Construction method of superfine tailing slurry pipe transportation resistance calculation model

Abstract

The invention relates to a construction method of a superfine tailing slurry pipe transportation resistance calculation model, and belongs to the technical field of metallurgical mine mining methods. According to the technical scheme, on the basis of analysis of physicochemical properties of tailings and cement, the relation between rheological parameters and mass concentration, the cement-sand ratio and slurry temperature test factors is discussed on the basis of a center composite design response curved surface method, the parameter ratio is optimized, so that the pipe conveying resistance reaches the minimum value, and the pipe conveying performance is improved. A pipeline conveying resistance loss calculation model comprehensively considering the multi-factor effect is established, and numerical simulation verification is carried out. The method has the beneficial effects that a theoretical guidance value can be provided for superfine tailing pipeline transportation, the filling pipeline transportation energy consumption is further reduced, pipeline transportation accidents are reduced, and the filling efficiency is improved.

Description

Technical Field

[0001] The present invention relates to a method for constructing a calculation model of the pipeline transportation resistance of ultrafine tailings slurry, belonging to the technical field of metallurgical mine mining methods. Background Art

[0002] In metal mine mining activities, as a green mining technology, the filling mining method has been widely used due to its significant advantages in improving the recovery rate of mine resources, reducing surface subsidence and decreasing the accumulation amount of tailings. However, due to its fine particles and large specific surface area, ultrafine tailings exhibit special rheological properties during the preparation of filling slurry and pipeline transportation, which puts higher requirements on its industrial application. During the process of preparing filling slurry using tailings, pipeline transportation is one of the important links. However, ultrafine tailings slurry often exhibits complex rheological properties during transportation, such as high viscosity, non-Newtonian flow behavior, etc., resulting in an increase in transportation resistance and energy consumption. Especially in the scenarios of long-distance and large-drop transportation, the influence of pipeline transportation resistance on filling efficiency and economy is particularly significant. In addition, the rheology of the slurry is easily affected by various factors such as mass concentration, ash-sand ratio and slurry temperature, further increasing the complexity of optimizing pipeline transportation resistance. Therefore, constructing a calculation model of the pipeline transportation resistance of fine tailings slurry and studying the rheological properties of ultrafine tailings filling slurry and the optimization of pipeline transportation resistance have important theoretical and practical significance.

[0003] At present, the research on the pipeline transportation resistance of filling slurry mainly includes empirical formula method, loop pipe test method and industrial test method, etc. The empirical formula method is based on a large amount of engineering practice data and can quickly describe the changing trend of pipeline transportation resistance; the loop pipe test can obtain more accurate pressure loss data by simulating the actual flow state of the slurry in the pipeline; the industrial test directly reflects the pipeline transportation performance of the slurry in actual application and provides an important basis for engineering optimization. Although the above methods reveal the pipeline transportation characteristics of filling slurry to a certain extent, they also have limitations. For example, the applicability of the empirical formula depends on the specific slurry composition and transportation conditions, and there are certain limitations in popularization and application; the loop pipe test and industrial test require a large amount of equipment and funds, and the test process is complex, making it difficult to comprehensively cover different working conditions. In contrast, the pipeline transportation resistance calculation model based on theoretical derivation can quickly calculate and optimize pipeline transportation parameters considering various test factors, and it has significant advantages in terms of model flexibility and practicability. In recent years, the application of multi-factor calculation models has provided new ideas for solving complex engineering problems. In the research on the pipeline transportation resistance of ultra-fine tailings filling slurry, by considering the influence of multi-factors such as mass concentration, ash-sand ratio and slurry temperature on rheological properties, a more reliable pipeline transportation resistance model can be constructed, which can effectively improve the prediction accuracy and applicability of the model. In the prior art, there is relatively little systematic research on the calculation model of the pipeline transportation resistance of ultra-fine tailings slurry under the combined action of multi-factors. In particular, how to optimize the pipeline transportation resistance loss through the properties of the slurry itself to improve the transportation efficiency still needs further research and exploration. Summary of the Invention

[0004] The object of the present invention is to provide a method for constructing a calculation model of the pipeline transportation resistance of ultra-fine tailings slurry. Based on the analysis of the physical and chemical properties of tailings and cement, and using the central composite design response surface method, the relationship between rheological parameters and test factors such as mass concentration, ash-sand ratio and slurry temperature is explored. By optimizing the parameter ratio to make the pipeline transportation resistance reach the lowest value, a calculation model of the pipeline transportation resistance loss considering the combined action of multiple factors is derived and established, further reducing the energy consumption of mine filling pipeline transportation, reducing pipeline transportation accidents, improving filling efficiency, and effectively solving the above problems existing in the background technology.

[0005] The technical solution of the present invention is: a method for constructing a calculation model of the pipeline transportation resistance of ultra-fine tailings slurry, comprising the following steps:

[0006] The first step is to conduct a response surface test design. First, analyze the physical and chemical properties of the test tailings and cement, then conduct an orthogonal test on the pipeline transportation resistance of the ultra-fine tailings slurry, and finally conduct a numerical simulation calculation of the pipeline transportation resistance to obtain a table of the pressure drop and pipeline transportation resistance results of the ultra-fine tailings slurry with different test variables;

[0007] Step 2: Test results and analysis. Perform variance analysis. Based on the results of orthogonal tests and response surface analysis, obtain a multiple regression analysis equation for the three variables of mass concentration, ash-sand ratio, and slurry temperature and the pipeline transportation resistance of ultra-fine tailings slurry, and conduct interaction analysis;

[0008] Step 3: Build a calculation model for the pipeline transportation resistance of ultra-fine tailings slurry under the influence of multiple factors;

[0009] Step 4: Conduct model applicability verification. Draw a comparison chart of the numerical simulation test values and model calculation values of the pipeline transportation resistance to further verify the reliability and applicability of the newly built model.

