CN-121997836-A - Finite-scale confined aquifer porous micro-water test model solving and parameter identification method

CN121997836ACN 121997836 ACN121997836 ACN 121997836ACN-121997836-A

Abstract

The invention discloses a method for solving a limited-scale confined aquifer porous micro-water test model and identifying parameters, which comprises the steps of constructing a radial non-steady flow mathematical model considering a shaft water storage effect and a remote constant head boundary constraint, performing dimensionless treatment, deducing an analytical expression representing the test well and the internal water head response of the aquifer in a frequency domain by utilizing Laplace transformation, and solving a transient water level semi-analytical solution in a time domain by matching with Stehfest numerical inverse transformation algorithm. In the parameter identification process, high-frequency high-precision water pressure sensors arranged at the test well and the observation wells at different positions are utilized to synchronously acquire water level response data after micro-water excitation. Before the unstable flow data is processed, the stable flow water injection test data before micro-water excitation can be utilized, and the permeability coefficient reference value is obtained through the logarithmic linear regression analysis of the water head and the distance by combining a radial steady well flow formula. And finally, decoupling and identifying the permeability coefficient and the water storage rate. The invention obviously improves the accuracy of the permeability coefficient and the water storage rate.

Inventors

Dong Xiaosong
ZHOU WEIJIAN
WANG FEIYUN
LIU YINAN
ZHAO YANRONG
HUANG YONG
WANG HAONAN
MAO SHILONG
ZHANG JIE
ZHANG YUXING
Xing Fuxin
HU CHENGJIE

Assignees

河海大学

Dates

Publication Date: 20260508
Application Date: 20260203

Claims (8)

