CN115809730B - Large crude oil storage tank heat loss prediction method - Google Patents

Abstract

The invention relates to a method for predicting heat loss of a large crude oil storage tank, which comprises: obtaining the real-time changing values of heat flux density, atmospheric temperature, soil temperature, and solar radiation heat at different positions of the large crude oil storage tank through on-site testing; Take a small amount of crude oil out of the tank, test the density, viscosity, and specific heat capacity of crude oil at different temperatures in the tank, establish a variable physical model of crude oil, measure the distribution of crude oil temperature field at different times, and determine the density, viscosity, and specific heat capacity of crude oil; The boundary heat loss is affected by the external dynamic thermal environment and the internal crude oil physical properties; the correlation between each influencing factor and the storage tank boundary heat flux is tested separately; a mathematical model of the waxy crude oil storage tank boundary heat flux loss is established to obtain the storage tank boundary heat flow The functional relationship between the density, the external dynamic thermal environment and the internal crude oil variable physical parameters is used to determine the overall heat loss of the storage tank. The invention realizes the accurate prediction of the heat loss of the storage tank.

Description

A method for predicting heat loss of large crude oil storage tanks

Technical field:

The invention belongs to the technical field of oil and gas storage and transportation, and in particular relates to a method for predicting heat loss of a large crude oil storage tank.

Background technology:

In recent years, the total oil storage capacity of my country's oil depots is nearly 85 million tons. The gas and oil consumption of heating furnaces used to maintain safe storage and external transmission of oil products each year accounts for more than 85% of the heat consumption of the ground production system, and also produces a large amount of carbon dioxide emissions. How to reduce the energy consumption of crude oil storage while ensuring the safe production of oil depots will play an important role in promoting energy conservation and consumption reduction for oilfield enterprises and implementing low-carbon development. During the crude oil storage process, the boundary of the crude oil storage tank is in direct contact with the external environment, resulting in a large temperature difference between the inside and outside of the storage tank, serious heat loss, and a large amount of energy waste, high fuel consumption, and increased carbon emissions. Therefore, it is necessary to grasp the overall heat loss of crude oil storage tanks, so as to provide theoretical support for oilfield enterprises to reduce carbon emissions from crude oil reserves and improve the utilization efficiency of reserve energy.

Theoretical calculation method is usually used to obtain the heat loss at the boundary of crude oil storage tanks. This calculation method determines the heat flux value by multiplying the temperature difference between the inside and outside of the tank with the heat transfer coefficient. On this basis, the heat loss at the boundary of the tank is determined by multiplying the surface area of the tank boundary and time. This method ideally simplifies the thermal environment of the tank into a fixed solution condition, resulting in the heat transfer coefficient being used as a fixed value to calculate the heat loss. However, in practice, the tank is affected by boundary factors such as atmospheric temperature, solar radiation, soil temperature, and the physical properties of the internal crude oil. The heat transfer process of crude oil from the inside to the outside changes in an oscillating and fluctuating manner, causing the heat transfer coefficient to change dynamically. Therefore, it is impossible to accurately measure the heat loss at the boundary of the tank. It can be seen that the theoretical calculation method has certain limitations for the determination of heat loss at the boundary of the tank. Therefore, it is necessary to establish a new prediction method for heat loss of large crude oil storage tanks to achieve accurate prediction of the overall heat loss of the tank.

In summary, the current measurement of heat loss in crude oil storage tanks has certain limitations and cannot scientifically and accurately predict the heat loss of large crude oil storage tanks.

Summary of the invention:

The purpose of the present invention is to provide a method for predicting heat loss of a large crude oil storage tank, which is used to solve the problem that the prior art cannot accurately measure the heat loss of the storage tank boundary.

The technical solution adopted by the present invention to solve the technical problem is: the heat loss prediction method of a large crude oil storage tank comprises the following steps:

Step 1: Use a heat flux meter, surface thermometer and solar radiation meter to conduct on-site tests on the heat flux density, atmospheric temperature, soil temperature and solar radiation heat at different locations on the boundary of a large crude oil storage tank, and obtain the real-time change values of the heat flux density, atmospheric temperature, soil temperature and solar radiation heat;

Step 2: Take a small amount of crude oil from a large crude oil storage tank, use a petroleum density meter, a crude oil rheology meter, and a differential scanning calorimeter to test the density, viscosity, and specific heat capacity of the crude oil at different temperatures in the tank, and establish a variable property model of crude oil; use a temperature sensing probe arranged on the guide column in the large crude oil storage tank to measure the temperature field distribution of the crude oil at different times, and determine the density, viscosity, and specific heat capacity of the crude oil;

The variable property model of the crude oil is as follows:

Crude oil density:

ρ _oil =ρ ₂₀ [1-ξ(t _oil -20)]

Wherein, ρ _oil is the crude oil density, kg·m ^-3 ; ρ ₂₀ is the crude oil density at 20℃, kg·m ^-3 ; t _oil is the crude oil temperature, ℃; ξ is the regression coefficient;

Specific heat capacity of crude oil:

Where, c _oil is the specific heat capacity of crude oil, J·(kg·℃) ^-1 ; b ₀ , b ₁ , b ₂ , b ₃ , b ₄ are the regression coefficients;

Crude oil viscosity:

Wherein, μ _oil is the dynamic viscosity of crude oil, Pa·s, K and m are regression coefficients;

Step 3: The heat loss at the tank boundary is affected by the external dynamic thermal environment and the internal crude oil properties. Considering the different dimensions of the factors affecting the external dynamic thermal environment and the internal crude oil physical properties, which will affect the results of data analysis, the data are normalized without changing the original distribution law of the data, eliminating the dimensional influence between the indicators and making the data indicators comparable.

