Method for reaction time-related calibration of the kf value

Abstract

Methods for calibrating k f -values ​​of porous aquifers characterized by the fact that the reaction time is calculated from the change in concentration of a substance dissolved in the groundwater between two groundwater monitoring wells or points under consideration in a porous aquifer and this is equated to the flow time related to the effective porosity, whereupon the k f The value is determined using the following equation: kf = − LGWM ⋅ k ⋅ neff ln ( c GWMU c GWMO ) ⋅ I with k f k f -value in m / d L GWM Distance between the upstream and downstream groundwater monitoring wells in m k First-order reaction rate in 1 / d n eff effective porosity C GWMU Concentration at the downstream groundwater monitoring station C GWMO Concentration at the upstream groundwater monitoring station Hydraulic gradient I = dh / L GWM

Description

[0001] The invention relates to a method for the reaction time-related calibration of k f -values. The method is suitable for use in model-based forecasting and management of groundwater based on quantity and quality, for in situ groundwater treatment, and for use in the treatment of groundwater containing contaminants, and thus for in situ groundwater remediation.

[0002] The k f -value according to DARCY (k f -value, permeability coefficient, permeability coefficient, filtration coefficient, saturated hydraulic conductivity, saturated water conductivity) with the unit [m / s] is generally defined as the quotient of filter velocity v f with the unit [m / s] and the corresponding hydraulic gradient I without a unit. The filter velocity v f is calculated from the quotient of the flow rate Q for water with the unit [m 3 / s] and the area flowed through with the unit [m 2 ]. The k f The value depends on the physical properties of the water (density, viscosity, temperature) and the properties of the aquifer (pores, fractures). It is determined using the Darcy equation (Darcy's law): kf=QF⋅I with Q = flow rate [m 3 / s], F = flow area [m 2 ] and I = hydraulic gradient.

[0003] The basic transport and migration processes in groundwater as well as the modeling methods used for this purpose can be found, for example, in Luckner / Schestakow (1991).

[0004] If groundwater quantity and quality are to be predicted within the scope of the above-mentioned application areas, this is done based on numerical groundwater models. The goal of such modeling is to simulate groundwater flow and transport processes as accurately as possible. First, a site-specific hydrogeological model is created, on which the numerical groundwater flow model is created. After calibration, the model is converted into a numerical groundwater transport model, which must also be calibrated.

[0005] According to DVGW W 107 (2016): Structure and application of numerical groundwater models in water abstraction areas, groundwater models describe the "relationship between volume, material and heat flows and observable quantities such as groundwater levels, concentrations and temperatures. Since these flows cannot be determined directly locally in their spatial distribution, but only summarily over a certain area, the relationship between the non-directly observable flows and the observed quantities is established in the calibration process. Measures for the deviations between measured and calculated values ​​(usually standpipe levels or concentrations) are used as quality criteria.Since the spatial and temporal distribution of the observed values ​​results from the spatial distribution of the flows and the parameters involved, these are varied during calibration, integrating the basic assumptions of the hydrogeological model, until certain quality specifications are achieved. A distinction must be made between steady-state and transient calibration according to the definitions in this worksheet (see 3.3). Where possible, the quality specifications should be agreed upon in advance, taking into account the associated cost aspects. If the measurement data are inaccurate or insufficient to capture the complex real-world conditions, it is not possible to achieve the agreed quality specifications.Deviations from the specifications of an otherwise adequate hydrogeological model therefore primarily arise from heterogeneities in pore and especially in hard rock aquifers that cannot be captured in detail.

