Method for establishing rheological model of deep-sea mining plume considering physical property changes

Abstract

The present invention provides a method for establishing a rheological model of deep-sea mining plume considering physical property changes, establishing a rheological database of deep-sea mining plume under different rheological models; analyzing and comparing the differences in rheological parameters of deep-sea mining plume under different rheological models; constructing a relationship between rheological parameters and density for the rheological model of deep-sea mining plume considering physical property changes. Through the technical solution of the present invention, the model uses the artificial sample kaolin plume with relatively stable properties to represent the sediment plume in the mining area, overcoming the current defects of lacking rheological test data of sediment in the mining area and the extremely large differences in rheological properties of deep-sea sediments in different regions. The model provides an important reference for the variation law of the rheological characteristics of sediment in the mining area with density, and based on this, a rheological model of deep-sea mining sediment plume under the full-life evolution cycle can be constructed.

Description

Technical Field

[0001] The present invention relates to the technical field of deep - sea mining. Specifically, it particularly relates to a method for establishing a rheological model of deep - sea mining plume considering the change of physical properties. Background Art

[0002] A rheological model refers to a model that describes the variation law of rheological parameters of a fluid (such as apparent viscosity, yield strength) with the increase of shear rate. The rheological model is used in the simulation of the propagation range of deep - sea mining sediment plumes.

[0003] Deep - sea mining will cause serious environmental pollution including plumes, which is one of the important factors restricting the commercial exploitation of deep - sea minerals. The plumes caused by deep - sea mining activities come from two aspects, namely, the mining vehicle plume caused by the mining vehicle during the ore - collecting process, and the tailing plume formed by discharging the treated tailings into the sea water. Among them, due to the higher discharge concentration and velocity, the tailing plume has a farther propagation distance and a longer residence time in the sea water. Currently, the most favorable means for predicting the propagation range of deep - sea mining plumes is numerical simulation. Since the rheological properties (such as viscosity) of the plume have an important impact on its propagation range, the accuracy of numerical simulation depends on the description of the rheological properties of the plume. During the entire life - cycle of the deep - sea mining plume from release to far - away propagation, due to the flocculation settlement of sediments and the dilution of the plume by the environmental fluid, its physical properties such as density will change significantly, resulting in the change of the rheological properties of the plume. However, current research regards plumes at different stages as Newtonian fluids and rarely considers the change of rheological parameters of the plume with its evolution process, which will have an important impact on the prediction of the plume. In order to describe the rheological characteristics of the plume, some scholars have carried out a large number of rheological tests using deep - sea sediment samples. Among them, the power - law model, Bingham model, and Herschel - Bulkley model show good applicability in describing the rheological characteristics of sediment plumes with a certain density. However, in these rheological models, only the influence of shear - rate change on rheological parameters is considered, and the change of physical parameters represented by density is not considered. This may cause a large error in the simulation result of the propagation range of deep - sea mining plumes. Summary of the Invention

[0004] In order to more realistically describe the change of rheological properties experienced by deep - sea mining plumes during the propagation process, it is necessary to improve the existing typical rheological models, such as the power - law model, Bingham model, and Herschel - Bulkley model. Specifically, it is necessary to quantify the influence of the change of plume physical parameters represented by density on its rheological parameters, and couple it with the typical rheological model, and finally construct a rheological model of deep - sea mining plume considering the change of plume density. In order to make up for the deficiencies of the existing technology, the present invention provides a method for establishing a rheological model of deep - sea mining plume considering the change of physical properties.

[0005] The present invention is realized through the following technical solutions: A method for establishing a rheological model of deep-sea mining plume considering physical property changes, characterized by specifically including the following steps:

[0006] Step S1. Establish a rheological database of deep-sea mining plume under different rheological models, specifically including the following steps:

[0007] Step S1-1. Determine the rheological models for describing the rheology of deep-sea mining plume with a certain density, including typical non-Newtonian fluid rheological models such as power-law model, Bingham model, and Herschel-Bulkley model;

[0008] Step S1-2. According to the physical property changes experienced during the evolution process of the deep-sea mining plume to be described, determine the physical property parameters representing the entire evolution process, and delimit the change range of this parameter during the sediment evolution process;

[0009] Step S1-3. Establish a rheological parameter database of deep-sea mining plume. According to different descriptions of the rheological models of deep-sea mining plume, establish a database of the variation of rheological property parameters of deep-sea mining plume with density under different rheological models;

