiments and is not intended to limit this application.

[0060] In the description of this application, the phrase "and / or" is an expression used to describe the logical relationship between objects, indicating that there can be three relationships. For example, A and / or B means: the existence of A, the existence of B, and the simultaneous existence of A and B. In addition, the character " / " in this article generally represents an "or" logical relationship between the associated objects before and after.

[0061] 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 or secondary, or order relationship between these entities or operations.

[0062] Without more limitations, in this application, the open-ended expressions such as "including", "comprising", "having" or other similar expressions used in the statement 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.

[0063] Similar to the understanding in the "Examination Guidelines", in this application, expressions such as "greater than", "less than", and "exceeding" are understood as not including the base number; expressions such as "above", "below", and "within" are understood as including the base number. In addition, in the description of the embodiments of this application, the meaning of "multiple" 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 clearly and specifically defined.

[0064] Please refer to Figures 1 to 6 , this embodiment provides a method for predicting the migration of DNA tracers and characterizing the site flow field, including the following steps:

[0065] S1. Construct a DNA tracer migration model, which is configured to be constructed according to the migration behavior of DNA tracers in the underground soil and water environment;

[0066] S2. Obtain the condition information of the DNA tracer migration model, which is configured to be generated through background value investigation and experimental site conditions, and the condition information includes initial conditions and boundary conditions;

[0067] S3. Input the dimensionless parameters into the tracer migration mathematical model, and with the help of Laplace transform and Fourier transform, obtain the analytical solution in the Laplace domain of the DNA tracer migration in the underground soil and water environment;

[0068] S4. Calculate the analytical solution through a numerical inversion algorithm to obtain the fast-region concentration expression and slow-region concentration expression of the DNA tracer in heterogeneous soil;

[0069] S5. Obtain the type information of the DNA tracer, the formation information where the DNA tracer is injected, and the well information where the DNA tracer is injected, and generate the necessary parameter information of the DNA tracer migration model. The well information includes the tracer monitoring concentration of the injection well and the spatial position information of the monitoring well;

[0070] S6. Output the tracer production curve through the genetic algorithm with the necessary parameter information, the fast-region concentration expression, and the slow-region concentration expression, and generate the site flow field characterization information according to the tracer production curve.

[0071] In step S1, based on the migration behavior of DNA tracers in the underground soil and water environment, a DNA tracer migration model is constructed.

[0072] In step S2, based on the background value investigation results and experimental site conditions, determine the initial conditions and boundary conditions of the DNA tracer migration model.

[0073] In step S3, based on Laplace transform, Fourier transform, and the DNA tracer migration model, a dimensionless parameter is introduced to obtain the analytical solution of the DNA tracer migration in the Laplace domain in the underground water and soil environment.

[0074] In step S4, based on the analytical solution in step S3 and the numerical inversion method, the concentration expressions of the DNA tracer in the fast zone and the slow zone are obtained.

[0075] In step S5, based on the type of the DNA tracer injected and the formation information of the injected DNA tracer, combined with the monitored concentration of the tracer in the well where the DNA tracer is injected and the spatial position of the monitoring well, the necessary parameters of the DNA tracer migration model are determined.

[0076] In step S6, based on the tracer in the monitoring well, combined with the genetic algorithm, by inputting the necessary parameter information, the concentration expressions in the fast zone and the slow zone, and generating curves, a fine characterization of the site flow field is achieved.

[0077] In this embodiment, by dividing the fast zone (preferential pathway) and the slow zone (matrix flow) of the soil, a prediction method for the migration of DNA tracers in heterogeneous soil that does not rely on simulation software, has accurate calculation results, and is convenient to use is obtained by using Laplace transform, Fourier transform, and numerical inversion, overcoming the defect that traditional models cannot describe the double-peak phenomenon; in addition, based on the site conditions, formation exploration data, and tracer experiment results, with the fitting degree between the prediction result and the monitored value as the control variable, the genetic algorithm is used to run the analytical model to search for the average linear velocity and porosity of the fast zone and the slow zone of the soil, achieving a low-cost fine characterization of the site flow field.

