CN112989644A - Numerical simulation method for mine water geological storage - Google Patents
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Abstract
The invention discloses a numerical simulation method for mine water geological storage, belonging to the technical field of geological storage, and the numerical simulation method for mine water geological storage can realize that the data parameter acquisition of different areas is carried out, the areas which are more suitable for carrying out deep geological storage on harmful waste liquid are selected, corresponding hydrogeological conceptual models and mathematical models are established, software is introduced for operation, preliminary data results are obtained by solving, then data simulation under parameter change is carried out through the change of viscosity, density and hydrogeological parameters, so that the change condition of the harmful waste liquid to be buried under different data conditions is simulated, the conclusion is obtained by combining with the preliminary data results, the influence of the harmful waste liquid to the surrounding ecological environment after being buried is discussed, and the success and the variability of the harmful waste liquid burying are improved, and the corresponding measures can be made in time when the relevant technical personnel face different conditions.
Description
Technical Field
The invention relates to the technical field of geological sequestration, in particular to a numerical simulation method for geological sequestration of mine water.
Background
With the acceleration of the industrialization process of China, some domestic and industrial waste liquid is continuously generated, is not easy to treat and is extremely harmful, the ecological environment is immeasurably damaged due to improper treatment, and the life safety of people is endangered, deep-well underground perfusion is one of important disposal modes of harmful waste liquid in some countries in the United states and Europe, according to the research of the United states Federal Environmental Protection Agency (EPA), chemical industrial waste liquid is selectively underground perfused to be safer than almost all other disposal modes, the risk analysis of the chemical industrial waste liquid is supposed to have the leakage probability of one to four parts per million, and in all cases, 19 states in the United states, have I-type perfusion wells 529, wherein the harmful waste perfusion wells 163 are filled with more than 3400 x 104m3 harmful waste liquid underground every year.
Through strict processes of design, construction, operation, monitoring and the like, the establishment of a class I harmful waste liquid injection well must provide a 'transfer-free' application, wherein 'flow confinement' certification requires that injected fluid does not vertically flow out of an injection zone within 10000 years, does not horizontally reach a discharge point (a well, a hydraulic fault, a fracture development zone and the like) or contact an underground drinking water source, so that simulation of migration of waste liquid in an underground injection layer is required in advance to ensure safety in the transportation and landfill processes, and over 20 years, many scholars research on migration of pollutants under deep well injection, and discuss treatment of harmful waste liquid through a deep geological sealing method.
Disclosure of Invention
1. Technical problem to be solved
Aiming at the problems in the prior art, the invention aims to provide a numerical simulation method for geological storage of mine water, which can realize that a region suitable for deep geological storage of harmful waste liquid is selected by acquiring data parameters of different regions, by establishing corresponding hydrogeological conceptual model and mathematical model, importing software for operation, solving to obtain preliminary data result, then performing data simulation under parameter change through viscosity, density and hydrogeological parameter change, thereby simulating the change condition of the landfill harmful waste liquid under different data conditions, obtaining a conclusion by combining with the primary data result, discussing the influence of the landfill harmful waste liquid on the surrounding ecological environment, therefore, the success and the variability of the harmful waste liquid landfill are improved, and the corresponding counter measures can be made in time when the technicians in the related field face different conditions.
2. Technical scheme
In order to solve the above problems, the present invention adopts the following technical solutions.
A numerical simulation method for geological storage of mine water comprises the following steps:
s1, data acquisition: collecting a plurality of suitable geographic area parameters, analyzing specific parameters, and selecting an optimal geographic area;
s2, establishing a model: classifying according to the collected geographic region parameters, and respectively establishing a hydrogeological concept model and a mathematical model;
s3, software operation: calculating the model through numerical simulation software, and simulating by adopting a region discretization method;
s4, model solving results: solving according to the data to obtain a preliminary simulation result;
s5, parameter change simulation: the operation parameters are modularized, and diversified simulation is carried out through changes of viscosity, density and hydrogeological parameters to obtain corresponding change data;
s6, obtaining a conclusion that: and combining and analyzing the preliminary simulation result and the change data to obtain a simulation conclusion.
