CN107808049A - DNAPL migration method for numerical simulation based on porous media three-dimensional microstructures model - Google Patents

Abstract

The invention provides a DNAPL migration numerical simulation method based on a three-dimensional microstructure model of a porous medium. By establishing a three-dimensional microstructure model of a regular square pyramid, the porosity of a translucent porous medium is accurately measured through visible light using visible light microscopic imaging technology. Then the permeability and capillary entry pressure are calculated using the model of the three-dimensional microstructure of porous media. Relative gradient errors are used to quantitatively assess the scale of typical unit cells based on precise measurements of permeability and capillary entry pressure in translucent porous media. The migration model of heavy non-aqueous pollutants was established with UTCHEM, and the two-dimensional translucent porous medium was subdivided with REV as the grid scale, so as to improve the simulation accuracy of DNAPL migration and realize the quantitative determination of the model subdivision grid. This method achieves a more accurate quantitative determination of the properties of porous media and grid scales, and has strong applicability in accurately simulating the migration and remediation process of DNAPL in aquifers and formulating corresponding pollutant remediation programs.

Description

Numerical Simulation Method of DNAPL Migration Based on 3D Microstructural Model of Porous Media

technical field

The invention relates to a heavy non-aqueous phase pollutant, in particular to a DNAPL migration numerical simulation method.

Background technique

With the rapid development of industry and agriculture, human activities release more and more dense nonaqueous phase liquid DNAPL into nature. The leaked DNAPL has low solubility and higher density than water. After entering the aquifer, the DNAPL will always infiltrate and migrate to the deep part of the aquifer, and it is easy to stay on the low-permeability medium to form a polluted pool and remain. Because DNAPL such as perchloroethylene (PCE) and polycyclic aromatic hydrocarbons (polycyclic aromatic hydrocarbons, PAHs) have stable chemical properties, low solubility, high toxicity, and carcinogenicity, the residual DNAPL in the aquifer will cause serious damage to the groundwater environment. Long-term pollution will cause serious harm to human health in the ecosystem. When DNAPL enters the underground environment, its migration and repair process in the aquifer will be greatly affected by the properties of the medium (such as permeability and capillary entry pressure), heterogeneity and the corresponding scale effect, as shown in Figure 1 , the abscissa in the figure represents the measurement scale L. It can be seen that the properties of porous media change with the measurement scale, and REV is located in the middle section. Therefore, accurate determination of the heterogeneity of the porous media of the aquifer and quantitative evaluation of the representative elementary volume (REV) are essential before simulating the migration of DNAPL in the aquifer and formulating a remediation plan. important link

In order to study the complex migration behavior of DNAPL in the groundwater environment, in general experiments, water and pollutants are usually allowed to migrate in translucent quartz sand, and the concentration of DNAPL in translucent quartz sand is monitored in real time. The nature of the sand is difficult to measure, making it difficult to determine the effect of the properties of the quartz sand material on the migration of DNAPL. With the development of science and technology, non-invasive high-precision technologies such as x-rays and gamma-rays are more and more widely used in the determination of the microstructural properties of materials. X-rays and γ-rays have been widely used in the determination of material properties and fluid saturation in porous media. However, in actual measurement, the size of material samples is usually required to be very small, so that X-rays and γ-rays can easily penetrate the material. At the same time, when applying x-ray and gamma-ray technology, complex equipment and more energy are required, and the risk of radioactivity is high during operation, and the process is complicated. In recent years, a new visible light transmission imaging technology has emerged, such as light transmission micro-tomography (LTM) and light transmission visualization (LTV), which can detect water, Fast, economical, efficient and accurate determination of the content of pollutants and the properties of translucent materials themselves. On the other hand, all porous media in nature can be regarded as fractal, and a large number of studies have been carried out on the tortuosity, permeability, and thermal conductivity of porous media through fractal methods. However, the research of these fractal methods on porous media is limited to the theoretical point of view, and the microstructure models of porous media constructed are mostly ideal two-dimensional models, but the actual microstructure of porous media is three-dimensional, so the properties of porous media in actual measurement are different. It is difficult to obtain accurately with the current fractal method. In addition, usually the numerical model of DNAPL migration determines the grid scale of the subdivision of the aquifer in a qualitative way, with great randomness. Therefore, the current visible light imaging technology and fractal methods cannot quantitatively and accurately measure the key parameters (permeability, capillary entry pressure) and corresponding REV of translucent porous media such as translucent quartz sand in practice. This will make it difficult to quantitatively determine the properties of porous media and the meshing scale of the numerical model of DNAPL migration in porous media, which will lead to simulation errors.

Contents of the invention

Purpose of the invention: The purpose of the present invention is to provide an efficient and accurate numerical simulation method for DNAPL migration based on a three-dimensional microstructural model of porous media for the deficiencies of the prior art.

Technical solution: the present invention provides a method for numerical simulation of DNAPL migration based on a porous medium three-dimensional microstructure model, comprising the following steps:

(1) Use visible light microscopic imaging technology to scan translucent porous media, and accurately measure the porosity of porous media;

(2) Establish a micro-fractal model of a three-dimensional regular pyramid for the micro-structure of porous media, and calculate the permeability through the micro-fractal model;

(3) Quantitatively determine the average pore diameter with the microscopic fractal model of the porous medium, thereby calculating the capillary entry pressure of the porous medium according to the Young-Laplace equation;

(4) Quantitative evaluation of the REV scale for the permeability of porous media and the capillary entry pressure;

(5) DNAPL is injected into a translucent porous medium for migration, and the distribution of DNAPL saturation is monitored by the light transmission method;

(6) Use the multi-component and multi-phase flow simulation program UTCHEM to establish a numerical model to simulate the migration of DNAPL, use the REV scale as the grid scale to subdivide the two-dimensional translucent porous medium, and use the three-dimensional microstructure model based on the porous medium Quantitatively determined porosity, permeability and capillary entry pressure data are converted into REV-scale data and input into UTCHEM, thereby improving simulation accuracy, avoiding qualitative determination of subdivided grid scales, and simulating the migration of DNAPL in porous media .

