Parameters evaluation in the process of solid phase pulp sedimentation in technological units of beneficiation plants

The aim of the research is the analysis and modeling of the process of sedimentation of the solid phase of the pulp in the technological units of processing plants to assess the density of particles of crushed ore. The paper analyzes domestic and foreign experience; methods of mathematical modeling were used, as well as methods of mathematical statistics and probability theory for processing the results of experiments. Scientific novelty consists in developing and substantiating a method for estimating the density of crushed ore particles in the process of their sedimentation directly in the process units of beneficiation plants. Practical value consists in developing a methodology for determining the characteristics of the enriched raw materials, which make it possible to form the degree of grinding necessary for the full disclosure of mineral formations. It was proposed to use the density of ore particles as an indicator of changes in the quality characteristics of the ore received for beneficiation, which is determined on the basis of measurements of the attenuation of volumetric ultrasonic waves and Lamb waves propagating in the pulp and the wall of the technological sump that is in contact with it. These measurements must be synchronized with the results of measurements of the pulp level in the sump during its working operation. The proposed method makes it possible to dynamically correct the parameters of the model of a closed ore grinding cycle, depending on the quality characteristics of the feedstock, and thereby form the conditions for the full disclosure of inclusions of the useful component in the product entering the magnetic separation or flotation.


Introduction
In the world practice of extraction and processing of minerals, geological reserves of ore with a high content of a valuable component are constantly declining [1,2].In this regard, mining and metallurgical enterprises are faced with the problem of rational use of ore with a high content of useful minerals and the development of technologies that allow efficient processing of low-grade ores [3].Many efforts are being made to rationally use poor ores to extend the life of developed deposits and achieve acceptable financial results, such as optimizing the cut-off grade of a useful component [4,5], mining production schedule optimization [6,7], improvement of technologies for enrichment of extracted raw materials [8,9].
In mineral processing, grinding is used to reduce the particle size of the ore in order to expose the valuable mineral component and recover it in subsequent processing operations such 1254 (2023) 012069 IOP Publishing doi:10.1088/1755-1315/1254/1/012069 2 as flotation or magnetic separation [10].The specific particle size of the crushed ore is the most important production indicator, which is a prerequisite for ensuring the quality of the resulting concentrate.The difficulty of achieving this condition is due to the fact that the process of grinding ore depends on a large number of operating parameters.In addition, the composition of iron ore is unstable and its quality deteriorates with a decrease in geological reserves [1].
Because of these difficulties, much attention has been paid to research into the grinding process [11].With the development of new intelligent modeling and control methods, many of them have been successfully implemented in the field of mineral processing.Recently, advanced methods based on predictive control with a model have been widely discussed [12,13], supervisory control with intelligent decision support system [14,15] and others to optimize the technological operations of ore beneficiation.
However, the grinding process is difficult to describe using mathematical models, since the real technological complex that implements it is a multiple input multiple output (MIMO) system with large inertia, nonlinearities, strong feedbacks, uncertainty, and the presence of a large number of perturbing factors [16].Moreover, due to the lack of high-quality information support, which makes it possible to obtain real-time data on the main variables of the grinding process, its optimal control cannot be realized even on the basis of the most advanced models [17].
Under these conditions, the combination of the advantages of various methods of analysis and modeling makes it possible to more accurately and comprehensively simulate the real operating conditions of technological units [18,19].
As the importance of process information grows [20,21], there is a growing need to develop methods that can automate the processing and interpretation of the received data.
In work [22] the importance of data quality assessment for the development of semi-rigorous and empirical models of the primary grinding scheme at the concentrator is emphasized.
The key task of information support for the effective management of ore grinding-classification processes is the operational measurement of its granulometric composition and determination of the degree of grinding required, depending on the physical-mechanical and chemicalmineralogical properties of the enriched raw material.A promising direction in the development of methods to solve this problem is the use of non-contact non-destructive testing tools based on ultrasonic, magnetometric and nuclear-physical measurements [23].
There are different mineralogical varieties of ore that enters the beneficiation process.These varieties differ in several characteristics of inclusions of a useful component (fineness of inclusions), which requires various degrees of grinding for its complete disclosure.As a marker of the changed qualitative composition of the crushed ore, it is proposed to use the density of particles of the solid phase of the pulp in the process of its deposition directly in the technological units of concentrating plants.This parameter is determined based on the results of measuring the attenuation of bulk ultrasonic waves and Lamb waves propagating in the iron ore pulp and metal platinum that is in contact with it, as well as the level of the pulp in the process tank in which it is located.