[0010] Step S2. Analyze and compare the differences in rheological parameters of deep-sea mining plume under different rheological models, specifically including the following steps:

[0011] Step S2-1. Visual analysis of data differences; Divide the entire range of physical parameter changes of the deep-sea mining plume, and then evaluate the distribution range of rheological parameters in a smaller physical parameter change interval by drawing box plots;

[0012] Step S2-2. Quantitative analysis of data differences; Calculate the range of rheological parameters within the physical parameter change interval of 0.5 g / cm 3 Calculate the average range, the ratio of the maximum range to the average value within the entire range of physical parameter changes of the deep-sea mining plume, and count the density interval where the maximum value is located; Based on the visual analysis of data differences, calculate the range of rheological test data within each single density interval with a density gradient of 0.05 g / cm3, and conduct quantitative analysis of data differences; The range of data within a certain interval is the difference between the maximum value and the minimum value of the data within this interval, indicating the size of the data distribution range within this interval;

[0013] Step S2-3. Selection of the rheological model for describing the rheological characteristics of deep-sea mining sediment plume; Considering the results of visual analysis and quantitative analysis of data differences comprehensively, select the rheological model with the smallest data difference, and build a rheological model of deep-sea mining plume considering physical property changes based on this model;

[0014] Step S3: Construct a rheological model for deep - sea mining plume considering physical property changes, and establish the relationship between rheological parameters and density. The specific steps are as follows:

[0015] Step S3 - 1: Establish the quantitative relationship between rheological parameters and physical parameters; include the relevant parameters of environmental water ρ = 1 g / cm 3 ; K = 0.001 Pa·s; n = 1 are incorporated into the fitting database, and ensure that the relevant parameters of water conform to the fitting results, ρ and K and n both show a relationship of three - parameter power - exponential function;

[0016] Step S3 - 2: Construct a rheological model for deep - sea mining plume considering physical property changes; determine the variation law of rheological parameters with physical parameters through data fitting. Through data fitting, it can be determined that there is a mathematical relationship of three - parameter power function between the rheological parameters and density of the deep - sea mining plume. Coupling it with the power - law model can obtain a rheological model for kaolin plume considering density changes. The specific coupling method is as follows:

[0017] Equations (1) and (2) are the relationships between rheological parameters K and n and density, and Equation (3) is the expression formula of the power - law model. Substituting Equations (1) and (2) into Equation (3), a rheological model for deep - sea mining plume considering plume density changes can be constructed, as shown in Equation (4).

[0018]

[0019] As a preferred solution, in Step S1 - 2, the determined density range of the deep - sea mining plume does not exceed 1.50 g / cm3.

[0020] As a preferred solution, in Step S2 - 1, the box plot shows the maximum value, minimum value, median, and upper and lower quartiles of the rheological test data within the density change range with a density gradient of 0.05 g / cm 3 interval, so as to describe the distribution range and dispersion degree of the data within this interval.

[0021] Due to the adoption of the above - mentioned technical solutions, the present invention has the following beneficial effects compared with the prior art: This model uses the kaolin plume of artificial samples with relatively stable properties to represent the sediment plume in the mining area, overcoming the defects of the current lack of rheological test data for sediment in the mining area and the extremely large differences in rheological properties of deep - sea sediments in different regions. This model provides an important reference for the law of the rheological characteristics of sediment in the mining area changing with density, and based on this, a rheological model for deep - sea mining sediment plume under the full - life evolution cycle can be constructed.

[0022] Additional aspects and advantages of the present invention will become apparent in the following description section, or be learned through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The above and / or additional aspects and advantages of the present invention will become apparent and be readily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0024] Figure 1 It is a rheological database diagram of kaolin plume, where (a) is the relationship between K and density under the power-law model, (b) is the relationship between n and density under the power-law model, (c) is the relationship between τy and density under the Bingham model, (d) is the relationship between K and density under the Bingham model, (e) is the relationship between K and density under the H-B model, (f) is the relationship between τy and density under the H-B model, and (g) is the relationship between n and density under the H-B model;

[0025] Figure 2 It is a visualization diagram of the difference in kaolin plume rheological test data; where (a) is the visualization of the difference in K under the power-law model, (b) is the visualization of the difference in n under the power-law model, (c) is the visualization of the difference in τy under the Bingham model, (d) is the visualization of the difference in K under the Bingham model, (e) is the visualization of the difference in K under the H-B model, (f) is the visualization of the difference in τy under the H-B model, and (g) is the visualization of the difference in n under the H-B model;

[0026] Figure 3 It is the relationship between the kaolin plume rheological parameters and density, where (a) is the relationship between K and density, and (b) is the relationship between n and density. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0027] In order to more clearly understand the above objects, features, and advantages of the present invention, the present invention will be further described in detail below in conjunction with the drawings and specific embodiments. It should be noted that, without conflict, the embodiments of the present application and the features in the embodiments may be combined with each other.