[0006] During the calibration process, system parameters or, in special cases, boundary conditions are varied. Changing both in a single calibration step will not lead to a clear result. The most important system parameters that can be determined during calibration are: • Permeability coefficients (k f -value according to DARCY) • Leakage coefficients at the boundary conditions of the third kind • Storage coefficients (for transient models) • Transport parameters (e.g. flow-effective porosity, dispersivity, sorption, degradation)"

[0007] When applying the above-mentioned state of the art, significant discrepancies can sometimes be observed between the values ​​calculated using numerical groundwater models and those determined at groundwater monitoring points. This particularly affects the concentrations of dissolved substances or contaminants in the groundwater. The main causes for this are identified in DVGW W 107 (2016): 1. The dependent parameters contained in the numerical groundwater models (see the paragraph before the "Permeability Coefficient" section). Dependent parameters are linked to each other by multiplication, division, or summation, or by their complex effect on the result. There are an infinite number of value combinations for these parameters that can produce a calculated value, such as groundwater standpipe levels or groundwater concentration. 2. The heterogeneity in the pore aquifer that cannot be captured in detail.

[0008] To improve the reason mentioned under 1, it is necessary to reduce the number of parameters to be calibrated. This is achieved using numerical groundwater transport models, preferably by determining the transport parameters of substance storage, microbial degradation, and substance transformation at the laboratory scale.

[0009] For example, Dost (2020) presents a laboratory management system (LMS) for the process-oriented planning, implementation, and evaluation of laboratory experiments to determine source and transport terms. This system enables the quantification of representative parameters of material storage, microbial degradation, and material transformation for the soil and groundwater sector, independent of the user's level of knowledge. The focus is on demonstrating the transferability of the parameters quantified at the laboratory scale to the field. Accordingly, Dost (2020) presents the developed equation (38) specifically on page 104, which enables an estimation of the microbial degradation rate from the results of groundwater analyses from groundwater monitoring wells, with the aim of achieving direct comparability with the microbial degradation rates quantified at the laboratory scale.

[0010] For improved capture of heterogeneity (see second cause), P. Keilholz, A. et al. (2018) Renz, J. Zwinger, and S. Rothermel: Model-based groundwater monitoring at Munich Airport, 14th Bavarian Water Days, on November 14-15, 2018 in Augsburg, presents a method known as "data fusion" for the automated blending of point-based measurement data with a spatial groundwater model. The model uncertainty is reduced through the use of statistical data evaluations. The result is a significant reduction in the differences between the groundwater levels calculated using a numerical groundwater transport model and those measured.

[0011] The known methods for calibrating numerical groundwater transport models have the following disadvantages: - The number of dependent parameters to be calibrated remains unchanged. This means that the permeability coefficient (kf -value according to Darcy) cannot be calibrated by including other methods. - For the calibration of the k f By calculating the Darcy permeability coefficient relative to the measured value of a groundwater measuring point (pressure head), the calibration can be objectively verified by the deviation between the calculated value and the measured value. However, this does not apply to its spatial validity, which depends heavily on the heterogeneity of the aquifer being studied.

[0012] The object of the present invention is to provide a method for calibrating the k f-value that is independent of the other dependent parameters of the numerical groundwater flow model and also homogenizes the heterogeneity of the aquifer between the groundwater measuring points under consideration or the points to be determined. This means that the objectification of the calibration of the k that has been achieved so far within the framework of the calibration of the geohydraulic model with reference to the measured value of a groundwater measuring point (pressure head) is no longer sufficient. f -value is extended to the area between two groundwater measuring points or points to be determined.

[0013] The object is achieved according to the invention with the method according to claim 1. Advantageous embodiments can be found in the dependent claims.

[0014] The solution to the problem is based on the realization that the spatial calibration of the k f-value is hardly possible due to the multitude and interdependence of the parameters in models that attempt to represent these causalities. Surprisingly, a phenomenological approach has proven successful, based on the idea that the k f -value has a temporal reference, but no relation to spatial heterogeneity. In contrast, the reduction in the concentration of substances or contaminants dissolved in groundwater depends on the effect of spatial heterogeneity and also on time. Accordingly, the spatial calibration of the k f -value the first-order reaction rate in 1 / d, which also has this time reference.

[0015] The first-order reaction rate is to be understood here in the reaction kinetic sense. The first-order reaction rate is the proportionality factor that describes how the change in concentration over time depends on the initial concentration. The first-order reaction rate can thus be determined from knowledge of the initial concentration, the current concentration, and the elapsed time (reaction time).

