Slurry Transportation Characteristics of Potash Mine Cemented Paste Backfills via Loop Test Processing

Abstract

This study evaluated the properties and processing of cemented paste backfills (CPBs) for potash mining through loop tests. The CPBs were made with steel slags as the binder, granulated potash tailings as the aggregate, and waste brine water as the liquid phase. The effects of solid concentration and steel slag dosage on the transport and mechanical properties of CPBs were assessed. The loop test demonstrated that all CPB slurries performed well, exhibiting strong long-distance pipeline transport capabilities. The 28-day compressive strength of the backfills exceeded 1 MPa, meeting the design requirements for backfill strength. The key rheological parameters, including yield stress (τ₀) and viscosity coefficient (η), were comprehensively and theoretically analyzed based on the variations in pressure loss per unit distance of the filling slurry measured during the loop test. The empirical formulas for CPB pressure loss, accounting for varying flow rates and pipeline diameters, were derived with an error margin under 2%. The response surface analysis showed that the affecting extents of factors on pressure loss in CPB slurry were ranked as follows: solid concentration > cementing agent content > flow rate. This study offered valuable guidance for the processing of potash mine backfill operations.

1. Introduction

As potash mining develops, the goaf left by underground mining can lead to surface subsidence if not properly filled. Additionally, by-products produced during the mining process can cause severe environmental pollution if left on the earth surface. The main wastes are tail salt and waste brine water, with sodium chloride and magnesium chloride solutions as the main components, respectively [1,2]. To address these issues, the potash mine backfilling process was used, where cemented paste backfill (CPB) was obtained by mixing tail salt, waste brine water, and binder, and backfilled into the goaf, creating a stable filling body that ensures continuous and safe mining operations [3,4,5,6]. However, the technology for potash mine backfilling is still under development, with only a few companies implementing it in practice [7].

The strength of the backfill material and the transport performance of the filling slurry are key design criteria for CPBs [8,9]. In potash mines, the 28-day compressive strength of CPBs must reach 1 MPa. Fluidity is a critical parameter for assessing flowability: gravity transport is feasible when fluidity exceeds 220 mm, and pumping is possible with a fluidity of 180 mm or more. However, early strength and fluidity are often inversely related. To address this, some researchers [10] added retarders, though this increases costs. Our previous studies [8,9] showed that using steel slag as a binder for potash mine CPBs results in s slow initial hydration process but continued hardening over time, maintaining fluidity above 200 mm for 8 h with excellent homogeneity and a 28-day strength greater than 1 MPa. Microanalysis revealed that the main hydration products are C-S-H gels and hydrocalumite (or Friedel’s salt), which interlock and enhance compressive strength. The results suggested that steel slag exhibits latent hydraulic properties and can effectively serve as a coagulant in CPBs for long-distance transport in potash mines.

However, before finalizing the formal preparation process for underground cemented filling materials, it is essential to evaluate the flow performance of the filling slurry in pipelines through loop pipe tests. To ensure system stability, it is important to measure pressure loss during slurry flow at various mix ratios, providing a foundation for engineering design. Since slurry flow is dynamic, relying solely on theoretical calculations can lead to significant errors [11]. Loop tests that measure flow, temperature, and pressure loss yield more accurate data, supporting the design of a reliable backfilling system and optimizing its processing in mining operations.

The rheological model describes the relationship between shear stress and shear rate in backfilling slurry within a pipeline. If the shear stress is directly proportional to the shear rate, the slurry is classified as Newtonian; if the relationship is nonlinear, the slurry is considered non-Newtonian. Non-Newtonian slurries can be further categorized into types like Bingham bodies, pseudo-plastic bodies, and yield-pseudo-plastic bodies [12]. When using steel slag powder, with calcium silicates as the primary components, as a binder, the slurry undergoes slow but continuous hydration reactions, leading to good fluidity performances at the early stages and allowing high concentration of cemented filling material. Due to the high concentration of cemented filling material, the prepared filling slurry does not undergo stratification or segregation. Furthermore, the solid particles in the filling slurry are relatively fine, and the high viscosity of the waste brine water causes these particles to adhere to each other, preventing free settling and segregation. Additionally, as the filling slurry remains in continuous flow within the pipeline, the particles do not settle at the bottom of the slurry but are uniformly distributed throughout the entire filling slurry. In the absence of external force, the slurry will retain its shape and volume. It only flows when the applied force exceeds the yield stress, exhibiting Bingham body rheological behavior. The flow of the slurry along the pipeline, influenced by the pressure difference between the pipeline ends, is illustrated in Figure 1.

