Research on heat transfer characteristic of crude oil during the tubular heating process in the floating roof tank

Author’s Accepted Manuscript Research on heat transfer characteristic of crude oil during the tubular heating process in the floating roof tank Jian Zhao, Hang Dong, Xiulian Wang, Xiaoming Fu www.elsevier.com/locate/csite

PII: DOI: Reference:

S2214-157X(16)30194-0 http://dx.doi.org/10.1016/j.csite.2017.05.006 CSITE187

To appear in: Case Studies in Thermal Engineering Received date: 23 December 2016 Revised date: 19 May 2017 Accepted date: 23 May 2017 Cite this article as: Jian Zhao, Hang Dong, Xiulian Wang and Xiaoming Fu, Research on heat transfer characteristic of crude oil during the tubular heating process in the floating roof tank, Case Studies in Thermal Engineering, http://dx.doi.org/10.1016/j.csite.2017.05.006 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Research on heat transfer characteristic of crude oil during the tubular heating process in the floating roof tank Jian Zhao*1, Hang Dong1, Xiulian Wang2, Xiaoming Fu2 1

Key Laboratory of Enhance Oil and Gas Recovery of Educational Ministry, Northeast Petroleum University, Daqing, P.R. China 2

Transportation and Storage and Marketing Subsidiary Company of Daqing Oil Field, Daqing, P.R. China

*Correspondence to: Northeast Petroleum University, Fazhan Road NO.199, Hi-tech Development Zone, Daqing, China. 163318. Tel: 8618345993453. [email protected].

Abstract By means of finite volume method, the heat transfer characteristic of crude oil under the tubular heating in the floating roof tank is investigated by numerical simulation. The evolution of temperature profile and its relationship with the flow pattern is presented in detail. A noticeable finding is that there exists the transformation of the flow pattern which affects the temperature profile apparently during the heating process. Special concern is taken on the evolution of temperature distribution on the interface between oil and the inner wall of the tank. The temperature profile on the top wall, sidewall and base wall of the tank is investigated. It is concluded that the plume induced by natural convection takes most responsibility for the formation of temperature field in the tank. The second factor is the boundary condition of the tank. Key words: crude oil; floating roof tank; tubular heating; numerical simulation; heat transfer Nomenclature c po specific heat of crude oil, J/kg·℃.

g gravitational acceleration, m/s2. H tank total height of the tank, m.

H jc thickness of the foundation, m. depth of the constant temperature layer, m. H soil surface heat transfer coefficient on the roof, W/m2℃. hroof hsidewall surface heat transfer coefficient on the sidewall, W/m2℃. ko heat conductivity coefficient of crude oil, W/m℃. ki heat conductivity coefficient of solid material i , W/m℃. kroof heat conductivity coefficient of roof, W/m℃. ksidewal heat conductivity coefficient of insulation, W/m℃. ksoil heat conductivity coefficient of soil, W/m℃. p * static pressure, p*  p  2  k . 3 external diameter of the tank, m. Rtank Rsoil external diameter of the soil region, m. t cooling time, s. Ttube surface temperature of the heating tube, ℃. Theat heating temperature of the tube, ℃. To oil temperature, ℃. Th temperature of constant temperature layer, ℃. T0 initial oil temperature, ℃. Troof temperature of the external wall of the roof, ℃. 1

Tsidewall Tsoil,r

temperature of the external wall of the sidewall, ℃. temperature of soil on the thermal influence boundary, ℃.

Ti temperature of solid material i , ℃. temperature of soil on the constant temperature layer, ℃. Tsoil,z

Tair u v u0 v0 x r

atmospheric temperature, ℃. axial velocity, m/s. radial velocity, m/s. initial axial velocity, m/s. initial radial velocity, m/s.

axial coordination. radial coordinate.

Greek letters  thermal diffusion coefficient of crude oil, m2/s.

t

turbulence thermal diffusion coefficient of crude oil, m2/s.

o kinetic viscosity of crude oil, Pa·s.

eff o

effective viscosity coefficient,

eff  o  t , t  oC k 2  .

density of crude oil, kg/m3.

Indices/exponents 0 initial moment. air atmospheric. h constant temperature layer. i solid material. jc foundation. o crude oil. p constant pressure. roof tank roof. top wall topwall of the tank . sidewall sidewall of the tank . soil soil below the tank.

tank oil tank.

