CN115081725B - Method and device for predicting pollutant solute distribution under karst landform - Google Patents
Method and device for predicting pollutant solute distribution under karst landform Download PDFInfo
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Abstract
The invention discloses a method and a device for predicting pollutant solute distribution under karst landforms, wherein the method comprises the following steps: collecting pollutant solute concentration and karst landform characteristics in a preset time period, and determining the arrival time and model parameters of pollutants through a plurality of migration paths based on the pollutant solute concentration and the karst landform characteristics in the preset time period; constructing a three-stage truncated fractional solute transport model based on the concentration of the contaminant solute in the preset time period, the arrival time of the contaminant through a plurality of transport paths and the model parameters; collecting the current concentration of the pollutant solute, and inputting the current concentration of the pollutant solute into the three-stage cut-off fractional order solute transport model to generate the distribution of the pollutant solute. According to the method, the solute transport process in the aquifer under karst landforms is simulated through a three-stage cut-off fractional order solute transport model, the pollutant solute distribution of a target area is identified, and data support is provided for underground karst water pollution assessment and restoration.
Description
Technical Field
The invention relates to the technical field of solute migration, in particular to a method and a device for predicting distribution of pollutant solutes in karst landforms.
Background
The karst landform is widely distributed in the world, the soluble rock occupies 10.2% of the earth area, the distribution area of the karst landform in China reaches 344 ten thousand square kilometers, and the karst landform is one third of the territory area, and the karst landform is mainly distributed in southwest areas.
Most of the existing researches on the pollution condition of lava water aim at a single underground pipeline, and the researches on the distribution of pollutants and solutes in lava water under a complex karst underground river basin are insufficient, so that the researches on the communication condition of the same underground river system under different hydraulic conditions are less common.
Disclosure of Invention
Therefore, the invention aims to overcome the defect that the prior art lacks in researching the distribution of pollutant solutes in lava water under the condition that complex karst underground river basin is communicated with the same underground river system under different hydraulic conditions, and further provides a method and a device for predicting the distribution of pollutant solutes under karst landforms.
The embodiment of the invention provides a method for predicting the distribution of pollutant solutes in karst landforms, which comprises the following steps:
collecting pollutant solute concentration and karst landform characteristics in a preset time period, and determining the arrival time and model parameters of pollutants through a plurality of migration paths based on the pollutant solute concentration and the karst landform characteristics in the preset time period;
constructing a three-stage truncated fractional solute transport model based on the concentration of the contaminant solute in the preset time period, the arrival time of the contaminant through a plurality of transport paths and the model parameters;
collecting the current concentration of the pollutant solute, and inputting the current concentration of the pollutant solute into the three-stage cut-off fractional order solute transport model to generate the distribution of the pollutant solute.
According to the method for predicting the solute distribution of the pollutants under the karst landform, the solute migration process in the aquifer under the karst landform is described through the three-stage cut-off fractional order solute migration model, the solute distribution of the pollutants in the target area is identified, and data support can be provided for underground karst water pollution assessment and restoration.
Optionally, the determining the time and model parameters of the arrival of the contaminant through a plurality of migration paths based on the contaminant solute concentration and the karst topographical features within the preset time period includes:
Constructing a solute transport graph based on the concentration of the pollutant solute in the preset time period, and determining the arrival time of the pollutant through a plurality of transport paths according to peaks in the solute transport graph; wherein the plurality of migration paths include a medium-range channel and a long-range channel;
model parameters are determined based on contaminant solute concentrations over a preset period of time, times at which the contaminants arrive through multiple migration paths, and the karst topographical features.
The solute concentration migration process of the pollutant is clearly represented through the solute migration curve graph, the model parameter and the arrival time of the pollutant through a plurality of migration paths are determined through the solute migration curve graph, the model parameter range is shortened, the pollutant solute concentration and karst landform characteristics in a preset time period are processed, and a three-stage cut-off fractional order solute migration model is constructed, so that the three-stage cut-off fractional order solute migration model is more in accordance with the karst landform characteristics, and the karst water solute migration process is more accurate.
Optionally, the determining, based on the peaks, a time at which the contaminant arrives through a plurality of migration paths includes:
according to the time sequence, taking the time corresponding to the first wave peak in the solute transport graph as the time for the contaminant to arrive through the short-range channel, and selecting the time corresponding to other wave peaks in the solute transport graph as the time for the contaminant to arrive through the medium-range channel and the time for the contaminant to arrive through the long-range channel; wherein the other peaks are the remaining peaks except the first peak.
The short-range channel, the medium-range channel and the long-range channel are more intuitively arranged through the wave peaks in the solute transport graph.
Optionally, the model parameters include:
flow parameters, diffusion parameters, fractional capacity coefficients, truncation coefficients, temporal fractional order, temporal truncation fractional derivative, and spatial fractional derivative.
Optionally, the determining the model parameter based on the solute concentration of the contaminant, the arrival time of the contaminant through the plurality of migration paths, and the karst landform feature within a preset time period includes:
determining the flow parameter, the diffusion parameter, and a fractional spatial derivative based on a concentration of a contaminant solute and a time of arrival of the contaminant through a plurality of migration paths over a predetermined period of time;
determining the fractional capacity coefficient, the truncation coefficient and the time fractional order by utilizing the karst landform characteristic;
extracting an initial time in the solute transport graph, and determining the time truncated fractional derivative based on the contaminant solute concentration, the initial time, the time fractional order and the truncated coefficient within the preset time period;
the spatial fractional derivative is determined based on the contaminant solute concentration and the temporal fractional order over the predetermined period of time.
