A method for simulating the co-migration of colloids and pollutants in porous media

Abstract

The present invention relates to a method for simulating the co-migration process of colloids and pollutants in a porous medium, the method comprising: S1, obtaining initial conditions and boundary conditions corresponding to the colloids and pollutants in the porous medium; S2, according to the initial conditions and boundary conditions, using a pre-acquired first mathematical model for simulating the migration of colloids after adsorption of pollutants, a second mathematical model for simulating the migration of dissolved pollutants, and a third mathematical model for simulating the migration of pollutants adsorbed on the surface of the colloid to obtain the simulated co-migration process of the colloids and pollutants in the porous medium. Since the pre-acquired first mathematical model, second mathematical model, and third mathematical model are used to comprehensively consider the mutual influence mechanism of the migration process of the colloids and pollutants in the porous medium, compared with the prior art, the co-migration process of the colloids and pollutants obtained by the method for simulating the co-migration process of the colloids and pollutants in the porous medium of the present invention is more accurate.

Description

Technical Field

[0001] The invention relates to the technical field of colloid migration research, and in particular to a method for simulating the co-migration process of colloid and pollutants in a porous medium. Background Art

[0002] The traditional view is that pollutants with strong adsorption, such as heavy metals, radionuclides, pharmaceuticals and personal care products (PPCPs), pesticides, etc., are mainly present in the solid phase of porous media and are usually considered to be stationary. Most of the colloid and pollutant co-migration models established based on this view do not consider the adsorption of colloids on pollutants. Therefore, the simulated colloid and pollutant co-migration process obtained by the colloid and pollutant co-migration model in the existing technology is not accurate. Summary of the invention

[0003] 1. Technical issues to be resolved

[0004] In view of the above-mentioned shortcomings and deficiencies of the prior art, the present invention provides a method for simulating the co-migration process of colloids and pollutants in porous media, which solves the technical problem that the simulated co-migration process of colloids and pollutants obtained by the co-migration model of colloids and pollutants in the prior art is not accurate.

[0005] (II) Technical solution

[0006] In order to achieve the above object, the main technical solutions adopted by the present invention include:

[0007] An embodiment of the present invention provides a method for simulating the co-migration process of colloids and pollutants in a porous medium, the method comprising:

[0008] S1. Obtaining initial conditions and boundary conditions corresponding to colloids and pollutants in porous media;

[0009] S2. According to the initial conditions and boundary conditions, a first mathematical model for simulating the migration of colloids after adsorption of pollutants, a second mathematical model for simulating the migration of dissolved pollutants, and a third mathematical model for simulating the migration of pollutants adsorbed on the surface of the colloid are used to obtain the simulated co-migration process of colloids and pollutants in the porous medium.

[0010] Preferably,

[0011] The first mathematical model includes:

[0012]

[0013]

[0014]

[0015] C represents the concentration of liquid colloid;

[0016] S1 represents the solid phase colloid concentration at the first kinetic point;

[0017] S2 represents the solid colloid concentration at the second kinetic point;

[0018] ρ b is the bulk density of the porous medium;

[0019] J w Darcy flux represents the flow of water in porous media;

[0020] D sh represents the diffusion coefficient of porous media;

[0021] t represents time;

[0022] z represents the spatial coordinate of the migration direction of colloids and pollutants in the porous medium;

[0023] μ cw It represents the decomposition coefficient of liquid colloid;

[0024] μ cs It represents the decomposition coefficient of solid colloid;

[0025] θ represents the volumetric water content of the porous medium;

[0026] S represents the solid phase colloid concentration;

[0027] S max Indicates the maximum solid phase colloid concentration;

[0028] k a1 It represents the colloid adhesion coefficient at the first kinetic point;

[0029] k d1 It represents the colloid separation coefficient at the first kinetic point;

[0030] k a2 Indicates the colloid adhesion coefficient at the second kinetic point;

[0031] k d2 It represents the colloid separation coefficient at the second kinetic point;

[0032] c represents the concentration of liquid phase pollutants;

[0033] s k Indicates the concentration of adsorbed pollutants at the kinetic point;

[0034] k amc represents the adsorption coefficient of pollutants on mobile colloids; k aic It represents the adsorption coefficient of pollutants on attached colloids;

[0035] k dmc It represents the desorption coefficient of pollutants on mobile colloids;

[0036] k dic It represents the desorption coefficient of pollutants on attached colloids.

[0037] c ref Expressed as adsorption rate k amc The corresponding pollutant concentration;

[0038] s max Expressed as adsorption rate k aic The corresponding adsorbed pollutant concentration; d 50 Represents the median particle size of porous media.