Further, in step (1), fill the translucent porous medium into the two-dimensional sand box and saturate it with water. The visible light source illuminates the sand box from one side, and the CCD camera receives the transmitted light signal penetrating through the two-dimensional translucent porous medium on the other side. Visible microscopic imaging measures the porosity of translucent porous media at each pixel:

in, n is the porosity of the semi-transparent porous medium, I _s is the transmitted light intensity of visible light penetrating the water-saturated semi-transparent porous medium, I _o is the original light intensity of the visible light source, C is the parameter for correcting the transmission error of visible light, α _s is the light absorption coefficient of the solid phase, d _s is the average diameter of the solid phase particles in the water-saturated translucent quartz sand material, L _T is the thickness of the translucent granular material, e is the Euler constant, τ _{s, w} is the solid phase - light transmittance at the liquid-water interface, d _o is the average diameter of the pores.

The further step (2) regards the porous medium as a collection of capillary bundles, and randomly selects a microelement with a fluid path length L and a cross-sectional area A _L , the viscosity of the fluid in the porous medium is μ, and the number of capillaries in the microelement for

Among them, N(L≥λ) represents the number of capillaries with a diameter greater than λ in the microelement, -d _N(L≥λ) is the derivative of N(L≥λ), λ is the diameter of capillaries in porous media, and δ is a constant parameter, D _f is the fractal dimension;

The flow is calculated according to Poiseuille's equation:

Among them, q represents the flow rate of the capillary in the micro-element, λ _min is the minimum diameter of the capillary, λ _max is the maximum diameter of the capillary, and ΔP is the pressure difference at both ends of the flow path of the fluid in the micro-element; west law Combined, the ratio of the smallest diameter of the capillary to the largest diameter of the capillary tends to 0, we can get:

where k is the permeability,

Further, step (3) selects a research unit (rightsquare pyramid microstructure, RSPM) from the porous medium microstructure, and its porosity and unit volume are respectively:

where V _r is the unit volume of the regular pyramid research unit, R _v is the radius of the solid phase particles in the porous medium, and L _r is the side length of the regular quadrangular pyramid research unit;

The side length and the pore volume of the research unit of the regular pyramid are:

where V _rp is the pore volume in the research unit of the regular pyramid;

Approximate the pores in the research unit of the regular pyramid as a sphere, and thus calculate the diameter λ _r1 of the sphere:

The bottom of the regular pyramid research unit is a square, and its corresponding total area and pore area are respectively:

Among them, Arb is the total volume of the bottom square, _Arbs is the area occupied by the solid phase, _{and Arbp} is the area occupied by the pores;

Approximate the area occupied by the pores in the bottom square as a circle, and calculate the diameter λ _r2 of the circle:

In the same way, the side of the regular pyramid research unit is a triangle, and the area occupied by the pores is also approximated as a circle, and the diameter λ _r3 of the circle is:

Among them, A _rsp is the pore area of the regular triangle on the side of the regular pyramid research unit,

In the regular quadrangular pyramid research unit, the distance ΔL _r of the gap between solid phase particles is:

When the fluid flows in the porous medium, it will not only pass through the middle pores, bottom and side pores in the unit, but also flow through the gaps between particles. Therefore, the pore diameter d _o is λ _r1 , λ _r2 , λ _r3 and The mean value of the interparticle interstitial distance ΔL _r :

Taking the pore diameter d _o in the research unit of the regular pyramid as the diameter λ of the capillary, the capillary entry pressure P _b can be calculated according to the Young-Laplace equation:

where ω=Fσcosθ, θ is the contact angle on the interface between the fluid and solid particles, σ is the surface tension on the interface, and F is a parameter related to the capillary shape and fluid flow direction in porous media.

Further, step (4) uses the relative gradient error To quantitatively evaluate the permeability of translucent porous media and the REV scale of capillary entry pressure:

in, is the parameter to be evaluated, such as the permeability of the porous medium or the capillary entry pressure, i is the ordinal number of the change from the small scale to the large scale when calculating the properties of the porous medium, and ΔL is the scale of each increase;

Divide the two-dimensional semi-transparent porous medium into large square grids, quantitatively evaluate the REV of the permeability and capillary entry pressure of each grid, and then perform statistical analysis on the REV scale of all grids to determine the translucency Mean REV of porous media.

Further, step (5) injects DNAPL into the two-dimensional translucent porous medium, allowing DNAPL to migrate in the porous medium, and the saturation S _DL of DNAPL in the translucent porous medium is measured by light transmission method:

Among them, I _s is the transmitted light intensity value after the visible light penetrates when the two-dimensional translucent porous medium is completely saturated by water, and I _DL is the transmitted light intensity value after the visible light penetrates when the two-dimensional translucent porous medium is completely saturated by DNAPL, Measured in the experiment, I is the transmitted light intensity.

Beneficial effects: the present invention establishes a new three-dimensional microstructure model of regular quadrangular pyramids for porous media, uses visible light microscopic imaging technology to accurately measure the porosity of translucent porous media through visible light, and then uses the model of three-dimensional microstructure of porous media Calculate the permeability and capillary entry pressure. Based on the precise measurement of the permeability and capillary entry pressure of translucent porous media, the relative gradient error is used to quantitatively evaluate the scale of representative elementary volume (REV). The migration model of heavy non-aqueous pollutants was established with UTCHEM, and the two-dimensional translucent porous medium was subdivided with REV as the grid scale, so as to improve the simulation accuracy of DNAPL migration and realize the quantitative determination of the model subdivision grid. This method is fast, economical, efficient, and high-precision. Compared with the previous two-dimensional microstructure model of porous media and the qualitative determination method of the subdivided mesh size in DNAPL simulation, it realizes the determination of the properties of porous media and the mesh size. The more accurate quantitative determination has taken an important step in the accurate simulation of DNAPL migration in aquifers, and has a strong application in the accurate simulation of DNAPL migration in aquifers and even the remediation process and the formulation of corresponding pollutant remediation programs. sex.

