Recharge pressure detection method of geothermal exploitation system and related equipment

Abstract

The invention provides a recharge pressure detection method of a geothermal exploitation system and related equipment. The method comprises the following steps: establishing a mathematical model of a pumping and recharging system; determining a first control equation, a first initial condition and a first boundary condition based on the mathematical model; performing Laplace transformation on the first control equation, the first initial condition and the first boundary condition to obtain a second control equation, a second initial condition and a second boundary condition; further, obtaining a drawdown analytic solution of the recharge well on the Laplacian domain; and converting the drawdown analytic solution of the recharge well on the Laplace domain into a pressure analytic solution of the recharge well on the Laplace domain, and obtaining a pressure analytic solution of the recharge well on the time domain according to a numerical inversion method of Laplace transformation. According to the method, the mathematical model of the pumping and recharging system is established, the laplace transformation method is used for solving the rule that the recharging pressure changes along with time, and therefore the recharging pressure change of the abandoned mine in the geothermal energy development process is accurately analyzed.

Description

Technical Field

[0001] The present application relates to the field of groundwater dynamics and mining engineering technology, and in particular to a method for detecting the reinjection pressure of a geothermal mining system and related equipment. Background Art

[0002] As an important part of traditional energy, the transformation, upgrading and structural adjustment of the coal industry are imperative.

[0003] Abandoned mines not only occupy valuable land resources, but the mine water accumulated inside them may also cause geological disasters if not managed properly, posing a potential threat to the surrounding ecological environment. Summary of the invention

[0004] In view of this, the purpose of the present application is to provide a reinjection pressure detection method and related equipment for a geothermal mining system.

[0005] As one aspect of the present application, a method for detecting reinjection pressure of a geothermal production system is provided, comprising:

[0006] Establishing a mathematical model of a pumping and irrigation system; the pumping and irrigation system comprises a pumping well and a recharging well; the mathematical model comprises a two-dimensional cylindrical coordinate system, the origin of the cylindrical coordinate system is the intersection of the well axis of the pumping well and the upper surface of the bottom plate of the pumping and irrigation system, the longitudinal axis of the cylindrical coordinate system is the well axis of the pumping well, the vertically upward direction is the positive direction, and the transverse axis of the cylindrical coordinate system is the line connecting the well axes of the pumping well and the recharging well on the upper surface of the bottom plate;

[0007] Based on the mathematical model, determining a first control equation, a first initial condition and a first boundary condition;

[0008] Performing Laplace transform on the first control equation, the first initial condition and the first boundary condition respectively to obtain a second control equation, a second initial condition and a second boundary condition;

[0009] Based on the second control equation, the second initial condition and the second boundary condition, an analytical solution of the drawdown of the reinjection well in the Laplace domain is obtained;

[0010] The drawdown analytical solution of the reinjection well in the Laplace domain is converted into the pressure analytical solution of the reinjection well in the Laplace domain. According to the numerical inversion method of Laplace transform, the pressure analytical solution of the reinjection well in the time domain is obtained to detect the distribution law of the reinjection pressure.

[0011] Optionally, the first control equation satisfies the following expression:

[0012]

[0013] Where s is the groundwater drawdown; r is the radial coordinate; t is the pumping time; S is the water release coefficient of the aquifer; K r is the hydraulic conductivity of the quasi-aquifer in the radial direction; d is the thickness of the quasi-aquifer;

[0014] The first initial condition satisfies the following expression:

[0015] s(r,0)=0;

[0016] s(∞,t)=0;

[0017] The first boundary condition satisfies the following expression:

[0018]

[0019] Among them, r w is the well radius; Q is the pumping rate.

[0020] Optionally, performing Laplace transform on the first control equation, the first initial condition and the first boundary condition respectively to obtain a second control equation, a second initial condition and a second boundary condition comprises:

[0021] Performing Laplace transformation on the first control equation to obtain the second control equation;

[0022] The second control equation satisfies the following expression:

[0023]

[0024] in, is the Laplace transform of groundwater drawdown; p is the Laplace variable;

[0025] Performing Laplace transformation on the first initial condition to obtain the second initial condition;

[0026] The second initial condition satisfies the following expression:

[0027]

[0028] Performing Laplace transformation on the first boundary condition to obtain the second boundary condition;

[0029] The second boundary condition satisfies the following expression:

[0030]

[0031] Optionally, Substitute into the second control equation to obtain the third control equation;

[0032] The third control equation satisfies the following expression:

[0033]

[0034] According to the Bessel equation, the third initial condition is obtained;

[0035] The third initial condition satisfies the following expression:

[0036] C1 = 0;

[0037]

[0038] wherein, the Bessel equation is I0(x) represents the modified Bessel function of the first kind, K0(x) represents the modified Bessel function of the second kind, and C1 and C2 are integration constants.

[0039] Optionally, obtaining the drawdown analytical solution of the recharge well in the Laplace domain based on the second control equation, the second initial condition, and the second boundary condition includes:

[0040] Determining the drawdown analytical solution of the pumping well in the Laplace domain;

[0041] The drawdown analytical solution of the pumping well in the Laplace domain satisfies the following expression:

[0042]

[0043] According to the drawdown analytical solution of the pumping well in the Laplace domain, determining the drawdown analytical solution of the recharge well in the Laplace domain; the pumping rates of the pumping well and the recharge well are opposite to each other;

[0044] The drawdown analytical solution of the recharge well in the Laplace domain satisfies the following expression:

[0045]

[0046] wherein, r1 is the distance from the center of the pumping well to any point p in the aquifer, r2 is the distance from the center of the recharge well to point p in the aquifer, l here represents the well spacing, l = r1 + r2, and l < R, R is the radius of influence, which can be expressed as:

[0047] Optionally, converting the drawdown analytical solution of the recharge well in the Laplace domain to the pressure analytical solution of the recharge well in the Laplace domain includes:

[0048] Based on the superposition principle, superimposing the drawdown analytical solutions of the pumping well and the recharge well in the Laplace domain to obtain the drawdown analytical solution of the pumping and recharge system in the Laplace domain;

[0049] The depth reduction analytical solution of the pumping system in the Laplace domain satisfies the following expression:

[0050]

[0051] Based on the conversion relationship between the drawdown analytical solution and the pressure analytical solution, the pressure analytical solution of the pumping and irrigation system in the Laplace domain is obtained;

[0052] The conversion relationship between the drawdown analytical solution and the pressure analytical solution satisfies the following expression:

[0053]

[0054] The analytical solution of the pressure of the pumping system in the Laplace domain satisfies the following expression:

[0055]

[0056] According to the analytical solution of the pressure of the pumping system in the Laplace domain, the analytical solution of the pressure of the reinjection well in the Laplace domain is determined.

[0057] Optionally, verify the analytical solution of the pressure of the reinjection well in the time domain.