1. Introduction In the northeast of china, the environment temperature in winter can reduce to -35 ℃. The extreme low temperature increases the risk of gelatinization of crude oil during the storage process. In order to reduce this risk, heating is always a preferred measure to ensure the safety storage of crude oil. Due to the high wax content in crude oil, the jelling point of crude oil produced in some oil field can approach to 32 ℃. That’s means a large amount of heat consumed during the heating. With the respect of reducing the energy consumption, the reasonable heating temperature and the heating measure becomes the key point. In order to accomplishing this goal, the precisely understanding of the heat transfer characteristic during different heating process is the theoretical basis. As the tubular heating is a conventional heating method, many scholars focused on the heat transfer behavior for 4 3

this heating measure. Yahong Lu and Jiang tao Wu[1] employed Fluent to simulate the heating process in a 10×10 m cylindrical vertical oil tank. Based on the thermal analysis, the rationality of the structure of the heater was discussed. Jia Liu [2,3] established a 2-D numerical simulation model for the heating process of oil tank. Eighteen typical cases carried out in winter were conducted to reflect the flow and temperature field. The height of the tank, the quantity of steam, environment temperature and the heating time were picked as the factor and the influence on the temperature field was investigated. Shuai Shao[4] simulated the heating process in the floating roof oil tank by Fluent. The evolution of temperature profile and flow structure in the tank was 2

presented under different height and storage volume of the oil tank. As the core process for the tubular heating is the heat transfer between the heating tubes and the surround oil. Some research was conducted on the heat transfer process around the heating tube. However, in most cases, water is taken as the medium. Kitamura[5] carried out the experiment research on the natural convection heat transfer around the horizontal cylinder and water was taken as the medium. The flow characteristic and temperature profile is presented by the visualization experiment method. Atmane[6] first introduced the PIV technology to investigate the formation and evolution of buoyancy plume induced by natural convection originated around the cylinder. And the heat transfer behavior and flow pattern under different distance from the cylinder to the surface was analyzed. The same method was used by Stig Grafsrφnningen[7] who carried out the research on the velocity field dominated by the plume when the Ra is within 2.05× 107~7.94×107. Special concern was taken on the transition from laminar flow to the turbulent flow. As there is always more than one tube in the heater, many researches were conducted on the heated tube bundle in the horizontal or vertical arrangement. Marsters[8] investigated the heat transfer characteristic by experiment. The diameter of the tube is 6.35mm. And the center distance is within 2D to 20D. Some feature which is different from the sole tube was presented. Based on the PIV technology, Stig Grafsrφnningen[9] established an experiment apparatus to study the flow pattern under the heated tube bundle. The evolution of the plume structure and its influence on the heat transfer characteristic was investigated. The analogous research was also conducted by Persoon[10] and Reymond[11]. Kuriyama and Tokanai[12] investigated the natural convection heat transfer under two conditions of three tubes and nine tubes. The diameter of the heating tube is 8mm, 15mm and 30mm. The result reflected that the heat transfer characteristic around the center tube and the side one is much different. And this difference is changed with the variation of the center distance between two adjacent tubes. Most of the former research focused on the natural convection heat transfer process of water. And the boundary condition for the research system was regarded as thermal isolation. However, for the tubular heating process in the oil tank, the crude oil is the research object, the property of which is much different from water. Besides, the boundary condition of the oil tank is not appropriate to be taken as the thermal isolation. In the practical working condition, the top wall and sidewall of the oil tank is exposed in the atmosphere. The heat transfer course involves the natural convection, heat conduction and heat radiation. Although there are some researches which are aiming at the oil tank, most of the researches were proceed from the engineering point of view. The absence of detailed description of evolution of temperature profile and the flow pattern was found in these documents. The relationship between the temperature profile and the flow pattern did not receive enough concern either. Considering the information in the literature on this research topic, the aim of this work is to investigate the heat transfer characteristic of crude oil under the tubular heating process in a floating roof tank. Taking in to consideration of the advantage of numerical simulation method, the heat transfer characteristic of oil is investigated by means of numerical simulation. The evolution of temperature profile and its relationship with the flow pattern is investigated. Special concern is taken on the evolution of temperature distribution on the interface between oil and the inner wall of the tank.

2. Problem definition 2.1 Computational domain The research object is the double-deck floating roof tank with the storage of crude oil in the northeast of china. The tank roof is constituted by double-deck steel plate with the interlayer between them. There is no insulating layer on the roof. But an insulating layer with the thickness of 80mm is installed on the sidewall. The tank is placed on the foundation which is constituted by the asphaltic sand, the sand, backfill and ring wall, below the foundation is the subsoil. In addition to these components, there are many accessories in the tank. With the respect of simplifying the real heat transfer process, some assumptions are adopted in this study: (1) The roof can be regarded as a double-deck steel plate with an air layer between them. With the aim of simplify the calculation, the entire roof is seen as a solid structure, the equivalent heat conductivity of 1.05 W/m K is used to represent the heat transfer property which is obtained from the test of a real tank. (2) The sidewall is simplified into an equal thickness steel plate. The insulating layer is placed close to the extern wall of the steel plate. For the floating roof tank, the sidewall is divided into two parts by the roof. The part which is above the roof is neglected as it does not contact to oil. (3) The accessories on the bottom plate are neglected. The bottom plate is simplified into an equal thickness steel plate. (4) The foundation is divided into three layers. Each one is seemed as an equal thickness structure and filled with the 3