Because the karst landform cracks develop very abundantly, the early arrival phenomenon of pollutant solutes is very easy to occur, the diffusion phenomenon is described by adopting a space fractional derivative, and the retention effect of geological structures such as dead caves and the like on the solute migration process is considered, so that the description of a time fractional derivative is adopted in time, and the setting of the model parameters enables the three-stage truncated fractional solute migration model to reflect the pollutant migration process in the karst landform more.
Optionally, the constructing a three-stage truncated fractional order solute transport model based on the concentration of the contaminant solute, the arrival time of the contaminant through a plurality of transport paths, and the model parameters within the preset time period includes:
the three-stage truncated fractional solute transport model is constructed based on the concentration of contaminant solutes within the preset time period, the time at which the contaminants arrive through multiple transport paths, the flow parameters, the diffusion parameters, the fractional capacity coefficients, the truncated coefficients, the temporal fractional order, the temporal truncated fractional derivative, and the spatial fractional derivative.
Optionally, the expression of the three-stage truncated fractional order solute transport model is:
In the above formula, x represents space, T represents time, C represents concentration of pollutant solute, and T 1 Time of arrival of contaminant through medium range channel, T 2 Indicating the time of arrival of the contaminant through the long-range channel, T 3 Represents total time of contaminant solute transport, β represents fractional capacity coefficient, λ represents cut-off coefficient, α represents time fractional order, γ represents space fractional order, TC represents time cut-off fractional derivative, v represents flow parameter, D represents diffusion parameter, a represents initial concentration of contaminant solute,representing the position along the boundary.
In a second aspect of the present application, a device for predicting a distribution of contaminant solutes under karst topography is also provided, comprising:
the determining module is used for collecting the solute concentration of the pollutant and the karst landform characteristics in a preset time period, and determining the arrival time and model parameters of the pollutant through a plurality of migration paths based on the solute concentration of the pollutant and the karst landform characteristics in the preset time period;
the construction module is used for constructing a three-stage truncated fractional order solute migration model based on the concentration of the pollutant solute in the preset time period, the arrival time of the pollutant through a plurality of migration paths and the model parameters;
The generation module is used for collecting the current concentration of the pollutant solute, inputting the current concentration of the pollutant solute into the three-stage cut-off fractional order solute migration model, and generating the distribution of the pollutant solute.
Optionally, the determining module includes:
the construction submodule is used for constructing a solute migration curve graph based on the concentration of the pollutant solute in the preset time period and determining the arrival time of the pollutant through a plurality of migration paths according to peaks in the solute migration curve graph; wherein the plurality of migration paths include a medium-range channel and a long-range channel;
the determining submodule is used for determining model parameters based on the solute concentration of the pollutant, the arrival time of the pollutant through a plurality of migration paths and the karst landform characteristics in a preset time period.
Optionally, the constructing sub-module includes:
according to the time sequence, taking the time corresponding to the first wave peak in the solute transport graph as the time for the contaminant to arrive through the short-range channel, and selecting the time corresponding to other wave peaks in the solute transport graph as the time for the contaminant to arrive through the medium-range channel and the time for the contaminant to arrive through the long-range channel; wherein the other peaks are the remaining peaks except the first peak.
Optionally, the model parameters include:
flow parameters, diffusion parameters, fractional capacity coefficients, truncation coefficients, temporal fractional order, temporal truncation fractional derivative, and spatial fractional derivative.
Optionally, the determining submodule includes:
a first determining unit for determining the flow parameter, the diffusion parameter and the spatial fractional derivative based on a concentration of a contaminant solute and a time at which the contaminant arrives through a plurality of migration paths within a preset time period;
the second determining unit is used for determining the fractional capacity coefficient, the truncation coefficient and the time fractional order by utilizing the karst landform characteristic;
a third determining unit configured to extract an initial time in the solute transport graph, determine the time truncated fractional derivative based on a contaminant solute concentration within the preset time period, the initial time, the time fractional order, and the truncation coefficient;
and a fourth determining unit for determining the spatial fractional order derivative based on the contaminant solute concentration and the temporal fractional order within the preset time period.
Optionally, the building module includes:
The three-stage truncated fractional solute transport model is constructed based on the concentration of contaminant solutes within the preset time period, the time at which the contaminants arrive through multiple transport paths, the flow parameters, the diffusion parameters, the fractional capacity coefficients, the truncated coefficients, the temporal fractional order, the temporal truncated fractional derivative, and the spatial fractional derivative.
Optionally, the expression of the three-stage truncated fractional order solute transport model is:
in the above formula, x represents space, T represents time, C represents concentration of pollutant solute, and T 1 Time of arrival of contaminant through medium range channel, T 2 Indicating the time of arrival of the contaminant through the long-range channel, T 3 Represents total time of pollutant solute transport, beta represents fractional capacity coefficient, lambda represents cut-off coefficient, alpha represents time fractional order, gamma represents space fractional order, TC represents time cut-off fractionThe first derivative, v, represents the flow parameter, D represents the diffusion parameter, a represents the initial concentration of contaminant solutes,representing the position along the boundary.
In a third aspect of the present application, there is also provided a computer device comprising a processor and a memory, wherein the memory is for storing a computer program, the computer program comprising a program, the processor being configured to invoke the computer program to perform the method of the first aspect described above.