[0058] As a second aspect of the present application, a reinjection pressure detection device for a geothermal mining system is provided, comprising: an establishment module, a determination module and a processing module;

[0059] The establishment module is used to establish a mathematical model of the pumping and irrigation system; the pumping and irrigation system includes a pumping well and a recharging well; the mathematical model includes a two-dimensional cylindrical coordinate system, the coordinate origin of the cylindrical coordinate system is the intersection of the well axis of the pumping well and the upper surface of the bottom plate of the pumping and irrigation system, the longitudinal axis of the cylindrical coordinate system is the well axis of the pumping well, the vertical upward direction is the positive direction, and the horizontal axis of the cylindrical coordinate system is the line between the well axes of the pumping well and the recharging well on the upper surface of the bottom plate;

[0060] The determination module is used to determine a first control equation, a first initial condition and a first boundary condition based on the mathematical model;

[0061] The processing module is used to perform Laplace transform on the first control equation, the first initial condition and the first boundary condition respectively to obtain a second control equation, a second initial condition and a second boundary condition;

[0062] The processing module is further used to obtain a drawdown analytical solution of the reinjection well in the Laplace domain based on the second control equation, the second initial condition and the second boundary condition;

[0063] The processing module is also used to convert the drawdown analytical solution of the reinjection well in the Laplace domain into the pressure analytical solution of the reinjection well in the Laplace domain, and obtain the pressure analytical solution of the reinjection well in the time domain according to the numerical inversion method of Laplace transform to detect the distribution law of the reinjection pressure.

[0064] Optionally, the first control equation satisfies the following expression:

[0065]

[0066] Where s is the groundwater drawdown; r is the radial coordinate; t is the pumping time; S is the water release coefficient of the aquifer; K r is the hydraulic conductivity of the quasi-aquifer in the radial direction; d is the thickness of the quasi-aquifer;

[0067] The first initial condition satisfies the following expression:

[0068] s(r,0)=0;

[0069]

[0070] The first boundary condition satisfies the following expression:

[0071]

[0072] Among them, r w is the well radius; Q is the pumping rate.

[0073] Optionally, the processing module is specifically used to perform Laplace transform on the first control equation to obtain the second control equation;

[0074] The second control equation satisfies the following expression:

[0075]

[0076] in, is the Laplace transform of groundwater drawdown; p is the Laplace variable;

[0077] Performing Laplace transformation on the first initial condition to obtain the second initial condition;

[0078] The second initial condition satisfies the following expression:

[0079] s(r,0)=0;

[0080] s(∞,p)=0;

[0081] Performing Laplace transformation on the first boundary condition to obtain the second boundary condition;

[0082] The second boundary condition satisfies the following expression:

[0083]

[0084] Optionally, the processing module is further configured to substitute into the second control equation to obtain a third control equation;

[0085] The third control equation satisfies the following expression:

[0086]

[0087] The processing module is further configured to obtain a third initial condition according to the Bessel equation;

[0088] The third initial condition satisfies the following expression:

[0089] C1 = 0;

[0090]

[0091] wherein, the Bessel equation is I0(x) represents the modified Bessel function of the first kind, K0(x) represents the modified Bessel function of the second kind, and C1 and C2 are integration constants.

[0092] Optionally, the processing module is further specifically configured to determine the drawdown analytical solution of the pumping well in the Laplace domain;

[0093] The drawdown analytical solution of the pumping well in the Laplace domain satisfies the following expression:

[0094]

[0095] Determine the drawdown analytical solution of the recharge well in the Laplace domain according to the drawdown analytical solution of the pumping well in the Laplace domain; the pumping rates of the pumping well and the recharge well are opposite to each other;

[0096] The drawdown analytical solution of the recharge well in the Laplace domain satisfies the following expression:

[0097]

[0098] wherein, r1 is the distance from the center of the pumping well to any point p in the aquifer, r2 is the distance from the center of the recharge well to point p in the aquifer, l represents the well spacing here, l = r1 + r2, and l < R, where R is the radius of influence and can be expressed as:

[0099] Optionally, the processing module is further specifically used to, based on the superposition principle, superimpose the depth reduction analytical solutions of the pumping well and the recharging well in the Laplace domain to obtain the depth reduction analytical solution of the pumping and recharging system in the Laplace domain;

[0100] The depth reduction analytical solution of the pumping system in the Laplace domain satisfies the following expression:

[0101]

[0102] Based on the conversion relationship between the drawdown analytical solution and the pressure analytical solution, the pressure analytical solution of the pumping and irrigation system in the Laplace domain is obtained;

[0103] The conversion relationship between the drawdown analytical solution and the pressure analytical solution satisfies the following expression:

[0104]

[0105] The analytical solution of the pressure of the pumping system in the Laplace domain satisfies the following expression:

[0106]

[0107] According to the analytical solution of the pressure of the pumping system in the Laplace domain, the analytical solution of the pressure of the reinjection well in the Laplace domain is determined.

[0108] Optionally, the well wall pressure of the pumping system is regarded as the well pressure, and r2=r w And r1≈l, the analytical solution of the pressure of the reinjection well in the Laplace domain satisfies the following expression:

[0109]

[0110] Optionally, the reinjection pressure detection device of the geothermal mining system further includes a verification module;

[0111] The verification module is used to verify the analytical solution of the pressure of the reinjection well in the time domain.

[0112] As a third aspect of the present application, an electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned reinjection pressure detection method for the geothermal extraction system when executing the program.

[0113] As a fourth aspect of the present application, a non-transitory computer-readable storage medium is provided, wherein the non-transitory computer-readable storage medium stores computer instructions, and the computer instructions are used to enable the computer to execute the reinjection pressure detection method of the above-mentioned geothermal extraction system provided in the present application.

