CN108614942B - Method for representing spatiotemporal scale correlation of solute transport in porous medium - Google Patents
Method for representing spatiotemporal scale correlation of solute transport in porous medium Download PDFInfo
- Publication number
- CN108614942B CN108614942B CN201810440742.4A CN201810440742A CN108614942B CN 108614942 B CN108614942 B CN 108614942B CN 201810440742 A CN201810440742 A CN 201810440742A CN 108614942 B CN108614942 B CN 108614942B
- Authority
- CN
- China
- Prior art keywords
- solute
- space
- time
- model
- derivative
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
- 238000000034 method Methods 0.000 title claims abstract description 52
- 230000035515 penetration Effects 0.000 claims abstract description 45
- 238000009792 diffusion process Methods 0.000 claims abstract description 43
- 238000012360 testing method Methods 0.000 claims abstract description 19
- 230000008569 process Effects 0.000 claims abstract description 17
- 238000011160 research Methods 0.000 claims abstract description 6
- 239000006185 dispersion Substances 0.000 claims description 21
- 238000013508 migration Methods 0.000 abstract description 24
- 230000005012 migration Effects 0.000 abstract description 24
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 abstract description 5
- 238000003900 soil pollution Methods 0.000 abstract description 3
- 238000003911 water pollution Methods 0.000 abstract description 3
- 238000011156 evaluation Methods 0.000 abstract 1
- 239000000243 solution Substances 0.000 description 14
- 238000004364 calculation method Methods 0.000 description 4
- 238000004458 analytical method Methods 0.000 description 3
- 230000001419 dependent effect Effects 0.000 description 3
- CURLTUGMZLYLDI-UHFFFAOYSA-N Carbon dioxide Chemical compound O=C=O CURLTUGMZLYLDI-UHFFFAOYSA-N 0.000 description 2
- 238000005516 engineering process Methods 0.000 description 2
- 238000002474 experimental method Methods 0.000 description 2
- 238000012886 linear function Methods 0.000 description 2
- 230000009466 transformation Effects 0.000 description 2
- 230000001052 transient effect Effects 0.000 description 2
- VEXZGXHMUGYJMC-UHFFFAOYSA-M Chloride anion Chemical compound [Cl-] VEXZGXHMUGYJMC-UHFFFAOYSA-M 0.000 description 1
- 235000010627 Phaseolus vulgaris Nutrition 0.000 description 1
- 244000046052 Phaseolus vulgaris Species 0.000 description 1
- YZCKVEUIGOORGS-NJFSPNSNSA-N Tritium Chemical compound [3H] YZCKVEUIGOORGS-NJFSPNSNSA-N 0.000 description 1
- 230000002159 abnormal effect Effects 0.000 description 1
- 230000002547 anomalous effect Effects 0.000 description 1
- 229910002092 carbon dioxide Inorganic materials 0.000 description 1
- 239000001569 carbon dioxide Substances 0.000 description 1
- 230000008859 change Effects 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 230000007613 environmental effect Effects 0.000 description 1
- 239000003344 environmental pollutant Substances 0.000 description 1
- 239000012530 fluid Substances 0.000 description 1
- 238000002347 injection Methods 0.000 description 1
- 239000007924 injection Substances 0.000 description 1
- 239000002245 particle Substances 0.000 description 1
- 231100000719 pollutant Toxicity 0.000 description 1
- 238000011002 quantification Methods 0.000 description 1
- 238000005295 random walk Methods 0.000 description 1
- 238000005067 remediation Methods 0.000 description 1
- 239000013535 sea water Substances 0.000 description 1
- 238000007789 sealing Methods 0.000 description 1
- 238000007711 solidification Methods 0.000 description 1
- 230000008023 solidification Effects 0.000 description 1
- 229910052722 tritium Inorganic materials 0.000 description 1
- 239000002699 waste material Substances 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
The invention discloses a method for representing spatiotemporal-temporal scale correlation of solute migration in a porous medium, which comprises the steps of selecting a specific solute migration process in the porous medium as a research object, determining test conditions and obtaining test data of a solute penetration curve; establishing a space-time fractal derivative convection diffusion model, and deducing an analytic solution of the space-time fractal derivative convection diffusion model; calculating parameters of a space-time fractal derivative convection diffusion model by combining test data of a solute penetration curve, quantizing the solute penetration curve by adopting analytical solution of the model, and analyzing early arrival and trailing characteristics of the penetration curve; and analyzing the degree of association between the model parameters and the time or space scale according to the values of the model parameters, and giving the quantitative relation between the model parameters and the time or space scale. According to the invention, the smaller the order of the time fractal derivative and the space fractal derivative is, the larger the degree of the time-space correlation is, and the more obvious the early arrival and trailing characteristics of the penetration curve are. The method can be used for prediction, evaluation, restoration and the like of underground water and soil pollution, and is convenient for engineering use.