[0078] In some embodiments, the DNA tracer migration model is represented by formula (1), and formula (1) is as follows:

[0079]

[0080] In formula (1), C f is the concentration of the DNA tracer in the fast zone, C s is the concentration of the DNA tracer in the slow zone, R df is the retardation factor of the DNA tracer in the fast zone, R ds is the retardation factor of the DNA tracer in the slow zone, r is the radial distance (perpendicular to the injection well) from the edge of the injection well, z is the axial distance (depth) from the top of the aquifer, t is the migration time of the DNA tracer, D fr is the hydrodynamic dispersion coefficient of the DNA tracer in the fast zone along the radial direction, D fz is the hydrodynamic dispersion coefficient of the DNA tracer in the fast zone along the axial direction, D sr is the hydrodynamic dispersion coefficient of the DNA tracer in the slow zone along the radial direction, Dsz is the hydrodynamic dispersion coefficient of the DNA tracer along the axial direction in the slow zone, v f is the average linear velocity in the fast zone, v s is the average linear velocity in the slow zone, θ f is the porosity of the fast zone, θ s is the porosity of the slow zone, and α is the mass transfer coefficient between the fast zone and the slow zone.

[0081] In some embodiments, the dimensionless parameters are expressed by formulas (2) to (4), and formula (2) is as follows:

[0082]

[0083] Formula (3) is as follows:

[0084]

[0085] Formula (4) is as follows:

[0086]

[0087] In formulas (2) to (4), C fD is the first dimensionless parameter, C sD is the second dimensionless parameter, t D is the third dimensionless parameter, r D is the fourth dimensionless parameter, z D is the fifth dimensionless parameter, X is the sixth dimensionless parameter, k is the seventh dimensionless parameter, R s is the eighth dimensionless parameter, R f is the ninth dimensionless parameter, λ f is the tenth dimensionless parameter, λ s is the eleventh dimensionless parameter, C0 is the peak concentration of the tracer in the injection well, β is the injection coefficient, α r is the dispersivity in the radial direction of the aquifer, α z is the dispersivity in the axial direction of the aquifer, ω f is the proportion of the fast zone pores, which is the ratio of the porosity of the fast zone to the total porosity of the soil (ω f = θ f / (θ f + θ s ))), and B is the thickness of the aquifer.

[0088] In some embodiments, the analytical solution is expressed by formulas (5) to (8), and formula (5) is as follows:

[0089]

[0090] Formula (6) is as follows:

[0091]

[0092] Equation (7) is as follows:

[0093]

[0094] Equation (8) is as follows:

[0095]

[0096] In Equations (5) to (8), is the dimensionless fast-region concentration of the DNA tracer in the Laplace domain, is the dimensionless slow-region concentration of the DNA tracer in the Laplace domain, and is of the first eigenvector of matrix A, and is the second eigenvector of matrix A, Y q is the concentration calculation parameter in the q region (q = 1 represents the fast region, q = 2 represents the slow region), is Y q is the parameter after Fourier transform of Y A is the Airy function, ξ 1n and ξ 2n are the third and fourth intermediate calculation parameters respectively, and M1 is the fifth intermediate calculation parameter.

[0097] In some embodiments, the fast-region concentration expression is represented by Equation (9), and Equation (9) is as follows:

[0098]

[0099] The slow-region concentration expression is represented by Equation (10), and Equation (10) is as follows:

[0100]

[0101] In Equations (9) and (10), C q (t) is the concentration of the DNA tracer in the q region (q = 1 represents the fast region, q = 2 represents the slow region), 0 < k < M, M is a fixed constant, γ k is the first Laplace inversion parameter, is the dimensionless concentration of the DNA tracer in the q region in the Laplace domain, δ k is the second Laplace inversion parameter. When k = 0, When k ≠ 0, i is the imaginary unit.

[0102] In some embodiments, the background value investigation is an investigation of the initial concentration of the DNA tracer in the in-situ soil before the injection experiment, and the initial condition is configured as the initial concentration of the DNA tracer;

[0103] The in-situ experiment conditions include the DNA tracer injection method and the in-situ aquifer structure. The boundary conditions are configured as the DNA tracer concentration function at the injection well, the top tracer concentration of the DNA tracer transport model, the bottom tracer concentration of the DNA tracer transport model, and the tracer concentration at infinity in the DNA tracer transport model. Alternatively, the boundary conditions are configured as the DNA tracer concentration function at the injection well, the top tracer concentration gradient of the DNA tracer transport model, the bottom tracer concentration gradient of the DNA tracer transport model, and the tracer concentration gradient at infinity in the DNA tracer transport model.