[0010] In the first step mentioned above, the specific steps are as follows:

[0011] (1) First, conduct an analysis of the physical and chemical properties of the test tailings and cement, including particle size composition and oxide composition analysis. Use a laser particle size analyzer to test the particle size composition of tailings and cement respectively, and test the oxide composition of tailings through an X-ray fluorescence energy spectrometer;

[0012] (2) Design an orthogonal test for the pipeline transportation resistance of ultra-fine tailings slurry. Take mass concentration, ash-sand ratio, and slurry temperature as test variables, and use Design Expert software to establish an orthogonal test table with a central composite design;

[0013] (3) Numerical simulation calculation of pipeline transportation resistance,

[0014] 1) Use a rotational rheometer to test the rheological properties of ultra-fine tailings filling slurry under different test variables, and obtain plastic viscosity and yield stress;

[0015] 2) According to the existing filling scheme in the mine, use COMSOL Multiphysics numerical simulation software to establish an L-pipe model with a diameter of 140 mm, an average slurry flow rate of about 2.5 m·s -1 , a filling multiple of 5. To ensure the accuracy of the test results, perform ultra-fine meshing and set the relative calculation tolerance to 10 -5 , and calculate and obtain the pressure drops at the inlet and outlet of the pipeline in combination with the orthogonal test table, calculate the frictional resistance loss along the way, and obtain a result table of the pressure drop and pipeline transportation resistance of ultra-fine tailings slurry under different test variables.

[0016] In step (2) above, for the test variables of the orthogonal test of the pipeline transportation resistance of ultra-fine tailings slurry, the mass concentration is 66% - 70%, the ash-sand ratio is 1:4 - 1:8, and the slurry temperature is 30°C - 50°C.

[0017] In the second step mentioned above, the specific steps are as follows:

[0018] (1) Analysis of variance. Combining the calculated values of the pipeline transportation resistance loss of ultra-fine tailings slurry and the orthogonal test table, analyze the sensitivity of the mass concentration, ash-sand ratio, and slurry temperature to the pipeline transportation resistance, obtain the analysis of variance result table of the pipeline transportation resistance of ultra-fine tailings slurry, and analyze and judge the reliability and rationality of the response surface analysis results;

[0019] (2) Construct a multiple regression analysis equation. Based on the orthogonal test and response surface analysis results, obtain a multiple regression analysis equation for the three variables of mass concentration, ash-sand ratio, and slurry temperature and the pipeline transportation resistance of ultra-fine tailings slurry, as shown in Equation (1).

[0020]

[0021] In the formula, i u is the pipeline transportation resistance of ultra-fine tailings slurry, Pa·m -1 ; A is the mass concentration, %; B is the ash-sand ratio; C is the slurry temperature, °C.

[0022] (3) Interaction analysis. To further analyze the influence weights of the mass concentration, ash-sand ratio, and slurry temperature on the pipeline transportation resistance of ultra-fine tailings slurry, based on the response surface test results, draw 3D surface diagrams of the interaction effects of different test variables on the pipeline transportation resistance of ultra-fine tailings slurry, including the interaction effects of the ash-sand ratio and mass concentration, slurry temperature and mass concentration, and slurry temperature and ash-sand ratio on the pipeline transportation resistance.

[0023] In the third step described above, the specific steps are as follows:

[0024] (1) The yield stress and plastic viscosity have an exponential and proportional relationship with the mass concentration, ash-sand ratio, and slurry temperature of ultra-fine tailings slurry, and the two can be expressed by the following Equations (2) and (3).

[0025]

[0026] In the formula, C m is the mass concentration of ultra-fine tailings slurry, %; R cs is the ash-sand ratio; a1, b1, c1, d1, a2, b2, c2, and d2 are all undetermined coefficients, and the other symbols are the same as above.

[0027] (2) Further optimize the density of the slurry, which is calculated by weighted averaging of the solid-phase particle density and water density according to the mass concentration, as shown in Equation (4).

[0028] ρ = ρ w + C m ·(ρ s - ρ w ) (4)

[0029] In the formula, ρ w is the density of water, kg·m-3 ; ρ s is the solid particle density kg·m -3 , with the other symbols the same as above. Substitute the corrected yield stress, plastic viscosity and density into the Bingham fluid pipeline transportation resistance model to obtain a new optimized model for the pipeline transportation resistance of the slurry considering the mass concentration, ash-sand ratio and slurry temperature, as shown in Equation (5).

[0030]

[0031] (3) Model parameter calculation and analysis

[0032] To solve the undetermined parameters in the pipeline transportation resistance calculation model, take the logarithm of Equations (2) and (3) to obtain

[0033] ln(τ0) = ln(a1) + b1ln(C m ) + c1ln(R cs ) - d1T (6)

[0034] ln(μ u ) = ln(a2) + b2ln(C m ) + c2ln(R cs ) - d2T (7)

[0035] Let ln(a1) = A1, ln(a2) = A2, and substitute them into Equations (6) and (7) respectively to obtain

[0036] ln(τ0) = A1 + b1ln(C m ) + c1ln(R cs ) - d1T (8)

[0037] ln(μ u ) = A2 + b2ln(C m ) + c2ln(R cs ) - d2T (9)

[0038] To improve the calculation efficiency and simplify the calculation difficulty, construct Equations (8) and (9) into a linear equation system

[0039]

[0040] According to the test results, construct a table of the plastic viscosity and yield stress of the ultra-fine tailings slurry under different parameter combinations. Combining the results of this table, use the least squares method to construct an analysis matrix and calculate the undetermined coefficients.

[0041]

[0042] where β = [A1, b1, c1, d1]T is the undetermined coefficient and ε is the residual vector.