As shown in Figure 1, a slurry microelement with radius (r) and length (l) is taken from the pipeline, where the pressures at the left and right ends are p₁ and p₂, and (τ) represents the shear stress exerted on the filling slurry, respectively. According to the static equilibrium theory for tube flow, the slurry resistance along the pipe equals the fluid friction on the pipe wall [13]. Thus, the following formula can be derived:

$$p_1\pi r^2=p_2\pi r^2+2\tau \pi rl$$

(1)

where p₁ and p₂ are pressure values, MPa; r is the radius of the slurry micro-element, m; the length of the slurry micro-element is l, m; τ is the shear stress, Pa. According to Formula (1), Formula (2) can be deduced as follows:

$$\tau ={\displaystyle \frac{r\left(p_1-p_2\right)}{2l}}$$

(2)

The CPB slurry with steel slag as a cementing agent belongs to the Bingham body, so the following relationship is obtained:

$$\tau ={\tau }_0+\eta {\displaystyle \frac{d_v}{d_r}}$$

(3)

where τ₀ is the yield stress, Pa; η is the viscosity coefficient, Pa·S⁻¹; d_v/d_r is the shear rate (S_r), s⁻¹.

In the calculation of the flow resistance of the backfilling slurry, the relationship between the shear stress and the shear rate of the backfilling slurry of Bingham body can be deduced. The resulting Buckingham equation [14] is as follows:

$${\displaystyle \frac{8V}{D}}={\displaystyle \frac{\tau }{\eta }}\left(1-{\displaystyle \frac{4{\tau }_0}{3\tau }}+{\displaystyle \frac{4{\tau }_0^4}{3\tau }}\right)$$

(4)

In this study, biquadratic high-order small amount is removed, and the approximate shear stress formula is obtained by combining Equation (2) as follows:

$$\tau ={\displaystyle \frac{r\left(p_1-p_2\right)}{2l}}={\displaystyle \frac{4{\tau }_0}{3}}+{\displaystyle \frac{8v\eta }{D}}$$

(5)

where D is the diameter of the pipe, m.

According to Formula (4), the shear rate [15] is as follows:

$${\displaystyle \frac{d_v}{d_r}}={\displaystyle \frac{8V}{D}}$$

(6)

According to Formulas (2) and (6), the shear stress and shear rate of each ratio under different speed conditions are calculated, and the relationship curve of τ~S_r is drawn. The intercept in the fitted curve is 4τ₀/3, and the slope of the curve is the viscosity coefficient η [16].

After calculating the yield stress and viscosity coefficient of the backfilling slurry under each ratio, the relationship between the pressure loss i and the diameter D and the flow velocity V is derived from Formulas (2) and (5). The pressure loss per unit length of slurry under different flow rates and different pipe diameters can be calculated as follows in Formula (7):

$$i={\displaystyle \frac{16}{3D}}{\tau }_0+{\displaystyle \frac{32V}{D^2}}\eta$$

(7)

This study used steel slag powder as a cementing agent, granulated potash tailings salt as an aggregate, and potash waste brine water as a water substitute to prepare CPBs. Loop tests were performed to assess their rheological properties. Based on pressure loss data from these tests, theoretical analysis and data processing were conducted. The simulated slurry rheological parameters aimed to inform the design of large-scale potash mine filling applications.

2. Materials and Methods

2.1. Materials

2.1.1. Steel Slag

Steel slag, a by-product of iron and steel smelting, is the largest solid waste generated in the steel production process [17]. The steel slag used in this test came from Ansteel company, Anshan, China. Chemical analysis on representative steel slag samples was conducted, with the main chemical compositions summarized in

Table 1. Chemical composition of steel slag (wt. %).

Chemical Composition	Content/%
SiO2	11–15
Al2O3	4–8
Fe2O3	11.2–14.2
FeO	5–7.5
MgO	11.5–15
CaO	35–40
TiO2	0–1.5
MnO	0–1.7
Loss	5–7

.

