CN117610319B - Osmotic coefficient and dispersion recognition method and system integrating concentration and conductivity - Google Patents
Osmotic coefficient and dispersion recognition method and system integrating concentration and conductivity Download PDFInfo
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Abstract
The invention discloses a method and a system for identifying permeability coefficient and dispersity of fusion concentration and conductivity. The method comprises the following steps: sampling from the prior distribution to generate a permeability coefficient K, a longitudinal dispersion alpha l and a transverse dispersion alpha t field; according to concentration data of solute concentration distribution fields and observation points at different observation moments; converting a concentration distribution field into a conductivity sigma field by using a lithology physical model, and acquiring ERT potential data at all observation moments according to a resistivity forward model; inputting the measured observation point dynamic concentration data in the field and ERT potential data obtained by geophysical investigation together with the concentration distribution field and ERT potential data obtained by deduction into ESMDA inversion algorithm, and obtaining a parameter field after inversion updating through data assimilation; and repeating the operation by using the parameter field updated by inversion, and finally updating to obtain the optimal estimation field. The invention can improve the permeability coefficient of the heterogeneous aquifer and the describing precision of the dispersion field.
Description
Technical Field
The invention relates to the field of groundwater numerical simulation, in particular to a method and a system for identifying permeability coefficient and dispersity of fusion concentration and conductivity.
Background
Accurate characterization of the heterogeneity of an underground aquifer is critical to understanding the migration trend of chemical components in groundwater. In recent decades, many studies have focused on the determination of aquifer hydraulic parameter fields, such as permeability coefficient K. One widely used characterization technique is groundwater model inversion, where the distribution of K is determined by an inversion method based on borehole measurement data (typically head and solute concentrations). Common inversion methods are: geostatistical methods such as principal component geostatistical algorithms and reduced order continuous linear estimators; aggregation-based methods such as an aggregate kalman filter (Ensemble KALMAN FILTER, ENKF) and an aggregate smoother (Ensemble Smoother with Multiple Data Assimilation, ESMDA) for multiple data assimilation.
Although model inversion methods have been fully studied and applied to the characterization of K fields, the related studies on the characterization of solute transport parameter (e.g., fringing) fields are still relatively limited. The dispersion describes the diffusion and dilution behavior of solutes in the subsurface fluids, representing an important transport mechanism. Diffusion can cause distortion of the profile of the pollution plume, and dilution can cause mixing of the pollution plume with the original groundwater body and increase the volume of fluid occupied by the pollution plume. Thus, accurate identification of the dispersion is critical in predicting solute transport in heterogeneous formations. Previous studies have generally considered unknown homogeneous dispersions in the inversion model because limited borehole data cannot accurately capture the inherent spatial variation of the dispersion. However, using spatially homogeneous dispersion while solute transport behavior in relatively homogeneous aquifers may be predicted, such simplification may not accurately predict solute transport behavior in highly heterogeneous aquifers and the diffusion characteristics of the breakthrough curves (Breakthrough Curves, BTCs). To solve this problem, in one study in 2006, novak and Cirpka（Geostatistical inference of hydraulic conductivity and dispersivities from hydraulic heads and tracer data.Water Resources Research. 42: W08416.） proposed the joint estimation of the spatial variation of K and dispersion (including longitudinal and lateral dispersion) in flask experiments by assimilating the hydraulic head and the time moment of BTCs using geostatistical methods. The results show that estimating the dispersion of spatial variations can predict BTCs more accurately than using spatially homogeneous dispersions. In another study in 2018 Priyanka et al （Estimating anisotropic heterogeneous hydraulic conductivity and dispersivity in a layered coastal aquifer of Dakshina Kannada District, Karnataka.Journal of Hydrology. 565: 302–317.） proposed estimating the spatial variation of K and longitudinal dispersion using GLMA inversion method based on hydraulic head and solute concentration data. The results also show that the hydraulic head and solute concentrations simulated using the initial model of spatial homogeneity K and dispersion are highly mismatched with the observed data, thus illustrating the importance of spatial inhomogeneities taking into account K and dispersion.
Although both of the above studies considered heterogeneity of dispersion, they only used invasive borehole data (i.e., head and solute concentration) for model inversion. Drilling is often costly and cannot be performed with high spatial density. Thus, in an actual field, the number of boreholes may be relatively limited. On the other hand, however, the inversion model requires a large amount of observation data and sufficient information about groundwater flow and migration to ensure the accuracy of estimation of the parameter field, since identifying the dispersion of spatial variations can significantly increase the number of unknown parameters. Inversion based on finite data collected from the borehole may result in lower accuracy in identifying K and fringing fields, failing to improve the accuracy of solute transport simulation.
