CN109856028B - Method for predicting saturated permeability coefficient of clay mineral in electrolyte solution - Google Patents
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- 239000002734 clay mineral Substances 0.000 title claims abstract description 160
- 239000008151 electrolyte solution Substances 0.000 title claims abstract description 77
- 230000035699 permeability Effects 0.000 title claims abstract description 59
- 238000000034 method Methods 0.000 title claims abstract description 35
- 229920006395 saturated elastomer Polymers 0.000 title claims abstract description 7
- 229940021013 electrolyte solution Drugs 0.000 claims abstract description 76
- 239000000243 solution Substances 0.000 claims abstract description 31
- 230000003204 osmotic effect Effects 0.000 claims abstract description 18
- 238000002474 experimental method Methods 0.000 claims abstract description 8
- 239000002245 particle Substances 0.000 claims description 58
- XNWFRZJHXBZDAG-UHFFFAOYSA-N 2-METHOXYETHANOL Chemical compound COCCO XNWFRZJHXBZDAG-UHFFFAOYSA-N 0.000 claims description 23
- 238000005341 cation exchange Methods 0.000 claims description 16
- 150000001768 cations Chemical class 0.000 claims description 11
- 229910001422 barium ion Inorganic materials 0.000 claims description 9
- 239000013078 crystal Substances 0.000 claims description 9
- 239000011777 magnesium Substances 0.000 claims description 9
- 238000004364 calculation method Methods 0.000 claims description 8
- FYYHWMGAXLPEAU-UHFFFAOYSA-N Magnesium Chemical compound [Mg] FYYHWMGAXLPEAU-UHFFFAOYSA-N 0.000 claims description 6
- 238000004220 aggregation Methods 0.000 claims description 6
- 229910052749 magnesium Inorganic materials 0.000 claims description 6
- WDIHJSXYQDMJHN-UHFFFAOYSA-L barium chloride Chemical compound [Cl-].[Cl-].[Ba+2] WDIHJSXYQDMJHN-UHFFFAOYSA-L 0.000 claims description 4
- 229910001626 barium chloride Inorganic materials 0.000 claims description 4
- 239000011164 primary particle Substances 0.000 claims description 4
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 claims description 4
- JLVVSXFLKOJNIY-UHFFFAOYSA-N Magnesium ion Chemical compound [Mg+2] JLVVSXFLKOJNIY-UHFFFAOYSA-N 0.000 claims description 3
- 229910001425 magnesium ion Inorganic materials 0.000 claims description 3
- 238000005342 ion exchange Methods 0.000 claims description 2
- 239000002798 polar solvent Substances 0.000 claims description 2
- 239000000523 sample Substances 0.000 claims description 2
- 238000005259 measurement Methods 0.000 claims 1
- 239000004927 clay Substances 0.000 abstract 1
- 239000002689 soil Substances 0.000 description 12
- 239000010410 layer Substances 0.000 description 9
- 229910000281 calcium bentonite Inorganic materials 0.000 description 8
- ONCZQWJXONKSMM-UHFFFAOYSA-N dialuminum;disodium;oxygen(2-);silicon(4+);hydrate Chemical compound O.[O-2].[O-2].[O-2].[O-2].[O-2].[O-2].[O-2].[O-2].[O-2].[O-2].[O-2].[O-2].[Na+].[Na+].[Al+3].[Al+3].[Si+4].[Si+4].[Si+4].[Si+4] ONCZQWJXONKSMM-UHFFFAOYSA-N 0.000 description 8
- 229910000280 sodium bentonite Inorganic materials 0.000 description 8
- 229940080314 sodium bentonite Drugs 0.000 description 8
- FAPWRFPIFSIZLT-UHFFFAOYSA-M Sodium chloride Chemical compound [Na+].[Cl-] FAPWRFPIFSIZLT-UHFFFAOYSA-M 0.000 description 4
- 230000002776 aggregation Effects 0.000 description 4
- 230000008859 change Effects 0.000 description 4
- 230000007613 environmental effect Effects 0.000 description 3
- 239000011229 interlayer Substances 0.000 description 3
- 239000000126 substance Substances 0.000 description 3
- UXVMQQNJUSDDNG-UHFFFAOYSA-L Calcium chloride Chemical compound [Cl-].[Cl-].[Ca+2] UXVMQQNJUSDDNG-UHFFFAOYSA-L 0.000 description 2
