DNA tracer migration prediction and site flow field description method

Abstract

The invention discloses a DNA tracer migration prediction and site flow field description method, and belongs to the field of environmental rock and soil. According to the method, Laplace transform, Fourier transform and numerical inversion are used for obtaining the expression of the concentration of the DNA tracer in a fast region and a slow region. On the basis, necessary model parameters such as a tracer molecular diffusion coefficient, aquifer thickness, dispersity and tracer injection attenuation rate are determined according to hydrogeological conditions disclosed by a stratum and a tracer concentration monitoring result of an injection well in a field tracer experiment. And an analytical solution provided by genetic algorithm coupling is adopted, and the fitting degree of a tracer output curve of a monitoring well and a prediction result is taken as a control quantity, so that the average linear flow velocity and the porosity of the fast area and the slow area of the field soil are determined, and the fine description of the flow field in the field heterogeneous soil is realized. The method combines an analytical model, a genetic algorithm and a field tracer experiment, the obtained prediction result is accurate and objective, calculation is convenient and fast without depending on software, and the method is suitable for engineering application.

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 to characterize the hydrogeological conditions of a site by injecting a tracer into groundwater and detecting its migration. Compared with the traditional physical sampling method, 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 the tracer, it can accurately characterize the movement of water flow 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 the existing tracers, the DNA tracer has the advantages of strong specificity, high sensitivity, good stability, controllable degradation characteristics, and environmental friendliness. Even in a complex environment, it can still maintain its integrity, which is convenient for long-term storage and use.

[0003] Existing indoor experiments and field experiments have found that the output curve of DNA tracers is very likely to show a double-peak phenomenon, and the existing models cannot describe the double-peak phenomenon. In addition, the currently commonly used prediction models often need to rely on finite element or finite volume software such as COMSOL and MODFLOW. The modeling process is complex and the time cost is high, 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 the 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] Acquire condition information of the DNA tracer migration model, 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;

[0008] 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.

[0009] The analytical solution is calculated by numerical inversion algorithm to obtain the fast zone concentration expression and slow zone concentration expression of DNA tracer in heterogeneous soil;

[0010] Obtaining information on the type of DNA tracer, the formation information where the DNA tracer is placed, and the well information where the DNA tracer is placed, and generating necessary parameter information for the DNA tracer migration model. The well information includes the tracer monitoring concentration of the injection well and the spatial location information of the monitoring well;

[0011] The necessary parameter information, fast zone concentration expression and slow zone concentration expression are output into a tracer production curve through a genetic algorithm, and the site flow field characterization information is generated according to the tracer production curve.

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

[0013] ;

[0014] In formula (1), is the concentration of DNA tracer in the fast zone, is the concentration of DNA tracer in the slow zone, is the blocking factor of DNA tracer in the fast zone, It is the blocking factor of DNA tracer in the slow zone. is the radial distance from the edge of the injection well when the DNA tracer is vertically injected into the well, is the axial distance between the DNA tracer and the top of the aquifer, is the migration time of the DNA tracer, is the radial hydrodynamic diffusion coefficient of the DNA tracer in the fast zone, is the hydrodynamic diffusion coefficient of the DNA tracer in the fast zone along the axial direction, is the radial hydrodynamic diffusion coefficient of the DNA tracer in the slow zone, is the hydrodynamic diffusion coefficient of the DNA tracer in the slow zone along the axial direction, is the average linear velocity in the fast zone, is the average linear velocity in the slow zone, is the porosity of the fast zone, is the porosity of the slow zone, is the mass transfer coefficient applicable to the fast zone and the slow zone.

[0015] In some embodiments, the dimensionless parameter is expressed by formula (2) to formula (4), and formula (2) is as follows:

[0016] ;

[0017] Formula (3) is as follows:

[0018] ;

[0019] Formula (4) is as follows:

[0020] ;

[0021] In formula (2) to formula (4), is the first dimensionless parameter, is the second dimensionless parameter, is the third dimensionless parameter, is the fourth dimensionless parameter, is the fifth dimensionless parameter, is the sixth dimensionless parameter, is the seventh dimensionless parameter, is the eighth dimensionless parameter, is the ninth dimensionless parameter, is the tenth dimensionless parameter, is the eleventh dimensionless parameter, is the peak concentration of the tracer in the injection well, is the injection coefficient, is the radial dispersion of the aquifer, is the axial dispersion of the aquifer, 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 ( ), is the thickness of the aquifer.

