DNAPL Simulation Method for Groundwater Coupled with Mathematical Model and Optimization Algorithm

Abstract

This invention provides a method for simulating heavy non-aqueous phase liquids in groundwater by coupling a mathematical model and an optimization algorithm. The steps include: acquiring dynamic change data of groundwater, environmental indicator change data, and DNAPL concentration data; analyzing the hydrogeological conditions of the site and the migration and transformation process of DNAPL pollution; performing simulation based on a coupled multiphase flow and solute transport model; constructing a simulation system coupled with the mathematical model and optimization algorithm; simulating and evaluating the DNAPL transport process in groundwater based on the acquired data; and obtaining simulation results consistent with actual monitoring data. This invention is programmed using Python and uses open-source programs to achieve full-process simulation of different phases of DNAPL pollution. Simultaneously, the model parameters are corrected based on the optimization algorithm, ultimately yielding optimal simulation results consistent with actual monitoring data, laying the foundation for further in-depth DNAPL simulation work.

Description

Technical Field

[0001] This invention relates to the field of groundwater pollution control technology, and more specifically, to a groundwater DNAPL simulation method that couples mathematical models and optimization algorithms. Background Technology

[0002] Dense non-aqueous phase liquids (DNAPLs) are a class of pollutants that have attracted much attention in the field of groundwater pollution. DNAPLs have the following special properties: (1) They are denser than water, which makes the pollutants migrate not only with groundwater in the horizontal direction, but also independently into the depth of the strata in the vertical direction; (2) They have low water solubility, with a small portion of the pollutants dissolving in water, thus presenting a state of multiphase coexistence of free and dissolved phases of DNAPLs, which greatly increases the complexity of pollution; (3) They have low viscosity and low interfacial tension, which promotes the migration of DNAPLs in the groundwater environment; (4) They have low biodegradability, which allows the pollutants to exist in the groundwater environment for a long time, making it difficult to eliminate the risks and hazards.

[0003] For groundwater DNAPLs pollution, accurately understanding the distribution characteristics of DNAPLs in contaminated sites is crucial for reducing remediation costs and improving the targeting of remediation methods, and is essential for formulating remediation plans. Currently, numerous software programs exist for groundwater pollution simulation. For simulating groundwater flow fields and solute transport, there are GMS, MODFLOW, VisualModflow, and FEFLOW, while for simulating multiphase flow of DNAPLs, TOUGH2's T2VOC and TMVOC modules are commonly used. However, two major drawbacks remain: firstly, these commonly used software programs are all commercial and cannot be open-sourced, limiting their application and promotion; secondly, multiphase flow simulation software and solute transport software are independent, making it impossible to unify them into a single platform for simulating multiphase flow of DNAPLs pollution, increasing the difficulty of coupling optimization algorithms. Summary of the Invention

[0004] In view of this, the present invention proposes a groundwater DNAPL simulation method that couples mathematical models and optimization algorithms to solve the problems existing in the prior art.

[0005] To achieve the above objectives, this invention proposes a groundwater DNAPL simulation method that couples a mathematical model and an optimization algorithm, comprising:

[0006] The system acquires dynamic change data of groundwater based on the groundwater online monitoring system, acquires change data of groundwater-related environmental indicators based on the water quality multi-parameter instrument, and acquires DNAPL concentration data of corresponding points based on regular groundwater sample collection and analysis.

[0007] Analyze the hydrogeological conditions of the site and the migration and transformation process of DNAPL contamination.

[0008] The model parameter range was initially estimated, the scenario to be corrected was set, and simulation was performed based on the multiphase flow and solute transport coupling model;

[0009] An optimization algorithm is used to construct a simulation system that couples the mathematical model with the optimization algorithm. Based on the dynamic change data of groundwater, the change data of environmental indicators, and the concentration data of DNAPL, the migration, transformation, and transport processes of DNAPL in groundwater are simulated and evaluated, and simulation results that are consistent with the actual monitoring situation are obtained.

[0010] Optionally, the process of simulating and evaluating the migration, transformation, and transport of DNAPL in groundwater based on the aforementioned groundwater dynamic change data, environmental indicator change data, and DNAPL concentration data includes:

[0011] The DNAPL phase migration process was simulated based on the multiphase flow module of the established simulation system.

[0012] A DNAPL dissolution mass transfer model was constructed, and the dissolution process of the DNAPL phase to the aqueous phase was simulated based on the DNAPL dissolution mass transfer model.

[0013] The migration and reverse diffusion processes of DNAPL were simulated using the groundwater flow field module and the halohydrocarbon dissolved phase transport module of the established simulation system.

[0014] Optionally, in simulating the DNAPL phase migration process based on the multiphase flow model, the release of pollutants, the heterogeneity of the aquifer, the constitutive relationship characterizing the correlation between permeability, saturation, and capillary pressure, as well as the influence of the DNAPL's own properties and the aquifer's permeability on the migration rate are considered.

[0015] Optionally, the DNAPL dissolution mass transfer model includes a REV-scale model and a site-scale model. The REV-scale model is used to obtain the influencing factors and variation patterns of DNAPL dissolution; the site-scale model is used to match the model with field measurement data.

[0016] Optionally, the simulation method for the DNAPL dissolution mass transfer model includes:

[0017] Based on the assumption of local equilibrium, the mass transfer rate is estimated according to the equilibrium distribution relationship to simulate the interphase mass transfer process, or based on the dissolution kinetics, an empirical rate constraint expression is established to simulate the interphase mass transfer process.

[0018] Optionally, the simulation method for the site-scale model includes:

[0019] Based on site size, soil heterogeneity, and NAPL distribution, the effective mass transfer coefficient at the field scale can be corrected, or a power-law relationship between effluent concentration and residual DNAPL mass can be established.

