Calculation of Mixed Oil Volume for Sequential Transportation of Crude Oil Pipelines with Variable Temperature and Low Reynolds Number

In order to meet the differentiated demand of oil refiners for crude oil, improve the operating load ratio of long-distance pipelines, and reduce one-time investment, sequential transportation process has been widely used in long-distance crude oil pipelines in China. There are many studies on the calculation method of the mixed oil quantity of sequential transportation of refined oil, but due to its complex influencing factors, there is no general calculation model accepted by everyone. For the sequential transportation of crude oil pipelines, most of them have the characteristics of variable temperature and low Reynolds number, and it is more difficult to accurately calculate the mixed oil quantity than the refined oil pipeline. Through the analysis of the characteristics of oil mixing and hydraulic characteristics of sequential oil transportation, combined with the operation example of an oil pipeline in China, the calculation results of the diffusion theory formula, the Austin-Palfrey empirical formula and the equivalent pipeline length formula were compared and analyzed. The results show that the “equivalent pipeline length method” considers the influence of flow, pipe diameter and conveying distance on oil mixing, and takes into account the oil mixture caused by the change of initial oil mix and Reynolds number, which is more suitable for calculating the mixed oil quantity of sequential transportation of crude oil pipelines. However, for the sequential transportation of crude oil pipelines with low Reynolds number and variable temperature, the amount of oil mixed will be increased. According to the comparative analysis of actual cases, the correction coefficient is increased by 1.5 times on the basis of theoretical calculation, and the calculated value is in good agreement with the actual value, and the deviation is within 5%. It can be used as a reference for the design and operation management of variable temperature and low Reynolds number crude oil sequential transportation pipeline.


Introduction
The method of continuously transporting multiple oils and petroleum products in a certain sequence in a pipeline is called sequential transportation, also known as "alternating transportation" [1].Sequential transportation can meet the differentiated demand of oil refiners for oil products, improve the operating load ratio of long-distance pipelines, and reduce one-time investment.Many pipelines such as crude oil pipelines and Yilong lines in western China have adopted multi-variety crude oil sequential transportation technology [2][3][4].In the process of sequential conveying, the physical properties (such as density and viscosity) of the oil products are different, and the oil products transported next to each other inevitably produce oil mixing phenomenon [5].The quality index of mixed oil does not meet any of the adjacent oil products, and can only be used as a defective product or downgraded, resulting in the depreciation of the oil product.Therefore, the estimation of oil mixing amount and oil mixing length is the key basis for guiding the cutting of the end oil, the selection of oil mixing treatment method, and the optimization of the delivery batch.The calculation method of the mixed oil quantity of sequential transportation of refined oil is relatively mature, and according to its establishment method, it can be divided into empirical model, semi-empirical model and model based on computational fluid dynamics (CFD) theory [6][7][8][9][10][11]. Due to the complexity of the oil mixing mechanism and the particularity of each pipeline itself, each calculation model has been simplified, and the calculation results are only applicable to specific pipelines, which has limitations, and there is no general calculation model for oil mixing that has been widely accepted by everyone [7].
For the sequential transportation of crude oil pipelines, scholars at home and abroad have carried out more research on the dynamic heat transfer characteristics of alternating cold and hot oil [12][13][14][15].Less attention has been paid to the calculation of oil mixtures.In recent years, China's crude oil prices have been in line with international oil prices, and have fluctuated with the rise and fall of international crude oil prices.According to the density of crude oil, the sales quality of crude oil is divided into four categories: light oil, medium I., medium II., and heavy oil.When the density is less than 846kg/m3, it is light oil, the density between 846~870kg/m3 is medium I., the density between 870~910kg/m3 is medium II., the density is greater than 910kg/m3 is heavy oil, the smaller the oil density, the higher the sales price, and the difference between the sales price of the adjacent two quality oil products reaches 200¥/t [16].Therefore, the calculation of crude oil sequential oil mixing volume, optimization of oil mixing quality, and improvement of oil sales efficiency have gradually attracted attention.

Characteristics of Sequential Transportation of Crude Oil
In recent years, due to the different origins and properties of various types of crude oil in the world, refiners usually need a variety of different quality crude oil in order to pursue maximum economic benefits, and the transportation of these crude oil is mostly sequential.Crude oil sequential transportation pipeline, usually according to the pipeline environmental temperature, oil freezing point, viscosity, heating conveying process, additive conveying process or cold and hot oil alternating transportation process, while refined oil pipeline is generally room temperature conveying process.Therefore, the sequential transportation process of crude oil is relatively complex, and there are unsteady hydraulic and thermal characteristics.The temperature of the oil in the pipeline decreases along the pipeline transportation distance, the viscosity increases, and the Reynolds number decreases, resulting in the flow state of the fluid in the later section of the pipeline may be in laminar flow.Most of the existing oil mixing formulas are suitable for the sequential transportation of refined oil, or the alternating transportation of crude oil under high throughput, which is characterized by the small change of temperature along the oil line with the conveying distance, the influence of temperature on the oil mixing volume is not considered, and most of the oil products are in a turbulent flow state.For the calculation of the oil mixing volume of crude oil sequential transportation with variable temperature and low Reynolds number, it is necessary to analyze the adaptability of the existing oil mixing formula by combining the physical properties of the oil and the pipeline transportation conditions.