homogeneity material. (5) The thermal influence region of the tank is introduced to translate the semi-infinite soil region into the finite region. According to the related research, it is believed that the soil 7 m away from the tank on the horizontal direction is practically free from the effect of the tank. As a result, the heat insulation condition is taken as the boundary on the horizontal direction of the soil. Furthermore, based on the test data, there exists the constant temperature layer of soil with the depth of 12.5 m. The temperature of which is nearly a constant throughout the entire year. So the constant temperature condition is regarded as the boundary on the vertical direction of soil. Besides, the soil is assumed as the homogeneous material. (6) The heating tube is regarded as the tube with the same diameter. In order to simplify the calculation domain, the inlet for the steam and outlet for the backwater is neglected. And the related support structure and accessory of the heating tubes are also neglected. Five heating tubes are evenly spaced on the same height. The surface temperature of the heating tube is regarded as a constant during the calculation. (7) Base on above simplifications and hypothesis, the tank is regarded as a vertical cylinder which is placed on a cylindrical foundation. Below the foundation is a cylindrical subsoil structure. On the basis of ignoring the heat transfer along the circumference direction, the three-dimensional heat transfer problem is simplified as the axial symmetry heat transfer process. Based on above assumptions and simplifications, a sketch map describing the computational domain for the thermal system of the floating roof oil tank under the tubular heating is illustrated in Fig. 1.

Roof

External surface of the roof

External surface of the sidewall Crude oil

External surface

Axis of symmetry

Heating Tubes

Insulation

of the soil

Ring wall

Asphaltic sand Sand

Thermal

Backfill

influence boundary

Constant temperature layer

Fig. 1 Computational domain for the thermal system

2.2 Physical properties For the waxy crude oil, the physical properties become complicated as the temperature drops. Due to the paraffin crystallization, the latent heat releases which affect the heat transfer process directly. With the amount of precipitated paraffin increases, the rheology behavior of waxy crude oil changes. The crude oil investigated in this study comes from Daqing oil field. The thermal parameters of crude oil used in the calculations are all obtained by the experiment. As the oil temperature is higher than the abnormal point during the heating, the data of viscosity as a function of temperature at the low rate shear which is measured by 4

the rheometer (Anton Paar-QC) is adopted in the simulation. The latent heat caused by the paraffin crystallization is represented by additional specific heat capacity. The data of specific heat capacity as a function of temperature measured by differential scanning calorimetry (TA-Q2000) is introduced. The density data of crude oil is measured by the densimeter (Anton Paar-DMA4500M). During the calculation, the density of crude oil is assumed as a constant except in the buoyance terms of the momentum equations (Boussinesq approximation). The data of heat conductivity is measured by the thermal constant analyzer (Hot Disk-TPS2500S). And the variation of heat conductivity is regarded as the linear relation with temperature. The measuring data of physical properties for waxy crude oil, as well as the related mathematical models are shown as follows: The mathematical models for the physical properties of crude oil are as follows: 0 . 0 T3 7  T  4 4℃，o  1 4e6  0 . 0 T 67  T  4 4℃，o  5 5 1 .e7 3

Kinetic Viscosity:

Specific Heat:

Heat Conductivity:

(1)

T  44℃，c po  4.833T  2113.1  4 3 2 T  44℃，c po  0.0224T  3.2339T  171.13T  3905.2T  29558 1  0.00054T ko  0.137  0.856

o  870.1 1  0.000795(T  20)

Density:

(2)

(3) (4)

The physical properties of insulation and other solid material are shown in Table 1. Table 1 Physical properties of solid material[13] Solid Material

Density(kg/m3)

Heat Conductivity(W/m·℃)

Specific Heat(J/Kg·℃)

insulating layer

60

0.055

800

steel

7800

40

460

sand

1500

0.56

837

asphaltic sand

1400

0.5

1000

backfill

1750

0.93

1062

ring wall (Beton)

2500

1.63

1170

subsoil

1600

1.74

1750

3. Mathematical model, numerical approach and verification process 3.1 Mathematical model

k   model, the governing equations for the heating process in the oil tank are shown as follows: o ( ou ) 1 ( o rv) Equation of Continuity (5)   0 t x r r Based on the standard