In a fourth aspect of the present application, embodiments of the present invention provide a computer-readable storage medium storing a computer program for execution by a processor to implement the method of the first aspect described above.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are needed in the description of the embodiments or the prior art will be briefly described, and it is obvious that the drawings in the description below are some embodiments of the present invention, and other drawings can be obtained according to the drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flowchart of a method for predicting the distribution of contaminant solutes in karst landforms according to example 1 of the present invention;
FIG. 2 is a flowchart of S101 in embodiment 1 of the present invention;
fig. 3 is a flowchart of step S1012 in embodiment 1 of the present invention;
FIG. 4 is a graph showing the fit of experimental data to simulated data in example 1 of the present invention;
FIG. 5 is a schematic block diagram of a device for predicting the distribution of contaminant solutes in karst landforms according to embodiment 2 of the present invention;
Fig. 6 is a block diagram of a determination module 51 in embodiment 2 of the present invention;
fig. 7 is a block diagram of a determination submodule 512 in embodiment 2 of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made apparent and fully in view of the accompanying drawings, in which some, but not all embodiments of the invention are shown. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
In the description of the present invention, it should be noted that the directions or positional relationships indicated by the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. are based on the directions or positional relationships shown in the drawings, are merely for convenience of describing the present invention and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a specific orientation, be configured and operated in a specific orientation, and thus should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In addition, the technical features of the different embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
Example 1
The embodiment provides a method for predicting the solute distribution of pollutants in karst landforms, as shown in fig. 1, comprising the following steps:
s101, collecting pollutant solute concentration and karst landform characteristics in a preset time period, and determining the arrival time and model parameters of pollutants through a plurality of migration paths based on the pollutant solute concentration and the karst landform characteristics in the preset time period.
The method comprises the steps of aiming at a target area, investigating karst landform characteristics of the area, selecting places with spring water flowing in and out as tracer adding points and receiving points, selecting sodium fluorescein as a tracer, completely dissolving a certain mass of tracer into 10L of water according to outlet flow, carrying out a tracer experiment by instantly adding the tracer into the adding points at one time, and continuously collecting and finishing the measured sodium fluorescein concentration (namely pollutant solute concentration) at the receiving points.
Further, in general, karst landform cracks are abundant, the development degree is high, and in order to simulate the karst landform conveniently, the karst landform cracks can be approximated to a three-channel fractional solute transport model, and the length of a transport path is divided into a long-range channel, a medium-range channel and a short-range channel.
S102, constructing a three-stage cut-off fractional solute migration model based on the concentration of the pollutant solute in the preset time period, the arrival time of the pollutant through a plurality of migration paths and the model parameters.
Wherein the model parameters include: flow parameters, diffusion parameters, fractional capacity coefficients, truncation coefficients, temporal fractional order, temporal truncation fractional derivative, and spatial fractional derivative.
Further, the three-stage truncated fractional solute transport model is constructed based on the concentration of the contaminant solute, the arrival time of the contaminant through a plurality of transport paths, the flow parameter, the diffusion parameter, the fractional capacity coefficient, the truncated coefficient, the time fractional order, the time truncated fractional derivative, and the space fractional derivative within the preset time period, wherein the expression of the three-stage truncated fractional solute transport model is as follows:
in the above formula, x represents space, T represents time, C represents concentration of pollutant solute, and T 1 Time of arrival of contaminant through medium range channel, T 2 Indicating the time of arrival of the contaminant through the long-range channel, T 3 Represents total pollutant solute transport time, beta represents fractional capacity coefficient, beta=1, lambda represents cut-off coefficient, 0.ltoreq.lambda.ltoreq.0.1, alpha represents time fractional order, 0.5.ltoreq.alpha.ltoreq.0.9 or 0.5.ltoreq.alpha.ltoreq.1, gamma represents space fractional order, 1.3.ltoreq.gamma.ltoreq.1.7, TC represents time cut-off fractional order derivative, v represents flow parameter V is more than or equal to 0 and less than or equal to 0.1, D is a diffusion parameter, D is more than or equal to 0 and less than or equal to 0.1, A is the initial concentration of pollutant solute,the boundary position is represented, wherein the fractional capacity coefficient beta and the time fractional order alpha are dimensionless, reflect the complexity degree of the karst landform underground channel, and respectively represent corresponding time periods (namely, the corresponding flow parameters from the initial time to the time when the pollutant arrives through the medium-range channel, and the total time when the pollutant arrives through the long-range channel) by subscripts of the fractional capacity coefficient beta, the cutoff coefficient lambda, the time fractional order alpha, the flow parameter v and the diffusion parameter D.
S103, collecting the current concentration of the pollutant solute, and inputting the current concentration of the pollutant solute into the three-stage cut-off fractional order solute migration model to generate the distribution of the pollutant solute.
Specifically, the trained three-stage cut-off fractional order solute transport model is utilized to predict the distribution of the pollutant solutes.