[0022] In some embodiments, the analytical solution is expressed by formula (5) to formula (8), where 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 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 For the matrix The two first eigenvectors of and For the matrix The two second eigenvectors of is The concentration calculation parameters of the zone are: Indicates the fast zone, Indicates the slow zone, yes The parameters after Fourier transformation are is the Fourier operator, is the Laplace operator, is the first intermediate calculation parameter, is the second intermediate calculation parameter, yes The Airy function in operation, yes The Airy function in operation, is the third intermediate calculation parameter, is the fourth intermediate calculation parameter, is the fifth intermediate calculation parameter.

[0031] In some embodiments, the fast zone concentration expression is expressed by formula (9), which is as follows:

[0032] ;

[0033] The Laplace first inversion parameter is expressed by formula (10), which is as follows:

[0034] ;

[0035] In formula (9) and formula (10), For DNA tracers The concentration of the area, , is a fixed constant, is the Laplace first inversion parameter, is the DNA tracer in the Laplace domain The dimensionless concentration of the region, is the Laplace second inversion parameter, hour, , , hour, , Is an imaginary unit.

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

[0037] 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.

[0038] In some embodiments, 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;

[0039] The necessary parameter information for obtaining the type information of DNA tracers, the formation information where the DNA tracers are placed, the well information where the DNA tracers are placed, and generating the DNA tracer migration model includes:

[0040] After the DNA tracer is injected, the concentration of the DNA tracer in the injection well is monitored;

[0041] The DNA tracer concentration was fitted using boundary conditions to obtain the decay rate of the DNA tracer, the location information of the concentration peak, and the standard deviation of the concentration distribution along the axial direction.

[0042] In some embodiments, 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:

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

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

[0045] 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 at the site;

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

[0047] Different from the existing technology, the above technical solution divides the soil into fast zones (dominant channels) and slow zones (matrix flow), 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, thereby overcoming the defect that traditional models cannot describe the double peak phenomenon; in addition, based on site conditions, formation exploration data and tracer experimental results, the fit between the predicted results and the monitored values ​​is used as the control quantity, and a genetic algorithm is used to run the analytical model to search for the average linear flow velocity and porosity in the fast and slow zones of the soil, thereby achieving low-cost and fine characterization of the site flow field.

[0048] The above-mentioned records related to the invention content are only an overview of the technical solution of the present application. In order to enable ordinary technicians in the field to more clearly understand the technical solution of the present application, and then implement it according to the text of the specification and the contents recorded in the drawings, and to make the above-mentioned purpose and other purposes, features and advantages of the present application easier to understand, the following is an explanation in combination with the specific implementation mode and drawings of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0050] In the drawings of the specification:

[0051] Figure 1 It is a flow chart of the site DNA tracer migration prediction and flow field characterization of the present invention;

[0052] Figure 2 is a comparison diagram of the DNA tracer migration analysis solution described in the embodiment and the experimental results;

[0053] Figure 3 This is a graph showing the fitting results of the tracer concentration at the injection well boundary in a case of an industrial legacy site as described in the embodiment;

[0054] Figure 4 A comparison chart of search results and monitoring results of a case study of a certain industrial legacy site using the genetic algorithm coupled analytical solution described in the embodiment;

[0055] Figure 5This is a graph showing the fitting results of the tracer concentration at the injection well boundary in a pesticide contaminated site as described in the embodiment;

[0056] Figure 6 A comparison chart of search results and monitoring results of a case study of a pesticide contaminated site using the genetic algorithm coupled analytical solution described in the embodiment. DETAILED DESCRIPTION

[0057] In order to explain in detail the possible application scenarios, technical principles, specific schemes that can be implemented, and the purposes and effects that can be achieved, the following is a detailed description of the specific embodiments listed in conjunction with the accompanying drawings. The embodiments described herein are only used to more clearly illustrate the technical solutions of the present application, and are therefore only used as examples, and cannot be used to limit the scope of protection of the present application.