Calculation Formula
Oil mixing refers to the oil containing both the front A oil and the rear Boil, the mixed oil section refers to the oil section containing two types of oil in the pipeline, that is, the concentration of the oil product in the front A oil in the mixing section changes from 1 to 0, the concentration of the oil product in the second B changes from 0 to 1, the volume of oil contained in the mixed oil section is called the oil mixing amount, and the length of the oil mixing section to the pipeline is called the oil mixing length.
So far, researchers from all over the world have conducted a lot of research on the calculation of the oil mixture generated by alternate transportation, and obtained some empirical or semi-empirical formulas for calculating the oil mixing volume.The current formula can be divided into two categories, one is the diffusion theory formula obtained through the empirical modification of the diffusion theory, and the other is the empirical formula summarized through the actual data analysis in the field.However, due to the huge number of factors affecting the amount of oil mixing, and the movement of the oil mixing interface in the oil pipeline is very complex, each formula has certain limitations, and no general formula has been found for the calculation of the oil mixing amount under any working conditions and any pipeline.Combined with the characteristics of crude oil sequential pipeline, three widely used oil mixing calculation methods were selected.They are the diffusion theory formula, the Austin-Palfrey empirical formula and the equivalent pipe length calculation formula.

Diffusion Theoretical Formula.
The theoretical calculation formula of oil mixing volume is obtained by the empirical modification of the diffusion theory, which can be called the theoretical formula or the semi-empirical formula [17].The formula assumes that the time when the oil mixing head reaches the end of the pipeline is t1, the time when the entire oil mixing section passes through the end of the pipeline is t2, and the amount of oil mixed formed by the batch of oil in the pipeline is expressed by Vh (unit m 3 ).
) ( where Q -the average amount of oil mixing flowing through the pipeline, m 3 /s; The turbulence correction coefficient is introduced to obtain the calculation formula of the length of the oil mixture.where C, D, L -represent the length of the mixture, the inner diameter of the pipe and the length of the pipe, respectively, m.
The distance between the two interfaces with a forward oil concentration of 99%~1% is defined as the length of the mixing section, so Z is 1.645; when the Reynolds number is small during sequential transportation, the correction coefficient is 2.00 for calculation.
The theoretical calculation formula does not take into account the error of the turbulent diffusion coefficient K and the viscous hysteresis effect of the boundary layer, and there is a large computational error in the flow regime corresponding to low Reynolds number [18], but because of its wide range of application and applicability, it is the original model for the study of oil mixtures diffusion in CFD theory.

Empirical Formula for Calculating the Amount of Austin-Palfrey Oil Mixture
Austin [19] found through experiments and field practice that with the increase of Reynolds number, the growth of oil mixing length slows down when it exceeds a certain critical value, and summarised the Austin-Palfrey formula, which is the most widely used for calculating oil mixing length.
The calculation formula is summarized on the basis of a large number of laboratory data and field data, which is widely used, and the formula is as follows.
When Re> Rej: In Formula: Kinematic viscosity of A oil at conveying temperature, m 2 /s; Kinematic viscosity of B oil at conveying temperature, m 2 /s; Calculated kinematic viscosity of oil mixture at conveying temperature, m 2 /s.
(2) The influence of the conveying sequence on the oil mixing is not considered; (3) According to the symmetry of concentration, the distance between the two interfaces with a concentration of 99%~1% of the preceding oil is defined as the length of the mixing section.
The Austin-Palfrey empirical formula can be applied to the diffusion prediction of different types of oil mixtures, but it lacks a theoretical foundation, so it cannot provide a detailed explanation of the mechanism behind the diffusion of oil mixtures, and it relies on the support of accurate and reliable oil mixtures data in practical engineering applications, which is a high requirement for field applications.

