Pipe transportation initial stage resistance calculation model based on waste stone tailing paste thixotropy

Abstract

The invention discloses a pipe transportation initial stage resistance calculation model based on waste stone tailing paste thixotropy, and belongs to the technical field of paste filling. According to the method, a stress relaxation test is carried out on the waste stone tailing paste, the test phenomenon and rule are analyzed, the time effect of rheological parameters of the waste stone tailing paste is analyzed, and a yield stress thixotropic model and a plastic viscosity thixotropic model of the waste stone tailing paste are constructed; and establishing a pipe transportation initial stage resistance calculation model based on the thixotropy of the waste stone tailing paste. According to the method, the time effect of the rheological parameters of the waste stone and tailing paste is illuminated, the constructed pipe transportation initial stage resistance calculation model based on the thixotropy of the waste stone and tailing paste has great significance for the arrangement and maintenance of mine filling pipelines, and the pipe transportation resistance under the time effect is accurately calculated to lay a solid foundation for the development of accurate filling; the method has important theoretical research significance and high popularization and application value.

Description

Technical Field

[0001] The invention discloses a resistance calculation model for the initial stage of pipeline transportation based on the thixotropy of waste rock tailings paste, and belongs to the technical field of paste filling. Background Art

[0002] The paste filling technology for solid waste in mines is the main supporting technology for green mining, among which pipeline transportation technology is the core of paste filling and is crucial to mine production. The resistance characteristics of paste pipeline transportation are an important part of paste filling. The size of the paste pipeline transportation resistance directly determines whether the layout of the mine filling pipeline is reasonable, which is related to the choice of mine filling pipeline transportation method (gravity or pumping), affects the selection of pipeline transportation equipment, and even the cost of mine pipeline transportation. The smooth progress of pipeline transportation is an important guarantee for the paste to achieve its target function underground.

[0003] The pipeline transportation of pastes belongs to the category of structural flow, but the stable plunger flow zone and shear flow zone in the structural flow are not formed immediately after entering the pipe, but after a period of time and a certain distance. This process is called the initial stage of paste pipeline transportation. Since the velocity at the wall is approximately 0, when the paste enters the pipeline, the fluid near the wall immediately slows down. Due to the viscosity effect, the fluid near the wall is delayed in expanding inward. According to the continuity equation of fluid mechanics, in the full pipe state, the cross-sectional fluid mass flux at any axial position remains unchanged. The slowing of the fluid velocity near the wall will cause the fluid in the center of the plunger flow zone to move faster, and eventually move along the flow direction to reach a fully developed state of flow. Therefore, the internal friction of the fluid in the initial section of the pipeline is greater than the internal friction of the fluid when it is fully expanded (such as Figure 2 shown).

[0004] Thixotropy is the main reason for this phenomenon; thixotropy is also called shaking, which refers to the property that when an object (such as paint or coating) is sheared, its viscosity decreases, and when the shear stops, its viscosity increases, or when it is sheared, its viscosity increases, and when the shear stops, its viscosity decreases. Thixotropy is a reversible sol phenomenon, which represents the dependence of fluid rheological parameters on time.

[0005] The initial stage of paste pipeline transportation is the most difficult stage in the entire pipeline transportation process of the paste. If the initial stage of pipeline transportation is overcome, then there will be no problem in the steady-state pipeline transportation process of the paste. However, most of the existing calculation models are aimed at the resistance characteristics of the paste in the steady-state pipeline transportation process, and there is a serious lack of research on the initial stage of pipeline transportation. In the initial stage of pipeline transportation, the waste rock tailings paste undergoes a dynamic evolution from a static state to a stable transportation state; in this process, the rheological properties of the paste show dependence on time; this dependence depends on the thixotropic properties of the rheological parameters of the paste; the present invention conducts a thixotropic experiment on the waste rock tailings paste, establishes a mathematical relationship between the rheological parameters of the waste rock tailings paste and time, and then obtains a resistance calculation model that takes into account the pipeline transportation time. This model can well reflect the resistance change characteristics of the paste in the initial stage of pipeline transportation, and has important guiding significance for the development of mine paste pipeline transportation technology. Summary of the invention

[0006] The object of the present invention is to provide a resistance calculation model for the initial stage of pipeline transportation based on the thixotropy of waste rock tailings paste, which specifically includes the following steps:

[0007] (1) Stress relaxation test of waste rock tailings paste to analyze the time effect of yield stress and plastic viscosity.