- XEEYBQQBJWHFJM-UHFFFAOYSA-N Iron Chemical compound [Fe] XEEYBQQBJWHFJM-UHFFFAOYSA-N 0.000 description 2
- XDFCIPNJCBUZJN-UHFFFAOYSA-N barium(2+) Chemical compound [Ba+2] XDFCIPNJCBUZJN-UHFFFAOYSA-N 0.000 description 2
- 239000001110 calcium chloride Substances 0.000 description 2
- 229910001628 calcium chloride Inorganic materials 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 238000005067 remediation Methods 0.000 description 2
- 238000011160 research Methods 0.000 description 2
- 239000011780 sodium chloride Substances 0.000 description 2
- 238000012360 testing method Methods 0.000 description 2
- 229910052783 alkali metal Inorganic materials 0.000 description 1
- 150000001340 alkali metals Chemical class 0.000 description 1
- 229910052784 alkaline earth metal Inorganic materials 0.000 description 1
- 150000001342 alkaline earth metals Chemical class 0.000 description 1
- 229910052782 aluminium Inorganic materials 0.000 description 1
- XAGFODPZIPBFFR-UHFFFAOYSA-N aluminium Chemical compound [Al] XAGFODPZIPBFFR-UHFFFAOYSA-N 0.000 description 1
- 229910000323 aluminium silicate Inorganic materials 0.000 description 1
- 238000004458 analytical method Methods 0.000 description 1
- 238000012512 characterization method Methods 0.000 description 1
- 238000005352 clarification Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 239000012530 fluid Substances 0.000 description 1
- 239000008187 granular material Substances 0.000 description 1
- 230000003993 interaction Effects 0.000 description 1
- 229910052742 iron Inorganic materials 0.000 description 1
- 230000001788 irregular Effects 0.000 description 1
- 238000002386 leaching Methods 0.000 description 1
- 229910052943 magnesium sulfate Inorganic materials 0.000 description 1
- CSNNHWWHGAXBCP-UHFFFAOYSA-L magnesium sulphate Substances [Mg+2].[O-][S+2]([O-])([O-])[O-] CSNNHWWHGAXBCP-UHFFFAOYSA-L 0.000 description 1
- 230000007246 mechanism Effects 0.000 description 1
- 229910021645 metal ion Inorganic materials 0.000 description 1
- 230000005012 migration Effects 0.000 description 1
- 238000013508 migration Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000008569 process Effects 0.000 description 1
- 238000009738 saturating Methods 0.000 description 1
- 229910052710 silicon Inorganic materials 0.000 description 1
- 239000010703 silicon Substances 0.000 description 1
- 230000002194 synthesizing effect Effects 0.000 description 1
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- Investigating Or Analysing Materials By Optical Means (AREA)
Abstract
The invention provides a method for predicting saturated permeability coefficient of clay mineral in electrolyte solution, which comprises the following steps: 1) establishing a relation model of the type and concentration of the electrolyte solution and the osmotic coefficient of the clay mineral; 2) acquiring physical parameters of the model and clay surface charge density parameters; 3) calculating the surface charge density of different types of clay minerals in the polar solution; 3) obtaining the permeability coefficients of different types of clay minerals in certain specified electrolyte solutions with different concentrations through a constant head experiment, and calculating relevant parameters required by a model based on a relation model and the surface charge density of the clay minerals in a polar solution; 4) and predicting the osmotic coefficient of the clay mineral in the electrolyte solution with the concentration based on the relation model of the substituted relevant parameters and the actually measured concentration of the electrolyte solution. Compared with the prior art, the method for accurately predicting the clay mineral permeability coefficient is theoretically provided.