According to the finding, the data parameter acquisition of different areas can be realized, the areas which are suitable for carrying out deep geological storage on harmful waste liquid are selected, corresponding hydrogeological conceptual models and mathematical models are established, the operation is carried out by leading-in software, a preliminary data result is obtained by solving, and then data simulation under parameter change is carried out through the change of viscosity, density and hydrogeological parameters, so that the change condition of the harmful waste liquid in landfill under different data conditions is simulated, the conclusion is obtained by combining with the preliminary data result, the influence of the harmful waste liquid on the surrounding ecological environment after the harmful waste liquid is landfill is discussed, the success and variability of the harmful waste liquid landfill are improved, and the relevant field technicians can conveniently and timely take corresponding measures in the face of different conditions.
Further, the mathematical model in S2, which temporarily does not take into account temperature changes and chemical reactions, includes a pressure control equation:
in the formula: ρ -liquid density;
ui-seepage velocity (Darcy flow rate);
xi-distance in the direction of the principal coordinate axis;
ρs-density of injected waste liquid;
q-rate of waste injection;
t-time;
phi-the effective porosity of the porous material,
the motion equation corresponding to the pressure control equation is as follows:
in the formula: k is a radical ofii-a permeability tensor;
mu-viscosity coefficient;
p-liquid pressure;
z-the height of the optical system,
the equation of motion quotes
Obtaining:
in the formula: rho0Reference pressure p0Density of the liquid at concentration 0.
Further, the mathematical model in S2 includes a solute transport equation, where the solute transport equation is:
in the formula: c-liquid concentration;
Dij-hydrodynamic diffusion coefficient tensor;
CI-the concentration of the injected waste liquid;
the solute transport equation is connected with a plurality of coupled parameter expressions, and the parameter expressions are as follows:
φ＝φo[1+CR(|p-po)]、
in the formula: phio-porosity at a reference pressure;
CR-the volume compressibility of the porous medium;
Cw-the volume compressibility of the liquid;
Cc-density difference rate;
c ^ the ratio of the concentration of the liquid to the concentration of the injected waste liquid, namely the relative concentration,
μR(C ^) -concentration-related empirical functions determined from given data material.
Further, in S2, the hydrogeological conceptual model has a selection range of 20km × 15km, the selection range is located at the center of the simulation area, the hydrogeological conceptual model includes a perfusion layer and a water barrier layer, the perfusion layer is generalized to a homogeneous isotropic aquifer, the fluid motion in the aquifer conforms to the darcy law, the water barrier layer includes an edge sandstone and a large fault, the water barrier layer can effectively prevent the fluid from moving vertically, and further, the two-dimensional mathematical model is simplified to the fluid moving in the porous medium, the sandstone edge can define the fact that the direction is sharp, and the large fault can define the water barrier boundary.
Further, the numerical simulation software in S3 is SWIFT numerical simulation software which is discretized by a block center finite difference method, and the SWIFT numerical simulation software operates on time and space domains by a central or backward weighting algorithm, and can be used for simulating the movement and migration rules of fluid, heat, salt and radionuclide in a saturated groundwater system, and simulating and analyzing the problems of deep well perfusion, high radioactive nuclear waste disposal analysis, seawater intrusion and radioactive nuclear aquifer thermal energy storage.
Furthermore, the change of the viscosity parameter in S5 adopts time change, the viscosity parameter is a constant that does not change with concentration, the constant is 0.00035Pa · S, and the viscosity parameter can reflect a comparison result of a fluid pressure rise value in a perfusion period and an original condition, and is defined as that, when the constant flow rate is injected, the permeability coefficient becomes large without considering that the viscosity of the perfusion waste liquid is greater than that of the fluid in the perfusion layer, so that the required perfusion pressure or pressure gradient changes.
Further, the viscosity change is ignored when the density parameter is changed in S5, the density parameter is set to be the same as the density of the fluid in the injection waste liquid and the perfusion layer, and the density parameter is 1010kg/m3The density parameter variation results in that for non-horizontal perfusion layers, the difference between the density of the fluid in the injected waste and the density of the fluid in the perfusion layer cannot be ignored, and the simulation simply using MODFLOW and MT3DMS can also result in wrong results.
Further, the hydrogeological parameters in S5 include porosity, permeability and dispersion, the porosity is reduced by half, the permeability and dispersion are doubled, and the uncertainty of the sequestration process is simulated through the parameter changes of the porosity, permeability and dispersion, so as to perform diversified analysis.