[0008] (2) A mathematical model of the yield stress thixotropy of waste rock tailings paste was established: This step is based on a large amount of experimental data. A time node is taken every 30 seconds before the equilibrium time of the stress relaxation curve, and regression analysis is performed to obtain the yield stress value at that moment. To construct a functional relationship to characterize the change law of yield stress over time, the following two conditions must be met:

[0009]

[0010] Where: τ 0(t＝0) ——yield stress when shear time is 0, Pa;

[0011] τ0——yield stress before thixotropy, Pa;

[0012] τ 0(t→∞) ——yield stress when shear time is infinite, Pa;

[0013] τ 0∞ ——Yield stress after thixotropy, Pa.

[0014] The exponential function model of yield stress-time is as follows:

[0015] τ 0t =(τ0-τ 0∞ )·exp(-m·t)+τ 0∞

[0016] Where: τ0t ——yield stress during thixotropic process, Pa;

[0017] τ0——yield stress before thixotropy, Pa;

[0018] τ 0∞ ——yield stress after thixotropy, Pa;

[0019] C v - volume concentration;

[0020] m——time parameter;

[0021] m is a time parameter. The larger its value, the shorter the thixotropic equilibrium time and the easier it is for the yield stress to tend to equilibrium. The value of m depends on the proportion of the paste. The proportion of the paste is mainly reflected in two aspects: volume concentration and aggregate packing density. Therefore, the solid filling rate of the paste can be used. To characterize the value of the time parameter m, the relationship between the solid filling rate and the time parameter m is as follows: Figure 7 As shown, there is a linear relationship between the time parameter m and the solid filling rate, so the relationship function between the time parameter and the paste solid filling rate can be constructed as:

[0022]

[0023] Where: C v - volume concentration;

[0024] - aggregate packing density;

[0025] c, d—Fitting parameters, time-dependent.

[0026] Therefore, a mathematical model of yield stress thixotropy of waste rock tailings paste can be established:

[0027]

[0028] The model calculation results are accurate, the effect is excellent, and the regression degree is high, such as Figure 6 shown.

[0029] The calculation formula of yield stress thixotropic equilibrium time is given:

[0030]

[0031] Where: ——yield stress thixotropic equilibrium time, s;

[0032] k——yield stress thixotropic equilibrium time accuracy parameter.

[0033] (3) Constructing a thixotropic model of the plastic viscosity of waste rock tailings paste: This step is based on a large amount of test data. A time node is taken every 30 seconds before the equilibrium time of the stress relaxation curve, and regression analysis is performed to obtain the plastic viscosity value at that moment. The relationship between plastic viscosity and shear time is as follows: Figure 8 As shown in the figure; the plastic viscosity generally tends to decrease with the increase of time, but at the beginning of shear, there will be a period of increase. In the initial stage, the viscosity increases rapidly with the increase of shear time until it reaches the highest point, then gradually decreases, and finally tends to be stable; when the shear time gradually increases from zero, a certain starting deformation occurs inside the slurry to respond to the changes caused by the shear effect; this is mainly due to the hysteresis characteristics of the fluid viscosity formed by the extrusion internal friction formed by the combination of the viscous medium inside the slurry and the high concentration of coarse and fine particles; the higher the concentration, the more obvious the extrusion effect between the medium and aggregate particles, and the more prominent the viscosity tip pulse phenomenon. When the concentration is small to a certain extent, the viscosity tip pulse effect disappears, and the curve becomes a monotonically decreasing function.