Step 4: Conduct a correlation test on each influencing factor and the heat flux density of the tank boundary separately, and use the correlation coefficient as the basis for correlation judgment. When the absolute value of the correlation coefficient is above 0.6, it is considered that the correlation between the two is significant. The influencing factors with an absolute value below 0.6 are eliminated to determine the main influencing factors;

表示第j个影响因素与储罐边界热流密度的相关系数，该系数绝对值在0.6以上时，表示两变量之间相关性显著，反之，则表示两变量之间相关性较弱；

表示第j个影响因素与储罐边界热流密度的协方差；

表示第j个影响因素的标准差、σ_q表示储罐边界热流密度标准差；

表示第j个影响因素的平均值；

表示储罐边界热流密度的平均值；In the formula,

It represents the correlation coefficient between the jth influencing factor and the heat flux density of the tank boundary. When the absolute value of the coefficient is above 0.6, it means that the correlation between the two variables is significant. Otherwise, it means that the correlation between the two variables is weak.

represents the covariance between the jth influencing factor and the heat flux density at the tank boundary;

represents the standard deviation of the jth influencing factor, σ _q represents the standard deviation of the heat flux density at the tank boundary;

represents the average value of the jth influencing factor;

represents the average value of the heat flux density at the tank boundary;

Step 5: Based on the multivariate nonlinear regression mathematical method, a mathematical model of heat flux loss at the boundary of the waxy crude oil storage tank is established to obtain the functional relationship between the heat flux density at the boundary of the tank and the external dynamic thermal environment and the internal crude oil variable property parameters. On this basis, the overall heat loss of the tank is determined by multiplying the area of the tank top, tank wall and tank bottom with time;

The crude oil storage tank boundary heat flux loss regression model is shown in the following formula:

表示第j个影响因素经归一化处理后在第i个边界热流密度的取值：a₀、a₁…a_j表示模型的回归系数，k为回归模型中影响因素的次幂系数。Where, q _i is the measured value of the heat flux density at the boundary of the i-th tank, W/m ² ;

represents the value of the heat flux density at the ith boundary after normalization of the jth influencing factor: a ₀ , a ₁ , … a _j represents the regression coefficient of the model, and k is the power coefficient of the influencing factor in the regression model.

Step 3 of the above scheme is specifically as follows:

The heat flux density at the boundary of the storage tank is taken as the reference series, and the external and internal influencing factors are taken as the comparison series, wherein the reference series is composed of the heat flux density at the boundary of the storage tank directly measured by the measuring instrument, denoted as {q _i }, i = 1, 2, 3…, n; the comparison series is composed of the external dynamic thermal environment of the storage tank and the internal crude oil variable property parameters, denoted as {X _j,i }, wherein j = 1, 2, 3, 4, 5, 6, i = 1, 2, 3…, n; X _j,i represents the value of the heat flux density of the jth influencing factor at the i-th boundary, the atmospheric temperature is denoted as {X _1,i }, the solar radiation heat is denoted as {X _2,i }, the crude oil density is denoted as {X _3,i }, the crude oil viscosity is denoted as {X _4,i }, the crude oil specific heat capacity is denoted as {X _5,i }, and the soil temperature is denoted as {X _6,i };

In order to eliminate the influence of different dimensions and magnitudes of influencing factors on the data analysis results, normalization processing is used on the basis of the original data distribution law to make the data change range in [0,1], as shown in the following formula:

表示第j个影响因素经归一化处理后在第i个边界热流密度的取值；X_j,i表示第j个影响因素在第i个边界热流密度的取值；max(X_j,i)表示在各影响因素比较数列当中的最大值、min(X_j,i)表示在各影响因素比较数列当中的最小值；In the formula,

represents the value of the heat flux density of the jth influencing factor at the i-th boundary after normalization; X _j,i represents the value of the heat flux density of the jth influencing factor at the i-th boundary; max(X _j,i ) represents the maximum value in the comparison series of each influencing factor, and min(X _j,i ) represents the minimum value in the comparison series of each influencing factor;

太阳辐射热记作为

原油密度记作为

原油粘度记作为

原油比热容记作为

土壤温度记作为

The new series obtained after normalization of the influencing factor comparison series includes the atmospheric temperature recorded as

Solar radiation heat

The density of crude oil is recorded as

The viscosity of crude oil is recorded as

The specific heat capacity of crude oil is recorded as

Soil temperature is recorded as

The present invention has the following beneficial effects:

The present invention comprehensively considers factors such as the dynamic changes in the environment outside the storage tank and the variable physical properties of the internal crude oil, and establishes a prediction method for heat loss of large crude oil storage tanks based on the multivariate nonlinear regression mathematical method. It breaks through the limitation that the heat transfer coefficient changes in real time due to internal and external factors in the theoretical calculation process, realizes the prediction of heat loss of storage tanks, and provides theoretical support for oil depot production management to achieve the goal of reducing energy consumption and reducing carbon emissions.