[0058] Reference to "embodiment" herein means that the specific features, structures or characteristics described in conjunction with the embodiment may be included in at least one embodiment of the present application. The term "embodiment" appearing in various places in the specification does not necessarily refer to the same embodiment, nor does it particularly limit its independence or association with other embodiments. In principle, in the present application, as long as there is no technical contradiction or conflict, the various technical features mentioned in the embodiments can be combined in any way to form a corresponding implementable technical solution.

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

[0060] 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 may exist, for example, A and / or B, which means: A exists, B exists, and A and B exist at the same time. In addition, the character " / " in this article generally indicates that the objects before and after are in an "or" logical relationship.

[0061] In the present application, terms such as “first” and “second” are merely used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship of quantity, priority or sequence between these entities or operations.

[0062] Without further limitations, in this application, the words "include", "comprises", "has" or other similar open-ended expressions used in sentences are intended to cover non-exclusive inclusion. These expressions do not exclude the presence of additional elements in the process, method or product including the elements, so that the process, method or product including a series of elements may include not only those limited elements, but also other elements not explicitly listed, or also include elements inherent to such process, method or product.

[0063] Similar to the understanding in the Examination Guidelines, in this application, expressions such as "greater than", "less than", "exceed" and the like are understood to exclude the number itself; expressions such as "above", "below", "within" and the like are understood to include the number itself. In addition, in the description of the embodiments of this application, "multiple" means more than two (including two), and similar expressions related to "multiple" are also understood in this way, such as "multiple groups", "multiple times", etc., unless otherwise clearly and specifically limited.

[0064] See also Figures 1 to 6 This embodiment provides a method for predicting the migration of a DNA tracer and describing a flow field, comprising the following steps:

[0065] S1. 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;

[0066] S2, obtaining condition information of the DNA tracer migration model, 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;

[0067] S3, input the dimensionless parameters into the mathematical model of tracer transport, and obtain the Laplace domain analytical solution of DNA tracer transport in groundwater and soil environment with the help of Laplace transform and Fourier transform;

[0068] S4, using the numerical inversion algorithm to calculate the analytical solution to obtain the fast zone concentration expression and the slow zone concentration expression of the DNA tracer in the heterogeneous soil;

[0069] S5, 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 migration model, the well information including the tracer monitoring concentration of the injection well and the spatial location information of the monitoring well;

[0070] S6. Output the necessary parameter information, fast zone concentration expression, and slow zone concentration expression into a tracer production curve through a genetic algorithm, and generate site flow field characterization information based on the tracer production curve.

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

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

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

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

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

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

[0077] In this embodiment, by dividing the fast region (preferential pathway) and slow region (matrix flow) of the soil, using the Laplace transform, Fourier transform, and numerical inversion, 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 convenient to use is obtained, overcoming the defect that traditional models cannot describe the double-peak phenomenon; in addition, based on the site working 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 region and slow region of the soil, realizing a low-cost fine characterization of the site flow field.

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

[0079] ;

[0080] In formula (1), is the concentration of the DNA tracer in the fast region, is the concentration of the DNA tracer in the slow region, is the retardation factor of the DNA tracer in the fast region, is the retardation factor of the DNA tracer in the slow region, is the radial distance (perpendicular to the injection well) from the edge of the injection well, is the axial distance (depth) from the top of the aquifer, is the migration time of the DNA tracer, is the radial hydrodynamic diffusion coefficient of the DNA tracer in the fast zone, is the hydrodynamic diffusion coefficient of the DNA tracer in the fast zone along the axial direction, is the radial hydrodynamic diffusion coefficient of the DNA tracer in the slow zone, is the hydrodynamic diffusion coefficient of the DNA tracer in the slow zone along the axial direction, is the average linear velocity in the fast zone, is the average linear velocity in the slow zone, is the porosity of the fast zone, is the porosity of the slow zone, are the mass transfer coefficients of the fast zone and the slow zone.

