CN104102852A - Computing method of preheating commissioning thermodynamic process of crude oil pipeline - Google Patents

Abstract

The invention discloses a computing method of preheating commissioning thermodynamic process of a crude oil pipeline. The computing method comprises the steps of reasonably simplifying the preheating commissioning process of the crude oil pipeline and building a physical model under a normal conveying working condition for describing heat exchange between a medium in the pipeline and soil surrounding the pipeline, eliciting a control equation according to the physical model and determining a computational domain and boundary conditions, building a mathematical model under a conveying stop working condition and mathematical model of restart security evaluation, discretizing the physical model under the normal conveying working condition, the mathematical model under the conveying stop working condition and the mathematical model of restart security evaluation and obtaining a discrete control equation by use of a finite volume method and a finite difference method, and performing iteration solution on the discrete control equation and output the result.

Description

The computing method of crude oil pipeline preheating operation thermal procession

Technical field

The present invention relates to the long-range conveying technology of oil field, relate in particular to a kind of computing method of crude oil pipeline preheating operation thermal procession.

Background technology

Pipeline transportation is as the important component part of modern transportation system, has that transportation cost is low, safe reliability is high and the unique advantage such as environmental pollution is little, is particularly suited for the long-distance transportation of the inflammable and explosive dangerous goods such as crude oil, product oil and rock gas.In recent years, along with the economic steady-state growth of world's emerging economy and developed economies economic recovery, world's major power improves day by day to the demand of the energy, and therefore the pace of construction of oil and gas pipes is also accelerated.By the end of the year 2008, world's crude oil pipeline main line total length has exceeded 40 × 10 ⁴km.China has also welcome the pipe-line construction climax of a new round, expects " 12 " latter stage, and China's pipeline total kilometrage will break through 15 × 10 ⁴km.When the time comes, long-distance transmission pipeline will be born the Crude Oil Transportation task of China 70%.

Along with the external interdependency of crude oil in China in recent years further improves, oil sources variation will become a kind of trend, and this just requires oil products to carry in same pipeline.Because the quality of crude oil that different blocks is produced may differ larger, after the crude oil blending of different qualities, carry and may produce harmful effect to refinery equipment and product.Therefore, this will ask long distance pipeline to have the ability of oil products batch transportation, thereby it is point defeated to realize the former oil content storage of different qualities.Be that the good crude oil of flow adopts normal temperature to carry, carry and part high pour point and viscous crude oil is carried out to heating.This just need to be switched to that heating is carried or be switched to from heating flow behavior good oil product the poor oil product of heating flow behavior carrying from normal temperature, a kind of out-station temperature of oil product before improving, thereby pipeline soil along the line is carried out to preheating, prevent after rear a kind of oil product inlet pipe that temperature drop rate is compared with large and increase solidifying manage-style danger.Such differential temperature is carried sensu lato hot oil pipeline preheating operation problem that also can be considered as.

The key of crude oil pipeline preheating operation process program is choosing of choosing of operational factor, particularly technological parameter and determining of preheating method.It has been generally acknowledged that throw only need meet after oil pipeline terminal oil temperature than condensation point of crude oil high 3 DEG C～5 DEG C, and often design preheating scheme with the minimized principle of total energy consumption, this not science do not meet engineering reality yet.Safety in production is the most important thing, ensures that the safety operation of newly-built pipeline or the smooth switching of differential temperature conveyance conduit are only the matter of utmost importance that pay close attention to.Because accident or planned shutdown in operation process and repairing are almost difficult to avoid, ensure that pipeline restarts after shutdown under bad working environments and successfully just should serve as the core principles that pipeline preheating operation plant designs.Simultaneously, existing most of stopping transportation is restarted research and is all moved the starting condition as stopping transportation using pipeline stabilization or quasi-steady, and in preheating operation process the Soil Temperature Field of pipeline all the time in unstable state changes, the therefore stopping transportation under this initial boundary condition and to restart problem also urgently to be resolved hurrily.

Summary of the invention

The object of the present invention is to provide a kind of computing method of crude oil pipeline preheating operation thermal procession, to address the above problem.