Table 1 shows that the main compositions of steel slag are CaO, MgO, Fe₂O₃, and SiO₂. To identify the main mineral constituents, XRD analysis was performed on representative samples, with results presented in Figure 2. The primary minerals include dicalcium Silicate (C₂S), tricalcium Silicate (C₃S), calcium aluminate (CA), dicalcium Ferrite (C₂F), the MgO-FeO-MnO solid solution (RO phase), and free CaO, with C₂S, C₃S, and the RO phase being the most prominent. Due to the slow cooling rate of steel slag, minerals like C₂S and C₃S have ample time to crystallize [18]. The metastable β-C₂S gradually transforms into the stable γ-C₂S, and C₃S undergoes changes during cooling. The stable phases exhibit low reactivity, while the RO phase is nearly inert and difficult to react under high temperature and alkaline conditions [19]. Therefore, the activation of steel slag is necessary, with the main activation methods including mechanical, chemical, and thermal activation. This study focused on mechanical activation, where grinding the raw steel slag with a small mill to defect the mineral lattices and to generate free radicals or ions on the particle surfaces. The method was expected to enhance the reactivity of the steel slag by facilitating its chemical interactions.

The enhanced activity of the steel slag was demonstrated by its rapid chemical reaction with waste brine water, allowing the filling slurry to harden quickly and form a solid body with strength. In this study, a grinding mill (model SM500×500) was employed to mechanically activate the steel slag. The mill was loaded with 100 kg of grinding media, operated at a rotational speed of 48 revolutions per minute, and powered by a 1.5 kW motor. Each batch of steel slag material weighed 5 kg. The fineness of the steel slag powder was regulated by controlling the grinding duration. When the grinding time was set to 30 min, the steel slag powder achieved a specific surface area of 400–500 m²/kg. Figure 3 shows the particle size distribution of the ground steel slag, which held particles mostly under 100 μm and a specific surface area of about 400–500 m²/kg. This meets the requirements for both fineness and reactivity, making it suitable for use as a binder.

2.1.2. Tail Salt Aggregate

The potash mine tail salt used in the loop test was granular, transparent, or milky white and turned grayish-white or yellow when impure. Its NaCl content exceeds 95%, with a maximum particle size of D_max = 9 mm. As a by-product of potash fertilizer production, tail salt was under supersaturation conditions in the waste brine water, serving as an aggregate in the cemented paste backfill materials. However, the original particle distribution of the tail salt can cause significant segregation and affect transport when used directly as an aggregate. To address this, the tail salt fraction was processed and redistributed using a screening device with a 2–3 mm mesh size to remove coarse particles. The remaining coarse tail salt was then ground in a grinding mill (SMφ500×500) for 5–10 min. The fine powder was mixed with the screened tail salt to form the final tail salt aggregate (referred to as “aggregate”). The particle size distribution before and after grinding is shown in Figure 4.

2.1.3. Waste Brine Water

The potash mine waste brine water was a clear, colorless solution, but it turned light or dark yellow when mixed with certain impurities. Its density was 1.31 g/cm³, and the solute content is approximately 35%. Elemental analysis was performed using an inductively coupled plasma (ICP) emission spectrometer, and the chemical compositions of the waste brine water are shown in

Table 2. Chemical compositions of the potash mine waste brine water.

Solute	Content/%
MgCl2	25–35
NaCl	0.7–1.2
CaCl2	0.1–0.25

. It is worth noting that NaCl is in a saturated state in the waste brine water, meaning that the tail salt aggregates, primarily composed of NaCl, do not dissolve in the brine water. Therefore, it served as aggregates in the cemented paste backfills.

2.2. Loop Test Scheme

The loop test is a crucial step before mine design, as it determines the fluid parameters for the filling process, serving as the foundation for the design [20]. It simulates onsite backfilling to verify whether the laboratory-prepared filler maintains good fluidity and the mortar block’s strength under expanded test conditions, ensuring both pumping efficiency and mechanical properties during processing. Additionally, it validates the reliability and stability of the filling ratio throughout the process. Conducting the loop test for the filler in the potash mine provides solid theoretical support for the filling station design. Following a small-scale pilot study in the lab, using steel slag as a single binder and fractional-treated tail salt as aggregate was feasible, with waste brine water replacing water, to prepare the backfill material. From the various ratios tested, four sets with the optimal results were selected for the loop test, and the mixing ratios are shown in

Table 3. The mixing ratio of the looping pipe test.