[0043] Similarly, the undetermined coefficient matrix related to the plastic viscosity is obtained. After the solution is completed, the specific values of the undetermined coefficients can be obtained. After calculation, the solution values of the undetermined parameters in the pipeline transportation resistance calculation model are obtained. This value and Equation (5) together constitute the calculation model for the pipeline transportation resistance loss of ultra-fine tailings slurry.

[0044] In the fourth step, taking the mass concentration, ash-sand ratio, and slurry temperature as variables, rheological tests on ultra-fine tailings slurry are carried out under different test variables to obtain rheological parameters. Subsequently, numerical simulation studies are carried out using COMSOL Multiphysics. The values of the pipe diameter and initial flow velocity are kept the same as those in the above simulation tests. The pressure change values at the inlet and outlet of the pipeline are obtained to calculate the pipeline transportation resistance loss. Then, the predicted value of the resistance loss is calculated through the constructed pipeline transportation resistance loss calculation model. The error between the two is compared and analyzed, and the error rate of the pipeline transportation resistance is calculated using Equation (14); a comparison diagram of the numerical simulation test values and model calculation values of the pipeline transportation resistance is drawn to further verify the reliability and applicability of the constructed new model.

[0045]

[0046] In the formula, α is the error rate between the numerical simulation test value and the model calculation value, %; i u-exp is the pipeline transportation resistance value obtained by the numerical simulation method, Pa·m -1 ; i u-pred is the pipeline transportation resistance value obtained by model calculation, Pa·m -1 .

[0047] The beneficial effects of the present invention are as follows: Based on the analysis of the physical and chemical properties of tailings and cement, and based on the central composite design response surface method, the relationship between rheological parameters and test factors such as mass concentration, ash-sand ratio, and slurry temperature is explored. The parameter ratio is optimized to minimize the pipeline transportation resistance. A calculation model for pipeline transportation resistance loss considering multiple factors is deduced and established, further reducing the energy consumption of mine filling pipeline transportation, reducing pipeline transportation accidents, and improving filling efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 is the flow chart of the present invention;

[0049] Figure 2 is the cumulative particle size curve of ultra-fine tailings and ordinary Portland cement materials in the embodiment of the present invention;

[0050] Figure 3 is the interaction projection diagram of the influence of different test factors of ash-sand ratio and mass concentration on pipeline transportation resistance in the embodiment of the present invention

[0051] Figure 4It is the projection diagram of the interaction effect between the slurry temperature and mass concentration of different test factors on the pipeline transportation resistance in the embodiments of the present invention;

[0052] Figure 5 It is the projection diagram of the interaction effect between the slurry temperature and sand - ash ratio of different test factors on the pipeline transportation resistance in the embodiments of the present invention;

[0053] Figure 6 It is the comparison diagram between the numerical simulation test value and the model calculation value of the pipeline transportation resistance in the embodiments of the present invention;

[0054] Figure 7 It is the difference in pipeline transportation resistance between the numerical simulation test and the model calculation in the embodiments of the present invention;

[0055] Figure 8 It is the error rate of the pipeline transportation resistance between the numerical simulation test and the model calculation in the embodiments of the present invention. Detailed implementation manners

[0056] To make the objectives, technical solutions, and advantages of the embodiments of the invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments. Obviously, the described embodiments are only a small part of the embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0057] A method for constructing a calculation model of the pipeline transportation resistance of ultra - fine tailings slurry includes the following steps:

[0058] The first step is to conduct a response surface experimental design. First, analyze the physical and chemical properties of the test tailings and cement. Then, conduct an orthogonal experiment on the pipeline transportation resistance of ultra - fine tailings slurry. Finally, conduct a numerical simulation calculation of the pipeline transportation resistance to obtain a table of pressure drops and pipeline transportation resistance results of ultra - fine tailings slurry with different test variables;

[0059] The second step is the test result and analysis. Conduct variance analysis. Based on the results of orthogonal experiments and response surface analysis, obtain a multiple regression analysis equation of the three variables of mass concentration, sand - ash ratio, and slurry temperature and the pipeline transportation resistance of ultra - fine tailings slurry, and conduct interaction analysis;

[0060] The third step is to construct a calculation model of the pipeline transportation resistance of ultra - fine tailings slurry under the influence of multiple factors;

[0061] The fourth step is to conduct model applicability verification. Draw a comparison diagram between the numerical simulation test value and the model calculation value of the pipeline transportation resistance to further verify the reliability and applicability of the newly constructed model.

[0062] In the first step, the specific steps are as follows:

[0063] (1) First, conduct the physical and chemical property analysis of the test tailings and cement, including particle size composition and oxide composition analysis. Use a laser particle size analyzer to test the particle size composition of the tailings and cement respectively, and use an X-ray fluorescence spectrometer to test the oxide composition of the tailings;

[0064] (2) Orthogonal test design for the pipeline transportation resistance of ultra-fine tailings slurry. Take the mass concentration, ash-sand ratio, and slurry temperature as test variables, and use Design Expert software to establish an orthogonal test table with a central composite design;

[0065] (3) Numerical simulation calculation of pipeline transportation resistance,

[0066] 1) Use a rotational rheometer to test the rheological properties of ultra-fine tailings filling slurry under different test variables, and obtain the plastic viscosity and yield stress;

[0067] 2) According to the existing filling scheme of the mine, use COMSOL Multiphysics numerical simulation software to establish an L-pipe model with a diameter of 140 mm, an average slurry flow velocity of about 2.5 m·s -1 , a filling multiple of 5. To ensure the accuracy of the test results, conduct ultra-fine meshing and set the relative calculation tolerance to 10 -5 , and combine the orthogonal test table to calculate and obtain the pressure drops at the inlet and outlet of the pipeline, calculate the frictional resistance loss along the way, and obtain the pressure drop and pipeline transportation resistance results table of ultra-fine tailings slurry under different test variables.