Further, in S1, the geographic area includes a depression area with good geological stability, a large fault for stopping geological activity is connected around the depression area, the geographic area includes a quasi-perfusion area, the quasi-perfusion area is about 2000m from the ground surface, the quasi-perfusion area includes blocky sandstone, siltstone and gray sandstone, the blocky sandstone, the siltstone and the gray sandstone have appropriate porosity and permeability, and a mudstone-based capping layer with low permeability and good continuity exists above and below the mudstone-based capping layer.
Further, the area discretization method in S3 includes a simulation area, where the simulation area is divided into 300 × 300 rectangular grid cells, the grid cells are encrypted by using perfusion wells, and an initial pressure distribution is obtained by calculating a pressure at a known point in a perfusion layer in the grid cells according to a static equilibrium principle.
3. Advantageous effects
Compared with the prior art, the invention has the advantages that:
(1) according to the finding, the data parameter acquisition of different areas can be realized, the areas which are suitable for carrying out deep geological storage on harmful waste liquid are selected, corresponding hydrogeological conceptual models and mathematical models are established, the operation is carried out by leading-in software, a preliminary data result is obtained by solving, and then data simulation under parameter change is carried out through the change of viscosity, density and hydrogeological parameters, so that the change condition of the harmful waste liquid in landfill under different data conditions is simulated, the conclusion is obtained by combining with the preliminary data result, the influence of the harmful waste liquid on the surrounding ecological environment after the harmful waste liquid is landfill is discussed, the success and variability of the harmful waste liquid landfill are improved, and the relevant field technicians can conveniently and timely take corresponding measures in the face of different conditions.
(2) The hydrogeology conceptual model includes filling layer and water barrier, and the filling layer is generalized to isotropic aquifer of homogeneity, and fluid motion accords with Darcy's law in the aquifer, and the water barrier includes marginal sandstone and big fault, and the water barrier can effectively prevent the vertical upward migration of fluid, and then simplifies to the two-dimensional mathematical model of fluid migration in porous medium, and marginal sandstone can delimit the fact that pinches in this direction, and big fault can delimit the water proof boundary.
(3) The SWIFT numerical simulation software is used for calculating time and space domains through a central or backward weighting algorithm, and can be used for simulating the movement and migration rules of fluid, heat, salt and radioactive nuclides in a saturated underground water system and simulating and analyzing the problems of deep well perfusion, high radioactive nuclide waste disposal analysis, seawater invasion and aquifer heat energy storage.
(4) The viscosity parameter is a constant which does not change along with concentration, the constant is 0.00035 Pa.s, the viscosity parameter can reflect the comparison result of the fluid pressure rise value and the original condition in the perfusion period, and the permeability coefficient is defined to be increased when the constant flow rate is injected without considering that the viscosity of the perfusion waste liquid is greater than that of the fluid in the perfusion layer, so that the required perfusion pressure or pressure gradient changes.
(5) The density parameter is set to be the same as the density of the fluid in the injected waste liquid and the perfusion layer, and the density parameter is 1010kg/m3The density parameter variation results in that for non-horizontal perfusion layers, the difference between the density of the fluid in the injected waste and the density of the fluid in the perfusion layer cannot be ignored, and the simulation simply using MODFLOW and MT3DMS can also result in wrong results.
(6) And S5, performing diversified analysis by simulating uncertainty of the sequestration process through the parameter changes of the porosity, the permeability and the dispersivity.
(7) The large fault for stopping geological activities is connected around the hollow area, the geographical area comprises a planned perfusion area, the planned perfusion area is about 2000m from the ground surface, the planned perfusion area comprises blocky sandstone, siltstone and gray sandstone, the blocky sandstone, the siltstone and the gray sandstone have proper porosity and permeability, and a cover layer which is mainly mudstone and has low permeability and good continuity is arranged above and below the blocky sandstone, the siltstone and the gray sandstone.
(8) The simulation area is divided into 300 x 300 rectangular grid cells, the grid cells are encrypted by using filling wells, and initial pressure distribution is obtained by calculating the pressure of a known point in a filling layer according to the static balance principle in the grid cells.