Description
Technical Field
The invention relates to the field of environmental ecology, in particular to a method for predicting saturated permeability coefficient of clay mineral in electrolyte solution.
Background
Clay minerals are generally referred to as layered aluminosilicates (sometimes containing other components such as iron, alkali metals and alkaline earth metals). Due to the isomorphous replacement effect commonly existing in clay minerals, silicon and aluminum in the clay mineral crystal structure can be replaced by low-valence metal ions, so that the clay mineral has permanent negative charges, has the characteristic of attracting positive charges, further has the characteristics of expansibility and low permeability, and is widely used. Meanwhile, the clay mineral has a permanent negative charge, and the structure of the clay mineral can also change greatly along with the types and concentrations of the surrounding cations.
The permeability coefficient is also called hydraulic conductivity coefficient, which is defined as unit flow rate per unit hydraulic gradient, represents the ease of fluid passing through the framework structure, and is an important parameter of soil. This parameter represents the strength of the soil permeability and thus further influences the migration of substances in the soil solution.
At present, the prediction research on the permeability coefficient of the clay mineral in different electrolyte solutions is very limited, few prediction formulas mostly belong to empirical formulas obtained by direct fitting according to experimental results, and the research on the influence mechanism of the electrolyte solution on various levels of structures of the clay mineral is not deep enough and has no specific theoretical support.
The importance of clay minerals is self-evident because clay minerals have a wide range of applications and the permeability coefficient is an important soil parameter that must be considered in environmental protection (e.g., landfill) and environmental remediation (e.g., chemical leaching remediation of soil). Because the determination of the permeability coefficient of soil is a time-consuming and labor-consuming task, and meanwhile, in the actual soil environment, the components of the soil solution are very complex, and the permeability coefficient of the soil solution can also have great difference even for the soil with basically the same components, especially the soil with more clay mineral content. Therefore, it is necessary to theoretically provide a prediction model for the influence of the type and concentration of the electrolyte solution on the clay mineral permeability coefficient.
Disclosure of Invention
The present invention aims to overcome the above-mentioned drawbacks of the prior art and provide a method for predicting the saturation permeability coefficient of clay minerals in an electrolyte solution.
The purpose of the invention can be realized by the following technical scheme:
a method for predicting the saturation permeability coefficient of clay minerals in an electrolyte solution comprises the following steps:
1) establishing a relation model of the type and concentration of the electrolyte solution and the osmotic coefficient of the clay mineral;
2) acquiring the temperature, the cation valence number of the electrolyte solution and the concentration of the electrolyte solution;
3) collecting the mass of the obtained clay mineral, the mass of ethylene glycol monomethyl ether adsorbed by the clay mineral in unit mass and the mass parameter of ethylene glycol monomethyl ether in each square meter when a monomolecular ethylene glycol methyl ether layer is formed, and calculating the specific surface area of the clay mineral in a polar solution; collecting the mass of the clay mineral, the amount of barium ions which can be exchanged into the clay mineral in a certain volume of barium chloride solution, calculating the cation exchange amount of the clay mineral, and calculating the surface charge density of the clay mineral by combining the mass and the amount of barium ions;
4) obtaining the permeability coefficient of the clay mineral in certain specific electrolyte solution with different concentrations through a constant head experiment,
5) calculating a fractal dimension, a relational formula proportionality coefficient of a permeability coefficient and particle size distribution, a formula proportionality coefficient of an average particle size after clay mineral aggregation and parameters related to the fractal dimension, the permeability coefficient and the particle size distribution required by the clay mineral in a relational model of a specific type of electrolyte solution based on the models and the parameters obtained in the steps 1), 2), 3) and 4);
6) substituting the obtained parameters into the relation model obtained in the step 1) to obtain a final relation model of the type and concentration of the electrolyte solution and the osmotic coefficient of the clay mineral;
7) and predicting the osmotic coefficient of the clay mineral in the electrolyte solution with the concentration according to the actually measured concentration of the electrolyte solution in the same clay mineral to be predicted based on the final relation model of the type and the concentration of the obtained electrolyte solution and the osmotic coefficient of the clay mineral.