Results
In many technological units of the processing plant, during their operation, particles of crushed ore are deposited in the pulp, i.e. in certain volumes, sedimentation and thickening of the solid phase of the pulp occurs.When performing operations such as desliming, thickening and clarification, these processes are part of the technology used, while in intermediate process tanks, sumps, they are a factor that introduces a disturbing effect, the effect of which on the technological process, in this regard, should be taken into account.
On figure 1 it is shown a typical technological scheme of the process of grinding ore during its enrichment, which is widely used in processing plants [22].Initial ore and water are supplied to the mill, which operates in a closed cycle with hydrocyclones.Their flow is monitored by WT, FT sensors and controlled by closed local automatic control systems (ACS) based on proportionalintegral-derivative (PID) controllers.The ore crushed in the mill is pumped through the Mill Discharge Sump to the Cyclone Clusters.Hydrocyclone sands are returned to the mill, and the overflow through the Rougher Feed Tank is fed further to flotation or magnetic separation.The diagram provides for the control of the mill rotation speed and the control loops for the additional water flow to the process sump and the performance of the pump supplying the pulp to the hydrocyclones.The control strategy and its technical implementation by the grinding cycle can differ significantly at different concentrators, As shown above, the task of the ore grinding cycle is the complete disclosure of inclusions of a useful mineral in the original ore for its subsequent extraction in concentrators.It follows from the above diagram that the characteristics of the product entering the hydrocyclones have a decisive influence on the conditions for its classification by size and specific gravity (density) of ore particles, and, consequently, on the results of extracting the useful component in the enrichment apparatus.Thus, the conditions and characteristics of the process of sedimentation of the solid phase of the pulp in the Mill Discharge Sump (taking into account the characteristics and conditions of the formation of input and output products, as well as additional water consumption) directly affect the quality indicators of the entire ore grinding cycle.
In accordance with the main position of the kinematic theory of sedimentation [24,25] the relative velocity v r of particles of the solid phase and liquid depends only on their local concentration.In this case, the flux density function is determined by the expression: where u is the dimensionless volume fraction of solid particles.For calculations of the designs of sedimentation tanks (thickeners) of continuous action, the transport term q(t)u is used, where q(t) is the controlled flow rate of the mixture [26,27].This where t is time and x is depth.The function h(u) depends on the material properties of the studied suspension [25,28].However, in order to use (2) to simulate continuous deposition, it is necessary to explicitly model the feed and discharge mechanisms and provide the boundary conditions [29].
On figure 2 it is shown the main notation and variables used in the mathematical model of the sump in the technological chain of the closed grinding cycle [22,30,31].Q(t) denotes the flows at the corresponding points of the technological process, W is the content of the solid phase of the pulp, M (t) is the mass of material in the technological units at time t.In addition, when modeling the grinding cycle, the following designations were adopted: P (x, t) is the cumulative yield of solid particles whose size is less than x; Xi = ∂P (x,t) ∂x i ∆xfraction of the crushed material, the particle size of which belongs to the size interval i.Consider the movement of crushed material through the technological sump.We will assume: Material mass balance equations in the technological sump [22,30]: Equation for the balance of mass and fineness of the crushed material for the technological sump: or in discrete form: In this expression, X 1 , X 5 and X 4 characterize the dynamics of the granulometric composition of the loaded, internal and output products of the technological sump [30].
System (10) can be written in the following form: where I. In steady state: Taking into account the fact that the output flow of the sump Q 4 is determined by the performance of the hydrocyclone feed pump, we can write: In the table 1 it is shown the density and grindability for 7 types of ores, which are mined and processed from one of the deposits of the Krivoy Rog iron ore basin.In this case, the following designations of ore types are accepted [32]: 1 -magnetite hornfelses; 2 -silicate-carbonatemagnetite hornfelses; 3 -red-banded magnetite; 4 -semi-oxidized and oxidized hornfelses; 5silicate schists, barren hornfelses, and quartz; 6 -magnetite-silicate-carbonate (poor) hornfelses; 7 -hematite-magnetite hornfelses.The density of a particular type of ore with known values of the mass fraction of minerals is calculated by the formula [32]: where ρ m , ρ n -mineral and rock density; β m , α -mass fraction of the component in the mineral and ore; V m , V p -the volume of the mineral and rock in the ore.
Variations in the qualitative properties of enriched raw materials lead to changes in the results of grinding, opening of mineral formations and precipitation conditions (function h(u)) in the expression 2 particles of crushed ore in the technological sump.
The basic level of modern automatic process control systems (APCS) for grinding are local automatic control systems (ACS) of individual process variables (figure 1).At the same time, the models of regulated objects are approximated by an aperiodic link of the first order with sufficient accuracy for practical problems.Variations of the mineralogical varieties and characteristics of the ore received for enrichment lead to ambiguous results of the operation of the mill, technological sump and hydrocyclones, as well as their models, as objects of automatic control [32].On figure 3 it is shown the results of the influence of this ambiguity based on the analysis of expressions ( 10), ( 14), (15).To maintain the degree of grinding of the initial ore necessary for the full disclosure of the useful component, when h(u) changes, the amount of additional water supplied to the technological sump is corrected.
It is proposed to estimate the changes in h(u) based on the results of determining the density of particles of the solid phase of the pulp during its working settling in technological sumps of the grinding cycle.
Consider the process of movement of the pulp in the technological sump (figure 4).The Bernoulli equation for the flow of a viscous liquid (pulp) has the form:  where ρ -pulp density.
Let the conditions: In this case, expression 17 will take the form: where ξ T P = ξ T P (W, ρ T , η); η c = const; η -controlled size class of crushed material in the pulp flow; H = Z 1 − Z 2 ; W -volume fraction of the solid phase of the pulp; ρ T is the density of particles of the solid phase of the pulp. Then: Let us denote by Q the volume of incoming pulp per unit time.From the condition of equality of the volumes of incoming and outgoing pulp for the velocity V 2 , the relation: Taking into account (21), we have: Let the distance from the top edge of the sump to the pulp surface be determined by the signal S 3 , which is a linear function of H, i.e.: where A and B are constants.
Then, taking into account expression 23, S 3 can be represented as: where . Thus, the signal S 3 is a function of three variables W ,ρ T ,η.In accordance with the scheme shown in figure 4 according to the method described in the works [33], two more signals can be formed: S 2 -based on measurements of the attenuation of Lamb waves propagating in the wall of the technological sump in contact with the pulp and S 1 -based on measurements of the amplitude of high-frequency volumetric ultrasonic waves that have traveled a fixed distance in the pulp.Thus, the following system of functional dependencies can be formed: Let's pretend that ξ T P -friction loss coefficient, directly proportional to pulp viscosity, i.e.: where D is a constant value; η B is the viscosity of water.
In this case: If W = 0, then the pure water signal is equal to: where A 2 = DB .Let's find the signal ratio S3 and S 2 as well as S 1 and S 2 : The resulting expressions relate the content of the control size class of the crushed material with the density of the solid phase of the pulp.Thus, measuring the value, in accordance with the methodology described in the works [33], and the magnitude of the signal.S 3 , you can determine the value t.
In connection with the fundamental importance for solving the problem of controlling the parameters of the fineness of the processed raw materials [34], supplied for enrichment, on the basis of the results obtained, the procedure for correcting the flow rate of additional water supplied to the process sump and the effect of this control action on the content of class -74 µm in the hydrocyclone discharge was modeled.On figure 5 it is shown the results of modeling the mass balance and dynamics of the granulometric composition of the processed ore in a closed grinding cycle.The root-mean-square discrepancy between the model and experiment was 0.92%.