[0034] According to the curve shape and change law, the change law of plastic viscosity with shear time can be expressed by Gaussian distribution function (normal distribution). According to the general form of Gaussian function, the viscosity-time evolution function can be constructed as follows:

[0035]

[0036] Where: η t ——Plastic viscosity during thixotropic process, Pa·s;

[0037] η max ——The maximum value of plastic viscosity during thixotropic process, Pa·s;

[0038] η ∞ ——Plastic viscosity after thixotropy, Pa·s;

[0039] t max ——The time when the plastic viscosity reaches the maximum value during the thixotropic process, s;

[0040] b——Plastic viscosity thixotropic equilibrium time parameter, which is the width of the Gaussian function and is used to measure the thixotropic time, s;

[0041] This model innovatively considers the tip pulse effect during plastic viscosity thixotropy, and more realistically reflects the time effect of plastic viscosity. The schematic diagram of the meaning of model parameters is shown in Fig. 9 As shown; regression analysis is performed on the test data, and the regression curve is shown Fig.10 As shown in the figure, the fitting degree is high and the model can well reflect the change law of plastic viscosity over time.

[0042] According to the 3σ rule of Gaussian distribution function, the thixotropic stabilization time of plastic viscosity can be estimated as:

[0043] t ∞(η) ≈t max +3b

[0044] Where: t ∞(η) ——Plastic viscosity thixotropic equilibrium time, s.

[0045] (4) A resistance calculation model for the initial stage of pipeline transportation based on the thixotropy of waste rock tailings paste was established: On the basis of constructing the thixotropy mathematical model of the yield stress of waste rock tailings paste and the thixotropy mathematical model of the plastic viscosity of waste rock tailings paste, the model was substituted into the Buckingham equation to obtain the resistance calculation model for the initial stage of pipeline transportation based on the thixotropy of waste rock tailings paste; the Buckingham equation is:

[0046]

[0047] Where: i——pipeline transportation resistance loss, Pa / m;

[0048] ΔP——pressure difference between the two ends of the pipeline, Pa;

[0049] L——pipeline length, m;

[0050] D——pipeline diameter, m;

[0051] v——pipeline speed, m / s;

[0052] τ0——yield stress, Pa;

[0053] η——plastic viscosity, Pa·s;

[0054] The resistance calculation model at the initial stage of pipeline transportation based on the thixotropy of waste rock tailings paste is:

[0055]

[0056] Beneficial effects of the present invention:

[0057] (1) The method described in the present invention fully considers the pipeline transportation time effect, and the pipeline transportation resistance calculation result can truly reflect the process of pipeline transportation from difficult to easy in the initial stage of pipeline transportation, making the pipeline design more accurate and having significant engineering significance.

[0058] (2) The stress relaxation test method used in the present invention can accurately consider the influence of time on the waste rock tailings paste. The constructed thixotropic model of rheological parameters of the waste rock tailings paste can accurately calculate the rheological parameters at different times, making the calculation of pipeline transportation resistance more accurate.

[0059] (3) The pipeline resistance calculated based on the method of the present invention is closer to engineering practice and more accurate than that calculated by traditional methods. The paste ratio designed based on the calculation results is more precise, which greatly reduces the occurrence of pipeline blockage accidents and improves filling efficiency, thus having significant engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 is a process flow chart of the present invention;

[0061] Figure 2 Schematic diagram of the initial stage of pipeline transportation;

[0062] Figure 3 Stress relaxation test loading method;

[0063] Figure 4 Stress relaxation test result curve;

[0064] Figure 5 Variation of yield stress with shear time;

[0065] Figure 6 Yield stress thixotropy model fitting results;

[0066] Figure 7 The variation law of time parameter m and the fitting curve;

[0067] Figure 8 Variation of plastic viscosity with shear time;

[0068] Fig. 9 Schematic diagram showing the meaning of parameters in the plastic viscosity thixotropy model;

[0069] Fig.10 Plastic viscosity thixotropy model fitting results;

[0070] Fig.11 Industrial verification of pipeline layout and location of pressure monitoring devices;

[0071] Fig.12 Calculated and monitored values.

[0072] Industrial Validation

[0073] The present invention is further described in detail below in conjunction with specific embodiments, but the protection scope of the present invention is not limited to the described contents.