Drawings
In order to more clearly illustrate the technical solutions of the present invention or the prior art, the drawings needed for the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and those skilled in the art can also obtain other drawings according to the drawings without creative efforts.
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a schematic diagram of discretized boundary conditions of the present invention;
FIG. 3 is a contour map of elevation of a grid center of a perfusion layer in accordance with the present invention;
FIG. 4 is a schematic diagram of the migration range of waste liquid according to the present invention;
FIG. 5 is a graph of net pressure versus time for the present invention;
FIG. 6 is a graph of concentration over time for the present invention;
FIG. 7 is a graph showing a comparison of the migration range of waste liquid according to the present invention.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention; it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments, and all other embodiments obtained by those skilled in the art without any inventive work are within the scope of the present invention.
In the description of the present invention, it should be noted that the terms "upper", "lower", "inner", "outer", "top/bottom", and the like indicate orientations or positional relationships based on those shown in the drawings, and are only for convenience of description and simplification of description, but do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and thus should not be construed as limiting the present invention. Furthermore, the terms "first" and "second" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In the description of the present invention, it should be noted that, unless otherwise specifically stated or limited, the terms "mounted," "disposed," "sleeved/connected," "connected," and the like are used in a broad sense, and for example, "connected" may be a fixed connection, a detachable connection, an integral connection, a mechanical connection, an electrical connection, a direct connection, an indirect connection through an intermediate medium, and a communication between two elements.
Example 1:
referring to fig. 1, a numerical simulation method for mine water geological storage includes the following steps:
s1, data acquisition: collecting a plurality of suitable geographic area parameters, analyzing specific parameters, and selecting an optimal geographic area;
s2, establishing a model: classifying according to the collected geographic region parameters, and respectively establishing a hydrogeological concept model and a mathematical model;
s3, software operation: calculating the model through numerical simulation software, and simulating by adopting a region discretization method;
s4, model solving results: solving according to the data to obtain a preliminary simulation result;
s5, parameter change simulation: the operation parameters are modularized, and diversified simulation is carried out through changes of viscosity, density and hydrogeological parameters to obtain corresponding change data;
s6, obtaining a conclusion that: and combining and analyzing the preliminary simulation result and the change data to obtain a simulation conclusion.
Referring to fig. 1-7, the mathematical model in S2, which does not consider temperature variation and chemical reaction for the moment, includes a pressure control equation:
in the formula: ρ -liquid density;
ui-seepage velocity (Darcy flow rate);
xi-distance in the direction of the principal coordinate axis;
ρs-density of injected waste liquid;
q-rate of waste injection;
t-time;
phi-effective porosity;
the motion equation corresponding to the pressure control equation is:
in the formula: k is a radical ofii-a permeability tensor;
mu-viscosity coefficient;
p-liquid pressure;
z-elevation;
equation of motion referencing
Obtaining:
in the formula: rho0Reference pressure p0Density of the liquid at concentration 0.
Further, the mathematical model in S2 includes a solute transport equation, where the solute transport equation is:
in the formula: c-liquid concentration;
Dij-hydrodynamic diffusion coefficient tensor;
CI-the concentration of the injected waste liquid;
the solute transport equation is connected with a plurality of coupled parameter expressions, and the parameter expressions are as follows:
φ＝φo[1+CR(|p-po)]、
in the formula: phio-porosity at a reference pressure;
CR-the volume compressibility of the porous medium;
Cw-the volume compressibility of the liquid;
Cc-density difference rate;
c ^ the ratio of the concentration of the liquid to the concentration of the injected waste liquid, namely the relative concentration,
μR(C ^) -concentration-related empirical functions determined from given data material.
Referring to fig. 2-3, the hydrogeological conceptual model in S2 has a selection range of 20km × 15km, the selection range is located at the center of the simulation area, the hydrogeological conceptual model includes a perfusion layer and a water barrier layer, the perfusion layer is generalized to a homogeneous isotropic water-containing layer, the fluid motion in the water-containing layer conforms to the darcy' S law, the water barrier layer includes edge sandstone and a large fault, the water barrier layer can effectively prevent the fluid from moving vertically, and further simplifies the two-dimensional mathematical model to the fluid moving in the porous medium, the edge sandstone can define the fact that the direction is sharp, the large fault can define the water barrier boundary, the numerical simulation software in S3 is SWIFT numerical simulation software which performs dispersion by using a block center difference limited method, the SWIFT numerical simulation software performs calculation on time and space domains by a center or backward weighting algorithm, and the SWIFT numerical simulation software can be used for simulating the fluid, water, and water, The motion and migration rules of heat, salt and radioactive nuclide are simulated and analyzed, and the problems of deep well perfusion, high radioactive nuclide waste disposal and analysis, seawater invasion and aquifer heat energy storage are solved.
