2.1. Mechanism of Flocculation Action
The process of separation of solid particles suspended in a fluid by gravity is called sedimentation. Brownian motion is an important factor affecting the settling process of solid particles. The diffusion caused by Brownian motion hinders the settling of particles in the dispersion system. The larger the particle size, the less obvious the Brownian effect. Therefore, increasing the particle size is an effective way to improve the settling speed. According to Stokes Settlement Law [
6], the settling velocity of solid particles in the dispersion system is directly proportional to the square of particle size, the density difference between solid and liquid, and inversely proportional to the viscosity of liquid. That is to say, the bigger the diameter of solid particles, the bigger the density difference between solid and liquid, the smaller the viscosity of liquid, and the faster the settling velocity.
In the formula, is the settling velocity in m/s; g is the gravitational acceleration, ; d is the particle size in m; is the density of particles in ; is the density of liquids in , is the viscosity coefficient of liquids in .
Organic macromolecule flocculation is a linear macromolecule polymer. Its molecular weight is high. Active functional groups on long carbon chains can adsorb particles [
7,
8] in the dispersion system. Each macromolecule compound can adsorb more than one particle, which plays a role of linking between particles. This role is called bridging effect. The bridging process of organic polymer flocculation is shown in
Figure 1. One end of the flocculation adsorbs particles to form unstable adsorbed particles. Many unstable adsorbed particles form stable clusters [
9,
10] through bridging.
The mechanism of flocculation is to increase the particle size, thereby greatly increasing the settling speed of particles, that is, the whole tailings particles are adsorbed together under the bridge action of the long chain structure of flocculation, forming larger flocs, and achieving a certain size and density, which is conducive to settling and achieving the purpose of turbidity-clearing separation [
11,
12].
The flocculation settling process can be divided into six stages: Turbulence influence stage, accelerated settling stage, final settling velocity stage, interference settling stage, compaction settling stage, and ultimate settling stage. In the early stage of settling, the slurry undergoes strong agitation, and the particles are affected by turbulence, resulting in coagulation. When the turbulence effect weakens gradually [
13], the particles settle naturally under gravity and the velocity increases gradually until the resistance and gravity are balanced to reach the ultimate velocity. When the particles continue to settle, the interference settlement will occur when they contact the decelerated settled particles at the bottom. As the particles continue to settle, the bottom concentration will gradually increase, and the water between the flocs will gradually be extruded. After reaching a certain degree, the water in the flocs will also be extruded, resulting in compaction settlement. When the particle reaches the ultimate settlement concentration, the settlement velocity approaches zero and the settlement process basically ends.
2.2. Input Factor Analysis of Flocculation Settlement Parameters of Whole Tailings
Under certain physical and mechanical properties of tailings and flocculation properties, the concentration of sand supply, flocculation consumption and flocculation concentration, and mortar pH value are the most important factors affecting the flocculation settling effect [
14].
(1) The higher the concentration of sand supply, the more solid particles contained, the more flocculation used, and the interaction between tailings particles increases, the settling speed decreases; the lower the concentration of sand supply, the lower the final settling concentration, which cannot meet the requirements of tailings.
(2) The larger the dosage of flocculation, the faster the settling speed of tailings, but the larger the dosage, the higher the cost of reagent [
15], and the higher the content of flocculation in overflow water and the difficulty of wastewater treatment; the lower the dosage of flocculation, the slower the settling speed, which cannot meet the requirement of continuous dynamic sand release in vertical sand silo, and the higher the solid content in overflow water, the higher the cost of wastewater treatment [
16].
(3) When the concentration of flocculation is high, the viscosity is high, the agitation is difficult, and it is difficult to disperse evenly into the slurry; when the concentration of flocculation is too small, the flocculation dosage per unit volume is small, it is difficult to fully interact with the whole tailings particles per unit volume in a short time, which affects the sedimentation effect.
(4) Although some studies have shown that the pH value of mortar has an effect on the results, increasing the pH adjusting device on the spot will greatly improve the operation difficulty, reduce the accuracy of settlement results, and is not conducive to efficient management. In addition, with the continuous renewal of flocculation, different pH values have corresponding flocculation matching with them [
17]. Therefore, it is considered that acidic neutralization and externalization (for pipeline storage) are necessary for the removal of strong acidic slurries. In corrosion, the effect of pH value is not considered.
In summary, the settling parameters of flocculation are mainly determined by the sand concentration (mass concentration, %), the flocculation consumption q(g/t) and the flocculation concentration (%) which can be used as input factors of the network.
