Low-permeability medium nuclide migration parameter inversion method in non-darcy stage

Abstract

The invention relates to a low-permeability medium nuclide migration parameter inversion method in a non-darcy stage, which comprises the following steps of: applying a stepped pressurization test on a known low-permeability medium to determine a nonlinear index and a proportionality coefficient in a non-darcy seepage stage; based on a non-Darcy flow control equation, calculating the flow velocity of the to-be-measured low-permeability medium flow area; based on a non-Darcy flow coupling model, the range of the numerical value of the core parameter is limited, an initial parameter value corresponding to the to-be-measured low-permeability medium is obtained, and the non-Darcy flow coupling model comprises the flow velocity and the core parameter of the to-be-measured low-permeability medium; iterating the initial parameter value based on a likelihood function; and when the likelihood function reaches a convergence state after multiple iterations, outputting a final parameter value of the nuclide migration parameter of the to-be-detected low-permeability medium in the non-Darcy stage. By dynamically adjusting the parameter value distribution variance, the convergence speed is increased by two times, an inversion parameter system covers physical imbalance and chemical imbalance parameters, and the coupling effect of nuclide migration can be comprehensively analyzed.

Description

Technical Field

[0001] This invention relates to the field of nuclear environmental engineering technology, and in particular to a method for inverting the migration parameters of nuclides in the non-Darcy stage of low-permeability media. Background Technology

[0002] The migration of key radionuclides such as Cs-137, Co-60, Sr-90, Ni-63, and Pu-238 exists in typical low-permeability media such as granite, dense sandstone, and argillaceous shale. Based on the migration of these radionuclides, it is necessary to conduct nuclear facility leakage risk assessments and nuclear contaminated site remediation.

[0003] Existing technologies mostly simplify seepage calculations for low-permeability media based on the Darcy flow assumption, and only correct non-Darcy flow using empirical formulas (such as the Forchheimer equation), without clearly defining the seepage stages. Although a few foreign studies (such as the Yucca Mountain project in the United States) mention the initiation pressure gradient, they have not established a quantitative correlation between it and the microscopic properties of the medium (clay content, pore size distribution), and only use linear fitting to process the velocity-pressure gradient curve, which cannot accurately describe the seepage characteristics of the entire stage from "no flow to nonlinear to Darcy flow", resulting in large calculation errors of seepage parameters (initiation pressure gradient λ, nonlinear exponent α) in the non-Darcy stage.

[0004] Existing inversion methods are mostly based on foreign models such as HYDRUS-1D and TOUGH2, which default to the Darcy flow assumption and do not consider the influence of non-Darcy flow on nuclide migration. Domestic research is mostly a secondary development of foreign models, and the inversion parameters only cover conventional parameters such as adsorption partition coefficient Kd and vertical dispersion αL, lacking the ability to invert other parameters (such as the exchange coefficient between the flow region and the non-flow region, and the volumetric water content in the non-flow region). Moreover, parameter inversion often uses the gradient descent method, which is prone to getting trapped in local optima, has a slow convergence speed (more than 1000 iterations), and the inversion error often exceeds 35%.

[0005] The above problems urgently need to be addressed. Summary of the Invention

[0006] This invention discloses a method for inverting the migration parameters of nuclides in the non-Darcy stage of low-permeability media, aiming to solve the technical problems existing in the prior art.

[0007] This invention employs the following technical solution: applying a stepped pressure test to a known low-permeability medium to determine the nonlinear index and proportionality coefficient of the non-Darcy flow stage; calculating the flow velocity in the flow zone of the low-permeability medium under test using the nonlinear index and the proportionality coefficient based on the non-Darcy flow control equation; limiting the range of the values ​​of the core parameters in the non-Darcy flow coupling model to obtain the initial parameter values ​​corresponding to the low-permeability medium under test in the non-Darcy flow stage, wherein the non-Darcy flow coupling model includes the flow velocity in the flow zone of the low-permeability medium under test and the core parameters of nuclide migration in the low-permeability medium under test in the non-Darcy flow stage; constructing a likelihood function and iterating the initial parameter values ​​based on the likelihood function, wherein the likelihood function includes the observed parameter values ​​of the low-permeability medium under test in the non-Darcy flow stage; and outputting the final parameter values ​​of the nuclide migration parameters of the low-permeability medium under test in the non-Darcy flow stage after multiple iterations of the likelihood function until it reaches convergence.

[0008] Optionally, the step of applying a stepped pressure test to a known low-permeability medium to determine the nonlinear index and proportionality coefficient of the non-Darcy flow stage includes: applying a stepped pressure test to the known low-permeability medium; determining the starting pressure gradient corresponding to the critical point where the flow velocity of the known low-permeability medium is 0 when the flow velocity is at a critical point where the flow velocity and pressure gradient have a linear relationship; determining the critical pressure gradient corresponding to the critical point where the flow velocity and pressure gradient have a linear relationship when the flow velocity of the low-permeability medium is at a critical point; calculating the permeability coefficient corresponding to the low-permeability medium based on the critical pressure gradient; obtaining the non-Darcy flow control equation for the relationship between flow velocity and pressure in the non-Darcy flow stage using the permeability coefficient and the starting pressure gradient; and determining the nonlinear index and proportionality parameter of the non-Darcy flow stage based on the non-Darcy flow control equation.