Further, the step of training the three-stage truncated fractional solute transport model is as follows: the time and space in the three-stage truncated fractional order solute transport model are discretized, and then the three-stage truncated fractional order solute transport model is solved by using an implicit finite difference method, and the specific calculation process is as follows:
Let the space step length be h, the space length be L, the number of space points n=L/h+1, at this time define g 0 ＝1，i＝1,2,...,n。
When t is E [0, T 1 ]At the time, the number of points is m, and the time step is τ=t 1 /m，t k+1 Represents the k+1 time, x l Represents the first spatial position, wherein,
when k=0:
when k=1:
when k is more than or equal to 1:
in the above equation, j represents a summation function.
t∈[T 1 ，T 2 ]At the time, the number of distribution points in time is m 1 Time step τ 1 ＝(T 2 -T 1 )/m 1 The space step length is still h, t k+1 Represents the k+1 time, x l Represents the first spatial position, wherein,
when k-m=0:
when k-m=1:
when k-m is more than or equal to 1:
when T is E [ T ] 2 ，T 3 ]At the time, the number of distribution points in time is m 2 Time step τ 2 ＝(T 3 -T 2 )/m 2 The space step length is still h, t k+1 Represents the k+1 time, x l Represents the first spatial position, wherein,
when k-m 1 ＝0：
When k-m 1 ＝1：
When k-m 1 ≥1：
Further, based on the contaminant solute concentration at the end time of the contaminant solute concentration extraction within the preset time period, comparing the result of the calculation, that is, the solute concentration distribution with the contaminant solute concentration at the end time; when the solute concentration distribution is different from the pollutant solute concentration at the ending moment, calibrating the model parameters until the solute concentration distribution is the same as the pollutant solute concentration at the ending moment, and outputting a trained three-stage cut-off fractional order solute transport model; when the solute concentration distribution is the same as the pollutant solute concentration at the ending time, directly outputting a trained three-stage cut-off fractional order solute transport model, and carrying out prediction simulation on the karst water solute transport process under karst landforms based on the current utilization of the trained three-stage cut-off fractional order solute transport model.
The model parameters after calibration reflect the characteristics of non-communicated cracks and the like of each channel, and the lower the model parameters are, the higher the detention effect of the aquifer is, and the possibility of excessive development of cracks and excessive dead spots is indicated.
According to the method for predicting the distribution of the pollutant solute under the karst landform, the solute migration process in the aquifer under the karst landform is described through the three-stage cut-off fractional order solute migration model, the distribution of the pollutant solute in the target area is identified, data support is provided for underground karst water pollution assessment and restoration, the concentration of the pollutant solute in a preset time period and the characteristics of the karst landform are processed, and the three-stage cut-off fractional order solute migration model is further constructed, so that the three-stage cut-off fractional order solute migration model is more in accordance with the characteristics of the karst landform, and the karst water solute migration process is more accurate.
Preferably, as shown in fig. 2, determining the time and model parameters of the arrival of the contaminant through the plurality of migration paths in step S101 based on the contaminant solute concentration and the karst landform characteristic in the predetermined period of time includes:
s1011, constructing a solute transport graph based on the concentration of the pollutant solute in the preset time period, and determining the arrival time of the pollutant through a plurality of transport paths according to the wave peaks in the solute transport graph; wherein the plurality of migration paths include a middle-range channel and a long-range channel.
Specifically, according to a time sequence, taking the time corresponding to the first peak in the solute transport graph as the time for the contaminant to arrive through the short-range channel, and selecting the time corresponding to other peaks in the solute transport graph as the time for the contaminant to arrive through the medium-range channel and the time for the contaminant to arrive through the long-range channel; wherein the other peaks are the remaining peaks except the first peak.
Further, since the length of the migration path is characterized by the length of each stage, the longer the length is, the longer the solute needs to reach the receiving point, which means that the longer the path of the long-range or medium-range channel is, so that the first peak in the solute migration graph is the corresponding time and concentration of the contaminant and the contaminant solute reached by the contaminant through the short-range channel, and further, the subsequent peak is manually selected as the medium-range channel and the long-range channel.
S1012, determining model parameters based on the concentration of pollutant solute in a preset time period, the arrival time of the pollutant through a plurality of migration paths and the karst landform characteristics.
The solute concentration migration process of the pollutant is clearly characterized through the solute migration curve chart, and model parameters and the arrival time of the pollutant through a plurality of migration paths are determined through the solute migration curve chart, so that the range of the model parameters is reduced.
Preferably, determining model parameters based on the concentration of contaminant solutes, the arrival time of the contaminant through a plurality of migration paths and the karst landform features in step S1012 within a preset time period includes:
s10121, determining the flow parameter, the diffusion parameter and the spatial fractional derivative based on the concentration of the contaminant solute and the arrival time of the contaminant through a plurality of migration paths within a preset period of time.
Specifically, the flow parameters and the diffusion parameters are estimated manually according to the solute transport curve graph constructed by the tracer experiments by using artificial experience.
S10122, determining the fractional capacity coefficient, the truncation coefficient and the time fractional order by utilizing the karst landform characteristic.
Specifically, the karst landform features comprise crack development conditions and open flow and dark flow conditions in the karst landform, and initial fractional capacity coefficients, cut-off coefficients and time fractional orders are manually set respectively by using human experience based on the crack development conditions and the open flow and dark flow conditions.
S10123, extracting initial time in the solute transport graph, and determining the time cut-off fractional order derivative based on the concentration of the pollutant solute in the preset time period, the initial time, the time fractional order and the cut-off coefficient.
Specifically, the calculation formula of the time-truncated fractional derivative is as follows:
where xi represents the functional integral of time t,for fractional derivative sign, TC is short for time-truncated fractional derivative, lambda represents the truncated coefficient, t represents time (i.e., the instant of the current calculation), t.epsilon.t 1 ,t 2 ]，t 1 The moment when the fractional derivative starts memorization, typically the initial moment of each phase, t 2 Terminating the record for fractional derivativeThe time of memory, typically the end time of each phase, e is a natural constant, its value is about 2.718281828459045, Γ () is a single-parameter Gamma function (Gamma function), where Gamma function is expressed as follows:
in the above formula, gamma represents a single parameter variable, s, in the gamma function γ-1 Representing a polynomial incrementing function, e -s Representing an exponential decreasing function.