[0039] Preferably,

[0040] The second mathematical model comprises:

[0041]

[0042] Among them, s e Indicates the concentration of adsorbed pollutants at the equilibrium adsorption point; μ s Indicates the degradation rate of solid-phase adsorbed pollutants;

[0043] μ w Indicates the degradation rate of dissolved pollutants in the liquid phase.

[0044] s mc It represents the concentration of pollutants adsorbed on the surface of mobile colloids;

[0045] s ic It represents the concentration of pollutants adsorbed on the surface of immobile colloids;

[0046] C ref is the adsorption rate k amc The corresponding mobile colloid concentration.

[0047] Preferably,

[0048] The third mathematical model includes:

[0049]

[0050] μ i It indicates the degradation rate of pollutants adsorbed on the surface of immobile colloids;

[0051] μ m Indicates the degradation rate of pollutants adsorbed on the surface of mobile colloids.

[0052] Preferably,

[0053] The initial conditions include: initial spatial distribution state of porous medium water potential, initial spatial distribution state of dissolved pollutant concentration, initial spatial distribution state of adsorbed pollutant concentration, and initial spatial distribution state of colloid concentration.

[0054] Preferably,

[0055] Boundary conditions include: water flow conditions, pollutant migration and colloid migration conditions on the boundaries of porous media in all directions.

[0056] Preferably,

[0057] Water flow conditions include: constant head or variable head conditions, constant flux or variable flux conditions;

[0058] The boundary conditions for pollutant and colloid migration include: concentration boundary conditions and concentration flux boundary conditions.

[0059] Preferably,

[0060] The S2 specifically includes: according to the initial conditions and boundary conditions, using the finite difference method or the finite element method to solve the first mathematical model, the second mathematical model and the third mathematical model acquired in advance respectively, so as to obtain the co-migration process of the colloid and the pollutant in the simulated porous medium.

[0061] (III) Beneficial effects

[0062] The beneficial effect of the present invention is that the method for simulating the co-migration process of colloids and pollutants in a porous medium of the present invention adopts the pre-acquired first mathematical model, the second mathematical model, and the third mathematical model to comprehensively consider the mutual influence mechanism of the colloids and pollutants in the migration process in the porous medium. Compared with the prior art, it can simulate the mutual influence of colloids and pollutants in the migration process, and achieves that the co-migration process of colloids and pollutants obtained by the method for simulating the co-migration process of colloids and pollutants in a porous medium of the present invention is more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 The present invention is a flow chart of a method for simulating the co-migration process of colloids and pollutants in porous media. DETAILED DESCRIPTION

[0064] In order to better explain the present invention and facilitate understanding, the present invention is described in detail below through specific implementation modes in conjunction with the accompanying drawings.

[0065] In order to better understand the above technical solution, exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments described herein. On the contrary, these embodiments are provided to enable a clearer and more thorough understanding of the present invention and to fully convey the scope of the present invention to those skilled in the art.

[0066] More and more studies have shown that the colloidal substances present in the soil (such as microorganisms, humus, suspended clay and metal oxides, etc.) can act as carriers of these pollutants and become an important pathway for the rapid migration of strongly adsorbed pollutants. The study of the migration of pollutants carried by colloids in saturated porous media requires the basic theoretical knowledge of the separate migration of colloids and soluble pollutants. In addition, it is necessary to comprehensively consider the interface processes between the components, such as the transient adsorption or kinetic adsorption process of pollutants on the surface of soil particles, and the adsorption process of pollutants on the surface of mobile or immobile (attached) colloids. In addition, it is also necessary to comprehensively consider the shielding or enhancement of the surface charge of the colloid by pollutants adsorbed on the surface of the colloid, thereby affecting the migration dynamics of the colloid. Based on this, this embodiment proposes a method for simulating the co-migration process of colloids and pollutants in porous media, see. Figure 1 , the method comprising:

[0067] S1. Obtain the initial conditions and boundary conditions corresponding to the colloid and the pollutant in the porous medium.

[0068] S2. According to the initial conditions and boundary conditions, a first mathematical model for simulating the migration of colloids after adsorption of pollutants, a second mathematical model for simulating the migration of dissolved pollutants, and a third mathematical model for simulating the migration of pollutants adsorbed on the surface of the colloid are used to obtain the simulated co-migration process of colloids and pollutants in the porous medium.

[0069] In the practical application of this embodiment, the first mathematical model includes:

[0070]

[0071]

[0072]

[0073] C represents the concentration of liquid colloid.

[0074] S1 represents the solid phase colloid concentration at the first kinetic point.

[0075] S2 represents the solid phase colloid concentration at the second kinetic point.

[0076] ρ bis the bulk density of the porous medium.

[0077] J w Represents the Darcy flux of water flow in porous media.

[0078] D sh represents the diffusion coefficient of porous media.

[0079] t represents time.

[0080] z represents the spatial coordinate in the migration direction of colloids and pollutants in the porous medium.