[0114] From the above, it can be seen that the reinjection pressure detection method and related equipment of the geothermal mining system provided by the present application, by establishing a two-dimensional cylindrical coordinate mathematical model including pumping wells and reinjection wells, converts complex groundwater flow problems into mathematical equations, and can more accurately simulate the flow of groundwater in the pumping system, making the problem easier to handle. In addition, through Laplace transform, the control equations, initial conditions and boundary conditions in the time domain are converted to the Laplace domain, simplifying the solution process and thus improving the calculation efficiency. Finally, through the numerical inversion method, the law of reinjection pressure change with time is directly obtained. When applied to abandoned mines in the process of geothermal energy development, it can accurately analyze the changes in the reinjection pressure of the geothermal mining system, realize further utilization of geothermal resources in abandoned mines, promote economic value and environmental benefits, and at the same time help to prevent geological disasters in advance, and provide a scientific basis for groundwater resource management and protection. BRIEF DESCRIPTION OF THE DRAWINGS

[0115] In order to more clearly illustrate the technical solutions in the present application or related technologies, the drawings required for use in the embodiments or related technical descriptions are briefly introduced below. Obviously, the drawings described below are only embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0116] Figure 1 A schematic flow chart of a method for detecting reinjection pressure of a geothermal mining system provided in an embodiment of the present application;

[0117] Figure 2 A schematic diagram of a mathematical model of a pumping and irrigation system provided in an embodiment of the present application;

[0118] Figure 3 A schematic flow chart of another method for detecting the reinjection pressure of a geothermal mining system provided in an embodiment of the present application;

[0119] Figure 4 A schematic flow chart of another method for detecting the reinjection pressure of a geothermal mining system provided in an embodiment of the present application;

[0120] Figure 5 A schematic flow chart of another method for detecting the reinjection pressure of a geothermal mining system provided in an embodiment of the present application;

[0121] Figure 6 A schematic flow chart of another method for detecting the reinjection pressure of a geothermal mining system provided in an embodiment of the present application;

[0122] Figure 7 A schematic diagram of a solution to the reinjection pressure of the present invention and related technologies provided in an embodiment of the present application;

[0123] Figure 8 A relationship diagram of the effect of pumping rate on recharging pressure provided in an embodiment of the present application;

[0124] Fig. 9 A relationship diagram showing the influence of the distance between a pumping well and a recharging well on the recharging pressure provided in an embodiment of the present application;

[0125] Fig.10 A distribution relationship diagram of a type of aquifer water release coefficient and recharge pressure over time provided in an embodiment of the present application;

[0126] Fig.11 A graph showing the relationship between radial hydraulic conductivity and groundwater drawdown of a type of aquifer provided in an embodiment of the present application;

[0127] Fig.12 A schematic diagram of the composition of a reinjection pressure detection device for a geothermal mining system provided in an embodiment of the present application;

[0128] Fig.13 A schematic diagram of the composition of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0129] In order to make the purpose, technical solutions and advantages of the present application more clearly understood, the present application is further described in detail below in combination with specific embodiments and with reference to the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in the field without creative work are within the scope of protection of the present application.

[0130] It should be noted that, in the embodiments of the present application, words such as "exemplarily" or "for example" are used to indicate examples, illustrations or descriptions. Any embodiment or design described as "exemplarily" or "for example" in the embodiments of the present application should not be interpreted as being more preferred or more advantageous than other embodiments or designs. Specifically, the use of words such as "exemplarily" or "for example" is intended to present related concepts in a concrete way. Unless otherwise defined, the technical terms or scientific terms used in the embodiments of the present application should have the usual meaning understood by people with ordinary skills in the field to which the present application belongs. SUMMARY OF THE INVENTION

[0132] In the relevant technologies, geothermal energy, as a clean and renewable energy, has the advantages of abundant reserves, stable supply and environmental friendliness. The use of geothermal resources in mines to provide clean heating or cooling for buildings has received increasing attention. China has a huge amount of abandoned mine resources, which are rich in geothermal resources, have broad application prospects and huge market potential. They are currently important research directions and development fields. At the same time, vigorously developing geothermal resources in abandoned mines not only provides new ideas for solving the problems of abandoned mine management, but also opens up new paths for promoting the transformation of the national energy structure and promoting green and low-carbon development. However, since abandoned mines are usually located hundreds of meters underground, geothermal gradients and thermal convection have become the main heat transfer modes for the temperature field changes of the aquifer in the pumping and irrigation system of abandoned mines. The geothermal gradient increases at an average rate of 1-3°C per 100 meters, continuously heating the thermal reservoir fluid in the abandoned mines, and the degree of thermal convection mainly depends on the flow characteristics of groundwater in the aquifer. Therefore, it is necessary to first clarify the flow characteristics of groundwater in abandoned mines.

[0133] The inventors of this application have found that the research on the recharge pressure of mine water in the pumping and recharging system of abandoned mines is still in its infancy, and there is little systematic and in-depth discussion. This situation not only limits the comprehensive understanding of the fluid dynamics behavior of relevant technical personnel during the recharge process, but also hinders the formulation of effective control strategies for recharge pressure under specific geological and hydrological conditions. In addition, aquifer parameters, such as permeability, porosity, groundwater flow velocity, etc., and well structure parameters, such as well depth, well diameter, well spacing, etc., as key factors affecting recharge pressure, their interaction mechanism and specific impact on the geological environment, currently lack detailed theoretical analysis and experimental verification, making it difficult to ensure the long-term stable operation of the pumping and recharging system.

[0134] In order to solve the above problems, the present application provides a reinjection pressure detection method for a geothermal mining system. By establishing a two-dimensional cylindrical coordinate mathematical model including pumping wells and reinjection wells, the complex groundwater flow problem is converted into a mathematical equation, which can accurately simulate the flow of groundwater in the pumping system, making the problem easier to handle. Furthermore, through the Laplace transform, the control equations, initial conditions and boundary conditions in the time domain are converted to the Laplace domain, simplifying the solution process and thus improving the calculation efficiency. Finally, through the numerical inversion method, the law of reinjection pressure change with time is directly obtained. When applied to the geothermal energy development process of abandoned mines, the reinjection pressure change of the geothermal mining system can be accurately analyzed, and further utilization of geothermal resources in abandoned mines can be achieved, promoting economic value and environmental benefits. At the same time, it is helpful to prevent geological disasters in advance and provide a scientific basis for groundwater resource management and protection.

[0135] After introducing the basic principles of the present application, various non-limiting implementation methods of the present application are described in detail below.

[0136] Figure 1 A schematic diagram of a flow chart of a method for detecting the reinjection pressure of a geothermal mining system provided in an embodiment of the present application. Figure 1 As shown, the reinjection pressure detection method of the geothermal mining system provided by the present application specifically includes the following steps:

[0137] S101. Establish a mathematical model of the pumping and irrigation system.

[0138] Among them, the pumping and irrigation system includes a pumping well and a recharging well; the mathematical model contains a two-dimensional cylindrical coordinate system, the coordinate origin of the cylindrical coordinate system is the intersection of the well axis of the pumping well and the upper surface of the bottom plate of the pumping and irrigation system, the vertical axis of the cylindrical coordinate system is the well axis of the pumping well, the vertical upward direction is the positive direction, and the horizontal axis of the cylindrical coordinate system is the line between the well axes of the pumping well and the recharging well on the upper surface of the bottom plate.

[0139] In some embodiments, a geothermal extraction system is a system that utilizes underground thermal energy for energy development and utilization. It mainly drills geothermal wells deep underground and uses the hot water or steam in the geothermal wells as a heat source for heating, power generation or other industrial purposes. In order to reduce the impact on groundwater resources and prevent environmental problems such as ground subsidence, the geothermal extraction system includes a pumping and injection system. During the geothermal extraction process, the pumping and injection system extracts underground hot water or steam to the ground (pumping) and reinjects the used water into the ground (reinjection) to maintain the groundwater level and the sustainable utilization of geothermal resources.