Description of the drawings:

Figure 1 is a schematic diagram of radial and axial measurement points on the outside of a large crude oil storage tank.

Specific implementation method:

The present invention will be further described below in conjunction with the accompanying drawings:

This method for predicting heat loss in large crude oil storage tanks includes the following:

Step 1: Taking large crude oil storage tanks as the research object, heat flux meters, surface thermometers and solar radiation meters are used to conduct on-site tests on the heat flux density, atmospheric temperature, soil temperature and solar radiation heat at different locations on the tank boundary to obtain various real-time change data.

The external environment test of the tank uses a heat flux meter, surface thermometer and solar radiation meter to conduct on-site tests on the heat flux density, atmospheric temperature, soil temperature and solar radiation heat at different locations on the outer surface of the tank. The tested tank is divided into multiple test areas. In each area, in order to ensure the accuracy of the measurement results and take into account the test efficiency, representative locations are selected and as many measurement points as possible are arranged. When the local test results show a large change gradient or abnormal changes, consider encrypting the test locations.

The heat flux density change data on the top of the tank can be directly measured by a heat flux meter, but the tank wall is affected by the insulation layer and the external reflective strip, which makes it impossible for the heat flux meter to measure the heat flux density of the steel tank wall. Therefore, it is necessary to arrange measuring points along the spiral staircase on the tank wall, and open the reflective strips and insulation materials at the measuring points to ensure the accuracy of the measured tank wall heat flux density data, which will be restored after the measurement. The bottom of the tank is in direct contact with the ground, so the heat flux density of the tank bottom cannot be measured, and the data from the tank wall measuring points close to the ground are used instead. The hourly atmospheric temperature, soil temperature, solar radiation heat, and heat flux density values are determined by taking the average of 10 test results, as shown in Figure 1.

Step 2: Take out a small amount of crude oil from the tank, and use indoor experimental instruments such as petroleum density meter, crude oil rheology meter, differential scanning calorimeter to test the change law of density, viscosity, specific heat capacity and other related physical properties of crude oil at different temperatures in the tank, establish a variable physical property model of crude oil, and use the temperature sensing probe arranged on the guide column in the tank to obtain the distribution of crude oil temperature field at different times, and determine the relevant physical property parameters such as crude oil density, viscosity, specific heat capacity, etc.

Since the density, viscosity and specific heat capacity of waxy crude oil will show different changing patterns with temperature, a small amount of crude oil needs to be extracted from the storage tank, and the physical properties of crude oil at different temperatures are measured by indoor experimental instruments such as oil density meter, crude oil rheology meter, differential scanning calorimeter, etc., and the measured data are fitted to obtain the curves of crude oil density, viscosity and specific heat capacity changing with temperature.

As the temperature of crude oil increases, the density gradually decreases in a linear pattern, the viscosity changes in an exponential pattern and is greatly affected by the change in crude oil temperature, while the specific heat capacity shows a trend of first increasing and then decreasing. The measured data are numerically fitted to obtain the relevant variable property model.

Density of crude oil:

ρ _oil =ρ ₂₀ [1-ξ(t _oil -20)]

Wherein, ρ _oil is the density of crude oil, kg·m ^-3 ; ρ ₂₀ is the density of crude oil at 20℃, kg·m ^-3 ; t _oil is the temperature of crude oil, ℃; ξ is the regression coefficient.

Specific heat capacity of crude oil:

Where, c _oil is the specific heat capacity of crude oil, J·(kg·℃) ^-1 ; b ₀ , b ₁ , b ₂ , b ₃ , b ₄ are the regression coefficients;

Crude oil viscosity:

Wherein, μ _oil is the dynamic viscosity of crude oil, Pa·s, and K and m are regression coefficients.

The temperature of the crude oil from the bottom to the top of the tank is monitored in real time by the temperature sensing probe arranged on the guide column inside the tank, and the temperature field distribution of the crude oil inside the tank is obtained. The average value is taken as the temperature of the crude oil in the tank. The measured value is determined by taking the average value of 10 test results. The relevant physical property parameters such as crude oil density, viscosity, specific heat capacity, etc. are determined through the established variable physical property model.

Step 3: The heat loss at the tank boundary is affected by the external dynamic thermal environment and the internal crude oil properties. Considering the different dimensions of the influencing factors such as the external dynamic thermal environment of the tank and the internal crude oil physical properties, which will affect the results of data analysis, the data is normalized without changing its original distribution law to eliminate the dimensional influence between indicators and make the data indicators comparable.

The heat flux density at the tank boundary is taken as the reference series, and the external and internal influencing factors are taken as the comparison series. The reference series is composed of the heat flux density at the tank boundary directly measured by the measuring instrument, denoted as {q _i }, where i = 1, 2, 3…, n; the comparison series is composed of the external dynamic thermal environment of the tank and the internal crude oil variable property parameters, denoted as {X _j,i }, where j = 1, 2, 3, 4, 5, 6, i = 1, 2, 3…, n; X _j,i represents the value of the jth influencing factor at the i-th boundary heat flux density, where the atmospheric temperature, solar radiation heat, crude oil density, crude oil viscosity, crude oil specific heat capacity and soil temperature are denoted as {X _1,i }, {X _2,i }, {X _3,i }, {X _4,i }, {X _5,i }, {X _6,i }, respectively.