[0009] Optionally, the step of calculating the flow velocity in the low-permeability medium flow region based on the nonlinear exponent and the proportionality coefficient according to the non-Darcy flow control equation includes: the non-Darcy flow control equation is calculated as follows: in, For flow rate, It is a non-linear exponent. Where K is the proportionality coefficient and K is the permeability coefficient. For the currently applied pressure gradient, To initiate the pressure gradient.

[0010] Optionally, the step of limiting the range of values ​​for the core parameters in the non-Darcy flow coupling model to obtain the initial parameter values ​​corresponding to the low-permeability medium under test in the non-Darcy permeation stage includes: determining an inversion parameter system based on the non-Darcy flow coupling model, wherein the inversion parameter system includes multiple core parameters; limiting the range of values ​​for the multiple core parameters in the inversion parameter system; randomly generating parameter sets for any two of the multiple core parameters based on the range of values ​​for the core parameters; and substituting the two generated parameter sets into the non-Darcy flow coupling model to obtain the values ​​corresponding to the other core parameters besides the parameter sets, thereby generating the initial parameter values.

[0011] Optionally, the construction of the likelihood function, and the iteration of the initial parameter values ​​based on the likelihood function, includes: collecting observed parameter values ​​of the low-permeability medium to be tested in the non-Darcy flow stage; quantifying the parameter fit using the variance between the observed parameter values ​​and the initial parameter values, and constructing a likelihood function; constructing a posterior probability distribution based on the initial parameter values, and calculating a first acceptance probability using Bayesian theory; adjusting the variance between the observed parameter values ​​and the initial parameter values ​​based on the first acceptance probability; correcting the parameter fit using the adjusted variance to obtain an adjusted likelihood function; determining candidate parameter values ​​based on the adjusted likelihood function, and determining a second acceptance probability using the candidate parameter values ​​and the current parameter value, wherein the current parameter value is used to indicate the parameter value output by the likelihood function before adjustment; updating the current parameter value based on the second acceptance probability, and completing one iteration.

[0012] Optionally, adjusting the variance between the observed parameter value and the initial parameter value based on the first acceptance probability includes: reducing the variance by an adjustment factor of 0.8 when the first acceptance probability is less than or equal to 20 percent; increasing the variance by an adjustment factor of 1.2 when the first acceptance probability is greater than or equal to 40 percent; and maintaining the variance of the candidate parameter value distribution unchanged when the first acceptance probability is between 20 percent and 40 percent.

[0013] Optionally, determining candidate parameter values ​​based on the adjusted likelihood function, and determining the second acceptance probability using the candidate parameter values ​​and the current parameter value, includes: the second acceptance probability is calculated as follows: in, Let y be the second acceptance probability, and y be the observed parameter value. Candidate parameter values, To determine the degree of matching between observed parameter values ​​and candidate parameter values, The variance of the candidate parameter values. The current parameter value. To observe the degree of matching between the current parameter value and the parameter value, This represents the variance of the current parameter value distribution.

[0014] Optionally, updating the current parameter value based on the second acceptance probability to complete one iteration includes: randomly generating a probability threshold, wherein the probability threshold is greater than 0 and less than 1; when the second acceptance probability is greater than or equal to the probability threshold, selecting the candidate parameter value as the output parameter value after iteration to complete one iteration; when the second acceptance probability is less than the probability threshold, selecting the current parameter value as the output parameter value after iteration to complete one iteration.

[0015] Optionally, after the likelihood function reaches convergence after multiple iterations, and before outputting the final parameter values ​​of the nuclide migration parameters of the low-permeability medium under test in the non-Darcy stage, the method further includes: calculating the goodness of fit based on the output parameter values ​​and observed parameter values ​​after multiple iterations; if the goodness of fit is less than 0.85, adjusting the numerical range of the core parameters in the non-Darcy flow coupling model, regenerating the initial parameter values, and iterating again; if the goodness of fit is greater than or equal to 0.85, outputting the output parameter values ​​after multiple iterations as the final parameter values.

[0016] Optionally, calculating the goodness of fit based on the output parameter values ​​and observed parameter values ​​after multiple iterations includes: the goodness of fit is calculated as follows: in, For the goodness of fit, Let i be the value of the observed parameter from the i-th acquisition. The output parameter value is the output of the i-th iteration. This represents the average value of the observed parameter.

[0017] The technical solution adopted in this invention can achieve at least one of the following beneficial effects: (1) The segmented control equation can be divided into three stages: "no flow, nonlinear flow, and Darcy flow", which effectively reduces the prediction error of the non-Darcy flow model for the migration of low-permeability media; (2) Establish a quantitative correlation between microscopic pore parameters (pore size) and macroscopic seepage, so that the model has microscopic mechanism support, the physical meaning of the parameters is clear, and the limitations of the traditional model's "black box" simulation are avoided; (3) By dynamically adjusting the variance of parameter value distribution, the convergence speed is increased by 2 times (from 1000 iterations to less than 500 iterations); the inversion parameter system covers physical nonequilibrium and chemical nonequilibrium parameters, which can comprehensively analyze the coupling effect of nuclide migration, with a fitting degree ≥0.85, meeting the engineering accuracy requirements; Attached Figure Description