Description
Technical Field
The invention relates to an environmental fluid technology method, in particular to a method for representing spatiotemporal scale correlation of solute transport in a porous medium.
Background
Engineering problems of oil gas collection and transportation, carbon dioxide solidification and sealing, deep burying and storage of nuclear waste, site selection of refuse landfill, seawater backflow and the like all relate to the common problem of the migration rule of solute in a porous medium. Numerous indoor and outdoor experiments have shown that the solute transport processes in porous media generally exhibit time-scale dependent characteristics, i.e. their diffusion coefficients or flow rates are no longer constant, but rather are linear or non-linear functions in time or space, such processes being referred to as non-fick, anomalous or non-gaussian transport processes. Therefore, the method for exploring and quantifying the spatial-temporal scale association rule of solute migration in the porous medium can provide reasonable methods and guidance for the development and utilization of natural resources, the control of pollutant migration process, the remediation and treatment of polluted water bodies and the like.
The diffusion coefficient and the flow velocity are assumed to be constant in the conventional convection diffusion model, so that the solute transport process related to the space-time scale cannot be accurately described. At present, a plurality of technologies are applied to a method for describing the spatio-temporal scale correlation characteristics of solute migration in a porous medium at home and abroad, such as a time-space scale dependent convection diffusion model, a fractional derivative convection diffusion model, a continuous time random walking model and the like. It should be noted that most of the convection diffusion models depending on the time-space scale are empirical models, and the physical meaning of the model parameters is not clear. The fractional derivative convection diffusion model is a special case of a continuous time random walking model, and has the main problem of high calculation cost, and although the meaning of model parameters is clear, the fractional derivative convection diffusion model cannot be directly connected with the geometric characteristics of a porous medium.
The prior art also relates to the problem of solute transport in porous media, for example, a random walk particle tracking method is adopted to simulate the solute transport in a single-crack medium to obtain the distribution of the solute, and the method is not combined with the actual solute transport problem; furthermore, the nature of the Markov chain is combined, a random walking model is utilized to simulate the underground water solute transport process, but the spatio-temporal scale correlation characteristics of the solute transport process are not considered; in addition, a time fractal derivative model is also used for numerically simulating the abnormal diffusion of the chloride ions, and the method does not consider spatial scale correlation; based on the problems existing in the above methods, a new method for characterizing the spatiotemporal scale correlation of solute transport in porous media is needed to solve the above problems.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to overcome the defects of the prior art and provide a method for accurately characterizing spatiotemporal scale correlation of solute transport in a porous medium.
The technical scheme is as follows: the invention provides a method for representing spatiotemporal scale correlation of solute transport in a porous medium, which comprises the following steps:
(1) selecting a specific solute transport process in a porous medium as a research object, determining test conditions, and obtaining test data of a solute penetration curve;
(2) establishing a space-time fractal derivative convection diffusion model, and deducing an analytic solution of the space-time fractal derivative convection diffusion model;
(3) calculating parameters of the space-time fractal derivative convection diffusion model in the step (2) by combining the test data of the solute penetration curve in the step (1), and analyzing the early arrival and trailing characteristics of the penetration curve by adopting the analytic solution of the model to quantize the solute penetration curve in the step (1);
(4) and (4) analyzing the correlation degree of the model parameters and the time or space scale according to the values of the model parameters in the step (3), and giving the quantitative relation between the model parameters and the time or space scale.