Referring to fig. 4, the change of the viscosity parameter in S5 adopts time change, the viscosity parameter is a constant that does not change with concentration, the constant is 0.00035Pa · S, the viscosity parameter can reflect the comparison result of the fluid pressure rise value in the perfusion period and the original condition, when the constant flow rate is injected, the permeability coefficient is increased without considering that the viscosity of the perfusion waste liquid is larger than that of the fluid in the perfusion layer, so that the required perfusion pressure or pressure gradient changes, referring to fig. 1-5, the viscosity change is ignored when the density parameter changes in S5, the density parameter is set to be the same as the density of the fluid in the perfusion layer, and the density parameter is 1010kg/m3For a non-horizontal perfusion layer, the difference between the density of the injected waste liquid and the density of the fluid in the perfusion layer cannot be ignored due to the variation of the density parameter, and an erroneous result can be obtained by simply using the MODFLOW and the MT3DMS for simulation, please refer to fig. 1-6, S5, in which the hydrogeological parameters include porosity, permeability and dispersion, the porosity is reduced by half, the permeability and dispersion are increased by one time, and the uncertainty of the sealing process is simulated through the variation of the porosity, permeability and dispersion parameters, so as to perform the diversified analysis.
Referring to fig. 1-7, in S1, a geographical area includes a depressed area with good geological stability, a large fault for terminating geological activity is connected around the depressed area, the geographical area includes a quasi-irrigation area, the quasi-irrigation area is about 2000m from the ground surface, the quasi-irrigation area includes massive sandstone, siltstone and gray sandstone, the massive sandstone, siltstone and gray sandstone have suitable porosity and permeability, and a mudstone-based capping layer with low permeability and good continuity exists above and below the quasi-irrigation area, the area discretization method in S3 includes a simulation area, the simulation area is partitioned into 300 × 300 rectangular grid cells, the grid cells are packed by using irrigation wells, and an initial pressure distribution is obtained by calculating the pressure at a known point in the irrigation layer according to the static equilibrium principle.
According to the finding, the data parameter acquisition of different areas can be realized, the areas which are suitable for carrying out deep geological storage on harmful waste liquid are selected, corresponding hydrogeological conceptual models and mathematical models are established, the operation is carried out by leading-in software, a preliminary data result is obtained by solving, and then data simulation under parameter change is carried out through the change of viscosity, density and hydrogeological parameters, so that the change condition of the harmful waste liquid in landfill under different data conditions is simulated, the conclusion is obtained by combining with the preliminary data result, the influence of the harmful waste liquid on the surrounding ecological environment after the harmful waste liquid is landfill is discussed, the success and variability of the harmful waste liquid landfill are improved, and the relevant field technicians can conveniently and timely take corresponding measures in the face of different conditions.
The above are merely preferred embodiments of the present invention; the scope of the invention is not limited thereto. Any person skilled in the art should be able to cover the technical scope of the present invention by equivalent or modified solutions and modifications within the technical scope of the present invention.
Claims (10)
1. A numerical simulation method for geological storage of mine water is characterized by comprising the following steps: the method comprises the following steps:
s1, data acquisition: collecting a plurality of suitable geographic area parameters, analyzing specific parameters, and selecting an optimal geographic area;
s2, establishing a model: classifying according to the collected geographic region parameters, and respectively establishing a hydrogeological concept model and a mathematical model;
s3, software operation: calculating the model through numerical simulation software, and simulating by adopting a region discretization method;
s4, model solving results: solving according to the data to obtain a preliminary simulation result;
s5, parameter change simulation: the operation parameters are modularized, and diversified simulation is carried out through changes of viscosity, density and hydrogeological parameters to obtain corresponding change data;
s6, obtaining a conclusion that: and combining and analyzing the preliminary simulation result and the change data to obtain a simulation conclusion.