In order to eliminate the influence of different dimensions and magnitudes of influencing factors on the data analysis results, normalization processing is used on the basis of the original data distribution law to make the data change range in [0,1], as shown in the following formula:

表示第j个影响因素经归一化处理后在第i个边界热流密度的取值；X_j,i表示第j个影响因素在第i个边界热流密度的取值；max(X_j,i)、min(X_j,i)分别表示在各影响因素比较数列当中的最大值、最小值。in,

represents the value of the heat flux density of the jth influencing factor at the i-th boundary after normalization; X _j,i represents the value of the heat flux density of the jth influencing factor at the i-th boundary; max(X _j,i ) and min(X _j,i ) respectively represent the maximum and minimum values in the comparison series of each influencing factor.

The new series obtained after normalization of the influencing factor comparison series include atmospheric temperature, solar radiation heat, crude oil density, crude oil viscosity, crude oil specific heat capacity and soil temperature, which are recorded as

Step 4: Conduct a correlation test on each influencing factor separately with the heat flux density of the tank boundary, and use the correlation coefficient as the basis for correlation judgment. When the absolute value of the correlation coefficient is above 0.6, it is considered that the correlation between the two is significant. The influencing factors with an absolute value below 0.6 are eliminated to determine the main influencing factors.

表示第j个影响因素与储罐边界热流密度的相关系数，该系数绝对值在0.6以上时，表示两变量之间相关性显著，反之，则表示两变量之间相关性较弱；

表示第j个影响因素与储罐边界热流密度的协方差；

σ_q分别表示第j个影响因素的标准差、储罐边界热流密度标准差；

表示第j个影响因素的平均值；

表示储罐边界热流密度的平均值。in,

It represents the correlation coefficient between the jth influencing factor and the heat flux density of the tank boundary. When the absolute value of the coefficient is above 0.6, it means that the correlation between the two variables is significant. Otherwise, it means that the correlation between the two variables is weak.

represents the covariance between the jth influencing factor and the heat flux density at the tank boundary;

σ _q represents the standard deviation of the jth influencing factor and the standard deviation of the heat flux density at the tank boundary;

represents the average value of the jth influencing factor;

Represents the average value of the heat flux density at the tank boundary.

Step 5: Based on the mathematical method of multivariate nonlinear regression, a mathematical model of heat flux density loss at the boundary of waxy crude oil storage tanks is established to obtain the functional relationship between the heat flux density at the boundary of the tank and the external dynamic thermal environment and the internal crude oil variable property parameters. On this basis, the overall heat loss of the tank is determined by multiplying the area of the tank top, tank wall and tank bottom with time.

On the premise of ensuring that the heat flux density at the tank boundary has a significant correlation with its influencing factors, a regression model of heat flux density loss at the crude oil tank boundary is established, as shown in the following formula:

表示第j个影响因素经归一化处理后在第i个边界热流密度的取值：a₀、a₁…a_j表示所建模型的回归系数，k为回归模型中影响因素的次幂系数。Where, q _i is the measured value of the heat flux density at the boundary of the i-th tank, W/m ² ;

represents the value of the heat flux density at the ith boundary after normalization of the jth influencing factor: a ₀ , a ₁ … a _j represents the regression coefficient of the established model, and k is the power coefficient of the influencing factor in the regression model.

将拟合优度R²作为评判回归模型是否优良的依据，当R²趋近于1时，说明所建模型与实际数据高度吻合，可以用来表示储罐边界热流密度与外界动态热环境、原油变物性参数之间的函数关系，如下式所示：After assigning the initial value to the regression model, the iterative solution is performed to obtain the regression coefficients a ₀ , a ₁ … a _j and the power coefficient k of the influencing factor. On this basis, the values of the external and internal influencing factors are brought into the constructed crude oil storage tank boundary heat flux loss regression model to obtain the calculated value of the tank boundary heat flux density, which is recorded as

The goodness of fit ^R2 is used as the basis for judging whether the regression model is good or not. When ^R2 approaches 1, it means that the established model is highly consistent with the actual data, and can be used to express the functional relationship between the heat flux density at the tank boundary and the external dynamic thermal environment and the crude oil variable physical property parameters, as shown in the following formula:

为第i个储罐边界热流密度的计算值，W/m²；SS_tot为总误差，对于总误差来源主要有两个：a.影响因素的多样，导致q_i的多样；b.随机误差SS_res。显然，随机误差SS_res越小，R²越接近于1。Where, q _i is the measured value of the heat flux density at the boundary of the i-th tank, W/m ² ;

is the calculated value of the heat flux density at the boundary of the i-th tank, W/m ² ; SS _tot is the total error, and there are two main sources of the total error: a. The diversity of influencing factors leads to the diversity of q _i ; b. Random error SS _res . Obviously, the smaller the random error SS _res , the closer R ² is to 1.