[0104] In this embodiment, step S2 is specifically as follows: the condition information of the DNA tracer transport model is configured to be generated through the background value investigation and the in-situ experiment conditions. Among them, based on the in-situ tracer background value investigation, the initial condition of the DNA tracer transport model is determined, that is, the concentration of the DNA tracer in the in-situ soil before the injection experiment. Among them, based on the in-situ experiment conditions, considering the influence of the DNA tracer injection method and the aquifer structure, the boundary conditions of the DNA tracer transport model are determined, that is, the DNA tracer concentration function at the injection well, the top DNA tracer concentration of the DNA tracer transport model, the bottom DNA tracer concentration of the DNA tracer transport model, and the tracer concentration at infinity in the DNA tracer transport model, or the DNA tracer concentration function at the injection well, the top DNA tracer concentration gradient of the DNA tracer transport model, the bottom DNA tracer concentration gradient of the DNA tracer transport model, and the DNA tracer concentration gradient at infinity in the DNA tracer transport model.

[0105] In some embodiments, the necessary parameter information includes the molecular diffusion coefficient of the DNA tracer, the aquifer thickness, the dispersivity in the radial direction of the aquifer, the dispersivity in the axial direction of the aquifer, the decay rate of the DNA tracer, the position parameter where the concentration peak of the DNA tracer appears, and the standard deviation of the axial distribution of the DNA tracer concentration;

[0106] Obtaining the type information of the DNA tracer, the formation information where the DNA tracer is placed, and the well information where the DNA tracer is placed, and generating the necessary parameter information of the DNA tracer transport model includes:

[0107] After injecting the DNA tracer, monitor the DNA tracer concentration in the injection well;

[0108] The concentration of the DNA tracer is fitted using boundary conditions to obtain the decay rate of the DNA tracer, the position information where the concentration peak appears, and the standard deviation of the axial distribution of the concentration.

[0109] In this embodiment, based on the type of the DNA tracer and the formation exploration results, the molecular diffusion coefficient of the DNA tracer, the thickness of the aquifer, the dispersion degree in the radial direction of the aquifer, the dispersion degree in the axial direction of the aquifer, the position parameter where the concentration peak of the DNA tracer appears, and the standard deviation of the axial distribution of the concentration of the DNA tracer are determined; that is, according to the type information of the DNA tracer, the formation information where the DNA tracer is injected, the well information where the DNA tracer is injected, and the spatial positions of the injection well and the monitoring well, the molecular diffusion coefficient of the DNA tracer, the thickness of the aquifer, the dispersion degree in the radial direction of the aquifer, the dispersion degree in the axial direction of the aquifer, the position parameter where the concentration peak of the DNA tracer appears, the standard deviation of the axial distribution of the concentration of the DNA tracer, and the migration distance of the tracer (the straight-line distance between the injection well and the monitoring well) are confirmed; after injecting the DNA tracer, the concentration of the tracer in the injection well is monitored, and boundary conditions are used for fitting to determine the decay rate of the DNA tracer, the position information where the concentration peak appears, and the standard deviation of the axial distribution of the concentration.

[0110] In some embodiments, the necessary parameter information, the fast-zone concentration expression, and the slow-zone concentration expression are used to output the tracer production curve through a genetic algorithm, and the site flow field characterization information is generated according to the tracer production curve, including:

[0111] The concentration of the DNA tracer in the monitoring well is monitored for a preset time period and the tracer production curve is plotted;

[0112] Curve error information is generated according to the tracer production curve;

[0113] The curve error information is input into the genetic algorithm coupling model to obtain the prediction results, which include the average linear velocity in the fast zone, the porosity in the fast zone, the average linear velocity in the slow zone, and the porosity in the slow zone of the soil where the site is located;

[0114] The site flow field characterization information is generated according to the prediction results.

[0115] In this embodiment, the concentration of the DNA tracer in the monitoring well is monitored for a preset time period, and a tracer production curve is plotted. Preferably, the concentration of the tracer in the monitoring well is monitored for 600 hours, and a tracer production curve is plotted. Curve error information is generated based on the tracer production curve, and the curve error information is input into the genetic algorithm coupling model. Using the error of the monitoring well tracer production curve as the control variable, the average linear velocity, porosity of the fast zone, average linear velocity, and porosity of the slow zone of the site soil are searched until a result with a prediction error within an acceptable range is obtained, and a prediction result is obtained. The prediction result includes the average linear velocity, porosity of the fast zone, average linear velocity, and porosity of the slow zone of the soil where the site is located. Site flow field characterization information is generated based on the prediction result, and fine characterization of the site flow field is realized.