[0016] According to the invention, the basic approach to calibrating the k f The method of calculating the reaction time, taking into account the distance between the measuring points, is equated with the flow time between the two measuring points based on the effective porosity. The reaction time is determined from the change in concentration of a substance between two groundwater measuring points or points of interest in a porous aquifer. The direct calculation of the k f-value is determined according to equation (2). kf=−LGWM⋅k⋅neffln(cGWMUcGWMO)⋅I with k f k f -value in m / d L GWM Distance between the upstream and downstream groundwater measuring point in m (see Fig. 1) k 1st order reaction rate in 1 / d n eff effective porosity C GWMU Concentration at the downstream groundwater measuring point (see Fig. 1) C GWMO Concentration at the upstream groundwater measuring point (see Fig. 1) I hydraulic gradient I = dh / L GWM (see Fig. 1)

[0017] The groundwater pressure head difference (dh) for determining the hydraulic gradient is in Fig. 1 is explained schematically.

[0018] The determination of the first-order microbial degradation rate as the first-order reaction rate k is preferably carried out using state-of-the-art methods. The method described in DE 10 2009 038 017 B4 is particularly suitable. This publication discloses a method for determining the first-order microbial degradation rate in a near-natural laboratory experiment. The term "near-natural" is to be understood here in the sense of DE 10 2009 038 017 B4.Order in fluid-saturated or partially fluid-saturated porous media of the soil and groundwater sector according to DE 10 2009 038 017 B4 provides that a water sample to be examined flows successively through several series-connected, open or closed and intermittently operated reactors filled with the fluid-saturated or partially fluid-saturated porous medium to be examined in natural or disturbed storage, in order to exchange one pore volume in each case after observing a standstill time, and that pore water samples are taken during the exchange or after the exchange of the pore volume, which are analyzed for environmental parameters and substance concentrations, whereby the standstill time between the pore volume exchanges is dimensioned such that the pore water samples show a significant concentration difference between two time steps of the ingredients to be examined in the taken pore water samples.During the exchange phase, the water sample to be examined flows successively through several reactors connected in series.

[0019] The reactors are filled with fluid-saturated or partially fluid-saturated porous media. The reactors preferably contain a slightly contaminated substrate from a soil or aquifer.

[0020] The porous medium can be filled into the reactors in either natural or disturbed storage. Disturbed storage refers to the filling with previously extracted porous medium in an artificial layered configuration. When filling with porous media in natural storage, an exact replica of the natural layered configuration is adopted; for this purpose, the substrate is extracted, for example, using a liner core drilling (for a detailed procedure, see DE 10 2009 038 017 B4).

[0021] In another approach, the first-order denitrification rate is used as the first-order reaction rate. The first-order denitrification rate is preferably determined analogously to the first-order microbial degradation rate using a method as described in DE 10 2009 038 017 B4.

[0022] Another approach involves using the first-order sulfate reduction rate for the reaction rate. The first-order sulfate reduction rate is preferably determined analogously to the first-order microbial degradation rate, using a method as described in DE 10 2009 038 017 B4.

[0023] Another method for determining the first-order reaction rate is component-specific isotope analysis. This method is described, for example, in Eisenmann (2010) or Hunkeler (US-EPA, 2008), and in a more detailed, preferred procedure in Haderlein (2015). It is based on the fact that different isotopes of an element are utilized to varying degrees in biological degradation processes over time. The first-order reaction rate can be determined from the change in the isotope ratio over time using a method such as that described in DE 10 2009 038 017 B4.

[0024] In another approach, the first-order reaction rate is determined based on the half-life of radionuclides. The first-order reaction rate is preferably determined analogously to the first-order microbial degradation rate, using a method as described in DE 10 2009 038 017 B4.

[0025] Effective porosity is often confused with drainable porosity. Drainable porosity correlates with the k f -value. The lower the k f The higher the value, the lower the drainable porosity and vice versa. Drainable porosity is used to calculate the volume of water that flows from the lowered area into the groundwater when the groundwater surface is lowered (see Fig. 2).