Description of drawings

Fig. 1 is the theoretical curve of the properties of porous media changing with the scale;

Fig. 2 is the position relationship diagram of the two-dimensional sand box filled with heterogeneous translucent quartz sand and the six selected observation grids for REV evaluation in the experiment;

Fig. 3 is the three-dimensional microstructure model of porous media RSPM;

Figure 4(a) is the transmitted light intensity distribution image of 2D translucent quartz sand saturated with visible light before PCE injection; (b) is the porosity distribution image obtained by LTM measurement; (c) is the 3D micro-fractal model of porous media The calculated permeability distribution image; (d) the capillary entry pressure distribution image calculated for the three-dimensional micro-fractal model of porous media;

Fig. 5 shows the properties of translucent quartz sand and their relative gradient errors at the six observation grids as a function of the measurement scale: (a) porosity; (b) relative gradient error of porosity; (c) permeability; (d ) relative gradient error of permeability; (e) capillary entry pressure; (f) relative gradient error of capillary entry pressure;

Fig. 6(a) Frequency distribution and cumulative frequency distribution of REV minimum scale of translucent quartz sand porosity; (b) variation of REV minimum scale of porosity of translucent quartz sand with average diameter of solid particles; (c) permeability (d) Frequency distribution and cumulative frequency distribution of REV minimum scale of capillary entry pressure;

Figure 7 is the PCE saturation S _PCE distribution image at different times during the experiment: (a) t=1.44min; (b) t=22min; (c) t=58min; (d) t=80min; (e) t=418min; (f) t=756min; (g) t=1095min; (h) t=1433min;

Figure 8 shows the comparison between the PCE pollution plumes at different times simulated using the microstructure model of porous media and without the microstructure model of porous media and the PCE pollution plume obtained from the experiment in the PCE infiltration stage: (a-d) Model-I, using porous media Microstructural model; (e-h) Model-II, without using the porous media microstructural model;

Figure 9 shows the comparison of the PCE pollution plumes at different times simulated using the porous media microstructure model and without the porous media microstructure model and the PCE pollution plume obtained from the experiment in the PCE subdivision stage: (a-d) Model-I, using porous Media microstructure model; (e-h) Model-II, without using porous media microstructure model;

Figure 10(a) shows the time-dependent variation of the infiltration distance of the PCE pollution plume simulated by the experiment and the two models; (b) shows the comparison between the vertical infiltration distance of the PCE pollution plume simulated by the two models and the experimental observations.

Detailed ways

The technical solutions of the present invention will be described in detail below, but the protection scope of the present invention is not limited to the embodiments.

Embodiment: a kind of DNAPL migration numerical simulation method based on porous medium three-dimensional microstructure model, concrete operation is as follows:

As shown in Figure 2, prepare a two-dimensional sand box with a length of 60 cm, a height of 45 cm, and a thickness of 1.6 cm. Fill it with translucent quartz sand of 6 different particle sizes, and set the sampling needle 1 and the injection needle 2 at the same time. The filled background medium is F20/30 mesh translucent quartz sand, and F70/F100, F70/F80, F40/F50, F50/F70 and F30/F40 mesh translucent quartz sand are filled into two-dimensional sand boxes as 5 low The permeable lens body, the top and bottom of the sand box are filled with a thin layer of F70/80 purpose low-permeability translucent quartz sand to prevent water and PCE from escaping from the top and bottom. The properties of the six kinds of quartz sand used in the experiment are shown in Table 1:

Table 1 Properties of translucent quartz sand with different particle sizes used in the experiment

Deionized water enters the sand box evenly from the water inlet I-1~I-3 on the right side of the sand box from the horizontal direction, and then flows out from the water outlet E-1~E-3 on the left side of the sand box. The flow velocity in the direction is set to 0.5m/d, so that the translucent quartz sand is in a saturated state. After the whole device is ready, the visible light source is placed on one side of the sand box so that the visible light penetrates the two-dimensional translucent quartz sand from one side of the sand box, and a CCD camera is set on the other side of the sand box to receive the transmitted light intensity. Figure 4(a). The porosity of two-dimensional translucent quartz sand is determined by LTM calculation:

in, n is the porosity of the semi-transparent porous medium, I _s is the transmitted light intensity of visible light penetrating the water-saturated semi-transparent porous medium, I _o is the original light intensity of the visible light source, C is the parameter for correcting the transmission error of visible light, α _s is the light absorption coefficient of the solid phase, d _s is the average diameter of the solid phase particles in the water-saturated translucent quartz sand material, L _T is the thickness of the translucent granular material, e is the Euler constant, τ _{s, w} is the solid phase - light transmittance at the liquid-water interface, d _o is the average diameter of the pores.

From a fractal point of view, the porous medium is regarded as a collection of capillary bundles, and a microelement is randomly selected from the two-dimensional translucent quartz sand, where the length of the fluid path is L _o , the cross-sectional area is A _L , and the diameter of the microelement is greater than or The number of capillaries equal to λ and the corresponding derivative are:

where λ is the capillary diameter, D _f is the fractal dimension, and δ is a constant.

The fluid viscosity is μ, the minimum and maximum diameters of the capillary bundles in the microcell are λ _min and λ _max respectively, and the pressure difference at both ends of the fluid flow path in the microcell is ΔP, so the flow rate can be calculated based on the Poiseuille equation:

Darcy's law Substituted into formula (4), the ratio of the minimum diameter to the maximum diameter of the capillary bundle in the micro-element tends to be The formula for calculating the permeability can be obtained:

in

Then the three-dimensional microstructure model of porous media is established to determine the capillary entry pressure. The porous medium is composed of stacked solid phase particles and pores, as shown in Figure 3, a research unit of a right square pyramid microstructure (RSPM) is selected from it, and its porosity and unit volume are respectively:

Among them, R _V is the radius of the medium particle, V _r is the total volume of the RSPM unit, and L _r is the edge length of the RSPM unit.

Then determine the edge length of the RSPM unit:

The pores in the RSPM unit are approximated as a sphere, so the diameter λ _r1 of the sphere can be obtained:

where _Vrp is the pore volume in the RSPM cell.

The bottom surface of the RSPM unit is a square, first determine the area occupied by the solid phase particles and pores, and approximate the area occupied by the pores as a circle to calculate the diameter λ _r2 of the circle:

Among them, Arb is the total area of the bottom surface of the RSPM unit, _Arbs is the area occupied by the solid phase particles in the square on the bottom surface, and _Arbp is the area occupied by the pores in the square _on the bottom surface.