[0116] The above technical solution divides the fast zone (preferred channel) and slow zone (matrix flow) of the soil, and uses Laplace transform, Fourier transform, and numerical inversion to obtain a prediction method for the migration of DNA tracers in heterogeneous soils that does not rely on simulation software, has accurate calculation results, and is easy to use, overcoming the defect that traditional models cannot describe the double-peak phenomenon. In addition, based on the site conditions, formation exploration data, and tracer experiment results, with the fitting degree between the prediction result and the monitoring value as the control variable, the genetic algorithm is used to run the analytical model to search for the average linear velocity and porosity of the fast and slow zones of the soil, realizing low-cost fine characterization of the site flow field.

[0117] For easy understanding, this embodiment also provides the following two examples to specifically illustrate the foregoing technical solution:

[0118] Taking the DNA tracer experiments and flow field characterization of an industrial legacy site and a pesticide-contaminated site as examples, the present invention will be further elaborated and described in combination with the drawings and tables. The technical features of each embodiment of the present invention can be combined accordingly without conflict. The specific implementation process of the present invention is as Figure 1 .

[0119] The first example: an industrial legacy site

[0120] S1: Construct a DNA tracer migration model, which is configured to be constructed according to the migration behavior of the DNA tracer in the underground water and soil environment.

[0121] The migration mathematical models of the DNA tracer in the fast zone (preferred channel) and slow zone (matrix flow) of heterogeneous soil are as follows:

[0122]

[0123] Where: C f and C sis the concentration of the DNA tracer in the fast and slow regions of heterogeneous soil, R df and R ds are the retardation factors of the tracer in the fast and slow regions, r is the distance; z is the axial distance; t is the migration time of the tracer; D FR and D fz are the hydrodynamic dispersion coefficients of the tracer in the radial and axial directions in the fast region; D sr and D sz are the hydrodynamic dispersion coefficients of the tracer in the radial and axial directions in the slow region; v f and v s are the average linear flow velocities of the fast and slow regions, θ f and θ s are the porosities of the fast and slow regions. The total porosity n of the soil can be regarded as the sum of the porosities of the fast and slow regions, i.e., n = θ f + θ s .

[0124] S2: Obtain the condition information of the DNA tracer migration model, and the condition information is configured to be generated through background value investigation and the working conditions of the experimental site. The condition information includes initial conditions and boundary conditions.

[0125] Generally, the natural environment does not contain DNA tracers. Therefore, the initial condition of the mathematical model can be defined as:

[0126] C I (r,z,0) = 0 (i = f,s) (13)

[0127] The concentration of the tracer at the injection point will be diluted and attenuated due to the groundwater flow. Then, the boundary condition at the injection well can be expressed as:

[0128]

[0129] In the formula: C0 is the initial concentration of the injection well after injecting the tracer, λ0 is the attenuation rate of the tracer, μ is the position where the peak concentration of the tracer appears in the injection well, B is the thickness of the aquifer, and σ is the standard deviation of the axial distribution of the tracer concentration in the injection well.

[0130] The top of the aquifer is an impermeable boundary, and the bottom is an aquitard. Therefore, the boundary fluxes of the DNA tracer at the top and bottom are both 0:

[0131]

[0132] The migration distance of the tracer is limited. Therefore, it is assumed that at infinity, the concentration of the DNA tracer is 0:

[0133] C i (r,z,t)| r→∞= 0 (i = f, s) (17)

[0134] S3. Input the dimensionless parameters into the mathematical model of tracer migration, and obtain the analytical solution in the Laplace domain of DNA tracer migration in the underground water and soil environment by means of Laplace transform and Fourier transform.

[0135] Introduce the following parameters to make the model dimensionless:

[0136]

[0137] Where: C Fd , C Sd , t d , r d , z d , χ, k, R s , R f , λ f , and λ s are all dimensionless parameters; Q is the injection rate; β is the injection coefficient, β = Q / (2πBn); α r and α z are the dispersivities in the radial and axial directions of the aquifer.

[0138] Then the governing equations (11) and (12) can be rewritten as:

[0139]

[0140] The initial conditions and boundary conditions can be changed to:

[0141] C fD (0, z D , t D ) = C sD (0, z D , t D ) = C0(z D , t D ) (20)

[0142] C fD (r D , z D , 0) = C sD (r D , z D , 0) = 0 (21)

[0143]

[0144] Introduce the Laplace transform, then equations (18) and (19) can be changed to:

[0145]

[0146] Where: m is the Laplace operator.