[0140] Figure 2 A schematic diagram of a mathematical model of a pumping and irrigation system according to an embodiment of the present application is shown.

[0141] In some embodiments, Figure 2 As shown in the figure, the pumping and recharging system includes two wells of the same size and shape in the horizontal direction of the quasi-aquifer, one of which is a pumping well and the other is a recharging well. The two wells can be connected through a pumping system. The pumping well is used to extract groundwater from the quasi-aquifer for heat extraction, while the recharging well is used to re-inject the treated water into the quasi-aquifer to achieve groundwater recycling and heat extraction. Among them, the quasi-aquifer extends in the horizontal direction, and the top and bottom plates are both impermeable layers. In order to further simplify the complexity of calculation and analysis without losing the essential characteristics of the problem, a two-dimensional cylindrical coordinate system model is established. In this model, the intersection of the axis of the pumping well and the upper surface of the quasi-aquifer bottom plate is taken as the coordinate origin 0, the z-axis of the cylindrical coordinate system is the axis of the pumping well, and the direction is vertically upward as the positive direction to reflect the vertical change of the groundwater level; at the same time, the r-axis of the cylindrical coordinate system is the line between the axis of the pumping well and the recharging well on the upper surface of the bottom plate, which is convenient for describing the flow characteristics of groundwater in the horizontal direction; r wis the radius of the pumping well or the recharging well; d is the thickness of the quasi-aquifer; l is the distance between the well axes of the pumping well and the recharging well; Q is the pumping rate.

[0142] It should be understood that the quasi-aquifer is a space formed by the accumulation of mine water due to natural elastic recovery after the mine is shut down and the pump stops running. In the analysis, the impact of single-well pumping or single-well recharge on the aquifer is first considered. Based on this analysis, the superposition principle is used to combine the effects of the pumping well and the recharge well to simulate the hydraulic behavior of the entire pumping and recharge system in the quasi-aquifer.

[0143] It should be noted that the mathematical model of the above pumping and irrigation system is only shown to facilitate understanding of the spirit and principle of the present application, and the embodiments of the present application are not limited in this respect. On the contrary, the embodiments of the present application can be applied to any applicable scenario.

[0144] S102. Determine a first control equation, a first initial condition, and a first boundary condition based on a mathematical model.

[0145] In some embodiments, the mathematical model in S101 satisfies the following aspects: the thickness of the quasi-aquifer is uniform, homogeneous and anisotropic, and extends infinitely in the horizontal direction; the top and bottom plates of the quasi-aquifer are both impermeable, with uniform thickness and homogeneous and isotropic; the flow of groundwater in the quasi-aquifer satisfies Darcy's law, and the storage or release of groundwater caused by the rise or fall of the water level is completed instantly, wherein Darcy's law shows that under steady-state conditions, the flow rate of groundwater is proportional to the pressure gradient; both the pumping well and the recharge well are complete wells, pumping and recharge are carried out simultaneously and the pumping and recharge rates are equal (pumping is +, recharge is -, represented by Q); the influence of temperature on parameters such as permeability coefficient and water storage coefficient is not considered, etc.

[0146] In some embodiments, the control equation is a partial differential equation, which is used in this solution to describe the change of groundwater drawdown over time and space. The first control equation satisfies the following expression:

[0147]

[0148] Where s is the groundwater drawdown; r is the radial coordinate; t is the pumping time; S is the water release coefficient of the aquifer; K r is the hydraulic conductivity of the quasi-aquifer in the radial direction; d is the thickness of the quasi-aquifer;

[0149] Before the start of pumping (t = 0), the groundwater drawdown in the entire quasi-aquifer is zero, that is, the groundwater level is in its initial state and has not changed due to pumping. In addition, the change in groundwater level far away from the pumping well is negligible, that is, at infinity (r = ∞) in the quasi-aquifer, the groundwater drawdown is always zero. Then the first initial condition satisfies the following expression:

[0150] s(r,0)=0;

[0151] s(∞,t)=0;

[0152] According to the well radius and the well storage effect (i.e., the influence of the water level change in the wellbore on the surrounding groundwater flow), the first boundary condition satisfies the following expression:

[0153]

[0154] Among them, r w is the well radius; Q is the pumping rate.

[0155] It should be understood that drawdown (water level drop) is the value of the groundwater level drop during pumping. The groundwater level before pumping is called the "static water level", and the groundwater level that drops during pumping is called the "dynamic water level". The water level drop is equal to the difference between the static water level and the dynamic water level.

[0156] S103, performing Laplace transform on the first control equation, the first initial condition and the first boundary condition respectively to obtain a second control equation, a second initial condition and a second boundary condition.

[0157] Among them, Laplace transform is an integral transform commonly used in engineering mathematics, also known as Laplace transform. Laplace transform is a linear transformation that can transform a function with a parameter real number t (t≥0) into a function with a parameter complex number s. In this scheme, the function in the time domain can be transformed into a function in the Laplace domain. This transformation helps to transform partial differential equations into ordinary differential equations, thereby simplifying the solution process.

[0158] In some embodiments, the time variable (such as t) is replaced with a Laplace variable (such as s), and then the integral definition of the Laplace transform is applied to convert the time derivative term in the original control equation into a function of s. Similarly, the time variable in the initial condition and boundary condition is replaced with a Laplace variable, and the Laplace transform is applied to obtain a second control equation, a second initial condition, and a second boundary condition.

[0159] In some embodiments, Figure 3 As shown, S103 can be specifically implemented as follows S1031-S1033:

[0160] S1031. Perform Laplace transform on the first control equation to obtain a second control equation.

[0161] In some embodiments, the second control equation satisfies the following expression:

[0162]

[0163] in, is the Laplace transform of groundwater drawdown; p is the Laplace variable.

[0164] S1032. Perform a Laplace transform on the first initial condition to obtain a second initial condition.

[0165] In some embodiments, the second initial condition satisfies the following expression:

[0166] s(r,0)=0;

[0167] s(∞,p)=0.

[0168] S1033. Perform Laplace transform on the first boundary condition to obtain a second boundary condition.

[0169] In some embodiments, the second boundary condition satisfies the following expression:

[0170]

[0171] In some embodiments, Figure 4 As shown, the reinjection pressure detection method of the geothermal mining system provided in the embodiment of the present application also includes the following S201-S202:

[0172] S201, will Substitute it into the second control equation to obtain the third control equation.

[0173] In some embodiments, Substituted into the second control equation, the third control equation satisfies the following expression:

[0174]

[0175] S202. According to the Bessel equation, a third initial condition is obtained.

