CN102183447A - Test system and test method for permeability coefficients of aquifer - Google Patents

Abstract

The invention discloses a method for testing the permeability coefficient of an aquifer, which comprises the following steps: digging a well at the aquifer to be tested; quickly injecting a uniformly mixed tracer liquid into the well; collecting the water level and the tracer in the well in real time concentration, and calculate the permeability coefficient of the aquifer according to the open hole impact test model. This test method overcomes the defect that the existing technology needs to be used with the casing, effectively combines the tracer technology and the impact test technology, and can use the open hole to obtain the permeability coefficient of the aquifer in the natural state, which is easy to carry, easy to operate, and Low cost of use. The invention also discloses a test system for the permeability coefficient of the aquifer.

Description

A kind of testing system and testing method for permeability coefficient of aquifer

technical field

The invention belongs to the technical field of measuring groundwater dynamic parameters, in particular to a system and method for in-situ testing of hydrogeological parameters.

Background technique

At present, in the measurement of groundwater dynamic parameters, both indoor and field test methods can be used to obtain hydrogeological parameters. Among them, the indoor test method is to apply Darcy's theorem in the room to obtain the field undisturbed soil permeability coefficient, while the field test method The permeability coefficient of the aquifer is mainly obtained by using the pumping method and the water pressure method. The pumping/pressing method mainly includes the constant flow pumping/pressing method, the constant drop deep pumping/pressing method, etc., wherein the constant flow pumping The water pressure method is to extract the water body in the logging at a fixed flow rate (that is, to inject water into the logging well at a constant flow rate), so that the flow movement between the aquifer and the logging well can reach a steady state. According to the flow rate and drawdown in the steady state The permeability coefficient of the aquifer is obtained through the relationship; while the constant drawdown pumping/pressurization method keeps the water level drawdown in the logging well constant by pumping/pressurizing water, and obtains the permeability coefficient of the aquifer according to the relationship between the flow rate and the drawdown.

However, the existing test methods have their shortcomings: the indoor test method needs to take the undisturbed soil back to the laboratory for measurement, which destroys the natural structure of the soil; Although the method can be carried out on the test site to obtain the hydrogeological parameters of the aquifer, the equipment is cumbersome and the operation is complicated, which requires a lot of manpower, material and financial resources, and the implementation cost is high.

Based on the above, an impact test method has been developed abroad, which is a field test method. When it is implemented, it is mainly to set a casing in the logging, isolate the inner wall of the logging, and set a filter at a specific position of the casing. , using the change of water level to test the permeability coefficient of the aquifer at this place. However, this test method is only suitable for the situation where the water level fluctuation caused is located on the upper part of the filter. If it is used for screw hole test, or the whole hole is equipped with filter In the case of a device, there will be a large error in the result; in addition, this test method must be implemented with a bushing, which limits its application range.

Based on the above analysis, the inventor conducted research and improvement on the existing permeability coefficient test method, and this case arose from it.

Contents of the invention

The technical problem to be solved by the present invention is to provide an aquifer permeability coefficient testing system and testing method for the above-mentioned defects and deficiencies in the background technology, which can use open holes to obtain the permeability coefficient of the aquifer in the natural state, and is easy to carry , easy to operate, and low cost.

The present invention is for solving above technical problem, and the technical solution adopted is:

An aquifer permeability testing system includes a sensor, a central controller, a communication module and a data processing module, wherein the data processing module is connected to the sensor via the central controller to control the start of the sensor; the sensor is set in the well logging, Monitor the water level and tracer concentration in the well logging in real time, and send them to the data processing module through the communication module, and the data processing module converts the electrical signal obtained by the sensor into the corresponding water level signal and tracer concentration signal, and based on this Calculate the permeability coefficient of the aquifer.

The above-mentioned sensors include a pressure sensor capable of monitoring water pressure and a concentration detector capable of monitoring tracer concentration, and the data processing module calculates and obtains the logging water level data according to the water pressure.