After testing the goodness of the regression model by the goodness of fit ^R2 , the final mathematical model of heat flux loss at the boundary of the crude oil storage tank was determined as shown in the following formula:

After establishing the functional relationship between the heat flux density at the tank boundary and the external dynamic thermal environment and the internal crude oil variable physical property parameters, the overall heat loss of the tank can be determined, as shown in the following formula:

分别表示储罐罐顶、罐壁以及罐底热流密度的计算值，W/m²；t为时间，s。Wherein, Q _tot represents the heat loss of the entire tank, J; Q _roof , Q _wall , Q _bottom represent the heat loss of the tank top, tank wall, and tank bottom, J; S _roof , S _wall , S _bottom represent the surface area of the tank top, tank wall, and tank bottom, m ² , S _roof ＝S _bottom ＝πr ² , S _wall ＝2πrh, where r is the tank radius, m, and h is the tank height, m;

Respectively represent the calculated values of heat flux density of the tank top, tank wall and tank bottom, W/m ² ; t is time, s.

In order to make the above contents of the present invention more clearly understandable, a storage tank of Daqing Oilfield is taken as a secret research object, and the heat loss of the storage tank during the heating process is predicted and described in detail as follows:

A 100,000 cubic meter floating roof tank in an oil depot of Daqing Oilfield has a bottom diameter of 80m and a wall height of 20m. The density of the oil at 20°C is 860kg/ ^m3 , the viscosity is 4.94Pa·s, and the specific heat capacity is 2986.53J·(kg·℃) ^-1 . Based on the multivariate nonlinear regression mathematical method, the present invention establishes a mathematical model of heat flux density loss at the boundary of crude oil tanks, obtains the functional relationship between the heat flux density at the boundary of the tank and the external dynamic thermal environment and the internal crude oil variable property parameters, thereby realizing the prediction of the overall heat loss of the tank. The specific method steps are as follows:

Step 1: Taking large crude oil storage tanks as the research object, heat flux meters, surface thermometers and solar radiation meters are used to conduct on-site tests on the heat flux density, atmospheric temperature, soil temperature and solar radiation heat at different locations on the tank boundary to obtain real-time change data. The specific changes are shown in the table.

Step 2: Take out a small amount of crude oil from the tank, and use indoor experimental instruments such as petroleum density meter, crude oil rheology meter, differential scanning calorimeter to test the change law of density, viscosity, specific heat capacity and other related physical properties of crude oil at different temperatures in the tank, establish a variable physical property model of crude oil, and use the temperature sensing probe arranged on the guide column in the tank to obtain the distribution of crude oil temperature field at different times, and determine the relevant physical property parameters such as crude oil density, viscosity, specific heat capacity, etc.

The physical properties of crude oil at different temperatures are measured by indoor experimental instruments such as petroleum density tester, crude oil rheology tester, differential scanning calorimeter, etc., and the measured data are fitted to obtain the variable physical property model of crude oil, as shown below:

The density of crude oil is negatively linearly correlated with temperature. As the temperature of crude oil increases, the density decreases. The viscosity of crude oil changes exponentially and is greatly affected by temperature changes. Taking 20℃ as the dividing point, the viscosity decreases rapidly from 2 to 20℃, from 36.46Pa·s to 4.94Pa·s; the viscosity decreases slowly from 20 to 50℃, only changing by 4.58Pa·s. The specific heat capacity of crude oil increases first and then decreases with the increase of temperature. At 20℃, the specific heat capacity of crude oil reaches a maximum value of 2986.53J·(kg·℃) ^-1 , and then begins to decrease with the increase of temperature. At 44℃, the specific heat capacity of crude oil reaches a minimum value of 2228.12J·(kg·℃) ^-1 . The crude oil variable property model is as follows:

Density of crude oil:

ρ _oil =870×[1-0.00061(t _oil -20)]

Specific heat capacity of crude oil:

Crude oil viscosity:

The real-time change of the temperature of the crude oil in the tank is obtained by the temperature sensing probe on the guide column in the tank. The variable property model of crude oil is used to obtain the real-time change values of the physical properties of the crude oil in the tank at different temperatures, as shown in the following table:

Step 3: The heat loss at the tank boundary is affected by the external dynamic thermal environment and the internal crude oil properties. Considering the different dimensions of the influencing factors such as the external dynamic thermal environment of the tank and the internal crude oil physical properties, which will affect the results of data analysis, the data are normalized without changing the original distribution law of the data to eliminate the dimensional influence between the indicators and make the data indicators comparable. The heat flux density and influencing factor measurement data measured at the top of the tank are taken as an example.