[0068] In the step (2), for the test variables of the orthogonal test of the pipeline transportation resistance of ultra-fine tailings slurry, the mass concentration is 66% - 70%, the ash-sand ratio is 1:4 - 1:8, and the slurry temperature is 30°C - 50°C.

[0069] In the second step, the specific steps are as follows:

[0070] (1) Variance analysis. Combine the calculated values of the pipeline transportation resistance loss of ultra-fine tailings slurry and the orthogonal test table to analyze the sensitivity of the mass concentration, ash-sand ratio, and slurry temperature to the pipeline transportation resistance, obtain the variance analysis result table of the pipeline transportation resistance of ultra-fine tailings slurry, and analyze and judge the reliability and rationality of the response surface analysis results;

[0071] (2) Construct a multiple regression analysis equation. Based on the orthogonal test and response surface analysis results, obtain a multiple regression analysis equation of the three variables of mass concentration, ash-sand ratio, and slurry temperature and the pipeline transportation resistance of ultra-fine tailings slurry, as shown in Equation (1),

[0072]

[0073] In the formula, i u is the pipeline transportation resistance of ultra-fine tailings slurry, Pa·m -1; A is the mass concentration, %; B is the ratio of ash to sand; C is the slurry temperature, °C.

[0074] (3) Interaction analysis: To further analyze the influence weights of mass concentration, ratio of ash to sand, and slurry temperature on the pipeline transportation resistance of ultrafine tailings slurry, based on the results of the response surface experiment, 3D surface plots of the interaction effects of different experimental variables on the pipeline transportation resistance of ultrafine tailings slurry are drawn, including the interaction effects of the ratio of ash to sand and mass concentration, slurry temperature and mass concentration, and slurry temperature and ratio of ash to sand on the pipeline transportation resistance.

[0075] In the third step, the specific steps are as follows:

[0076] (1) The yield stress and plastic viscosity have an exponential and proportional relationship with the mass concentration, ratio of ash to sand, and slurry temperature of the ultrafine tailings slurry, and the two can be expressed by the following formulas (2) and (3)

[0077]

[0078] In the formula, C m is the mass concentration of the ultrafine tailings slurry, %; R cs is the ratio of ash to sand; a1, b1, c1, d1, a2, b2, c2, and d2 are all undetermined coefficients, and the other symbols are the same as above.

[0079] (2) Further optimize that the density of the slurry is calculated by weighting the solid-phase particle density and water density according to the mass concentration, as shown in formula (4),

[0080] ρ = ρ w + C m ·(ρ s - ρ w ) (4)

[0081] In the formula, ρ w is the density of water, kg·m -3 ; ρ s is the solid-phase particle density kg·m -3 , and the other symbols are the same as above. Substitute the corrected yield stress, plastic viscosity, and density into the Bingham fluid pipeline transportation resistance model to obtain a new optimized model for the pipeline transportation resistance of the slurry considering mass concentration, ratio of ash to sand, and slurry temperature, as shown in formula (5).

[0082]

[0083] (3) Model parameter calculation and analysis

[0084] To solve the undetermined parameters in the pipeline transportation resistance calculation model, logarithmize formulas (2) and (3) to obtain

[0085] ln(τ0) = ln(a1) + b1ln(Cm ) + c1ln(R cs ) - d1T (6)

[0086] ln(μ u ) = ln(a2) + b2ln(C m ) + c2ln(R cs ) - d2T (7)

[0087] Let ln(a1) = A1, ln(a2) = A2, and substitute them into Equation (6) and Equation (7) respectively, we can get

[0088] ln(τ0) = A1 + b1ln(C m ) + c1ln(R cs ) - d1T (8)

[0089] ln(μ u ) = A2 + b2ln(C m ) + c2ln(R cs ) - d2T (9)

[0090] To improve the calculation efficiency and simplify the calculation difficulty, Equation (8) and Equation (9) are constructed into a linear equation system

[0091]

[0092] According to the test results, construct a table of the plastic viscosity and yield stress of ultra-fine tailings slurry under different parameter combinations. Combining the results of this table, use the least squares method to construct an analysis matrix and calculate the undetermined coefficients

[0093]

[0094] where β = [A1, b1, c1, d1]T is the undetermined coefficient, and ε is the residual vector

[0095] Similarly, find the undetermined coefficient matrix related to the plastic viscosity. After the solution is completed, the specific values of the undetermined coefficients can be obtained. After calculation, the solution values of the undetermined parameters in the pipeline transportation resistance calculation model are obtained. This value and Equation (5) together constitute the calculation model of the pipeline transportation resistance loss of ultra-fine tailings slurry

[0096] In the fourth step, with the mass concentration, sand - ash ratio, and slurry temperature as variables, perform rheological tests on ultra - fine tailings slurry under different test variables to obtain rheological parameters. Subsequently, conduct numerical simulation research using COMSOL Multiphysics, where the values of the pipe diameter and initial flow velocity are kept the same as those in the above - mentioned simulation test. Calculate the pressure change values at the inlet and outlet of the pipeline to obtain the pipe - transportation resistance loss, and then calculate the predicted value of the resistance loss through the constructed pipe - transportation resistance loss calculation model. Compare and analyze the error between the two, and calculate the error rate of the pipe - transportation resistance using Equation (14); draw a comparison chart of the numerical simulation test value and the model calculation value of the pipe - transportation resistance to further verify the reliability and applicability of the newly constructed model.

[0097]

[0098] In the formula, α is the error rate between the numerical simulation test value and the model calculation value, %; i u-exp is the pipe - transportation resistance value obtained by the numerical simulation method, Pa·m -1 ; i u-pred is the pipe - transportation resistance value obtained by model calculation, Pa·m -1 .

