Construction method of superfine tailing paste thixodynamic rheological model

Abstract

The invention discloses a construction method of a thixodynamic rheological model of superfine tailing paste, and belongs to the technical field of metal mine paste filling, the method comprises the following steps: firstly, constructing a structural kinetic equation that the internal structural coefficient of the superfine tailing paste dynamically evolves along with the shearing rate and the shearing time; secondly, constructing a state equation for associating the structure coefficient with the macroscopic rheological parameters of the paste; finally, the equations are coupled, a thixodynamic rheological model containing seven parameters representing the dynamic damage and recovery process of the internal structure of the paste is obtained, and the model parameters can be calibrated by fitting a paste thixotropic rheological characteristic curve. The applicability of the model is verified under different conditions, and a time-varying paste pipeline conveying resistance calculation model is further established. The method effectively solves the problem that the traditional rheological model is difficult to describe the thixotropic rheological characteristics of the paste, and the constructed model provides theoretical basis and data support for optimizing pipeline transportation design and reducing the energy consumption of a filling system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of metal ore paste filling, and particularly relates to a method for constructing a rheological model of thixotropic dynamics of superfine tailings paste. BACKGROUND

[0002] As a safe, green and efficient mining method, paste filling technology has been widely used in coal mines, metal mines and other mining industries. This technology can not only dispose of industrial solid waste such as tailings, but also effectively support underground stope, thereby solving the problems of waste disposal and stope stability at the same time, which meets the goal of sustainable development. In recent years, with the exhaustion of high-grade mineral resources, major mines have turned to mining low-grade ores, which leads to more fine grinding in the beneficiation process, thereby producing a large amount of superfine tailings. Such superfine tailings usually have the characteristics of high content of superfine particles, large specific surface area, and strong adsorption capacity of cement and free water. These physical properties make the superfine tailings easily self-flocculate after mixing with cement and water, forming a complex and interconnected flocculation network structure in the slurry, which makes the paste exhibit a complex thixotropic rheological property. Thixotropy refers to the reversible destruction of the internal structure of the paste when it is subjected to shear, which is manifested in the macroscopic reduction of the rheological parameters of yield stress and plastic viscosity. When the shear action stops, the internal structure gradually recovers under the action of mutual attraction between particles, and the rheological parameters also rise to the level before the shear action, which is a time-dependent rheological property that is crucial for the pipeline transportation behavior of the paste.

[0003] In the prior art, in order to describe the rheological properties of the paste, traditional rheological models such as Bingham model, Herschel-Bulkley model, etc. are usually used. However, these traditional models have a fundamental problem: they all regard the rheological properties of the paste filling slurry as a non-thixotropic fluid independent of time. That is, it is assumed that the yield stress and plastic viscosity do not change with time under constant shear rate. This assumption is seriously inconsistent with the actual rheological behavior of superfine tailings paste which exhibits significant thixotropy. Therefore, these traditional models cannot capture and describe the dynamic evolution process of the macroscopic rheological parameters of the paste during pipeline transportation due to structural damage.

[0004] Due to the ignorance of the thixotropy of the paste, the prior art often only calculates the pipeline transportation resistance loss value based on the initial highest yield stress and plastic viscosity of the paste before being sheared and damaged when designing the pipeline transportation of the filling slurry. This will cause a serious overestimation of the pipeline transportation resistance value. For the filling system using pumping transportation, this means that higher specification pumping equipment needs to be selected, which directly increases the equipment investment and operating energy consumption; and for the filling system using gravity flow transportation, the overestimated resistance will cause the conservative selection of the pipeline slope, pipe diameter and other design parameters, which increases the difficulty and cost of engineering construction. Therefore, developing a new model capable of accurately describing the thixotropic rheological properties of ultra-fine tailings paste to realize accurate modeling of the pipeline transportation process of the time-varying paste is a technical problem to be solved in the field. SUMMARY

[0005] In view of the above shortcomings of the prior art, the present application proposes a method for constructing a thixotropic dynamic rheological model of ultra-fine tailings paste.