The side of the RSPM is a regular triangle, and the diameter λ _r3 of the circle is calculated by approximating the area occupied by the pores in it as a circle:

where _Arsp is the area occupied by pores in the side equilateral triangle,

When the fluid flows in the porous medium, it will not only pass through the intermediate pores in the RSPM unit, the pores on the bottom and side of the RSPM, but also flow through the gaps between particles. Therefore, the pore diameter d _o is λ _r1 , λ _r2 , The average value of λ _r3 and interparticle interstitial distance ΔL _r :

Taking the pore diameter d _o of the cell as the capillary diameter λ, the capillary entry pressure P _b can be calculated:

where ω=Fσcosθ, θ is the contact angle on the interface between the fluid and solid particles, σ is the surface tension on the interface, and F is a parameter related to the capillary shape and fluid flow direction in porous media.

The porosity n, permeability k and capillary entry pressure Pb of translucent quartz sand measured by LTM and the three-dimensional microscopic model of porous media are shown in Fig. 4( _b )-(d), respectively. In the REV evaluation, the two-dimensional translucent quartz sand is divided into 30 layers and 40 columns with a total of 1200 grids, and the grid size is 0.015m×0.015m. Select 6 observation grids from the translucent quartz sand filled with 6 different particle sizes to observe the change of permeability and capillary entry pressure with the measurement scale, in which CA in Figure 2 belongs to lens A, and CB belongs to lens B, CC belongs to lens body C, CD belongs to lens body D, CE belongs to lens body E, CF belongs to F20/30 mesh translucent quartz sand filled in the background. When performing REV evaluation, the cuboid grid gradually increases from the center of each grid, and the change of medium properties and relative gradient errors with the measurement scale is calculated.

Curves of the porosity n, permeability k and capillary entry pressure P _b of the six observation grids as the measurement scale L increases, as shown in Fig. 5(a), (c) and (e), the observation grid CA, CB, CC, CD, CE and CF are respectively selected from the lens body A, B, C, D, E and the background medium F20/30 mesh quartz sand filled in the sand box. The porosity n and permeability k show a steady trend with the change of the measurement scale, while the curves of partial capillary entry pressure P _b with the change of the measurement scale show a decreasing trend, but most of these curves are stable and do not change with the measurement scale. Obvious changes, it is difficult to identify the stable interval II of the porous media properties with the measurement scale from the changes of these curves, which makes it difficult for the REV scale to change the porosity n, permeability k and capillary entry pressure _Pb with the measurement scale can be identified directly on the curve. In addition, the curves of properties measured by observation grids on lens bodies with different particle sizes versus measurement scales have different characteristics.

Based on obtaining the change curve of porous media properties with the measurement scale, the corresponding relative gradient error is then calculated to make the REV platform more obvious:

in, is the relative gradient error, is the property to be evaluated, such as porosity n, permeability k, and capillary entry pressure P _b , i is the ordinal number of the cuboid grid changing from small scale to large scale when calculating the properties of porous media, and ΔL is the scale of each increase of cuboid grid.

As shown in Figure 5(b), (d) and (f), the relative gradient error Make the fluctuation of the curve more obvious: when the measurement scale is small, the relative gradient error The fluctuation of the relative error curve is relatively large; with the increase of the measurement scale, the fluctuation of the relative error curve gradually weakens, and the curve also tends to be gentle correspondingly, and a stable platform of REV appears. In Fig. 5(b), (d) and (f), the REV platform of translucent quartz sand with small particle size is narrower, while the REV platform of translucent quartz sand with large particle size is wider. When measuring When the scale is further increased, the variation curve of permeability with measurement scale fluctuates again due to the influence of macroscopic heterogeneity. The curve of relative gradient error versus scale can make the stable interval of REV more significant, which is beneficial to the evaluation of REV. However, it is difficult to accurately identify the REV scale due to the large fluctuations in the gradient error versus scale curve. In order to smooth this fluctuation so as to accurately identify the scale of REV, the present invention utilizes the 5-point average value of the relative gradient error As a standard for identifying REV:

The statistical results of the minimum REV scale of porosity n, permeability k and capillary entry pressure P _b of translucent quartz sand and the minimum REV scale of capillary entry pressure are shown in Figure 6(a), (c) and (d). The results show that the scale distribution of porosity REV is between 0-12mm, and the frequency is close to Gaussian distribution, which is consistent with the normal distribution of most of the material properties in nature; the minimum scale distribution of REV of permeability is between 0.0-9.0mm, showing the characteristics of Gaussian distribution; The REV minimum scale of the capillary entry pressure is evenly distributed in the range of 0.0-15.0mm. The cumulative frequency of REV minimum scale for porosity and permeability shows a nonlinear increasing trend, while the REV minimum scale for capillary entry pressure shows a linear increasing trend. When the accumulative frequency exceeds 80%, the corresponding minimum REV scales of porosity and permeability are 9.0mm and 8.0mm, respectively, while the minimum REV scale of capillary entry pressure reaches 12.0mm. Considering the REV evaluation results of permeability and capillary entry pressure, the average REV scale of the two-dimensional translucent quartz sand in the experiment is 10.0 mm. In addition, statistical results show that there is a significant positive correlation between the minimum scale of porosity REV and the average particle diameter (p<0.05). The larger the distribution range.

After quantitatively determining the permeability, capillary entry pressure, and corresponding REV of the translucent quartz sand, inject PCE from the injection needle from the top of the sand box to make it migrate in the two-dimensional translucent quartz sand. 40 ml of dyed PCE was injected into the flask from the top of the flask over 80 minutes. During the whole process of the experiment, LTV technology was used to measure the saturation S _DL of DNAPL in two-dimensional translucent quartz sand in real time:

Among them, I _DL is the transmitted light intensity value after visible light penetrates when the two-dimensional translucent porous medium is completely saturated by DNAPL, which can be measured in experiments, and I is the transmitted light intensity.

The pollution plume of PCE at different times during the experiment is shown in Fig. 7(a-h). At the beginning of the experiment, the injected PCE was in the shape of water droplets and infiltrated downwards under the action of gravity, as shown in Figure 7(a). When the PCE pollution plume encountered the low-permeability lens, the PCE could not overcome the pressure of the lens. The capillary entry pressure thus accumulates on the lens body, and then flows out from one side of the lens body and continues to migrate to the deep part, as shown in Figure 7(b-d). Affected by the lateral water flow in the horizontal direction, no PCE flows out from the right side of lens bodies C and D, and PCE only flows out from the left side of lens body C and D. This indicates that the migration of PCE in porous media is closely related to the heterogeneity of the media and the groundwater flow rate, and the larger heterogeneity makes the shape of the PCE pollution plume more irregular.