[0099] Example:

[0100] The first step is the response surface experimental design.

[0101] (1) First, analyze the physical and chemical properties of the test tailings and cement. The tailings are selected from an iron mine in Hebei Province, and the cement is P.O32.5 ordinary Portland cement. The particle size compositions of the tailings and cement are respectively tested using an NKT - 6100D laser particle size analyzer, as Figure 2 shown. Figure 2 It shows that the d 60 of the tailings = 22.77μm < 74μm, so it is ultra - fine tailings. In addition, its uniformity coefficient Cu and curvature coefficient Cc are 0.75 and 5.33 respectively, indicating that the gradation is not excellent enough. The oxide components of the tailings are tested using an X - ray fluorescence spectrometer (XRF), as shown in Table 1. It can be seen from Table 1 that the vast majority of the ultra - fine tailings is SiO2, which is the main component to improve the strength of the filling body, and it does not contain harmful components such as S and Cl, indicating that it can be used as a filling aggregate.

[0102] Table 1 Chemical element composition of ultra - fine tailings

[0103]

[0104] (2) Orthogonal experimental design for the pipeline transportation resistance of ultra-fine tailings slurry. Taking the mass concentration (66% - 70%), the ash-sand ratio (1:4 - 1:8), and the slurry temperature (30°C - 50°C) as the experimental variables, the Design Expert software was used to establish an orthogonal experimental table with central composite design, as shown in Table 2.

[0105] Table 2 Analysis table of orthogonal experiment for the pipeline transportation resistance of ultra-fine tailings slurry

[0106]

[0107]

[0108] (3) Numerical simulation calculation of pipeline transportation resistance.

[0109] 1) The rheological properties of ultra-fine tailings filling slurry under different experimental variables were tested using a rotational rheometer to obtain the plastic viscosity and yield stress.

[0110] 2) According to the existing filling scheme of the mine, a L-pipe model with a diameter of 140 mm, an average slurry flow velocity of about 2.5 m·s -1 , and a filling multiple of 5 was established using the COMSOL Multiphysics numerical simulation software. To ensure the accuracy of the test results, ultra-fine meshing was carried out and the relative calculation tolerance was set to 10 -5 . Combining with the orthogonal experimental table, the pressure drops at the inlet and outlet of the pipeline were calculated, the frictional resistance loss along the way was calculated, and a result table of the pressure drop and pipeline transportation resistance of ultra-fine tailings slurry under different experimental variables was obtained, as shown in Table 3.

[0111] Table 3 Pressure drop and pipeline transportation resistance of ultra-fine tailings slurry under different experimental variables

[0112]

[0113] The second step is the test results and analysis.

[0114] (1) Variance analysis. Combining the calculated values of the pipeline transportation resistance loss of ultra-fine tailings slurry and the orthogonal experimental table, the sensitivity of the mass concentration, ash-sand ratio, and slurry temperature to the pipeline transportation resistance was analyzed, and a result table of the variance analysis of the pipeline transportation resistance of ultra-fine tailings slurry was obtained, as shown in Table 4.

[0115] Table 4 Results of variance analysis of pipeline transportation resistance of ultra-fine tailings slurry

[0116]

[0117] As can be seen from Table 4, in the results of the analysis of variance, the F value of the fitting model is 101.71 > 1, and the P value < 0.0001, which proves that the fitting result is significant. Moreover, both the correlation coefficient and the adjusted correlation coefficient of the fitting model remain at a relatively high value, indicating that the model has high precision. The lack-of-fit term F = 0.0651 < 1, and the P value is 0.3471 > 0.05, indicating that the lack-of-fit term is not significant, and the results of the response surface analysis are reliable and reasonable. The coefficient of variation CV and the signal-to-noise ratio Adequate precision can reflect the authenticity of the test results and the reliability of the model. Generally speaking, the smaller the coefficient of variation, the more authentic the test results, and the higher the signal-to-noise ratio, the higher the reliability of the model. In Table 4, the coefficient of variation CV is 3.65%, and the signal-to-noise ratio Adequate precision is 33.44, further indicating that the test results are real and the model is significant.

[0118] Regarding the significance of factors, when the P value is less than 0.05 and the F value is higher than 1, it indicates that the factor has a significant impact on the response value. Therefore, from Table 4, it can be obtained that the mass concentration, the ratio of ash to sand, and the slurry temperature are all key factors affecting the pipeline transportation resistance of ultra-fine tailings slurry, with relatively high significance. In the interaction terms, the interaction between the mass concentration and the ratio of ash to sand, and the interaction between the mass concentration and the slurry temperature are not significant, while the interaction between the ratio of ash to sand and the slurry temperature is significant.

[0119] (2) Construct a multiple regression equation

[0120] Based on the results of the orthogonal experiment and the response surface analysis, a multiple regression analysis equation for the three variables of mass concentration, ratio of ash to sand, and slurry temperature and the pipeline transportation resistance of ultra-fine tailings slurry is obtained, as shown in Equation (1).

[0121]

[0122] In the formula, iu is the pipeline transportation resistance of ultra-fine tailings slurry, Pa·m -1 ; A is the mass concentration, %; B is the ratio of ash to sand; C is the slurry temperature, °C.

[0123] Interaction analysis. To further analyze the influence weights of the mass concentration, the ratio of ash to sand, and the slurry temperature on the pipeline transportation resistance of ultra-fine tailings slurry, based on the results of the response surface experiment, 3D surface plots of the interaction effects of different test variables on the pipeline transportation resistance of ultra-fine tailings slurry are drawn, including the interaction effects between the ratio of ash to sand and the mass concentration, between the slurry temperature and the mass concentration, and between the slurry temperature and the ratio of ash to sand on the pipeline transportation resistance. As Figure 3 --5 shown.