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

[0082] ;

[0083] Formula (3) is as follows:

[0084] ;

[0085] Formula (4) is as follows:

[0086] ;

[0087] In formula (2) to formula (4), is the first dimensionless parameter, is the second dimensionless parameter, is the third dimensionless parameter, is the fourth dimensionless parameter, is the fifth dimensionless parameter, is the sixth dimensionless parameter, is the seventh dimensionless parameter, is the eighth dimensionless parameter, is the ninth dimensionless parameter, is the tenth dimensionless parameter, is the eleventh dimensionless parameter, is the peak concentration of the tracer in the injection well, is the injection coefficient, is the radial dispersion of the aquifer, is the axial dispersion of the aquifer, 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 ( ), is the thickness of the aquifer.

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

[0089] ;

[0090] Formula (6) is as follows:

[0091] ;

[0092] Formula (7) is as follows:

[0093] ;

[0094] Formula (8) is as follows:

[0095] ;

[0096] 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 is the first eigenvector of matrix A, and is the second eigenvector of matrix A, is district( Represents the fast zone, represents the slow zone) concentration calculation parameter, yes The parameters after Fourier transformation are is the Fourier operator, is the Laplace operator, and are the first and second intermediate calculation parameters, respectively, is the Airy function, and are the third and fourth intermediate calculation parameters, respectively, is the fifth intermediate calculation parameter.

[0097] In some embodiments, the fast zone concentration expression is expressed by formula (9), which is as follows:

[0098] ;

[0099] The slow zone concentration expression is expressed by formula (10), which is as follows:

[0100] ;

[0101] In formula (9) and formula (10), For DNA tracers The concentration of the area ( Represents the fast zone, represents the slow zone), , is a fixed constant, is the Laplace first inversion parameter, For DNA tracers in the Laplace domain The dimensionless concentration of the region, is the Laplace second inversion parameter, hour, , , hour, , Is an imaginary unit.

[0102] In some embodiments, the background value survey is a survey of the initial concentration of the DNA tracer in the soil of the field before injection into the experiment, and the initial condition is configured as the initial concentration of the DNA tracer;

[0103] 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.

[0104] In this embodiment, step S2 specifically comprises that the condition information of the DNA tracer migration model is configured to be generated through a background value survey and experimental site conditions; wherein, based on the site tracer background value survey, the initial conditions of the DNA tracer migration model are determined, that is, the DNA tracer concentration in the site soil before the injection experiment; wherein, based on the experimental site conditions, considering the influence of the DNA tracer injection method and the aquifer structure, the boundary conditions of the DNA tracer migration model are determined, that is, the DNA tracer concentration function at the injection well, the DNA tracer concentration at the top of the DNA tracer migration model, the DNA tracer concentration at the bottom of the DNA tracer migration model, and the tracer concentration at infinity of the DNA tracer migration model, or the DNA tracer concentration function at the injection well, the DNA tracer concentration gradient at the top of the DNA tracer migration model, the DNA tracer concentration gradient at the bottom of the DNA tracer migration model, and the DNA tracer concentration gradient at infinity of the DNA tracer migration model.

[0105] In some embodiments, 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;

[0106] The necessary parameter information for obtaining the type information of DNA tracers, the formation information where the DNA tracers are placed, the well information where the DNA tracers are placed, and generating the DNA tracer migration model includes:

[0107] After the DNA tracer is injected, the concentration of the DNA tracer in the injection well is monitored;

[0108] The DNA tracer concentration was fitted using boundary conditions to obtain the decay rate of the DNA tracer, the location information of the concentration peak, and the standard deviation of the concentration distribution along the axial direction.

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

[0110] In some embodiments, 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:

[0111] Monitor the concentration of the DNA tracer in the monitoring well for a preset time period and draw a tracer output curve;

[0112] Generate curve error information based on 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 at the site;

[0114] Generate site flow field characterization information based on 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 output curve is drawn; preferably, the concentration of the tracer in the monitoring well is monitored for 600 hours, and a tracer output curve is drawn; curve error information is generated according to the tracer output curve, and the curve error information is input into the genetic algorithm coupling model, and the error of the tracer output curve of the monitoring well is used as a control quantity to search for the average linear flow velocity in the fast zone, the porosity in the fast zone, the average linear flow velocity in the slow zone, and the porosity in the slow zone of the site soil until a prediction error is obtained within an acceptable range, and a prediction result is obtained, the prediction result including the average linear flow velocity in the fast zone, the porosity in the fast zone, the average linear flow velocity in the slow zone, and the porosity in the slow zone of the soil in the site; site flow field characterization information is generated according to the prediction result; and a fine characterization of the site flow field is achieved.