As a non-invasive method, geophysical techniques such as natural potential (SP) and resistivity Tomography (ELECTRICAL RESISTIVITY tomograph, ERT) can provide a relatively inexpensive indirect large amount of continuous data about groundwater solute migration. Many studies use geophysical information to characterize permeability coefficient K fields by constructing a hydrogeophysical inversion framework. For example, by coupled hydrogeophysical inversion methods, the average arrival time of ERT potential (caused by tracer migration) and hydraulic head data are inverted to estimate K distribution in sand box experiments. However, only a few studies identify dispersion through geophysical data. For example, revil and Jardani proposed to jointly identify K and dispersion of porous media based on time-series SP data by stochastic inversion methods in 2010 （Stochastic inversion of permeability and dispersivities from time lapse self-potential measurements: A controlled sandbox study.Geophysical Research Letters. 37: L11404.）. Straface and De Biase proposed using SP data to estimate longitudinal dispersion by the hydrogeophysical inversion method in 2013 （Estimation of longitudinal dispersivity in a porous medium using self-potential signals.Journal of Hydrology. 505: 163–171.）. However, in these studies, the dispersion was assumed to be homogeneous. Due to the low resolution of the SP method, it would be difficult to estimate the spatially varying K and fringing fields from the SP data alone. On the other hand, since ERT signals are very sensitive to conductive tracers, this geophysical approach can also be used to identify dispersion. Beaujean et al in 2014, （Calibration of seawater intrusion models: inverse parameter estimation using surface electrical resistivity tomography and borehole data.Water Resources Research. 50 (8): 6828–6849.）, propose to jointly estimate K and longitudinal dispersion in a seawater intrusion model by ERT data. However, the parametric field of its model is described as a two-phase system, and the dispersion is assumed to be homogeneous within each phase. Therefore, the study did not adequately consider the heterogeneity of the dispersion. Furthermore, there was a large difference between the estimated and reference (true) dispersion values in their study. Possible reasons include: (i) They interpret and invert ERT data by a non-coupled hydrogeophysical inversion method, applying isotropic smoothing regularization, which may reduce the accuracy of the interpretation results; and (ii) they only implement surface ERT electrode measurements, resulting in less accurate parameter estimation for deeper formations.
By way of introduction to the above more detailed background, it can be appreciated that the observed data based on borehole concentration is limited by the actual conditions (human, material, financial and field conditions) and the amount of data that can be obtained is generally limited. Under the condition of limited observation data, the estimation results of the heterogeneous permeability coefficient and the fringing field are difficult to describe the fine structure of the real field, and then the simulation and prediction results of solute migration are affected.
Disclosure of Invention
The invention aims to: for the problem that only limited borehole data is insufficient to finely describe the heterogeneous permeability coefficient and the dispersion field of the aquifer, the invention provides that an ERT method in geophysical technology is applied to indirectly and cheaply acquire a large amount of continuous data about the migration of the solute of the groundwater, so that enough constraint is provided for the estimation of the heterogeneous permeability coefficient field and the dispersion field, and further the precision of solute migration simulation and prediction is improved.
The technical scheme is as follows: in order to achieve the above object, the present invention provides a method for identifying permeability coefficient and dispersion of fusion concentration and conductivity, comprising the steps of:
(1) Sampling from the prior distribution to generate N r groups of permeability coefficients K, longitudinal dispersion alpha l and transverse dispersion alpha t fields;
(2) Operating an underground water flow forward model according to N r permeability coefficient K fields to obtain N r stable flow fields, and operating an underground water solute transport model according to N r groups of longitudinal dispersion alpha l and transverse dispersion alpha t fields corresponding to the permeability coefficient K fields to obtain N r concentration distribution fields at all observation moments;
(3) Converting N r concentration distribution fields into N r conductivity sigma fields by using a lithology physical model, and acquiring ERT potential data at all observation moments according to a resistivity forward model operated by the conductivity sigma fields;
(4) The measured observation point dynamic concentration data in the field and ERT potential data obtained by geophysical investigation are input into a multi-data assimilation set smoother ESMDA inversion algorithm together with the concentration distribution field and ERT potential data obtained by deduction in the steps (3) and (4), and the permeability coefficient K, the longitudinal dispersity alpha l and the transverse dispersity alpha t field after inversion updating are obtained through data assimilation;
(5) And (3) repeating the operations of the steps (2) - (4) by using the updated permeability coefficient K, the longitudinal dispersion alpha l and the transverse dispersion alpha t field by inversion until the iteration times reach the specified maximum iteration rounds, and finally updating the obtained permeability coefficient K, the longitudinal dispersion alpha l and the transverse dispersion alpha t field to obtain the optimal estimated field.
Further, in the step (1), a spectrum-based Gaussian generating method is adopted to generate a permeability coefficient K field conforming to Gaussian distribution; the longitudinal dispersion alpha l field is formed by overlapping and combining a Gaussian distribution field and a linear model which is related to the distance along the water flow direction; the transverse dispersion α t field is obtained by multiplying the anisotropy ratio λ, which is a linear model that is related to distance along the direction of water flow, by the longitudinal dispersion α l.
Further, in the step (2), the forward model of the groundwater flow is expressed as:
，
wherein K is the permeability coefficient, and h is the hydraulic head.
Further, in the step (2), the groundwater solute transport model is expressed as:
，
wherein θ is the porosity, D is the hydrodynamic diffusion tensor, C is the solute concentration, q represents the flow, and Darcy's law is adopted And calculating, wherein t represents time, and the calculation formula of the hydrodynamic dispersion tensor D is as follows:
，
Wherein v represents seepage velocity, and the calculation formula is V i represents the component of the velocity vector in the i-direction, v j represents the component of the velocity vector in the j-direction,/>Is Kronecker sign, 1 when i=j, otherwise 0, d m represents the diffusion coefficient, α represents the dispersion in the main direction, longitudinal dispersion is taken as the dispersion in the main direction,/>Λ is the anisotropic ratio.