[0124] Figure 3It can be seen that, compared with the ash-sand ratio, the change trend of the pipeline transportation resistance caused by the increase of the mass concentration from 66% to 70% is more significant. When the ash-sand ratio is a certain value, the change trend of the pipeline transportation resistance caused by the change of the mass concentration is approximately the same. Similarly, when the mass concentration is a certain value, the change range of the pipeline transportation resistance caused by the change of the ash-sand ratio is relatively small. Therefore, the interaction between the two is not significant. Figure 4 It shows that the interaction trend between the slurry temperature and the mass concentration is similar to that between the ash-sand ratio and the mass concentration, both from the perspective of the change range of the pipeline transportation resistance caused by the change of the mass concentration. The contour lines between the slurry temperature and the mass concentration are approximately parallel. Combining the P-value of the interaction term between the two in the variance analysis is 0.0645 > 0.05, so the interaction between the two is also not significant. Through Figure 5 It can be seen that the interaction between the slurry temperature and the ash-sand ratio is significant. This is because on the projection diagram, the contour lines of the two are parabolic, indicating that when fixing one variable and changing the level value of the other variable, the change trend of the pipeline transportation resistance is different. At the same time, combining the P-value of the interaction term between the two in the variance table is 0.0387 < 0.05. Therefore, among the above three interaction terms, only the interaction between the slurry temperature and the ash-sand ratio is significant. In addition, by comprehensively comparing the P-values and F-values of the three single factors, their sensitivity order is mass concentration > ash-sand ratio ≈ slurry temperature.

[0125] The third step is to construct a calculation model for the pipeline transportation resistance of ultra-fine tailings slurry under the influence of multiple factors.

[0126] (1) Classical pipeline transportation resistance calculation model.

[0127] Ultra-fine tailings slurry belongs to plastic fluid, and the classical Bingham plastic fluid model can better describe the flow characteristics of non-Newtonian slurry. In a circular pipeline, the pipeline transportation resistance loss of Bingham fluid can be expressed by Equation (1).

[0128]

[0129] In the formula, i u is the pipeline transportation resistance of ultra-fine tailings slurry, Pa·m -1 ; τ0 is the initial yield stress of ultra-fine tailings slurry, Pa; τ u is the shear stress of ultra-fine tailings slurry, Pa; μ u is the plastic viscosity of ultra-fine tailings slurry, Pa·s; is the shear rate of ultra-fine tailings slurry, s -1 . ΔP is the pressure drop in the pipeline, Pa; L is the total distance of slurry flow, m; D is the pipeline diameter, mm; ρ is the slurry density, kg·m -3 ; V is the average slurry flow velocity, m·s -1 , and the rest of the symbols are the same as above.

[0130] (2) Build a new model for calculating pipeline transportation resistance.

[0131] In the model (1), the variable parameters are usually set as constants, and the complex rheological properties of the slurry, such as the influence of mass concentration, ash-sand ratio, and temperature on yield stress and plastic viscosity, are not fully considered. Therefore, based on the model (1), combined with the actual characteristics of the slurry, a more applicable pipeline transportation resistance loss model is derived.

[0132] 1) Experimental studies have shown that there are exponential and proportional relationships between yield stress and plastic viscosity and the mass concentration, ash-sand ratio, and slurry temperature of ultra-fine tailings slurry, and the two can be expressed by the following formulas (2) and (3).

[0133]

[0134] In the formula, C m is the mass concentration of ultra-fine tailings slurry, %; R cs is the ash-sand ratio; a1, b1, c1, d1, a2, b2, c2, d2 are all undetermined coefficients, and the rest of the symbols are the same as above.

[0135] 2) Further optimize that the density of the slurry is calculated by weighting the solid-phase particle density and water density according to the mass concentration, as shown in formula (4).

[0136] ρ = ρ w + C m ·(ρ s - ρ w ) (4)

[0137] In the formula, ρ w is the density of water, kg·m -3 ; ρ s is the solid-phase particle density kg·m -3 , and the rest of the symbols are the same as above. Substitute the corrected yield stress, plastic viscosity, and density into the Bingham fluid pipeline transportation resistance model (1) to obtain a new optimized model for the pipeline transportation resistance of the slurry considering mass concentration, ash-sand ratio, and slurry temperature, as shown in formula (5)

[0138]

[0139] (3) Calculation and analysis of model parameters.

[0140] To solve the undetermined parameters in the pipeline transportation resistance calculation model, take the logarithm of formulas (2) and (3), and we can get

[0141] ln(τ0) = ln(a1) + b1ln(C m ) + c1ln(R cs ) - d1T (6)

[0142] ln(μu ) = ln(a2) + b2ln(C m ) + c2ln(R cs ) - d2T (7)

[0143] Let ln(a1) = A1, ln(a2) = A2, and substitute them into Equation (6) and Equation (7) respectively, we can get

[0144] ln(τ0) = A1 + b1ln(C m ) + c1ln(R cs ) - d1T (8)

[0145] ln(μ u ) = A2 + b2ln(C m ) + c2ln(R cs ) - d2T (9)

[0146] To improve the calculation efficiency and simplify the calculation difficulty, Equation (8) and (9) are constructed into a linear equation system

[0147]

[0148] According to the test results, a table of the plastic viscosity and yield stress of ultra-fine tailings slurry under different parameter combinations is constructed, and the results are shown in Table 5.

[0149] Table 5 Plastic viscosity and yield stress of ultra-fine tailings slurry under different test parameters

[0150]

[0151]

[0152] Combined with the test results in Table 5, the least squares method is used to construct an analysis matrix and calculate the undetermined coefficients.

[0153]

[0154] Among them, β = [A1, b1, c1, d1]T is the undetermined coefficient, and ε is the residual vector.