Further, the space-time fractal derivative convection dispersion model for characterizing the space-time correlation of solute transport in the porous medium in the step (2) is as follows:
wherein u (x, t) is the concentration of solute at the position x and the moment t, 0< α ≤ 1 is the order of time fractal derivative, 0< β ≤ 1 is the order of space fractal derivative, D is dispersion coefficient, V is flow velocity, and D and V are independent of time and space, and according to the property of the fractal derivative, the solute concentration of the model at the instantaneous point source is deduced, i.e. the model is resolved as:
wherein c is a constant, D is a dispersion coefficient, V is a flow velocity, 0<α is not more than 1, which is the order of time fractal derivative, 0<β is not more than 1, is the order of the spatial fractal derivative, the initial condition is that u (x, t ═ 0) ═ 0, the boundary condition is that when x → ∞,
further, the equivalent form of the space-time fractal derivative convection diffusion model in the step (2) is as follows:
wherein u (x, t) is the concentration of the solute at the position x and the moment t, 0< α ≤ 1 is the order of the time fractal derivative, 0< β ≤ 1 is the order of the space fractal derivative, D is the dispersion coefficient, and V is the flow velocity.
Further, the step (3) adopts a least square method, parameters of a space-time fractal derivative convection diffusion model are calculated through Matlab software, the model parameters comprise a diffusion coefficient D, a flow velocity V, the order α of a time fractal derivative and the order β of a space fractal derivative, the solute penetration curve in the step (1) is analyzed, solved and quantified through the model, the value corresponding to the solute penetration curve is the measured value of the solute concentration, the analytic solution of the model is the predicted value of the solute concentration, and the space-time fractal derivative convection diffusion model is compared with the existing time or space scale correlation convection diffusion model to analyze the early arrival and trailing characteristics of the penetration curve.
Further, in the step (4), the spatial scale is a solute transport distance, and the quantitative relationship between the model parameter and the spatial scale includes a quantitative relationship between the order of the time fractal derivative and the solute transport distance and a quantitative relationship between the order of the space fractal derivative and the solute transport distance, where a linear relationship is formed between the order of the time fractal derivative and the solute transport distance, and the expression is as follows:
α＝-0.045x+0.837；
r2＝0.996；
wherein α represents the order of the time fractal derivative, x represents the solute transport distance, and r represents the goodness of fit;
the order of the spatial fractal derivative and the solute transport distance are in approximate linear relation, and the expression is as follows:
β＝-0.055x+0.99；
r2＝0.989；
where β represents the order of the spatial fractal derivative, x represents the solute transport distance, and r represents the goodness of fit.
Has the advantages that: compared with the prior art, the method is characterized in that test data of a solute penetration curve are obtained based on a specific solute transport process in the porous medium as a research object, then a space-time fractal derivative convective dispersion model is established, an analytic solution of the convective dispersion model is deduced, parameters of the space-time fractal derivative convective dispersion model are determined by combining test conditions and the test data, the solute penetration curve in the porous medium is quantized, and finally the quantitative relation between the model parameters and time or space scale is investigated. The order of the time fractal derivative and the space fractal derivative of the invention describes the correlation degree of the spatiotemporal scale of solute migration in the porous medium and the early arrival and trailing characteristics of the penetration curve, and the smaller the order, the larger the spatiotemporal correlation degree is, and the more obvious the early arrival and trailing characteristics of the penetration curve are. The invention has wide engineering application prospect and can be used for predicting, evaluating and treating underground water and soil pollution and the like. Compared with the prior art, the method is more convenient for engineering use.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
fig. 2 is a graph of the corresponding solute penetration curves for different models describing migration distances x of 4 m;
fig. 3 is a graph of the corresponding solute penetration curves for different models describing migration distances x of 6 m;
fig. 4 is a graph of the corresponding solute penetration curves for different models describing the migration distance x of 8 m;
FIG. 5 is a graph of time-fractal derivatives versus migration distance;
FIG. 6 is a graph of spatial fractal derivatives versus migration distance.
Detailed Description
The technical solution of the present invention is described in detail below with reference to the accompanying drawings and specific embodiments, but the scope of the present invention is not limited to the embodiments.
