The present disclosure relates to a method of reversing aquifer parameter, and more particularly to a method of reversing aquifer parameter with skin effect by a drawdown record of a slug test.
The statements in this section merely provide background information related to the present disclosure and do not necessarily constitute prior art.
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In particular, the well skin effect means that there is an annular region (i.e., the well skin layer 4) between the well pipe 2 and the aquifer 5 with poor (or better) water permeability than that of the aquifer 5, and the well skin effect is divided into a positive skin effect and a negative skin effect. It is inferred that the formation of the positive well skin effect is due to the infiltration of drilling mud into the soil pores around the well during the well setting process, forming an annular area with poorer water permeability than the aquifer 5. The formation of the negative well skin effect is that during the well setup process, the filter material filled around the well or the water permeability around the well is increased due to excessive well flushing. Therefore, assuming that the monitoring well has a positive skin effect, jet flushing or other equivalent methods (such as shaking or back flushing) can be used for maintenance (see Table 1 for detailed maintenance method).
Table 1 shows the criteria for selecting an appropriate next well completion method based on the well skin effect.
However, although the “Groundwater Quality Monitoring Well Maintenance and Management Reference Manual” provides guidelines for selecting the next well completion method, there is no method for determining the well skin effect. Therefore, when performing monitoring well maintenance operations, only the appearance of the monitoring well and the inside conditions of the well pipe 2 and the well screen 3 can be observed, but the characteristics of the aquifer 5 outside the well screen 3 cannot be grasped.
In order to solve the above-mentioned problems, a method of reversing aquifer parameter with skin effect is provided. The method is implemented by a drawdown record of a slug test. The method includes steps of: performing a slug test on the monitoring well, and measuring a first water level change of the monitoring well by a water level meter; setting a parameter assembly having a plurality of hypothetical aquifer parameters; converting the hypothetical aquifer parameters through a programming language, and then respectively calculating a plurality of second water level changes; respectively calculating a plurality of function values through an objective function according to the first water level change and the second water level changes, and selecting one hypothetical aquifer parameter corresponding to one function value that meets a convergence condition from the function values; taking the hypothetical aquifer parameter that meets the convergence condition as the aquifer parameter.
In one embodiment, the aquifer parameter includes an aquifer hydraulic conductivity coefficient, an aquifer water storage coefficient, a well skin hydraulic conductivity coefficient, a well skin water storage coefficient, and a well skin radius.
In one embodiment, the function values are acquired by the sum of squares of differences between the first water level change and the second water level changes.
In one embodiment, the function value is selected from the function values by a symbiotic organisms search algorithm that meets the convergence condition.
In one embodiment, the symbiotic organisms search algorithm comprises a mutualism algorithm, a commensalism algorithm, and a parasitism algorithm.
In one embodiment, the mutualism algorithm includes steps of: (a1) selecting a first function value and a second function value from the function values to perform a mutualism calculation so as to recalculate function values for the first function value and the second function value; (a2) selecting the one with the smaller value as a first selection function.
In one embodiment, the commensalism algorithm includes steps of: (b1) selecting a third function value and the first selection function to perform a commensalism calculation so as to substitute at least one value of the third function value for the corresponding value in the first selection function to recalculate function values; (b2) selecting the one with the smaller value as a second selection function.
In one embodiment, the parasitism algorithm includes steps of: (c1) adjusting a value in the second selection function and performing a parasitism calculation to generate a mutation function; (c2) comparing the second selection function and the mutation function, and selecting the one with the smaller value as a third selection function.
In one embodiment, the method further includes a step of: repeating steps (a1) to (c2) until all function values are calculated.
The main purpose and effect of the present disclosure is that the present disclosure utilizes the above-mentioned drawdown record of a slug test to inversely deduce aquifer parameters with skin effect, and then calculate the ratio of hydraulic conductivity between the aquifer and the well skin layer to determine the well skin effect of the monitoring well, thereby selecting the appropriate next well completion method to achieve the purpose of maintenance and management of the monitoring well.