Momentum Equation

Energy Equation

Turbulence

k Equation

Turbulence



Equation

( ou ) ( ouu ) ( o vu ) p *  2u 1 u  2u     eff ( 2   )  o g t x r x x r r r 2

(6)

( o v) ( ouv) ( o vv) p  2v 1 v  2v v      eff ( 2    ) t x r r x r r r 2 r 2

(7)

( 0To ) ( 0uTo ) ( 0vTo )    2T 1 To  2To     0 (  t )  2o    t x r  t  x r r r 2 

(8)

( o k ) ouk o vk   eff k  1   eff k          r     Gk  o t x r x   k x  r r   k r 

(9)

( o ) ou o v   eff   1   eff            r     (C 1Gk  C 2 o ) (10) t x r x    x  r r    r  k 5

Where,

  u v v  u v 2  Gk  eff 2 ( ) 2  ( ) 2  ( ) 2   (  )  r r  r x    x

(11)

C 1  1.44 , C 2  1.92 ,  k  1.0 ,    1.3

( iTi ) ki  t C pi

Differential equation of heat conduction for solid structure

  2Ti 1 Ti  2Ti    2   r r r 2   x

(12)

Boundary conditions:

Ttube  Theat

Tube surface External surface of the roof External surface of the sidewall

(13)

Troof  hroof (Tair  Troof ) x Tsidewall  hsidewall (Tair  Tsidewall ) r

x  H t a n,k  Rtank  r  0 , kroof 0  x  H t a n ,k r   Rtank , ksidewall

(14) (15)

Other walls which contact with air are also set as the third kind of boundary condition.

( H jc  Hsoil )  x   H jc , r   Rsoil , ksoil

Thermal influence boundary on horizontal direction

Tsoil,r r

0

x  ( H jc  Hsoil ) ,  Rsoil  r  0 , Tsoil,z  Th

Constant temperature layer

( H jc  Hsoil )  x  H tank , r  0 , ki

Symmetry plane

Ti 0 r

(16)

(17) (18)

The thermal contact resistance is neglected as different structures are closely contact to each other. The connecting boundary conditions between different structures are as follows: On the axial direction On the radial direction

Ti x T ki i r

ki

x  X i

r  Ri

Ti 1 x Ti 1  ki 1 r

 ki 1

x  X i

r  Ri

i  1, 2,..., N  1

(19)

i  1, 2,..., N  1

(20)

At the initial time, the oil is still and the temperature in the tank is homogeneous. Initial condition

T0 (r , x)  T0 , u0 (r , x)  v0 (r, x)  0

(21)

The temperature field of the soil and other solid structure is calculated by the differential equation of heat conduction.

3.2 Numerical approach The governing equations together with the boundary conditions have been integrated over the whole domain including the fluid, insulating layer and other solid structure by means of finite-volume techniques with fully implicit first order temporal differentiation. Diffusive terms have been evaluated using a second order central differences scheme, while convective terms have been approximated by means of the high order QUICK scheme. The coupling between pressure and velocity fields has been solved by the PISO algorithm with additional correction to improve the efficiency of pressure-velocity coupling calculation. The Body Force Weighted scheme has been used for the discretization of pressure in consideration of the existence of buoyancy force caused by convection. The algebraic system of equations resulting for each variable has been solved by using a multigrid method. Taking into consideration of the structural feature of the thermal system, the structured and unstructured quadrilateral mesh have been used to discretize the calculation domain. With the objective of describing the boundary layer near the walls or the surface of the heating tubes (where the temperature and velocity gradients are the largest) more precisely and acquiring the detailed evolution of temperature and flow structure, the mesh at the interface between the fluid and the wall has been concentrated. Meanwhile the computational domain for the solid has been discretized into non-uniform meshes which are more concentrated near the oil. 6