1. The method for solving the finite-scale confined aquifer porous micro-water test model and identifying the parameters is characterized by comprising the following steps: 1) Aiming at a finite scale well-aquifer system in an initial stable flow field state, constructing an underground water flow control equation and a solution condition which consider the water storage effect of a shaft and the boundary constraint of a remote constant head to form a mathematical model, and carrying out dimensionless treatment on the mathematical model by defining dimensionless factors to obtain the dimensionless model; 2) Deducing analytic solutions of the test well and the internal water head of the aquifer in a frequency domain by using Laplace transformation based on a dimensionless model, and obtaining a transient water level response semi-analytic solution in a time domain by matching with a numerical inversion algorithm; 3) Constructing a physical model consisting of a cylindrical sand tank, a central test well and an observation well, constructing an initial background flow field through a steady flow water injection test, and acquiring whole process response data of a micro water test by adopting instantaneous water injection excitation; 4) Based on a radial steady well flow theoretical formula, calculating and obtaining a basic reference value of the permeability coefficient of the aquifer by establishing a linear regression model between the water head response and the radial distance logarithm by utilizing observation data of a steady flow water injection test stage before the micro water test excitation; 5) And a nonlinear optimization algorithm program based on a least square method is adopted, a datum reference value of the permeability coefficient is used as a constraint condition, and high-precision decoupling identification calculation of the permeability coefficient and the water storage rate is realized by fitting the porous measured data and a semi-analytical solution.
2. The method for solving and identifying parameters of the finite-scale confined aquifer porous micro-water test model according to claim 1, wherein in the step 1), the mathematical model construction method is as follows: establishing a polar coordinate system with a well axis of a test well as a center to obtain a radial unsteady flow control equation in an aquifer: ; transient response of the micro-water test is superimposed on the background steady-state flow field, and initial conditions are given by radial steady-state well flow solution in the limited confined aquifer: ; The outer boundary maintains constant head conditions: ; the inner boundary water head is equal to the sum of the initial background water head and the instantaneous disturbance water head: ; Considering the superposition of a shaft water storage effect and a background flow field, a water conservation equation of a well-aquifer and an initial condition thereof are established at the junction of the well wall and the aquifer through a water conservation law and a Darcy law together: ; ; Wherein H, H (R, T) are respectively represented as a total water head [ L ] of an aquifer, H (R, 0) is background stable flow field distribution [ L ] at an initial moment, H w is initial background water head [ L ] in a test well, H L is water head [ L ] at an outer boundary, w (T) are respectively represented as instantaneous variation [ L ] of water level in the test well relative to H w , w 0 is initial water head difference [ L ] excited by micro water test in the test well, R is radial distance [ L ] of each point in the aquifer from the center of the test well, R w is pipe radius [ L ] of the test well, R c is sleeve radius [ L ] of the test well, R L is limited outer boundary distance [ L ] of the aquifer, T is time [ T ], S s is water storage rate [1/L ] of the aquifer, K is permeability coefficient [ L/T ] of the aquifer, and B is the aquifer thickness [ L ].
3. The method for solving and identifying parameters of the finite-scale confined aquifer porous micro-water test model according to claim 2 is characterized in that in the step 1), the method for carrying out dimensionless treatment on the mathematical model by defining dimensionless factors comprises the following dimensionless variables: ; Will be described in Is substituted into the non-dimensional variable in (a) - The dimensionless treatment is carried out to obtain the dimensionless solution problem, wherein the dimensionless radial unstable flow control equation is as follows: ; The dimensionless initial conditions are: ; the dimensionless boundary conditions are: ; ; the dimensionless water conservation equation and the initial conditions are as follows: ; ; Wherein R D is the dimensionless radial distance, R LD is the dimensionless outer boundary distance, t D is the dimensionless time, w D , w D (t D ) are dimensionless water head variable in a test well, H D , H D (r D , t D ) are dimensionless water head variable in an aqueous layer, and S sD is the dimensionless water storage rate.
4. The method for solving and identifying parameters of the finite-scale confined aquifer porous micro-water test model according to claim 3, wherein the specific steps of the step 2) include the following steps: The Laplace transform defining a dimensionless time t D : ; wherein s is a Laplace variable; as a time domain function Is a function of the image of (a); Opposite type - Carrying out Laplace transformation, and obtaining a frequency domain solution in the Laplace domain by utilizing a general solution form of a Bessel equation and combining boundary conditions; For dimensionless control equation Applying Laplace transformation and using initial conditions The method comprises the following steps of: ; And The Bessel equation is modified for the zero order, which is solved: ; Laplacian transform is performed on boundary conditions: ; ; Will be described in Substitution of boundary conditions And : ; ; Combined type - The undetermined coefficients A and B can be obtained: ; ; The generation A and the generation B are processed in a back-to-back way In (3) obtaining the water head distribution: ; Next, the conservation equation of water quantity is changed Using the differential properties of the Laplace transform and the initial conditional expression : ; Opposite type Derivative relation is used for obtaining: ; Will be described in Substituted formula : ; And (3) finishing to obtain: ; And And-type Namely, the solution is a frequency domain solution of the dimensionless water head variation in the aquifer and the test well; wherein the auxiliary function is defined as: ; ; To obtain the time domain solutions w D and H D , the Stehfest algorithm pair-wise is used And (d) the Performing numerical inversion: ; ; Wherein the method comprises the steps of Are all indicated Is a laplace transform of (a); Are all indicated Is a laplace transform of (a); The method is characterized by comprising the steps of Laplace variables, A and B are to-be-determined coefficients, I 0 and K 0 are zero-order modified Bessel functions of a first type and a second type respectively, I 1 and K 1 are first-order modified Bessel functions of the first type and the second type respectively, N is a truncated term number, an even number between 8 and 16 is usually taken, 12 is calculated, V i is a weight coefficient related to N, I is an index variable in a sum cycle, and K is an auxiliary index variable in a sum formula when the weight coefficient is calculated.
5. The method for solving and identifying parameters of the limited-scale confined aquifer porous micro-water test model according to any one of claims 1-4 is characterized in that in the step 3), a physical model adopts a cylindrical sand tank to simulate a limited-scale confined aquifer, the top and the bottom of the tank body are subjected to seepage-proofing sealing, homogeneous water-bearing medium is filled in the tank body, the center of the tank body is provided with a fully-penetrating test well, more than two observation wells are distributed at different radial radiuses, the test well and the bottom of each observation well are respectively provided with a high-frequency high-precision water pressure sensor, the radially outer boundary of the aquifer is communicated with an external water tank, a constant water head boundary is maintained through an overflow port, constant flow water is injected to the test well before the water level is stabilized, a background flow field is formed, instantaneous water injection induction system response is carried out to the test well on the basis of the background flow field, and water head response overall process data of the test well and each observation well are synchronously collected.
6. The method for solving and identifying parameters of the limited-scale confined aquifer porous micro-water test model according to claim 5, wherein step 4) is implemented by collecting steady-state background flow field water level and flow data to calculate a permeability coefficient reference value after the water level is stabilized to form a background flow field in step 3), and calculating through the following mathematical regression analysis and formula: under the condition that peristaltic pumps are used for continuously injecting water into a test well and maintaining constant flow, a test system achieves a steady-state radial flow state, and for a limited confined aquifer with constant head boundary control, the steady-state radial head distribution is represented by the formula A representation; Will be described in Rewrites into a log-linear form, which can be obtained: ; ; The flow Q (t) and the water head gradient meet the requirement by combining the radial steady state Darcy law ; Will be described in Substituted formula The permeability coefficient can be directly calculated by the logarithmic fit slope A 1 ; Wherein A 1 and A 2 respectively represent the slope and intercept of logarithmic fit, and Q (t) is steady-state water injection flow in unit time; the permeability coefficient K is used as a base reference value of the permeability coefficient of the aquifer.
7. The method for solving and identifying parameters of the limited-scale confined aquifer porous micro-water test model according to claim 1, wherein in the step 5), a benchmark reference value of an aquifer permeability coefficient is used as a priori constraint condition in a subsequent parameter automatic decoupling inversion link, and rationality verification and robustness assessment of a geological parameter identification result are realized by comparing consistency of a steady-state benchmark value and a transient inversion value; The parameter automatic decoupling inversion link is realized by a nonlinear optimization algorithm program written based on Python language; In the inversion process, an algorithm program utilizes the strong correlation between the effective decoupling permeability coefficient of the test well and the data of a plurality of observation wells and the water storage rate to eliminate the problem of different parameter and same effect caused by low sensitivity of the water storage rate in the traditional single Kong Fanyan, thereby automatically identifying and outputting a high-precision calculation identification result with physical uniqueness of the permeability coefficient and the water storage rate.
8. The method for solving the finite-scale confined aquifer porous micro-water test model and identifying parameters according to claim 7, wherein the specific steps of automatically identifying and outputting the permeability coefficient and the water storage rate through iterative operation are as follows: Extracting the time series data of the measured water level drop after logarithmic resampling processing in the step 5) and taking the time series data as a nonlinear least square fitting target vector, executing nonlinear optimization iteration, outputting a final parameter identification result when the target function meets the convergence accuracy requirement, and calculating a formula of the permeability coefficient and the water storage rate by a pass type In the method, the dimensionless water storage rate and dimensionless time conversion relation are reversely determined 。