2. The numerical simulation method for geological storage of mine water according to claim 1, characterized in that: the mathematical model in S2, which temporarily does not take into account temperature changes and chemical reactions, includes a pressure control equation:
in the formula: ρ -liquid density;
ui-seepage velocity (Darcy flow rate);
xi-distance in the direction of the principal coordinate axis;
ρs-density of injected waste liquid;
q-rate of waste injection;
t-time;
phi-effective porosity;
the motion equation corresponding to the pressure control equation is as follows:
in the formula: k is a radical ofii-a permeability tensor;
mu-viscosity coefficient;
p-liquid pressure;
z-elevation;
the equation of motion quotes
Obtaining:
in the formula: rho0Reference pressure p0Density of the liquid at concentration 0.
3. The numerical simulation method for geological storage of mine water according to claim 1, characterized in that: the mathematical model in S2 includes a solute transport equation, the solute transport equation being:
in the formula: c-liquid concentration;
Dij-hydrodynamic diffusion coefficient tensor;
CI-the concentration of the injected waste liquid;
the solute transport equation is connected with a plurality of coupled parameter expressions, and the parameter expressions are as follows:
φ＝φo[1+CR(|p-po)]、
in the formula: phio-porosity at a reference pressure;
CR-the volume compressibility of the porous medium;
Cw-the volume compressibility of the liquid;
Cc-density difference rate;
c ^ the ratio of the concentration of the liquid to the concentration of the injected waste liquid, namely the relative concentration,
μR(C ^) -the phase of concentration determined from given dataAn empirical function of the relationship.
4. The numerical simulation method for geological storage of mine water according to claim 1, characterized in that: the hydrogeological conceptual model in the S2 is selected within a range of 20km multiplied by 15km, the selected range is located in the center of a simulation area, the hydrogeological conceptual model comprises a perfusion layer and a water barrier, the perfusion layer is generalized to be a homogeneous isotropic aquifer, fluid motion in the aquifer accords with Darcy' S law, and the water barrier comprises edge sandstone and a large fault.
5. The numerical simulation method for geological storage of mine water according to claim 1, characterized in that: the numerical simulation software in the S3 is SWIFT numerical simulation software which performs discretization by a block center finite difference method, and the SWIFT numerical simulation software performs operations on time and space domains by a center or backward weighting algorithm.
6. The numerical simulation method for geological storage of mine water according to claim 1, characterized in that: in S5, the change of the viscosity parameter is a time change, and the viscosity parameter is a constant that does not change with concentration, and the constant is 0.00035Pa · S.
7. The numerical simulation method for geological storage of mine water according to claim 1, characterized in that: neglecting viscosity change when the density parameter changes in S5, wherein the density parameter is set to be the same as the density of the fluid in the injection waste liquid and the perfusion layer, and the density parameter is 1010kg/m3。
8. The numerical simulation method for geological storage of mine water according to claim 1, characterized in that: the hydrogeological parameters in S5 include porosity, permeability and diffusivity, the porosity is reduced by half, and the permeability and diffusivity are doubled.
9. The numerical simulation method for geological storage of mine water according to claim 1, characterized in that: the geographic area in the S1 comprises a hollow area with good geological stability, a large fault for stopping geological activity is connected around the hollow area, the geographic area comprises a quasi-perfusion area, the quasi-perfusion area is about 2000m from the ground surface, and the quasi-perfusion area comprises massive sandstone, siltstone and gray sandstone.
10. The numerical simulation method for geological storage of mine water according to claim 1, characterized in that: the area discretization method in S3 includes a simulation zone partitioned into 300 × 300 rectangular grid cells, the grid cells being infilled with a pour well.
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| CN114117759A (en) * | 2021-11-12 | 2022-03-01 | 大连海事大学 | Large ship shafting inherent frequency uncertainty analysis method based on nonparametric model |
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| CN114117759A (en) * | 2021-11-12 | 2022-03-01 | 大连海事大学 | Large ship shafting inherent frequency uncertainty analysis method based on nonparametric model |
| CN114117759B (en) * | 2021-11-12 | 2024-11-01 | 大连海事大学 | Large ship shafting natural frequency uncertainty analysis method based on non-parametric model |
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