[0020] Optionally, the simulation process of the groundwater flow field model includes:

[0021] Constructing a differential equation for groundwater flow based on Darcy's law;

[0022] The finite difference method is used to solve the differential equation of groundwater flow. The set of discrete points in the simulation area is used to replace the seepage zone, and the difference quotient is used to approximate the differential quotient. The differential equation and its boundary conditions are transformed into a difference equation with the approximate value of the unknown function at the discrete points as the unknown quantity. The difference equation is solved to obtain the approximate value of the solution of the differential equation of groundwater flow at the discrete points.

[0023] The difference equation is embedded in the groundwater flow field module, and the relevant parameters are set according to hydrogeological information during the simulation.

[0024] Optionally, the simulation process of the halohydrocarbon dissolved phase transport model includes:

[0025] Convection-dispersion equations were constructed based on the groundwater flow field model and Fick's law to describe the dual processes of flow and dispersion of dissolved halogenated hydrocarbons in the groundwater system.

[0026] The convection-dispersion equation describes the injection or extraction process of pollutants, while also considering the adsorption process of halogenated hydrocarbons on the soil and the degradation process of halogenated hydrocarbons.

[0027] The convection-dispersion equation is embedded in the halohydrocarbon dissolved phase transport module, and the relevant parameters are set according to information such as pollutant leakage and pollutant properties during simulation.

[0028] Optionally, the process of constructing a simulation system that couples the optimization algorithm with the mathematical model includes:

[0029] The DNAPL migration and transformation simulation model was adapted into a function with the parameters to be determined as dependent variables, and the function was imported into the optimization algorithm model.

[0030] The model parameters are optimized based on the optimization algorithm, and the training is repeated. When the convergence condition is met, the optimal solution output by the coupled model is obtained.

[0031] Optionally, the process of optimizing the model parameters based on the optimization algorithm includes:

[0032] Set constraints and convergence conditions;

[0033] The decision variable parameters are initialized based on the population size to form the first generation population;

[0034] Based on the first-generation population, the DNAPL migration and transformation simulation program was invoked to obtain simulation results;

[0035] Determine whether the simulation results meet the constraints, calculate the objective function value, evaluate each feasible solution, and obtain a new generation population;

[0036] When the convergence condition is met, the optimal solution output by the coupled model is obtained.

[0037] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0038] This invention helps to solve the two major drawbacks of current DNAPL simulations.

[0039] On the one hand, this invention establishes a groundwater DNAPL pollution migration and transformation simulation system based on the Python language, including a multiphase flow module for simulating NAPL phase migration, a groundwater flow field, and a halohydrocarbon dissolved phase transport module, realizing open-source simulation of the entire DNAPL process, which is scalable.

[0040] On the other hand, the simulation system established in this invention, which couples the mathematical model with the optimization algorithm, unifies the simulation of the DNAPL contamination process and the optimization of model parameters on the Python platform, enhancing the convenience of model setup. Most importantly, the introduction of the optimization algorithm can determine the optimal model parameters, thereby ensuring that the simulation prediction results match the actual monitoring data and improving the model's accuracy. Attached Figure Description

[0041] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings:

[0042] Figure 1 This is a schematic diagram of the DNAPL simulation method for groundwater based on optimization algorithms in an embodiment of the present invention;

[0043] Figure 2 This is a schematic diagram of the groundwater online monitoring system in an embodiment of the present invention;

[0044] Figure 3 This is a schematic diagram of the appearance of the Leveline-mini-CTD monitoring device in an embodiment of the present invention;

[0045] Figure 4 This is a schematic diagram of the AP2000 water quality multi-parameter analyzer in an embodiment of the present invention;

[0046] Figure 5 This is a plan view of the simulated area pollution source and observation well in Example 1 of this invention;

[0047] Figure 6 The above are the simulation results of multiphase flow in Case 1 of the present invention.

[0048] Figure 7 This is a schematic diagram of the simulated area in Example 2 of the present invention;

[0049] Figure 8 The figures show a comparison of steady-state simulation results of the groundwater flow field model in the embodiments of the present invention; where (a) is the simulation result of the present invention using the Flopy module, and (b) is the simulation result of the GMS software.

[0050] Figure 9 This is a comparative diagram of the unsteady-state simulation results of the groundwater flow field model in the embodiments of the present invention; where (a) is the simulation result run by the Flopy module in the present invention, and (b), (c), and (d) are the results run by the GMS software;

[0051] Figure 10 This is a schematic diagram of the simulated area in Example 4 of the present invention;

[0052] Figure 11 This is a comparison chart of simulation results in Case 4 of the present invention.

[0053] Figure 12 This is the structural framework of the DNAPL simulation system in the embodiments of the present invention;

[0054] Figure 13 The results are as follows: (a) is the NAPL phase distribution result simulated based on the DNAPL whole process in the embodiments of the present invention, and (b) is the dissolved phase distribution result simulated based on the Flopy module.

[0055] Figure 14 This is the model structure framework of the coupling optimization algorithm in the embodiments of the present invention;

[0056] Figure 15 This is the convergence curve of the objective function (RMSE) of the coupled model in this embodiment of the invention. Detailed Implementation

[0057] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the disclosure to those skilled in the art. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0058] This embodiment proposes a groundwater DNAPL simulation method that couples a mathematical model and an optimization algorithm, such as... Figure 1 As shown, it includes:

[0059] Groundwater flow field monitoring scheme

[0060] (1) Layout of pollution monitoring stations

[0061] The hydrogeological environment of sites contaminated with halogenated hydrocarbons is investigated, and groundwater pollution monitoring stations are selected at several locations to form a monitoring network for the contaminated site. The basic principles for the layout of the groundwater pollution monitoring network are as follows: 1) The monitoring stations are established based on the investigation of the hydrogeochemical environment, pollutant composition, and major pollution sources in the monitoring area; 2) The network should be able to control urban residential areas, industrial and mining areas, and existing and planned water supply sources; 3) The number of monitoring stations should be increased in key investigation areas, such as severely polluted areas, water sources, and major pollution sources, and decreased in other areas; 4) Monitoring stations should also be set up in non-polluted areas as control points.