Further, in the step 1), the relational model expression between the type and concentration of the electrolyte solution and the permeability coefficient of the clay mineral is as follows:
P＝PDDL-Pvdv
in the formula, PDDLDue to repulsion resulting from the overlapping of the electric double layers, PvdwIs the intermolecular force, P is the external pressure, specifically,
PDDL＝2CRT[coshym-1]
wherein C is the concentration of the electrolyte solution, R is the universal gas constant, T is the temperature, K is the permeability coefficient of clay minerals, v is the cation valence of the electrolyte solution, F is the Faraday constant, sigma0Is the surface charge density of the clay mineral,0in order to obtain the absolute dielectric constant,ris the relative dielectric constant of water and,kappa is the reciprocal of the Debye length, AHIs Hammetk constant, DpIs the thickness of the clay mineral crystal structure, c1And c2Is a constant.
Further, said c1And c2The expression of (1) is;
in the formula, q is an index and a fractal dimension D of clay mineralFAnd (3) correlation:
t1and t2Is a proportional coefficient of a relation formula of permeability coefficient and particle size distribution, t is the ratio of the 10 th percentile particle size to the average particle size, d10Is the particle size of the 10 th percentile particle,
is the average particle size r of clay mineral after aggregation0Is the primary particle size of the clay mineral, and k is the proportional coefficient of the formula of the average particle size after the clay mineral is aggregated.
Further, in the step 3), the specific surface area is determined by an ethylene glycol methyl ether method, that is, a measuring probe used for the determination is a polar solvent molecule, and the cation exchange capacity is determined by a positive divalent barium ion exchange method.
Further, the calculation formula of the specific surface area is as follows:
in the formula, SEGMEIs the specific surface area of clay mineral, WaIs the mass of ethylene glycol monomethyl ether adsorbed by a unit mass of clay mineral, m is the mass of the clay mineral, m iss＝0.000286g/m2Mass of ethylene glycol monomethyl ether per square meter when forming a monomolecular ethylene glycol methyl ether layer.
Further, the calculation formula of the cation exchange capacity is as follows:
wherein CEC is cation exchange amount of clay mineral, C0And C is the mass of magnesium in the solution before and after the addition of the positive divalent magnesium ions, V is the volume of the solution in the system, M is the mass of the clay mineral, M isMgIs the molecular weight of magnesium.
Further, the calculation formula of the surface charge density is as follows:
in the formula, σ0Is the surface charge density.
Further, in the step 4), the same electrolyte solution is adopted for a series of permeability coefficients measured by a constant head experiment.
Further, in the step 5), the calculation method is as follows: determining the types of clay minerals and electrolyte solutions, establishing different relation model equations by changing the concentration of the electrolyte solutions to form an equation set, and solving the optimal solution of unknown parameters by adopting a regression method.
Compared with the prior art, the invention has the following advantages:
(1) the method is established based on an extended DLVO theory, a fractal theory and a sea clarification formula, and a method for predicting the clay mineral permeability coefficient is theoretically provided;
(2) the method considers the influence of the type and concentration of the electrolyte solution on the clay mineral permeability coefficient, so that the result is more suitable for the situation of practical application;
(3) the same electrolyte solution is adopted for measuring a series of permeability coefficients in a constant head test, so that the relevant parameters are ensured to be unchanged;
(4) tests prove that the method has high coincidence degree between the predicted value and the measured value and high prediction accuracy;
drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic view of a microstructure of a clay mineral;
FIG. 3 is a schematic diagram of clay mineral fractal structure;
FIG. 4 is a schematic diagram showing the correlation between the structure of clay minerals at different levels
FIG. 5 is a graph of measured and predicted results for sodium bentonite permeability coefficients for a specific embodiment of the present invention;
fig. 6 is a graph of measured and predicted results of the permeability coefficient of calcium bentonite in accordance with an embodiment of the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.