S10124, determining the spatial fractional order derivative based on the contaminant solute concentration and the time fractional order within the preset time period.
Specifically, the calculation formula of the spatial fractional derivative is as follows:
in the above formula, ζ represents the functional integral of the space x, and RL represents the abbreviation of the spatial fractional derivative.
A method for predicting contaminant solute distribution in karst topography is described below by way of a specific example.
Mao Cun the underground river basin is located in the tide field county of Gui Lin Shi Lingchun county, is about 35km away from Guilin, the underground river outlet is Mao Cun, the longitude and latitude coordinates are N25 DEG 11'38", E110 DEG 31'35", the elevation is 178m, and the river basin area is about 11.2km 2 The method is a typical karst landform, a research area is positioned at the north section of a south polder-sand fracture, is structurally positioned at the east side of tide Tian Xiangxie, mainly develops a north east tide field, a large rock front area fracture and associated NEE and NW fracture, has quartz sandstone, siltstone shale, east hillside group ash, a dark gray layer Kong Danni limestone and dolomite interbedded, gray black brecciated dolomite, a mud basin system county group shallow ash, a gray white thick layer blocky mud bright oolitic sand grain gritty limestone, a mud crystal gritty and dolomite, a fourth system sediment and the like, wherein the exposed stratum in the watershed is provided with quartz sandstone, siltstone shale, a dark gray layer Kong Danni limestone and dolomite interbedded, and the like; the watershed containsThe water rock group mainly comprises limestone of Rong county group and dolomite of Dong gang group, the lithology is purer, under the effects of construction and running water erosion, the karst in the river basin is very developed, and karst water is reserved in karst cave and erosion cracks of the carbonate rock water rock group.
The karst water solute transport simulation of Gui Linmao village underground river comprises the following steps:
Step 1: aiming at Guilin: the threshing ground-Mao Cun is subjected to field tracer experiments, experimental data are collected, the tracer experiments are positioned at the downstream of the underground river, a large rock front water falling hole is injected with a fluorescein tracer, the monitoring is performed at Mao Cun, two sumps are 100 meters apart, and the experimental data are shown in fig. 4;
step 2: analyzing solute transport mechanism in karst water according to experimental data, wherein the karst landform is easy to develop rich cracks, open flow and dark flow alternately exist, and experimental data in FIG. 5 show that tail is multimodal, so that a plurality of pollutant transport paths exist;
step 3: according to the analysis result of the step 2, a multi-stage fractional order convection diffusion model applicable to the Gui Linmao village underground river is established, and a three-stage truncated fractional order solute transport model is adopted to describe the migration rule of solutes in a karst water three-way underground medium, wherein the expression is as follows:
in the above formula, x represents space, T represents time, C represents concentration of pollutant solute, and T 1 Time of arrival of contaminant through medium range channel, T 2 Indicating the time of arrival of the contaminant through the long-range channel, T 3 Represents total time of contaminant solute transport, β represents fractional capacity coefficient, λ represents cut-off coefficient, α represents time fractional order, γ represents space fractional order, TC represents time cut-off fractional derivative, v represents flow parameter, D represents diffusion parameter, a represents initial concentration of contaminant solute, Representing the position along the boundary.
The time-truncated fractional derivative is defined as:
ζ represents the functional integral of the time t,for fractional derivative sign, TC is short for time-truncated fractional derivative, lambda represents the truncated coefficient, t represents time (i.e., the instant of the current calculation), t.epsilon.t 1 ,t 2 ]，t 1 The moment when the fractional derivative starts memorization, typically the initial moment of each phase, t 2 The moment when the memory is terminated for the fractional derivative, typically the end moment of each phase, e is a natural constant, its value is about 2.718281828459045, Γ () is a single-parameter gamma function.
The calculation formula of the spatial fractional derivative is as follows:
in the above formula, ζ represents the functional integral of the space x, and RL represents the abbreviation of the spatial fractional derivative.
Step 4: the calibration model parameters are shown in table 1 below:
table 1:
as can be seen from the above table, the time fractional order α in the model parameters in the simulation domain is 0.75, and the fractional capacity coefficient β is 1.
Step 5: therefore, the convection coefficient and diffusion coefficient of the solute under the local fracture geological condition are very high, the diffusion speed is 50, the time fractional order is 0.75, the parameters of the three channels are not obviously changed, the underground solute migration process is mainly based on convection effect, the average migration time is short, the tracer recovery rate is high, the water-containing medium is relatively uniform, the pipeline development is not obvious, and karst water solute is easy to store in the corrosion fracture; and referring to fig. 4, the data simulated by the three-stage truncated fractional solute transport model is similar to experimental data, so that the three-stage truncated fractional solute transport model can be used for describing the solute transport process in karst water in the whole flow area, and the method has popularization and application values in southwest karst areas.
Example 2
The embodiment provides a device for predicting solute distribution of pollutants in karst landforms, as shown in fig. 5, including:
the determining module 51 is configured to collect a solute concentration of the contaminant and karst landform characteristics in a preset time period, and determine a time and model parameters of arrival of the contaminant through a plurality of migration paths based on the solute concentration of the contaminant and the karst landform characteristics in the preset time period.