[0147] The boundary conditions can be changed to:

[0148]

[0149] Transpose and combine like terms for the governing equations (25) and (26) in the Laplace domain:

[0150]

[0151] Convert the above equations into matrix format:

[0152] L{C} = AC (33)

[0153]

[0154]

[0155] The eigenvalues of matrix A are:

[0156]

[0157] Where, M1 is an operation parameter and can be expressed as:

[0158]

[0159] Therefore, the eigenvectors of matrix A are:

[0160]

[0161] Since the eigenvectors are not equal, matrix A can be diagonalized using the following matrix:

[0162]

[0163] Assume there exists a matrix Y such that C = PY. According to equation (32), we can get:

[0164] L{PY} = APY (42)

[0165] Since P is linear, therefore:

[0166] PL{Y} = APY (43)

[0167] L{Y} = P -1 APY (44)

[0168] Substitute equation (44) into equations (33) to (35):

[0169]

[0170] Therefore, only two identical equations need to be solved. For Y1, the form of Y1 is as follows:

[0171]

[0172] Introduce the finite Fourier cosine transform:

[0173]

[0174] Equation (46) can be transformed into:

[0175]

[0176] ω n = nπ (49)

[0177] For this partial differential equation, there is a general solution:

[0178]

[0179] where Ai A is the Airy function, and Ai B is the related function of Ai A .

[0180] C is a linear expression about Y. Therefore, according to the boundary condition equation (16), it can be known that when r D tends to infinity, Y is also 0. Therefore, N2 = 0.

[0181] Introduce the injection well boundary condition into the Fourier domain:

[0182]

[0183] Assume that the pollution source is normally distributed and decays with time, then it can be expressed as:

[0184]

[0185] Since Y = P -1 C, where P -1 can be calculated according to the following formula:

[0186]

[0187] Then

[0188]

[0189] So it can be obtained:

[0190]

[0191] Further perform the finite Fourier transform

[0192]

[0193] Therefore, it can be obtained that:

[0194]

[0195] Therefore, N1 can be calculated as:

[0196]

[0197] Similarly, N3 is:

[0198]

[0199] According to equations (56) and (57), the analytical solutions of the DNA tracer migration in the subsurface soil and water environment in the Laplace domain are as follows:

[0200]

[0201] Where: and are the DNA tracer concentrations in the fast and slow regions in the Laplace domain, and the remaining parameters are all calculation parameters, which can be expressed as:

[0202]

[0203] S4. Obtain the fast-region concentration expression and slow-region concentration expression of the DNA tracer in heterogeneous soil by operating the analytical solution through a numerical inversion algorithm.

[0204] Adopt a numerical inversion method to solve the concentration expressions of the DNA tracer in the fast and slow regions based on the Laplace-domain analytical solution obtained in step 3:

[0205]

[0206] Where: i is the imaginary number, and M is a fixed constant (usually taken as 64).

[0207] Verify the accuracy of the proposed concentration expressions based on the soil column experiment carried out by Liu et al. in 2023; this experiment used the T12-DNA tracer containing 88 nucleotides developed by their team; since the soil column experiment is approximately a one-dimensional experiment, the molecular diffusion coefficients in the axial and radial directions are the same, equal to 2.2×10 -7 m 2 / s; the tracer was injected into the top of the soil column through the device at the beginning of the experiment, and the injection time was 2 s; the standard deviation of the tracer concentration distribution along the axial direction at the injection position can be regarded as infinite (take 10 when calculating); a peristaltic pump was used in the experiment to simulate the groundwater flow in the soil, and the pumping rate was 1.25×10 -4m / s; The total length of the soil column is 10 cm, the total porosity of the internal soil is 0.44, and the porosities of the fast and slow soil regions are 0.25 and 0.19 respectively; the average linear velocities of the fast and slow regions are 1.5×10 -4 m / s and 9.2×10 -5 m / s respectively, and the mass transfer coefficient is assumed to be 10 -5 / s; The comparison between the predicted results of the proposed expression and the soil column experiment results is shown in Figure 2 ; As can be seen from the figure, the proposed expression can accurately predict the double-peak phenomenon of the DNA tracer production curve, and the fitting degree of the prediction results can reach 0.94; therefore, it can be used for engineering design.

[0208] S5. Obtain the type information of the DNA tracer, the formation information where the DNA tracer is injected, and the well information where the DNA tracer is injected, and generate the necessary parameter information for the DNA tracer migration model. The well information includes the monitored concentration of the tracer in the injection well and the spatial position information of the monitoring well.