The invention provides a method for predicting saturated permeability coefficient of clay mineral in electrolyte solution, as shown in figure 1, the method comprises the following steps:
1) establishing a relation model of the type and concentration of the electrolyte solution and the osmotic coefficient of the clay mineral;
2) acquiring the temperature, the cation valence number of the electrolyte solution and the concentration of the electrolyte solution;
3) collecting the mass of the obtained clay mineral, the mass of ethylene glycol monomethyl ether adsorbed by the clay mineral in unit mass and the mass parameter of ethylene glycol monomethyl ether in each square meter when a monomolecular ethylene glycol methyl ether layer is formed, and calculating the specific surface area of the clay mineral in a polar solution; acquiring the mass of the clay mineral and the amount of barium ions capable of being exchanged into the clay mineral in a certain volume of barium chloride solution, calculating the cation exchange amount of the clay mineral, and calculating the surface charge density of the clay mineral according to the cation exchange amount;
4) obtaining the permeability coefficient of the clay mineral in certain specific electrolyte solution with different concentrations through a constant head experiment,
5) calculating a fractal dimension, a relational formula proportionality coefficient of a permeability coefficient and particle size distribution, a formula proportionality coefficient of an average particle size after clay mineral aggregation and parameters related to the fractal dimension, the permeability coefficient and the particle size distribution required by the clay mineral in a relational model of a specific type of electrolyte solution based on the models and the parameters obtained in the steps 1), 2), 3) and 4);
6) substituting the obtained parameters into the relation model obtained in the step 1) to obtain a final relation model of the type and concentration of the electrolyte solution and the osmotic coefficient of the clay mineral;
7) and predicting the osmotic coefficient of the clay mineral in the electrolyte solution with the concentration according to the actually measured concentration of the electrolyte solution in the same clay mineral to be predicted based on the final relation model of the type and the concentration of the obtained electrolyte solution and the osmotic coefficient of the clay mineral.
1. Establishing a relation model of the type and concentration of the electrolyte solution and the osmotic coefficient of the clay mineral
The relation model of the type and concentration of the electrolyte solution and the permeability coefficient of the clay mineral is obtained by integrating three submodels, wherein the three submodels are respectively as follows:
11) the electrolyte solution influences a model of the original particle size of the clay mineral;
12) a relation model of the original particle size of the clay mineral and the particle size distribution of the aggregated particles;
13) a relation model of particle size distribution and permeability coefficient.
1.1 model of influence of electrolyte solution on size of original particles of clay mineral
The model that the original granule size of clay mineral is influenced to electrolyte solution is according to extension DLVO theory, reachs the relation between the concentration three of the distance between the interaction force between the clay mineral layer, clay mineral crystal structure and electrolyte solution, and then reachs this model, and the expression of relation is:
P＝PDDL-Pvdw+PCSS(1)
in the formula, PDDLDue to repulsion resulting from the overlapping of the electric double layers, PvdwIs intermolecular force, PCSSIs repulsion generated when cation between clay mineral layers is hydrated, P is external pressure, specifically,
(1) according to the theory of electric double layers, for PDDLComprises the following steps:
PDDL＝2CRT[coshym-1](2)
wherein C is the concentration of the electrolyte solution, R is the universal gas constant, T is the temperature, v is the cation valence of the electrolyte solution, F is the Faraday constant, σ0Is the surface charge density of the clay mineral,0in order to obtain the absolute dielectric constant,rk is the reciprocal of the debye length, which is the relative dielectric constant of water.
(2) According to DLVO theory, for PvdwComprises the following steps:
in the formula, AHIs Hammetk constant, DpIs the thickness of the clay mineral crystal structure, h is the distance between two clay mineral crystal structures,
when clay mineral is in saturation state DpThe value of (A) is determined only by the type of interlayer cations of the clay mineral, for example when the interlayer cations are Na+When D ispIs 0.96 nm.