The invention principle is as follows: compared with fractional order derivatives, the basic concept of the fractional derivatives is simple in mathematical form, convolution integral is not included in the expression, the fractional order derivatives are local operators, the calculation amount is greatly reduced compared with that of non-local fractional order derivatives, and the calculation efficiency is high. The fractal derivative can also be regarded as a scale transformation, and the main idea is to convert integer-dimensional time and space into fractal space-time through the scale transformation, and the fractal space-time is directly used for describing a space-time scale dependent system. The presently widely used spread gaussian distribution and spread exponential decay, also known as non-debye decay, spread relaxation, can be directly deduced from the fractal derivative model. The statistical mechanical basis is clear, and the method is completely different from the statistical background of the Levy stable distribution of the fractional derivative and the Mittag-Leffler function attenuation. From the aspect of fractal geometry, the dimension of the fractal derivative in space in the spatial definition is the fractal dimension of the fractal body.
A large number of experiments show that the solute migration process in the porous medium usually shows a time scale correlation characteristic, and the dispersion coefficient or the flow velocity of the porous medium is not a constant, but a linear or nonlinear function of time or space and is non-Fick migration. In order to overcome the limitation of the existing method, the invention provides a space-time fractal derivative convection diffusion model, deduces an analytic solution of the convection diffusion model and represents the space-time scale correlation characteristic of solute transport.
As shown in FIG. 1, the method for characterizing spatiotemporal scale correlation of solute transport in porous media of the present invention comprises the following specific operation steps:
(1) selecting a specific solute transport process in a porous medium as a research object, determining test conditions, and obtaining test data of a solute penetration curve;
in the embodiment, bean gravel is filled in a cylinder with the length of 8m and the inner diameter of 30cm, 5 liters of tritium-containing isotope solution is injected into one end of the cylinder, samples are collected at positions 4m, 6m and 8m downstream of the injection end, the concentrations of solutes of the samples at positions 4m, 6m and 8m downstream at different times are recorded, and a penetration curve of the solutes is drawn according to the change value of the solute concentration along with time.
(2) Establishing a space-time fractal derivative convection diffusion model, and deducing an analytic solution of the space-time fractal derivative convection diffusion model;
a space-time fractal derivative convection dispersion model for characterizing solute transport space-time correlation in porous media is as follows:
wherein u (x, t) is the concentration of solute at position x and time t, 0< α ≤ 1 is the order of time fractal derivative, 0< β ≤ 1 is the order of space fractal derivative, D is dispersion coefficient, V is flow velocity, and D and V are independent of time and space.
Wherein c is a constant, D is a dispersion coefficient, V is a flow velocity, 0<α is not more than 1, which is the order of time fractal derivative, 0<β is not more than 1, is the order of the spatial fractal derivative, the initial condition is that u (x, t ═ 0) ═ 0, the boundary condition is that when x → ∞,
further, the step (2) may also adopt an equivalent form of a space-time fractal derivative convection diffusion model, that is:
wherein u (x, t) is the concentration of the solute at the position x and the moment t, 0< α ≤ 1 is the order of the time fractal derivative, 0< β ≤ 1 is the order of the space fractal derivative, D is the dispersion coefficient, and V is the flow velocity.
(3) And (3) calculating parameters of the space-time fractal derivative convection diffusion model in the step (2), namely the diffusion coefficient, the flow velocity, the order of the time fractal derivative and the order of the space fractal derivative, by combining the test data of the solute penetration curve in the step (1). And (3) analyzing early arrival and trailing characteristics of the penetration curve by adopting the solute penetration curve in the step (1) of analytical solution quantification of the model.
In the step, a least square method is adopted, parameters of a space-time fractal derivative convection diffusion model are calculated through Matlab software, the model parameters comprise a diffusion coefficient D, a flow velocity V, the order α of a time fractal derivative and the order β of a space fractal derivative, a solute penetration curve in the step (1) is quantified through analysis and solution of the model, the value corresponding to the solute penetration curve is an actually measured value of solute concentration, the analysis and solution of the model is a predicted value of solute concentration, and the space-time fractal derivative convection diffusion model is compared with an existing time or space scale associated convection diffusion model, so that the significance of the order of the space-time fractal derivative is determined.