[0209] Select the polylactic acid-superparamagnetic iron oxide nanoparticle-DNA tracer provided by IDT DNA Company of the United States. The molecular diffusion coefficient of this tracer is 4.4×10 -1 m 2 / s; The geological exploration results show that the main soil type in the research area is silty clay, the thickness of the aquifer is 10 m, the porosity is 0.4, and the dispersivities in the radial and axial directions are 2 m and 0.018 m respectively; the injection well is set at the northernmost end of the research area, the well radius is 0.5 m, and the injection flow rate is 100 m 3 / d; The monitoring well is installed 20 m downstream of the injection well in a straight line; Monitor the concentration of the DNA tracer in the injection well within 300 h after injection; It should be noted that the tracer concentration difference at different positions in the well is not significant. Therefore, the position where the tracer concentration peak appears and the standard deviation of the tracer concentration distribution along the axial direction are 5 m and 10 respectively; Fit the data in the injection well based on the boundary condition (Equation 4) to obtain the decay rate λ0; From Figure 3 it can be seen that the decay rate λ0 is 0.0176 h -1 ; In addition, the adopted boundary condition can effectively describe the change of the tracer concentration, and the fitting degree can reach 0.95.

[0210] S6. Output the tracer production curve through the genetic algorithm with the necessary parameter information, the fast-region concentration expression, and the slow-region concentration expression, and generate the site flow field characterization information based on the tracer production curve.

[0211] Observe the DNA tracer concentration in the monitoring wells within 600 h after injection, and plot the tracer production curve; use the genetic algorithm to couple with the proposed analytical solution, and search for the average linear velocity and porosity of the fast and slow zones of the site soil with the fitting degree between the monitoring well tracer production curve and the prediction result as the control variable; the fitting degree can be calculated according to the following formula:

[0212]

[0213] where: n is the number of tracer concentration samples in the monitoring well, y i is the tracer concentration in the i-th sample, is the predicted tracer concentration, is the mean value of the prediction results.

[0214] The parameters of the genetic algorithm are set as follows: the number of individuals in the population is 500, the number of generations of evolution is 500, the crossover probability is 0.15, and the mutation probability is 0.2; the search results are as Figure 4 shown. It can be seen that as the number of generations of evolution increases, the error between the prediction result and the actual production curve becomes smaller and smaller. When the number of generations of evolution (g n ) is 100, 200, and 500 generations, the fitting degrees of the prediction results are 0.63, 0.86, and 0.99 respectively; the search results reveal that the average linear velocities of the fast and slow zones of the site are 1.27×10 -4 m / s and 1.98×10 -5 m / s respectively; in addition, the porosity ratios of the fast and slow zones in the site soil are 0.098 and 0.302 respectively; according to the search results, the site flow field can be accurately characterized.

[0215] The second example: a pesticide-polluted site

[0216] When the present invention is applied to a landfill, steps 1 to 4 are the same as those in Case 1, so they will not be elaborated here.

[0217] S5. Obtain the type information of the DNA tracer, the formation information of the injected DNA tracer, and the well information of the injected DNA tracer, and generate the necessary parameter information of the DNA tracer migration model. The well information includes the tracer monitoring concentration of the injection well and the spatial position information of the monitoring well.

[0218] Select the polylactic acid-superparamagnetic iron oxide nanoparticle-DNA tracer provided by IDT DNA Company of the United States. The molecular diffusion coefficient of this tracer is 4.4×10 -12 m 2 / s; The geological exploration results show that the soil type in the study area is mainly clay, the thickness of the aquifer is 15 m, the porosity is 0.38, and the dispersivities in the radial and axial directions are 1.28 m and 0.03 m, respectively; The injection well is set in the western part of the study area, with a well radius of 0.5 m and an injection flow rate of 100 m 3 / d; The monitoring well is installed 15 m away from the injection well downstream in a straight line; Monitor the concentration of the DNA tracer in the injection well within 300 h after injection; The position where the peak value of the tracer concentration appears and the standard deviation of the axial distribution of the tracer concentration are 7.5 m and 10, respectively; Fit the data in the injection well based on the boundary conditions (Equation 4) to obtain the attenuation rate λ0; From Figure 5 It can be seen that the attenuation rate λ0 is 0.0132 h -1 ; In addition, the boundary conditions adopted can effectively describe the change of the tracer concentration, and the fitting degree can reach 0.93.

[0219] S6. Output the tracer production curve through the genetic algorithm with the necessary parameter information, the fast-region concentration expression, and the slow-region concentration expression, and generate the site flow field characterization information based on the tracer production curve.

