# Oil Sludge Deposition in Storage Tanks: A Case Study for Russian Crude Oil in Mo-he Station
## 2 Methods
### Sedimentation Ratio (\(k_{a}\))
#### 2.3.1 Polarizing Microscope Observation  
One of the methods of observing wax crystal is polarized light microscopy (PLM) [11]. It takes advantage of the crystal characteristics. The wax crystal has the anisotropic property, which can deflect the polarized light, thus it shows the different phenomenon from the surrounding medium in optics. The purpose of using this method is to obtain the particle size distribution and quantity of wax crystals. Then the method proposed by [PERSON] [2 ] can be used. Based on [PERSON]'s [2 ] settlement equilibrium theory, [PERSON] gives an equation for calculating the molecular weight of critical particles according to the equal sedimentation and upward diffusion. Considering the influence of liquid hydrocarbon in the formation of flocs, a formula for calculating the packing factor is proposed. [PERSON] [2 ] et al. used PLM to observe the distribution of wax crystal, and used software to process the pictures in order to obtain the particle size and volume of wax crystal. She drew the distribution curves of wax molecule size and volume, verified that the particle distribution of wax crystal conforms to gamma distribution. By calculating the critical particle size, the total number of settled and unsettled wax particles can be determined. The sedimentation ratio was obtained. She predicted the indoor simulated deposition of several crude oil and the field deposition of Tarim crude oil. We used the PLM to obtain the area fraction and average particle size of wax at the sedimentation temperature. As previously assumed, the average environment temperature is 0 \({}^{\circ}\)C, the wax precipitation point of Russian oil is about 12 \({}^{\circ}\)C and the condensation point is about \(-\)23 \({}^{\circ}\)C. It is better to eliminate the thermal history of wax crystals before experiment. However, because of the large content of light components in Russian oil, it is easy to volatilize. So, we did not heat the oil and the experiment is carried out at room temperature 18 \({}^{\circ}\)C, higher than wax precipitation point. Experimental process:  
Slides were cleaned, and proper amount of oil samples were taken using a pipette. Then, oil drops were gently placed in the middle of the slide. To avoid the existence of bubbles, the oil drops should be covered gently by cover glass at one end. The slide was put on the plate, where the temperature can be adjusted. Then, the temperature of plate was reduced 3 \({}^{\circ}\)C at a time. During the process, the objective lens was adjusted to find the wax crystal and the field of vision was continuously observed on the computer. We found that when the temperature was reduced to 9 \({}^{\circ}\)C, the wax crystals were observed. With the decrease of temperature, more and more wax crystals were separated out. When the temperature is reduced to the 0 \({}^{\circ}\)C, the wax crystals were observed for a period of time to let the wax precipitate completely. A suitable view was chosen to take the pictures, and the area contains impurities was avoided  
Pictures processing:  
Image-J software was used to analyze the micrographs of the wax crystals. It is a simple and convenient software widely used in medicine and biology. It is mainly used for statistical screening of cells and bacteria. The wax crystals are also small particles in crude oil, so ImageJ-J is well used too. It was applied to binary and boundary segmentation of the wax crystals micrographs. The function particle analysis can output the parameters such as the size, quantity and area of the wax crystal in the image by Excel, which is convenient for subsequent statistics. We obtained the particles area fraction was 0.0102% and the average wax grain size was 1.82 \(\upmu\)m.  
Two-Dimensional Particle Deposition Simulation Program  
Some scholars have done some research in this direction, such as [PERSON] et al. [2 ] and [PERSON] et al. [2 ] have carried out three-dimensional simulation of the accumulation and deposition of sediment particles. [PERSON] et al.