[0028] In the following description, many specific details are set forth in order to fully understand the present invention. However, the present invention may be implemented in other ways different from those described herein. Therefore, the protection scope of the present invention is not limited by the specific embodiments disclosed below.

[0029] The following will specifically describe Figures 1 to 3 a method for establishing a deep-sea mining plume rheological model considering physical property changes for the embodiments of the present invention.

[0030] The present invention proposes a method for establishing a deep-sea mining plume rheological model considering physical property changes, specifically including the following steps:

[0031] Step S1. Establish a rheological database of deep-sea mining plumes under different rheological models, which specifically includes the following steps:

[0032] Step S1-1. Determine the rheological models for describing the density of deep-sea mining plumes, including typical non-Newtonian fluid rheological models such as the power-law model, Bingham model, and Herschel-Bulkley model. Non-Newtonian fluids refer to fluids that do not satisfy Newton's law of internal friction. Time-independent non-Newtonian fluid is a common type of non-Newtonian fluid, whose shear stress is only related to the shear rate, and its apparent viscosity is represented by the ratio of shear stress to shear rate. The non-Newtonian fluid models widely used to describe the mechanical property changes of deep-sea sediment flows are the power-law model, Bingham model, and Herschel-Bulkley model. The sediment plume caused by seabed mining belongs to a type of seabed sediment flow. Therefore, it can also be described by the above three models.

[0033] Step S1-2. According to the physical property changes experienced during the evolution process of the deep-sea mining plume to be described, determine the physical property parameters representing the entire evolution process and delimit the range of changes in this parameter during the sediment evolution process; Currently, the density of the mining vehicle plume monitored is relatively low, not exceeding 1.01 g / cm 3 , but the maximum amount of resuspensible sediment caused by deep-sea mining activities depends on the saturated density and water content of the seabed sediment, thus affecting the density of the seabed sediment plume. For example, the saturated density of the seabed sediment in the polymetallic nodule deposit area in the Peru Basin varies between 1.10 and 1.27 g / cm 3 . Therefore, the density of the head of the mining vehicle plume may exceed the monitored density. In addition, during the process of transporting tailings from the surface mother ship to the seawater through the pipeline, the volume concentration of the sediment flow in the pipeline does not exceed 30%. That is, under the condition that the density of the seabed sediment is 2.63 - 2.65 g / cm 3 , and the density of nodule debris is about 2.00 g / cm 3 , the density of the sediment flow in the pipeline will be close to 1500 kg / m 3 . Thus, it is inferred that the density of the tailings plume discharged into the middle water layer through the pipeline at the release point can reach nearly 1500 kg / m 3 . Considering comprehensively the maximum density that the mining vehicle plume and the tailings plume can reach, finally determine that the density range of the deep-sea mining plume does not exceed 1.50 g / cm 3 .

[0034] Step S1-3: Establish a rheological parameter database for deep-sea mining plumes. According to different descriptions of the rheological models of deep-sea mining plumes, establish a database of the rheological property parameters of deep-sea mining plumes varying with density under different rheological models. Therefore, at the laboratory temperature (20 - 25°C), the rheological test data of kaolin plumes with a density not exceeding 1.50 g / cm³ were screened. Then, the data were classified according to the different rheological models applied, and the relationship between the density of kaolin plumes and the rheological parameters under different models was analyzed, as Figure 1 shown.

[0035] Step S2: Analyze and compare the differences in rheological parameters of deep-sea mining plumes under different rheological models, which specifically includes the following steps:

[0036] Step S2-1: Visual analysis of data differences; divide the entire range of physical parameter changes of deep-sea mining plumes, and then evaluate the distribution range of rheological parameters within a smaller physical parameter change interval by drawing box plots. The visualization of data differences is achieved by drawing box plots, and a box plot is a statistical chart describing the data distribution. The box plot shows the maximum value, minimum value, median, and upper and lower quartiles of the rheological test data within the density change interval with a density gradient of 0.05 g / cm3, thereby describing the distribution range and dispersion degree of the data within this interval, as Figure 2 shown in (b); Figure 2 shows the visualization results of the differences in rheological test data under different models. Specifically, within this interval, the larger the distribution range and the higher the dispersion degree of the rheological parameters, the greater the difference in rheological test data, and the interval with the largest data difference is marked with a blue shadow. The gray broken line is the connection of the medians of different intervals, intuitively reflecting the change of rheological parameters within the density range of 1.0 - 1.5 g / cm³.