Further, in the step (3), the lithology physical model is expressed as:
，
Where σ is the bulk conductivity, m represents the cementation index, n represents the saturation index, S w is the water saturation, and σ w is the pore fluid conductivity.
Further, the pore fluid conductivity σ w is calculated as follows:
，
Where F is Faraday constant, i represents the number of the ith ion in the pore fluid, k ions are total, u i represents the electric mobility of ion i, C i is the molar concentration of ion i, and z i represents the valence of ion i.
Further, in the step (4), the resistivity forward model is expressed as:
，
Wherein, Is a dirac function,/>Is a single current electrode, I is the amperage.
The invention also provides a permeability coefficient and dispersion recognition system for fusing concentration and conductivity, comprising:
The analog data acquisition module is used for sampling from prior distribution to generate N r groups of permeability coefficient K, longitudinal dispersion alpha l and transverse dispersion alpha t fields;
The concentration deduction module operates an underground water flow forward model according to N r permeability coefficient K fields to obtain N r stable flow fields, and operates an underground water solute transport model according to N r groups of longitudinal dispersion alpha l and transverse dispersion alpha t fields corresponding to the permeability coefficient K fields to obtain N r concentration distribution fields at all observation moments;
The potential deduction module converts N r concentration distribution fields into N r conductivity sigma fields by using a lithology physical model, and operates a resistivity forward model according to the conductivity sigma fields to obtain ERT potential data at all observation moments;
The inversion updating module is used for inputting the measured observation point dynamic concentration data in the field and ERT potential data obtained by geophysical investigation, together with the concentration distribution field and ERT potential data obtained by the concentration deduction module and the potential deduction module, into a multi-data assimilation set smoother ESMDA inversion algorithm, and obtaining an permeation coefficient K, a longitudinal dispersion alpha l and a transverse dispersion alpha t field after inversion updating through data assimilation;
And the iteration control module repeatedly calls the concentration deduction module, the potential deduction module and the inversion updating module to carry out iteration treatment by using the permeability coefficient K, the longitudinal dispersity alpha l and the transverse dispersity alpha t field data after inversion updating until reaching the specified maximum iteration turn, and finally updating to obtain the permeability coefficient K, the longitudinal dispersity alpha l and the transverse dispersity alpha t field which are the optimal estimated fields.
The present invention also provides a computer device comprising: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, which when executed by the processors, implement the steps of the permeability coefficient and dispersion identification method of fusion concentration and conductivity as described above.
The present invention also provides a computer readable storage medium having stored thereon a computer program which when executed by a processor realizes the steps of the permeation coefficient and dispersion identification method of fusion concentration and conductivity as described above.
The beneficial effects are that: the invention constructs a coupled hydrologic geophysical inversion framework, and jointly estimates the permeability coefficient and the fringing field of spatial heterogeneity by fusing tracer concentration data and ERT data in the geophysics and adopting a data assimilation algorithm ESMDA as an inversion method. The effectiveness of the proposed method was verified by numerical cases in ideal aquifers with highly heterogeneous permeability coefficient K and fringing fields. The invention can improve the osmotic coefficient of the heterogeneous aquifer and the describing precision of the dispersion field, thereby improving the simulation and prediction results of the groundwater solute transport model.
Drawings
FIG. 1 is a coupled hydrogeophysical inversion frame model in accordance with the present invention;
FIG. 2 is an image of an ideal aquifer and reference field set in the numerical case of the present invention;
FIG. 3 is a depiction of the spatial homogeneity and spatial variation of the assumed dispersion based on tracer concentration data alone;
FIG. 4 is a parameter field estimated with simultaneous assimilation of the tracer concentration and potential data from ERT surveys;
FIG. 5 is a fit of estimated permeability coefficient K and dispersion to true permeability coefficient K and dispersion;
fig. 6 is a schematic of the concentration profile of the reference and simulated tracers at 80 days.
Detailed Description
The technical scheme of the invention is further described below with reference to the accompanying drawings.
In order to jointly estimate the spatial distribution of the heterogeneous permeability coefficient field and the dispersion field, the invention provides a coupled hydrogeophysical inversion framework for fusing concentration and ERT data. In this framework, for the fringing fields, the two parameter fields of longitudinal fringing alpha l and anisotropy ratio lambda are estimated jointly, instead of directly estimating the fields of longitudinal fringing alpha l and transverse fringing alpha t jointly, so as to avoid the problem of the uncomfortable inversion caused by the "aliasing" phenomenon. In the method of the invention, the dispersion has the following properties: (1) They are spatially varying variables and have a scale effect (increasing with increasing solute transport distance). (2) As in the conventional practice of estimating the lnK field, the lnalpha l and lnlambda fields of natural logarithmic transformation are estimated to avoid the occurrence of negative values of dispersion during inversion. Finally, the respective parameter fields are restored according to k=exp (ln K), α l= exp(ln αl), and λ=exp (lnλ).