[0116] The above technical solution divides the soil into fast zones (dominant channels) and slow zones (matrix flow), 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, thereby overcoming the defect that traditional models cannot describe the double peak phenomenon. In addition, based on site conditions, formation exploration data and tracer experimental results, and with the degree of fit between the predicted results and the monitored values ​​as the control quantity, a genetic algorithm is used to run the analytical model to search for the average linear flow velocity and porosity in the fast and slow zones of the soil, thereby achieving low-cost and fine characterization of the site flow field.

[0117] For ease of understanding, this embodiment also provides the following two examples to illustrate the specific application of the above technical solution:

[0118] The DNA tracing experiment and flow field characterization of a certain industrial legacy site and a certain pesticide contaminated site will be taken as examples, and the present invention will be further described and illustrated in conjunction with the accompanying drawings and tables. The technical features of each embodiment of the present invention can be combined accordingly without conflicting with each other; the specific implementation process of the present invention is as follows Figure 1 .

[0119] The first example: an industrial legacy site

[0120] S1: Construct a DNA tracer migration model. The DNA tracer migration model is configured to be constructed based on the migration behavior of the DNA tracer in the groundwater and soil environment.

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

[0122]

[0123]

[0124] Where: and is the concentration of DNA tracer in the fast and slow zones of heterogeneous soil, and is the retardation factor of the tracer in the fast and slow zones, for distance; is the axial distance; is the migration time of the tracer; and is the hydrodynamic diffusion coefficient of the tracer in the fast zone along the radial and axial directions; and is the hydrodynamic diffusion coefficient of the tracer in the slow zone along the radial and axial directions; and is the average linear velocity of the fast and slow zones, and is the porosity of the fast zone and the slow zone. The total porosity of the soil It can be regarded as the sum of the porosity of the fast zone and the slow zone, that is, .

[0125] S2: Obtaining condition information of the DNA tracer migration model. The condition information is configured to be generated through background value investigation and experimental field conditions. The condition information includes initial conditions and boundary conditions.

[0126] In general, there is no DNA tracer in the natural environment, so the initial conditions of the mathematical model can be defined as:

[0127]

[0128] The concentration of the tracer at the injection point will be diluted and attenuated by groundwater flow, so the boundary condition at the injection well can be expressed as:

[0129]

[0130] Where: is the initial concentration of the injection well after the tracer is placed, is the decay rate of the tracer, is the location where the peak tracer concentration occurs in the injection well, is the thickness of the aquifer, is the standard deviation of the axial distribution of the tracer concentration in the injection well.

[0131] The top of the aquifer is an impermeable boundary and the bottom is an aquiclude; therefore, the boundary flux of the DNA tracer is zero at both the top and bottom:

[0132]

[0133]

[0134] The tracer has a finite migration distance, so it is assumed that at infinite distance, the concentration of the DNA tracer is 0:

[0135]

[0136] S3. Input the dimensionless parameters into the mathematical model of tracer migration, and with the help of Laplace transform and Fourier transform, obtain the analytical solution of the Laplace domain of DNA tracer migration in the groundwater and soil environment.

[0137] The following parameters are introduced to make the model dimensionless:

[0138]

[0139]

[0140]

[0141] Where: , , , , , , , , , ,and They are all dimensionless parameters; is the injection rate; is the injection coefficient, ; and is the radial and axial dispersion of the aquifer.

[0142] Then the control equations (11) and (12) can be changed to:

[0143]

[0144]

[0145] The initial and boundary conditions can be changed to:

[0146]

[0147]

[0148]

[0149]

[0150]

[0151] By introducing the Laplace transform, equations (18) and (19) can be transformed into:

[0152]

[0153]

[0154] Where: is the Laplace operator.