2.3. Analysis of Output Factor of Flocculation Settlement Parameters of Whole Tailings
The evaluation indexes of flocculating settling effect of whole tailings include settling velocity (m/h), sand discharge amount (mass concentration, %), and overflow water concentration (mass concentration, %) as follows:
(1) Settlement velocity. During the laboratory test, the measured settlement velocity of the settlement interface is the tailings settlement velocity. In order to achieve the dynamic settlement of tailings in vertical sand silos and continuous releasing of sand, it is necessary to ensure that the amount of sand stored in the silos remains unchanged, that is, the settling speed of tailings is greater than or equal to the releasing speed. On the premise of ensuring that the amount of sand input is satisfied [
18], the settling velocity
v of the whole tailings settlement should meet the requirement of the sand releasing capacity
Q, which is related to the cross-sectional area
S of the vertical sand silo where the tailings are located.
When the filling capacity is designed according to , dry sand is required per h, and the sand release rate is designed to be calculated by . In a vertical sand silo with a diameter of 11 m, can achieve dynamic settlement and continuous sand release by means of full tailings settlement velocity . In actual production, under certain cost, the faster settlement speed is required, the better. During the test, the settlement velocity is calculated by measuring the variation of the settlement height with time.
(2) The amount of sand released and the concentration of sand released. That is, the mass concentration of bottom tailings after flocculation settlement. In order to configure high concentration slurry, the higher the concentration of sand release, the better. Generally, the concentration of sand release is more than 50%.
(3) The concentration of overflow water, the mass concentration of overflow water in the process of flocculation and sedimentation, and the solid content of overflow water commonly used in engineering. In vertical silo flocculation settling, if the flocculation performance, concentration, and dosage are fixed, the settling speed will be determined, the amount of sand released and the concentration of sand released will be determined accordingly. Therefore, the settling speed and the amount of sand released [
19] and the concentration of sand released are actually three aspects of a problem, which should not be considered repeatedly in the study. The former is chosen in this paper. If the feed concentration is constant and the total mass of slurry and solid tailings remains unchanged in the established vertical sand silo, the following relationship exists:
In the formula, is the mass concentration of sand feeding; is the total mass of sand feeding; is the mass concentration of sand releasing; is the total mass of sand releasing; is the mass concentration of overflow water.
The quality concentration of overflow water is contradictory to the amount of sand released. Generally speaking, the larger the amount of sand released, the lower the quality concentration of overflow water, and vice versa. Therefore, when network output is carried out, a comprehensive evaluation output factor must be formulated, taking into account the settling speed, the amount of sand released [
20], and the concentration of sand released and the concentration of overflow water. In order to simplify the network system, the settling velocity is taken as a comprehensive evaluation index to evaluate the flocculation settling parameters, which is the only optimization parameter in this study.
2.4. Parameter Optimization of Spatial Difference Algorithm
2.4.1. Inverse Distance Weighted (IDW) Difference Method
IDW method is a deterministic difference method based on the principle of similar similarity. It is assumed that each sampling point of flocculation settling velocity of tailings has a local influence [
21,
22]. Some points closest to the sampling point have the greatest contribution to the value of the unsampled point, and their contribution is inversely proportional to the distance. The expression is as follows:
In the formula: is the settlement velocity of the sampling point studied. is the different settlement velocity , which is used to evaluate the distance between sampling stations. is the power parameter defined by analysis, and represents the number of stations used for evaluation and calculation.
The main factor affecting the accuracy of IDW method is p value, which is linear distance attenuation difference when p equals one, and non-linear distance attenuation difference when p is greater than one. For larger powers, the nearest sampling stations are given a higher weight share; for smaller powers, the weights are evenly distributed to each sampling station. The advantage of this method is that the structure of spatial difference isoline can be adjusted by weight. The disadvantage of this method is that unreasonable weighting will lead to large deviation if we do not understand the structural distribution characteristics of interpolation attributes in the study area, and it is easy to be affected by extreme values. The simulation results of several commonly used p parameters are compared. In addition, the size and number of adjacent points also affect the accuracy of the results. The value of the nearest sampling point is 12, and the range of maximum distance is set to 1.7 m.
2.4.2. Spline Method
Spline method is a method of approaching the surface by mathematical function, which is piecewise polynomial [
23] joined together according to certain smoothness requirements. This method has the advantages of small calculation amount, fast speed, retaining local variation characteristics, good visual effect, and is suitable for smooth surface. Generally, it requires continuous first and second derivatives. The disadvantage of this method is that it is difficult to estimate the error of function interpolation, and it is difficult for spline method to meet the requirements of interpolation accuracy when simulating limited monitoring data.