[0062] (2) Composition of groundwater online monitoring system

[0063] like Figure 2 As shown, the groundwater online monitoring system mainly consists of multiple water quality parameter probes, a data communication host, a wireless network, and a monitoring center station. The center station exchanges information with each monitoring instrument via the wireless network, completing the collection of monitoring data and management of the monitoring equipment. Field testing instruments include an automatic monitoring and data transmission system for groundwater environmental parameters. Long-term automatic monitoring of groundwater environmental parameters is achieved through composite probes. Monitoring data can be exchanged and communicated periodically via wireless network according to agreed protocols, realizing an intelligent monitoring network for data acquisition, transmission, monitoring, and management.

[0064] (3) On-site installation

[0065] The water level gauge is placed into the groundwater monitoring well, and the water level sensor terminal is placed inside the protective device at the wellhead. The water level gauge cable is fixed at the wellhead baffle with a cylindrical load-bearing rod, so that the load-bearing rod supports the weight of the water level gauge and the cable. This not only prevents the water level gauge from dragging the sensor terminal, but also eliminates the risk of the water level gauge falling into the well.

[0066] (4) Description of the technical performance of the main equipment

[0067] The Leveline-mini-CTD is the online automatic groundwater flow field monitoring device selected in this embodiment. This device is used for long-term automatic monitoring of groundwater level, temperature, and conductivity. The sensors for groundwater level, temperature, and conductivity provide highly consistent and accurate measurements, and respond rapidly to instantaneous changes in water head. The sensors are easy to install. By forming a monitoring network with data communication equipment, remote data transmission can be achieved.

[0068] like Figure 3 As shown, this instrument employs a high-precision piezoresistive ceramic pressure sensor and a four-electrode conductivity sensor. Using standard data protocols, Levelline can be integrated into third-party monitoring systems to measure absolute or gauge pressure, water temperature, and conductivity at depths up to 100m. Its relevant parameters are shown in Table 1.

[0069] Table 1

[0070]

[0071] (5) Monitoring indicators

[0072] Dynamic data on groundwater level, temperature, and conductivity were measured using an online monitoring system, providing data support for the establishment of a groundwater flow model. The groundwater flow field monitoring indicators are shown in Table 2.

[0073] Table 2

[0074]

[0075] Groundwater quality monitoring program

[0076] Water quality monitoring was conducted based on the groundwater flow field monitoring scheme. Using the pollution monitoring stations established during the development of the online groundwater monitoring system, a portable multi-parameter water quality analyzer was used to collect relevant groundwater quality data on-site.

[0077] (1) Description of the technical performance of the main equipment

[0078] The groundwater quality monitoring equipment selected in this embodiment is the AP-2000 portable multi-parameter water quality analyzer. The standard configuration of the AP-2000 system includes basic parameters such as optical dissolved oxygen, pH, ORP, EC, and temperature. In addition to these five probes, the AP-2000 also has an ISE electrode interface and an optical probe interface, allowing for the installation of optional probes. The system can read data on-site via the Aquaread GPS Aquameter and save data via the Aquaread Logger.

[0079] like Figure 4 As shown, the AP2000 main unit has a built-in GPS system, can store 3000 monitoring data points, and outputs them via USB port, overlaying them with maps or satellite images using operating software. It boasts a high level of protection, making it suitable for field use. The device's probes offer rapid response, requiring no preheating or immersion in electrolyte, and are unaffected by sulfides, sulfates, chlorides, carbon dioxide, or ammonia nitrogen. The AP-2000 offers unique advantages for groundwater, especially borehole water quality measurement. Its ultra-compact size accommodates most boreholes, and each water quality probe has its own flow cell, allowing sample water to enter directly into the probe, which is ideal for groundwater monitoring and some process applications. Furthermore, its marine-grade aluminum alloy casing provides ample protection for the instrument's measuring probes. Relevant parameters are shown in Table 3.

[0080] Table 3

[0081]

[0082]

[0083] (2) Monitoring indicators

[0084] In this embodiment, the AP2000 water quality multi-parameter analyzer is mainly used for some conventional water chemical parameters in groundwater, such as pH, oxidation-reduction potential (ORP), total dissolved solids (TDS), and optically dissolved oxygen (DO). Table 4 lists the measurement range and accuracy of some detectable items.

[0085] Table 4

[0086]

[0087] DNAPL contamination migration and transformation process

[0088] After DNAPL is released into the soil-groundwater system, its pollution formation process is as follows:

[0089] The first stage involves the migration of DNAPL. Due to its high density and low viscosity, once a leak occurs, DNAPL will infiltrate deep into the formation, pass through the vadose zone, contaminate the groundwater aquifer, and eventually accumulate at the top of the impermeable layer, forming a pool. Under the influence of soil heterogeneity, hydraulic gradient, capillary forces, and other factors, DNAPL forms a highly irregular and complex distribution pattern along its seepage path, such as ganglia (porosity of 1-20% of the pore space, also known as residual saturation) and continuous pools (porosity of more than 50% of the pore openings). The infiltrated DNAPL can exist stably in this form for a long time and slowly dissolve into the groundwater, becoming a source area for groundwater contamination.