In order to improve the mesh quality, the calculation domain of oil is divided into five parts. Four parts have the rectangle structure. And the structured quadrilateral mesh has been used to discretize these domains. In these domains, the mesh concentrates in the boundary layer between oil and the interface of the walls. And the relatively coarse mesh is used in the interior. The nearest grid-point is located at 0.5mm away from these walls, and expands at a rate of 2% up to 42.3 mm away from the wall. After that the grid size increases to 1.3 mm. And then the grid size gradually increases to 13.4 mm with different extended factor for different domains until the mesh reaches to the interface between different domains. Five heating tubes are segregated in an independent rectangle domain. The grid size on the surface of the tube is 1 mm, and the total amount of mesh is 500 on each tube surface. From the surface of the tubes to the boundary of the independent rectangle domain, the grid size gradually increases to10 mm conforming to the unstructured mesh scheme. The total amount of quadrilateral mesh in this domain is 195259 and the largest equisize skew is 0.56. The total amount of quadrilateral mesh of other four domains is 276200. As the calculation domain is very large and the temperature variation is slow, a large amount of calculation time is needed for one case. Concerning the temporal discretization, with the respect of increasing the calculation efficiency as well as the computational accuracy, different time steps have been adapted for one simulation. At the beginning of the calculation, a small time step is used to calculate the flow and heat transfer process. The time step of 0.5s is used to obtain the accuracy and steady solution. As the calculation proceeding, a larger time step of 1s is attempted and the convergence is reached after a number of iterations. After that, the calculation gradually gets steady, but as the temperature increases, the flow becomes more intense. Only a little larger time step of 2s is attempted and the calculation can keep steady but the convergence is achieved after more iterations. So the time step of 2s is used through the rest of calculation process.

3.3 Solutions verification In order to verify the reliability of numerical solutions, the heat convective heat transfer coefficient at the surface of the tubes obtained from the numerical simulation is contrasted to the result based on the following correlation:

Nu  0.125Ra 0.333 Pr 0.047

(22)

The above correlation is derived from Morgan’s research [14]. While take into consideration of the physical property of crude oil is different from water, the additional correction of Pr is adopted based on Fand’s research [15]. The comparison between the results from correlation and the numerical simulation results is calculated. The average deviation between the numerical simulation result and correlation result is 5.4%. As the natural convection around the tubes is the main heat transfer course during the heating in the tank, this verification demonstrates the reliability of numerical solutions. 4. Results and discussion 4.1 Simulation cases Seven simulation cases were carried out involving different heating temperature. For different cases, the physical structure of the tank and the physical properties of crude oil is the same. The heating temperature for cases 1 is 50 ℃, while for case 2 is 60 ℃ and for case 3 is 70, 80℃ for case 4, 90℃ for case 5, 100℃ for case 6 and 110℃ for case 7. The environment temperature for different cases is -20 ℃. And the initial temperature of oil is 40 ℃ for different cases. According to the calculating results, there is the similar temperature profile and flow structure during the heating process, so case 6 is taken as an example to illustrate the flow and heat transfer characteristic during the tubular heating process.

4.2 Evolution of temperature field during the heating process

a. 1/3h

b. 1h 7

c. 2h

d. 5h

e. 10h

f. 20h

g. 30h

h. 50h Fig 2 Temperature profile in the tank during the heating process

i. 100h

a. 1/3h

d. 5h

g. 30h

b. 1h

e. 10h

h. 50h 8

c. 2h

f. 20h

i. 100h

Fig 3 Streamline profile in the tank during the heating process As illustrated in Fig 2 and Fig 3, the temperature profile and flow structure in the tank for case 6 evolves as the heating proceeds. The detailed profile of oil temperature is affected by the heating tubes and the boundary conditions of the tank. The plume created by the natural convection is derived from the heating tubes and dominates the heat transfer process. As shown in Fig 2a, in the first instant, the oil near the tubes is heated by heat conduction under the large temperature difference between the tube and the oil. The oil temperature increases quickly which contributes the decreasing of the oil density. Under the density difference between the hot oil and the cold oil, the hot oil rises to the region above the tube by the buoyancy. Different from the flow pattern when the heating tube stays in an infinite large space, the flow pattern formed by the hot oil is affected apparently by the space structure and thermal boundary condition of the oil tank. The plumes induced by the buoyancy force leaves away from each tube and converge together in the area not far from the tubes. Instead of rising straightly to the area above the tubes, the converging plumes moves and shifts to the sidewall of the tank. And then the plume ascends straightly to the upper part of the tank along the sidewall. In Fig 3a, it is shown how the flow pattern appears during this moment. The plume induces a main vortex which covers most regions in the tank. In this big vortex, there exist two small vortexes in pairs. One is directly induced by the plume and stays in the area above the heating tubes. Another vortex exists in the center part of the tank. There is another smaller vortex generating in the corner between the top wall and sidewall. This small vortex is believed to be created by the descending of cold oil which is formed by the heat loss from the top wall and sidewall. At this moment, the hot temperature region overlaps with the path of the plume, while the temperature of other regions is nearly unchanged. As the heating proceeds, the plume makes the temperature profile turn to be a further evolution. The region affected by the plume enlarges from the top wall to the center part of the tank (see Fig. 2b). The main vortex is divided into four small ones, and the larger one near the plume becomes smaller than that in the former stage (see Fig. 3b). Fig. 2 c and 2 d illustrates the further evolution of the temperature profile and flow pattern. The vortex in the corner between the top wall and sidewall extends towards to the center of the tank along the radial direction, except for the existence of vortex near the plume, the main flow pattern is nearly the parallel streamlines from the top wall to the base wall (see Fig. 3c and 3d). Under this flow field, the temperature profile in the tank appears the thermal stratification feature. Especially in the lower part of the tank, except for the region covered by the plume, the temperature on the radial is nearly uniform, and the temperature gradient in the axis is more pronounced. However, the region near walls has the least influence from the heating which makes these regions still turn to be the low temperature region in the tank. When the heating continues, the vortex originated from the top corner continues to grow up and covers the upper part of the tank (see 3e~3h). Affected by this flow pattern, the temperature distribution becomes more homogeneous and is higher in the upper part than that in the lower part of the tank (see 2e~2h). Squeezed by this vortex, the region on the sidewall which is covered by the plume shrinks apparently (see 3e~3h). From then on, the extension of the vortex in the upper part continues to squeeze the lower one. Under this circumstance, the temperature field in the tank can be divided into two parts by the plume path. The temperature profile is rather uniform in each part. And the temperature on the plume path is the highest with the largest temperature gradient in the tank. As this evolution proceeds, the plume finally changes its path and leaves away from the sidewall (see Fig. 3i). The vortex originated from the top corner finally turns to be the main vortex, another small vortex lies surrounded by the base wall and the axis of the tank. The two vortex structure makes the temperature field appears more uniform than any former stage. 4.3 Variation of oil temperature as a function of time