The method comprises the steps of aiming at a target area, investigating karst landform characteristics of the area, selecting places with spring water flowing in and out as tracer adding points and receiving points, selecting sodium fluorescein as a tracer, completely dissolving a certain mass of tracer into 10L of water according to outlet flow, carrying out a tracer experiment by instantly adding the tracer into the adding points at one time, and continuously collecting and finishing the measured sodium fluorescein concentration (namely pollutant solute concentration) at the receiving points.
Further, in general, karst landform cracks are abundant, the development degree is high, and in order to simulate the karst landform conveniently, the karst landform cracks can be approximated to a three-channel fractional solute transport model, and the length of a transport path is divided into a long-range channel, a medium-range channel and a short-range channel.
A construction module 52 is configured to construct a three-stage truncated fractional order solute transport model based on the concentration of the contaminant solute during the predetermined time period, the arrival time of the contaminant through the plurality of transport paths, and the model parameters.
Wherein the model parameters include: flow parameters, diffusion parameters, fractional capacity coefficients, truncation coefficients, temporal fractional order, temporal truncation fractional derivative, and spatial fractional derivative.
Further, the three-stage truncated fractional solute transport model is constructed based on the concentration of the contaminant solute, the arrival time of the contaminant through a plurality of transport paths, the flow parameter, the diffusion parameter, the fractional capacity coefficient, the truncated coefficient, the time fractional order, the time truncated fractional derivative, and the space fractional derivative within the preset time period, wherein the expression of the three-stage truncated fractional solute transport model is as follows:
in the above formula, x represents space, T represents time, C represents concentration of pollutant solute, and T 1 Time of arrival of contaminant through medium range channel, T 2 Indicating the time of arrival of the contaminant through the long-range channel, T 3 Represents total transport time of pollutant solute, beta represents fractional capacity coefficient, beta=1, lambda represents cut-off coefficient, 0.ltoreq.lambda.ltoreq.0.1, alpha represents time fractional order, 0.5.ltoreq.alpha.ltoreq.0.9 or 0.5.ltoreq.alpha.ltoreq.1, gamma represents space fractional order, 1.3.ltoreq.gamma.ltoreq.1.7, TC represents time cut-off fractional derivative, v represents flow parameter, 0.ltoreq.v.ltoreq.0.1, D represents diffusion parameter, 0.ltoreq.D.ltoreq.0.1, A represents initial concentration of pollutant solute, The boundary position is represented, wherein the fractional capacity coefficient beta and the time fractional order alpha are dimensionless, reflect the complexity degree of the karst landform underground channel, and respectively represent corresponding time periods (namely, the corresponding flow parameters from the initial time to the time when the pollutant arrives through the medium-range channel, and the total time when the pollutant arrives through the long-range channel) by subscripts of the fractional capacity coefficient beta, the cutoff coefficient lambda, the time fractional order alpha, the flow parameter v and the diffusion parameter D.
The generating module 53 is configured to collect a current concentration of a contaminant solute, input the current concentration of the contaminant solute into the three-stage truncated fractional order solute transport model, and generate a contaminant solute distribution.
Specifically, the trained three-stage cut-off fractional order solute transport model is utilized to predict the distribution of the pollutant solutes.
Further, the step of training the three-stage truncated fractional solute transport model is as follows: the time and space in the three-stage truncated fractional order solute transport model are discretized, and then the three-stage truncated fractional order solute transport model is solved by using an implicit finite difference method, and the specific calculation process is as follows:
Let the space step length be h, the space length be L, the number of space points n=L/h+1, at this time define g 0 ＝1，i＝1,2,...,n。
When t is E [0, T 1 ]At the time, the number of points is m, and the time step is τ=t 1 /m，t k+1 Represents the k+1 time, x l Represents the first spatial position, wherein,
when k=0:
when k=1:
when k is more than or equal to 1:
in the above equation, j represents a summation function.
t∈[T 1 ，T 2 ]At the time, the number of distribution points in time is m 1 Time step τ 1 ＝(T 2 -T 1 )/m 1 The space step length is still h, t k+1 Represents the k+1 time, x l Represents the first spatial position, wherein,
when k-m=0:
when k-m=1:
when k-m is more than or equal to 1:
when T is E [ T ] 2 ，T 3 ]At the time, the number of distribution points in time is m 2 Time step τ 2 ＝(T 3 -T 2 )/m 2 The space step length is still h, t k+1 Represents the k+1 time, x l Represents the first spatial position, wherein,
when k-m 1 ＝0：
When k-m 1 ＝1：
When k-m 1 ≥1：
/>
Further, based on the contaminant solute concentration at the end time of the contaminant solute concentration extraction within the preset time period, comparing the result of the calculation, that is, the solute concentration distribution with the contaminant solute concentration at the end time; when the solute concentration distribution is different from the pollutant solute concentration at the ending moment, calibrating the model parameters until the solute concentration distribution is the same as the pollutant solute concentration at the ending moment, and outputting a trained three-stage cut-off fractional order solute transport model; when the solute concentration distribution is the same as the pollutant solute concentration at the ending time, directly outputting a trained three-stage cut-off fractional order solute transport model, and carrying out prediction simulation on the karst water solute transport process under karst landforms based on the current utilization of the trained three-stage cut-off fractional order solute transport model.
The model parameters after calibration reflect the characteristics of non-communicated cracks and the like of each channel, and the lower the model parameters are, the higher the detention effect of the aquifer is, and the possibility of excessive development of cracks and excessive dead spots is indicated.