Specifically, the solute migration test in this embodiment may be regarded as a transient point source solute migration problem, and an analytic solution fitting step (1) is performed by using a space-time fractal derivative convection diffusion model corresponding to a transient point source to obtain solute penetration curves corresponding to three migration distances x, where the values of x are 4, 6, and 8, respectively. Determining the values of the model parameters by means of a least-squares method, wherein the dispersion coefficient D is 0.0064m2The flow velocity V is 1.4m/h, and the order α of the time fractal derivative and the order β of the space fractal derivative are shown in the table 1. As shown in the table 1, the smaller the order of the time fractal derivative is, the larger the correlation degree of the space-time scale of the solute migration process is.
TABLE 1 parameter values of space-time fractal derivative order convection diffusion model corresponding to different migration distances
And (3) according to the parameter values in the step (2) and the analytic solutions of the space-time fractal derivative convection diffusion model corresponding to the instantaneous point source, drawing solute penetration curves corresponding to different migration distances x of 4m, 6m and 8m in the step (1), comparing the solute penetration curves with the existing space correlation model and space-time correlation model, and analyzing the early arrival and trailing characteristics of the solute penetration curves, wherein the early arrival and trailing characteristics are respectively shown in fig. 2, fig. 3 and fig. 4. As can be seen from fig. 2, 3 and 4, as the migration distance increases, the early arrival (i.e., the left end of the solute penetration curve, the concentration value of the solute is larger when the time is smaller) and the trailing features (i.e., the right end of the solute penetration curve, the duration of the process of the concentration of the solute decaying to 0 is longer) of the solute penetration curve become more obvious, and the fractal derivative convection model can more accurately describe the features of non-fick migration than the spatial correlation model and the spatial-temporal correlation model. The more obvious the early arrival characteristic of the penetration curve corresponds to the smaller value of the spatial fractal derivative, the more obvious the trailing characteristic is, and the corresponding value of the time fractal derivative is smaller.
(4) And (4) analyzing the correlation degree of the model parameters and the time or space scale according to the values of the model parameters in the step (3), and giving the quantitative relation between the model parameters and the time or space scale. The method comprises the following steps of calculating parameters of a model corresponding to different time or space scales, analyzing the degree of association between the model parameters and the time or space scales, and giving out the linear or nonlinear relation between the model parameters and the time or space scales.
Specifically, the relation between the order of the time and space fractal derivatives and the solute transport distance is analyzed according to the values of the parameters of the space-time fractal derivative convection diffusion model in the step (3). Through calculation and analysis, the linear relation between the order of the time fractal derivative and the migration distance can be obtained, and the slope of a straight line is-0.045, as shown in figure 5; the linear relational expression is:
α＝-0.045x+0.837；
r2＝0.996；
wherein α represents the order of the time fractal derivative, x represents the solute transport distance, and r represents the goodness of fit;
the order of the spatial fractal derivative is also approximated as a linear function of the migration distance, and the slope of the straight line is-0.055, see fig. 6; the linear functional relationship expression is:
β＝-0.055x+0.99；
r2＝0.989；
where β represents the order of the spatial fractal derivative, x represents the solute transport distance, and r represents the goodness of fit.
Therefore, the solute transport process in the porous medium has the spatial-temporal scale correlation characteristics, and the spatial-temporal fractal derivative convection diffusion model can be adopted to characterize the characteristics.
The method comprises the steps of obtaining test data of a solute penetration curve based on a solute transport process in a specific porous medium as a research object, then establishing a space-time fractal derivative convection dispersion model, deducing an analytic solution of the convection dispersion model, determining parameters of the space-time fractal derivative convection dispersion model by combining test conditions and the test data, quantizing the solute penetration curve in the porous medium, and finally inspecting the quantitative relation between the model parameters and time and space scales. In the method for representing the correlation of the solute transport spatio-temporal scale in the porous medium, the order of the time fractal derivative and the space fractal derivative describes the correlation degree of the solute transport spatio-temporal scale in the porous medium and the early arrival and trailing characteristics of a penetration curve, and the smaller the order, the larger the correlation degree, and the more obvious the early arrival and trailing characteristics of the penetration curve. The invention has wide engineering application prospect and can be used for predicting, evaluating, repairing and the like of underground water and soil pollution. Compared with the prior art, the method is more convenient for engineering use.