[0081] μ cw Represents the decomposition coefficient of liquid colloid.

[0082] μ cs Represents the decomposition coefficient of solid phase colloid.

[0083] θ represents the volumetric water content of the porous medium.

[0084] S represents the solid phase colloid concentration.

[0085] S max Indicates the maximum solid phase colloid concentration.

[0086] k a1 It represents the colloid adhesion coefficient at the first kinetic point.

[0087] k d1 It represents the colloid separation coefficient at the first kinetic point.

[0088] k a2 It represents the colloid adhesion coefficient at the second kinetic point.

[0089] k d2 It represents the colloid separation coefficient at the second kinetic point.

[0090] c represents the liquid phase pollutant concentration.

[0091] s k Represents the concentration of adsorbed pollutants at the kinetic point.

[0092] k amc It represents the adsorption coefficient of pollutants on mobile colloids.

[0093] k aic It represents the adsorption coefficient of pollutants on attached colloids.

[0094] k dmc It represents the desorption coefficient of pollutants on mobile colloids.

[0095] k dic It represents the desorption coefficient of pollutants on attached colloids.

[0096] c ref Expressed as adsorption rate k amc The corresponding pollutant concentration.

[0097] s max Expressed as adsorption rate k aic The corresponding adsorbed pollutant concentration.

[0098] d 50 Represents the median particle size of porous media.

[0099] The first mathematical model in this embodiment takes into account the influence of the concentration of pollutants adsorbed on the surface and their adsorption coefficient on the colloid attachment process, and the influence of the concentration of pollutants adsorbed on the surface and their adsorption coefficient on the colloid separation process.

[0100] In the practical application of this embodiment, the second mathematical model includes:

[0101]

[0102] Among them, s e Represents the concentration of adsorbed pollutants at the equilibrium adsorption point.

[0103] μ s Indicates the degradation rate of solid-phase adsorbed pollutants.

[0104] μ w Indicates the degradation rate of dissolved pollutants in the liquid phase.

[0105] s mc It represents the concentration of pollutants adsorbed on the surface of mobile colloids.

[0106] s ic It indicates the concentration of pollutants adsorbed on the surface of immobile colloids.

[0107] C ref is the adsorption rate k amc The corresponding mobile colloid concentration.

[0108] In the practical application of this embodiment, the third mathematical model includes:

[0109]

[0110] μ i Indicates the degradation rate of pollutants adsorbed on the surface of immobile colloids.

[0111] μ m Indicates the degradation rate of pollutants adsorbed on the surface of mobile colloids.

[0112] The third mathematical model in this embodiment incorporates the migration flux of pollutants adsorbed on the mobile colloid and moving therewith.

[0113] In practical applications of this embodiment, the initial conditions include: initial spatial distribution of water potential of porous media, initial spatial distribution of dissolved pollutant concentration, initial spatial distribution of adsorbed pollutant concentration, and initial spatial distribution of colloid concentration.

[0114] In the practical application of this embodiment, the boundary conditions include: water flow conditions, pollutant migration and colloid migration conditions on the boundaries of the porous medium in all directions.

[0115] In practical applications of this embodiment, water flow conditions include: constant head conditions (such as a Malchow flask), variable head conditions (such as intermittent furrow irrigation), constant flux conditions (such as drip irrigation) or variable flux conditions (such as precipitation).

[0116] The boundary conditions for the migration of pollutants and colloids include: concentration boundary conditions (for example, the concentration of pollutants and colloids at a certain location in the soil of a contaminated site is known) and concentration flux boundary conditions (for example, the concentration of pollutants and colloids in the water entering the medium is known).

[0117] In the practical application of this embodiment, S2 specifically includes: according to the initial conditions and boundary conditions, using the finite difference method or the finite element method to solve the pre-acquired first mathematical model, the second mathematical model, and the third mathematical model respectively, so as to obtain the simulated co-migration process of colloids and pollutants in the porous medium.

[0118] The method for simulating the co-migration process of colloids and pollutants in a porous medium in the present embodiment adopts the pre-acquired first mathematical model, the second mathematical model, and the third mathematical model to comprehensively consider the mutual influence mechanism of the colloids and pollutants in the migration process in the porous medium. Compared with the prior art, it can simulate the mutual influence of colloids and pollutants in the migration process (for example, it considers that the pollutants adsorbed on the surface of the mobile colloid are promoted to migrate, the pollutants adsorbed on the surface of the attached colloid are co-retained, and the pollutants adsorbed on the surface of the colloid affect the surface properties of the colloid itself, thereby changing the adhesion and separation coefficients of the colloid), so that the co-migration process of colloids and pollutants obtained by the method for simulating the co-migration process of colloids and pollutants in a porous medium of the present invention is more accurate.