FIG. 1 is a schematic diagram of a coupled hydrogeophysical inversion framework. Referring to fig. 1, the method for identifying permeability coefficient and dispersity of various fusion concentrations and conductivities provided by the invention comprises the following steps:
In step S1, N r sets of lnK, lnalpha l and lnalpha t fields meeting the prior condition are randomly generated.
And generating an ln K field conforming to the Gaussian distribution by adopting a Gaussian generating method based on a spectrum. The method requires geostatistical parameters (i.e., mean, variance and correlation length) of the input field to randomly generate a gaussian field. Where the N r sets of ln K fields are generated by inputting a priori geostatistical parameter (mean, variance, correlation length) values (gaussian distribution fields).
The spatial distribution mode of the lnalpha l field is formed by overlapping and combining a Gaussian distribution field and a linear model which is related to the distance along the water flow direction, namely: Wherein/> Is a linear coefficient of the linear model, d represents a vertical distance from the boundary to the observation point along the water flow direction, and G is a gaussian geostatistical field. Specifically, N r sets of gaussian distribution fields are generated by inputting l a priori geostatistical parameters (mean, variance, correlation length). N r sets of linear coefficients/>, obtained from uniform sampling within a priori range (estimated by field investigation)N r sets of distance-dependent linear fields are generated. The two fields (Gao Sichang and linear) are superimposed, resulting in a N r set lnα l field.
The lnλ field is expressed by a linear model: Wherein/> Is the linear coefficient of the model,/>Is a constant. N r sets of linear coefficients/>, obtained from uniform sampling within a priori range (estimated by field investigation)Sum constant/>Generating N r sets of lnλ fields. According to/>The final calculation generates the corresponding lnα t field of the N r sets.
And S2, simulating concentration distribution fields of solutes at different observation moments and concentration data of observation points.
And (3) inputting the initial estimated ln K field into an underground water flow (steady flow) model, and calculating a steady flow field (hydraulic head h field). Inputting the stable flow field and the corresponding lnalpha l and lnalpha t fields into a groundwater solute transport model, and calculating to obtain the solute concentration (C) distribution field at different observation moments and dynamic concentration data of observation points.
The underground water flow model, namely the underground water flow control equation of the steady flow is as follows:
（1）
wherein K is the permeability coefficient (m/d), h is the hydraulic head (m), Representing the differential operator.
The groundwater solute transport model, the convection-dispersion equation that controls solute transport, is as follows:
（2）
Wherein θ is the porosity, D is the hydrodynamic diffusion tensor (m 2/D), C is the solute concentration (mg/L), q represents the flow (m/D), and Darcy's law Calculated, t represents time in days (d). The calculation formula of the hydrodynamic dispersion tensor D is as follows:
（3）
wherein v represents seepage velocity (m/d), and the calculation formula is V i represents the component of the velocity vector in the i-direction, v j represents the component of the velocity vector in the j-direction,/>Is the Kronecker symbol (1 when i=j, otherwise 0), D m represents the diffusion coefficient (m 2/D), α represents the dispersion in the principal direction, and the longitudinal dispersion is typically taken as the principal dispersion, i.e./>，Is the lateral dispersion (m), and λ is the anisotropic ratio.
And S3, converting the concentration field simulated in the step S2 into a bulk conductivity sigma field at each moment by using a lithology physical model, and operating a resistivity forward model according to the sigma field to calculate ERT potential data at different observation moments.
According to the lithology physical model, in clay-free or low clay media, the bulk conductivity σ can be calculated from the water saturation S w and the pore fluid conductivity σ w (S/m) (azi' S law):
（4）
wherein m represents the cementation index, An m-power exponent representing porosity, n representing saturation exponent,/>An nth power exponent representing water saturation. In the method of the present invention, the case of saturation conditions is considered, i.e. S w is equal to 1. The pore fluid conductivity σ w has the following linear combination relationship with the concentration of the ionic tracer in the fluid:
（5）
Where F is Faraday constant (96, 485C/mol), i represents the serial number of the ith ion in the pore fluid, k ions are shared, u i represents the electric mobility of the ion i (m 2·V-1·s-1）,Ci is the molar concentration (mol/L) of the ion i, and z i represents the valence of the ion i. It is to be noted that the electrical resistivity is the name of ERT method, the electrical conductivity is the inverse of the electrical resistivity, and the two are essentially the same.
With respect to the resistivity forward model (poisson's equation for electric potential), the geophysical forward model may predict electric potential Φ (V) by solving the partial differential equation:
（6）
Wherein, Is a dirac function,/>Is a single current electrode, is idealized as a point source of origin, and has a current intensity of I (A).
And S4, updating the parameter field by using ESMDA inversion algorithm.
Inputting the measured observation point location dynamic concentration data in the field and ERT potential data obtained by geophysical investigation, and the simulated observation point location dynamic concentration data and ERT potential data in the steps S2-S4 to ESMDA algorithm, and outputting the obtained inversion updated ln K, ln alpha l and ln alpha t fields through data assimilation.