Claims (4)
1. A method of characterizing a spatiotemporal scale correlation of solute transport in a porous medium, comprising the steps of:
(1) selecting a specific solute transport process in a porous medium as a research object, determining test conditions, and obtaining test data of a solute penetration curve;
(2) establishing a space-time fractal derivative convection diffusion model, and deducing an analytic solution of the space-time fractal derivative convection diffusion model;
(3) calculating parameters of the space-time fractal derivative convection diffusion model in the step (2) by combining the test data of the solute penetration curve in the step (1), and analyzing the early arrival and trailing characteristics of the penetration curve by adopting the analytic solution of the model to quantize the solute penetration curve in the step (1);
(4) analyzing the correlation degree of the model parameters and the time or space scale according to the values of the model parameters in the step (3), and giving the quantitative relation between the model parameters and the time or space scale; specifically, the method comprises the following steps:
the space scale is solute transport distance, the quantitative relation between the model parameter and the space scale comprises the quantitative relation between the order of the time fractal derivative and the solute transport distance and the quantitative relation between the order of the space fractal derivative and the solute transport distance, wherein the order of the time fractal derivative and the solute transport distance are in linear relation, and the expression is as follows:
α＝-0.045x+0.837；
r2＝0.996；
wherein α represents the order of the time fractal derivative, x represents the solute transport distance, and r represents the goodness of fit;
the order of the spatial fractal derivative and the solute transport distance are in approximate linear relation, and the expression is as follows:
β＝-0.055x+0.99；
r2＝0.989；
where β represents the order of the spatial fractal derivative, x represents the solute transport distance, and r represents the goodness of fit.
2. The method for characterizing the spatiotemporal-spatial scale correlation of solute transport in porous media according to claim 1, wherein the spatiotemporal fractal derivative convective dispersion model for characterizing the spatiotemporal correlation of solute transport in porous media in step (2) is as follows:
wherein u (x, t) is the concentration of solute at the position x and the moment t, 0< α ≤ 1 is the order of time fractal derivative, 0< β ≤ 1 is the order of space fractal derivative, D is dispersion coefficient, V is flow velocity, and D and V are independent of time and space, and according to the property of the fractal derivative, the solute concentration of the model at the instantaneous point source is deduced, i.e. the model is resolved as:
wherein c is a constant, D is a dispersion coefficient, V is a flow velocity, 0<α is not more than 1, which is the order of time fractal derivative, 0<β is not more than 1, is the order of the spatial fractal derivative, the initial condition is that u (x, t ═ 0) ═ 0, the boundary condition is that when x → ∞,
3. the method for characterizing the spatiotemporal scale correlation of solute transport in porous media according to claim 1, wherein the equivalent form of the spatiotemporal fractal derivative convective dispersion model in step (2) is:
wherein u (x, t) is the concentration of the solute at the position x and the moment t, 0< α ≤ 1 is the order of the time fractal derivative, 0< β ≤ 1 is the order of the space fractal derivative, D is the dispersion coefficient, and V is the flow velocity.