[0090] In the second stage, through interphase mass transfer, some DNAPL dissolves in the groundwater. When groundwater flows through the DNAPL contamination source area, a significant concentration gradient exists in the boundary layer region, promoting DNAPL dissolution. Notably, the dissolution rate varies at different locations within the source area due to the influence of the contamination concentration in the upstream water. Most DNAPLs have low water solubility, and coupled with the low groundwater flow rate, the dissolution process of the NAPL phase is slow and persistent.

[0091] The third stage involves the transport of dissolved phases. Dissolved DNAPL flows with groundwater, forming a contamination plume downstream of the source area. This plume can extend hundreds or even thousands of meters from the source area, expanding the contamination range. The distribution and lifespan of the plume are influenced by a combination of factors, including groundwater flow, soil heterogeneity, source area dissolution intensity, and biodegradation.

[0092] The fourth stage involves the reverse diffusion of DNAPL from low-permeability to high-permeability areas. Over a long period, the DNAPL source region continuously dissolves and is consumed. Simultaneously, some dissolved DNAPL diffuses from the high-permeability area to the low-permeability area, where it is intercepted and accumulates—this is the forward diffusion process (the first three stages). When the source region is depleted and the concentration gradient between the two regions reverses, reverse diffusion (the fourth stage) occurs, and the contaminant migrates backward from the low-permeability area to the aquifer. Reverse diffusion significantly increases the persistence of the contamination plume, allowing the contamination concentration in groundwater to remain above the MCL (Medium-Clearance Level) for decades or even centuries.

[0093] Simulation of DNAPL migration, transformation, and transport processes in groundwater

[0094] (1) Simulation of DNAPL phase migration process based on multiphase flow model

[0095] From a spatial perspective, key factors influencing DNAPL migration include contaminant release, aquifer heterogeneity, and the permeability-saturation-capillary pressure (K-pressure) characteristic. r,N -S w -P c The constitutive relationship of the correlation. From a time-scale perspective, the migration rate of DNAPL is mainly affected by its own properties (density and viscosity) and the permeability of the aquifer. Therefore, these factors need to be carefully considered when setting up a multiphase model.

[0096] (2) Dissolution process of DNAPL phase to aqueous phase based on mass transfer model

[0097] Mass transfer models describing the DNAPL dissolution process are mainly divided into three categories: pore-scale models, REV-scale models, and site-scale models. Pore-scale models reveal the details of mass transfer during the DNAPL source region dissolution process; REV-scale models study the influencing factors and variation patterns of DNAPL dissolution; and site-scale models enable the models to match field measurement data and accurately predict pollutant concentration distribution.

[0098] There are two main categories of methods for simulating interphase mass transfer processes. One category is based on the assumption of local equilibrium, estimating the mass transfer rate according to the equilibrium distribution relationship. The other category is based on dissolution kinetics, establishing empirical rate-limiting expressions, such as:

[0099]

[0100] In the formula, J is the mass flux from the NAPL phase to the aqueous phase during the dissolution process, [ML -3 T -1 ]; Let [LT] be the average mass transfer coefficient at the NAPL-water interface. -1 ];a nw [L] represents the effective specific interfacial area between the NAPL phase and the aqueous phase. -1 ];C s The concentration of the aqueous phase under equilibrium conditions, i.e., the effective solubility, [ML -3 [C] represents the aqueous phase concentration, [ML] -3 ].

[0101] Scale-up models for site-scale applications can be divided into two main categories. One category considers the combined effects of site size, soil heterogeneity, and NAPL distribution, and focuses on the effective mass transfer coefficient K at the site scale. eff Methods for correction. For example, the widely used expression for the effective mass transfer coefficient at the field scale:

[0102]

[0103] In the formula, C out Let L be the average concentration at the descending boundary, and L be the source region length parallel to the flow direction. The average Darcy flow velocity of groundwater. For effective saturated hydraulic conductivity, M0 and M are the initial and current residual concentrations of DNAPL, respectively, and k o α and β are model parameters.

[0104] Another type is to establish a power-law relationship between the effluent concentration and the remaining DNAPL mass, i.e., the source strength function.

[0105] Widely adopted source strength functions, such as

[0106]

[0107] In the formula, C s M(t) and M(t) correspond to the concentration of DNAPL dissolved in the source region and the mass of residual DNAPL at time t, respectively. C0 and M0 correspond to the concentration of DNAPL dissolved in the initial source region and the mass of residual DNAPL, respectively. Γ is the model parameter.

[0108] (3) Dissolved phase transport process

[0109] The factors to consider in the DNAPL dissolved phase transport process mainly include groundwater flow velocity, water level, dispersion mixing, and biodegradation. This process is usually simulated by coupling groundwater flow field models and solute transport models. Most studies use assumed source strength functions to characterize the dissolved phase source region release process, while a few studies couple it with multiphase flow models to simulate the entire DNAPL migration process.

[0110] (4) Reverse diffusion

[0111] Reverse diffusion refers to the process by which contaminants accumulated in low-permeability areas migrate back to high-permeability areas due to the reversal of the concentration gradient between high-permeability and low-permeability zones. Essentially, it is a long-term process of DNAPL dissolution and reverse migration. When the source region's contaminants are depleted or isolated and remediated, reverse diffusion will occur after the contaminant concentration in the aquifer decreases to a certain level, becoming a secondary pollution source and causing the plume concentration to remain above the MCL for a long period. Factors affecting reverse diffusion include solubility, heterogeneity, adsorption-desorption, and degradation. Simulations of the reverse diffusion process are generally divided into two stages, marked by source region removal or isolation. Stage 1: With the source region present, contaminants accumulate in low-permeability areas through forward diffusion. Stage 2: With the source region removed, simulations continue over a longer time range, studying the reverse diffusion process by observing the plume tailing phenomenon.