[0006] To achieve the above object, the technical scheme adopted by the present application is as follows: a method for constructing a thixotropic dynamic rheological model of ultra-fine tailings paste, comprising the following steps: S1, establishing a structure dynamic equation for describing the dynamic evolution of the internal structure coefficient of the ultra-fine tailings paste with shearing time and shearing rate, wherein the structure coefficient is used to quantitatively characterize the dynamic damage and recovery process of the internal flocculation network structure of the paste under the action of shearing; In order to quantitatively describe the dynamic evolution of the internal flocculation network structure of the ultra-fine tailings paste, i.e. the thixotropy, the present application first introduces a dimensionless structure coefficient (Structural coefficient, S ). This coefficient is used to represent the completeness of the internal structure of the paste, and its value range is set to 0 to 1. When S = 1, it represents that a completely developed and ideal flocculation network structure is formed inside the paste; when S = 0, it represents that the network structure is completely damaged under the action of strong shearing, and the particle structure inside the paste is in an extreme dispersion state.

[0007] As a preferred embodiment of the present application, the thixotropy of the ultra-fine tailings paste is the result of the joint action of two kinds of dynamic processes competing with each other under the action of shearing: structure damage: caused by the external applied shearing action, the flocculation network structure is disintegrated and dispersed into smaller flocculation structures; structure recovery: driven by the mutual attraction force (such as van der Waals force, electrostatic force) between particles, the damaged structure is re-flocculated and aggregated; Therefore, the structure coefficient S evolves with timet the rate of change of the structure (d S / d t ) can be expressed as the difference between the rate of structure recovery and the rate of structure damage.

[0008] Further, the rate of structure recovery is considered to be proportional to the difference between the ideal structure and the current structure, i.e. proportional to (S S max - S ), where S S max is the maximum structure coefficient, representing a fully developed ideal internal structure, which has a value of 1.

[0009] Further, the rate of structure damage is considered to be proportional to the difference between the current structure state and the limit damage state, i.e. proportional to (S S - S min ), where S S min is the minimum structure coefficient, representing a fully damaged limit dispersed state of the structure, which has a value of 0.

[0010] In addition, the rate of damage is further proportional to the applied shear rate .

[0011] The specific expression of the differential equation of structural dynamics proposed in the present application is as follows: (1) In the formula, S R is the structure recovery coefficient; b is the structure damage coefficient.

[0012] After substituting the two preferred values of S S max = 1 and S S min = 0, formula 1 is simplified as: The first-order explicit integral form of the structural dynamics equation is constructed as follows: In the formula, S S init is the initial state structure coefficient, S eq is the equilibrium state structure coefficient, k is the decay rate coefficient related to the structure recovery, damage and shear rate; Based on the first-order explicit integral form constructed, the way to solve the differential equation for accurate analytical solution is as follows: To solve the above differential equation 1, this invention defines two key boundary conditions: Initial boundary conditions: at the initial moment when shearing begins ( t =0), the paste slurry is in a static state, and due to factors such as Brownian motion, there is also slight structural damage and recovery within it. Therefore, its flocculation network is not in the most ideal fully developed state. Thus, the initial condition defined in this invention is: when... t When = 0, S = S init .in S init This is the initial structural coefficient, and its value is close to 1.

[0013] Equilibrium boundary conditions: at a constant shear rate Under the influence of shearing, after a certain shearing time, the structural destruction rate and structural recovery rate inside the paste reach a dynamic equilibrium. At this point, the structural coefficient no longer changes with time, i.e., d S / d t = 0. The structural coefficient at this point is defined as the equilibrium structural coefficient. S eq . d S / d t Substituting 0 into equation 1, we get: (2) Integrating differential equation 1 using the method of separation of variables, we obtain: After integration, we get: Initial boundary conditions t =0, S = S init Substituting into the above equation, the integral constant C can be solved as: Integral constant C Substituting back into the original equation and rearranging, the structure coefficients can finally be obtained. S With shearing time t and shear rate The explicit expression for the change, namely the integral expression of the first-order exact structural dynamics equation constructed in this invention, is as follows: (3) S2. Establish a state equation to correlate the structural coefficients with the macroscopic rheological parameters of the paste; The rheological behavior of ultrafine tailings paste is described using the Bingham model, namely: (4) wherein t is the shear stress, t is the yield stress, m is the plastic viscosity, is the shear rate.