And S5, repeating the steps S2-S4 according to the updated ln K, the updated lnalpha l and the updated lnalpha t field until the iteration times reach a specified maximum value N a. And finally, the updated lnK, lnalpha l and lnalpha t fields are the optimal estimation fields.
Having described the general implementation of the method of the present invention, the method is further demonstrated by the following specific examples and illustrate the performance of the proposed inversion framework. The effectiveness of the technical scheme is verified by an ideal tracing test based on potassium chloride. The tracer test is carried out on an ideal two-dimensional confined aquifer. Figure 2 shows an ideal aquifer and its reference field. The aquifer size was 30 m x 6 m, the spatial dispersion was 120 x 24 grids, each of which was 0.25 x m in length, see (a) in fig. 2, where circles represent electrodes and diamonds represent concentration sampling wells. By using a spectrum-based gaussian generation method, a reference (real) ln K (cm/s) field is generated. The overall mean and variance of the ln K field were-4.63 and 0.6, respectively. The horizontal correlation length is 5m and the vertical correlation length is 1 m. This spatial statistical design is consistent with the geological features of the Borden aquifer. The reference ln l field consists of two parts, one part being a gaussian distribution field characterizing the heterogeneity and the other part characterizing the linear trend related to the distance traveled in the flow direction. The reference lnα t field is generated from a linear trend model of the logarithmic anisotropy ratio lnλ. The fringing fields are designed in a manner consistent with Nowak and Cirpka（Geostatistical inference of hydraulic conductivity and dispersivities from hydraulic heads and tracer data.Water Resources Research. 42: W08416.）. The horizontal and vertical correlation lengths of lnα l were set to 7.5 m and 0.5 m, respectively. The final longitudinal dispersion is in the range of about 0.35 to 3.03 meters, which is common in field trials. The relevant geostatistical parameters are listed in table 1, and the generated reference lnk, lnα l and lnα t fields are shown in fig. 2 (b), (c), (d), respectively. All other parameters required in the groundwater flow and solute transport model are summarized in table 1. To mitigate the effects of boundary conditions on the hydraulic and electrical signals, the investigation region is surrounded by a large homogeneous buffer zone (200 meters long by 10 meters high) with constant hydraulic parameters and conductivity. Since confined aquifers are typically located at a depth below the surface of the earth, it is assumed that there is a 2.0m thick non-confined aquifer and a 0.5 m thick aquifer above the investigation region (i.e., the confined aquifer), see (a) in fig. 2. The groundwater level is set at a depth of 1.0 m. The water saturation of the upper unsaturated zone was set to 40%. The conductivities of the water-resistant layer, the non-pressure-bearing saturated zone and the non-saturated zone were set to 10 -3S/m、10-2 S/m and 1.6X10 -3 S/m, respectively.
For the groundwater flow model, the top and bottom of the buffer zone are considered to be watertight (i.e., no flux boundary). Constant head boundary conditions were applied on the left and right sides, with heads 52 m and 50m, respectively, corresponding to an average hydraulic gradient of 0.01.
For the solute transport model, it was assumed that the tracer was released uniformly over the left boundary of the study area for ten days with an initial concentration of 3000 mg/L. The simulation time period was set to 160 days, divided into 32 equal time steps. The initial tracer concentration over the whole area was set to 0.
For the resistivity forward model, the top of the buffer is set as an insulating boundary condition, while the remaining boundaries are assumed to be zero potential boundaries. Since the resistivity forward model requires knowledge of the conductivity field, a lithologic physical relationship (equations 4 and 5) is employed to relate the tracer concentration calculated by the solute transport model to conductivity. The relevant parameters in all lithologic physical relationships (e.g., cementation index) are assumed to be known, the values of which are provided in table 1.
Table 1 ideal tracer experiment parameter settings
Hypothetical observations were generated by running a forward model using the referenced K and fringing fields, simulating the context of collecting data from a real field survey. Five boreholes were placed in the aquifer, see (a) in fig. 2. For each borehole, tracer concentrations can be measured at six depth levels, 3.5, 4.5, 5.5, 6.5, 7.5 and 8.5 meters, respectively. To record ERT potential responses caused by tracer migration, 61 ERT electrodes were placed at the surface and 30 electrodes were placed at the locations of the concentration sampling wells. The electrodes were mounted in horizontal and drilled holes at intervals of 0.5 meters and 1 meter, respectively. Current injections of 1A and-1A were performed in succession, potential data were collected using a dipole-dipole configuration, and a total of 704 measurements were obtained for each ERT investigation. The observation was continued for 60 days, and tracer concentration and potential signals were collected every 5 days. A total of 30×12=360 concentration data and 704×12= 8,448 potential data were obtained by borehole-based sampling and ERT investigation. Both sets of hypothetical observations were perturbed by gaussian random noise with standard deviations of 5% and 15% of the mean of the concentration and potential data, respectively.