[0155] The boundary conditions can be changed to:

[0156]

[0157]

[0158]

[0159]

[0160] The governing equations (25) and (26) in the Laplace domain are shifted and similar terms are merged:

[0161]

[0162]

[0163] Convert the above equation into matrix format:

[0164]

[0165]

[0166]

[0167] matrix The characteristic roots of are:

[0168]

[0169]

[0170] in, is the operation parameter, which can be expressed as:

[0171]

[0172] Therefore, the matrix The eigenvectors of are:

[0173]

[0174]

[0175] Since the eigenvectors are not equal, we can use the following matrix to convert Diagonalization:

[0176]

[0177] Assume that there is a matrix , so that = According to equation (32), we can get:

[0178]

[0179] because is linear, so:

[0180]

[0181]

[0182] Substituting equation (44) into equations (33) to (35):

[0183]

[0184] So we only need to solve two identical equations. , The form is as follows:

[0185]

[0186] Introduce the finite Fourier cosine transform:

[0187]

[0188] Equation (46) can be transformed into:

[0189]

[0190]

[0191] For this partial differential equation, there exists a general solution:

[0192]

[0193]

[0194] in is the Airy function, yes The related functions.

[0195] About Therefore, according to the boundary condition equation (16), we know As it approaches infinity is also 0. Therefore, .

[0196] Introduce the injection well boundary condition into the Fourier domain:

[0197]

[0198] Assuming that the pollution source is normally distributed and decays over time, it can be expressed as:

[0199]

[0200] because ,in It can be calculated according to the following formula:

[0201]

[0202] but

[0203]

[0204] So we can get:

[0205]

[0206]

[0207] Further finite Fourier transform

[0208]

[0209]

[0210] Therefore, we can get:

[0211]

[0212] Therefore, it can be calculated :

[0213]

[0214] Similarly, for:

[0215]

[0216] According to equations (56) and (57), the analytical solution of the migration of DNA tracer in groundwater and soil environment in the Laplace domain is as follows:

[0217]

[0218]

[0219] Where: and is the concentration of DNA tracer in the fast and slow zones in the Laplace domain, and the remaining parameters are calculated parameters, which can be expressed as:

[0220]

[0221]

[0222]

[0223] S4. The analytical solution is calculated through a numerical inversion algorithm to obtain the fast zone concentration expression and slow zone concentration expression of the DNA tracer in the heterogeneous soil.

[0224] The numerical inversion method is used to solve the expression of the concentration of DNA tracer in the fast zone and the slow zone based on the Laplace domain analytical solution obtained in step 3:

[0225]

[0226]

[0227]

[0228]

[0229]

[0230] Where: is an imaginary number, is a fixed constant (usually 64).

[0231] The accuracy of the proposed concentration expression was verified based on a soil column experiment conducted by Liu et al. in 2023; the experiment used the 88-nucleotide T12-DNA tracer developed by their team; since the soil column experiment is approximately a one-dimensional experiment, the axial and radial molecular diffusion coefficients are the same, equal to ; The tracer was injected into the top of the soil column through the equipment at the beginning of the experiment, and the injection time was 2 s; the standard deviation of the tracer concentration along the axial distribution at the injection position can be regarded as infinite (10 can be used for calculation); the experiment used a peristaltic pump to simulate the groundwater flow in the soil, and the pumping rate was The total length of the soil column is 10 cm, the total porosity of the internal soil is 0.44, the porosity of the fast zone and slow zone of the soil is 0.25 and 0.19 respectively; the average linear flow velocities in the fast zone and slow zone are and , the mass transfer coefficient is assumed to be The comparison between the prediction results of the proposed expression and the soil column test 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 output curve, and the fitting degree of the prediction result can reach 0.94; therefore, it can be used in engineering design.

[0232] S5. Obtain 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. The well information includes the tracer monitoring concentration of the injection well and the spatial location information of the monitoring well.