[0220] Observe the concentration of the DNA tracer in the monitoring well within 600 h after injection and plot the tracer production curve; Use the genetic algorithm to couple the proposed analytical solution, and search for the average linear velocities and porosities of the fast and slow regions of the site soil with the fitting degree between the monitoring well tracer production curve and the prediction result as the control variable; The parameter settings of the genetic algorithm are the same as those in Case 1; The search results are as Figure 6 shown. When the number of generations of evolution (g n ) is 100, 200, and 500 generations, the fitting degrees of the prediction results are 0.51, 0.69, and 0.99, respectively; The search results reveal that the average linear velocities of the fast and slow regions of the site are 8.18×10 -5 m / s and 1.22×10 -5 m / s, respectively. In addition, the void ratios of the fast and slow regions in the site soil are 0.11 and 0.27, respectively.

[0221] The above-described embodiments are only two preferred solutions of the present invention, but they are not intended to limit the present invention; Those of ordinary skill in the relevant technical field can still make various changes and modifications without departing from the spirit and scope of the present invention; Therefore, all technical solutions obtained by adopting equivalent substitution or equivalent transformation methods fall within the protection scope of the present invention.

[0222] Finally, it should be noted that although the above embodiments have been described in the text of the specification and the drawings of the present application, the patent protection scope of the present application cannot be limited thereby. Any technical solutions resulting from equivalent structural or equivalent process substitutions or modifications made based on the essential concept of the present application and using the content recorded in the text of the specification and the drawings 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 method for predicting DNA tracer migration and describing site flow field, characterized in that: include: Constructing a DNA tracer migration model, wherein the DNA tracer migration model is configured to be constructed according to the migration behavior of the DNA tracer in the underground water and soil environment; Acquiring condition information of the DNA tracer migration model, wherein the condition information is configured to be generated through background value investigation and experimental field conditions, and the condition information includes initial conditions and boundary conditions; The dimensionless parameters were input into the mathematical model of tracer migration, and the Laplace domain analytical solution of DNA tracer migration in groundwater and soil environment was obtained by means of Laplace transform and Fourier transform. The analytical solution is calculated by a numerical inversion algorithm to obtain a fast zone concentration expression and a slow zone concentration expression of the DNA tracer in the heterogeneous soil; Acquire the type information of the DNA tracer, the formation information where the DNA tracer is placed, and the well information where the DNA tracer is placed, and generate the necessary parameter information of the DNA tracer migration model, wherein the well information includes the tracer monitoring concentration of the injection well and the spatial position information of the monitoring well; Outputting the necessary parameter information, the fast zone concentration expression, and the slow zone concentration expression into a tracer production curve through a genetic algorithm, and generating site flow field characterization information according to the tracer production curve; The DNA tracer migration model is expressed by formula (1), which is as follows: In formula (1), C f is the concentration of DNA tracer in the fast zone, C s is the concentration of DNA tracer in the slow zone, R df is the blocking factor of DNA tracer in the fast zone, R ds is the retardation factor of the DNA tracer in the slow zone, r is the radial distance between the DNA tracer and the edge of the injection well when the DNA tracer is vertically injected into the well, z is the axial distance between the DNA tracer and the top of the aquifer, t is the migration time of the DNA tracer, and D fr is the radial hydrodynamic diffusion coefficient of the DNA tracer in the fast zone, D fz is the hydrodynamic diffusion coefficient of the DNA tracer in the fast zone along the axial direction, D sr is the radial hydrodynamic diffusion coefficient of the DNA tracer in the slow zone, D sz is the hydrodynamic diffusion coefficient of the DNA tracer in the slow zone along the axial direction, v f is the average linear velocity in the fast zone, v s is the average linear velocity in the slow zone, θ f is the porosity of the fast zone, θ s is the porosity of the slow zone, and α is the mass transfer coefficient applicable to both the fast zone and the slow zone.

2. The method for predicting DNA tracer migration and describing site flow field according to claim 1, characterized in that: The dimensionless parameters are expressed by formulas (2) to (4), and formula (2) is as follows: Formula (3) is as follows: Formula (4) is as follows: In formula (2) to formula (4), C fD is the first dimensionless parameter, C sD is the second dimensionless parameter, t D is the third dimensionless parameter, r D is the fourth dimensionless parameter, z D is the fifth dimensionless parameter, χ is the sixth dimensionless parameter, k is the seventh dimensionless parameter, R s is the eighth dimensionless parameter, R f is the ninth dimensionless parameter, λ f is the tenth dimensionless parameter, λ s is the eleventh dimensionless parameter, C0 is the peak concentration of the tracer in the injection well, β is the injection coefficient, α r is the radial dispersion of the aquifer, α z is the axial dispersion of the aquifer, ω f is the porosity ratio of the fast zone, is the ratio of the porosity of the fast zone to the total porosity of the soil (ω f =θ f / (θ f +θ s )), B is the thickness of the aquifer.