A series of numerical cases were set up to investigate the benefits of improving the accuracy of solute transport prediction by jointly estimating the spatially heterogeneous permeability coefficient and the fringing field, as well as increasing ERT data. Table 2 lists four cases with different types of data and different prior assumptions. Case 1 assumes that the dispersion is homogeneous and only the tracer concentration data is used to jointly estimate K and dispersion. In case 2, the heterogeneity and scale dependence of the dispersion are considered. In case 3 ERT data is combined, while assuming that the dispersion is homogeneous. Case 4 estimates K and heterogeneous dispersion simultaneously by fusing the multi-source data. Since case 1 and case 3 estimate the homogeneous dispersion, the range of the sum anisotropy ratio is given for both cases, respectively, as a priori information on the homogeneous dispersion.
Table 2a priori information for four cases
Fig. 3 shows the estimated ln K and dispersion fields for case 1 and case 2, while fig. 4 shows the results of the estimation for case 3 and case 4. In fig. 3, (a), (b), (c) are the lnk, lnα l and lnα t fields, respectively, estimated in case 1; (d) (e) and (f) are the lnk, lnα l and lnα t fields, respectively, estimated for case 2; (g) (h), (i) are the reference lnK, lnα l and lnα t fields, respectively. In fig. 4, (a), (b), (c) are the lnk, lnα l and lnα t fields, respectively, estimated for case 3; (d) (e), (f) are the lnk, lnα l and lnα t fields, respectively, estimated for case 4; (g) (h), (i) are the reference lnK, lnα l and lnα t fields, respectively. The accuracy of the estimation results was evaluated using Root Mean Square Error (RMSE):
（7）
Where Nu represents the number, x and Representing the actual and estimated values of the unknown parameter, respectively. Table 3 lists the RMSE for each case.
TABLE 3 RMSE calculated for four cases
The advantages of heterogeneous dispersion and incorporation into ERT data are discussed in terms of the above calculations.
Fig. 3 compares the characterization results assuming spatial homogeneity and spatial variation of the dispersion based on tracer concentration data alone (i.e., case 1 and case 2). In case 1, the information about the diffusion of solute transport contained in the tracer concentration observation data is assimilated mainly by adjusting the spatial mode of the ln K field, since the spatial variation of the dispersion is not considered. In other words, the estimated permeability field compensates for the lack of spatial variability in the dispersion in the process of jointly adjusting K and dispersion to fit the tracer concentration data. Thus, there is a large difference between the estimated ln K field and the reference field. Conversely, when considering the inhomogeneity of the dispersion (i.e. case 2), the estimated ln K field is improved to some extent, the ln K depicted in case 2 is closer to the reference field (e.g. spatial pattern within the dashed ellipse in fig. 3). And, RMSE of ln K improved from 0.81 to 0.74 for case 1 (as in table 3).
In case 3 and case 4, the tracer concentration and the potential data of ERT investigation were assimilated simultaneously. The corresponding estimated parameter fields are shown in fig. 4. In case 3, homogenous dispersion was considered. The resolution of the inverted ln K image is limited due to the inadequate assumption of the spatial distribution of the dispersion. In case 4, the spatial variability of the dispersion is considered, the resolution of the obtained ln K image is significantly improved, the spatial structure is closer to the reference field, and RMSE is significantly reduced.
The benefits of incorporating ERT data in joint inversion K and dispersion were next explored. When assuming a homogeneous distribution of the fringing fields (i.e., case 1 and case 3), the ln K field estimated using the multisource data (case 3) is close to the ln K field estimated using only the tracer concentration data (case 1). In both cases, the estimated ln K field only macroscopically reproduces the dominant spatial pattern of the reference ln K field. The RMSE for case 1 was 0.81 and case 3 was 0.78. As for the identified dispersion field, in case 1, the estimated longitudinal and transverse dispersions were 0.81 meters and 0.13 meters, respectively. In case 3, the estimated longitudinal and transverse dispersions were 0.77 meters and 0.14 meters, respectively. The estimated longitudinal dispersion of these two cases is relatively small compared to the average value of the reference ln K field of 1.08 meters. This is because the tracer has not yet completely reached the right boundary of the aquifer until the last observation time (i.e. day 60). In both cases, the scale effect of the dispersion is not considered, and the characteristic that the dispersion increases with time (or migration distance) is ignored. Furthermore, since the observed data is assimilated primarily by the adjustment of the ln K field, the determined dispersion values in case 1 and case 3 are not very different.
Adding ERT data can significantly improve the accuracy of the characterization of K and dispersion when considering the heterogeneity and scale effects of dispersion (i.e., case 2 and case 4). Fig. 5 shows a comparison between true ln K and dispersion values and an estimation value, where (a), (b), (c) are the true ln K, lnα l, and lnα t fields of case 2, respectively; (d) (e) and (f) are the actual lnK, lnα l and lnα t fields of case 4, respectively. Although the estimated ln K field in case 2 can capture large scale patterns in the reference ln K field, some fine features are missing (as in fig. 3). Furthermore, fig. 5 shows that the specific ln K values in each grid of the study area in case 2 do not fit well with the true values, which results in a relatively large RMSE for ln K. In contrast, when the tracer concentration and ERT data (i.e., case 4) are used simultaneously, the accuracy of the estimated ln K field is significantly improved. The ln K field of case 4 is highly accurate in characterizing the dominant spatial mode of the reference field and the fine scale features. The RMSE of ln K was reduced to 0.58, which was the smallest in four cases. For dispersion, in case 2, although the estimated lnα l field captures the dominant spatial mode and scale effect features in the reference field, some fine scale features are not fully reproduced. As for lnα t, since α l and the anisotropy ratio λ are poorly characterized, it is estimated that lnα t field deviates significantly from the reference field. However, adding ERT data helps better characterize the heterogeneous distribution of dispersions. The lnα l and lnα t fields depicted in case 4 show spatial modes that are more similar to the reference field. Thus, comparison of these four cases shows that assimilation of multi-source data only helps to jointly estimate K and the fringing field when fringing non-uniformity is considered.