Based on the evaluation results of REV, a numerical model of PCE migration was established with UTCHEM. Taking the REV scale of 10.0mm as the grid scale of the numerical model, the two-dimensional translucent quartz sand is subdivided, and the porosity, permeability and capillary entry pressure are also converted into corresponding scale data and input into UTCHEM. In order to further prove the effect of the PCE migration simulation based on the new porous media three-dimensional microstructure model, the previous simulation method was used to simulate the PCE migration to compare the simulation effect. Model-I is a numerical simulation model of PCE migration using a new 3D microstructural model of porous media, and Model-II is a numerical simulation model of PCE migration without using a new 3D microstructural model of porous media. In Model-I and Model-II, the injection of PCE is simulated by the injection well, and 40ml of PCE is injected into the two-dimensional translucent sand box within 0-80min, and the injection rate is 0.5ml/min. The top and bottom are set as zero-flux boundaries, and the left and right sides are set as pressure boundaries, so that the water flows horizontally from right to left to maintain a flow rate of 0.5m/d. Porosity, permeability and capillary entry pressure are converted into corresponding scale data and input into the three models. The whole migration process of PCE is divided into three stages: the correction period is 0-22 minutes, the test period is 22-58 minutes, and the verification period is 58-80 minutes. The corrected other parameters related to PCE and water are listed in Table 1.

Figure 8(a-h) is the comparison between the simulation results of Model-I and Model-II on the migration of PCE in the infiltration stage and the experimental results, and Figure 9(a-h) is the simulation results and experimental results of Model-I and Model-II on the PCE redistribution stage Comparison of PCE pollution plumes obtained from experimental observations. The simulation results of all models show that PCE infiltrates downward from the injection point and accumulates on top of the low-permeability lens, which is basically consistent with the experimental results. However, in the process of PCE infiltration simulated by Model-II, the vertical infiltration speed of PCE is slower than that obtained by experimental observation, as shown in Fig. 9(e-h), which shows that the error of Model-II is relatively large. However, the PCE migration speed simulated by Model-I is similar to the experimental observation, and the size of the PCE pollution plume is also consistent with the experimental results. An overall comparison of the PCE pollution plume shows that the simulation results obtained by Model-I are in the highest agreement with the experiment in the whole simulation process.

Further quantitative comparison of the simulation results of the three models is shown in Figure 10(a)(b). Figure 10a shows the vertical infiltration distance of the PCE plume as a function of time obtained from experiments and Model-I and Model-II simulations. In the first few minutes when PCE is injected into the sand box, the vertical infiltration distance of the PCE pollution plume increases rapidly with time. When the PCE pollution plume hits the lens in the sand box, the vertical infiltration speed becomes slow. When t=4～12min, the PCE pollution plume reaches the upper part of the lens body A, and as time goes by, the PCE pollution plume reaches the upper part of the lens body B and E respectively at t=11.8～31.8min and t=34.3～54.4min. Finally, the PCE contamination plume reaches the bottom of the sand box and accumulates. The mean absolute error MAE, root mean square error RMSE and coefficient of determination R2 of Model-I are 1.63cm, 2.60cm and 0.96 respectively, while the mean absolute error MAE, root mean square error RMSE and coefficient of determination R2 of Model ^{- II} are respectively are 2.00cm, 3.21cm and 0.94, indicating that when the three-dimensional microstructure model of porous media is not used, the numerical simulation of the migration of PCE in porous media by Model-II will have greater errors. In general, the simulation results of Model-I using the three-dimensional microstructure model of porous media are more in line with the experimental observations.

In addition, for the vertical distance between the centroid of the PCE pollution plume and the injection point, the second-order moment of the PCE pollution plume in the horizontal direction, and the second-order moment of the PCE pollution plume in the vertical direction, the experimental results and the simulation results of the three models are consistent. For comparison, see Tables 2 and 3:

Table 2 The vertical distance between the centroid of the PCE pollution plume and the injection point as a function of time obtained from experiments and two models

VDIP ^a , the vertical distance between the centroid of the PCE pollution plume and the injection point

AE ^b , absolute error, negative sign means smaller than the observed value, positive sign means higher than the actual observed value

RE ^c , the relative error, is equal to the ratio of the absolute error to the actual observed value

Table 3 The horizontal and vertical second moments of the PCE pollution plume obtained from the experiment and the two models vary with time

SMHD ^a , the second moment of the pollution plume in the horizontal direction

SMVD ^b , the second moment of the vertical pollution plume

In Table 2, the relative error of Model-II in the early stage of PCE infiltration (t=1.44min) exceeds 30%. In comparison, the relative error of Model-I is smaller and does not change during the entire simulation period. Big, both lower. The comparison of the vertical distance between the centroid of the PCE pollution plume and the injection point shows that the simulation results of Model-I are in good agreement with the experiment.

For the second moment of the PCE pollution plume in the horizontal direction in Table 3, Model-I is consistent with the experimental observations, and its relative error is always lower than that of Model-II. Therefore, the PCE pollution obtained by Model-I The second moment of the feather in the horizontal direction is most accurate. For the second moment of the PCE pollution plume in the vertical direction, the maximum relative errors of Model-I and Model-II are 68.42% and 74.75%, respectively. During the verification period, the relative error gradually decreased. During the whole simulation period, the relative error of the second moment of the PCE pollution plume obtained by Model-I in the vertical direction is the smallest. Based on the comparison of the first-order moments and second-order moments of the PCE pollution plume in Table 2-3, the simulation results of Model-I are in good agreement with the experiments, indicating that the 3D microstructure model based on porous media can accurately describe the microstructural characteristics of porous media, thereby Quantitatively measure the permeability and capillary entry pressure of porous media, significantly reduce the error of simulation, and improve the simulation accuracy of DNAPL migration in porous media.