[0014] In order to macroscopically characterize the thixotropic rheological behavior of the ultrafine tailings paste UCPB, its rheological parameters, i.e. the yield stress t 0 and the plastic viscosity m , are considered as time-dependent quantities, which are made a function of the internal structure coefficient of the paste. This link makes the shear stress t of the paste a function of the shear rate and of the shear time t. Thus, the present invention proposes a state equation to link the microscopic structure coefficient to the macroscopic Bingham model rheological parameters. The basic assumption is that as the internal structure decays from an initial, well-developed state S init to a disturbed, shearing-destroyed state S eq , the rheological parameters, yield stress and plastic viscosity, decrease and a linear relationship between the rheological parameters and the structure coefficient is assumed, i.e. the state equation constructed in the present invention, as shown in equation 5: (5) wherein t 0( t ) and m ( t ) are the instantaneous yield stress and the instantaneous plastic viscosity of the paste at a certain shear time, corresponding to the instantaneous structure state S ( t ); t init and m init are the initial (maximum) yield stress and the initial (maximum) plastic viscosity, corresponding to the initial structure state S init ; t eq and m eq are the equilibrium yield stress and the equilibrium plastic viscosity, corresponding to the equilibrium structure state S eq ; S ( t ) is the instantaneous structure state coefficient at a specific shear time, calculated from the structure dynamics equation 3 in step S1.

[0015] S3, coupling the structural dynamics equation of S1 with the state equation of S2, so as to obtain a thixotropic dynamics rheological model containing a group of undetermined parameters; In order to construct a comprehensive rheological model capable of completely and accurately describing the thixotropic behavior of the ultra-fine tailing paste, the structural dynamics equation (the result of step S1) describing the microstructure evolution is coupled with the state equation (the result of step S2) connecting the microstructure and the macrostructure, so as to obtain the thixotropic dynamics rheological model of the ultra-fine tailing paste.

[0016] The specific steps of the equation coupling are as follows: firstly, the explicit expression (formula 3) of the structural coefficient solved in step S1 is substituted into the state equation (formula 5) of step S2. Through the substitution, the specific function expressions of the instantaneous yield stress t 0( t ) and the instantaneous plastic viscosity m ( t ) varying with the shear time t and the shear rate are obtained. Then, the function expressions of the above obtained t 0( t ) and m ( t ) are further substituted into the Bingham rheological equation (formula 4), and finally, a complete thixotropic dynamics rheological model of the ultra-fine tailing paste capable of explicitly describing the shear stress t as the function of the shear time t and the shear rate is obtained. The final expression is shown in the following formula: (6) The above thixotropic dynamics rheological model is determined by a group of seven parameters with certain physical meanings. The seven parameters completely describe the dynamic destruction and recovery process of the internal structure of the ultra-fine tailing paste and the embodiment thereof on the macroscopic rheological characteristics. The seven undetermined parameters are respectively: the initial yield stress t init , the initial plastic viscosity m init , the equilibrium yield stress t eq , the equilibrium plastic viscosity m eq , the structure recovery coefficient R , the structure destruction coefficient b and the initial structure coefficient S init .

[0017] S4, the non-linear fitting is conducted on the paste thixotropic rheological property curve measured by the rheological test, so as to calibrate the set of undetermined parameters in the S3 model.

[0018] As the preferred embodiment of the present application, the specific step of the undetermined parameter calibration is that the ultra-fine tailings paste sample to be measured is placed in a rheometer, then a single constant shear rate ( ) is applied to the sample, and the shear stress ( t ) of the paste is continuously monitored with the shear time ( t ). Through the test, a key curve reflecting the thixotropic property of the paste, that is, the shear stress-shear time ( t - t ) thixotropic rheological property curve, can be obtained. The curve records the whole dynamic evolution process of the shear stress of the paste from the initial state to the equilibrium state under the specific constant shear rate.

[0019] The thixotropic dynamic rheological model (formula 6) finally obtained in the step S3 is taken as the fitting function, and all the seven parameters ( t init , m init , t eq , m eq , R , b , S init ) contained in the formula are taken as the undetermined fitting parameters. The model is used to conduct the non-linear fitting on a series of data points on the single shear stress-shear time curve measured in the previous constant shear rheological test. By minimizing the residual sum of squares between the theoretical model prediction value and the experimental data points, the seven parameters can be fitted and calibrated.