[0112] Example 1: Modeling and Verification of Multiphase Flow Module

[0113] Equilibrium equations for different phases are established based on the different occurrence states of DNAPL. Furthermore, based on the transformation laws between haloalkanes, the multiphase equations are coupled together to establish the following multiphase flow migration equations:

[0114] For the aqueous phase:

[0115]

[0116] For free phases of haloalkanes:

[0117]

[0118] in, This describes the process by which free-phase haloalkanes dissolve into the aqueous phase. This indicates the process of halogenated hydrocarbons in the aqueous phase being adsorbed by soil particles and then desorbed.

[0119] This embodiment uses the open-source program UTCHEM to simulate and determine the distribution of the NAPL phase in groundwater during DNAPL contamination.

[0120] Case 1: The simulated research site is a three-dimensional area of ​​140m × 60m × 20m, containing a groundwater aquifer with a homogeneous and isotropic aquifer medium. The model is discretized in space. Planarly, the research area is divided into 70 rows and 30 columns, totaling 2100 elements; vertically, the research area is divided into 10 layers. Each element has a volume of 2 × 2 × 2m³. 3 The groundwater flows from left to right. The left and right boundaries are isobaric boundaries (102.972 kPa on the left and 101.325 kPa on the right), while the remaining boundaries are impermeable. Within the study area, there is a nitrobenzene leak point with a leakage rate of 8 m³. 3 / d, leakage time is 10 days. Nitrobenzene concentration is 70% (volume fraction). Initial pollutant concentration in the unconfined aquifer is 0. Simulation was conducted under this scenario for 300 days. Parameter values ​​in the model are shown in Table 5. The planar locations of the pollution source and observation wells within the study area are shown in Table 5. Figure 5 .

[0121] Table 5

[0122]

[0123] Simulation results are as follows Figure 6 As shown. For the DNAPL free phase, the concentration is expressed as saturation. During the first 10 days of the pollutant leakage phase, a small amount of pollutant was found in the 5th stratum, indicating that DNAPL would take several days to infiltrate to this soil depth under gravity. From days 10 to 30, as the sparingly soluble DNAPL gradually infiltrated, a DNAPL free phase distribution area formed around the leakage point, and the saturation gradually increased. At this time, the DNAPL free phase showed an accumulation trend, and the effect of gravity migration was greater than that of groundwater convection diffusion. From days 90 to 300, the distribution range of the DNAPL free phase did not change significantly, but the saturation showed a gradual decreasing trend, indicating that the DNAPL free phase had stabilized in the soil at this stage. Under the influence of groundwater convection diffusion, a small portion of DNAPL gradually dissolved into the aqueous phase, leading to a decrease in saturation. At the same time, the dissolved DNAPL diffused with the water flow, increasing the pollution range, making it possible to detect different concentrations (in mg / L) of DNAPL pollutants at various monitoring wells.

[0124] Example 2: Modeling and Verification of Groundwater Flow Field Module and Halogenated Hydrocarbon Dissolved Phase Transport Module

[0125] Groundwater flow field model

[0126] Groundwater flow field models are fundamental to simulating groundwater pollution transport. Based on Darcy's law, a differential equation for groundwater flow is established:

[0127]

[0128] This embodiment is programmed using the Python language and runs MODFLOW through the open-source program Flopy. It realizes the spatiotemporal discretization of the contaminated field and the solution of the model difference equation, and obtains the distribution of groundwater level and flow direction at the contaminated site.

[0129] Halogenated hydrocarbon dissolved phase transport model

[0130] For halogenated hydrocarbon pollutants dissolved in groundwater, their flow is single-phase, controlled by both convection and dispersion. Therefore, by coupling a groundwater flow field model and Fick's law, a convection-dispersion equation describing the dual processes of flow and dispersion of dissolved halogenated hydrocarbons in the groundwater system is established:

[0131]

[0132] This embodiment uses the open-source program Flopy to run MT3DMS, and realizes the simulation of the concentration distribution of soluble halogenated hydrocarbon pollutants.

[0133] Model testing

[0134] For the groundwater flow field model program and the halohydrocarbon dissolution phase migration model program that have been written, different case scenarios were set up to verify them. The simulation results were compared with the results of GMS software operation to verify the feasibility and accuracy of the established models.

[0135] (1) Groundwater flow field model under steady-state conditions

[0136] Case 2: For example Figure 7 As shown, the simulation area is a single-layer rectangular region with an x-axis elevation of 190m and a y-axis elevation of 250m. The top elevation of the region is 5m and the bottom elevation is -15m. The region is discretized into a uniform grid of 26 rows and 20 columns. Under steady-state conditions, the upper and lower boundaries of the simulation area are constant head boundaries, and the left and right boundaries are flux-free boundaries. The initial water level of the entire region is 3m. The permeability coefficient hk = 1m / d, and the rainfall recharge = 0.001m / d.

[0137] A comparison diagram of the results with those from the GMS software is shown below. Figure 8As shown, in this scenario, rainfall falls as a surface source in the simulated area and flows out from the upper and lower boundaries. Calculations show that in steady state, the rainfall amount ≈ the sum of the outflow from the upper and lower boundaries, which is theoretically reasonable. In steady state, the water level is highest in the central part of the area, approximately 3.4m. From the central part to the upper and lower boundaries, the water level gradually decreases to a constant head boundary value of 3m. This is consistent with the simulation results from the GMS software.