(3)PCSSCan be generally expressed in the form of an index
Wherein k and l are constants
When the interlayer cations of the clay minerals are fully hydrated, namely the external pressure is not large, and the clay minerals are in a saturated state, the term can be ignored.
For the external pressure P, when the clay mineral is not subjected to the external pressure or is shallow soil, the value of P can be regarded as a certain value, and the atmospheric pressure can be directly taken as a value.
(4) Accordingly, the stress condition of the clay mineral crystal structure can be expressed as P ═ PDDL-Pvdw(10)
The variables of the formula are only the distance between the electrolyte solution and the crystal structure, and therefore can be regarded as a function of the distance of the clay mineral crystal structure and the electrolyte solution.
1.2 model of relationship between original particle size of clay mineral and particle size distribution after aggregation
Due to the irregular movement of clay mineral particles, the original particles of clay mineral in water collide with other surrounding particles to form clay mineral particles, and the clay mineral particles continue to collide to form larger clay mineral particles, as shown in fig. 3. According to the fractal theory, the particle size of the particles composed of a large number of primary particles satisfies
Wherein v and r represent the volume and the particle diameter of the particles, respectively, and v0And r0Respectively representing the volume and the particle size of the primary particles, DFIs a fractal dimension, and
r0＝Dp+h (12)
and the frequency of particle collisions can be expressed as
The change in the number density N of the particles over time can thus be expressed as
In the formula, n (v)i) Is a volume viThe particle number density of (a).
Using average particle size
Instead of the number density of the particles, the above formula can be written as
Wherein
Wherein k is Boltzmann's constant, T is temperature, ρ is particle density, a, φ, v are constants, and c is the sum of r0The number of correlations.
The solution of this equation is
Wherein also according to the fractal theory there are
Can be substituted by formula (22)
Wherein the content of the first and second substances,
therefore, when the time is long enough, the first term on the right side of the above equation is negligible, and thus
Wherein k is a scale factor, and k is a constant,
1.3 relationship model of particle size distribution and permeability coefficient
According to the Haichang formula, the relation between the permeability coefficient and the particle size satisfies
Wherein t is1Is a proportionality coefficient, d10Is the particle size of the 10 th percentile particle.
For clay minerals, the particle size distribution mostly satisfies the lognormal distribution, and the average particle size and d can be considered at this time10Proportionally, therefore the above formula can be written as
In the formula, K is the permeability coefficient of clay mineral, d10Is the particle size of the 10 th percentile particle, t1And t2Is a proportionality coefficient, wherein
t is the ratio of the 10 th percentile particle size to the average particle size.
1.4 model of relationship between type and concentration of electrolyte solution and osmotic coefficient of clay mineral
And (3) synthesizing the three sub-models to obtain a relation model of the type and concentration of the electrolyte solution and the permeability coefficient of the clay mineral, wherein the relation is as follows:
P＝PDDL-Pvdw(29)
wherein
PDDL＝2CRT[coshym-1](30)
In the above formula c1And c2Is a constant
2. Density of surface charge
2.1, the calculation formula of the clay mineral surface charge density is as follows:
in the formula, σ0Is the surface charge density, SEGMECEC is the cation exchange capacity of clay minerals, which is the specific surface area of clay minerals.
2.2, the specific surface area is measured by an Ethylene Glycol Methyl Ether (EGME) method, and the calculation formula of the specific surface area is as follows:
in the formula, SEGMEIs the specific surface area of clay mineral, WaIs the mass of ethylene glycol monomethyl ether adsorbed by a unit mass of clay mineral, m is the mass of the clay mineral, m isS＝0.000286g/m2Mass of ethylene glycol monomethyl ether per square meter when forming a monomolecular ethylene glycol methyl ether layer.
2.3, use of Ba2+The cation exchange amount of clay mineral is determined by exchange method, namely 1mol/L Ba is adopted2+Repeatedly saturating clay mineral, and adding MgSO4Solution exchange of Ba on clay minerals2+. The cation exchange capacity is calculated by the formula：
Wherein CEC is cation exchange amount of clay mineral, C0And C is the mass of magnesium in the solution before and after the addition of the positive divalent magnesium ions, V is the volume of the solution in the system, M is the mass of the clay mineral, M isMgIs the molecular weight of magnesium.