The advantages of adding ERT data and jointly estimating spatial heterogeneous dispersion are further illustrated by solute transport using K and dispersion fields estimated in four cases. Fig. 6 shows the concentration profile of the reference and simulated tracers at 80 days, where (a) is the tracer plume profile simulated using the reference K and the fringing fields, (b) - (e) are the tracer plume profiles simulated using the K and fringing fields estimated using cases 1-4, respectively, (f) - (i) are the residual fields between the tracer plume concentration profile simulated for cases 1-4 and the reference tracer plume concentration profile. In four cases, with the same observation, the tracer feathers simulation results using spatially heterogeneous dispersion are better than the simulation results using spatially homogeneous dispersion (compare cases 1, 3 with cases 2, 4 in fig. 6). This demonstrates the importance of considering the spatial heterogeneity of the dispersion.
Regarding the addition of ERT data, the simulated tracer plume concentration profile at 80 days, taking into account the multisource information in case 3, was not significantly improved over case 1, indicating that ERT data is not necessarily beneficial for solute transport simulation when considering homogeneous dispersion. That is, adding geophysical data does enhance the data assimilation process, but if homogeneous dispersion is considered, the predictive power of the model is not guaranteed to be improved. Conversely, blending ERT data has significant advantages when considering heterogeneous dispersion. In case 4, the tracer plume concentration profile predicted using the multi-source data is closest to the reference tracer plume concentration profile in all four cases with very little residual. These findings indicate that the additional ERT data can only be effective in improving the joint inversion method, improving the simulation accuracy of solute transport, when considering the appropriate assumption of dispersion (inhomogeneity).
Based on the same technical concept as the method embodiment, the invention also provides a permeability coefficient and dispersion recognition system integrating concentration and conductivity, which comprises the following steps:
The analog data acquisition module is used for sampling from prior distribution to generate N r groups of permeability coefficient K, longitudinal dispersion alpha l and transverse dispersion alpha t fields;
The concentration deduction module operates an underground water flow forward model according to N r permeability coefficient K fields to obtain N r stable flow fields, and operates an underground water solute transport model according to N r groups of longitudinal dispersion alpha l and transverse dispersion alpha t fields corresponding to the permeability coefficient K fields to obtain N r concentration distribution fields at all observation moments;
The potential deduction module converts N r concentration distribution fields into N r conductivity sigma fields by using a lithology physical model, and operates a resistivity forward model according to the conductivity sigma fields to obtain ERT potential data at all observation moments;
The inversion updating module is used for inputting the measured observation point dynamic concentration data in the field and ERT potential data obtained by geophysical investigation, together with the concentration distribution field and ERT potential data obtained by the concentration deduction module and the potential deduction module, into a multi-data assimilation set smoother ESMDA inversion algorithm, and obtaining an permeation coefficient K, a longitudinal dispersion alpha l and a transverse dispersion alpha t field after inversion updating through data assimilation;
And the iteration control module repeatedly calls the concentration deduction module, the potential deduction module and the inversion updating module to carry out iteration treatment by using the permeability coefficient K, the longitudinal dispersity alpha l and the transverse dispersity alpha t field data after inversion updating until reaching the specified maximum iteration turn, and finally updating to obtain the permeability coefficient K, the longitudinal dispersity alpha l and the transverse dispersity alpha t field which are the optimal estimated fields.
The present invention also provides a computer device comprising: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, which when executed by the processors, implement the steps of the permeability coefficient and dispersion identification method of fusion concentration and conductivity as described above.
The present invention also provides a computer readable storage medium having stored thereon a computer program which when executed by a processor realizes the steps of the permeation coefficient and dispersion identification method of fusion concentration and conductivity as described above.
It will be appreciated by those skilled in the art that embodiments of the invention may be provided as a method, system, computer device, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The invention is described with reference to flow charts of methods according to embodiments of the invention. It will be understood that each flow in the flowchart, and combinations of flows in the flowchart, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create a system for implementing the functions specified in the flowchart flow or flows.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows.