[0026] The effective porosity quantifies that portion of the pore volume that characterizes the heterogeneity of an aquifer. The lower the heterogeneity of an aquifer, the greater the effective porosity, and vice versa. The effective porosity cannot be greater than the total porosity. The difference between total porosity and effective porosity is referred to as immobile porosity. In this porosity fraction, groundwater flows much more slowly than in the effective porosity fraction. Fig.3, the relationship between effective and immobile porosity and the heterogeneity of an aquifer was schematically illustrated using a representative elementary volume (REV). The REV should be large compared to the characteristic dimensions of the heterogeneity of the groundwater area to be monitored (e.g., pore sizes) in order to be able to introduce locally statistical mean values ​​for the physical and chemical parameters or measured values. On the other hand, the REV must be small compared to the characteristic dimensions of the entire groundwater area to be considered in order to be able to consider the locally statistical mean values ​​as differentially small field quantities (Luckner / Schestakow, 1991). The REV is figuratively a cube with an edge length of 1 (see Fig.3). The corresponding length dimension is determined by the heterogeneity of the groundwater area under consideration. Thus, the edge length can be 1 cm for silts and clays, 1 dm to 1 m for sands and gravels, and 1 km for fractured aquifers.

[0027] Determining the effective porosity n eff is carried out by evaluating tracer experiments, from which the hydrodynamic dispersivity and the mass transfer coefficient (exchange rate between n eff and n im) can be determined. It is assumed that the tracer breakthrough curve for a porous system without immobile porosity corresponds to a Gaussian normal distribution. This means that the tracer breakthrough curve is mirror-symmetrical with respect to the 50% passage. When displaying the tracer breakthrough curve in a Gaussian probability grid, the straight part of the tracer breakthrough curve corresponds to the concentration curve influenced by the hydraulically effective porosity component. The second, curved part of the curve, which deviates from the mirror-symmetrical curve, is influenced by the hydraulically less effective porosity component (Nitsche, 1981). The first, straight curve is extended by a straight line, with the help of which the influence of the hydraulically less effective pore space (deviation from mirror symmetry) is graphically visible. From this straight line, the t 50-point at which 50% of the initial tracer concentration has been broken through (see Fig. 4). The effective porosity is determined according to equation (3). Based on this evaluation method, M. Rostan (see (Rostan, 2011)) developed a digital evaluation sheet with which both the effective porosity and dispersity can be determined. neff=vfL*t50 with n eff effective porosity v f Filter speed according to Darcy in m / s L Length of the tracer flow path in m t 50 Time at which 50% of the initial tracer concentration has been broken through in seconds (see Fig. 4)

[0028] Preferably, the calibration of the k f -value as follows (for more details see Fig. 5): Based on the hydraulically calibrated groundwater flow model, the groundwater transport model is constructed by defining the time steps for mass transport. Subsequently, the groundwater monitoring points suitable for reaction- or flow-time-related model calibration are selected based on the following additional criteria: • The groundwater measuring points to be used must be located within a groundwater flow path (see Fig. 6). • In hydraulically unsteady conditions, a flow-time-related time offset of the measured values ​​between the two groundwater measuring points under consideration must be taken into account in accordance with DIN 38 402-13: 2021-12. Figures Fig.1: Schematically shown vertical section through an aquifer with a groundwater flow direction from left to right, marked groundwater surface (V) and the groundwater pressure head difference (dh) acting between the two groundwater measuring points Fig. 2: Schematically shown vertical section through an aquifer with lowered groundwater surface and inflowing groundwater Fig. 3: Schematically depicted relationship between effective porosity and immobile porosity to the heterogeneity of an aquifer using a representative elementary volume (REV): left figure: REV cube with an edge length of 1; middle figure: section through the REV cube for a homogeneous aquifer in which the effective porosity n eff is equal to the total porosity n; right figure: section through the REV cube for a highly heterogeneous aquifer in which neff due to the immobile porosity n im is reduced and thus n = n eff + n im is. Fig. 4: Exemplary tracer test evaluation according to Nitsche (1981), (C* = normalized tracer concentration at time t; C*= Ct / C0; C0 = input concentration of the tracer; Ct = tracer concentration at the end of the flow path at time t). Fig. 5: Schematically illustrated workflow for the reaction time-related calibration of the k f -value; geol. GB: geological validity range of the k f -value Fig. 6: Schematically represented hydroisohypse plan with lines of equal groundwater pressure levels (136) and the resulting groundwater flow direction from hydroisohypse 136 via groundwater isohypse 135 to groundwater hydroisohypse 134; only GWM A and GWM B lie within a groundwater flow path Example