[0018] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below, forming part of the present invention. The illustrative embodiments of the present invention and their descriptions explain the present invention and do not constitute an improper limitation of the present invention. In the accompanying drawings: Figure 1 This is a flowchart of a method for inverting radionuclide migration parameters in a low-permeability medium during the non-Darcy stage, according to Embodiment 1 of the present invention. Figure 2 This is a flow stage division diagram in a non-Darcy stage nuclide migration parameter inversion method for low-permeability media according to Embodiment 1 of the present invention; Figure 3 This is a flowchart of parameter iteration in a method for inverting radionuclide migration parameters in a low-permeability medium during the non-Darcy stage, according to Embodiment 1 of the present invention. Figure 4 This is a diagram showing the migration test results and fitting effect of feldspar sandstone Sr-90 in Example 2 of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. In the description of this invention, it should be noted that the term "or" is generally used to include the meaning of "and / or," unless otherwise expressly indicated.

[0020] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or a magnetic connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances. Furthermore, in the description of this application, the terms "first," "second," etc., are used only for distinguishing descriptions and should not be construed as indicating or implying relative importance. In the description of this invention, "a plurality of" means at least two, such as two, three, or more, unless otherwise explicitly specified.

[0021] Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0022] First, to facilitate understanding of the embodiments of the present invention, some terms or nouns involved in the present invention will be explained below: Darcy's Law is the fundamental law describing the low-velocity, linear flow of fluids in porous media. The non-Darcy flow regime is the flow stage in which fluids do not conform to Darcy's Law when flowing in porous media (such as rocks, soil, filter materials, etc.).

[0023] Low-permeability medium is a type of porous medium with extremely low permeability, resulting in high seepage resistance and extremely slow flow velocity of fluids (water, oil, gas, waste liquid, etc.) in it, and even making it difficult for effective flow to occur under normal pressure gradients.

[0024] To address the problems existing in related technologies, this application provides a method for inverting the migration parameters of nuclides in the non-Darcy stage of low-permeability media.

[0025] Example 1 This embodiment provides a method for inverting radionuclide migration parameters in the non-Darcy stage of low-permeability media, such as... Figure 1 As shown, Figure 1 This is a flowchart of a method for inverting radionuclide migration parameters in a low-permeability medium during the non-Darcy stage, according to Embodiment 1 of the present invention. The method includes: Step S102: Apply a stepped pressure test to a known low-permeability medium to determine the nonlinear index and proportionality coefficient of the non-Darcy flow stage; In some preferred embodiments, a stepped pressure test is applied to a known low-permeability medium to determine the nonlinear index and proportionality coefficient of the non-Darcy flow stage. This includes: applying a stepped pressure test to the known low-permeability medium; determining the starting pressure gradient corresponding to a flow velocity of 0 when the flow velocity of the known low-permeability medium is at a critical point from 0 to greater than 0; determining the critical pressure gradient corresponding to a linear relationship between the flow velocity and pressure gradient when the flow velocity of the low-permeability medium is at a critical point; calculating the permeability coefficient corresponding to the low-permeability medium based on the critical pressure gradient; obtaining the non-Darcy flow control equation for the relationship between flow velocity and pressure in the non-Darcy flow stage using the permeability coefficient and the starting pressure gradient; and determining the nonlinear index and proportionality parameter of the non-Darcy flow stage based on the non-Darcy flow control equation.

[0026] Optionally, the non-Darcy stage seepage characteristics can be calculated segmentally using a known low-permeability medium, referring to... Figure 2 , Figure 2 This is a seepage stage division diagram in a low-permeability medium non-Darcy stage nuclide migration parameter inversion method in Embodiment 1 of the present invention. Specifically, the seepage stage is first divided, and the seepage interpretation includes a no-flow stage, a nonlinear flow stage (non-Darcy core stage), and a Darcy flow stage.

[0027] Optionally, stepped pressure tests can be conducted on known low-permeability media using a 0 to 70 MPa high-pressure seepage test apparatus, according to the pressure gradient ( The relationship between P / L and flow velocity (v) divides the seepage process into three stages: No flow stage ( Figure 2 (Section D in the middle): When When P / L≤λ (v is at the critical starting pressure gradient of 0), the flow velocity v=0, and the fluid in the medium pores does not flow effectively. Nonlinear flow stage (non-Darcy core stage) Figure 2 (Section E in the middle): When λ < P / L≤ When the critical pressure gradient is reached, a power-law equation is used. Fitting, where β is the proportionality coefficient, K is the permeability coefficient, and α is the nonlinear exponent (the nonlinear characteristics are significant when α>1); Darcy's Stream Phase ( Figure 2 (in section F): when P / L> At that time, the modified Darcy's law was adopted. or Description, in which, Let g be the fluid density and g be the acceleration due to gravity. This represents the flow velocity value corresponding to the critical pressure gradient. This is based on the apparent starting pressure gradient.

[0028] Optionally, after completing the seepage stage division, it is necessary to calculate the non-Darcy seepage parameters, specifically: Initiation pressure gradient λ ( Figure 2 Point A in the test): Determined by the "pressure gradient of the previous stage when the flow rate is first non-zero" in the stepped pressurization test, combined with the blank test (no sample, only the pipeline is tested) to deduct the systematic error; Critical pressure gradient ( Figure 2 Point C in the equation: The inflection point identification algorithm (second derivative mutation method) is used to analyze v- Analyzing the P / L curve, the point where the absolute value of the second derivative of the curve is maximized corresponds to... P / L is Ge; Depending on the starting pressure gradient ( Figure 2 Point B in the equation: that is, the intercept of the linear segment along the pressure gradient axis; Nonlinear exponent α and proportionality coefficient β: The power exponent equation is fitted using the least squares method for the nonlinear stage data, and the goodness of fit R0 is... 2 ≥0.95; Permeability coefficient K: In the Darcy flow stage, it is calculated according to the modified Darcy's law, and the formula is as follows: or .