Aiming at the limitations of the existing research on the microstructure of porous media and the meshing method of the numerical model of DNAPL migration, this method proposes a new three-dimensional microstructure model of porous media based on the fractal method, combined with the visible light microscopic imaging technology (light transmission micro -tomography, LTM), can realize the quick, economical and efficient quantitative determination of the porosity, permeability and capillary entry pressure of translucent porous media. Then, the REV of the porous medium is quantitatively evaluated by the relative gradient error, and the porous medium is segmented with the REV scale. Finally, based on the three-dimensional microstructure model of porous media and the evaluation of REV, the migration of DNAPL in porous media is accurately simulated with UTCHEM. Through this method, properties such as permeability and capillary entry pressure of translucent porous media can be quantitatively determined more accurately, and the grid division scale of the numerical model for the migration of DNAPL in translucent materials can be determined quantitatively, which is useful for studying the microstructure of porous media. The understanding and accurate simulation of DNAPL migration and repair in aquifers play an important role.

Claims (6)

1. A DNAPL migration numerical simulation method based on porous media three-dimensional microstructure model, is characterized in that: comprise the following steps: (1) Use visible light microscopic imaging technology to scan translucent porous media, and accurately measure the porosity of porous media; (2) Establish a micro-fractal model of a three-dimensional regular pyramid for the micro-structure of porous media, and calculate the permeability through the micro-fractal model; (3) Quantitatively determine the average pore diameter with the microscopic fractal model of the porous medium, thereby calculating the capillary entry pressure of the porous medium according to the Young-Laplace equation; (4) Quantitative evaluation of the REV scale for the permeability of porous media and the capillary entry pressure; (5) DNAPL is injected into a translucent porous medium for migration, and the distribution of DNAPL saturation is monitored by the light transmission method; (6) Use the multi-component and multi-phase flow simulation program UTCHEM to establish a numerical model to simulate the migration of DNAPL, use the REV scale as the grid scale to subdivide the two-dimensional translucent porous medium, and use the three-dimensional microstructure model based on the porous medium The quantitatively determined data of porosity, permeability and capillary entry pressure were converted into REV-scale data and input into UTCHEM to simulate the migration of DNAPL in porous media. 2. the DNAPL migration numerical simulation method of porous medium three-dimensional microstructure model according to claim 1, is characterized in that: step (1) fills translucent porous medium in the two-dimensional sand box and is saturated with water, and visible light source is irradiated from one side On the other side of the sand box, the CCD camera receives the transmitted light signal that penetrates the two-dimensional translucent porous medium, and uses visible light microscopic imaging technology to measure the porosity of the translucent porous medium on each pixel: <mrow><mi>n</mi><mo>=</mo><mfrac><mrow><mi>ln</mi><mi></mi><msub><mi>I</mi><mi>s</mi></msub><mo>-</mo><mi>&amp;beta;</mi></mrow><mi>&amp;gamma;</mi></mfrac></mrow> in, n is the porosity of the semi-transparent porous medium, I _s is the transmitted light intensity of visible light penetrating the water-saturated semi-transparent porous medium, I _o is the original light intensity of the visible light source, C is the parameter for correcting the transmission error of visible light, α _s is the light absorption coefficient of the solid phase, d _s is the average diameter of the solid phase particles in the water-saturated translucent quartz sand material, L _T is the thickness of the translucent granular material, e is the Euler constant, τ _{s, w} , are the solid Light transmittance at the phase-liquid water interface, d _o is the average diameter of the pores. 3. the DNAPL migration numerical simulation method of porous medium three-dimensional microstructure model according to claim 1, is characterized in that: step (2) regards porous medium as the collection of capillary bundle, therefrom arbitrarily gets a fluid path length and is L, The _microelement with cross-sectional area AL, the viscosity of the fluid in the porous medium is μ, and the number of capillaries in the microelement is <mrow><mi>N</mi><mrow><mo>(</mo><mi>L</mi><mo>&amp;GreaterEqual;</mo><mi>&amp;lambda;</mi><mo>)</mo></mrow><mo>=</mo><msub><mi>A</mi><mi>L</mi></msub><msup><mi>&amp;delta;&amp;lambda;</mi><mrow><mo>-</mo><msub><mi>D</mi><mi>f</mi></msub></mrow></msup></mrow> <mrow><mo>-</mo><msub><mi>d</mi><mrow><mi>N</mi><mrow><mo>(</mo><mi>L</mi><mo>&amp;GreaterEqual;</mo><mi>&amp;lambda;</mi><mo>)</mo></mrow></mrow></msub><mo>=</mo><msub><mi>A</mi><mi>L</mi></msub><msub><mi>&amp;delta;D</mi><mi>f</mi></msub><msup><mi>&amp;lambda;</mi><mrow><mo>-</mo><msub><mi>D</mi><mi>f</mi></msub><mo>-</mo><mn>1</mn></mrow></msup><msub><mi>d</mi><mi>&amp;lambda;</mi></msub></mrow> Among