According to the predicting device for the solute distribution of the pollutants under the karst landform, the solute migration process in the aquifer under the karst landform is described through the three-stage cut-off fractional solute migration model, the solute distribution of the pollutants in the target area is identified, data support is provided for underground karst water pollution assessment and restoration, the concentration of the pollutants in the preset time period and the characteristics of the karst landform are processed, and the three-stage cut-off fractional solute migration model is further constructed, so that the three-stage cut-off fractional solute migration model is more in accordance with the characteristics of the karst landform, and the karst water solute migration process is more accurate.
Preferably, as shown in fig. 6, the determining module 51 includes:
a constructing submodule 511, configured to construct a solute transport graph based on the concentration of the contaminant solute in the preset time period, and determine a time when the contaminant arrives through a plurality of transport paths according to peaks in the solute transport graph; wherein the plurality of migration paths include a middle-range channel and a long-range channel.
Specifically, according to a time sequence, taking the time corresponding to the first peak in the solute transport graph as the time for the contaminant to arrive through the short-range channel, and selecting the time corresponding to other peaks in the solute transport graph as the time for the contaminant to arrive through the medium-range channel and the time for the contaminant to arrive through the long-range channel; wherein the other peaks are the remaining peaks except the first peak.
Further, since the length of the migration path is characterized by the length of each stage, the longer the length is, the longer the solute needs to reach the receiving point, which means that the longer the path of the long-range or medium-range channel is, so that the first peak in the solute migration graph is the corresponding time and concentration of the contaminant and the contaminant solute reached by the contaminant through the short-range channel, and further, the subsequent peak is manually selected as the medium-range channel and the long-range channel.
A determination sub-module 512 for determining model parameters based on a contaminant solute concentration over a predetermined period of time, a time of arrival of the contaminant through a plurality of migration paths, and the karst landform characteristic.
Preferably, as shown in fig. 7, the determining submodule 512 includes:
a first determining unit 5121 is configured to determine the flow parameter, the diffusion parameter, and the spatial fractional derivative based on a concentration of a contaminant solute and a time at which the contaminant arrives through a plurality of migration paths within a preset period of time.
Specifically, the flow parameters and the diffusion parameters are estimated manually according to the solute transport curve graph constructed by the tracer experiments by using artificial experience.
A second determining unit 5122 is configured to determine the fractional capacity coefficient, the truncation coefficient, and the temporal fractional order by using the karst landform characteristic.
Specifically, the karst landform features comprise crack development conditions and open flow and dark flow conditions in the karst landform, and initial fractional capacity coefficients, cut-off coefficients and time fractional orders are manually set respectively by using human experience based on the crack development conditions and the open flow and dark flow conditions.
A third determining unit 5123 is configured to extract an initial time in the solute transport graph, and determine the time truncated fractional derivative based on the contaminant solute concentration, the initial time, the time fractional order, and the truncated coefficient within the preset time period.
Specifically, the calculation formula of the time-truncated fractional derivative is as follows:
where xi represents the functional integral of time t,for fractional derivative sign, TC is short for time-truncated fractional derivative, lambda represents the truncated coefficient, t represents time (i.e., the instant of the current calculation), t.epsilon.t 1 ,t 2 ]，t 1 The moment when the fractional derivative starts memorization, typically the initial moment of each phase, t 2 The moment when the memory is terminated for the fractional derivative, typically the end moment of each phase, e is a natural constant, its value is about 2.718281828459045, Γ () is a Gamma function (Gamma function) of a single parameter, where the Gamma function is expressed as follows:
in the above formula, gamma represents a single parameter variable, s, in the gamma function γ-1 Representing a polynomial incrementing function, e -s Representing an exponential decreasing function.
A fourth determining unit 5124 is configured to determine the spatial fractional derivative based on the concentration of the contaminant solute and the temporal fractional order within the preset time period.
Specifically, the calculation formula of the spatial fractional derivative is as follows:
in the above formula, ζ represents the functional integral of the space x, and RL represents the abbreviation of the spatial fractional derivative.
Example 3
The embodiment provides a computer device, which comprises a memory and a processor, wherein the processor is used for reading instructions stored in the memory to execute the method for predicting the distribution of pollutant solutes under karst landforms in any of the method embodiments.
It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Example 4
The present embodiment provides a computer-readable storage medium storing computer-executable instructions that are capable of performing a method for predicting contaminant solute distribution under karst topography in any of the above-described method embodiments. Wherein the storage medium may be a magnetic Disk, an optical Disk, a Read-Only Memory (ROM), a random access Memory (Random Access Memory, RAM), a Flash Memory (Flash Memory), a Hard Disk (HDD), or a Solid State Drive (SSD); the storage medium may also comprise a combination of memories of the kind described above.
It is apparent that the above examples are given by way of illustration only and are not limiting of the embodiments. Other variations or modifications of the above teachings will be apparent to those of ordinary skill in the art. It is not necessary here nor is it exhaustive of all embodiments. While still being apparent from variations or modifications that may be made by those skilled in the art are within the scope of the invention.