[0020] The beneficial effects of the present application are: (1) The present application fundamentally solves the technical problem that the traditional rheological model cannot describe the time-varying rheological property of the paste by innovatively introducing the structure coefficient to quantitatively characterize the evolution of the flocculation network inside the paste. The structure dynamic equation describing the evolution of the internal structure of the paste, the state equation connecting the microstructure and the macro rheological parameter, and the complete thixotropic dynamic rheological model containing seven parameters with clear physical meanings are systematically established, and the two are effectively coupled. The model not only provides a theoretical framework for understanding and analyzing the thixotropy of the paste, but also can accurately describe the thixotropy time-varying rheological behavior of the ultra-fine tailings paste.

[0021] (2) Based on the constructed thixotropic rheological model, this invention further establishes a time-varying calculation model for the friction resistance along the pipeline transport of paste, thereby solving the engineering application problem of the prior art relying on the initial highest rheological parameters for conservative estimation, which leads to a serious overestimation of the transport resistance. The model proposed in this invention can accurately calculate that as the shearing action continues during the paste pipeline transport process, the pipeline resistance will dynamically decrease from a high initial value to a significantly lower steady-state value. Therefore, in a pumping transport system, it is possible to avoid selecting pumping equipment with excessive specifications and power consumption, thereby significantly saving equipment investment and operating energy consumption; while in a gravity-flow transport system, a more optimized pipeline slope and diameter design can be adopted, reducing construction difficulty and engineering costs. In summary, by accurately modeling the thixotropic rheological characteristics exhibited by ultrafine tailings paste, this invention not only provides a theoretical basis for understanding the thixotropic properties of paste, but also improves the scientificity and economy of the design of the filling system, effectively reduces the filling cost, and is more conducive to the further promotion and development of filling mining methods. Attached Figure Description

[0022] Figure 1 This is a flowchart illustrating the method for constructing a thixotropic dynamics rheological model of ultrafine tailings paste according to the present invention. Figure 2 This is a schematic diagram of the dynamic reversible evolution process of the internal structure of the ultrafine tailings paste described in Example 1; Figure 3 This is a diagram showing the control shear rate mode rheological test procedure settings for the rheometer described in Example 1; Figure 4 The fitting results of the thixotropic rheological property curves described in Example 1 are as follows: (a) is the fitting result of the thixotropic rheological property curve of the ultrafine tailings paste under a mass concentration of 66%; (b) is the fitting result of the thixotropic rheological property curve of the ultrafine tailings paste under a mass concentration of 68%; and (c) is the fitting result of the thixotropic rheological property curve of the ultrafine tailings paste under a mass concentration of 70%. Figure 5 This is a comparison chart of the model calculation values ​​and actual monitoring values ​​for the industrial test of the paste pipeline transportation described in Example 1; Figure 6 This is a flowchart illustrating the application of the thixotropic dynamics rheological model described in Example 1 to the design of a practical filling pipeline. Detailed Implementation

[0023] To better illustrate the purpose, technical solution, and advantages of the present invention, the present invention will be further described below in conjunction with specific embodiments.

[0024] like Figure 1 As shown, a method for constructing a thixotropic dynamics rheological model of ultrafine tailings paste is described in detail below: S1, establishing a structure dynamics equation for describing dynamic evolution of the internal structure coefficient of the ultra-fine tailings paste with shearing time and shearing rate, wherein the structure coefficient is used for quantitatively characterizing a dynamic destruction and recovery process of the internal flocculation network structure of the paste under shearing action; As shown in Figure 2 , it is a schematic diagram of the dynamic reversible evolution process of the internal structure of the ultra-fine tailings paste described in the embodiment. As can be seen from the figure, in the particle dispersion stage, the ultra-fine tailings particles and cement particles are uniformly dispersed in water. Under the condition of static or low shearing, due to the interaction between the tailings particles and the cement particles, such as van der Waals force and electrostatic attraction, the dispersed particles begin to spontaneously flocculate and agglomerate, forming an initial flocculation network structure, and in this process, a part of free water is adsorbed and wrapped, forming non-flowing water. This process is the self-flocculation development stage, as shown in Figure 2 Process (a). With the passage of time or under the condition of continuous weak interaction, the network structure will further develop, and finally reach a mature flocculation structure stage with a certain shearing strength, as shown in Figure 2 Process (b).