[0233] The polylactic acid-superparamagnetic iron oxide nanoparticle-DNA tracer provided by IDT DNA Company of the United States was selected. The molecular diffusion coefficient of the tracer is ; The geological survey results show that the soil type in the study area is mainly silty clay, the aquifer thickness is 10m, the porosity is 0.4, the radial and axial dispersions are 2m and 0.018m respectively; the injection well is set at the northernmost end of the study area, the well radius is 0.5m, and the injection flow rate is ; The monitoring well was installed 20 m downstream of the injection well; the DNA tracer concentration in the injection well was monitored within 300 h after injection; it should be noted that the tracer concentration at different positions in the well was not much different, so the position where the tracer concentration peak appeared and the standard deviation of the tracer concentration along the axial distribution were 5 m and 10, respectively; the data in the injection well were fitted based on the boundary conditions (Eq. 4) to obtain the decay rate ;from Figure 3 It can be seen that the decay rate 0.0176 ; In addition, the adopted boundary conditions can effectively describe the changes in tracer concentration, and the fitting degree can reach 0.95.

[0234] S6. Output the necessary parameter information, fast zone concentration expression, and slow zone concentration expression into a tracer production curve through a genetic algorithm, and generate site flow field characterization information based on the tracer production curve.

[0235] The DNA tracer concentration in the monitoring well within 600 h after injection was observed, and the tracer output curve was drawn. The analytical solution proposed by genetic algorithm coupling was used to search for the average linear flow velocity and porosity in the fast and slow zones of the site soil, taking the fit between the tracer output curve of the monitoring well and the predicted result as the control quantity. The fit can be calculated according to the following formula:

[0236]

[0237] Where: is the number of tracer concentration samples in the monitoring well, It is The tracer concentration in each sample, is the predicted tracer concentration, is the mean of the predicted results.

[0238] The parameters of the genetic algorithm are set as follows: the number of individuals in the population is 500, the number of generations is 500, the crossover probability is 0.15, and the mutation probability is 0.2; the search results are as follows Figure 4 As shown in the figure, it can be seen that with the increase of evolutionary generations, the error between the predicted results and the actual output curve becomes smaller and smaller. Evolutionary generations ( ) for 100, 200 and 500 generations, the fitting degrees of the prediction results were 0.63, 0.86 and 0.99 respectively; the search results revealed that the average linear flow velocities in the fast and slow zones of the site were and ; In addition, the porosity ratios of the fast zone and slow zone in the site soil are 0.098 and 0.302 respectively; Based on the search results, the site flow field can be accurately characterized.

[0239] Second example: A pesticide contaminated site

[0240] When the present invention is applied in a landfill, steps 1 to 4 are the same as those in case 1, and thus will not be described in detail.

[0241] S5. Obtain 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. The well information includes the tracer monitoring concentration of the injection well and the spatial location information of the monitoring well.

[0242] The polylactic acid-superparamagnetic iron oxide nanoparticle-DNA tracer provided by IDT DNA Company of the United States was selected. The molecular diffusion coefficient of the tracer is ; The geological survey results show that the soil type in the study area is mainly clay, the aquifer thickness is 15 m, the porosity is 0.38, and the radial and axial dispersions are 1.28 m and 0.03 m respectively; the injection well is set in the west of the study area, with a well radius of 0.5 m and an injection flow rate of ; The monitoring well was installed 15 m downstream of the injection well; the DNA tracer concentration in the injection well was monitored within 300 h after injection; the position of the tracer concentration peak and the standard deviation of the tracer concentration along the axial distribution were 7.5 m and 10, respectively; the data in the injection well were fitted based on the boundary conditions (Eq. 4) to obtain the decay rate ;from Figure 5 It can be seen that the decay rate 0.0132 ; In addition, the adopted boundary conditions can effectively describe the changes in tracer concentration, and the fitting degree can reach 0.93.

[0243] S6. Output the necessary parameter information, fast zone concentration expression, and slow zone concentration expression into a tracer production curve through a genetic algorithm, and generate site flow field characterization information based on the tracer production curve.