A method for testing the permeability coefficient of an aquifer, comprising the steps of:

(1) Excavating logging wells at the aquifer to be tested;

(2) Rapidly inject the uniformly mixed tracer fluid into the well logging;

(3) Collect the water level and tracer concentration in the well log in real time, and calculate the permeability coefficient of the aquifer according to the open hole impact test model.

In the above-mentioned step (3), the water level acquisition method in the well logging is: a pressure sensor is set in the well logging, the water pressure in the well logging is collected in real time, and the water pressure is converted into the water level in the well logging at this moment according to the following formula:

$\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>\frac{\text{<span class="notranslate"> p</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;g</span>}}$

Among them, H is the height of the water level relative to the water level;

p is the measured water pressure value;

ρ is the density of water;

g is the acceleration due to gravity.

In above-mentioned step (3), the expression of described open hole impact test model is:

$\left\{\begin{array}{c}\frac{{<span\; class="notranslate">\; \&PartialD;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; h</span>}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="r"\; filenames="110308093239.png,110308093416.png"\; state="\{\{state\}\}">r</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; r</span>}}\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; K</span>}}\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; t</span>}}\\ \mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; <</span><span\; class="notranslate">\; \&infin;</span>\\ \mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ \mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; \&infin;</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}\mathrm{<span\; class="notranslate">\; KB</span>}\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\end{array}\right.$

In the formula: h is the water head drawdown of the aquifer;

r is the radial distance;

Ss is the water storage rate;

K is the radial permeability coefficient;

t is time;

H(t) is the water head drawdown of well logging at time t;

_H0 is the initial water head drawdown in the logging;

r _w is the radius of the effective filter tube;

B is the thickness of the aquifer;

Q ₂ (t) represents the amount of water flowing into the aquifer at time t during the test, and its expression is:

${\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; \&Integral;</span>\frac{\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}}}{\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; \&Integral;</span>\frac{\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}}}{\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; d\; h</span>}}\mathrm{<span\; class="notranslate">\; d\; h</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&Integral;</span>\frac{\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}}}{\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; d\; h</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&Integral;</span>\frac{\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}}}{\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; d\; h</span>}}<span\; class="notranslate">\; \&Integral;</span>\frac{\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}}}{\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; \&Integral;</span>\frac{\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}}}{\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; d\; h</span>}}\mathrm{<span\; class="notranslate">\; d\; h</span>}<span\; class="notranslate">\; ]</span>$

Among them, c(h ₀ , t) is the concentration value of the tracer at the time point t during the test, when the water head drawdown of the aquifer is h ₀ .

After adopting the above-mentioned scheme, the present invention changes the existing test method, effectively combines the tracer technology and the impact test technology, and uses the change of the tracer concentration in the well logging to calculate and obtain the permeability coefficient of the aquifer. The present invention is applicable to bare The hole test overcomes the defect that the existing technology must be used in conjunction with the casing. Since the casing is no longer used, the requirements for well logging are correspondingly reduced, and the applicability is wide. cost; in addition, the test system provided by the present invention is easy to operate and portable.

Description of drawings

Fig. 1 is a schematic diagram of the overall architecture of the present invention;

Fig. 2 is a flow chart of the present invention;

Fig. 3 is a schematic view of the working state of the present invention.

Detailed ways

The structure and working principle of the present invention will be described in detail below with reference to the drawings and specific embodiments.

First with reference to shown in Fig. 1, the present invention provides a kind of aquifer permeability testing system, comprises sensor 1, central controller 2, communication module 3 and data processing module 4, and wherein, data processing module 4 connects central controller 2, and The output end of the central controller 2 is connected to the sensor 1, and the data processing module 4 sends a test command to the central controller 2, and then the central controller 2 controls the sensor 1 to start and start data monitoring; the sensor 1 includes pressure The sensor and the concentration detector are both arranged in the well logging, and are respectively used to monitor the water pressure and the concentration of the tracer in the well logging, and transmit them to the data processing module 4 through the communication module 3, and the data processing module 4 sends the sensor 1 The obtained electrical signal is converted into the corresponding water pressure signal and tracer concentration signal, and the water level data is calculated according to the water pressure, and then the permeability coefficient of the aquifer is calculated based on this.