[0025] When the paste is subjected to external shearing action, the input mechanical energy will destroy the mature flocculation network. First, larger flocculation bodies are broken into smaller agglomerates under the action of shearing force, as shown in Figure 2 Process (c); with the continuous shearing action, these agglomerates will be further dispersed into smaller flocculation bodies or single particles, and return to the initial particle dispersion state. This structure destruction process, in the macroscopic aspect, is manifested as the time-varying decrease of the paste yield stress and plastic viscosity, as shown in Figure 2 Process (d). Therefore, the thixotropy of the ultra-fine tailings paste is a dynamic reversible process containing two mutually competitive mechanisms of structure destruction and structure recovery.

[0026] In order to quantitatively describe the dynamic evolution process of the internal flocculation network structure of the ultra-fine tailings under external shearing action, i.e. the thixotropy, the present application first introduces a dimensionless structure coefficient ( S ) for characterizing the completeness of the internal structure of the paste, and the value range thereof is set to 0 to 1. The change rate (d S / dt) of the structure coefficient with time can be expressed as the difference between the structure recovery rate and the structure destruction rate. The structure recovery is driven by the mutual attraction between the particles, and the rate thereof is considered to be proportional to the difference between the ideal structure (maximum structure coefficient S max =1) and the current structure; while the structure destruction is caused by the external applied shearing, and the rate thereof is considered to be proportional to the difference between the current structure and the limit destruction state (minimum structure coefficient S min =0), and further proportional to the applied shearing rate is proportional.

[0027] In summary, the specific expression of the structural dynamics differential equation is as follows: (1) In the formula, R is the structure recovery coefficient; b is the structure damage coefficient.

[0028] In the formula, S max =1 and S min =0, formula 1 is simplified as: The first-order explicit integral form of the structural dynamics equation is as follows: In the formula, S init is the initial state structure coefficient, S eq is the equilibrium state structure coefficient, k is the decay rate coefficient related to the structure recovery, damage and shear rate; Based on the first-order explicit integral form, the accurate analytical solution of the differential equation is as follows: In order to solve the above differential equation (1), the application defines two key boundary conditions: Initial boundary condition: at the initial time (t=0) when the shear time starts, the paste slurry is in a static state, and there is also weak structure damage and recovery in the internal due to Brownian motion and other factors, so the flocculation network is not in the most ideal fully developed state. Therefore, the application defines the initial condition as: when t =0, t S = S init ; wherein S init is the initial structure coefficient, which is close to 1.

[0029] Equilibrium boundary condition: under the action of constant shear rate , when a certain shear time is reached, the structure damage rate and the structure recovery rate in the paste reach dynamic equilibrium, at this time the structure coefficient no longer changes with time, that is, dS / dt =0. At this time, the structure coefficient is defined as the equilibrium structure coefficient S eq . Substituting dS / dt =0 into formula (1) can obtain: (2) ​Integrating differential equation 1 by separation of variables, we get After integration, we get The initial boundary condition t =0, S = S init Substituting the above formula, the integral constant C is: Substituting the integral constant C back into the original equation and rearranging, the structural coefficient S can be finally solved to obtain the explicit expression that varies with shear time t and shear rate , i.e. the first-order accurate structural dynamics equation constructed in the present application: (3) S2, establishing a state equation for associating the structural coefficient with the macroscopic rheological parameters of the paste; The rheological behavior of the ultra-fine tailings paste is described by the Bingham model, i.e. (4) where t is the shear stress, t 0 is the yield stress, m is the plastic viscosity, is the shear rate.

[0030] In order to macroscopically characterize the thixotropic rheological behavior of the ultra-fine tailings paste UCPB, its rheological parameters, i.e. the yield stress t 0 and the plastic viscosity m , need to be regarded as quantities that vary with time, making them functions of the internal structural coefficient of the paste. This connection makes the shear stress t of the paste a function of the shear rate and the shear time t. Therefore, the present application proposes a state equation to connect the microscopic structural coefficient with the macroscopic Bingham model rheological parameters. The basic assumption is that as the internal structure decays from an initial, well-developed state (S0) S init to a disturbed, shear-damaged state (S1) S eq , the rheological parameters, the yield stress and the plastic viscosity, also decrease, and it is assumed that there is a linear relationship between the rheological parameters and the structural coefficient, i.e. the state equation constructed in the present application, as shown in formula 5: (5) In the formula, t 0( t )and m ( t These represent the instantaneous yield stress and instantaneous plastic viscosity of the paste at a certain shear time, corresponding to the instantaneous structural state. S ( t ); t init and m init These represent the initial (maximum) yield stress and the initial (maximum) plastic viscosity, respectively, corresponding to the initial structural state. S init ; t eq and m eq These represent the equilibrium yield stress and equilibrium plastic viscosity, respectively, corresponding to the equilibrium structural state. S eq ; S ( t ) represents the instantaneous structural state coefficient at a specific shear moment, which is calculated from structural dynamics equation 3 in step S1.