[0037] Step S2-2: Quantitative analysis of data differences; calculate the range of rheological parameters within the density change interval of 0.5 g / cm 3 , and calculate the average range, the ratio of the maximum range to the average value, and count the density interval where the maximum value is located within the entire range of physical parameter changes of deep-sea mining plumes. Based on the visual analysis of data differences, calculate the range of rheological test data within each single density interval with a density gradient of 0.05 g / cm 3 to carry out quantitative analysis of data differences. The range of data within a certain interval is the difference between the maximum value and the minimum value of the data within this interval, indicating the size of the data distribution range within this interval. Table 1 shows the results of quantitative analysis of data differences, including the full density range (1.0 - 1.5 g / cm 3The average value of the within-range difference, the ratio of the maximum range value to the average value, and the range of the interval where the maximum range value is located were statistically analyzed. Among them, the average value of the range difference reflects the overall level of data differences of the rheological parameters within the full density change range.

[0038] Table 1 Quantitative analysis of the differences in rheological parameters under different rheological models

[0039]

[0040] Step S2-3: Selection of the rheological model to describe the rheological characteristics of deep-sea mining sediment plumes; comprehensively considering the visual analysis and quantitative analysis results of data differences, select the rheological model with the smallest data difference, and based on this model, construct a rheological model of deep-sea mining sediment plumes considering physical property changes; the quantitative results show that K The data difference is the smallest under the power-law model, and the ratio of the maximum range value to the average value is 240.76%. The difference is the largest under the Herschel-Bulkley model, and the ratio of the maximum range value to the minimum value is as high as 426.27%. τ y The data difference under the Bingham model is smaller than that under the Herschel-Bulkley model, while n Although the quantitative results of the data differences under the power-law model and the Herschel-Bulkley model are not very different, the visual results of the data differences show that the data distribution under the power-law n is more concentrated and the data difference is smaller. Therefore, comprehensively considering the visual and quantitative results of the data differences, the data difference of the rheological test data is the smallest under the power-law model.

[0041] Step S3: Construction of a rheological model of deep-sea mining sediment plumes considering physical property changes. Establish the relationship between rheological parameters and density, which specifically includes the following steps:

[0042] Step S3-1: Establish the quantitative relationship between rheological parameters and physical parameters; during the process of the plume spreading from release to a distance, due to the flocculation and sedimentation of sediments and the dilution of the plume by the ambient fluid, the density of the plume gradually decreases and finally approaches the density of the ambient water. Therefore, to simulate the evolution of the rheological properties of the plume over its entire life cycle, relevant parameters of the ambient water ( ρ = 1 g / cm 3 ; K = 0.001 Pa·s; n = 1) are incorporated into the fitting database, and it is ensured that the relevant parameters of water conform to the fitting results. Figure 3 The data fitting results of density and rheological parameters under the power-law are shown. Here, ρ and K and nAll show the relationship of a three-parameter power exponential function, and the fitting curve can better reflect the change trend of rheological parameters with density.

[0043] Through data fitting, it can be determined that there is a mathematical relationship of a three-parameter power function between the rheological parameters and density of the deep-sea mining plume. Coupling it with the power-law model can obtain a rheological model of kaolin plume considering density changes. The sediments in the deep-sea mining area have the property of shear thinning like kaolin, so the three-parameter power function relationship provided by this model can also be used to describe the change of rheological properties of the deep-sea mining plume with density.

[0044] Step S3-2: Construct a rheological model of the deep-sea mining plume considering physical property changes; determine the change law of rheological parameters with physical parameters through data fitting. Through data fitting, it can be determined that there is a mathematical relationship of a three-parameter power function between the rheological parameters and density of the deep-sea mining plume. Coupling it with the power-law model can obtain a rheological model of kaolin plume considering density changes. The specific coupling method is as follows:

[0045] Equations (1) and (2) are the rheological parameters K and n The relationship with density, and Equation (3) is the expression formula of the power-law model. Substituting Equations (1) and (2) into Equation (3), a rheological model of the deep-sea mining plume considering plume density changes can be constructed, as shown in Equation (4).

