In the actual measurement, different source positions have different measurement results. In order to maximize the measurement efficiency, the relationship between the different distances of the radiation source from the sample and the results is simulated. The change curve of the normalized value of the source position is shown in Figure 2. The results show that the influence of the source location on the measurement results accords with the law of exponential decay. On the one hand, the attenuation of the radiation emitted by the radioactive source in the air follows the law of exponential decay. On the other hand, the sample is assumed to be uniformly distributed. When the source distance is 7 cm, the normalized value is 1, and the detector count is optimized. When the distance exceeds and is lower than 7 cm, the detector count is obviously different. Therefore, in the actual operation process, the specified radiation source distance is 7 cm.

In the actual measurement, different detector distances have different measurement results. In order to maximize the measurement efficiency, the effects of different detector distances on the measurement results are simulated. Considering the influence of the simulate source distance on the measurement result, when the source distance is 7 cm, the detection efficiency reaches the optimal effect, so the variable of the control source is 7 cm. Detector position-normalized value changes as shown in Figure 3. The results show that the overall effect of the detector on the counting rate is small, and the counting rate decreases linearly with the detector distance before 14 mm.

The source distance is 5 cm and the detector distance is 12 mm. Considering that the particle size of iron concentrate is more difficult for Monte Carlo simulation, it is assumed that the particle size of each sample is uniform, and the particle size of the iron concentrate is changed by the proportion of air. Assuming that the volume of iron concentrate is V_iron, the volume of air is V_air, the volume of water is V_water, the volume of container is V, and the iron concentrate is insoluble in water, and without considering the presence of air, the following formula exists:

V = V iron + V water (3-1)

when air is present, the density of air is ρ air : 1.29 × 10⁻³ g/cm³ (under standard conditions), and the density of iron concentrate is ρ iron . Assuming that the percentage of air in the iron concentrate is k, the content of iron concentrate is 1 − k, and the density of the iron concentrate containing air is:

ρ air-containing-iron = ρ iron ⋅ ( 1 − k ) + ρ a i r ⋅ k (3-2)

The volume of the above iron concentrate is V_iron. After adding air, it is assumed that the volume of V_iron remains the same but the density becomes smaller. It is ρ air-containing-iron .

If the volume of air-containing iron concentrate is V_{air-containing-air} = V − V_water, the overall density of the sample is:

ρ sample = ρ air-containing-iron ⋅ V air-containing-iron V sample + ρ water ⋅ V water V sample (3-3)

Assuming that the proportion of air in the iron concentrate is 1%, 2%, 3%, 4%, 5%, 6%, 7%, 8%, 9%, 10%. V is 1000 cm³, V_{air-containing-iron} is 500 cm³, for the sample with 1% air, the density is:

ρ air-containing-iron = 2.3   g / cm 3 × ( 1 − 0.01 ) + 1.29 × 10 − 3   g / cm 3 × 0.01 = 2.277   g / cm 3

ρ sample = 2.277   g / cm 3 × 1 2 + 1   g / cm 3 × 1 2 = 1.6385   g / cm 3 (3-4)

Similarly, according to the above formula, the sample density of different air proportions is obtained, as shown in Table 1 below.

Figure 4 shows the variation curve of the normalized value with the particle size. When the particle size is 7%, the normalized value of the count rate tends to be flat. For iron concentrates with a particle size of 7%, the size of the iron concentrate cannot be distinguished by the counting rate. Before the particle size is 7%, the particle size shows a linear growth trend with the change of the normalized value.

Because the concentration plant has more than 10,000 tons of beneficiation tasks every day, the influence of ore quantity and ball mill and other factors makes the concentration of the sample different, so the simulated sample concentration is of great significance to the actual operation. In the simulation process, it is assumed that the iron concentrate has no air and the volume of water is a variable, then V_iron = V − V_water, the density of the simulated sample: ρ sample = ρ iron ⋅ V iron V + ρ water ⋅ V water V . The source distance is 6 cm and the detector distance is 12 mm.

The volume of V is 1000 cm³, and the volume of water is assumed to be 10%, 15%, 20%, 25%, 30%, 35%, 40%, 50%, 60%, and 70%. The density of the slurry with different concentrations is shown in Table 2 below.

The volume of different water represents the concentration of slurry under different conditions, and the experiment simulates the counting rate of slurry under different source locations. Figure 5 shows the change curve of the count rate of different iron concentrate slurry concentration. Before the water volume is 40%, the detector count rate fluctuates less, and after the water volume is 40%, the count rate suddenly increases. When the volume of water increases, iron concentrate pulp concentration decreases, and the count rate measured by the detector is gradually increased at this time. The increase is mainly due to the reduction of water, the penetration ability of the particles is enhanced, which leads to an increase in the count.