[0029] Optionally, based on the above division of seepage stages, the division of seepage stages can be simplified. For rapid engineering assessment scenarios (such as nuclear leak emergency response), the second derivative catastrophe method identification can be omitted. The solution is obtained by directly using the intersection of the extended line of the velocity-pressure gradient curve and the horizontal axis. ,possible The calculation error increased to 8% to 10%, but the time for dividing the stages can be shortened from 24 hours to 8 hours, meeting the timeliness requirements of emergency scenarios.

[0030] Optionally, to address the correlation between microscopic and macroscopic parameters in low-permeability media, a quantitative model of non-Darcy flow parameters and the microscopic properties of the medium needs to be established, as follows: The starting pressure gradient λ is approximately calculated using microscopically collected data such as clay content, porosity, and average pore size. The specific calculation method is as follows: in, The clay content of the medium is % (%). Let d represent porosity (%) and d represent the average pore size (nm). The goodness-of-fit of the starting pressure gradient obtained from the calculation using the parameters of the low-permeability medium actually collected above, compared with the starting pressure gradient obtained through a pressurization experiment, is calculated. In practical applications, the goodness-of-fit obtained by the above method can reach R²=0.91. This indicates that the accuracy of the starting pressure gradient calculated using some parameters of the low-permeability medium meets the usage standards and is close to the true value. Therefore, in the absence of a pressurization experiment, the starting pressure gradient can be estimated using the quantitative correlation formula between the starting pressure gradient and the microscopic properties of the medium (clay content, pore size distribution).

[0031] Step S104: Based on the non-Darcy flow control equation, calculate the flow velocity in the flow region of the low-permeability medium to be tested using the nonlinear exponent and the proportionality coefficient. In some preferred embodiments, the flow velocity in the low-permeability medium flow region is calculated based on the non-Darcy flow control equations, using a nonlinear exponent and a proportionality coefficient. This includes calculating the non-Darcy flow control equations as follows: in, For flow rate, It is a non-linear exponent. Where K is the proportionality coefficient and K is the permeability coefficient. For the currently applied pressure gradient, To initiate the pressure gradient.

[0032] Optionally, based on the calculated nonlinear exponent, proportionality coefficient, and permeability coefficient, a non-Darcy flow coupled nuclide migration model can be constructed. Using the non-Darcy flow coupled nuclide migration model, when a low-permeability medium to be tested is present, the known data in the low-permeability medium to be tested can be input to obtain the required flow rate of the low-permeability medium.

[0033] Specifically, based on the convection-dispersion equation (CDE), a non-Darcy flow governing equation and a two-zone model of two-point adsorption are introduced to construct a non-Darcy flow coupled nuclide migration model. The specific form of the non-Darcy flow governing equation is as follows: when When P / L≤λ, v=0, and the nuclide does not migrate; When λ < P / L≤ hour, Substitute the convection term; when P / L> hour, Substitute the convection term into the equation.

[0034] Step S106: Based on the non-Darcy flow coupling model, the values ​​of the core parameters in the non-Darcy flow coupling model are limited to obtain the initial parameter values ​​corresponding to the low-permeability medium under test in the non-Darcy permeation stage. The non-Darcy flow coupling model includes the flow velocity in the flow zone of the low-permeability medium under test and the core parameters of nuclide migration in the low-permeability medium under test in the non-Darcy permeation stage. Optionally, based on the obtained non-Darcy governing equations, the flow velocity in the flow zone of the low-permeability medium to be tested can be obtained. By inputting the flow velocity into the two-zone model equation of the two-point adsorption of the non-Darcy flow coupling model, the seven core parameters can be calculated step by step.

[0035] in: The concentration of the dissolved phase in the flowable region, Bq / cm³ 3 ; The concentration of the dissolved phase in the non-flowing region is Bq / cm³. 3 ; The equilibrium adsorbate concentration in the flowable region is Bq / g; The concentration of the non-equilibrium adsorbed phase is Bq / g; The concentration of the non-equilibrium adsorbed phase in the flowable region under equilibrium conditions is Bq / g; The concentration of the adsorbed phase in the non-flowing region; Bq / g; The water content in the flowable zone (cm) 3 ; Moisture content in the non-flowing zone, cm 3 ; The proportion of adsorption sites that come into contact with flowing water; The proportion of equilibrium adsorption sites in contact with flowing water; The velocity of the water flow in the flow zone is expressed in cm / d. d is the first-order kinetic coefficient for solute exchange between the flowing and non-flowing regions. -1 ω is the first-order rate coefficient between the dissolved phase and the non-equilibrium adsorbed phase in the flow region, and d -1 ; For balanced distribution coefficients; m is the dispersion coefficient. 2 / d; V is the vertical dispersion, in meters; V is the seepage velocity, in meters per day.