It is to be understood that both the foregoing general description and the following detailed description are exemplary, and are intended to provide further explanation of the present disclosure as claimed. Other advantages and features of the present disclosure will be apparent from the following description, drawings, and claims.
The present disclosure can be more fully understood by reading the following detailed description of the embodiment, with reference made to the accompanying drawing as follows:
Reference will now be made to the drawing figures to describe the present disclosure in detail. It will be understood that the drawing figures and exemplified embodiments of present disclosure are not limited to the details thereof.
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The method of reversing aquifer parameter with skin effect is mainly used to reverse the aquifer parameter in the monitoring well. The method includes steps of: performing a slug test on the monitoring well and a surrounding area thereof to measure a first water level change (S100) and inputting the record results into a computer. The surrounding area of the monitoring well 100 may cover several meters or tens of meters (i.e., the well skin layer 4 and the aquifer 5 are included). Specifically, the first water level change is mainly to measure the change (drawdown and recovery) of groundwater level through the slug test described above. Afterward, setting a parameter assembly having a plurality of hypothetical aquifer parameters (S200). Specifically, the aquifer parameter includes an aquifer hydraulic conductivity coefficient, an aquifer water storage coefficient, a well skin hydraulic conductivity coefficient, a well skin water storage coefficient, and a well skin radius. Therefore, the method of reversing aquifer parameter with skin effect mainly inversely deduces the above five values, when the actual influence of the well skin layer 4 cannot be known by observation, the inverse deduction of the actual well skin effect belongs to the positive well skin effect or the reverse well skin effect, and the effect of the well skin effect on the water level in the monitoring well 100.
Moreover, the hypothetical aquifer parameters are mainly based on the above known five values, and are based on the first water level change, and can be determined from the appearance or historical parameters of the monitoring well (wellhead 1 diameter, borehole diameter, aquifer thickness, well screen 3 length, drilling data and well string map, well setup data, confined aquifer or uncompressed aquifer, et), take out all possible values, and then put all possible values combination as the hypothetical aquifer parameters. Therefore, the parameter assembly includes 1 to N hypothetical aquifer parameters, and each hypothetical aquifer parameter includes at least the above five values (that is, each hypothetical aquifer parameter at least includes: the aquifer hydraulic conductivity coefficient, the aquifer water storage coefficient, the well skin hydraulic conductivity coefficient, the well skin water storage coefficient, and the well skin radius). The number of N is possible from several hundreds to tens of thousands, mainly based on the number of possible values.
Afterward, respectively calculating a plurality of second water level changes according to the plurality of hypothetical aquifer parameters (S300). Specifically, the hypothetical aquifer parameters need to be converted into a computer programming language through a programming language, and then a second water level change corresponding to each hypothetical aquifer parameter in the parameter assembly can be calculated through the operation of the software. The calculation of the second water level change can refer to the research of Yeh and Chen (2007), based on Moench and Hsieh (1985) to solve the analytical solution of the slug test, and the Laplace domain analytical solution formula for deriving the time-varying well water level is as follows:
In which,
The programming language may be implemented by programming languages such as, but not limited to, Python language, C language, R language, etc. The present disclosure mainly converts the above formula and parameter assembly into computer programming language through the above-mentioned example programming language, and then calculates the second water level change corresponding to each set of hypothetical aquifer parameters through computer operation. In particular, the programming language uses the Python language as the best implementation, which has the advantages of easy to use and wide versatility. Afterward, respectively calculating a plurality of function values through an objective function according to the first water level change and the second water level changes, and selecting one hypothetical aquifer parameter corresponding to one function value that meets a convergence condition from the function values (S400). In step (S400), the function values are acquired by the sum of squares of differences between the first water level change and the second water level changes (S420). Afterward, it is determined whether there is a function value that meets the convergence condition (S440). If step (S440) finds a function value that can meet the convergence condition, it means that the hypothetical aquifer parameter corresponding to the function value is correct. Therefore, taking the hypothetical aquifer parameter that meets the convergence condition as the aquifer parameter (S500) to determine the well skin effect of the monitoring well 100, and an appropriate next well completion method is selected to achieve the purpose of maintenance and management of the monitoring well 100. If the determination of step (S440) is “No”, the process returns to step (S200) to reset the parameter assembly.