[0176] In some embodiments, the general solution to the Bessel equation is I0(x) represents the first kind of modified Bessel function, K0(x) represents the second kind of modified Bessel function, C1 and C2 are integration constants, so the third initial condition satisfies the following expression:

[0177] C1=0;

[0178]

[0179] It should be understood that the Bessel equation is a second-order ordinary differential equation, and its standard solution function needs to be represented by two independent functions. Typically, the first-kind Bessel function and the second-kind Bessel function are used to represent the standard solution function. In addition, the Bessel equation is obtained when solving the Laplace equation and the Helmholtz equation using the separation of variables method in cylindrical coordinates or spherical coordinates.

[0180] S104. Based on the second control equation, the second initial condition, and the second boundary condition, obtain the analytical solution of the drawdown of the recharge well in the Laplace domain.

[0181] In some embodiments, according to the above S201 - S202, convert the second control equation into a third control equation and the second initial condition into a third initial condition. Then, taking the partial derivative with respect to the parameter r gives:

[0182]

[0183] Furthermore, according to the second boundary condition, obtain that the integral constant C2 satisfies the following expression:

[0184]

[0185] By substituting the expression of C2 into the expression of the third initial condition, obtain that the analytical solution of the drawdown of the pumping well in the Laplace domain satisfies the following expression:

[0186]

[0187] According to the pumping and recharge in the pumping - recharge system in S102 being carried out simultaneously and at equal rates (pumping is +, recharge is -, represented by Q), that is, the pumping rates of the pumping well and the recharge well are opposite to each other, the analytical solution of the drawdown of the recharge well in the Laplace domain satisfies the following expression:

[0188]

[0189] Wherein, r1 is the distance from the center of the pumping well to any point p in the aquifer, r2 is the distance from the center of the recharge well to point p in the aquifer, l here represents the well spacing, l = r1 + r2, and l < R, where R is the radius of influence and can be expressed as:

[0190] S105. Convert the analytical solution of the drawdown of the recharge well in the Laplace domain into the analytical solution of the pressure of the recharge well in the Laplace domain. According to the numerical inversion method of the Laplace transform, obtain the analytical solution of the pressure of the recharge well in the time domain to detect the distribution law of the recharge pressure.

[0191] Among them, the numerical inversion method of the Laplace transform includes the Stehfest algorithm. This algorithm approximately calculates the inverse Laplace transform through numerical integration to obtain the analytical solution of the pressure in the time domain.

[0192] In some embodiments, the drawdown and the pressure are in a proportional relationship. By substituting the pressure expression for the drawdown, further convert the analytical solution of the drawdown of the recharge well in the Laplace domain into the analytical solution of the pressure of the recharge well in the Laplace domain.

[0193] In some embodiments, Figure 5 As shown, S105 can be specifically implemented as follows S1051-S1053:

[0194] S1051. Based on the superposition principle, the drawdown analytical solutions of the pumping well and the recharging well in the Laplace domain are superimposed to obtain the drawdown analytical solution of the pumping and recharging system in the Laplace domain.

[0195] In some embodiments, according to the superposition principle, the pumping and recharging system operates at the same flow rate. At this time, the drawdown generated at any point P in the quasi-aquifer is the sum of the drawdowns of the pumping well and the recharging well, and the following expression is satisfied:

[0196] s(r,t)=s1(r1,t)+s2(r2,t);

[0197] By performing Laplace transform on the above formula, we can get:

[0198]

[0199] Furthermore, the depth reduction analytical solution of the pumping system in the Laplace domain satisfies the following expression:

[0200]

[0201] S1052. Based on the conversion relationship between the drawdown analytical solution and the pressure analytical solution, obtain the pressure analytical solution of the pumping and irrigation system in the Laplace domain.

[0202] In some embodiments, the conversion relationship between the drawdown analytical solution and the pressure analytical solution satisfies the following expression:

[0203]

[0204] The analytical solution of the pressure of the pumping system in the Laplace domain satisfies the following expression:

[0205]

[0206] S1053. Determine the analytical solution for the pressure of the recharging well in the Laplace domain according to the analytical solution for the pressure of the pumping system in the Laplace domain.

[0207] In some embodiments, Figure 2 As shown in the figure, the well wall pressure of the pumping system is regarded as the well pressure, and r2 = r w And r1≈l, the analytical solution of the pressure of the reinjection well in the Laplace domain satisfies the following expression:

[0208]

[0209] In some embodiments, Figure 6As shown, after S105, the reinjection pressure detection method of the geothermal mining system provided in the embodiment of the present application further includes the following S106:

[0210] S106. Verify the analytical solution of the pressure of the recharging well in the time domain.

[0211] In some embodiments, the pressure distribution of the mathematical model of the pumping and irrigation system is solved. As an example, the model parameters are shown in Table 1 below.

[0212] Table 1

[0213] parameter Value unit Pumping volume Q 40 m3 h-1 Recharge volume Q 40 m3 h-1 Aquifer thickness d 60 m Well spacing l 27 m Well radius rw 0.1 m Water release coefficient S 0.007 m-1 Horizontal permeability coefficient Kr 1.25 MH-1 Vertical permeability coefficient Kz 0.01 MH-1

[0214] As shown in Table 1, the parameter pumping volume Q is 40m3h-1; the parameter reinjection volume Q is 40m3 h-1; the parameter aquifer thickness d is 60m; the parameter well spacing l is 27m; the parameter well radius rw is 0.1m; the parameter water release coefficient S is 0.07m-1; the parameter horizontal permeability Kr is 1.25mh-1; the parameter pumping volume Kz is 0.01mh-1. Further, by using the Stehfest numerical inversion method and writing relevant MATLAB programs, the model parameters set in Table 1 are brought in to obtain the results of the reinjection pressure of the abandoned mine pumping system changing with time. The relevant technology establishes a three-dimensional hydrothermal coupling numerical model to simulate and predict the evolution of groundwater seepage field and temperature field under different pumping well layout schemes, such as Figure 7 As shown, the analytical solution of the reinjection pressure of the abandoned mine water source heat pump well pumping system obtained by the present invention is almost completely consistent with the results obtained by the analytical solution obtained by the relevant technology, indicating that the analytical solution of the reinjection pressure obtained by this scheme is accurate.