4. The method for characterizing the spatiotemporal correlation of solute transport in porous media according to claim 1, wherein the step (3) adopts a least square method, and calculates the parameters of a spatiotemporal fractal derivative convective diffusion model through Matlab software, the model parameters include diffusion coefficient D, flow velocity V, order α of time fractal derivative and order β of space fractal derivative, the solute penetration curve in the step (1) is analyzed and quantified by the model, the value corresponding to the solute penetration curve is the measured value of solute concentration, the analytic solution of the model is the predicted value of solute concentration, and the spatiotemporal fractal derivative convective diffusion model is compared with the existing time or space scale correlation convective diffusion model to analyze the early arrival and trailing characteristics of the penetration curve.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810440742.4A CN108614942B (en) | 2018-05-10 | 2018-05-10 | Method for representing spatiotemporal scale correlation of solute transport in porous medium |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810440742.4A CN108614942B (en) | 2018-05-10 | 2018-05-10 | Method for representing spatiotemporal scale correlation of solute transport in porous medium |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN108614942A CN108614942A (en) | 2018-10-02 |
| CN108614942B true CN108614942B (en) | 2020-05-05 |
Family
ID=63662714
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201810440742.4A Expired - Fee Related CN108614942B (en) | 2018-05-10 | 2018-05-10 | Method for representing spatiotemporal scale correlation of solute transport in porous medium |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN108614942B (en) |
Families Citing this family (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111323344B (en) * | 2020-04-17 | 2020-12-22 | 吉林大学 | Simulation device and experimental method for three-dimensional solute transport in porous medium |
| CN111690831B (en) * | 2020-05-29 | 2022-05-24 | 江西理工大学 | Liquid injection process optimization method of ionic rare earth ore |
| CN112206553B (en) * | 2020-09-24 | 2022-06-03 | 天津大学 | Method for evaluating competitive adsorption of polystyrene microspheres and humic acid in sand filtration |
| CN113484210B (en) * | 2021-05-28 | 2022-11-18 | 河海大学 | On-site scale test determination method for dispersity of strongly weathered layer |
| CN113588916B (en) * | 2021-07-09 | 2022-04-29 | 河海大学 | Method for predicting water accumulation adsorption in expansive soil |
Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2007149766A3 (en) * | 2006-06-18 | 2009-04-02 | Chevron Usa Inc | Reservoir simulation using a multi-scale finite volume including black oil modeling |
| CN103412142A (en) * | 2013-09-10 | 2013-11-27 | 河海大学 | Device and method for monitoring and testing seepage speed of porous medium structural body |
| CN204536168U (en) * | 2015-04-24 | 2015-08-05 | 长安大学 | A kind of test unit measuring sediment infiltration coefficient for pneumatic process |
| US9169579B2 (en) * | 2005-03-11 | 2015-10-27 | New Jersey Institute Of Technology | Carbon nanotube mediated membrane extraction |
| CN106202746A (en) * | 2016-07-14 | 2016-12-07 | 南京大学 | The Yeh multi-level finite element modeling method of simulation Water in Porous Medium stream Darcy velocity |
| CN106248546A (en) * | 2016-06-16 | 2016-12-21 | 水利部交通运输部国家能源局南京水利科学研究院 | A kind of multiple dimensioned thermal transport synchronous monitoring pilot system and test method |
| CN106951617A (en) * | 2017-03-10 | 2017-07-14 | 河海大学 | A kind of point shape derivative analogue method of chlorion unusual dispersion ability data reconstruction in concrete |
| CN104865165B (en) * | 2015-06-05 | 2018-01-12 | 武汉大学 | The on-site soil solute transfer dispersion coefficient method for measuring of overall process flux conservation |
Family Cites Families (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20140057814A1 (en) * | 2010-12-07 | 2014-02-27 | Tufts University | Gum arabic encapsulation of reactive particles for enhanced delivery during subsurface restoration |
| CN102073796B (en) * | 2011-02-21 | 2012-11-21 | 南京大学 | Lattice traveling method for simulating solute three-dimensional transport process |
| CN106886682B (en) * | 2017-01-04 | 2020-01-07 | 中国环境科学研究院 | Random walking particle tracking method for solute transport numerical simulation in single fracture |
-
2018
- 2018-05-10 CN CN201810440742.4A patent/CN108614942B/en not_active Expired - Fee Related
Patent Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US9169579B2 (en) * | 2005-03-11 | 2015-10-27 | New Jersey Institute Of Technology | Carbon nanotube mediated membrane extraction |