The main purpose and effect of the present disclosure is that the present disclosure utilizes the above-mentioned drawdown record of a slug test to inversely deduce aquifer parameters with skin effect, and then calculate the ratio of hydraulic conductivity between the aquifer 5 and the well skin layer 4 to determine the well skin effect of the monitoring well 100, thereby selecting the appropriate next well completion method to achieve the purpose of maintenance and management of the monitoring well 100.
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In the mutualism algorithm A, another set of function values is randomly selected from the remaining function values (i.e., the second function value Fj(Xj) is randomly selected, in step (S600)) to perform mutualism algorithm calculation. The mutualism algorithm calculation mainly involves generating two new function values Fim(Xi) and Fjm(Xj) according to the mutualism relationship (step S620), and then determining whether the function value Fim(Xi) is less than the function value Fjm(Xj) (step S640). The detailed calculation method of the mutualism algorithm calculation is a technology well known to those skilled in the art, and will not be repeated here. When the determination in step (S640) is “Yes”, replacing the function value Fi(Xi) with function value Fim(Xi) as the first selection function (step S660) so as to enter into the commensalism algorithm B. On the contrary, the function value Fi(Xi) is used as the first selection function (step S680) so as to enter into the commensalism algorithm B.
In the commensalism algorithm B, randomly selecting the third function value (i.e., Fk(Xk)) and the first selection function (Fi(Xi) or Fim(Xi)) for the commensalism algorithm calculation. The commensalism algorithm calculation is mainly to replace part of the value (at least one) in the third function value Fk(Xk) with the corresponding value in the first selection function (Fi(Xi) or Fim(Xi)) to recalculate the function value Fic(Xi) (step S700). The detailed calculation method of the commensalism algorithm calculation is a technology well known to those skilled in the art, and will not be repeated here. Afterward, it is determined whether the function value Fic(Xi) is less than the first selection function (the function Fi(Xi) or Fim(Xi) selected in the preceding steps (step S720). When the determination in step (S720) is “Yes”, replacing the first selection function (the function Fi(Xi) or Fim(Xi) selected in the previous steps) with the function value Fic(Xi) as the second selection function (step S740) to enter the parasitism algorithm C. On the contrary, the first selection function (the function Fi(Xi) or Fim(Xi) selected in the preceding steps) is used as the second selection function (step S760) to enter the parasitism algorithm C.
In the parasitism algorithm C, randomly mutating (changing) a certain value in the second selection function (the function Fic(Xi), Fi(Xi) or Fim(Xi) selected in the previous steps), and perform parasitism algorithm calculation. The parasitism algorithm calculation is mainly to adjust a certain value in the second selection function (the function Fic(Xi), Fi(Xi) or Fim(Xi) selected in the previous steps) to recalculate the function value Fi(Xi′) (step S800). The detailed calculation method of the parasitism algorithm calculation is a technology well known to those skilled in the art, and will not be repeated here. Afterward, it is determined whether the function value Fi(Xi′) is less than the second selection function (the function Fic(Xi), Fi(Xi) or Fim(Xi) selected in the preceding steps) (step S820). If the determination in step (S820) is “Yes”, replacing the second selection function (the function Fic(Xi), Fi(Xi) or Fim(Xi) selected in the previous steps) with the function value Fi(Xi′) as the third selection function (step S840). On the contrary, using the second selection function (the function Fic(Xi), Fi(Xi) or Fim(Xi) selected in the previous steps) as the third selection function (step S860).
After completing the mutualism algorithm A, the commensalism algorithm B, and the parasitism algorithm C (refer to
Although the present disclosure has been described with reference to the preferred embodiment thereof, it will be understood that the present disclosure is not limited to the details thereof. Various substitutions and modifications have been suggested in the foregoing description, and others will occur to those of ordinary skill in the art. Therefore, all such substitutions and modifications are intended to be embraced within the scope of the present disclosure as defined in the appended claims.