[0031] S3. Couple the structural dynamics equations described in S1 with the state equations described in S2 to obtain a thixotropic dynamics rheological model containing a set of undetermined parameters. To construct a comprehensive rheological model that can fully and accurately describe the thixotropic behavior of ultrafine tailings paste, this invention couples the structural dynamics equations describing the evolution of the microstructure (the result of step S1) with the state equations connecting the micro- and macro-level relationships (the result of step S2), thereby obtaining a thixotropic dynamics rheological model of ultrafine tailings paste.

[0032] The specific steps for equation coupling are as follows: First, substitute the explicit expression of the structural coefficients obtained in step S1 (Equation 3) into the state equation (Equation 5) in step S2. Through this substitution, the instantaneous yield stress can be obtained. t 0( t and instantaneous plastic viscosity m ( t With shearing time t and shear rate The specific functional expression for the evolution. Then, the above-obtained... t 0( t )and m ( t The functional expression of ) is further substituted into the Bingham rheological equation (Equation 4) to finally obtain a function that can clearly describe the shear stress. tas a function of the shearing time t and the shearing rate The complete rheological model of the thixotropic dynamics of the ultra-fine tailings paste. The final expression is shown in the following formula: (6) The thixotropic dynamics rheological model is determined by a set of seven parameters with physical meaning. The seven parameters completely describe the dynamic destruction and recovery process of the internal structure of the ultra-fine tailings paste, and the embodiment on the macro rheological characteristics. The seven undetermined parameters are respectively: the initial yield stress ( t init ), the initial plastic viscosity ( m init ), the equilibrium yield stress ( t eq ), the equilibrium plastic viscosity ( m eq ), the structure recovery coefficient ( R ), the structure destruction coefficient ( b ) and the initial structure coefficient ( S init ).

[0033] S4, the rheological characteristics curve of the paste thixotropy is nonlinearly fitted by the rheological test, so as to calibrate the set of undetermined parameters in the S3 model.

[0034] In this embodiment, the ultra-fine tailings collected from a mine are selected, and the particle content with a particle size less than 20 μm is 53.9%. The ultra-fine tailings, ordinary Portland cement (P.O 42.5) and tap water are mixed according to the predetermined ratio to prepare the ultra-fine tailings paste filling slurry. In order to ensure that the prepared filling slurry has good fluidity to meet the requirements of the pipeline conveying process, based on the slump test, the sand-cement ratio (the mass ratio of cement to tailings) is fixed at 1:4, and three mass concentrations which can meet the engineering fluidity requirements (the slump is in the range of 250-290 mm) are selected, which are 66%, 68% and 70%.

[0035] In this embodiment, the rheometer of RHEOCAD500 type is used to carry out the constant shearing rheological test on the three kinds of slurry with different concentration ratios. The test adopts the control shearing rate mode, and the rheological test program is set as shown in Figure 3 In order to further verify the universality and accuracy of the thixotropic dynamics rheological model proposed in the present application under different constant shearing rates, four constant shearing rate levels are set in this embodiment, which are 30 s -1 , 60 s -1 , 90 s -1 and 120 s -1The total duration of each constant shear test was 820 seconds, including a pre-shear process of 20 seconds to ensure that all samples had a consistent initial state before the test began.

[0036] Through the above rheological test, 12 shear stress-time (t) curves of the thixotropic rheological properties of the ultra-fine tailings paste under different conditions were obtained. t t The thixotropic rheological model (equation 6) constructed in step S3 was used as a fitting function to perform nonlinear fitting on the 12 curves, respectively, to determine the seven undetermined parameters of the model under different conditions. To evaluate the universality and accuracy of the model proposed in the present application, the fitting determination coefficients R 2 of the fitting results were further calculated, and the parameter fitting results and the corresponding R 2 values are shown in Table 1, and the nonlinear fitting results of each curve are shown in parts a, b and c of Figure 4 .