[0155] Similarly, the undetermined coefficient matrix related to the plastic viscosity is obtained. After the solution is completed, the specific values of the undetermined coefficients can be obtained. After calculation, the solution values of the undetermined parameters in the pipeline transportation resistance calculation model are obtained, as shown in Table 6 below. Table 6 and Equation (5) together constitute the calculation model of the pipeline transportation resistance loss of ultra-fine tailings slurry.

[0156] Table 6 Solution values of undetermined parameters in the pipeline transportation resistance calculation model

[0157]

[0158] Step 4: Model applicability verification.

[0159] To verify the reliability and applicability of the model, taking the mass concentration, sand-to-ash ratio, and slurry temperature as variables, conduct rheological tests on ultra-fine tailings slurry under different test variables to obtain rheological parameters. Subsequently, use COMSOL Multiphysics for numerical simulation research (the values of pipe diameter and initial flow rate are kept the same as those in the above simulation test), obtain the pressure change values at the inlet and outlet of the pipeline to calculate the pipeline transportation resistance loss, and then calculate the predicted value of the resistance loss through the constructed pipeline transportation resistance loss calculation model. Compare and analyze the error between the two, and calculate the error rate of the pipeline transportation resistance using Equation (14); draw a comparison chart of the numerical simulation test value and the model calculation value of the pipeline transportation resistance to further verify the reliability and applicability of the newly constructed model.

[0160]

[0161] In the formula, α is the error rate between the numerical simulation test value and the model calculation value, %; i u-exp is the pipeline transportation resistance value obtained by the numerical simulation method, Pa·m -1 ; i u-pred is the pipeline transportation resistance value obtained by model calculation, Pa·m -1 .

[0162] Table 7 Numerical simulation test parameters

[0163]

[0164] Table 7 shows the simulation test parameters. Figure 6 is the comparison and verification chart of the test resistance loss value and the predicted resistance loss value. Figure 7 is the difference in pipeline transportation resistance between the numerical simulation test and the model calculation. Figure 8 is the error rate of the pipeline transportation resistance between the numerical simulation test and the model calculation in the embodiment of the present invention. Combining Figure 6 with Figure 7 It can be seen that taking the mass concentration, sand-to-ash ratio, and slurry temperature as test variables, the difference between the pipeline transportation resistance loss value of ultra-fine tailings slurry obtained by the numerical simulation method and the value calculated by the established pipeline transportation resistance calculation model is small. And through Figure 8 it can be seen that the absolute value of the calculation error between the two is between 1.81% and 9.98%, indicating that the present invention has reliability and applicability.

[0165] Based on the calculation model of the resistance loss in the circular pipeline transportation of Bingham fluid, this invention fully considers the complex rheological properties of the slurry, such as the influence of mass concentration, ash-sand ratio, and temperature on the yield stress and plastic viscosity. Combining with the actual properties of the slurry, a more applicable pipeline transportation resistance loss model is derived. Taking mass concentration, ash-sand ratio, and slurry temperature as variables, rheological tests of ultra-fine tailings slurry are carried out under different test variables to obtain rheological parameters. COMSOL Multiphysics is used for numerical simulation to obtain the pressure change values at the inlet and outlet of the pipeline to calculate the pipeline transportation resistance loss. The absolute value of the calculation error between the two is between 1.81% and 9.98%, further verifying the reliability and applicability of the newly constructed model. It can provide theoretical guiding value for the pipeline transportation of ultra-fine tailings, further reduce the energy consumption of mine filling pipeline transportation, reduce pipeline transportation accidents, and improve the filling efficiency.

Claims

1. A method for constructing a calculation model for pipeline transportation resistance of ultrafine tailings slurry, characterized in that The following steps are involved: The first step is to conduct response surface test design. First, the physical and chemical properties of the test tailings and cement are analyzed. Then, the orthogonal test of the pipeline resistance of ultrafine tailings slurry is carried out. Finally, the numerical simulation calculation of pipeline resistance is carried out to obtain the result table of ultrafine tailings slurry pressure drop and pipeline resistance for different test variables. The second step is the test results and analysis. A variance analysis is performed. Based on the results of orthogonal test and response surface analysis, the multiple regression analysis equations of mass concentration, lime-sand ratio and slurry temperature and the pipeline transportation resistance of ultrafine tailings slurry are obtained to conduct interaction analysis. The third step is to construct a calculation model for the pipeline transportation resistance of ultrafine tailings slurry under the influence of multiple factors; The fourth step is to verify the applicability of the model and draw a comparison chart between the numerical simulation test values ​​of pipeline resistance and the model calculation values ​​to further verify the reliability and applicability of the newly constructed model.

2. The method for constructing a superfine tailings slurry pipeline transportation resistance calculation model according to claim 1, characterized in that: In the first step, the specific steps are as follows: (1) First, the physical and chemical properties of the test tailings and cement were analyzed, including particle size composition and oxide composition analysis. The particle size composition of the tailings and cement was tested by a laser particle size analyzer, and the oxide composition of the tailings was tested by an X-ray fluorescence spectrometer; (2) Orthogonal test design of pipeline transport resistance of ultrafine tailings slurry, with mass concentration, lime-sand ratio and slurry temperature as test variables, using Design Expert software and central composite design to establish an orthogonal test table; (3) Numerical simulation calculation of pipeline transportation resistance, 1) The rheological properties of the ultrafine tailings filling slurry under different test variables were tested using a rotational rheometer to obtain the plastic viscosity and yield stress; 2) Based on the existing filling plan of the mine, COMSOL Multiphysics numerical simulation software was used to establish a slurry with a diameter of 140 mm and an average flow rate of about 2.5 m·s -1 , the L-tube model with a filling factor of 5, and the ultra-fine mesh is used to ensure the accuracy of the test results and the relative calculation tolerance is set to 10 -5 , combined with the orthogonal test table, the pressure drop between the pipeline inlet and outlet is calculated, the resistance loss along the way is calculated, and the result table of ultrafine tailings slurry pressure drop and pipeline transportation resistance for different test variables is obtained.