[0029] The groundwater flow path between the groundwater measuring points GWM 1 and GWM 2 was used with the following parameters: L GWM 384 m k 0,0026 1 / d n eff 0,211 C GWM2 1.60 µg / L C GWM1 5.20 µg / L V f 0.30 m / d I 0.0030 (dH = 1.15 m) Inserted into equation (2) it was calculated: k f = 7.15 E-04 m / s In comparison, the model calibration carried out for 2018 for the aquifer in which the two groundwater monitoring wells GWM 3 and GWM 6 are located resulted in a k f -value of 3.83 E-05 m / s.

[0030] The k calculated using equation (2) f -value of k f = 7.15 E-04 m / s was used in the geohydraulic model for this area. The model run yielded the following differences between calculated and measured groundwater pressure heads and distance velocities for the two groundwater monitoring wells, which can be seen in Table 1 in comparison to the hydraulic calibration. Table 1: Comparison of the differences achieved as a result of the hydraulic and reaction time calibration of the kf value between the groundwater pressure heads (dh) measured and calculated at GWM 6 and GWM 3 and the calculated distance velocities (va) Groundwater measuring point yes hydraulische Kalibrierung V a hydraulische Kalibrierung yes reaktionszeitbezogene Kalibrierung Va reaktionszeitbezogene Kalibrierung GWM 3 4 cm 0.27 m / d -34 cm 0.8 m / d GWM 6 29 cm 65 cm

[0031] The concentration calculated for the GWM 6 using the distance velocities from the hydraulic and reaction time calibration (actual value) was compared with the concentrations obtained during the 2018 groundwater monitoring (target value). The results are shown in Table 2. Table 2: Target-actual comparison of the differences between the measured and calculated PSM concentrations at the GWM 6 as a result of the hydraulic and reaction time-related calibration of the kf value Groundwater measuring point C hydraulische Kalibrierung C reaktionszeitbezogene Kalibrierung GWM 6 - Target 1.60 µg / L 1.60 µg / L GWM 6 - Is < 0.05 µg / L 1.58 µg / L Deviation from the target value 96,88 % 1,25 %

[0032] Fig.Figure 5 shows a schematic implementation of the procedure for reaction time-related calibration of the k f -value, as applied in the present embodiment. Reference symbols and abbreviations geol. GB geological scope of the k f -value GWM groundwater measuring point G WM A, ...B, ...C Groundwater measuring points A, B and C GWMo upper groundwater measuring point (seen in the direction of groundwater flow) GWMu lower groundwater measuring point (seen in the direction of groundwater flow) k f -value permeability coefficient according to DARCY L GWM Distance between groundwater measuring points n Total porosity n eff effective porosity n im immobile porosity RB boundary conditions REV representative elementary volume 134, 135, 136 Hydroisohypses 134, 135 and 136 ∇ Groundwater surface Cited non-patent literature

[0033] DOST, Philipp: Process-oriented planning, implementation, and evaluation of laboratory experiments for source and transport term determination, Dresden University of Technology, Faculty of Environmental Sciences, Dissertation, 2020, pp. 1-150. URL: https: / / nbnresolving.org / urn:nbn:de:bsz:14-qucosa2-725277 [accessed on September 19, 2023]