[0037] Table 1: Fitting results of the thixotropic rheological model of each group of paste As can be seen from Table 1, the R 2 values of all 12 groups are higher than 0.98, indicating that the thixotropic rheological model constructed in the present application can accurately describe and predict the thixotropic behavior of ultra-fine tailings paste under different conditions, and has good universality.

[0038] To further illustrate the practical engineering application value of the present application, based on the parameter fitting results of the thixotropic rheological model, a time-varying paste pipeline resistance calculation model was constructed, and it was compared and verified with the industrial test data.

[0039] For a structural fluid such as paste, the frictional resistance loss (Pa / m) in the pipeline can usually be calculated using the Buckingham equation: (7) In the equation, Δ P is the total pressure drop of the pipeline, L is the length of the pipeline, D is the inner diameter of the pipeline, is the pipe velocity; t 0 and m are the yield stress and plastic viscosity of the paste, respectively. In the prior art, the t 0 and m are usually considered as constant constants. This approach ignores the thixotropy of the paste, which can lead to a serious overestimation of the resistance. To solve this problem, the time-varying instantaneous yield stress​t 0( t ) and instantaneous plastic viscosity m ( t ) (Formula 5) to replace the constant in Formula 7 t 0 and m . Through this substitution, a time-varying paste pipe resistance calculation model capable of describing the dynamic evolution of the pipe resistance with the conveying time can be obtained, and the specific expression is as follows: (8) In the formula, the value of the instantaneous structure coefficient S ( t ) is calculated by Formula 3.

[0040] In order to evaluate the practical applicability of the time-varying paste pipe resistance calculation model proposed in the present application, the present embodiment takes the ultra-fine tailings paste filling material slurry with a mass concentration of 68% as an example to carry out industrial verification. The seven parameters of the thixotropic dynamics model of the slurry have been calibrated in advance in step S4. The industrial test is carried out in a filling pipeline with a total length of 1500 m and an inner diameter of 150 mm, and the slurry conveying speed is 1.7 m / s. Pressure monitoring probes are installed along the pipeline to monitor the pressure values at different positions in real time, so as to obtain the actual pipe resistance. The industrial test results are shown in Figure 5 , which compares the calculated pipe resistance value calculated by the model (Formula 8) of the present application with the actual monitoring value in the industrial field. As can be seen from the figure, the model calculation value is in good agreement with the measured data, and the average error between them is only 5.7%. As shown in the figure, the pipe resistance significantly decreases in the initial stage of conveying, and gradually stabilizes after about 420 seconds of flow. This fully confirms the thixotropic destruction behavior of the paste, and the final steady-state pipe resistance is only about 40% of the initial resistance.

[0041] The industrial test results prove that the thixotropic dynamics rheological model constructed by the present application and the time-varying pipe resistance calculation model can accurately predict the pipe conveying resistance value of the paste in actual engineering. Based on the present application, a more economical and reasonable steady-state resistance value can be used as the design basis for the design of the filling system, thereby avoiding overdesign of equipment and engineering and reducing energy consumption and filling cost.

[0042] Figure 6 The application steps of the thixotropic dynamics rheological model constructed by the present application systematically applied to the actual filling pipeline conveying design are shown in the figure, which includes the following steps: First, according to the specific filling engineering requirements, the material ratio of the ultra-fine tailings paste is determined, and the average conveying speed of the slurry in the pipeline is calculated according to the pipeline design flow and the pipe diameter, and one or more shear rates are determined as the test conditions.

[0043] For the paste formulation determined in step one, a constant shear rheological test is conducted under the corresponding shear rate conditions according to the method described in step S4 to obtain its shear stress-shear time (SST). t - t Thixotropic rheological property curves.

[0044] Using the thixotropic dynamics rheological model (Equation 6) constructed in this invention, the results obtained in step two are analyzed. t - t The curve is nonlinearly fitted to determine all seven parameters characterizing the thixotropic properties of the specific paste. t init , m init , t eq , m eq , R , b , S init ).

[0045] By substituting the seven parameters calibrated in step three into the structural dynamics equation (Equation 3) and state equation (Equation 5) of this invention, the internal structural coefficient of the paste when it flows in the pipe can be calculated. S ( t Instantaneous yield stress t 0( t and instantaneous plastic viscosity m ( t With delivery time t The evolutionary pattern.