[0036] Optionally, based on the parameters required in the two-zone model equations for two-point adsorption, core parameters are screened to identify seven core parameters to be inverted (covering non-Darcy flow coupling parameters and nuclide migration parameters). Based on the non-Darcy flow coupling model, the core inversion parameters include: vertical dispersion. Volumetric water content in the non-flowing zone The proportion of adsorption sites in the medium that come into contact with flowing water The proportion of equilibrium adsorption sites among the adsorption sites in contact with flowing water. Exchange of first-order kinetic coefficients between the flow region and the non-flow region The first-order rate coefficient ω between the dissolved phase and the non-equilibrium adsorbed phase in the flow region, and the equilibrium partition coefficient. This establishes a parameter inversion system covering the entire process of "seepage-adsorption-migration". The parameter value range is set based on previous experimental data (seepage test, static adsorption test, HTO tracer test).

[0037] In some preferred embodiments, based on a non-Darcy flow coupling model, the values ​​of the core parameters in the non-Darcy flow coupling model are limited to a range to obtain the initial parameter values ​​corresponding to the low-permeability medium under test in the non-Darcy permeation stage. This includes: determining an inversion parameter system based on the non-Darcy flow coupling model, wherein the inversion parameter system includes multiple core parameters; limiting the range of values ​​of the multiple core parameters in the inversion parameter system; randomly generating parameter sets for any two of the multiple core parameters based on the range of values ​​of the core parameters; and substituting the two generated parameter sets into the non-Darcy flow coupling model to obtain the values ​​corresponding to the other core parameters besides the parameter sets, thereby generating the initial parameter values.

[0038] Step S108: Construct a likelihood function, and iterate the initial parameter values ​​based on the likelihood function. The likelihood function includes the observed parameter values ​​of the low-permeability medium under test during the non-Darcy flow stage; for example... Figure 3 As shown, Figure 3 This is a flowchart of parameter iteration in a method for inverting radionuclide migration parameters in a low-permeability medium during the non-Darcy stage, as described in Embodiment 1 of the present invention.

[0039] In some preferred embodiments, a likelihood function is constructed, and the initial parameter values ​​are iterated based on the likelihood function, including: collecting observed parameter values ​​of the low-permeability medium to be tested in the non-Darcy flow stage; quantifying the parameter fit using the variance between the observed parameter values ​​and the initial parameter values, and constructing the likelihood function; constructing a posterior probability distribution based on the initial parameter values, and calculating a first acceptance probability using Bayesian theory; adjusting the variance between the observed parameter values ​​and the initial parameter values ​​based on the first acceptance probability; correcting the parameter fit using the adjusted variance to obtain an adjusted likelihood function; determining candidate parameter values ​​based on the adjusted likelihood function; determining a second acceptance probability using the candidate parameter values ​​and the current parameter value, wherein the current parameter value is used to indicate the parameter value output by the likelihood function before adjustment; updating the current parameter value based on the second acceptance probability, and completing one iteration.

[0040] Optionally, the sum of squared residuals between the observed parameter values ​​and the model simulation data (candidate parameter values) is used to construct a likelihood function P(y|θ), where y is the observed parameter value and θ is the parameter to be inverted (candidate parameter value). The degree of matching between the candidate parameter value θ (candidate parameter value) and the observed parameter value y is quantified. in, Let i be the value of the observed parameter from the i-th acquisition. (θ) represents the candidate parameter value for the i-th output, σ represents the standard deviation of the observation error, and n represents the number of data points.

[0041] Combining prior information (parameter values ​​are set based on seepage and static adsorption test results), a posterior probability distribution is constructed: P( |y)∝P(y| ) P( The optimal solution for the parameters is approximated by sampling, which is an adaptive sampling and convergence optimization.

[0042] Optionally, sampling can be performed within the constructed likelihood function, specifically initial sampling, to obtain initial parameter values: from the prior distribution P( Randomly generate the initial parameter set in ) Substitute the non-Darcy flow coupled nuclide migration model (including the segmented seepage control equation and the two-zone model of two-point adsorption) into the candidate simulated values ​​to calculate the simulated values. ( The first acceptance probability is calculated based on the likelihood function.

[0043] In some preferred embodiments, the variance between the observed parameter values ​​and the initial parameter values ​​is adjusted based on the first acceptance probability, including: reducing the variance by an adjustment factor of 0.8 when the first acceptance probability is less than or equal to 20 percent; increasing the variance by an adjustment factor of 1.2 when the first acceptance probability is greater than or equal to 40 percent; and keeping the variance of the candidate parameter value distribution unchanged when the first acceptance probability is between 20 percent and 40 percent.

[0044] Optionally, the variance can be adaptively adjusted based on the first acceptance probability, thereby adjusting the parameter fit and consequently the likelihood function, so that the candidate parameter values ​​obtained from the likelihood function are closer to the observed parameter values.

[0045] Optionally, in the first 500 iterations, the distribution variance corresponding to the candidate parameter values ​​is dynamically adjusted based on the first acceptance probability. If the first acceptance probability is <20% (low sampling efficiency), the variance is reduced (adjustment coefficient is 0.8). If the first acceptance probability is >40% (insufficient exploration range), the variance can be increased (adjustment coefficient is 1.2). The target first acceptance probability is controlled between 20% and 40%, which can effectively balance sampling efficiency and parameter space exploration capability.