them, N(L≥λ) represents the number of capillaries with a diameter larger than λ in the microelement, -d _N(L≥λ) is the derivative of N(L≥λ), λ is the diameter of capillaries in porous media, and δ is a constant parameter, D _f is the fractal dimension; The flow is calculated according to Poiseuille's equation: <mrow><mi>Q</mi><mo>=</mo><msubsup><mo>&amp;Integral;</mo><msub><mi>&amp;lambda;</mi><mi>min</mi></msub><msub><mi>&amp;lambda;</mi><mi>max</mi></msub></msubsup><msub><mi>d</mi><mi>p</mi></msub><mo>=</mo><msubsup><mo>&amp;Integral;</mo><msub><mi>&amp;lambda;</mi><mi>min</mi></msub><msub><mi>&amp;lambda;</mi><mi>max</mi></msub></msubsup><mfrac><mrow><mi>&amp;pi;</mi><msup><mrow><mo>(</mo><mfrac><mi>&amp;lambda;</mi><mn>2</mn></mfrac><mo>)</mo></mrow><mn>4</mn></msup><mi>&amp;Delta;</mi><mi>P</mi></mrow><mrow><mn>8</mn><mi>&amp;mu;</mi><mi>L</mi></mrow></mfrac><msub><mi>A</mi><mi>L</mi></msub><msub><mi>&amp;delta;D</mi><mi>L</mi></msub><msup><mi>&amp;lambda;</mi><mrow><mo>-</mo><msub><mi>D</mi><mi>f</mi></msub><mo>-</mo><mn>1</mn></mrow></msup><msub><mi>d</mi><mi>&amp;lambda;</mi></msub><mo>=</mo><mfrac><mrow><msub><mi>&amp;pi;&amp;delta;D</mi><mi>f</mi></msub><msub><mi>A</mi><mi>L</mi></msub><mi>&amp;Delta;</mi><mi>P</mi></mrow><mrow><mn>128</mn><mi>&amp;mu;</mi><mi>L</mi><mrow><mo>(</mo><mn>4</mn><mo>-</mo><msub><mi>D</mi><mi>f</mi></msub><mo>)</mo></mrow></mrow></mfrac><mrow><mo>(</mo><msubsup><mi>&amp;lambda;</mi><mi>max</mi><mrow><mn>4</mn><mo>-</mo><msub><mi>D</mi><mi>f</mi></msub></mrow></msubsup><mo>-</mo><msubsup><mi>&amp;lambda;</mi><mi>min</mi><mrow><mn>4</mn><mo>-</mo><msub><mi>D</mi><mi>f</mi></msub></mrow></msubsup><mo>)</mo></mrow></mrow> Among them, q represents the flow rate of the capillary in the micro-element, λ _min is the minimum diameter of the capillary, λ _max is the maximum diameter of the capillary, and ΔP is the pressure difference at both ends of the flow path of the fluid in the micro-element; west law Combined, the ratio of the smallest diameter of the capillary to the largest diameter of the capillary tends to 0, we can get: where k is the permeability, 4. the DNAPL migration numerical simulation method of porous medium three-dimensional microstructure model according to claim 1 is characterized in that: step (3) selects the research unit of a regular quadrangular pyramid from porous medium microstructure, its porosity and unit volume They are: <mrow><mi>n</mi><mo>=</mo><mfrac><mrow><msub><mi>V</mi><mi>r</mi></msub><mo>-</mo><mfrac><mn>4</mn><mn>9</mn></mfrac><msubsup><mi>&amp;pi;R</mi><mi>v</mi>mi><mn>3</mn></msubsup></mrow><msub><mi>V</mi><mi>r</mi></msub></mfrac></mrow> <mrow><msub><mi>V</mi><mi>r</mi></msub><mo>=</mo><mfrac><mrow><mn>4</mn><msubsup><mi>&amp;pi;R</mi><mi>v</mi><mn>3</mn></msubsup></mrow><mrow><mn>9</mn><mrow><mo>(</mo><mn>1</mn><mo>-</mo><mi>n</mi><mo>)</mo></mrow></mrow></mfrac></mrow> Among them, V _r is the unit volume of the regular pyramid research unit, R _v is the radius of the solid phase particle in the porous medium, L _r is the side length of the regular square pyramid research unit; The side length and the pore volume of the research unit of the regular pyramid are: <mrow><msub><mi>V</mi><mi>r</mi></msub><mo>=</mo><mfrac><msqrt><mn>2</mn></msqrt><mn>6</mn></mfrac><msubsup><mi>L</mi><mi>r</mi><mn>3</mn></msubsup></mrow> <mrow><msub><mi>L</mi><mi>r</mi></msub><mo>=</mo><msub><mi>R</mi><mi>v</mi></msub><mroot><mfrac><mrow><mn>8</mn><mi>&amp;pi;</mi></mrow><mrow><mn>3</mn><msqrt><mn>2</mn></msqrt><mrow><mo>(</mo><mn>1</mn><mo>-</mo><mi>n</mi><mo>)</mo></mrow></mrow></mfrac><mn>3</mn></mroot></mrow> <mrow><msub><mi>V</mi><mrow><mi>r</mi><mi>p</mi></mrow></msub><mo>=</mo><msub><mi>V</mi><mi>r</mi></msub><mo>-</mo><mfrac><mn>4</mn><mn>9</mn></mfrac><msubsup><mi>&amp;pi;R</mi><mi>v</mi><mn>3</mn></msubsup><mo>=</mo><mfrac><mrow><mn>4</mn><msubsup><mi>&amp;pi;R</mi><mi>v</mi><mn>3</mn></msubsup><mi>n</mi></mrow><mrow><mn>9</mn><mrow><mo>(</mo><mn>1</mn><mo>-</mo><mi>n</mi><mo>)</mo></mrow></mrow></mfrac></mrow> where V _rp is the pore volume in the research unit of the regular pyramid; Approximate the pores in the research unit of the regular pyramid as a sphere, and thus calculate the diameter λ _r1 of the sphere: <mrow><msub><mi>V</mi><mrow><mi>r</mi><mi>p</mi></mrow></msub><mo>=</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mi>&amp;pi;</mi><msup><mrow><mo>(</mo><mfrac><msub><mi>&amp;lambda;</mi><mrow><mi>r</mi><mn>1</mn></mrow></msub><mn>2</mn></mfrac><mo>)</mo></mrow><mn>3</mn></msup></mrow> <mrow><msub><mi>&amp;lambda;</mi><mrow><mi>r</mi><mn>1</mn></mrow></msub><mo>=</mo><mn>2</mn><msub><mi>R</mi><mi>v</mi></msub><mroot><mfrac><mi>n</mi><mrow><mn>3</mn><mrow><mo>(</mo><mn>1</mn><mo>-</mo><mi>n</mi><mo>)</mo></mrow></mrow></mfrac><mn>3</mn></mroot></mrow> The bottom of the regular pyramid research unit is a square, and its corresponding total area and pore area are respectively: <mrow><msub><mi>A</mi><mrow><mi>r</mi><mi>b</mi></mrow></msub><mo>=</mo><msubsup><mi>L</mi><mi>r</mi><mn>2</mn></msubsup></mrow> <mrow><msub><mi>A</mi><mrow><mi>r</mi><mi>b</mi><mi>s</mi></mrow></msub><mo>=</mo><msubsup><mi>&amp;pi;R</mi><mi>v</mi><mn>2</mn></msubsup></mrow> <mrow><msub><mi>A</mi><mrow><mi>r</mi><mi>b</mi><mi>p</mi></mrow></msub><mo>=</mo><msubsup><mi>L</mi><mi>r</mi><mn>2</mn></msubsup><mo>-</mo><msubsup><mi>&amp;pi;R</mi><mi>v</mi><mn>2</mn></msubsup></mrow> Among