[0138] (2) Groundwater flow field model under unsteady conditions

[0139] Case 3: Unsteady-state simulation test based on the simulated area in Case 2. Under unsteady-state conditions, the upper and lower boundaries of the simulation area are constant head boundaries, and the left and right boundaries are flux-free boundaries. The initial water level of the entire area is 3m, and the permeability coefficient hk = 1m / d. Unlike the steady-state test, the rainfall (recharge) is divided into three stress periods: days 1-10: 0.001m / d; days 10-20: 0.0015m / d; days 20-30: 0.0005m / d.

[0140] The simulation results comparison chart is as follows Figure 9 As shown, the overall trend of water level distribution is similar to that in steady state, i.e., the water level is highest in the central part of the region, and gradually decreases from the central part to the upper and lower boundaries to the constant head boundary value. Reading the water level data, we can find that the highest water levels in the central part are approximately 3.4m on the 10th day, approximately 3.6m on the 20th day, and approximately 3.3m on the 30th day, which is basically consistent with the distribution of GMS data.

[0141] (3) Model of dissolved phase transport of haloalkanes

[0142] Case 4: For example Figure 10 As shown, the simulation area is a single-layer rectangular region with an x-axis elevation of 190m and a y-axis elevation of 250m. The top elevation of the region is 5m and the bottom elevation is -15m. The region is discretized into a uniform grid of 26 rows and 20 columns. The water level at the upper boundary of the simulation area is 3m, the water level at the lower boundary is 4m, and the left and right boundaries are flux-free boundaries. The initial water level of the entire region is 3m. The permeability coefficient hk = 1m / d. There is a pumping well at (5, 5) with a pumping rate of 5m³ / d; and an injection well at (15, 15) with an injection rate of 5m³ / d. 3 / d. The pollutant concentration in the injected water is 50 mg / L. The porosity is 0.3, the longitudinal dispersion is 20 m, trpt = 0.2, and trpv = 0.01.

[0143] The simulation results comparison chart is as follows Figure 11 As shown, the water flow direction is from bottom to top. After the pollutants are injected, they are transported along the water flow direction. At the same time, under the influence of dispersion, the pollution range in the left and right directions also expands to a certain extent. The simulation results on day 61 and day 361 are basically consistent with the GMS simulation.

[0144] Example 3: A migration and transformation simulation system was constructed by coupling the multiphase flow module with the groundwater flow field module and the halohydrocarbon dissolved phase transport module.

[0145] The key to coupling these two aspects lies in transforming the permeability and saturation fields of the NAPL distribution source region. The relevant formulas can be used as follows:

[0146] K eff =K i ·K r

[0147]

[0148] Where: K i —Inherent hydraulic conductivity (permeability coefficient); S rw —Residual liquid phase saturation, 0.2; λ b — Brooks-Corey model parameters. The above parameters can be set to a fixed value, 2.0.

[0149] On the other hand, it is important to set up the mass transfer model appropriately.

[0150] like Figure 12 As shown, the constructed simulation system consists of three parts. The first part is the simulation of the DNAPLs free phase. By importing the UTCHEM program input file and inputting relevant model parameters, the DNAPLs free phase distribution is calculated and solved, with the results characterized by saturation. Under the condition of DNAPLs in the free phase, the soil permeability to groundwater changes, and the free phase distribution also affects DNAPLs dissolution. Therefore, the key parameters of solute transport under the condition of free phase presence are corrected using formulas and models. This is coupled to the second part, the simulation of the DNAPLs dissolved phase. The open-source program Flopy calls the MODFLOW and solute transport MT3D models for calculation, obtaining the hydraulic head distribution H and the DNAPLs dissolved phase distribution Cn.

[0151] Case 5: Based on the NAPL phase simulation results of Case 1, the groundwater flow field module and the halohydrocarbon dissolved phase transport module are further coupled to predict the distribution of the dissolved phase. The results are as follows: Figure 13 As shown.

[0152] Example 4: Establish a groundwater DNAPL simulation method based on optimization algorithm, determine DNAPL source information based on monitoring data, and then achieve more accurate simulation prediction.

[0153] The key to establishing a DNAPL (Genetic Algorithm for Groundwater) simulation method based on optimization algorithms lies in transforming the forward simulation model (DNAPL simulation program) into a callable subroutine form of the inverse optimization model (optimization algorithm), thereby embedding it into the optimization process and achieving seamless data transfer between the two. Taking the genetic algorithm used in this embodiment as an example, its optimization is a cyclical process. When the loop begins, the parameters in the decision variables need to be initialized according to the set population size to form the first generation population. This population is used as the feasible solution set, and each individual in it needs to call the Python simulation program once to perform groundwater flow field and dissolved phase transport simulation calculations under the corresponding scheme, obtaining the corresponding simulation results. Then, the optimization algorithm will determine whether the scheme meets the set constraints based on the simulation results, calculate the objective function value, evaluate each feasible solution, and obtain a new generation population. The above steps are repeated until the convergence condition is reached. The specific process architecture of the coupled optimization algorithm model is as follows: Figure 14 As shown.

[0154] Case 6: Groundwater DNAPL Inversion Case Based on Optimization Algorithm

[0155] Scenario Setting: Assume a halogenated hydrocarbon contaminant leak occurs at a certain location on a site. Horizontally, the site is 50m × 30m in size and homogeneous. The planar region is discretized into a uniform grid of 25 rows and 15 columns. Vertically, the site has a top elevation of 2m and a bottom elevation of -10m, and can be divided into three strata. The left and right boundaries of the simulation area are constant head boundaries (left 1.5m, right 0m), and the top and bottom boundaries are flux-free boundaries, with an initial head of 1.5m for the entire area. The contaminant leak point is located at (row 7, column 5, stratum 1), with a leak rate of 5 m³ / d. The concentration of the leaked chlorobenzene contaminant is 50 mg / L. The leak lasts for 30 days, after which measures are taken to terminate the pollution source. During contaminant transport, the porosity is 0.3, the longitudinal dispersion is 0.5m, the ratio of transverse to longitudinal dispersion (TRPT) is 0.1, and the ratio of vertical to longitudinal dispersion (TRVT) is 0.01. The unsteady-state simulation was conducted in this scenario, with a simulation duration of 100 days, during which pollutants flowed in during the first 30 days.