[0046] Optionally, for low-precision parameter requirements (such as preliminary screening of repair schemes), the adaptive variance adjustment algorithm can be replaced with the Metropolis-Hastings algorithm (which uses a fixed distribution variance). In this case, the convergence speed decreases by 30% (800 to 1000 iterations), but the algorithm complexity is reduced, and fast inversion can be achieved on a regular computer (4-core CPU), with the inversion error controlled within 15%.

[0047] In some preferred embodiments, candidate parameter values ​​are determined based on the adjusted likelihood function, and a second acceptance probability is determined using the candidate parameter values ​​and the current parameter value, including: the second acceptance probability is calculated as follows: in, Let y be the second acceptance probability, and y be the observed parameter value. Candidate parameter values, To determine the degree of matching between observed parameter values ​​and candidate parameter values, The variance of the candidate parameter values. The current parameter value. To observe the degree of matching between the current parameter value and the parameter value, This represents the variance of the current parameter value distribution.

[0048] In some preferred embodiments, updating the current parameter value based on the second acceptance probability to complete one iteration includes: randomly generating a probability threshold, wherein the probability threshold is greater than 0 and less than 1; if the second acceptance probability is greater than or equal to the probability threshold, selecting the candidate parameter value as the output parameter value after iteration to complete one iteration; if the second acceptance probability is less than the probability threshold, selecting the current parameter value as the output parameter value after iteration to complete one iteration.

[0049] Optionally, candidate parameter values ​​are generated in each iteration. Calculate its relationship with the current parameter Second acceptance probability ,like Accepts ≥ random number (probability threshold) (between 0 and 1) Used as parameters for new samples; otherwise, retained. This completes one iteration.

[0050] Step S110: After the likelihood function reaches convergence after multiple iterations, the final parameter values ​​of the nuclide migration parameters of the low-permeability medium under test in the non-Darcy stage are output.

[0051] Optionally, during the iterative process, convergence testing is required, along with parameter output. The specific convergence test is as follows: When the latent scaling factor statistic (Gelman-Rubin) is <1.1, it is determined that multi-chain sampling tends to be consistent (no significant difference); the latent scaling factor statistic is calculated as follows: First, calculate the sample mean for each chain. and the overall mean of all chains ; Next, calculate the inter-chain variance. ; Then calculate the sample variance for each chain. Then calculate the average variance within the chain. ; Estimate the variance of the target distribution: ; Latent scaling factor statistic: .

[0052] When the sampling converges, B will approach 0. It will approach 1; if A value much greater than 1 indicates significant differences between chains, suggesting that sampling has not converged.

[0053] When the multi-chain sampling tends to be consistent, trace plot analysis is performed. The parameter sample traces show no obvious trend and the fluctuations are stable, indicating that the sampling has converged. When convergence occurs, parameter extraction is required, that is, the "burning period" samples (the first 50% of the iteration results) before convergence are removed; the mean, median and confidence interval (such as 95% confidence interval) are calculated for the remaining samples as the final inversion parameters (final parameter values).

[0054] In some preferred embodiments, after the likelihood function reaches convergence after multiple iterations, and before outputting the final parameter values ​​of the nuclide migration parameters of the low-permeability medium under test in the non-Darcy stage, the method further includes: calculating the goodness of fit based on the output parameter values ​​and observed parameter values ​​after multiple iterations; if the goodness of fit is less than 0.85, adjusting the numerical range of the core parameters in the non-Darcy flow coupling model, regenerating the initial parameter values, and iterating again; if the goodness of fit is greater than or equal to 0.85, outputting the output parameter values ​​after multiple iterations as the final parameter values.

[0055] Optionally, before outputting the final parameter values, verification is required. This involves substituting the final parameter values ​​into the non-Darcy flow coupling model and ensuring that the goodness of fit between the simulated and observed parameter values ​​is ≥0.85. Otherwise, the prior range should be readjusted and the inversion repeated.

[0056] Optionally, the specific model verification and solution process is as follows: Local verification: Verify the accuracy of the segmented non-Darcy flow control equations in characterizing the seepage stage, and ensure the rationality of the division of the flow zone or non-flow zone; Global solution: Input the nuclide concentration data of the dynamic migration experiment, start the adaptive Markov chain Monte Carlo algorithm (MCMC algorithm) (adaptive adjustment algorithm) for iterative inversion, and output the final parameter values ​​and confidence intervals; Accuracy calibration: Compare the simulated values ​​of the inversion parameters with the experimentally observed values ​​to calculate the goodness of fit. ;like If the value is less than 0.85, adjust the range of the prior parameters (e.g., expand the range of α to [0.001, 40]). -1 Repeated sampling and inversion until... ≥0.85.

[0057] In some preferred embodiments, the goodness of fit is calculated based on the output parameter values ​​and observed parameter values ​​after multiple iterations, including: the goodness of fit is calculated as follows: in, For the goodness of fit, Let i be the value of the observed parameter from the i-th acquisition. The output parameter value is the output of the i-th iteration. This represents the average value of the observed parameter.