3. Detailed description of the preferred embodiments
Preferably, the specific implementation manner of the step (4) adopted by the invention is to determine the permeability coefficient of the clay mineral by adopting a constant head method. The method is characterized in that the adopted solutions are the same electrolyte solutions with different concentrations, the surface charges of the clay minerals characterized in the step (3) are combined, and then the c is obtained according to the model deduced in the step (1)1And c2Two constants. When the electrolyte solution is the same kind of solution, it is considered that the aggregation mode of the clay mineral does not change, i.e. the constant c1And c2The clay mineral and the electrolyte solution do not change when the clay mineral and the electrolyte solution are of the same type.
Preferably, the step (7) is implemented by determining the components of the solution in the clay mineral and determining the concentration thereof, and predicting the permeability coefficient of the clay mineral in the electrolyte solution with the determined concentration by combining with a model.
4. Examples of the applications
The following is a case where the prediction method is used in combination with specific examples, and the clay minerals used are sodium bentonite and calcium bentonite.
4.1 characterization of basic Properties of Clay mineral
The specific surface area of the sodium bentonite measured by the EGME method is 448.1g/m2The specific surface area of the calcium bentonite is 520.3g/m2. With Ba2+The cation exchange capacity of the sodium bentonite measured by an exchange method is 0.769mol/kg, and the cation exchange capacity of the calcium bentonite is 1.096 mol/kg. The surface charge density of the sodium bentonite is calculated to be-0.166C/m2The surface charge density of the calcium bentonite is-0.203C/m2。
4.2 prediction of clay mineral permeability coefficient
Firstly, a constant head experiment is adopted to measure the permeability coefficients of sodium bentonite in sodium chloride solutions with different concentrations and the permeability coefficients of calcium bentonite in calcium chloride solutions with different concentrations. The results are shown in tables 1 and 2.
Calculating a constant c from the measured permeability coefficient in combination with equation (29)1And c2. When the unit of the permeability coefficient K is cm/s and the unit of the original particle size of the clay mineral is m, for the sodium bentonite c1＝0.92×10-9，c2-0.144. For calcium bentonite c1＝1.14×10-1，c2＝-0.436。
C to be fitted out1And c2Substituting into equation (29), a prediction curve of permeability coefficient was calculated, and it was found that the predicted value matched well with the measured value. As shown in fig. 5 and 6
TABLE 1 osmotic coefficient of sodium bentonite in sodium chloride solutions of different concentrations
TABLE 2 permeability coefficient of calcium bentonite in calcium chloride solutions of different concentrations
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.
Claims (8)
1. A method for predicting the saturation permeability coefficient of clay minerals in an electrolyte solution is characterized by comprising the following steps:
1) establishing a relation model between the type and concentration of the electrolyte solution and the osmotic coefficient of the clay mineral,
2) collecting the temperature, the cation valence number of the electrolyte solution and the concentration of the electrolyte solution,
3) collecting the mass of the obtained clay mineral, the mass of ethylene glycol monomethyl ether adsorbed by the clay mineral in unit mass and the mass parameter of ethylene glycol monomethyl ether in each square meter when a monomolecular ethylene glycol methyl ether layer is formed, and calculating the specific surface area of the clay mineral in a polar solution; collecting the mass of the clay mineral, the amount of barium ions in the barium chloride solution with a certain volume capable of exchanging into the clay mineral, calculating the cation exchange amount of the clay mineral, and calculating the surface charge density of the clay mineral by combining the mass and the amount of barium ions in the barium chloride solution,
4) obtaining the permeability coefficient of the clay mineral in certain specific electrolyte solution with different concentrations through a constant head experiment,
5) based on the models and parameters obtained in the steps 1), 2), 3) and 4), calculating the fractal dimension, the formula proportionality coefficient of the relation between the osmotic coefficient and the particle size distribution, the formula proportionality coefficient of the average particle size after the clay mineral is aggregated and the parameters related to the three components,