[0074] Example 1

[0075] The resistance calculation model for the initial stage of pipeline transportation based on the thixotropy of waste rock tailings paste described in the present invention can take into account the unstable transportation process at the initial stage of pipeline transportation, making the calculation of pipeline transportation resistance more accurate. The specific implementation method is as follows:

[0076] (1) Background

[0077] A phosphate mine uses pipeline transportation to fill paste slurry, using waste rock-tailings coarse and fine aggregate mixed filling slurry. The company designed to use 78% weight concentration for transportation, and the proportion is shown in the following table:

[0078] Table 1 Ratio of filler slurry used in a phosphate mine

[0079]

[0080] (2) Stress relaxation test of waste rock tailings paste: A constant shear test was conducted on the waste rock tailings paste. The test loading method was as follows: Figure 3 As shown; This step takes into account the effect of shear time on the rheological parameters of the waste rock tailings paste. The test shear time is set to 1200s to ensure that the waste rock tailings paste can enter the thixotropic equilibrium period, and the shear rate is set to 30s -1 , 60s -1 , 90s - 1,120s -1 , regressing the yield stress and plastic viscosity at each moment.

[0081] (3) Regressing the parameters in the yield stress thixotropic model of the phosphate waste rock tailings paste: This step is based on a large amount of test data. A time node is taken every 30 seconds before the equilibrium time of the stress relaxation curve, and regression analysis is performed to obtain the yield stress value at that moment. Using τ 0t =(τ0-τ 0∞ )·exp(-m·t)+τ 0∞ Regress the test data and get τ0, τ 0∞ , the value of m. The regression results are shown in the following table:

[0082] Table 2 Thixotropic yield stress regression results

[0083] <![CDATA[Initial yield stress τ0 (Pa)]]> <![CDATA[Stable yield stress τ 0∞ (Pa)]]> Time parameter m 69.409 41.723 0.00683

[0084] (4) Regressing the parameters in the plastic viscosity thixotropic model of the phosphate waste rock tailings paste: This step is based on a large amount of test data. A time node is taken every 30 seconds before the equilibrium time of the stress relaxation curve, and regression analysis is performed to obtain the plastic viscosity value at that moment. Regress the test data and get η max , η ∞ , t max , the value of b.

[0085] Where: η t ——Plastic viscosity during thixotropic process, Pa·s;

[0086] η max——The maximum value of plastic viscosity during thixotropic process, Pa·s;

[0087] η ∞ ——Plastic viscosity after thixotropy, Pa·s;

[0088] t max ——The time when the plastic viscosity reaches the maximum value during the thixotropic process, s;

[0089] b——Plastic viscosity thixotropic equilibrium time parameter, which is the width of the Gaussian function and is used to measure the thixotropic time, s.

[0090] Table 3 Thixotropic plastic viscosity regression results

[0091]

[0092] (5) Substituting the values ​​of regression parameters into the established model for calculating the resistance at the initial stage of pipeline transportation based on the thixotropy of waste rock tailings paste: In this step, based on the established model for calculating the yield stress and plastic viscosity thixotropy of waste rock tailings paste, the values ​​of regression parameters are substituting into the established model for calculating the resistance at the initial stage of pipeline transportation based on the thixotropy of waste rock tailings paste to obtain the value of the pipeline transportation resistance at the initial stage of pipeline transportation.

[0093] The resistance calculation model at the initial stage of pipeline transportation based on the thixotropy of waste rock tailings paste is:

[0094]

[0095] In order to verify the accuracy and reliability of the model in the early stage of pipeline transportation, an industrial verification of waste rock tailings paste pipeline transportation was carried out in a phosphate mine in Yunnan; the locations of the filling pipeline and pressure monitoring device in this industrial test are as follows: Fig.11 As shown, a pressure detection probe is set every 100m on the pipeline to monitor the pressure; thus, the pipeline resistance and resistance stabilization time are monitored and compared with the model calculation results to verify the reliability of the model; the industrial test plan is shown in the following table:

[0096] Table 4 Industrial test plan

[0097]

[0098] The calculated values ​​and monitored values ​​are shown in Table 5:

[0099] Table 4 Calculated and monitored values ​​of pipeline transport resistance