9

70 Top wall

Sidewall

Base wall

Average

65

Temperature(℃)

60 55 50 45 40 35 0

10

20

30

40

50 Time(h)

60

70

80

90

100

Fig.4 Variation of representative oil temperature as a function of time In order to investigate the temperature evolution during the heating more thoroughly, the variation of some representative temperature is collected in Fig. 4. The average oil temperature is calculated based on the volume weighted method. As seen in Fig. 4, the average oil temperature increases as a function of the heating time nearly in the form of the linear rule. The average temperature increasing rate during the heating process is nearly 0.26 ℃/h. Relatively speaking, the evolution of the average temperature on different walls appears more complicated. The average temperature on the top wall decreases in the first one hour and increases slowly until to the 10th hour during the heating. During this period, the plume created by the heating tube gradually develops in the tank. The heat loss on the top wall contributes the decreasing of the temperature on the top wall. With the development of the plume, the cooling rate gets slowly until the circumstance of temperature rise comes out on the top wall. After that, the temperature on the top wall increases with the same rate as the average oil temperature. However, corresponding to transformation of flow pattern, there are some fluctuations during the temperature variation. As the plume covers the sidewall during the first instant of the heating, the temperature on the sidewall is higher than that on the base wall and top wall before the 50th hours. But as the transformation of the flow pattern comes out, the temperature increasing rate slows down and the temperature difference expands. Since the plume directly acts on the sidewall, there is hardly the temperature decrease on the sidewall during the entire heating process. The temperature on the base wall decreases apparently in the first instant during the heating. And the period in which the temperature on the base wall decreases lasts longer than that on the top wall which reflects that the influence from the heating tube is presented on the base wall at the latest time. As the heat transfer by the development of plume is the main form of the heating in the tank, the base wall which lies under the heating tube begins to be affected by the plume until the plume fully develops in the tank. Therefore, under the tubular heating, affected by the plume, the sidewall is first affected by the heating and then is the region near the top wall, and the base wall is the region which finally obtained the influences from the heating. 4.4 Variation of temperature profile on the walls as a function of time

10

Temperature(℃)

64 62 60 58 56 54 52 50 48 46 44 42 40 38 36 34

1/3h 30h 0

1

1h 50h

2

3

5h 70h 4

10h 90h

5 H(m)

6

7

8

9

10

Temperature(℃)

Fig.5 a Variation of temperature profile on the sidewall, b Variation of temperature profile on the top wall, c Temperature profile on the base wall 64 62 60 58 56 54 52 50 48 46 44 42 40 38 36 34 32 30

1/3h 30h -14

1h 50h -12

5h 70h -10

10h 90h -8

-5

-3

-1

-3

-1

r(m)

65 62 59

Temperature(℃)

56 53 50 47 44 41 38

1/3h 30h

1h 50h

5h 70h

10h 90h

35 -14

-12

-10

-8

-5 r(m)