Claims (10)
1. A method for identifying permeability coefficient and dispersion of fusion concentration and conductivity, comprising the steps of:
(1) Sampling from the prior distribution to generate N r groups of permeability coefficients K, longitudinal dispersion alpha l and transverse dispersion alpha t fields;
(2) Operating an underground water flow forward model according to N r permeability coefficient K fields to obtain N r stable flow fields, and operating an underground water solute transport model according to N r groups of longitudinal dispersion alpha l and transverse dispersion alpha t fields corresponding to the permeability coefficient K fields to obtain N r concentration distribution fields at all observation moments;
(3) Converting N r concentration distribution fields into N r conductivity sigma fields by using a lithology physical model, and acquiring ERT potential data at all observation moments according to a resistivity forward model operated by the conductivity sigma fields;
(4) The measured observation point dynamic concentration data in the field and ERT potential data obtained by geophysical investigation are input into a multi-data assimilation set smoother ESMDA inversion algorithm together with the concentration distribution field and ERT potential data obtained by deduction in the steps (3) and (4), and the permeability coefficient K, the longitudinal dispersity alpha l and the transverse dispersity alpha t field after inversion updating are obtained through data assimilation;
(5) And (3) repeating the operations of the steps (2) - (4) by using the updated permeability coefficient K, the longitudinal dispersion alpha l and the transverse dispersion alpha t field by inversion until the iteration times reach the specified maximum iteration rounds, and finally updating the obtained permeability coefficient K, the longitudinal dispersion alpha l and the transverse dispersion alpha t field to obtain the optimal estimated field.
2. The method according to claim 1, wherein in the step (1), a gaussian-based gaussian generation method is used to generate a K field of permeability coefficients conforming to a gaussian distribution; the longitudinal dispersion alpha l field is formed by overlapping and combining a Gaussian distribution field and a linear model which is related to the distance along the water flow direction; the transverse dispersion α t field is obtained by multiplying the anisotropy ratio λ, which is a linear model that is related to distance along the direction of water flow, by the longitudinal dispersion α l.
3. The method of claim 1, wherein in step (2), the groundwater flow forward model is expressed as:
，
wherein K is the permeability coefficient, and h is the hydraulic head.
4. The method of claim 1, wherein in step (2), the groundwater solute transport model is represented as:
，
wherein θ is the porosity, D is the hydrodynamic diffusion tensor, C is the solute concentration, q represents the flow, and Darcy's law is adopted Calculating, wherein h is a hydraulic head, t represents time, and a calculation formula of the hydrodynamic dispersion tensor D is as follows:
，
Wherein v represents seepage velocity, and the calculation formula is V i represents the component of the velocity vector in the i-direction, v j represents the component of the velocity vector in the j-direction,/>Is Kronecker sign, 1 when i=j, otherwise 0, d m represents the diffusion coefficient, α represents the dispersion in the main direction, longitudinal dispersion is taken as the dispersion in the main direction,/>Λ is the anisotropic ratio.
5. The method according to claim 1, wherein in the step (3), the lithology physical model is expressed as:
，
Wherein σ is bulk conductivity, θ is porosity, m represents a cementation index, n represents a saturation index, S w is water saturation, and σ w is pore fluid conductivity.
6. The method of claim 5, wherein the pore fluid conductivity σ w is calculated as follows:
，
Where F is Faraday constant, i represents the number of the ith ion in the pore fluid, k ions are total, u i represents the electric mobility of ion i, C i is the molar concentration of ion i, and z i represents the valence of ion i.
7. The method according to claim 1, wherein in the step (4), the resistivity forward model is expressed as:
，
Wherein, Is of potential,/>Is a dirac function,/>Is a single current electrode, I is the amperage.
8. A permeability coefficient and dispersion identification system that fuses concentration and conductivity, comprising:
The analog data acquisition module is used for sampling from prior distribution to generate N r groups of permeability coefficient K, longitudinal dispersion alpha l and transverse dispersion alpha t fields;
The concentration deduction module operates an underground water flow forward model according to N r permeability coefficient K fields to obtain N r stable flow fields, and operates an underground water solute transport model according to N r groups of longitudinal dispersion alpha l and transverse dispersion alpha t fields corresponding to the permeability coefficient K fields to obtain N r concentration distribution fields at all observation moments;
The potential deduction module converts N r concentration distribution fields into N r conductivity sigma fields by using a lithology physical model, and operates a resistivity forward model according to the conductivity sigma fields to obtain ERT potential data at all observation moments;
The inversion updating module is used for inputting the measured observation point dynamic concentration data in the field and ERT potential data obtained by geophysical investigation, together with the concentration distribution field and ERT potential data obtained by the concentration deduction module and the potential deduction module, into a multi-data assimilation set smoother ESMDA inversion algorithm, and obtaining an permeation coefficient K, a longitudinal dispersion alpha l and a transverse dispersion alpha t field after inversion updating through data assimilation;
And the iteration control module repeatedly calls the concentration deduction module, the potential deduction module and the inversion updating module to carry out iteration treatment by using the permeability coefficient K, the longitudinal dispersity alpha l and the transverse dispersity alpha t field data after inversion updating until reaching the specified maximum iteration turn, and finally updating to obtain the permeability coefficient K, the longitudinal dispersity alpha l and the transverse dispersity alpha t field which are the optimal estimated fields.
9. A computer device, comprising:
one or more processors;
A memory; and
One or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, which when executed by the processor, implement the steps of the fusion concentration and conductivity permeation coefficient and dispersion identification method of any one of claims 1-7.
10. A computer readable storage medium, on which a computer program is stored, characterized in that the computer program, when being executed by a processor, carries out the steps of the method for identifying permeability coefficient and dispersion of fusion concentration and conductivity according to any one of claims 1-7.
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