[0119] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0120] The present invention is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems) and computer program products according to the embodiments of the present invention. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions.

[0121] It should be noted that in the claims, any reference numerals placed between brackets shall not be construed as limiting the claims. The word "comprising" does not exclude the presence of components or steps not listed in the claims. The word "a" or "an" preceding a component does not exclude the presence of a plurality of such components. The invention may be implemented by means of hardware comprising several different components and by means of a suitably programmed computer. In the claims enumerating several means, several of these means may be embodied by the same hardware. The use of the words first, second, third, etc., is for convenience of expression only and does not indicate any order. These words may be understood as part of the component name.

[0122] In addition, it should be noted that, in the description of this specification, the description of the terms "one embodiment", "some embodiments", "embodiment", "example", "specific example" or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, unless they are contradictory.

[0123] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments after knowing the basic creative concept. Therefore, the claims should be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present invention.

[0124] Obviously, those skilled in the art can make various modifications and variations to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention should also include these modifications and variations.

Claims

1. A method for simulating the co-migration of colloids and pollutants in a porous medium, characterized in that: The method comprises: S1. Obtaining initial conditions and boundary conditions corresponding to colloids and pollutants in porous media; The initial conditions include: initial spatial distribution state of porous medium water potential, initial spatial distribution state of dissolved pollutant concentration, initial spatial distribution state of adsorbed pollutant concentration, and initial spatial distribution state of colloid concentration; Boundary conditions include: water flow conditions, pollutant migration and colloid migration conditions on the boundaries of porous media in all directions; Water flow conditions include: constant head or variable head conditions, constant flux or variable flux conditions; Pollutant and colloid migration boundary conditions include: concentration boundary conditions, concentration flux boundary conditions; S2. According to the initial conditions and boundary conditions, a first mathematical model for simulating the migration of colloids after adsorption of pollutants, a second mathematical model for simulating the migration of dissolved pollutants, and a third mathematical model for simulating the migration of pollutants adsorbed on the surface of the colloid are used to obtain the simulated co-migration process of colloids and pollutants in the porous medium.

2. The method according to claim 1, characterized in that: The first mathematical model comprises: C represents the concentration of liquid colloid; S1 represents the solid phase colloid concentration at the first kinetic point; S2 represents the solid colloid concentration at the second kinetic point; ρ b is the bulk density of the porous medium; J w Darcy flux represents the flow of water in porous media; D sh represents the diffusion coefficient of porous media; t represents time; z represents the spatial coordinate of the migration direction of colloids and pollutants in the porous medium; μ cw It represents the decomposition coefficient of liquid colloid; μ cs It represents the decomposition coefficient of solid colloid; θ represents the volumetric water content of the porous medium; S represents the solid phase colloid concentration; S max Indicates the maximum solid phase colloid concentration; k a1 It represents the colloid adhesion coefficient at the first kinetic point; k d1 It represents the colloid separation coefficient at the first kinetic point; k a2 Indicates the colloid adhesion coefficient at the second kinetic point; k d2 It represents the colloid separation coefficient at the second kinetic point; c represents the concentration of liquid phase pollutants; s k It represents the concentration of adsorbed pollutants at the kinetic point; k amc It represents the adsorption coefficient of pollutants on mobile colloids; k aic It represents the adsorption coefficient of pollutants on attached colloids; k dmc It represents the desorption coefficient of pollutants on mobile colloids; k dic It represents the desorption coefficient of pollutants on attached colloids; c ref Expressed as adsorption rate k amc The corresponding pollutant concentration; s max Expressed as adsorption rate k aic The corresponding adsorbed pollutant concentration; d 50 Represents the median particle size of porous media.

3. The method according to claim 2, characterized in that The second mathematical model comprises: Among them, s e It represents the concentration of adsorbed pollutants at the equilibrium adsorption point; μ s Indicates the degradation rate of solid-phase adsorbed pollutants; μ w It indicates the degradation rate of pollutants dissolved in liquid phase; s mc It represents the concentration of pollutants adsorbed on the surface of mobile colloids; s ic It represents the concentration of pollutants adsorbed on the surface of immobile colloids; C ref is the adsorption rate k amc The corresponding mobile colloid concentration.

4. The method according to claim 3, characterized in that The third mathematical model includes: μ i It indicates the degradation rate of pollutants adsorbed on the surface of immobile colloids; μ m Indicates the degradation rate of pollutants adsorbed on the surface of mobile colloids.

5. The method according to claim 4, characterized in that The S2 specifically includes: according to the initial conditions and boundary conditions, using the finite difference method or the finite element method to solve the first mathematical model, the second mathematical model and the third mathematical model acquired in advance respectively, so as to obtain the co-migration process of the colloid and the pollutant in the simulated porous medium.

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