3. The method for predicting DNA tracer migration and describing site flow field according to claim 2, characterized in that: The analytical solution is expressed by formula (5) to formula (8), and the formula (5) is as follows: The formula (6) is as follows: The formula (7) is as follows: The formula (8) is as follows: In formula (5) to formula (8), is the dimensionless fast zone concentration of the DNA tracer in the Laplace domain, is the dimensionless slow zone concentration of the DNA tracer in the Laplace domain, and are the two first eigenvectors of matrix A, and are the two second eigenvectors of matrix A, Y q It is the concentration calculation parameter in the q zone, q=1 represents the fast zone, q=2 represents the slow zone, Yes q The parameter after Fourier transformation, n is the Fourier operator, m is the Laplace operator, N1 is the first intermediate calculation parameter, N3 is the second intermediate calculation parameter, Ai A [ξ 1n (r D )]yes Airy function in operation, Ai A [ξ 2n (r D )]yes The Airy function in operation, ξ 1n is the third intermediate calculation parameter, ξ 2n is the fourth intermediate calculation parameter, and M1 is the fifth intermediate calculation parameter.

4. The method for predicting DNA tracer migration and describing site flow field according to claim 3, characterized in that: The fast zone and slow zone concentration expressions are expressed by formula (9), which is as follows: The Laplace first inversion parameter is expressed by formula (10), which is as follows: In Formula (9) and Formula (10), C q (t) is the concentration of the DNA tracer in region q, where 0 < k < M and M is a fixed constant, and γ k is the first Laplace inversion parameter, is the dimensionless concentration of the DNA tracer in region q in the Laplace domain, and δ k is the second Laplace inversion parameter. When k = 0, When k ≠ 0, where i is the imaginary unit.

5. The method for predicting DNA tracer migration and describing site flow field according to claim 1, characterized in that: The background value investigation is an investigation of the initial concentration of the DNA tracer in the soil of the site before injection into the experiment, and the initial condition is configured as the initial concentration of the DNA tracer; The experimental field conditions include the DNA tracer injection method and the site aquifer structure, and the boundary conditions are configured as the DNA tracer concentration function at the injection well, the top tracer concentration of the DNA tracer migration model, the bottom tracer concentration of the DNA tracer migration model, and the tracer concentration at infinity of the DNA tracer migration model, or the boundary conditions are configured as the DNA tracer concentration function at the injection well, the top tracer concentration gradient of the DNA tracer migration model, the bottom tracer concentration gradient of the DNA tracer migration model, and the tracer concentration gradient at infinity of the DNA tracer migration model.

6. The method for predicting DNA tracer migration and describing site flow field according to claim 1, characterized in that: The necessary parameter information includes the molecular diffusion coefficient of the DNA tracer, the thickness of the aquifer, the radial dispersion of the aquifer, the axial dispersion of the aquifer, the attenuation rate of the DNA tracer, the position parameter of the peak concentration of the DNA tracer, and the standard deviation of the concentration distribution of the DNA tracer along the axial direction; The acquisition of the type information of the DNA tracer, the formation information where the DNA tracer is placed, the well information where the DNA tracer is placed, and the necessary parameter information for generating the DNA tracer migration model include: After the DNA tracer is injected, the concentration of the DNA tracer in the injection well is monitored; The concentration of the DNA tracer is fitted using boundary conditions to obtain the decay rate of the DNA tracer, the position information of the peak concentration, and the standard deviation of the concentration distribution along the axial direction.

7. The method for predicting DNA tracer migration and describing site flow field according to claim 1, characterized in that: The necessary parameter information, the fast zone concentration expression, and the slow zone concentration expression are outputted into a tracer production curve through a genetic algorithm, and the site flow field characterization information is generated according to the tracer production curve, including: Monitoring the concentration of the DNA tracer in the monitoring well for a preset time period and drawing a tracer output curve; generating curve error information according to the tracer production curve; Inputting the curve error information into the genetic algorithm coupling model to obtain a prediction result, wherein the prediction result includes the average linear velocity in the fast zone, the porosity in the fast zone, the average linear velocity in the slow zone, and the porosity in the slow zone of the soil at the site; The site flow field characterization information is generated according to the prediction result.

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