In the formula,
is used to study the settlement velocity of sampling points;
is the number of stations;
is the coefficient of solutions of a series of linear equations;
is the distance between estimated points and
i stations;
and
are expressed as follows:
In the formula, is the weight coefficient, is the modified Bessel function, is the constant, is the number of linear equations. Two types of spline interpolation methods, regularized and tension, were used to verify the interpolation. The weight coefficient was 0.1 and the number of model samples was 12.
2.4.3. Kriging Method
Kriging method is an interpolation method based on geostatistics. It is based on regionalized variable theory [
24,
25,
26]. It considers that any attributes that change continuously in space are irregular. It cannot be simulated by simple smooth mathematical functions, and can be described appropriately by random surface. Kriging method focuses on the determination of weight coefficients, thus providing the best linear unbiased estimation for the variable values of blank stations.
In formula: is the weight coefficient of the settlement velocity of station i, indicating the contribution of the settlement velocity of each station to the estimated value . In order to achieve linear unbiased estimation and minimize the variance of estimation, the weight coefficients are obtained from the equations.
In the formula, is the covariance between the sample points, is the covariance between the sample points and the interpolation points, and is the Lagrange multiplier.
The spatial structure characteristics of interpolated data are expressed by semi-variogram
as follows:
In the formula, is the settlement velocity of station i; is the settlement velocity of point h from station i; n represents the number of paired stations with distance h. According to the experimental semi-variogram, a reasonable theoretical model of variogram is determined. Five variogram models, spherical, circular, exponential, Guassian and linear, were used to verify the validity. The latest sampling point was 12 and the range was set to maximum distance of 1.7.
2.5. Verification of the Accuracy of the Results of Spatial Difference Optimization Model
Combined with the depth learning algorithm, the optimization effect of each difference model is verified by cross-test. The principle is to remove the settlement velocity of each monitoring station once from the data column [
27]. In-depth learning algorithm, unsupervised learning is used to train layer by layer, mapping high-dimensional and non-linear data features into low-dimensional feature space, automatically establishing dimension mapping relationship and acquiring hierarchical feature representation, so as to obtain better feature expression and classification. The self-coding network model in deep learning is used to extract network features, and the feature data are classified by soft Max classifier to optimize the difference model. The structure of deep network in deep learning is consistent with that of neural network. The neuron model is shown in
Figure 2. Among them,
represents input signals transmitted by neurons,
represents cumulative output,
represents the weight of the current neuron, and a formula is obtained:
Based on the neuron model, the settlement velocity is estimated by the difference between the measured values of surrounding stations, and then the error between the optimized values and the measured values is calculated to obtain the optimized settling velocity of the whole tailings flocculation [
28]. Pearson correlation coefficient (Corr), mean error (ME), mean absolute error (MAE), and mean square error (RMSE) of optimized and measured values were used as criteria for evaluating the difference method. Corr reflects the degree of coincidence between validation value and optimization value, ME reflects the error of overall optimization value, MAE reflects the possible error range of optimization value, RMSE reflects the sensitivity and extremum effect of optimization value. The formulas are as follows:
In the formula, represents the optimal settlement velocity value of monitoring station, and represents the actual settlement velocity value of monitoring station.
The difference of settlement velocity measured by the optimal difference model is compared with RI.
When the RI value is between zero and one, the difference between the optimized settlement velocity and the actual settlement velocity is small and the similarity is high. When the value is greater than one or less than zero, the difference between the optimized settlement velocity and the actual settlement velocity is large.
Taking the whole tailings filling system of an Iron Mine as an example, this method is used to optimize the settling speed of the whole tailings. A large number of studies have shown that the dosage of flocculation and the concentration of tailings are the main factors affecting the flocculation settling effect when the physical and mechanical properties of tailings and flocculation characteristics are certain [
29]. The main factors influencing the settling parameters of flocculation are the consumption of flocculation
Q and the concentration of tailings
(mass concentration, %). The comparison index of the experiment is the relationship between the settling parameters of the whole tailings and the settling velocity
v, and the results obtained are compared with the actual situation. In order to realize dynamic releasing of tailings in vertical silos, the settling velocity should be greater than or equal to the releasing velocity. The control group did not consider the effect of flocculation dosage and tailings concentration on the settling speed. The genetic algorithm is used to solve the settlement velocity of the whole tailings.