In order to achieve the above object, technical scheme of the present invention is achieved in that

Computing method for crude oil pipeline preheating operation thermal procession, comprise the steps:

Crude oil pipeline preheating operation process is carried out to Rational Simplification, set up the physical model of the interior medium of the description pipe of normally carrying under operating mode and pipeline soil heat exchange; Derive governing equation according to described physical model, and definite zoning and boundary condition;

Set up the mathematical model under stopping transportation operating mode and restart the mathematical model of safety evaluation;

Adopt different grid systems respectively the physical model under described normal conveying operating mode, mathematical model under stopping transportation operating mode and the mathematical model of restarting safety evaluation to be carried out discrete, application Finite Volume Method for Air and method of finite difference obtain discrete governing equation;

Described discrete governing equation is carried out to iterative Output rusults.

Preferably, in described pipe, medium comprises pre-thermal medium, pumped (conveying) medium.

Preferably, described crude oil pipeline preheating operation process is carried out to Rational Simplification, set up the physical model of medium and pipeline soil heat exchange in the normal description pipe of carrying under operating mode; Derive governing equation according to described physical model, and definite zoning and boundary condition, specifically comprise the steps:

For simplifying computation process, make following basic assumption:

(1) normally carry in operating mode and think that managing medium temperature, pressure, flow velocity and density on interior same cross section is uniformly, thinks that these variablees are the function of time and pipeline axial position; (2) pipeline soil is considered as to uniform dielectric, thinks that its physical property is respectively to identical; (3) because soil is along the thermograde of pipeline axial much smaller than along pipeline thermograde radially, ignoring the heat conduction between adjacent soil cross section, is two-dimension unsteady state heat conduction by problem reduction; (4) do not consider that pre-thermal medium and pumped (conveying) medium (being water and crude oil, crude oil of low-coagulation and crude oil with high solidifying point etc.) in the blending of interface, think " piston-type " displacement; (5) think that the rectangular area of the vertical center line of the pipeline wide 10m in left and right, dark 10m is the soil heating power zone of influence;

Based on above hypothesis and simplification, set up following mathematical model:

In described pipe, continuity equation, the equation of momentum and the energy equation of medium are followed successively by:

$\frac{\∂}{\∂\mathrm{\τ}}\left(\mathrm{\ρA}\right)+\frac{\∂}{\∂z}\left(\mathrm{\ρVA}\right)=0;$

$\frac{\∂V}{\∂\mathrm{\τ}}+V\frac{\∂V}{\∂z}=-g\sin \mathrm{\α}-\frac{1}{\mathrm{\ρ}}\frac{\∂p}{\∂z}-\frac{f}{D}\frac{V^2}{2};$

$\frac{\∂}{\∂\mathrm{\τ}}\left[\left(\mathrm{\ρA}\right)(u+\frac{V^2}{2}+\mathrm{gs})\right]+\frac{\∂}{\∂z}\left[\left(\mathrm{\ρVA}\right)(h+\frac{V^2}{2}+\mathrm{gs})\right]=-\mathrm{\πDq};$

Obtained the heat exchange equation of pipe flow medium and tube wall by above three equations:

$C_p\frac{\mathrm{dT}}{\mathrm{d\τ}}-\frac{T}{\mathrm{\ρ}}\mathrm{\β}\frac{\mathrm{dp}}{\mathrm{d\τ}}-\frac{{\mathrm{fV}}^3}{2D}=-\frac{4q}{\mathrm{\ρD}};$ It is formula 2.5;

Wherein, τ is the time, s; Z is the distance apart from pipeline starting point, m; ρ is the average density of the interior medium of pipe at section, kg/m ³; V is the mean speed of pipe flow medium, m/s; A is the sectional area of pipeline, m ²; G is acceleration of gravity, m/s ²; α is the angle of pipeline axial and horizontal direction; P is the mean pressure of medium at section, Pa; F is the darcy coefficient of friction resistance; D is the diameter of the effective flow area of pipeline, m; U is medium specific internal energy in pipe, J/kg; S is the difference of elevation between adjacent cells, m; H is the specific enthalpy of unit mass medium in pipe, J/kg; Q is the tube wall of medium and unit area in the pipe heat exchange amount within the unit interval, W/m ²; C _pfor managing the specific heat at constant pressure of interior medium, J/ (kg DEG C); T is medium temperature in pipe, DEG C; β is the expansion coefficient of medium in pipe, DEG C ^-1;