[0034] Ludwig Luckner, Vsevolod M. Shestakov; Migration Processes in the Soil and Groundwater Zone, CRC Press LLC, 1991 ISBN: 9780873713023, EAN: 9780873713023

[0035] Rostan, M.; Investigation of the suitability of schwertmannite agglomerates for arsenic removal from groundwater, diploma thesis, Technical University of Dresden, Institute of Groundwater Management (2012)

[0036] Nitsche, C.; Contribution to mathematical modeling and digital simulation of mass transport, exchange, storage, and transformation processes in the aeration zone, dissertation, Technical University of Dresden (1981)

[0037] Keilholz, A., Renz, J. Zwinger, and S. Rothermel: Model-based groundwater monitoring at Munich Airport, 14th Bavarian Water Days, Proceedings, 2018

[0038] Eisenmann, H.; Fischer, A.; Isotope investigations in contaminated site assessment. In: V. Franzius, T. Gerhold, M. Altenbockum (Eds.), Handbook of Contaminated Site Remediation, (2010).

[0039] US EPA - Hunkeler, D.; Meckenstock, R.U.; Sherwood-Lollar, B.; Schmidt, T.C.; Wilson, J. T. (2008). A guide for assessing biodegradation and source identification of organic ground water contaminants using compound specific isotope analysis (CSIA). EPA 600 / R-08 / 148.

[0040] Prof. Dr. Stefan Haderlein, Dr. Daniel Buchner: Guide to the Determination and Interpretation of Isotopic Fingerprints, Stuttgart, November 27, 2015, Download link: https: / / pudi.lubw.de / detailseite / - / publication / 95237-Leitfaden_zur_Ermittlung_und_Interpretation_isotopischer_Fingerabdrücke.pdf, as of December 8, 2022

Claims

[1] Procedure for calibrating k f -values ​​of porous aquifers characterized by the fact that the reaction time is calculated from the change in concentration of a substance dissolved in the groundwater between two groundwater measuring points or points to be considered in a porous aquifer and this is equated to the flow time related to the effective porosity, whereupon the k f -value is determined using the following equation: kf=−LGWM⋅k⋅neffln(cGWMUcGWMO)⋅I with k f k f -value in m / d L GWM Distance between the upstream and downstream groundwater measuring point in m k 1st order reaction rate in 1 / d n eff effective porosity C GWMU Concentration at the downstream groundwater measuring point C GWMO Concentration at the upstream groundwater measuring point I hydraulic gradient I = dh / LGWM [2] The method according to claim 1, wherein the first-order microbial degradation rate is used for the reaction rate. [3] The process according to claim 1, wherein the first order denitrification rate is used for the reaction rate. [4] The process according to claim 1, wherein the first order sulfate reduction rate is used for the reaction rate. [5] Method according to claim 1, wherein component-specific isotope analysis is used to determine the first-order reaction rate. [6] Method according to claim 1, wherein the half-life of radionuclides is used to determine the first-order reaction rate. [7] Method for determining the k f -value, at least the following steps: a. Determination of the groundwater flow direction, b. Determination of the distance between an upstream groundwater measuring point and a downstream groundwater measuring point, c. Determination of the level difference between the upstream and downstream groundwater measuring points and determination of the hydraulic gradient, d. Determination of the concentration of a substance dissolved in groundwater at the upstream groundwater measuring point and determination of the concentration of the same substance dissolved in groundwater at the downstream groundwater measuring point, e. Determination of the first-order reaction rate, f. Determination of k f -value. [8] Method according to claim 7, characterized by that the upstream and downstream groundwater measuring points are located on the same groundwater flow determined in step a. [9] Method according to claim 7, characterized by that the determination of the hydraulic gradient I according to the formula I=dh / LGWM occurs, with ie height difference between the water levels at the upstream and downstream groundwater measuring point L GWM Distance between the upstream and downstream groundwater measuring point in m [10] Method according to one of claims 7 to 9, characterized by that the determination of the first-order reaction rate is carried out in a near-natural laboratory experiment.

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