3. The method for constructing a superfine tailings slurry pipeline transportation resistance calculation model according to claim 2, characterized in that: In the step (2), the test variables of the orthogonal test of the pipeline transport resistance of the ultrafine tailings slurry are mass concentration of 66%-70%, lime-sand ratio of 1:4-1:8, and slurry temperature of 30°C-50°C.

4. The method for constructing a superfine tailings slurry pipeline transportation resistance calculation model according to claim 1, characterized in that: In the second step, the specific steps are as follows: (1) Variance analysis: Combined with the calculated value of pipeline transportation resistance loss of ultra-fine tailings slurry and the orthogonal test table, the sensitivity of mass concentration, lime-sand ratio and slurry temperature to pipeline transportation resistance is analyzed, and the variance analysis result table of pipeline transportation resistance of ultra-fine tailings slurry is obtained to analyze and judge the reliability and rationality of the response surface analysis results; (2) Construct a multiple regression analysis equation. Based on the results of orthogonal test and response surface analysis, obtain the multiple regression analysis equation of mass concentration, ash-sand ratio and slurry temperature and the pipeline transportation resistance of ultrafine tailings slurry, as shown in formula (1). In the formula, i u is the pipe transportation resistance of ultrafine tailings slurry, Pa·m -1 ; A is mass concentration, %; B is lime-sand ratio; C is slurry temperature, ℃. (3) Interaction analysis: In order to further analyze the influence weights of mass concentration, ash-sand ratio and slurry temperature on the pipeline transportation resistance of ultrafine tailings slurry, a 3D surface diagram of the interaction of different experimental variables on the pipeline transportation resistance of ultrafine tailings slurry was drawn based on the response surface test results, including the interaction between ash-sand ratio and mass concentration, slurry temperature and mass concentration, and slurry temperature and ash-sand ratio on the pipeline transportation resistance.

5. The method for constructing a superfine tailings slurry pipeline transportation resistance calculation model according to claim 1, characterized in that: In the third step, the specific steps are as follows: (1) The yield stress and plastic viscosity have an exponential and proportional relationship with the mass concentration of ultrafine tailings slurry, the lime-sand ratio and the slurry temperature. The two can be expressed by the following equations (2) and (3): In the formula, C m is the mass concentration of ultrafine tailings slurry, %; R cs is the lime-sand ratio; a1, b1, c1, d1, a2, b2, c2 and d2 are all unknown coefficients, and the other symbols are the same as above. (2) The density of the slurry is further optimized by weighting the solid particle density and water density according to the mass concentration, as shown in formula (4): p=p w +C m ·(r s -r w ) (4) In the formula, ρ w is the density of water, kg·m -3 ρ s is the solid particle density kg·m -3 , the other symbols are the same as above, the modified yield stress, plastic viscosity and density are introduced into the Bingham fluid pipeline resistance model, and a new slurry pipeline resistance optimization model considering mass concentration, lime-sand ratio and slurry temperature is obtained, as shown in formula (5), (3) Model parameter calculation and analysis In order to solve the unknown parameters in the pipeline resistance calculation model, equations (2) and (3) are logarithmized to obtain ln(τ0)=ln(a1)+b1ln(C m )+c1ln(R cs )-d1T (6) ln(μ u )=ln(a2)+b2ln(C m )+c2ln(R cs )-d2T (7) Let ln(a1) = A1, ln(a2) = A2, and substitute them into equation (6) and equation (7), we can get ln(τ0)=A1+b1ln(C m )+c1ln(R cs )-d1T (8) in(μ u )=A2+b2ln(C m )+c2ln(R cs )-d2T (9) In order to improve the computational efficiency and simplify the computational difficulty, equations (8) and (9) are constructed as a linear equation system: According to the test results, the table of plastic viscosity and yield stress of ultrafine tailings slurry under different parameter combinations was constructed. Combined with the results of the table, the least squares method was used to construct the analysis matrix and calculate the unknown coefficients. Among them, β=[A1,b1,c1,d1]T is the unknown coefficient, ε is the residual vector, Similarly, the matrix of undetermined coefficients related to plastic viscosity is obtained. After the solution is completed, the specific values ​​of the undetermined coefficients can be obtained. After calculation, the solution values ​​of the undetermined parameters in the pipeline transportation resistance calculation model are obtained. This value and formula (5) together constitute the calculation model of the pipeline transportation resistance loss of ultrafine tailings slurry.

6. The method for constructing a superfine tailings slurry pipeline transportation resistance calculation model according to claim 1, characterized in that: In the fourth step, with mass concentration, ash-sand ratio and slurry temperature as variables, rheological tests of ultrafine tailings slurry under different test variables are carried out to obtain rheological parameters, and then numerical simulation research is carried out using COMSOL Multiphysics, in which the values ​​of pipe diameter and initial flow velocity are kept consistent with the above simulation test, and the pressure change value at the pipeline inlet and outlet is obtained to calculate the pipeline resistance loss, and then the resistance loss prediction value is calculated by the constructed pipeline resistance loss calculation model, and the error between the two is compared and analyzed, and the error rate of pipeline resistance is calculated using formula (14); a comparison chart of the pipeline resistance numerical simulation test value and the model calculation value is drawn to further verify the reliability and applicability of the constructed new model. Where α is the error rate between the numerical simulation test value and the model calculation value, %; i u-exp is the pipeline resistance value obtained by numerical simulation method, Pa·m -1 ; i u-pred is the pipeline resistance value calculated by the model, Pa·m -1 .

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