NO.	Steel Slag/%	Tail Salt Aggregate/%	Waste Brine Water/%	Solid Concentration/(wt.%)
1	5	65	30	70
2	5	70	25	75
3	5	73	22	78
4	10	60	30	70

.

The loop test system consists of several subsystems: batching, pumping, detection, pipeline, and automatic control. The pipeline has an inner diameter of 80 mm, with a maximum stirring capacity of 0.4 m³ and a theoretical maximum flow rate of 40 m³/h. It was designed for pumping pressures between 2 and 4 MPa, a slump of over 150 mm, and a rated power of 70 kW at 380 V. The optimal test temperature range was 10–35 °C, with a maximum flow speed of 2.2 m/s. Metered waste brine water was mixed in the agitator and transferred to the pump for circulation. The transfer pump then delivered the material to the 80 mm loop pipe for processing. Test parameters such as pressure, temperature, flow, and differential pressure were monitored through sensors, and data were collected by the computer monitoring software. The results were analyzed using dedicated software.

2.3. Test Methods

The steel slag, tail salt aggregate, and waste brine water were mixed according to the specified ratio to produce the backfilling slurry, which was then subjected to a processing loop test. During the process, the circulating slurry was sampled regularly, and its fluidity and slump were measured according to “GB/T 2419-2005” [21] and “GBT50080-2016” [22] standards for cement mortar and fresh concrete. The remaining slurry was poured into a standard 100 mm × 100 mm × 100 mm mold and vibrated on a concrete vibrating table. The test simulated actual goaf conditions, with a temperature range of 35–42 °C and 25–30% relative humidity. The backfill materials with molds were placed in a controlled chamber with 40 °C and 27 ± 3% humidity inside condition. When the test block hardened, the molds were removed before the blocks were put back into the chamber for a curing process lasting 28 days. Finally, the compressive strength of the cured block was tested according to “GB50107-2010” [23].

3. Results

3.1. Results of Fluidity Performance Test

A loop test was conducted, and samples were taken to measure the fluidity and slump of the filler slurry over time, based on the test ratio above. The results are shown in Figure 5 and Figure 6.

As the mining depth of potash deposits increases, the distance between underground goaf areas and filling stations also becomes progressively longer. This requires stricter conditions for backfilling materials, specifically ensuring no delamination, water seepage, or solidification during transportation. In addition to meeting strength standards, the fluidity of the filler is also crucial for the processing of the slurry. Zhou [24] found that to meet pipeline transportation requirements, the backfilling slurry’s slump should generally be between 180 and 220 mm. Figure 5 and Figure 6 show that the slurry prepared with four different ratios maintains a fluidity above 200 mm for 8 h and a slump above 215 mm for 2 h. Moreover, the slurry exhibits no delamination, water seepage, or solidification, demonstrating good flow properties that allow it to travel long distances in the pipeline. This ensures efficient long-distance backfilling and processing in potash mines. Based on conventional flow rate calculations, backfilling and conveying operations are easily achievable within a pipe length of 0–5 km.

3.2. Mechanical Properties Results

Figure 7 presents the compressive strength results of test blocks after 28 days of curing under onsite simulation conditions, using steel slag as a binder at various ratios. The strength of the 28-day cured blocks ranges from 1 to 2 MPa. It is evident that compressive strength increases with higher solid concentrations, assuming the cement content remains constant. Conversely, at the same solid concentration, strength increases with higher cement content. Steel slag’s dense crystalline grains and stable crystal lattice result in slow hydration, which is reflected in the relatively low compressive strength (2 MPa) of the backfilling block at 28 days. While steel slag has a slower hydration rate compared to other binders, its hydration products increase steadily [25], enhancing long-term strength [26,27,28]. The slow hydration and increased strength over time are beneficial for the backfilling process, as steel slag also leads to microdilatancy [29], aiding in further fill tightening work in potash mine backfill application. In conclusion, the four mix ratios demonstrate theoretical relevance, as both the flowability of the slurry and the 28-day compressive strength meet the required standards, indicating the need for further cyclic testing.