[0156] Reference field: The above simulated scenario is used as the reference field to determine the amount and concentration of pollutants leaking at the pollution source. To obtain the monitoring data required for the inversion model, it is assumed that three monitoring wells are set up in the contaminated site, with coordinates J1(7, 9, 1), J2(6, 15, 2) and J3(9, 20, 1) (the third digit indicates the stratum being monitored).

[0157] Based on the simulation calculations performed at the reference site, under otherwise unchanged conditions, when the pollution leakage rate is 5 m³ / d and the pollutant concentration is 50 mg / L, the pollutant concentrations at the three monitoring wells after 100 days of simulation are C1 (34.27 mg / L), C2 (0.65 mg / L), and C3 (1.32 mg / L). These reference values ​​were then used as the actual monitoring values ​​(true values) for the inversion model.

[0158] Inversion Scenario Setting: Assume that a pollutant leak occurred at a known point P(7, 5, 1) in the study area of ​​the above case. The pollution source was discovered and measures were taken to terminate it 30 days later. The amount and concentration of the leaked pollutants are unknown. Site remediation began 100 days later. The concentrations of pollutants in the groundwater measured at the three established monitoring wells were C1 (34.27), C2 (0.65), and C3 (1.32), respectively. This monitoring data was used to invert the pollution source strength (leakage amount and concentration) to accurately determine the pollution source information and achieve accurate pollution plume prediction.

[0159] In this example, the classic genetic algorithm is used for inversion solution, and the relevant parameters are set as follows:

[0160] (1) Calling the forward simulation model. Since the forward model itself is a code program that can run successfully, in order to make it a subroutine that the optimization algorithm can call, the model needs to be adapted into a function with the parameters to be calculated as dependent variables. In this embodiment, the forward simulation model is defined as the `forwardingmodel` function, and the variables of the function are the parameters to be calculated, namely the leakage amount and leakage concentration of the pollution source. At the same time, the return value of the function is set to the required model simulation value so as to read the simulation results. In this case, it is the pollutant concentration at the three monitoring wells. Finally, the forward model function to be called is imported into the optimization model program to realize the coupling between the forward simulation model and the inversion optimization model.

[0161] (2) Setting up the inversion optimization model. The optimization model has three elements: objective function, decision variables, and constraints.

[0162] Objective function: The root mean square error, composed of simulated and observed values, is used as the objective function to determine the degree of agreement between the measured pollutant concentration in the monitoring well and the model-simulated pollutant concentration. The formula is as follows:

[0163]

[0164] Decision variables: i.e. parameters to be determined, in this case, the amount of pollutant leakage P[0] and the concentration P[1].

[0165] Constraints: Upper and lower limits are imposed on the decision variables. In this case, 0 ≤ P[0] ≤ 10m is set. 3 / d;40≤P[1]≤60mg / L;

[0166] Inversion Result Analysis

[0167] This embodiment uses a genetic algorithm to invert the source and sink terms of the pollution source leakage amount and concentration in the forward model. When the population size is 30 and the simulation lasts for 100 generations, the convergence curve of the corresponding objective function (RMSE) is as follows. Figure 15 As shown, during the optimization process, the objective function value decreased significantly after about 10 iterations; and after about 38 iterations, the objective function value basically converged. This demonstrates that solving the optimization model based on the genetic algorithm can find the global optimum at a relatively fast speed.

[0168] The optimal solution obtained by solving the above nonlinear optimization model is the identification result of pollutant leakage amount and concentration in this embodiment. The pollutant leakage amount at the pollution source obtained by inversion is 5.05 m³. 3 / d, compared to the true value 5m 3 The simulated value was only 1% higher than the actual value per day; the inverted pollutant leakage concentration was 49.63 mg / L, which was only 0.7% lower than the actual value of 50 mg / L. The root mean square error (RSME) of the final simulation result was 0.05, indicating that the inversion result was relatively accurate.