Description

Finite-scale confined aquifer porous micro-water test model solving and parameter identification method Technical Field The invention relates to a method for testing and inverting hydrogeologic parameters of an aquifer, in particular to a method for solving an analytical model and identifying permeability coefficient and water storage rate with high precision by a porous micro-water test aiming at a limited-scale confined aquifer system under an initial background stable flow field, belonging to the technical field of testing the hydrogeologic parameters of the aquifer and evaluating groundwater resources. Background The accurate acquisition of hydrogeologic parameters such as aquifer permeability coefficient, water storage rate and the like is a core foundation for developing groundwater resource evaluation, engineering precipitation design and geological environment protection. The micro-water test is used as an in-situ test technology for inducing the water head response of the aquifer by instantaneously changing the water level in the well, has the remarkable advantages of short test period, simple and convenient equipment, small disturbance on the physical structure of the stratum and the like, and is widely applied to indoor physical model tests and on-site in-situ tests. However, existing theoretical models of micro-water testing are mostly built on the assumption of unconfined domain space, considering the aquifer as a medium that extends indefinitely in the radial direction. In an actual indoor sand tank experiment or an engineering site with a physical barrier, the geometric dimension of a test medium is often strictly limited by a rigid wall surface or a drainage boundary, and if inversion calculation is directly carried out by using a traditional unconfined domain theory, serious systematic deviation can be generated due to neglecting the boundary effect, so that the calculated hydrogeologic parameters are distorted. Meanwhile, the traditional single-hole micro-water test is generally faced with the dilemma of different parameters and the uniformity of the inverted parameters is often lacking due to the low sensitivity of the water level response of a single test well to the water storage rate. In addition, the existing data processing mode is mostly dependent on manual drawing of standard curves and visual matching, and the manual wiring method is low in efficiency and large in subjective error, and the data advantages of multi-observation hole monitoring are difficult to develop. Therefore, a novel solving method capable of accurately marking a limited-scale fixed water head boundary, balancing background flow field influence and realizing automatic decoupling inversion of porous data is developed, and the method has important academic value and practical significance for improving the refinement level of aquifer parameter test. Disclosure of Invention The invention aims to: the invention aims to provide a method for solving a finite-scale confined aquifer porous micro-water test model and performing parameter inversion, wherein a mathematical model considering an initial background flow field, a shaft water storage effect and a remote constant head boundary constraint is constructed, and decoupling identification and physical verification of a permeability coefficient and a water storage rate are realized by utilizing an automatic inversion program based on a least square method. The method aims to eliminate the uniqueness problems of boundary effect errors and parameter identification, and provides an intelligent and refined technical paradigm for parameter evaluation under complex working conditions. In order to solve the technical problems, the technical scheme adopted by the invention is as follows: A method for solving a finite-scale confined aquifer porous micro-water test model and identifying parameters comprises the following steps: 1) Aiming at a finite scale well-aquifer system in an initial stable flow field state, constructing an underground water flow control equation and a solution condition which consider the water storage effect of a shaft and the boundary constraint of a remote constant head to form a mathematical model, and carrying out dimensionless treatment on the mathematical model by defining dimensionless factors to obtain the dimensionless model; 2) Deducing analytic solutions of the test well and the internal water head of the aquifer in a frequency domain by using Laplace transformation based on a dimensionless model, and obtaining a transient water level response semi-analytic solution in a time domain by matching with a numerical inversion algorithm; 3) Constructing a physical model consisting of a cylindrical sand tank, a central test well and an observation well, constructing an initial background flow field through a steady flow water injection test, and acquiring whole process response data of a micro water test by adopting instantaneous water injection excit