Claims (9)
1. The method for predicting the solute distribution of the pollutants under the karst landform is characterized by comprising the following steps of:
collecting pollutant solute concentration and karst landform characteristics in a preset time period, and determining the arrival time and model parameters of pollutants through a plurality of migration paths based on the pollutant solute concentration and the karst landform characteristics in the preset time period;
constructing a three-stage truncated fractional solute transport model based on the concentration of the contaminant solute in the preset time period, the arrival time of the contaminant through a plurality of transport paths and the model parameters;
collecting the current concentration of the pollutant solute, and inputting the current concentration of the pollutant solute into the three-stage cut-off fractional order solute transport model to generate the distribution of the pollutant solute; the expression of the three-stage truncated fractional solute transport model is as follows:
in the above formula, x represents space, T represents time, C represents concentration of pollutant solute, and T 1 Time of arrival of contaminant through medium range channel, T 2 Indicating the time of arrival of the contaminant through the long-range channel, T 3 Represents total time of contaminant solute transport, β represents fractional capacity coefficient, λ represents cut-off coefficient, α represents time fractional order, γ represents space fractional order, TC represents time cut-off fractional derivative, v represents flow parameter, D represents diffusion parameter, a represents initial concentration of contaminant solute, The subscripts representing the boundary positions, fractional capacity coefficient β, cutoff coefficient λ, time fractional order α, flow parameter v, and diffusion parameter D, respectively represent the corresponding time periods.
2. The method for predicting the solute distribution of contaminants in a karst landform according to claim 1, wherein said determining the time and model parameters for the arrival of contaminants through a plurality of migration paths based on the contaminant solute concentration and the karst landform characteristics in said predetermined period of time comprises:
constructing a solute transport graph based on the concentration of the pollutant solute in the preset time period, and determining the arrival time of the pollutant through a plurality of transport paths according to peaks in the solute transport graph; wherein the plurality of migration paths include a medium-range channel and a long-range channel;
model parameters are determined based on contaminant solute concentrations over a preset period of time, times at which the contaminants arrive through multiple migration paths, and the karst topographical features.
3. A method of predicting contaminant-solute distribution under karst topography as defined in claim 2, wherein said determining the time of arrival of a contaminant through a plurality of migration paths from peaks in said solute migration profile comprises:
According to the time sequence, taking the time corresponding to the first wave peak in the solute transport graph as the time for the contaminant to arrive through the short-range channel, and selecting the time corresponding to other wave peaks in the solute transport graph as the time for the contaminant to arrive through the medium-range channel and the time for the contaminant to arrive through the long-range channel; wherein the other peaks are the remaining peaks except the first peak.
4. A method of predicting contaminant solute distribution under karst topography as claimed in claim 2 or 3, in which the model parameters comprise:
flow parameters, diffusion parameters, fractional capacity coefficients, truncation coefficients, temporal fractional order, temporal truncation fractional derivative, and spatial fractional derivative.
5. The method for predicting a contaminant-solute distribution under karst topography of claim 4, wherein determining model parameters based on a contaminant-solute concentration over a predetermined period of time, a time at which the contaminant arrives through a plurality of migration paths, and the karst topography features comprises:
determining the flow parameter, the diffusion parameter, and a fractional spatial derivative based on a concentration of a contaminant solute and a time of arrival of the contaminant through a plurality of migration paths over a predetermined period of time;
Determining the fractional capacity coefficient, the truncation coefficient and the time fractional order by utilizing the karst landform characteristic;
extracting an initial time in the solute transport graph, and determining the time truncated fractional derivative based on the contaminant solute concentration, the initial time, the time fractional order and the truncated coefficient within the preset time period;
the spatial fractional derivative is determined based on the contaminant solute concentration and the temporal fractional order over the predetermined period of time.
6. The method for predicting a contaminant-solute distribution under karst topography according to claim 5, wherein said constructing a three-stage truncated fractional order solute migration model based on the contaminant-solute concentration, the time of arrival of the contaminant through a plurality of migration paths, and the model parameters within the predetermined period of time comprises:
the three-stage truncated fractional solute transport model is constructed based on the concentration of contaminant solutes within the preset time period, the time at which the contaminants arrive through multiple transport paths, the flow parameters, the diffusion parameters, the fractional capacity coefficients, the truncated coefficients, the temporal fractional order, the temporal truncated fractional derivative, and the spatial fractional derivative.
7. A device for predicting the solute distribution of pollutants in karst landforms, comprising:
the determining module is used for collecting the solute concentration of the pollutant and the karst landform characteristics in a preset time period, and determining the arrival time and model parameters of the pollutant through a plurality of migration paths based on the solute concentration of the pollutant and the karst landform characteristics in the preset time period;
the construction module is used for constructing a three-stage truncated fractional order solute migration model based on the concentration of the pollutant solute in the preset time period, the arrival time of the pollutant through a plurality of migration paths and the model parameters;
the generation module is used for collecting the current concentration of the pollutant solute, inputting the current concentration of the pollutant solute into the three-stage cut-off fractional order solute migration model, and generating the distribution of the pollutant solute; the expression of the three-stage truncated fractional solute transport model is as follows:
in the above formula, x represents space, T represents time, C represents concentration of pollutant solute, and T 1 Time of arrival of contaminant through medium range channel, T 2 Indicating the time of arrival of the contaminant through the long-range channel, T 3 Represents total time of contaminant solute transport, β represents fractional capacity coefficient, λ represents cut-off coefficient, α represents time fractional order, γ represents space fractional order, TC represents time cut-off fractional derivative, v represents flow parameter, D represents diffusion parameter, a represents initial concentration of contaminant solute, The subscripts representing the boundary positions, fractional capacity coefficient β, cutoff coefficient λ, time fractional order α, flow parameter v, and diffusion parameter D, respectively represent the corresponding time periods.
8. A computer device comprising a processor and a memory, wherein the memory is for storing a computer program, the processor being configured to invoke the computer program to perform the steps of the method according to any of claims 1-6.
9. A computer readable storage medium having stored thereon computer instructions which, when executed by a processor, implement the steps of the method according to any of claims 1-6.
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