Conclusions and further research
Under the conditions of the changing quality of the initial ore and the state of the technological equipment, in order to ensure the optimal operation of the subsequent technological stagemagnetic separation or flotation, the mathematical model of a closed grinding cycle, including a mill, a sump and a hydrocyclone, must contain a circuit that corrects its parameters depending on current physical-mechanical and chemical-mineralogical characteristics of processed raw materials.
It is proposed to use the density of its particles as an indicator of changes in the quality characteristics of the ore received for beneficiation, which is determined on the basis of measurements of the attenuation of volumetric ultrasonic waves and Lamb waves propagating in the pulp and the wall of the technological sump that is in contact with it.These measurements must be synchronized with the results of measurements of the pulp level in the sump during its working operation.
The proposed method makes it possible to dynamically correct the parameters of the model of a closed ore grinding cycle, depending on the quality characteristics of the feedstock, and thereby form the conditions for the full disclosure of inclusions of the useful component in the product entering the magnetic separation or flotation.The root-mean-square discrepancy between the model and experiment was 0.92%.
The direction of further research should be the approbation of the proposed approach in relation to spiral classifiers and concentrators.

Figure 1 .
Figure 1.Technological scheme of the closed cycle of ore grinding [22].

Figure 2 .
Figure 2. Balance of ore flows and granulometric composition of processed ore in the technological sump.

Figure 3 .
Figure 3.The family of frequency characteristics of the object of treatment with variation of parameters in the model.

Figure 4 .
Figure 4. Scheme of measurements and movement of the pulp in the technological sump.

Figure 5 .
Figure 5.The results of modeling the mass balance and dynamics of the granulometric composition of the processed ore in a closed grinding cycle: a -input signal (consumption of additional water in the technological sump, c.u.); b -object output (class content -74 µm in the hydrocyclone drain, %); c is the output of the model (the content of the -74 µm class in the hydrocyclone drain, %); d -error signal, %.

Table 1 .
The results of the analysis of ores of various types.