The heat flux density of the tank top measured by the experimental instrument is recorded as {q _i }, and the atmospheric temperature, solar radiation heat of the tank top, crude oil density, crude oil viscosity, and crude oil specific heat capacity as the influencing factors of the tank top heat flux density are recorded as {X _1,i }, {X _2,i }, {X _3,i }, {X _4,i }, and {X _5,i }, respectively, as shown below:

{q _i }＝{82.34,81.79,81.13,80.04,78.86,77.60,73.20,69.39,65.92,63.30,61.74,61.33,61.86,63.58,66.46,69.95,74.21,78.50,80.10, 81.45,82.70,83.59, 84.23,84.45}

{X _1,i }＝{-30.01,-29.61,-28.98,-28.15,-27.19,-26.15,-25.12,-24.15,-23.32,-22.69,-22.29,-22.15,-22.28,-22.68, -23.32,-24.14,-25.11,-26.14,-27.18,-28.14,-28.97,-29.61,-30.01,-30.15}

{X _2,i }＝{0,0,0,0,0,0,0,48.27,91.82,126.38,148.57,156.21,148.57,126.38,91.82,48.27,0,0,0,0,0, 0,0,0}

{ _, 853.47,853.51,853.52,853.53,853.53, 853.55,853.54,853.53}

_{ 1.42,1.42,1.42}

{ , _{2599.46,2601.58,2604.88,2608.55,2609.40,2610.30,2610.36} , 2611.50,2611.39,2610.01}

Similarly, the heat flux density of the tank wall is also affected by five factors: atmospheric temperature, solar radiation heat of the tank wall, crude oil density, crude oil viscosity, and crude oil specific heat capacity, and is recorded as:

{q _i }＝{21.70,21.62,21.43,21.19,20.69,20.43,18.93,19.10,19.00,18.94,19.00,19.01,19.01,18.98,19.05,18.99,18.96,20.45,20.78, 21.12,21.58,21.77, 21.80,21.88}

{X _1,i }＝{-30.01,-29.61,-28.98,-28.15,-27.19,-26.15,-25.12,-24.15,-23.32,-22.69,-22.29,-22.15,-22.28,-22.68, -23.32,-24.14,-25.11,-26.14,-27.18,-28.14,-28.97,-29.61,-30.01,-30.15}

{X _2,i }＝{0,0,0,0,0,0,128.69,125.60,122.82,120.60,119.19,118.70,119.19,120.60,122.82,

125.60,128.69,0,0,0,0,0,0,0}

{X _3,i }＝{853.72,853.70,853.68,853.66,853.64,853.61,853.55,853.51,853.47,853.44,

853.41,853.40,853.39,853.41,853.41,853.43,853.47,853.51,853.52,853.53,853.53,

853.55,853.54,853.53}

_{

1.39,1.40,1.41,1.41,1.42,1.42,1.42,1.42,1.42}

_{

2602.29,2599.47,2598.37,2597.89,2599.70,2599.46,2601.58,2604.88,2608.55,2609.40,

2610.30,2610.36,2611.50,2611.39,2610.01}

Since the bottom of the storage tank is in direct contact with the soil, its heat flux density change is not affected by the atmospheric temperature and solar radiation heat, but is only related to the crude oil density, crude oil viscosity, crude oil specific heat capacity and soil temperature. The tank bottom heat flux density, crude oil density, crude oil viscosity, crude oil specific heat capacity and soil temperature can be recorded in turn as:

{q _i }＝{50.08,49.76,49.28,48.63,47.87,47.03,46.23,45.46,44.84,44.33,44.04,43.98,44.12,

44.50,45.08,45.78,46.62,47.53,48.41,49.27,49.96,50.55,50.91,50.97}

{X _3,i }＝{853.72,853.70,853.68,853.66,853.64,853.61,853.55,853.51,853.47,853.44,

853.41,853.40,853.39,853.41,853.41,853.43,853.47,853.51,853.52,853.53,853.53,

853.55,853.54,853.53}

_{

1.39,1.40,1.41,1.41,1.42,1.42,1.42,1.42,1.42}

_{

2602.29,2599.47,2598.37,2597.89,2599.70,2599.46,2601.58,2604.88,2608.55,2609.40,

2610.30,2610.36,2611.50,2611.39,2610.01}

_{

-18.78,-19.18,-19.82,-20.64,-21.61,-22.64,-23.68,-24.64,-25.47,-26.11,-26.51,-26.65}

Taking the atmospheric temperature as an example of the factors affecting the heat flux density at the tank top, the maximum value max(X _{1,i ) in the sequence {X 1 ,i} } is -22.15, and the minimum value max(X _1,i ) is -30.15. The values in the sequence are normalized as follows:

Similarly, the normalized values of each item in the series are shown in the following table:

This gives a new series of normalized atmospheric temperature:

Similarly, the normalized series of other factors affecting the heat flux density on the tank top can be obtained:

Similarly, the normalized new series of factors affecting the heat flux density of the tank wall and tank bottom are obtained;

The normalized series of factors affecting the heat flux density of the tank wall:

The normalized series of factors affecting the heat flux density at the bottom of the tank:

Step 4: Conduct a correlation test on each influencing factor separately with the heat flux density of the tank boundary, and use the correlation coefficient as the basis for correlation judgment. When the absolute value of the correlation coefficient is above 0.6, it is considered that the correlation between the two is significant. The influencing factors with an absolute value below 0.6 are eliminated to determine the main influencing factors.