[0058] Example 2 Based on the above embodiments, the present invention also proposes a specific implementation method taking the Sr-90 migration process in sandstone as an example, referring to... Figure 2 and Figure 4 , Figure 2 The non-Darcy stage division diagram of feldspathic sandstone Sr-90 in Embodiment 2 of the present invention is still shown. Figure 4 This is the result of the Sr-90 migration test in feldspathic sandstone and the fitting effect diagram in Example 2 of the present invention. Taking the calculation of seepage characteristics and parameter inversion of the non-Darcy stage of the Sr-90 migration process in feldspathic sandstone as an example, the specific implementation steps are as follows: Step S1, Sample Preparation: Sandstone was cut with a diamond saw and processed into thin cylindrical samples with a length of 8 mm and a diameter of 8.834 cm. After removing surface debris by ultrasonic cleaning, the samples were treated using a "vacuum evacuation-step pressure saturation" process: first, a vacuum was applied to 0.098 MPa and maintained for 4 hours, then pressure was applied in steps of 0.1 MPa → 0.3 MPa → 0.5 MPa (holding pressure for 8 hours at each step). The saturation was verified by the "drying and weighing method" (saturation = (mass after saturation - mass after drying) / (pore volume × water density) × 100%), and the sandstone reached 95.2%, meeting the experimental requirements. Step S2, seepage test: A feldspar sandstone sample from a certain location was used to conduct a stepped pressure test using a 0-70 MPa high-pressure seepage device. The pressure gradient increased from 0.1 MPa / cm (each step was 0.1 MPa / cm, and the pressure was maintained for 24 hours). The flow velocity data were measured. The flow velocity is non-zero for the first time when P / L = 6.25 MPa / cm (λ = 6.25 MPa / cm). When P / L = 15 MPa / cm, the velocity-pressure gradient curve enters the linear segment. =15.0 MPa / cm); using power exponent equation Fitting yields the nonlinear exponent. =1.68, proportionality constant β=1.02×10⁹; above 15MPa / cm is the Darcy flow stage, according to the modified Darcy law. (Where, ρ = 1 g / cm³, g = 9.8 m / s², =15MPa / cm), the calculated permeability coefficient is K=6.1606×10 -7 cm / d.

[0059] Step S3, Microscopic Correlation Verification: Substitute λ = 0.02 × / The value is calculated as λ = 0.02 × 4 / 0.0235 × (10 / 7.5)² ≈ 6.05 MPa / cm, which has an error of 3.2% compared with the experimental value (6.25 MPa / cm), thus verifying the effectiveness of the correlation model.

[0060] Step S4, radionuclide migration assay: Using a high-pressure dynamic migration device, inject Sr-90 standard solution (specific activity 105 Bq / mL, volume 1 mL), control the flow rate at 3 mL / d, and obtain the breakthrough curve (peak time 44 d, peak concentration 764.91 Bq / mL).

[0061] Step S5, Parameter Inversion: Construct a non-Darcy flow coupled nuclide migration model, set the prior parameter range, and iterate 600 times using the Metropolis-Hastings algorithm. For the initial 500 iterations, dynamically adjust the distribution variance based on an acceptance rate of 20%–40%. Finally, the Gelman-Rubin statistic = 1.04 < 1.1, indicating convergence. The inversion yields: =0.02048cm, =0.02, =4.865d -1 , ω=17.55d -1 , =9.791×10 -1 mL / g =0.8856、 =0.08637, goodness of fit =0.993, which meets the engineering accuracy requirements.

[0062] The above are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for inverting radionuclide migration parameters in a low-permeability medium during the non-Darcy stage, characterized in that, include: A stepped pressurization test was conducted on a known low-permeability medium to determine the nonlinear index and proportionality coefficient of the non-Darcy flow stage. Based on the non-Darcy flow control equation, the flow velocity in the flow region of the low-permeability medium under test is calculated using the nonlinear exponent and the proportional coefficient. Based on the non-Darcy flow coupling model, the values ​​of the core parameters in the non-Darcy flow coupling model are limited to a range to obtain the initial parameter values ​​of the low-permeability medium under test in the non-Darcy permeation stage. The non-Darcy flow coupling model includes the flow velocity in the flow zone of the low-permeability medium under test and the core parameters of nuclide migration in the low-permeability medium under test in the non-Darcy permeation stage. Construct a likelihood function, and iterate the initial parameter values ​​based on the likelihood function, wherein the likelihood function includes the observed parameter values ​​of the low-permeability medium under test in the non-Darcy flow stage; When the likelihood function reaches convergence after multiple iterations, the final parameter values ​​of the nuclide migration parameters of the low-permeability medium under test in the non-Darcy stage are output.

2. The method for inverting radionuclide migration parameters in a low-permeability medium during the non-Darcy stage according to claim 1, characterized in that, The step-pressure test applied to a known low-permeability medium to determine the nonlinear index and proportionality coefficient of the non-Darcy flow stage includes: A stepped pressurization test is applied to the known low-permeability medium. When the flow rate of the known low-permeability medium is at the critical point from 0 to greater than 0, the starting pressure gradient corresponding to the critical point when the flow rate is 0 is determined. When the flow rate of the low-permeability medium is at the critical point where the flow rate and pressure gradient have a linear relationship, the critical pressure gradient corresponding to the critical point where the flow rate has a linear relationship is determined. Based on the critical pressure gradient, the permeability coefficient corresponding to the low-permeability medium is calculated. Using the permeability coefficient and the starting pressure gradient, the non-Darcy flow control equations for the relationship between velocity and pressure in the non-Darcy seepage stage are obtained; Based on the non-Darcy flow control equations, the nonlinear index and proportional parameters of the non-Darcy seepage stage are determined.