[0169] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A DNAPL simulation method for groundwater coupled with a mathematical model and an optimization algorithm, characterized in that, Includes the following steps: The system acquires dynamic change data of groundwater based on the groundwater online monitoring system, acquires change data of groundwater-related environmental indicators based on the water quality multi-parameter instrument, and acquires DNAPL concentration data of corresponding points based on regular groundwater sample collection and analysis. Analyze the hydrogeological conditions of the site and the migration and transformation process of DNAPL contamination. The model parameter range was initially estimated, the scenario to be corrected was set, and simulation was performed based on the multiphase flow and solute transport coupling model; An optimization algorithm is used to construct a simulation system that couples the mathematical model with the optimization algorithm. Based on the dynamic change data of groundwater, the change data of environmental indicators and the concentration data of DNAPL, the migration, transformation and transport process of DNAPL in groundwater is simulated and evaluated, and simulation results that are consistent with the actual monitoring situation are obtained. The process of simulating and evaluating the migration, transformation, and transport of DNAPL in groundwater based on the aforementioned groundwater dynamic change data, environmental indicator change data, and DNAPL concentration data includes: The DNAPL phase migration process was simulated based on the multiphase flow module of the established simulation system. A DNAPL dissolution mass transfer model was constructed, and the dissolution process of the DNAPL phase to the aqueous phase was simulated based on the DNAPL dissolution mass transfer model. The migration and reverse diffusion processes of DNAPL were simulated based on the groundwater flow field module and the halohydrocarbon dissolved phase transport module of the established simulation system. The simulation process of the groundwater flow field module includes: Constructing a differential equation for groundwater flow based on Darcy's law; The finite difference method is used to solve the differential equation of groundwater flow. The set of discrete points in the simulation area is used to replace the seepage zone, and the difference quotient is used to replace the differential quotient. The differential equation and its boundary conditions are transformed into a difference equation with the unknown function as the unknown quantity at the discrete points. The solution of the differential equation of groundwater flow at the discrete points is obtained by solving the difference equation. The difference equation is embedded in the groundwater flow field module, and the relevant parameters are set according to hydrogeological information during the simulation. The simulation process of the halohydrocarbon dissolved phase transport module includes: Convection-dispersion equations were constructed based on the groundwater flow field model and Fick's law to describe the dual processes of flow and dispersion of dissolved halogenated hydrocarbons in the groundwater system. The convection-dispersion equation describes the injection or extraction process of pollutants, while also considering the adsorption process of halogenated hydrocarbons on the soil and the degradation process of halogenated hydrocarbons. The convection-dispersion equation is embedded in the halohydrocarbon dissolved phase transport module, and the relevant parameters are set according to the pollutant leakage situation and pollutant property information during the simulation. Specifically, equilibrium equations for different phases are established based on the different occurrence states of DNAPL. Furthermore, based on the transformation laws between haloalkanes, the multiphase equations are coupled together to establish the following multiphase flow migration equation: For the aqueous phase: For free phases of haloalkanes: in, This describes the process by which free-phase haloalkanes dissolve into the aqueous phase. This indicates the process of haloalkanes in the aqueous phase being adsorbed by soil particles and then desorbed. The groundwater flow field model is the foundation for simulating groundwater pollution transport. Based on Darcy's law, a differential equation for groundwater flow is established: For halogenated hydrocarbon pollutants dissolved in groundwater, their flow is a single phase controlled by both convection and dispersion. Therefore, by coupling a groundwater flow field model and Fick's law, a convection-dispersion equation describing the dual processes of flow and dispersion of dissolved halogenated hydrocarbons in the groundwater system is established: The key to coupling these two aspects lies in transforming the permeability and saturation fields of the NAPL distribution source region, using the following relevant formulas: K eff =K i ·K r Where: K i —Inherent hydraulic conductivity; S rw —Residual liquid phase saturation, 0.2; λ b — Brooks-Corey model parameters. The above parameters can be set to a fixed value, 2.0; The constructed simulation system consists of three parts. The first part is the simulation of the DNAPLs free phase. By importing the UTCHEM program input file and inputting the relevant model parameters, the DNAPLs free phase distribution is calculated and solved, and the results are characterized by saturation. Under the condition of DNAPLs free phase, the soil permeability to groundwater changes, and the free phase distribution also affects the dissolution of DNAPLs. Therefore, the key parameters of solute transport under the condition of free phase are corrected by formula and model. This is coupled to the second part, the simulation of the DNAPLs dissolved phase. The open-source program Flopy calls MODFLOW and the solute transport MT3D model for calculation to obtain the hydraulic head distribution H and the DNAPLs dissolved phase distribution Cn.

2. The groundwater DNAPL simulation method based on the coupled mathematical model and optimization algorithm according to claim 1, characterized in that, In simulating the DNAPL phase migration process based on a multiphase flow model, the release of pollutants, the heterogeneity of the aquifer, the constitutive relationship characterizing the correlation between permeability, saturation, and capillary pressure, as well as the influence of the DNAPL's own properties and the aquifer's permeability on the migration rate are considered.

3. The groundwater DNAPL simulation method according to claim 1, characterized in that, The DNAPL dissolution mass transfer model includes a REV-scale model and a site-scale model. The REV-scale model is used to obtain the influencing factors and variation patterns of DNAPL dissolution. The site-scale model is used to match the model with field measurement data.

4. The groundwater DNAPL simulation method based on the coupled mathematical model and optimization algorithm according to claim 3, characterized in that, The simulation method for the DNAPL dissolution mass transfer model includes: Based on the assumption of local equilibrium, the mass transfer rate is estimated according to the equilibrium distribution relationship to simulate the interphase mass transfer process, or based on the dissolution kinetics, an empirical rate constraint expression is established to simulate the interphase mass transfer process.

5. The groundwater DNAPL simulation method according to claim 3, characterized in that, The simulation method for the site-scale model includes: Based on site size, soil heterogeneity, and NAPL distribution, the effective mass transfer coefficient at the field scale can be corrected, or a power-law relationship between effluent concentration and residual DNAPL mass can be established.

6. The groundwater DNAPL simulation method according to claim 1, characterized in that, The process of constructing a simulation system that couples optimization algorithms with mathematical models includes: The DNAPL migration and transformation simulation model was adapted into a function with the parameters to be determined as dependent variables, and the function was imported into the optimization algorithm model. The model parameters are optimized based on the optimization algorithm, and the training is repeated. When the convergence condition is met, the optimal solution output by the coupled model is obtained.

7. The groundwater DNAPL simulation method according to claim 6, characterized in that, The process of optimizing the model parameters based on the aforementioned optimization algorithm includes: Set constraints and convergence conditions; The decision variable parameters are initialized based on the population size to form the first generation population; Based on the first-generation population, the DNAPL migration and transformation simulation program was invoked to obtain simulation results; Determine whether the simulation results meet the constraints, calculate the objective function value, evaluate each feasible solution, and obtain a new generation population; When the convergence condition is met, the optimal solution output by the coupled model is obtained.

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