Taking the heat flux density on the top of the storage tank and the atmospheric temperature as an example, the correlation test is carried out. The specific calculation process is as follows:

计算：average value

calculate:

σ_Q计算：Standard Deviation

σ _Q calculation:

计算：Covariance

calculate:

Correlation coefficient between heat flux density at tank top boundary and atmospheric temperature

After calculation, the correlation coefficient between the atmospheric temperature and the heat flux density on the tank top is -0.975, and the correlation between the two is significant. Similarly, according to the same calculation steps, the correlation coefficients between the heat flux density on the tank top and the solar radiation heat on the tank top, crude oil density, crude oil viscosity and crude oil specific heat capacity can be obtained, which are:

Similarly, the correlation coefficients between the heat flux density of the tank wall and tank bottom and their respective influencing factors are calculated:

The correlation coefficients between the tank wall heat flux density and the tank wall solar radiation heat, crude oil density, crude oil viscosity and crude oil specific heat capacity are:

The correlation coefficients between the heat flux density at the bottom of the tank and the crude oil density, crude oil viscosity, crude oil specific heat capacity and soil temperature are:

Usually, when the absolute value of the correlation coefficient is above 0.6, it is considered that two variables have a strong correlation. It can be seen that the changes in the heat flux density of the tank top, tank wall and tank bottom are significantly correlated with each corresponding influencing factor. Therefore, a mathematical relationship can be established between the external dynamic thermal environment, crude oil variable physical properties and the heat flux density of the tank boundary to characterize the changes in the heat flux density of the tank boundary.

Step 5: Based on the mathematical method of multivariate nonlinear regression, a mathematical model of heat flux loss at the boundary of a waxy crude oil storage tank is established to obtain the functional relationship between the heat flux at the boundary of the tank and the external dynamic thermal environment and the internal crude oil variable physical property parameters. On this basis, the overall heat loss of the tank is determined by multiplying the area of the tank top, tank wall and tank bottom with time. Taking the establishment of a mathematical model of heat flux loss at the tank top as an example, the heat flux at the tank top is used as the dependent variable q _i , and the atmospheric temperature, solar radiation heat at the tank top, crude oil density, viscosity and specific heat capacity are used as independent variables respectively.

Tank top heat flux loss regression model:

After multivariate nonlinear regression, the coefficients and power coefficients are:

a ₀ =84.3451, a ₁ =-25.9386, a ₂ =2.5873, a ₃ =-28.0169, a ₄ =3.8357, a ₅ =21.4503, k =2.

The values of external and internal influencing factors are introduced into the established crude oil tank top heat flux loss regression model to obtain the calculated value of the tank top heat flux density, which is recorded as

In order to verify the accuracy of the constructed model, it is necessary to calculate the goodness of fit ^R2 of the model. When the goodness of fit approaches 1, it means that the constructed tank top heat flux loss regression model is consistent with the actual situation.

Random error SS _res calculation:

Calculation of total error SS _tot :

Therefore, the goodness of fit ^R2 is:

After calculation, the goodness of fit ^R2 is close to 1, which proves that the established tank top heat flux loss regression model can fully reflect the actual loss of tank top heat flux density. Therefore, the mathematical model of tank top heat flux loss can be determined as:

The same calculation steps can be used to obtain the mathematical models of heat flux loss on the tank wall and tank bottom.

The mathematical model of heat flux loss of the tank wall has a goodness of fit of R ² = 0.988:

The mathematical model of heat flux loss at the tank bottom has a goodness of fit of R ² = 0.999:

可得到储罐升温过程中，一天内储罐边界向外界散失的总热量Q_tot。After calculating the heat flux loss value of the tank boundary, the formula

The total heat Q _tot lost from the tank boundary to the outside in one day during the tank heating process can be obtained.

S _roof ＝S _bottom ＝πr ² ＝3.14×40 ² ＝5024(m ² )

S _wall = 2πrh = 2 × 3.14 × 40 × 20 = 5024 (m ² )

Heat loss at the tank top:

Heat loss at tank wall:

Heat loss at the bottom of the tank:

Overall heat loss of the tank:

Q _tot ＝Q _roof +Q _wall +Q _bottom ＝32333419.01+8775623.93+20532223.87＝61641266.81(KJ)

According to calculation, the overall heat loss of the storage tank in one day is 61641266.81KJ, among which the heat loss at the top of the tank is the most serious at 32333419.01KJ; the heat loss at the tank wall is 8775623.93KJ; and the heat loss at the bottom of the tank is 20532223.87KJ.

In general, this large crude oil storage tank heat loss prediction method directly converts the difficult problem of the heat transfer coefficient in the theoretical calculation method being dynamically affected by internal and external factors into a functional relationship between the heat flux density at the tank boundary and the external dynamic thermal boundary conditions and the variable physical properties of the crude oil, thereby achieving an accurate prediction of the heat loss of the tank. This prediction method can provide a theoretical basis for oilfield enterprises to save energy and reduce consumption in oil depot production management.