Please refer to shown in Fig. 2 again, be the flowchart of a kind of aquifer permeability testing method provided by the present invention, comprise the steps:

(1) Excavating logging wells at the aquifer to be tested;

(2) Dissolve a certain amount of tracer in a certain volume of water, mix it evenly to make a tracer liquid, and quickly inject it into the well logging, so that a certain water head difference will be generated in the well logging instantaneously;

(3) Put the sensor into the well logging, as shown in Fig. 3, at this time, the tracer fluid injected in the well logging will penetrate into the inner wall of the logging well in order to achieve hydraulic balance. The concentration of the tracer will also decrease; at this time, the pressure sensor and the concentration detector respectively collect the water pressure and tracer concentration in the well logging in real time, and send them to the data processing module through the communication module in the form of electrical signals;

(4) The data processing module converts the received electric signal into a water pressure signal and a tracer concentration signal in the well logging respectively, and converts the water pressure into a water level signal, and the described water pressure conversion formula is:

$\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>\frac{\text{<span class="notranslate"> p</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;g</span>}}$

Among them, H is the height of the water level relative to the water level;

p is the measured water pressure value;

ρ is the density of water;

g is the acceleration due to gravity.

Then, calculate the permeability coefficient of the aquifer according to the open hole impact test model again, and the described open hole impact test model is as follows:

$\left\{\begin{array}{c}\frac{{<span\; class="notranslate">\; \&PartialD;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; h</span>}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="r"\; filenames="110308093239.png,110308093416.png"\; state="\{\{state\}\}">r</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; r</span>}}\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; K</span>}}\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; t</span>}}\\ \mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; <</span><span\; class="notranslate">\; \&infin;</span>\\ \mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ \mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; \&infin;</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}\mathrm{<span\; class="notranslate">\; KB</span>}\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\end{array}\right.$

In the formula: h is the water head drawdown of the aquifer;

r is the radial distance;

Ss is the water storage rate;

K is the radial permeability coefficient;

t is time;

H(t) is the water head drawdown of well logging at time t;

_H0 is the initial water head drawdown in the logging;

r _w is the radius of the effective filter tube;

B is the thickness of the aquifer;

Q ₂ (t) represents the amount of water flowing into the aquifer at time t during the test.

The analytical formula of the above open hole impact test model is as follows:

$\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}{{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}\mathrm{<span\; class="notranslate">\; KB</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; \&infin;</span>}\frac{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; d\&tau;du</span>}$

In the above formula, the expression of the parameter Q ₂ (t) is as follows:

${\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; \&Integral;</span>\frac{\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}}}{\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; \&Integral;</span>\frac{\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}}}{\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; d\; h</span>}}\mathrm{<span\; class="notranslate">\; d\; h</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&Integral;</span>\frac{\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}}}{\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; d\; h</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&Integral;</span>\frac{\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}}}{\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; d\; h</span>}}<span\; class="notranslate">\; \&Integral;</span>\frac{\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}}}{\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; \&Integral;</span>\frac{\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}}}{\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; d\; h</span>}}\mathrm{<span\; class="notranslate">\; d\; h</span>}<span\; class="notranslate">\; ]</span>$

Among them, c(h ₀ , t) is the concentration value of the tracer at the time point t during the test, when the water head drawdown of the aquifer is h ₀ .