[0046] The time-varying rheological parameters obtained in step four t 0( t )and m ( t Substituting these values ​​into Buckingham's equation (Equation 7), we can finally obtain an accurate prediction model of the frictional resistance of the ultrafine tailings paste filling slurry in the pipeline over time. This model can provide theoretical basis and data support for the optimized design, energy consumption assessment, and safe operation of the filling system.

[0047] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the essence and scope of the technical solutions of the present invention.

Claims

1. A method for constructing a rheological model of thixotropic dynamics of an ultrafine tailings paste, characterized by the fact that It comprises the following steps: S1, establishing a structure dynamics equation for describing the dynamic evolution of the internal structure coefficient of the ultra-fine tailings paste with the shearing time and the shearing rate, wherein the structure coefficient is used for quantitatively characterizing the dynamic destruction and recovery process of the internal flocculation network structure of the paste under the shearing action; The structure dynamics equation is obtained by integrating the structure dynamics differential equation through the separation of variables method; S2, establishing a state equation for associating the structure coefficient with the macroscopic rheological parameter of the paste; S3, coupling the structure dynamics equation in S1 with the state equation in S2, thereby obtaining a thixotropic dynamics rheological model containing a group of undetermined parameters; the set of pending parameters includes: initial yield stress τ init , initial plastic viscosity μ init , equilibrium yield stress τ eq , equilibrium plastic viscosity μ eq , structure recovery coefficient R , structure destruction coefficient b , and initial structure coefficient S init ; S4, completing the construction of the thixotropic dynamics rheological model of the ultra-fine tailings paste by performing nonlinear fitting on the thixotropic rheological characteristic curve of the paste measured through the rheological test, so as to calibrate the group of undetermined parameters in the S3 model.

2. The method according to claim 1, wherein, The structural dynamics equation in S1 relates the structural coefficients S Rate of change over time d S / d t Is expressed as the difference between a rate of structural recovery and a rate of structural damage.

3. The method according to claim 2, wherein, The structural recovery rate is related to a maximum structural coefficient. S max and current structural coefficients S The difference between them is proportional, and the structural failure rate is further related to the applied shear rate condition. Proportional; the rate of structural failure is related to a current structural coefficient. S and minimum structural coefficient S min The difference between them is proportional; the maximum structural coefficient S max A value of 1 represents a fully developed ideal internal structure; the minimum structure coefficient S min The value of 0 represents the ultimate dispersion state where the structure is completely destroyed.

4. The method according to claim 1, wherein, The structure dynamics equation in S1 is specifically expressed as a differential equation as shown in the following: wherein R is the structure repair coefficient, b is the structure damage coefficient, S max is the maximum structure coefficient, S is the structure coefficient, is the shear rate, S min is the minimum structure coefficient.

5. The method according to claim 1, wherein, S1 The first-order display integration form of the structural dynamics equation described in S1 is used to directly calculate the structural coefficients at any shear moment under the condition of constant shear rate t The expression is as follows: wherein S init is the initial state structure coefficient, S eq is the equilibrium state structure coefficient, k is the decay rate coefficient related to structure recovery, damage and shear rate.

6. The method according to claim 5, wherein, The expression of the attenuation rate coefficient related to the structure recovery, destruction and shearing rate is as follows: wherein R is a structure recovery coefficient, b is a structure destruction coefficient.

7. The method according to claim 1, wherein, The state equation in S2, the macro-rheological parameters, including yield stress and plastic viscosity, are expressed as linear functions of the structure coefficient S The specific expressions are as follows: wherein τ init and μ init are the initial yield stress and initial plastic viscosity, respectively; τ eq and μ eq are the equilibrium yield stress and initial plastic viscosity, respectively; S init is the initial structure coefficient, denotes the instantaneous structure state at a specific shear time t .

8. The method according to claim 1, wherein, The coupling step in the S3, specifically: the linear function of the structure coefficient S is substituted into the Bingham rheological equation, thereby obtaining the thixotropic dynamics rheological model.

9. The method according to claim 1, wherein, The rheological test in S4 is a constant shear rheological test, and the paste thixotropic rheological property curve is a shear stress-shear time curve measured under a single constant shear rate - τ t curve.​ 10. The method according to claim 1, wherein, The specific steps of the nonlinear fitting in S4 are as follows: the data points on the single shearing stress-shearing time curve are fitted by using the thixotropic dynamics rheological model, thereby calibrating all the parameters.

Images