Claims (4)

1. The method for predicting the heat loss of the large crude oil storage tank is characterized by comprising the following steps of:

step one: the method comprises the steps of performing field test on heat flux density, atmospheric temperature, soil temperature and solar radiation heat at different positions of the boundary of a large crude oil storage tank by adopting a heat flux meter, a surface thermometer and a solar radiation measuring instrument to obtain real-time change values of the heat flux density, the atmospheric temperature, the soil temperature and the solar radiation heat;

step two: taking out a small amount of crude oil from a large crude oil storage tank, and using a petroleum density tester, a crude oil rheological tester and a differential scanning calorimeter to test the change rules of density, viscosity and specific heat capacity of the crude oil at different temperatures in the tank to establish a variable physical property model of the crude oil; the distribution condition of the crude oil temperature field at different moments is measured through a temperature sensing probe arranged on a guide column in a large crude oil storage tank, and the density, viscosity and specific heat capacity of the crude oil are determined;

step three: the boundary heat loss of the storage tank is comprehensively influenced by the external dynamic thermal environment and the physical properties of the internal crude oil, the data analysis result is influenced by considering the difference of dimension between the external dynamic thermal environment of the storage tank and the physical property parameter influence factors of the internal crude oil, the data is normalized on the basis of not changing the original distribution rule of the data, the dimension influence among indexes is eliminated, and the data indexes are comparable;

step four: performing relevance test on each influence factor and the boundary heat flux density of the storage tank independently, taking a relevance coefficient as a relevance judgment basis, when the absolute value of the relevance coefficient is more than 0.6, obviously judging the relevance between the two, and eliminating influence factors with absolute values below 0.6;

in the method, in the process of the invention,

the correlation coefficient of the j-th influencing factor and the boundary heat flux density of the storage tank is represented, when the absolute value of the coefficient is more than 0.6, the correlation between the two variables is obvious, otherwise, the correlation between the two variables is weaker;

Representing covariance of j-th influencing factors and boundary heat flux density of the storage tank;

Standard deviation sigma representing the jth influencing factor _q Representing the standard deviation of the boundary heat flux density of the storage tank;

Mean value of j-th influencing factors;

Representing an average value of the boundary heat flux density of the storage tank;

step five: based on a multiple nonlinear regression mathematical method, a mathematical model of the boundary heat flux density loss of the waxy crude oil storage tank is established, and the product of the functional relation between the boundary heat flux density of the storage tank, the external dynamic heat environment and the variable physical parameters of the internal crude oil, the tank top, the tank wall and the tank bottom area and the time is obtained to determine the integral heat loss of the storage tank.

2. The method for predicting heat loss of a large crude oil storage tank according to claim 1, wherein: the variable property model of the crude oil is as follows:

crude oil density:

ρ _oil ＝ρ ₂₀ [1-ξ(t _oil -20)]

wherein ρ is _oil Is the density of crude oil, kg.m ^-3 ；ρ ₂₀ The density of crude oil at 20 ℃ is kg.m ^-3 ；t _oil Is the temperature of crude oil, DEG C; ζ is a regression coefficient;

specific heat capacity of crude oil:

wherein, c _oil Is the specific heat capacity of crude oil, J (kg · DEG C) ^-1 ；b ₀ 、b ₁ 、b ₂ 、b ₃ 、b ₄ Is the regression coefficient of each item;

viscosity of crude oil:

wherein mu is _oil The dynamic viscosity of crude oil is Pa.s, K, m, and the regression coefficient.

3. The method for predicting heat loss of a large crude oil storage tank according to claim 2, wherein: the third step is specifically as follows:

taking the boundary heat flux density of the storage tank as a reference sequence and external and internal influence factors as a comparison sequence, wherein the reference sequence consists of the boundary heat flux density of the storage tank directly measured by a measuring instrument and is recorded as { q } _i I=1, 2,3 …, n; the comparative series is composed of dynamic thermal environment outside the storage tank and variable physical property parameters of crude oil inside the storage tank and is marked as { X } _j,i -j = 1,2,3,4,5,6, i = 1,2,3 …, n; x is X _j,i The value of the heat flux density of the jth influencing factor at the ith boundary is represented, and the atmospheric temperature is recorded as { X ] _1,i Solar radiation heat is recorded as { X } _2,i Density of crude oil is recorded as { X } _3,i Viscosity of crude oil is recorded as { X } _4,i Specific heat capacity of crude oil as { X } _5,i The temperature of the soil is recorded as { X } _6,i }；

In order to eliminate the influence of different scales and magnitude orders among influence factors on the data analysis result, on the basis of the original data distribution rule, normalization processing is adopted to ensure that the data change interval is in [0,1], and the following formula is shown:

in the method, in the process of the invention,

representing the value of the heat flux density of the ith boundary after normalization treatment of the jth influencing factor; x is X _j,i Representing the value of the heat flux density of the jth influencing factor at the ith boundary; max (X) _j,i ) Represents the maximum value, min (X _j,i ) Representing the minimum value among the comparative series of each influencing factor;

the new series obtained by normalizing the influence factor comparison series comprises atmospheric temperature record as

Solar radiation heat mark as->

Crude oil density is recorded as->

The viscosity of crude oil was recorded as->

Specific heat capacity of crude oil as

Soil temperature is recorded as->

4. A method for predicting heat loss from a bulk crude oil storage tank as set forth in claim 3, wherein: the crude oil storage tank boundary heat flux density loss regression model is shown as the following formula:

wherein q _i W/m is a measure of the boundary heat flux density of the ith tank ² ；

The value of the heat flux density at the ith boundary after normalization treatment is represented by the jth influencing factor: a, a ₀ 、a ₁ …a _j And (3) representing regression coefficients of the model, wherein k is the power coefficient of the influencing factors in the regression model. />

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