[0215] For example, the influence of different quasi-aquifer parameters and pumping and recharging system structure parameters on the recharging pressure change of abandoned mines in quasi-aquifers is further analyzed. Figure 8 This is a graph showing the effect of pumping rate on recharging pressure. Figure 8 As shown, the pumping rate has a significant effect on the recharging pressure. The greater the pumping rate, the greater the injection pressure. Fig. 9 This is a graph showing the effect of the distance between the pumping well and the recharging well on the recharging pressure. Fig. 9 As shown, the distance between wells in the early stage has little effect on the reinjection pressure, while the greater the distance between wells, the greater the reinjection pressure in the later stage. Fig.10 This is the distribution relationship diagram of the water release coefficient and recharge pressure of aquifers over time, such as Fig.10 As shown in the figure, in the early stage of the pumping and irrigation system, the larger the water release coefficient, the smaller the reinjection pressure; in the later stage, the influence of the water release coefficient on the reinjection pressure can be ignored, and no matter how the water release coefficient changes, the reinjection pressure eventually approaches the same value. Fig.11 It is a graph showing the relationship between the radial hydraulic conductivity of aquifers and groundwater drawdown, such as Fig.11 As shown, the larger the radial hydraulic conductivity is, the smaller the reinjection pressure is.

[0216] The reinjection pressure detection method for the geothermal mining system provided in the present application converts the complex groundwater flow problem into a mathematical equation by establishing a two-dimensional cylindrical coordinate mathematical model including a pumping well and a reinjection well, and can accurately simulate the flow of groundwater in the pumping system, making the problem easier to handle. Furthermore, through the Laplace transform, the control equations, initial conditions and boundary conditions in the time domain are converted to the Laplace domain, simplifying the solution process and thus improving the calculation efficiency. Finally, through the numerical inversion method, the law of reinjection pressure change with time is directly obtained. When applied to the geothermal energy development process of abandoned mines, the reinjection pressure change of the abandoned geothermal mining system can be accurately analyzed, so as to further utilize the geothermal resources in the abandoned mines, promote economic value and environmental benefits, and at the same time help to prevent geological disasters in advance, providing a scientific basis for groundwater resource management and protection.

[0217] Furthermore, through the superposition principle, the influence of pumping wells and reinjection wells is comprehensively considered to obtain the analytical solution of the drawdown of the pumping and injection system, and then the reinjection pressure is obtained. Then, by comparing and verifying with actual observation data or other numerical methods, the accuracy and scope of application of the analytical solution can be evaluated, providing a reliable basis for practical application. At the same time, the verification process also helps to discover problems in the analytical solution and correct and improve it.

[0218] It should be noted that the method of the embodiment of the present application can be performed by a single device, such as a computer or server. The method of this embodiment can also be applied to a distributed scenario and completed by multiple devices cooperating with each other. In the case of such a distributed scenario, one of the multiple devices can only perform one or more steps in the method of the embodiment of the present application, and the multiple devices will interact with each other to complete the described method.

[0219] It should be noted that the above describes some embodiments of the present application. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in an order different from that in the above embodiments and still achieve the desired results. In addition, the processes depicted in the accompanying drawings do not necessarily require the specific order or continuous order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0220] Based on the same inventive concept, corresponding to any of the above-mentioned embodiments and methods, the present application also provides a reinjection pressure detection device for a geothermal mining system.

[0221] refer to Fig.12 , the reinjection pressure detection device of the geothermal mining system includes: an establishment module 1201, a determination module 1202 and a processing module 1203;

[0222] The establishment module 1201 is used to establish a mathematical model of the pumping and irrigation system; the pumping and irrigation system includes a pumping well and a recharging well; the mathematical model includes a two-dimensional cylindrical coordinate system, the origin of the cylindrical coordinate system is the intersection of the well axis of the pumping well and the upper surface of the bottom plate of the pumping and irrigation system, the longitudinal axis of the cylindrical coordinate system is the well axis of the pumping well, the vertical upward direction is the positive direction, and the horizontal axis of the cylindrical coordinate system is the line between the well axes of the pumping well and the recharging well on the upper surface of the bottom plate;

[0223] The determination module 1202 is used to determine a first control equation, a first initial condition and a first boundary condition based on the mathematical model;

[0224] The processing module 1203 is used to perform Laplace transform on the first control equation, the first initial condition and the first boundary condition respectively to obtain a second control equation, a second initial condition and a second boundary condition;

[0225] The processing module 1203 is further used to obtain a drawdown analytical solution of the reinjection well in the Laplace domain based on the second control equation, the second initial condition and the second boundary condition;

[0226] The processing module 1203 is also used to convert the depth drawdown analytical solution of the reinjection well in the Laplace domain into the pressure analytical solution of the reinjection well in the Laplace domain, and obtain the pressure analytical solution of the reinjection well in the time domain according to the numerical inversion method of Laplace transform to detect the distribution law of the reinjection pressure.

[0227] In some embodiments, the first control equation satisfies the following expression:

[0228]

[0229] Where s is the groundwater drawdown; r is the radial coordinate; t is the pumping time; S is the water release coefficient of the aquifer; K r is the hydraulic conductivity of the quasi-aquifer in the radial direction; d is the thickness of the quasi-aquifer;

[0230] The first initial condition satisfies the following expression:

[0231] s(r,0)=0;

[0232] s(∞,t)=0;

[0233] The first boundary condition satisfies the following expression:

[0234]

[0235] Among them, r w is the well radius; Q is the pumping rate.

[0236] In some embodiments, the processing module 1203 is specifically used to perform Laplace transform on the first control equation to obtain the second control equation;

[0237] The second control equation satisfies the following expression:

[0238]

[0239] in, is the Laplace transform of groundwater drawdown; p is the Laplace variable;

[0240] Performing Laplace transformation on the first initial condition to obtain the second initial condition;

[0241] The second initial condition satisfies the following expression:

[0242] s(r,0)=0;

[0243] s(∞,p)=0;

[0244] Performing Laplace transformation on the first boundary condition to obtain the second boundary condition;

[0245] The second boundary condition satisfies the following expression:

[0246]

[0247] In some embodiments, the processing module 1203 is further configured to: Substitute into the second control equation to obtain the third control equation;

[0248] The third control equation satisfies the following expression:

[0249]

[0250] The processing module 1203 is also used to obtain a third initial condition according to the Bessel equation;

[0251] The third initial condition satisfies the following expression:

[0252] C1=0;

[0253]

[0254] Among them, the Bessel equation is I0(x) represents the modified Bessel function of the first kind, K0(x) represents the modified Bessel function of the second kind, and C1 and C2 are integration constants.