3.3. Results of Rheological Property Test

The CPB slurry was prepared using the four proportions above and tested in a continuous pipeline circulation. Pressure loss per unit distance was measured, and the raw data were filtered and averaged to generate the trend line shown in Figure 8.

As shown in Figure 8, the pressure loss in the pipeline increases linearly with flow rate for all four CPB slurry proportions. Using the measured data and substituting them into Equations (2) and (6), the shear stress (τ) and shear rates at different flow rates are calculated. These values are then substituted into Formula (5), and the data points for τ and S_r are obtained. MATLAB is used to process linear regression via the least squares method to generate the fitting curves and formulas. From the fitting curve, the 4τ₀/3 and τ₀ are obtained. The viscosity coefficient (η) is the slope of the curve. The analysis results are presented in Figure 9 and

Table 4. Calculation results of yield stress and viscosity coefficient.

Mixture Ratio	Fitting Formula	R2	τ0/Pa	η/Pa·S−1
ss5%, co70%	y = 0.1658x + 23.935	0.9115	17.951	0.1658
ss5%, co75%	y = 0.1977x + 25.623	0.9641	19.217	0.1977
ss5%, co78%	y = 0.3550x + 57.300	0.9394	42.975	0.3550
ss10%, co70%	y = 0.2710x + 31.380	0.9735	23.535	0.2710

.

As shown in Figure 9 and Table 4, both the yield stress (τ₀) and viscosity coefficient (η) of the four backfilling slurry mixtures increase with higher solid concentrations and greater cement content. This trend aligns with the findings of Ma [30] and Zhang [31]. The R² values of the fitted relationship curves exceed 0.9, indicating a strong fit and reliable results.

3.4. Determination of the Simulation Formula

Using the yield stress (τ₀) and viscosity coefficient (η) data from Table 4, the empirical formulas for each mixture ratio are derived by substituting the values into Equation (7). The flow rate and pressure loss data from Figure 8 are then processed using these formulas, with the actual pipe diameter (0.08 m) from the loop test equipment. The backfilling slurry pressure for each ratio is calculated based on the pressure loss data, and the resulting errors and error rates are presented in

Table 5. The empirical formula of pressure loss at different potash mine CPB proportions.

Mixture Ratio	Empirical Formula of Pressure Loss	Error Rate
ss5%, co70%	$i_1={\displaystyle \frac{95.74}{D}}+{\displaystyle \frac{5.306v}{D^2}}$	0.89%
ss5%, co75%	$i_2={\displaystyle \frac{102.49}{D}}+{\displaystyle \frac{6.326v}{D^2}}$	1.25%
ss5%, co78%	$i_3={\displaystyle \frac{229.20}{D}}+{\displaystyle \frac{11.360v}{D^2}}$	0.93%
ss10%, co70%	$i_4={\displaystyle \frac{125.52}{D}}+{\displaystyle \frac{8.672v}{D^2}}$	1.92%

.

Table 5 shows that, for a given flow rate, pressure loss in the backfilling material decreases as pipe diameter increases, while pressure loss increases with flow rate at a constant pipe diameter. Additionally, for a fixed pipe diameter and flow rate, a higher solid concentration or cement content leads to increased pressure loss during processing. Comparing the calculated data with loop test results, the formula’s error rates are as follows: 0.89% for 5% steel slag and 70% solid concentration; 1.25% for 5% steel slag and 75% solid concentration; 0.93% for 5% steel slag and 78% solid concentration; and 1.92% for 10% steel slag and 70% solid concentration. These error rates, all under 2%, suggest the formulas are reliable and have practical significance, providing a solid theoretical foundation for real-world backfilling systems. The simulation results in Table 5 also show calculations for various pipe diameters (80–200 mm) and flow rates (20–120 m³/h), with increments of 20 mm and 20 m³/h, respectively. Using the known volume flow rate and pipe diameter, flow rates are calculated using Formula (8).

$$v={\displaystyle \frac{Q}{360\pi D^2}}$$

(8)

Q represents the volume flow rate (m³/h). The volume flow rate and corresponding pipe diameter data are substituted into the empirical formulas for each mixture ratio, with a linear fit applied to generate the pressure loss curve shown in Figure 10.