3. The method for inverting radionuclide migration parameters in a low-permeability medium during the non-Darcy stage according to claim 1, characterized in that, The calculation of the flow velocity in the low-permeability medium flow region based on the non-Darcy flow control equation, using the nonlinear exponent and the proportionality coefficient, includes: The non-Darcy flow governing equations are calculated as follows: in, For flow rate, It is a non-linear exponent. Where K is the proportionality coefficient and K is the permeability coefficient. For the currently applied pressure gradient, To initiate the pressure gradient.

4. The method for inverting radionuclide migration parameters in a low-permeability medium during the non-Darcy stage according to claim 1, characterized in that, The non-Darcy flow coupling model limits the range of values ​​for its core parameters to obtain initial parameter values ​​for the low-permeability medium under test during the non-Darcy permeation stage, including: Based on the non-Darcy flow coupling model, an inversion parameter system is determined, wherein the inversion parameter system includes multiple core parameters; The range of values ​​for several core parameters in the inversion parameter system is limited; Based on the numerical range of the core parameters, a parameter set is randomly generated for any two of the multiple core parameters; By substituting any two generated parameter sets into the non-Darcy flow coupling model, the numerical values ​​of other core parameters besides the parameter sets are obtained, and initial parameter values ​​are generated.

5. The method for inverting radionuclide migration parameters in a low-permeability medium during the non-Darcy stage according to claim 1, characterized in that, The construction of the likelihood function, and the iteration of the initial parameter values ​​based on the likelihood function, includes: Collect the observed parameter values ​​of the low-permeability medium to be tested in the non-Darcy flow stage; The variance between the observed parameter values ​​and the initial parameter values ​​is used to quantify the parameter fit, and a likelihood function is constructed. Based on the initial parameter values, a posterior probability distribution is constructed, and the first acceptance probability is calculated using Bayesian theory. Based on the first acceptance probability, adjust the variance between the observed parameter value and the initial parameter value; The adjusted variance is used to correct the parameter fit, resulting in the adjusted likelihood function. Based on the adjusted likelihood function, candidate parameter values ​​are determined, and a second acceptance probability is determined by comparing the candidate parameter values ​​with the current parameter value, wherein the current parameter value is used to indicate the parameter value output by the likelihood function before adjustment; Based on the second acceptance probability, the current parameter value is updated to complete one iteration.

6. The method for inverting radionuclide migration parameters in a low-permeability medium during the non-Darcy stage according to claim 5, characterized in that, The step of adjusting the variance between the observed parameter value and the initial parameter value based on the first acceptance probability includes: If the first acceptance probability is less than or equal to 20 percent, the variance is reduced by an adjustment factor of 0.8; If the first acceptance probability is greater than or equal to 40%, the variance is increased by an adjustment factor of 1.

2. When the first acceptance probability is between 20% and 40%, the variance of the candidate parameter value distribution remains unchanged.

7. The method for inverting radionuclide migration parameters in a low-permeability medium during the non-Darcy stage according to claim 5, characterized in that, The process of determining candidate parameter values ​​based on the adjusted likelihood function, and determining the second acceptance probability using the candidate parameter values ​​and the current parameter value, includes: The second acceptance probability is calculated as follows: in, Let y be the second acceptance probability, and y be the observed parameter value. Candidate parameter values, To determine the degree of matching between observed parameter values ​​and candidate parameter values, The variance of the distribution of candidate parameter values. The current parameter value. To observe the degree of matching between the current parameter value and the parameter value, This represents the variance of the current parameter value distribution.

8. The method for inverting radionuclide migration parameters in a low-permeability medium during the non-Darcy stage according to claim 5, characterized in that, The step of updating the current parameter value based on the second acceptance probability to complete one iteration includes: A probability threshold is randomly generated, wherein the probability threshold is greater than 0 and less than 1; If the second acceptance probability is greater than or equal to the probability threshold, the candidate parameter value is selected as the output parameter value after iteration, and one iteration is completed. If the second acceptance probability is less than the probability threshold, the current parameter value is selected as the output parameter value after iteration, and one iteration is completed.

9. The method for inverting radionuclide migration parameters in a low-permeability medium during the non-Darcy stage according to claim 1, characterized in that, After the likelihood function reaches convergence after multiple iterations, and before outputting the final parameter values ​​of the nuclide migration parameters of the low-permeability medium under test in the non-Darcy stage, the method further includes: The goodness of fit is calculated based on the output parameter values ​​and observed parameter values ​​after multiple iterations. If the goodness of fit is less than 0.85, adjust the numerical range of the core parameters in the non-Darcy flow coupling model, regenerate the initial parameter values, and iterate again. If the fit is greater than or equal to 0.85, the output parameter values ​​after multiple iterations are output as the final parameter values.

10. The method for inverting radionuclide migration parameters in a low-permeability medium during the non-Darcy stage according to claim 9, characterized in that, The calculation of the goodness of fit based on the output parameter values ​​and observed parameter values ​​after multiple iterations includes: The fit degree is calculated as follows: in, For the goodness of fit, Let i be the value of the observed parameter from the i-th acquisition. The output parameter value is the output of the i-th iteration. This represents the average value of the observed parameter.

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