[0255] In some embodiments, the processing module 1203 is further specifically configured to determine the drawdown analytical solution of the pumping well in the Laplace domain;

[0256] The drawdown analytical solution of the pumping well in the Laplace domain satisfies the following expression:

[0257]

[0258] According to the drawdown analytical solution of the pumping well in the Laplace domain, determine the drawdown analytical solution of the recharge well in the Laplace domain; the pumping rates of the pumping well and the recharge well are opposite to each other;

[0259] The drawdown analytical solution of the recharge well in the Laplace domain satisfies the following expression:

[0260]

[0261] Among them, r1 is the distance from the center of the pumping well to any point p in the aquifer, r2 is the distance from the center of the recharge well to point p in the aquifer, l represents the well spacing here, l = r1 + r2, and l < R, where R is the radius of influence and can be expressed as:

[0262] In some embodiments, the processing module 1203 is further specifically configured to, based on the superposition principle, superimpose the drawdown analytical solutions of the pumping well and the recharge well in the Laplace domain to obtain the drawdown analytical solution of the pumping and recharge system in the Laplace domain;

[0263] The drawdown analytical solution of the pumping and recharge system in the Laplace domain satisfies the following expression:

[0264]

[0265] Based on the conversion relationship between the drawdown analytical solution and the pressure analytical solution, obtain the pressure analytical solution of the pumping and recharge system in the Laplace domain;

[0266] The conversion relationship between the drawdown analytical solution and the pressure analytical solution satisfies the following expression:

[0267]

[0268] The pressure analytical solution of the pumping and recharge system in the Laplace domain satisfies the following expression:

[0269]

[0270] According to the analytical solution of the pressure of the pumping system in the Laplace domain, the analytical solution of the pressure of the reinjection well in the Laplace domain is determined.

[0271] In some embodiments, the reinjection pressure detection device of the geothermal mining system further includes a verification module 1204;

[0272] The verification module 1204 is used to verify the analytical solution of the pressure of the reinjection well in the time domain.

[0273] For the convenience of description, the above device is described in terms of functions divided into various modules. Of course, when implementing the present application, the functions of each module can be implemented in the same or multiple software and / or hardware.

[0274] The device of the above embodiment is used to implement the reinjection pressure detection method of the geothermal mining system corresponding to any of the above embodiments, and has the beneficial effects of the corresponding method embodiment, which will not be repeated here.

[0275] Based on the same inventive concept, corresponding to any of the above-mentioned embodiments and methods, the present application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the reinjection pressure detection method for the geothermal extraction system described in any of the above embodiments is implemented.

[0276] Fig.13 A more specific schematic diagram of the hardware structure of an electronic device provided in this embodiment is shown, and the device may include: a processor 1010, a memory 1020, an input / output interface 1030, a communication interface 1040, and a bus 1050. The processor 1010, the memory 1020, the input / output interface 1030, and the communication interface 1040 are connected to each other through the bus 1050 in the device.

[0277] The processor 1010 can be implemented by a general-purpose CPU (Central Processing Unit), a microprocessor, an application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of this specification.

[0278] The memory 1020 may be implemented in the form of ROM (Read Only Memory), RAM (Random Access Memory), static storage device, dynamic storage device, etc. The memory 1020 may store an operating system and other application programs. When the technical solutions provided in the embodiments of this specification are implemented by software or firmware, the relevant program codes are stored in the memory 1020 and are called and executed by the processor 1010.

[0279] The input / output interface 1030 is used to connect the input / output module to realize information input and output. The input / output module can be configured in the device as a component (not shown in the figure), or it can be externally connected to the device to provide corresponding functions. The input device may include a keyboard, a mouse, a touch screen, a microphone, various sensors, etc., and the output device may include a display, a speaker, a vibrator, an indicator light, etc.

[0280] The communication interface 1040 is used to connect a communication module (not shown) to realize communication interaction between the device and other devices. The communication module can realize communication through a wired mode (such as USB, network cable, etc.) or a wireless mode (such as mobile network, WIFI, Bluetooth, etc.).

[0281] The bus 1050 includes a path that transmits information between the various components of the device (eg, the processor 1010, the memory 1020, the input / output interface 1030, and the communication interface 1040).

[0282] It should be noted that, although the above device only shows the processor 1010, the memory 1020, the input / output interface 1030, the communication interface 1040 and the bus 1050, in the specific implementation process, the device may also include other components necessary for normal operation. In addition, it can be understood by those skilled in the art that the above device may also only include the components necessary for implementing the embodiments of the present specification, and does not necessarily include all the components shown in the figure.

[0283] The electronic device of the above embodiment is used to implement the reinjection pressure detection method of the geothermal mining system corresponding to any of the above embodiments, and has the beneficial effects of the corresponding method embodiment, which will not be repeated here.

[0284] Based on the same inventive concept, corresponding to any of the above-mentioned embodiment methods, the present application also provides a non-transitory computer-readable storage medium, wherein the non-transitory computer-readable storage medium stores computer instructions, and the computer instructions are used to enable the computer to execute the reinjection pressure detection method of the geothermal extraction system as described in any of the above embodiments.

[0285] The computer-readable medium of this embodiment includes permanent and non-permanent, removable and non-removable media, and information storage can be implemented by any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, read-only compact disk read-only memory (CD-ROM), digital versatile disk (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device.

[0286] The computer instructions stored in the storage medium of the above embodiment are used to enable the computer to execute the reinjection pressure detection method of the geothermal mining system as described in any of the above embodiments, and have the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0287] Based on the same inventive concept, corresponding to the reinjection pressure detection method of the geothermal mining system described in any of the above embodiments, the present disclosure also provides a computer program product, which includes a computer program. In some embodiments, the computer program is executable by one or more processors so that the processor executes the reinjection pressure detection method of the geothermal mining system. Corresponding to the execution subject corresponding to each step in each embodiment of the reinjection pressure detection method of the geothermal mining system, the processor that executes the corresponding step may belong to the corresponding execution subject.

[0288] The computer program product of the above embodiment is used to enable the processor to execute the reinjection pressure detection method of the geothermal mining system as described in any of the above embodiments, and has the beneficial effects of the corresponding method embodiment, which will not be repeated here.

[0289] Those skilled in the art should understand that the discussion of any of the above embodiments is merely illustrative and is not intended to imply that the scope of the present application (including the claims) is limited to these examples. In line with the concept of the present application, the technical features in the above embodiments or different embodiments may be combined, the steps may be implemented in any order, and there are many other variations of the different aspects of the embodiments of the present application as described above, which are not provided in detail for the sake of simplicity.

[0290] In addition, to simplify the description and discussion, and in order not to make the embodiments of the present application difficult to understand, the known power supply / ground connection with the integrated circuit (IC) chip and other components may or may not be shown in the provided drawings. In addition, the device can be shown in the form of a block diagram to avoid making the embodiments of the present application difficult to understand, and this also takes into account the fact that the details of the implementation of these block diagram devices are highly dependent on the platform to be implemented in the embodiments of the present application (that is, these details should be fully within the scope of understanding of those skilled in the art). In the case of elaborating specific details (e.g., circuits) to describe exemplary embodiments of the present application, it is obvious to those skilled in the art that the embodiments of the present application can be implemented without these specific details or when these specific details are changed. Therefore, these descriptions should be considered to be illustrative rather than restrictive.