6) substituting the obtained parameters into the relation model obtained in the step 1) to obtain a final relation model of the type and the concentration of the electrolyte solution and the osmotic coefficient of the clay mineral,
7) predicting the osmotic coefficient of the clay mineral in the electrolyte solution with the concentration according to the actually measured concentration of the electrolyte solution in the same clay mineral to be predicted based on the final relation model of the type and the concentration of the obtained electrolyte solution and the osmotic coefficient of the clay mineral;
in the step 1), the relational model expression of the type and concentration of the electrolyte solution and the permeability coefficient of the clay mineral is as follows:
P＝PDDL-Pvdw
in the formula, PDDLDue to repulsion resulting from the overlapping of the electric double layers, PvdwIs the intermolecular force, P is the external pressure, specifically,
PDDL＝2CRT[coshym-1]
wherein C is the concentration of the electrolyte solution, R is the universal gas constant, T is the temperature, K is the permeability coefficient of clay minerals, v is the cation valence of the electrolyte solution, F is the Faraday constant, sigma0Is the surface charge density of the clay mineral,0in order to obtain the absolute dielectric constant,ris the relative dielectric constant of water, κ is the reciprocal of the Debye length, AHIs Hammetk constant, DpIs the thickness of the clay mineral crystal structure, c1And c2Is a constant.
2. The method as claimed in claim 1, wherein c is the saturation permeability coefficient of clay mineral1And c2The expression of (1) is;
in the formula, q is an index and a fractal dimension D of clay mineralFAnd (3) correlation:
t1and t2Is a proportional coefficient of a relation formula of permeability coefficient and particle size distribution, t is the ratio of the 10 th percentile particle size to the average particle size, d10Is the particle size of the 10 th percentile particle,
is the average particle size r of clay mineral after aggregation0Is the primary particle size of the clay mineral, and k is the proportional coefficient of the formula of the average particle size after the clay mineral is aggregated.
3. The method for predicting the saturation permeability coefficient of the clay mineral in the electrolyte solution according to claim 1, wherein in the step 3), the specific surface area is determined by an ethylene glycol methyl ether method, that is, a measurement probe is adopted for determining polar solvent molecules, and the cation exchange capacity is determined by a positive divalent barium ion exchange method.
4. The method for predicting the saturation permeability coefficient of clay mineral in electrolyte solution according to claim 3, wherein the calculation formula of the specific surface area is as follows:
in the formula, SEGMEIs the specific surface area of clay mineral, WaIs the mass of ethylene glycol monomethyl ether adsorbed by a unit mass of clay mineral, m is the mass of the clay mineral, m isS＝0.000286g/m2Mass of ethylene glycol monomethyl ether per square meter when forming a monomolecular ethylene glycol methyl ether layer.
5. The method for predicting saturated permeability coefficient of clay mineral in electrolyte solution according to claim 3, wherein the cation exchange amount is calculated by the following formula:
wherein CEC is cation exchange amount of clay mineral, C0And C is the mass of magnesium in the solution before and after the addition of the positive divalent magnesium ions, V is the volume of the solution in the system, M is the mass of the clay mineral, M isMgIs the molecular weight of magnesium.
6. The method of claim 4, wherein the formula for calculating the surface charge density is as follows:
in the formula, σ0Is the surface charge density.
7. The method for predicting the saturation permeability coefficient of the clay mineral in the electrolyte solution according to claim 1, wherein in the step 4), the same electrolyte solution is adopted for a series of permeability coefficients measured by a constant head experiment.
8. The method for predicting the saturation permeability coefficient of clay mineral in the electrolyte solution according to claim 2, wherein in the step 5), the calculation method comprises: determining the types of clay minerals and electrolyte solutions, establishing different relation model equations by changing the concentration of the electrolyte solutions to form an equation set, and solving the optimal solution of unknown parameters by adopting a regression method.
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