11

Fig.5a illustrates the detailed variation of temperature profile on the sidewall. In accord with the temperature field shown in Fig.2. There are apparently two kinds of temperature distribution features on the sidewall which is divided by the plume. At the 1/3th hour, there is no prominent affection on the sidewall from the heating tubes. However, at the 1th hour, the influence from the heating tube begins to present on the sidewall. The temperature on the region from 0.4m to 4m on the sidewall increases apparently. From 1th hour to the 5th hour, although the temperature near the top wall and base wall continues to decrease, the temperature in the region from 0.4m to 8m on the sidewall increases apparently and is nearly 1.2 ℃ higher than that on the upper part of the sidewall. From the 5th to the 10th hour, the temperature on the sidewall increases apparently in the lower part, and the temperature difference between the two regions increases to 5 ℃. There are still the low temperature regions near the top wall and base wall. However, the temperature on these low temperature regions increases too. As shown in Fig.2 and Fig.3, the transformation of flow pattern contributes the variation of temperature profile along the sidewall, and the high temperature region on the sidewall shrinks as the top vortex continues to squeezing the plume. From the 10th to the 70th hour, the temperature profile accords with the similar feature. There are four regions with different characteristic of temperature profile along the sidewall. Below 0.4m, there is the low temperature region near the base wall which is caused by the heat loss from the base wall and the absence of the influence from the heating tube. Above this region, there is a high temperature region, the temperature in which is homogeneous. This region is created by the plume from the heating tube. However, as the heating proceeds, this region continues to decreases. Above this high temperature region, another region with a lower temperature lies on the sidewall. These two regions are divided by the plume from the heating tube. Near the top wall, there is the fourth region with the lowest temperature on the sidewall. This region is induced by the heat loss from the top wall. As the heating proceeds, the high temperature region on the sidewall continues to decrease and finally vanishes. At the 100th hour, there are three regions left on the sidewall. Except for the low temperature regions near the top wall and base wall, the temperature in the most parts on the sidewall is the same. As seen in Fig.2 and 3, at this moment, the plume changes its path and develops away from the sidewall. Under the heating mode of tubular, the sidewall is heated prominently which brings about two consequences. Due to the high temperature on the sidewall, the heat loss on the sidewall increase a lot. However, as the lower part on the sidewall is heated, the sending and receiving oil process obtains the benefit. Normally, the inlet and outlet of the tank lies on the sidewall and at about 1.5 m higher than the base wall. Benefit from the heating, the oil in this region is heated and the viscosity of oil decreases which makes the oil good fluidity during the operating process. Fig.5b shows the temperature profile on the top wall as the heating proceeds. Different from the sidewall, the influence from the heating tubes on the top wall begin to present until the 5th hour. At the 5th hour, the temperature increases on the position which is about 1 m away from the sidewall, and the highest temperature appears on the position which is 2.5 m from the sidewall. This is believed to be caused by the heating tube. Away from this region, the temperature on the top wall decreases as the heat loss on the top wall dominates the heat transfer and there is less influence from the heating tube far away from the sidewall. However, as the heating proceeds, the temperature profile on the top wall changes. The high temperature region shifts to the area far away from the sidewall due to the development of the plume. And due to the heat loss from the top wall, other region which is less affected by the plume continues to decreases. From then on, the influence from the heating increases and gradually surpasses the influence from the heat loss. Although the temperature on the top wall increases together, there is still the low temperature region near the sidewall which lies near the sidewall. The base wall begins to obtain the influence from the heating tube at the latest time. As shown in Fig. 5c, till the 10th hour, there begins to generate the prominent temperature increases on the base wall at the 1.4 m away from the sidewall. As seen in Fig.3, at this moment, the vortex induced by the plume completes the coverage of the main part in the tank, and the streamlines assemble below the tubes. The region where the streamlines cover has an apparent temperature increment on the base wall. In contrast, away from the tubes, especially in the region between the tubes and the sidewall, there is absence of the main streamlines. And there is no noticeable variation of temperature increment there. Far away from the tubes and towards the center of the tank, the temperature of there is also less affected by the heating. As the heating proceeds, the temperature on the whole region of the base wall increases apparently. However, there is uneven temperature profile on the base wall. According to the data from 30th hour to 70th hour, the high temperature region always lies directly below the tubes. There is always the low temperature region in the corner between the tubes and the sidewall. Until the 70th hour, the 12