Therefore, the expression of the aquifer permeability coefficient can be obtained as:

In summary, a test system and test method for aquifer permeability coefficient of the present invention focus on combining tracer technology and impact test technology, dissolving a certain amount of tracer in a certain volume of water to make a tracer solution , inject it into the well logging quickly, so that a certain water head difference is generated in the well logging instantaneously, and then track and record the recovery process of the water level in the well logging and the change process of the tracer concentration in the well logging, and use the open hole impact test model to calculate The permeability coefficient of the aquifer. The invention can obtain the permeability coefficient of the aquifer in the natural state by utilizing the open holes, is convenient and quick, has low use cost, does not need the use of casing, and has wide applicability.

The above embodiments are only to illustrate the technical ideas of the present invention, and can not limit the protection scope of the present invention with this. All technical ideas proposed in accordance with the present invention, any changes made on the basis of technical solutions, all fall within the protection scope of the present invention. Inside.

Claims (5)

1. a kind of aquifer permeability test system, it is characterized in that: comprise sensor, central controller, communication module and data processing module, wherein, data processing module connects sensor via central controller, the start-up of control sensor; Described sensor Set in well logging, monitor the water level and tracer concentration in the well logging in real time, and send them to the data processing module through the communication module, and the data processing module converts the electrical signal obtained by the sensor into the corresponding water level signal and tracer Concentration signal, and calculate the permeability coefficient of the aquifer based on it. 2. a kind of aquifer permeability testing system as claimed in claim 1, is characterized in that: described sensor comprises the pressure sensor that can monitor water pressure and the concentration detector that can monitor tracer concentration, and data processing module according to The water pressure is calculated to obtain the logging water level data. 3. a test method that adopts the aquifer permeability test system as claimed in claim 1, is characterized in that comprising the steps: (1) Excavating logging wells at the aquifer to be tested; (2) Rapidly inject the uniformly mixed tracer fluid into the well logging; (3) Collect the water level and tracer concentration in the well log in real time, and calculate the permeability coefficient of the aquifer according to the open hole impact test model. 4. a kind of aquifer permeability testing method as claimed in claim 3, is characterized in that: in described step (3), the water level acquisition method in the well logging is: a pressure sensor is set in the well logging, real-time acquisition measurement The water pressure in the well, and convert the water pressure to the water level in the well logging at this time according to the following formula: $\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;g</span>}}$ Among them, H is the height of the water level relative to the water level; p is the measured water pressure value; ρ is the density of water; g is the acceleration due to gravity. 5. a kind of aquifer permeability test method as claimed in claim 3, is characterized in that: in described step (3), the expression of described open hole impact test model is: $\left\{\begin{array}{c}\frac{{<span\; class="notranslate">\; \&PartialD;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; h</span>}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; r</span>}}\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; K</span>}}\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; t</span>}}\\ \mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; <</span><span\; class="notranslate">\; \&infin;</span>\\ \mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ \mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; \&infin;</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}\mathrm{<span\; class="notranslate">\; KB</span>}\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\end{array}\right.$ In the formula: h is the water head drawdown of the aquifer; r is the radial distance; Ss is the water storage rate; K is the radial permeability coefficient; t is time; H(t) is the water head drawdown of well logging at time t; _H0 is the initial water head drawdown in the logging; r _w is the radius of the effective filter tube; B is the thickness of the aquifer; Q ₂ (t) represents the amount of water flowing into the aquifer at time t during the test, and its expression is: ${\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; \&Integral;</span>\frac{\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}}}{\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; \&Integral;</span>\frac{\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}}}{\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; d\; h</span>}}\mathrm{<span\; class="notranslate">\; d\; h</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&Integral;</span>\frac{\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}}}{\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; d\; h</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&Integral;</span>\frac{\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}}}{\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; d\; h</span>}}<span\; class="notranslate">\; \&Integral;</span>\frac{\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}}}{\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; \&Integral;</span>\frac{\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}}}{\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; d\; h</span>}}\mathrm{<span\; class="notranslate">\; d\; h</span>}<span\; class="notranslate">\; ]</span>$ Among them, c(h ₀ , t) is the concentration value of the tracer at the time point t during the test, when the water head drawdown of the aquifer is h ₀ .

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