The pipe diameter is a key factor influencing pressure loss in filling slurry pipelines process. Figure 10 shows that, for the same flow rate, pressure loss decreases as pipe diameter increases, while for the same diameter, pressure loss rises with flow rate, which is in line with another study [32]. A larger pipe diameter reduces pressure loss, benefiting slurry flow, but also complicates pipeline installation and assembly. Beyond a certain diameter, further increases yield minimal reductions in pressure loss. Therefore, considering engineering feasibility and cost, the optimal pipe diameter is in the range of 140 mm to 160 mm, with 150 mm as the recommended size.

Using a 150 mm pipe diameter, the pressure loss for the four slurry mixtures was calculated during the processing of different flow conditions, based on the formula in Table 5. The results are shown in Figure 11.

As shown in Figure 11, when the pipe diameter is 150 mm, pressure loss varies at the range of 0.65~2.5 kPa/m, with different slurry ratios. It increases with both solid concentration and steel slag content. For a given ratio, pressure loss also rises with flow rate. At a flow rate of 120 m³/h, the pressure loss reaches its maximum values of 1.08 kPa/m, 1.21 kPa/m, 1.56 kPa/m, and 2.48 kPa/m, respectively. In designing the backfilling system, the specific scheme can be flexibly selected based on filling times, pipeline layout, and tailings or waste brine water utilization requirements. After finalizing the scheme, a resistance calculation can be used to select the appropriate pressure pump for the processing system. The pumping pressure should be designed to exceed 2 MPa, the typical starting pressure for industrial pumps [33].

3.5. Response Surface Analysis

To assess the effects of solid concentration, flow rate, and steel slag content on filling pressure loss, response surface analysis was conducted using Design Expert software 12. This method fits a regression equation to model the relationship between the factors and the response variable, analyzing the response surface contour to identify optimal process parameters. In this study, pressure loss was chosen as the response variable, influenced by three main factors: solid concentration (70–78%), flow rate (1.4–2.0 m/s), and cement slag content (5–10%). Response surface analysis was performed within these ranges. The findings provided valuable insights into on-site backfilling design and contributed to the theoretical understanding of backfilling system formulation [34].

As shown in Figure 12a, with a constant solid concentration, pressure loss in the backfilling slurry is influenced by both the flow rate and the amount of cementing agent during the processing. The pressure loss peaks at 10% cementing agent content and a flow rate of 2.0 m/s, while it is at a minimum with 5% cementing agent and a flow rate of 1.4 m/s. Among these factors, the cementing agent content has a more pronounced effect on pressure loss. Figure 12b reveals that, for a constant flow rate, solid concentration has a greater impact on pressure loss than the cementing agent content. When the solid concentration increases from 70% to 78%, the variation in pressure loss is significant. However, when the binder content increases from 5% to 10%, the change in pressure loss is relatively insignificant.

In conclusion, the influence on pressure loss, in order of significance, is solid concentration, cementing agent content, and flow rate.

4. Conclusions

Through experimental studies, it was demonstrated that steel slag can be used as a binder for potash mine CPB slurry. This not only helped in processing large amounts of tail salt and waste brine water from potash fertilizer production but also provided environmental benefits.

Loop tests showed that the four types of CPB slurries performed well, with good long-distance pipeline transportability. The 28-day compressive strength of the backfill exceeded 1 MPa, meeting design requirements for strength.

Simulation formulas for pressure loss at various pipe diameters and flow rates were developed, with the calculated and measured pressure loss values differing by less than 2%, confirming the reliability of the empirical formulas. The formula was validated under specific mix proportions, such as when the steel slag binder content was 5% with a solid concentration of 70%, 5% with a solid concentration of 75%, 5% with a solid concentration of 78%, and 10% with a solid concentration of 70%. However, under more complex mix proportion conditions, it is challenging to determine whether the variations in pressure loss align with the formula’s predicted changes. Therefore, the formula exhibits certain limitations.

Response surface analysis revealed that the factors influencing pressure loss in CPB slurry were ranked as follows: solid concentration > cementing agent content > flow rate.

Through experimental studies, it was demonstrated that steel slag can be used as a binder for potash mine CPB slurry. This not only helped to recycle large amounts of tail salt and waste brine water from potash fertilizer production but also provided environmental benefits.