them, Arb is the total volume of the bottom square, _Arbs is the area occupied by the solid phase, _{and Arbp} is the area occupied by the pores; Approximate the area occupied by the pores in the bottom square as a circle, and calculate the diameter λ _r2 of the circle: <mrow><msub><mi>A</mi><mrow><mi>r</mi><mi>b</mi><mi>p</mi></mrow></msub><mo>=</mo><mi>&amp;pi;</mi><msup><mrow><mo>(</mo><mfrac><msub><mi>&amp;lambda;</mi><mrow><mi>r</mi><mn>2</mn></mrow></msub><mn>2</mn></mfrac><mo>)</mo></mrow><mn>2</mn></msup></mrow> <mrow><msub><mi>&amp;lambda;</mi><mrow><mi>r</mi><mn>2</mn></mrow></msub><mo>=</mo><mn>2</mn><msqrt><mfrac><msub><mi>A</mi><mrow><mi>r</mi><mi>b</mi><mi>p</mi></mrow></msub><mi>&amp;pi;</mi></mfrac></msqrt></mrow> In the same way, the side of the regular pyramid research unit is a triangle, and the area occupied by the pores is also approximated as a circle, and the diameter λ _r3 of the circle is: <mrow><msub><mi>&amp;lambda;</mi><mrow><mi>r</mi><mn>3</mn></mrow></msub><mo>=</mo><mn>2</mn><msqrt><mfrac><msub><mi>A</mi><mrow><mi>r</mi><mi>s</mi><mi>p</mi></mrow></msub><mi>&amp;pi;</mi></mfrac></msqrt></mrow> Among them, A _rsp is the pore area of the regular triangle on the side of the regular pyramid research unit, In the regular quadrangular pyramid research unit, the distance ΔL _r of the gap between solid phase particles is: <mrow><msub><mi>&amp;Delta;L</mi><mi>r</mi></msub><mo>=</mo><msub><mi>L</mi><mi>r</mi></msub><mo>-</mo><mn>2</mn><msub><mi>R</mi><mi>v</mi></msub><mo>=</mo><msub><mi>R</mi><mi>v</mi></msub><mrow><mo>(</mo><mroot><mfrac><mrow><mn>8</mn><mi>&amp;pi;</mi></mrow><mrow><mn>3</mn><mrow><mo>(</mo><mn>1</mn><mo>-</mo><mi>n</mi><mo>)</mo></mrow></mrow></mfrac><mn>3</mn></mroot><mo>-</mo><mn>2</mn><mo>)</mo></mrow></mrow> When the fluid flows in the porous medium, it will not only pass through the middle pores, bottom and side pores in the unit, but also flow through the gaps between particles. Therefore, the pore diameter d _o is λ _r1 , λ _r2 , λ _r3 and The mean value of the interparticle interstitial distance ΔL _r : <mrow><msub><mi>d</mi><mi>o</mi></msub><mo>=</mo><mfrac><mrow><msub><mi>&amp;lambda;</mi><mrow><mi>r</mi><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>&amp;lambda;</mi><mrow><mi>r</mi><mn>2</mn></mrow></msub><mo>+</mo><msub><mi>&amp;lambda;</mi><mrow><mi>r</mi><mn>3</mn></mrow></msub><mo>+</mo><msub><mi>&amp;Delta;L</mi><mi>r</mi></msub></mrow><mn>4</mn></mfrac></mrow> Taking the pore diameter d _o in the research unit of the regular pyramid as the diameter λ of the capillary, the capillary entry pressure P _b can be calculated according to the Young-Laplace equation: <mrow><msub><mi>P</mi><mi>b</mi></msub><mo>=</mo><mfrac><mi>&amp;omega;</mi><mi>&amp;lambda;</mi></mfrac><mfrac><mrow><mn>1</mn><mo>-</mo><mi>n</mi></mrow><mi>n</mi></mfrac></mrow> where ω=Fσcosθ, θ is the contact angle on the interface between the fluid and solid particles, σ is the surface tension on the interface, and F is a parameter related to the capillary shape and fluid flow direction in porous media. 5. the DNAPL migration numerical simulation method of porous medium three-dimensional microstructure model according to claim 1 is characterized in that: step (4) uses relative gradient error To quantitatively evaluate the permeability of translucent porous media and the REV scale of capillary entry pressure: in, is the parameter to be evaluated, such as the permeability of the porous medium or the capillary entry pressure, i is the ordinal number of the change from the small scale to the large scale when calculating the properties of the porous medium, and ΔL is the scale of each increase; Divide the two-dimensional semi-transparent porous medium into large square grids, quantitatively evaluate the REV of the permeability and capillary entry pressure of each grid, and then perform statistical analysis on the REV scale of all grids to determine the translucency Mean REV of porous media. 6. the DNAPL migration numerical simulation method of porous medium three-dimensional microstructure model according to claim 1 is characterized in that: step (5) injects DNAPL in two-dimensional translucent porous medium, allows DNAPL to migrate in porous medium, The saturation S _DL of DNAPL in translucent porous media is determined by light transmission method: <mrow><msub><mi>S</mi><mrow><mi>D</mi><mi>L</mi></mrow></msub><mo>=</mo><mfrac><mrow><mi>ln</mi><mi></mi><msub><mi>I</mi><mi>S</mi></msub><mo>-</mo><mi>ln</mi><mi></mi><mi>I</mi></mrow><mrow><mi>ln</mi><mi></mi><msub><mi>I</mi><mi>S</mi></msub><mo>-</mo><mi>ln</mi><mi></mi><msub><mi>I</mi><mrow><mi>D</mi><mi>L</mi></mrow></msub></mrow></mfrac></mrow> Among them, I _s is the transmitted light intensity value after the visible light penetrates when the two-dimensional translucent porous medium is completely saturated by water, and I _DL is the transmitted light intensity value after the visible light penetrates when the two-dimensional translucent porous medium is completely saturated by DNAPL, Measured in the experiment, I is the transmitted light intensity.