[0291] Although the present application has been described in conjunction with specific embodiments of the present application, many replacements, modifications and variations of these embodiments will be apparent to those skilled in the art from the foregoing description. For example, other memory architectures (e.g., dynamic RAM (DRAM)) may use the embodiments discussed.

[0292] The embodiments of the present application are intended to cover all such substitutions, modifications and variations that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the embodiments of the present application should be included in the scope of protection of the present application.

Claims

1. A method for detecting the reinjection pressure of a geothermal mining system, characterized in that: The method comprises: Establishing a mathematical model of a pumping and irrigation system; the pumping and irrigation system comprises a pumping well and a recharging well; the mathematical model comprises a two-dimensional cylindrical coordinate system, the origin of the cylindrical coordinate system is the intersection of the well axis of the pumping well and the upper surface of the bottom plate of the pumping and irrigation system, the longitudinal axis of the cylindrical coordinate system is the well axis of the pumping well, the vertically upward direction is the positive direction, and the transverse axis of the cylindrical coordinate system is the line connecting the well axes of the pumping well and the recharging well on the upper surface of the bottom plate; Based on the mathematical model, determining a first control equation, a first initial condition and a first boundary condition; Performing Laplace transform on the first control equation, the first initial condition and the first boundary condition respectively to obtain a second control equation, a second initial condition and a second boundary condition; Based on the second control equation, the second initial condition and the second boundary condition, an analytical solution of the drawdown of the recharge well in the Laplace domain is obtained; The drawdown analytical solution of the reinjection well in the Laplace domain is converted into the pressure analytical solution of the reinjection well in the Laplace domain. According to the numerical inversion method of Laplace transform, the pressure analytical solution of the reinjection well in the time domain is obtained to detect the distribution law of the reinjection pressure.

2. The method according to claim 1, characterized in that The first control equation satisfies the following expression: Where S is the groundwater drawdown; r is the radial coordinate; t is the pumping time; S is the water release coefficient of the aquifer-like layer; K r is the hydraulic conductivity of the quasi-aquifer in the radial direction; d is the thickness of the quasi-aquifer; The first initial condition satisfies the following expression: s(r,0)＝0； s(∞,t)=0; The first boundary condition satisfies the following expression: Among them, r w is the well radius; Q is the pumping rate.

3. The method according to claim 2, characterized in that The step of performing Laplace transform on the first control equation, the first initial condition and the first boundary condition to obtain a second control equation, a second initial condition and a second boundary condition comprises: Performing Laplace transformation on the first control equation to obtain the second control equation; The second control equation satisfies the following expression: in, is the Laplace transform of groundwater drawdown; p is the Laplace variable; Performing Laplace transformation on the first initial condition to obtain the second initial condition; The second initial condition satisfies the following expression: s(r,0)＝0； s(∞,p)=0; Performing Laplace transformation on the first boundary condition to obtain the second boundary condition; The second boundary condition satisfies the following expression:

4. The method according to claim 3, characterized in that The method further comprises: Will Substitute into the second control equation to obtain the third control equation; The third control equation satisfies the following expression: According to Bessel's equation, the third initial condition is obtained; The third initial condition satisfies the following expression: C1＝0； Wherein, the Bessel equation is I0(x) represents the first kind modified Bessel function, K0(x) represents the second kind modified Bessel function, C1 and C2 are integration constants.

5. The method according to claim 4, characterized in that The method of obtaining the drawdown analytical solution of the recharging well in the Laplace domain based on the second control equation, the second initial condition and the second boundary condition includes: determining an analytical drawdown solution for the pumping well in a Laplace domain; The analytical solution of the drawdown of the pumping well in the Laplace domain satisfies the following expression: Determine the drawdown analytical solution of the recharging well in the Laplace domain according to the drawdown analytical solution of the pumping well in the Laplace domain; the pumping rates of the pumping well and the recharging well are inverse numbers of each other; The analytical solution of the drawdown of the recharge well in the Laplace domain satisfies the following expression: Among them, r1 is the distance from the center of the pumping well to any point p in the aquifer, r2 is the distance from the center of the recharge well to point p in the aquifer, l here represents the well spacing, l = r1 + r2, and l < R, where R is the radius of influence, which can be expressed as:

6. The method according to claim 5, characterized in that The step of converting the drawdown analytical solution of the reinjection well in the Laplace domain into the pressure analytical solution of the reinjection well in the Laplace domain comprises: Based on the superposition principle, the drawdown analytical solutions of the pumping well and the recharging well in the Laplace domain are superimposed to obtain the drawdown analytical solution of the pumping and recharging system in the Laplace domain; The depth reduction analytical solution of the pumping system in the Laplace domain satisfies the following expression: Based on the conversion relationship between the drawdown analytical solution and the pressure analytical solution, the pressure analytical solution of the pumping and irrigation system in the Laplace domain is obtained; The conversion relationship between the drawdown analytical solution and the pressure analytical solution satisfies the following expression: The analytical solution of the pressure of the pumping system in the Laplace domain satisfies the following expression: According to the analytical solution of the pressure of the pumping system in the Laplace domain, the analytical solution of the pressure of the reinjection well in the Laplace domain is determined.

7. The method according to claim 1, characterized in that The method further comprises: Verify the analytical solution of the pressure of the reinjection well in the time domain.

8. A reinjection pressure detection device for a geothermal mining system, characterized in that: The device comprises: an establishing module, a determining module and a processing module; The establishment module is used to establish a mathematical model of the pumping and irrigation system; the pumping and irrigation system includes a pumping well and a recharging well; the mathematical model includes a two-dimensional cylindrical coordinate system, the coordinate origin of the cylindrical coordinate system is the intersection of the well axis of the pumping well and the upper surface of the bottom plate of the pumping and irrigation system, the longitudinal axis of the cylindrical coordinate system is the well axis of the pumping well, the vertical upward direction is the positive direction, and the horizontal axis of the cylindrical coordinate system is the line between the well axes of the pumping well and the recharging well on the upper surface of the bottom plate; The determination module is used to determine a first control equation, a first initial condition and a first boundary condition based on the mathematical model; The processing module is used to perform Laplace transform on the first control equation, the first initial condition and the first boundary condition respectively to obtain a second control equation, a second initial condition and a second boundary condition; The processing module is further used to obtain a drawdown analytical solution of the reinjection well in the Laplace domain based on the second control equation, the second initial condition and the second boundary condition; The processing module is also used to convert the drawdown analytical solution of the reinjection well in the Laplace domain into the pressure analytical solution of the reinjection well in the Laplace domain, and obtain the pressure analytical solution of the reinjection well in the time domain according to the numerical inversion method of Laplace transform to detect the distribution law of the reinjection pressure.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the method according to any one of claims 1 to 7 when executing the program. 10 . A non-transitory computer-readable storage medium storing computer instructions, wherein the computer instructions are used to cause a computer to execute the method according to claim 1 .

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