[0244] The DNA tracer concentration in the monitoring well within 600 hours after injection was observed, and the tracer output curve was drawn. The analytical solution proposed by genetic algorithm coupling was used to search for the average linear flow velocity and porosity in the fast and slow zones of the site soil, taking the fitting degree between the tracer output curve of the monitoring well and the predicted result as the control quantity. The parameter setting of the genetic algorithm was the same as that of Case 1. The search results are shown in Figure 2. Figure 6 As shown, the evolutionary algebra ( ) for 100, 200 and 500 generations, the fitting degrees of the prediction results were 0.51, 0.69 and 0.99 respectively; the search results revealed that the average linear flow velocities in the fast and slow zones of the site were and In addition, the void ratios of the fast zone and slow zone in the site soil were 0.11 and 0.27, respectively.

[0245] The embodiments described above are only two preferred solutions of the present invention, but they are not intended to limit the present invention. Ordinary technicians in the relevant technical field can make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, all technical solutions obtained by equivalent replacement or equivalent transformation fall within the protection scope of the present invention.

[0246] Finally, it should be noted that although the above embodiments have been described in the specification and drawings of this application, this does not limit the scope of patent protection of this application. All technical solutions generated by replacing or modifying equivalent structures or equivalent processes based on the essential concept of this application using the contents recorded in the specification and drawings of this application, as well as directly or indirectly implementing the technical solutions of the above embodiments in other related technical fields, are included in the scope of patent protection of this 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; The necessary parameter information, fast zone concentration expression, and slow zone concentration expression are outputted into a tracer production curve through a genetic algorithm, and site flow field characterization information is generated according to the tracer production curve.

2. The method for predicting DNA tracer migration and describing site flow field according to claim 1, characterized in that: The DNA tracer migration model is expressed by formula (1), which is as follows: ； In formula (1), is the concentration of DNA tracer in the fast zone, is the concentration of DNA tracer in the slow zone, is the blocking factor of DNA tracer in the fast zone, It is the blocking factor of DNA tracer in the slow zone. is the radial distance from the edge of the injection well when the DNA tracer is vertically injected into the well, is the axial distance between the DNA tracer and the top of the aquifer, is the migration time of the DNA tracer, is the radial hydrodynamic diffusion coefficient of the DNA tracer in the fast zone, is the hydrodynamic diffusion coefficient of the DNA tracer in the fast zone along the axial direction, is the radial hydrodynamic diffusion coefficient of the DNA tracer in the slow zone, is the hydrodynamic diffusion coefficient of the DNA tracer in the slow zone along the axial direction, is the average linear velocity in the fast zone, is the average linear velocity in the slow zone, is the porosity of the fast zone, is the porosity of the slow zone, is the mass transfer coefficient applicable to the fast zone and the slow zone.

3. The method for predicting DNA tracer migration and describing site flow field according to claim 2, 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), is the first dimensionless parameter, is the second dimensionless parameter, is the third dimensionless parameter, is the fourth dimensionless parameter, is the fifth dimensionless parameter, is the sixth dimensionless parameter, is the seventh dimensionless parameter, is the eighth dimensionless parameter, is the ninth dimensionless parameter, is the tenth dimensionless parameter, is the eleventh dimensionless parameter, is the peak concentration of the tracer in the injection well, is the injection coefficient, is the radial dispersion of the aquifer, is the axial dispersion of the aquifer, 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 ( ), is the thickness of the aquifer.

4. The method for predicting DNA tracer migration and describing site flow field according to claim 3, 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 For the matrix The two first eigenvectors of and For the matrix The two second eigenvectors of is The concentration calculation parameters of the zone are: Indicates the fast zone, Indicates the slow zone, yes The parameters after Fourier transformation are is the Fourier operator, is the Laplace operator, is the first intermediate calculation parameter, is the second intermediate calculation parameter, yes The Airy function in operation, yes The Airy function in operation, is the third intermediate calculation parameter, is the fourth intermediate calculation parameter, is the fifth intermediate calculation parameter.

5. The method for predicting DNA tracer migration and describing site flow field according to claim 4, 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), For DNA tracers The concentration of the area, , is a fixed constant, is the Laplace first inversion parameter, For DNA tracers in the Laplace domain The dimensionless concentration of the region, is the Laplace second inversion parameter, hour, , , hour, , Is an imaginary unit.

6. 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.

7. 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.

8. 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 characterization information is generated according to the prediction result.

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