[0046]

[0047] In the description of this specification, the descriptions of terms such as "one embodiment", "some embodiments", "specific embodiments", etc. mean that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or instance. Moreover, the specific features, structures, materials or characteristics described can be combined in a suitable manner in any one or more embodiments or examples.

[0048] The above is only the preferred embodiment of the present invention and is not used to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for establishing a rheological model of deep - sea mining plume considering physical property changes, characterized in that , specifically including the following steps: Step S1. Establish a rheological database of deep-sea mining plumes under different rheological models, specifically including the following steps: Step S1-1. Describe the rheological models of deep-sea mining plumes with determined density, including typical non-Newtonian fluid rheological models such as the power-law model, Bingham model, and Herschel-Bulkley model. Non-Newtonian fluids refer to fluids that do not satisfy Newton's law of internal friction. Step S1-2. Determine the physical property parameters representing the entire evolution process according to the physical property changes experienced during the evolution of the deep-sea mining plume to be described, and delimit the change range of this parameter during the sediment evolution process. Step S1-3. Establish a rheological parameter database of deep-sea mining plumes. According to the different descriptions of the rheological models of deep-sea mining plumes, establish a database of the variation of rheological property parameters of deep-sea mining plumes with density under different rheological models. Step S2. Analyze and compare the differences in rheological parameters of deep-sea mining plumes under different rheological models, specifically including the following steps: Step S2-1, Visual analysis of data differences; divide the entire range of physical parameter changes of the deep-sea mining plume, and then evaluate the distribution range of rheological parameters within the physical parameter change interval by plotting a box plot for 0.5 g / cm 3 ; Step S2-2, quantitative analysis of data differences; calculate 0.5 g / cm 3 the range of rheological parameters within the physical parameter change interval, and calculate the average value of the ranges, the ratio of the maximum range value to the average value within the entire range of physical parameter changes of the deep-sea mining plume, and count the density interval where the maximum value is located; based on the visual analysis of data differences, calculate the range of rheological test data within each single density interval with a density gradient of 0.05 g / cm 3 to conduct quantitative analysis of data differences; the range of data within a certain interval is the difference between the maximum value and the minimum value of the data within that interval, indicating the size of the data distribution range within that interval; Step S2-3. Select the rheological model describing the rheological characteristics of deep-sea mining sediment plumes; comprehensively consider the visual analysis and quantitative analysis results of data differences, select the rheological model with the smallest data difference, and construct a rheological model of deep-sea mining plumes considering physical property changes based on this model. Step S3. Construct a rheological model of deep-sea mining plumes considering physical property changes to establish the relationship between rheological parameters and density, specifically including the following steps: Step S3-1: Establish the quantitative relationship between rheological parameters and physical parameters; include the relevant parameters of environmental water ρ = 1 g / cm 3 ; K = 0.001 Pa·s; n = 1 into the fitting database, and ensure that the relevant parameters of water conform to the fitting results, ρ and K and n both show a relationship of a three-parameter power exponential function; Step S3-2. Construct a rheological model of deep-sea mining plumes considering physical property changes; determine the variation law of rheological parameters with physical parameters through data fitting. It is determined through data fitting that there is a mathematical relationship of a three-parameter power function between the rheological parameters and density of deep-sea mining plumes. Coupling it with the power-law model can obtain a rheological model of kaolin plumes considering density changes. The specific coupling method is as follows: Equations (1) and (2) are rheological parameters K and n their relationships with density. Equation (3) is the expression formula of the power-law model. By substituting Equations (1) and (2) into Equation (3), a rheological model of deep-sea mining plume considering the change of plume density can be constructed, as shown in Equation (4). （1） （2） （3） （4）。 2. The method for establishing a rheological model of deep - sea mining plume considering physical property changes according to claim 1, characterized in that , in step S1-2, it is determined that the density range of the deep-sea mining plume does not exceed 1.50 g / cm 3 .

3. The method for establishing a rheological model of a deep - sea mining plume considering physical property changes according to claim 1, wherein , in the box plot in the step S2-1, the rheological test data shows the maximum value, minimum value, median, and upper and lower quartiles within the density change range with a density gradient of 0.05 g / cm 3 interval, so as to describe the distribution range and dispersion degree of the data within this interval.

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