streamlines formed by the plume did not cover this low temperature region. When the temperature in the region from the tubes to the axis of the tank gets higher during the heating is accords with the transformation of the streamlines in this region. When it comes to the 90th hour, the former low temperature region converts to the high temperature region and the temperature on other positions also changes a lot. According to Fig.3i, at this moment, the plume has changed its shape which contributes the variation of temperature profile on the base wall. This reflects that the temperature profile in the tank is largely determined by the flow pattern. 4.5 Uncertainty analysis The results based on the simulation mainly present the general evolution of temperature profile and natural convection, but there are still some factors that confine the application of the conclusions. First, due to the fluctuation of environment condition, such as the wind speed and environment temperature, the oil temperature near the inner surface of the tank wall may vary during the heating process. However, as the tank volume is so large, the influence range by the environment condition most confines into a small region near the inner surface. And on consideration of the long term of heating, the influence from the fluctuation of environment condition is not so significant to transform the temperature profile. Secondly, the physical property of crude oil is measured through the experiment. But since there is the inevitable experimental error, this may affects the simulation findings. In order to minish the experimental error, every test is always conducted for more than three times, and the repeatability is taken into consideration. Besides, the sectional deviation of experiment data from the real condition can not affect the peculiarity of the physical property of crude oil. So the representative temperature profile and natural convection can still be obtained. Lastly, in order to minish the discretization error from the simulation, the discrete algorithm and solution parameters are all carefully selected, and the simulation result is testified by the empirical correlation, and the calculation error is confined in a permitted range within 7%. 5. Conclusions By means of finite volume method, the heat transfer characteristic of crude oil under the tubular heating in the floating roof tank is investigated by numerical simulation. The detailed profile of oil temperature is affected by the plume derived from the

heating tubes and the boundary conditions of the tank. The plume first leaves away from each tube and converge together. The converging plumes moves and shifts to the sidewall. And then the plume ascends straightly to the upper part of the tank along the sidewall. A main vortex induced by the plume covers most regions in the tank. Another small vortex created by the descending of cold oil generates in the corner between the top wall and sidewall. As the heating proceeds, the vortex in the top corner extends towards to the center of the tank. And the path of the plume is forced to be changed. Except for the existence of vortex near the plume, the main flow pattern is nearly the parallel streamlines from the top wall to the base wall. When the heating continues, the vortex originated from the top corner continues to grow up and squeeze the plume. The plume finally changes its path and leaves away from the sidewall. The vortex originated from the top corner finally turns to be the main vortex, another small vortex lies surrounded by the base wall and the plume. Affected by the evolution of flow pattern, the hot temperature region always overlaps with the path of the plume. The temperature profile in the tank first appears the thermal stratification feature. And then the temperature field is divided into two parts by the plume. In each part the temperature profile is homogeneous. As the heating proceeds, the areas of two regions change. Finally, the temperature of the main part in the tank is homogeneous, except for the region which is surrounded by the plume and the boundary. There are four regions with different characteristic of temperature profile along the sidewall. There is the low temperature region near the base wall which is caused by the heat loss from the base wall and the absence of the influence from the heating tube. Above this region, there is a high temperature region, the temperature in which is homogeneous. Above this high temperature region, another region with a lower temperature lies on the sidewall. These two regions are divided by the plume. Near the top wall, there is the fourth region with the lowest temperature on the sidewall. As the heating proceeds, the high temperature region on the sidewall continues to decrease and finally vanishes. Under the heating mode of tubular, the sidewall is heated prominently which brings about two consequences. Due to the high temperature on the sidewall, the heat loss on the sidewall increase a lot. However, as the lower part on the sidewall is heated, the sending and receiving oil process obtains the benefit. Different from the sidewall, the influence from the heating tubes on the top wall begins to present in a later time. The 13

highest temperature appears on the position which is 2.5 m away from the sidewall caused by the heating tube. As the heating proceeds, the high temperature region shifts to the area far away from the sidewall due to the development of the plume. Due to the heat loss released from the top wall, the temperature on the top wall is the lowest during the heating. The base wall begins to obtain the influence from the heating tubes at the latest time. From 30th hour to 70th hour, the high temperature region always lies directly below the tubes. The low temperature region is always in the corner between the tubes and the sidewall. When it comes to the 90th hour, the plume has changed its shape, the former low temperature region converts to the high temperature region and the temperature on other positions also changes a lot.

CONFLICT OF INTEREST There is no conflict of interest.

Acknowledgements This paper was supported by PetroChina Innovation Foundation (2014D-5006-0607). This paper was supported by Youth Fund of Northeast Petroleum University (NEPUBS201505). This paper was supported by the Fostering Foundation for the University Nursing Program for Young Scholars with Creative Talents in Heilongjiang Province of China (SCXHB201601). This work was financially supported by the University Nursing Program for Young Scholars with Creative Talents in Heilongjiang Province of China. This work was financially supported by the University Nursing Program for Young Scholars with Creative Talents in Heilongjiang Province of China (Grant No. UNPYSCT-2015074).

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