[0100] Pipeline transportation time(s) Pipeline distance (m) Calculation results of pipeline transport resistance (Pa / m) Pipeline resistance monitoring results (Pa / m) error 67 100 3783.18 3894.25 2.94％ 133 200 3619.63 3775 4.29％ 200 300 3477.89 3602 3.57％ 267 400 3325.91 3497 5.14％ 333 500 3172.15 3311 4.38％ 400 600 3041.14 3253 6.97％ 467 700 2948.81 3005 1.91％ 533 800 2894.28 2927 1.13％ 600 900 2866.46 2905 1.34％ 667 1000 2853.52 2975 4.26％ 733 1100 2847.56 2921 2.58％ 800 1200 2844.60 2938 3.28％ 867 1300 2842.95 2949 3.73％ 933 1400 2841.97 2950 3.80％ 1000 1500 2841.35 2909 2.38％

[0101] For example Fig.12As shown, the average error between the calculated value and the monitored value of the model of the present invention is only 3.45%, which proves the accuracy and reliability of the model of the present invention; in actual measurement, the resistance balance time is 533s, the balance time of the model of the present invention is 500s, and the error is only 6.6%.

Claims

1. A resistance calculation model for the initial stage of pipeline transportation based on the thixotropy of waste rock tailings paste, characterized in that: The specific steps include: (1) Stress relaxation test of waste rock tailings paste to analyze the time effect of yield stress and plastic viscosity; (2) Constructing a thixotropic model of the yield stress of waste rock tailings paste: Based on the stress relaxation test data and the analysis of the thixotropic law of yield stress, a mathematical model of the thixotropic yield stress of waste rock tailings paste was constructed; (3) Constructing a thixotropic model of plastic viscosity of waste rock tailings paste: Based on the stress relaxation test data and the analysis of the thixotropic law of plastic viscosity, a thixotropic mathematical model of plastic viscosity of waste rock tailings paste was constructed; (4) A resistance calculation model for the initial stage of pipeline transportation based on the thixotropy of waste rock tailings paste was established: On the basis of constructing the thixotropic mathematical model of the yield stress of waste rock tailings paste and the thixotropic mathematical model of the plastic viscosity of waste rock tailings paste, the model was substituted into the Buckingham equation to obtain the resistance calculation model for the initial stage of pipeline transportation based on the thixotropy of waste rock tailings paste.

2. According to claim 1, a resistance calculation model for the initial stage of pipeline transportation based on the thixotropy of waste rock tailings paste, characterized in that: The mathematical model of yield stress thixotropy of waste rock tailings paste in step (2) is as follows: Where: τ 0t ——yield stress during thixotropic process, Pa; τ0——yield stress before thixotropy, Pa; τ 0∞ ——yield stress after thixotropy, Pa; C v - volume concentration; - aggregate packing density; t——time, s; c, d—fitting parameters, time-dependent; The calculation formula of yield stress thixotropic equilibrium time is given: Where: k——yield stress thixotropic equilibrium time accuracy parameter; m——time parameter, calculated as follows:

3. According to claim 1, a resistance calculation model for the initial stage of pipeline transportation based on the thixotropy of waste rock tailings paste, characterized in that: The thixotropic mathematical model of the plastic viscosity of the waste rock tailings paste in step (3) is as follows: Where: η t ——Plastic viscosity during thixotropic process, Pa·s; η max ——The maximum value of plastic viscosity during thixotropic process, Pa·s; η ∞ ——Plastic viscosity after thixotropy, Pa·s; t max ——The time when the plastic viscosity reaches the maximum value during the thixotropic process, s; b——Plastic viscosity thixotropic equilibrium time parameter; The thixotropic equilibrium time of plastic viscosity is as follows: t ∞(η) ≈t max +3b Where: t ∞(η) ——Plastic viscosity thixotropic equilibrium time, s.

4. According to claim 1, a resistance calculation model for the initial stage of pipeline transportation based on the thixotropy of waste rock tailings paste, characterized in that: The calculation model of the resistance in the initial stage of pipeline transportation based on the thixotropy of waste rock tailings paste in step (4) is as follows: The parameters in the formula are as described above.

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