Equivalent Pipeline Length Method Calculation Formula for Oil
Mixing.There are many distribution points and large changes in oil transmission along the refined oil pipeline, while the oil quality of crude oil pipelines is high, the temperature along the line changes greatly, and the oil quality changes greatly.If the calculation of oil mixing volume directly according to the average Reynolds number will lead to a large error, Chen Qingxun [20] scholars proposed the equivalent pipeline length calculation method, which fully considered the influence of Reynolds number change on oil mixture.The equivalent pipeline length method is to divide the pipeline into several sections according to the working conditions or pipeline length, and the initial oil mixture or the oil mixture formed in the previous section is converted into the pipe length that should have to produce the same amount of oil mixture under the current working conditions (the next section of pipeline), the pipeline length is the equivalent pipeline length, and the equivalent pipeline length and the pipe length to be calculated are added as the equivalent pipeline length to calculate the oil mixing amount of the pipe section.
Suppose the oil mixing head is transported by distance L1, and the Reynolds number is Re1, forming the oil mixing length C1; When the flow state changes and the Reynolds number is Re2, it is calculated from the oil mixture length C1 that the equivalent length of the pipeline L ' which forms the C1 length oil mixture, is formed with the Reynolds number Re2: When the oil mixing head is transported at a distance of L2, the length of the oil mixture formed at this time is: Equivalent pipeline length calculation method is simple and intuitive, which can realise the rapid estimation of pipeline length required for oil blending and diffusion, and is applicable to a variety of oil blending systems and engineering scenarios, but the accuracy of the results depends on the accuracy of the assumptions of oil blending system, and there are certain limitations for complex oil blending systems.

Calculation Examples
SH line is the only external pipeline in the eastern area of the northern Xinjiang oil ring network, with a pipe diameter of D426×10 (7/8) straight seam steel pipe (made of 16Mn steel), with a total length of 101.12km.At present, two types of oil are transported sequentially, namely Medium I and Medium II.

Comparison of Calculation Results of Mixed Oil.
According to the basic data of SH line, different seasonal operating conditions are selected for calculation.The calculation results of the oil mixing derived from the diffusion theory are shown in table 1.The results of the calculation of the Austin-Palfrey empirical formula are shown in table 2. By sorting out the on-site oil mixing data of the SH line in the past two years, it is found that some data have problems such as errors and incompleteness, and the data quality will affect the correction of the calculation formula of oil mixing quantity.Remove the obvious erroneous data, compare the statistical results of the actual oil mixture on site with the theoretical calculated values, see table 4, and the comparison trend of the calculated values of each theoretical formula and the actual values is shown in figure 1.The diffusion theory formulation does not consider the viscous hysteresis effect of the boundary layer, which leads to a large error in the calculation of flow regimes with small Reynolds numbers; whereas the equivalent pipe length method introduces an equivalent pipe diameter parameter to further extend the Austin-Palfrey empirical formulation, with a higher computational accuracy.The equivalent pipe length method considers the change of Reynolds number during transportation, and the curve trend is basically consistent with the actual situation, due to the characteristics of low Reynolds number of SH line, the actual oil mixing amount is much greater than the calculated oil mixing amount.Therefore, the equivalent tube length formula needs to be modified.By comparing the conditions used, the variables considered, and the hypotheses proposed by the three calculation methods, it is concluded that the equivalent pipeline length method is more suitable for calculating the amount of oil mixed in the sequential transportation of low Reynolds number variable temperature crude oil pipeline.

Modification of the Calculation
Formula for the Amount of Oil Mixed in the SH Line.At present, the SH line sequentially transports intermediate I. and intermediate II.crude oil, of which the density and viscosity of medium II are large, the outbound temperature of the SH line is higher, the temperature along the line changes greatly, and the viscosity change leads to the change of Reynolds number.The oil mixing amount of SH line is calculated by equivalent pipe length method, the step length is set to 1km, and it is divided into 101 pipe sections, and the oil mixing amount change caused by the change of Reynolds number is considered in turn.However, it cannot be directly calculated by the equivalent pipeline length formula, because the transmission volume of the SH line is small, the Reynolds number is much lower than the critical Reynolds number during operation, and there will occasionally be laminar flow at the end of the pipeline, and the actual oil mixing amount should be slightly greater than the oil mixing amount calculated directly by the formula.Therefore, it is necessary to correct the calculation formula of the oil mixing quantity under the equivalent pipeline length method based on the actual oil mixing amount, and the correction results are shown in table 5.

1 ) 1 2 1 2
In Formula: C is the length of the oil mixture, m; L is the conveying distance, m; d is the inner diameter of the pipe, m; Re is the Reynolds number; Rej is the critical Reynolds number, The kinematic viscosity of the mixed oil is calculated by the following empirical formula, and the Reynolds number is calculated from this viscosity; (  × 10 6 + 0.89) = (   × 10 6 + 0.89) + (   × 10 6 + 0.89) By analogy, the calculated equivalent pipe length is superimposed on the previous section, and the calculated final oil mixing length is:

Figure 1 .
Figure 1.Comparison curve of the calculation results of the three formulas.

Table 1 .
Calculation results of oil mixture theory derived from diffusion theory.

Table 2 .
Results of the calculation formula of Austin-Palfrey oil mixture.The calculation results of the equivalent pipe length method are shown in table3. 6

Table 3 .
Calculation results of equivalent equivalent pipe length formula.

Table 4 .
Comparison of the actual oil mixing amount on site with the oil mixing amount calculated by the three formulas.

Table 5 .
Correction of the formula for calculating the amount of mixed oil.