| WO2007149766A3 (en) * | 2006-06-18 | 2009-04-02 | Chevron Usa Inc | Reservoir simulation using a multi-scale finite volume including black oil modeling |
| CN103412142A (en) * | 2013-09-10 | 2013-11-27 | 河海大学 | Device and method for monitoring and testing seepage speed of porous medium structural body |
| CN204536168U (en) * | 2015-04-24 | 2015-08-05 | 长安大学 | A kind of test unit measuring sediment infiltration coefficient for pneumatic process |
| CN104865165B (en) * | 2015-06-05 | 2018-01-12 | 武汉大学 | The on-site soil solute transfer dispersion coefficient method for measuring of overall process flux conservation |
| CN106248546A (en) * | 2016-06-16 | 2016-12-21 | 水利部交通运输部国家能源局南京水利科学研究院 | A kind of multiple dimensioned thermal transport synchronous monitoring pilot system and test method |
| CN106202746A (en) * | 2016-07-14 | 2016-12-07 | 南京大学 | The Yeh multi-level finite element modeling method of simulation Water in Porous Medium stream Darcy velocity |
| CN106951617A (en) * | 2017-03-10 | 2017-07-14 | 河海大学 | A kind of point shape derivative analogue method of chlorion unusual dispersion ability data reconstruction in concrete |
Non-Patent Citations (6)
| Title |
|---|
| Homotopy perturbation method for solving the space–time fractional advection–dispersion equation;Ahmet Yıldırım 等;《Advances in Water Resources》;20091022;第1711-1713页 * |
| Modelling solute dispersion in periodic heterogeneous porous media: Model benchmarking against intermediate scale experiments;Samer Majdalani 等;《Journal of Hydrology》;20180328;第427-443页 * |
| 一维均质与非均质土柱中溶质迁移的分数微分对流-弥散模拟;陈静 等;《水科学进展》;20060531;第17卷(第3期);第299-304页 * |
| 改进时间分数阶模型模拟非Fick溶质运移;夏源 等;《水科学进展》;20130531;第349-357页 * |
| 空间-时间分数阶变系数对流扩散方程微分阶数的数值反演;贾现正 等;《计算数学》;20140531;第113-132页 * |
| 陈静 等.一维均质与非均质土柱中溶质迁移的分数微分对流-弥散模拟.《水科学进展》.2006,第17卷(第3期),第299-304页. * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN108614942A (en) | 2018-10-02 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN108614942B (en) | Method for representing spatiotemporal scale correlation of solute transport in porous medium | |
| Anderson et al. | The role of the postaudit in model validation | |
| Carrera | An overview of uncertainties in modelling groundwater solute transport | |
| US6035701A (en) | Method and system to locate leaks in subsurface containment structures using tracer gases | |
| Guneshwor et al. | Identification of groundwater contamination sources using meshfree RPCM simulation and particle swarm optimization | |
| Peck | Field variability of soil physical properties | |
| Seuntjens et al. | Sensitivity analysis of physical and chemical properties affecting field-scale cadmium transport in a heterogeneous soil profile | |
| CN113772804B (en) | Groundwater pollution monitoring natural attenuation restoration prediction method, system and device | |
| CN112697849B (en) | Dynamic pollution source positioning method | |
| Ghosh et al. | Subsurface fate and transport of cyanide species at a manufactured-gas plant site | |
| CN115828508B (en) | Automatic ground water critique prediction method based on GIS platform | |
| Fiori et al. | Groundwater contaminant transport: Prediction under uncertainty, with application to the MADE transport experiment | |
| CN117010217A (en) | Groundwater pollution visualization method and system based on model analysis | |
| Fogg et al. | Modeling contaminant transport in the vadose zone: Perspective on state of the art | |
| Freedman et al. | Elements of complexity in subsurface modeling, exemplified with three case studies | |
| Desnoyers et al. | Geostatistical methodology for waste optimization of contaminated premises | |
| Antonov et al. | Determination of soil hydrological parameters of a multi-layered loess complex using HYDRUS-2D and field infiltration experiments | |
| Ichige et al. | Stochastic model for the fluctuations of the atmospheric concentration of radionuclides and its application to uncertainty evaluation | |
| Brookfield et al. | Interpreting temporal variations in river response functions: an example from the Arkansas River, Kansas, USA | |
| Estrada et al. | Numerical modeling and data-worth analysis for characterizing the architecture and dissolution rates of a multicomponent DNAPL source | |
| Arnold et al. | Groundwater Transport Modeling to Investigate Contaminant Back-Diffusion from the Rock Matrix | |
| CN117057262A (en) | NAPLs pollutant characterization method based on aquifer structure information | |
| Holt et al. | Uncertainty in vadose zone flow and transport prediction | |
| Michalak et al. | A geostatistical data assimilation approach for estimating groundwater plume distributions from multiple monitoring events | |
| Pasetti et al. | Development of a Coupled Hydrological and Buildup/Washoff Watershed Model |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20200505 |