Determine the heat conduction equation of tube wall and anticorrosive coat:

${\mathrm{\ρ}}_i{C}_i\frac{{\∂T}_i}{\∂\mathrm{\τ}}=\frac{1}{r}\frac{\∂}{\∂r}\left({\mathrm{\λ}}_{i}r\frac{{\∂T}_i}{\∂r}\right)+\frac{1}{r^2}\frac{\∂}{\∂\mathrm{\θ}}\left({\mathrm{\λ}}_i\frac{{\∂T}_i}{\∂\mathrm{\θ}}\right);$ It is formula 2.6;

Wherein, when the newly-built pipeline of preheating, i=1,2, represent respectively tube wall and anticorrosive coat; When preheating in-service pipeline (crude oil of low-coagulation changes defeated crude oil with high solidifying point), i=1,2,3, represent respectively wax deposition layer, tube wall and anticorrosive coat; In two kinds of situations, ρ _ibe the density of i layer, kg/m ³; C _ibe the specific heat capacity of i layer, J/ (kg DEG C); T _ibe the temperature of i layer, DEG C; λ _ibe the coefficient of heat conductivity of i layer, W/ (m DEG C); R is radial position, m; θ is hoop radian;

Determine the heat conduction equation of pipeline soil:

${\mathrm{\ρ}}_s{C}_s\frac{{\∂T}_s}{\∂\mathrm{\τ}}=\frac{\∂}{\∂x}\left({\mathrm{\λ}}_s\frac{{\∂T}_s}{\∂x}\right)+\frac{\∂}{\∂y}\left({\mathrm{\λ}}_s\frac{{\∂T}_s}{\∂y}\right);$

Wherein, ρ _sfor the density of soil, kg/m ³; C _sfor the specific heat capacity of soil, J/ (kg DEG C); Ts is the temperature of soil, DEG C; λ _sfor the coefficient of heat conductivity of soil, W/ (m DEG C); X is the lateral separation apart from pipeline center's vertical section, m; Y is the longitudinal degree of depth apart from earth's surface, m;

Consider the symmetry of zoning, only get the right half part (the rectangle heating power influence district of 10m × 10m) of pipeline and study, boundary condition is:

In the time of y=0, ${\mathrm{\λ}}_s\frac{{\mathrm{dT}}_s}{\mathrm{dy}}={\mathrm{\α}}_a(T_a-T_s);$

Work as x=0, and-(h ₀-R)≤y≤0 or y≤-(h ₀+ R) time,

In the time of y=-H, T _s=T _n;

In the time of x=L, ${\mathrm{\λ}}_s\frac{{\mathrm{dT}}_s}{\mathrm{dx}}=0;$

Wherein, h ₀for pipeline center's buried depth, m; R is the pipeline radius comprising after anticorrosive coat, m; α _afor the coefficient of heat transfer of earth's surface and atmosphere, W/ (m ²dEG C); T _afor temperature, DEG C; T _nfor the temperature of soil thermostat layer, DEG C; H is longitudinal degree of depth of the pipeline heating power zone of influence, m; L is the half of the transverse width of the pipeline heating power zone of influence, m.

Guarantee to manage in the diabatic process of interior medium, tube wall, anticorrosive coat and soil, also should meet preheating pipe system heat exchange linked list:

Described preheating pipe system heat exchange Correlation Criteria is listed as follows:

Preferably, the described mathematical model of setting up under stopping transportation operating mode, specifically comprises the steps:

Do as follows and suppose: (1) definition equivalent heat conductivity, is converted into Heat Conduction Problems processing by the natural convection after medium stopping transportation in pipe; (2) if when pipeline shutdown, in pipe, in medium, contain waxy crude oil, and have wax partial crystallization to go out in whole temperature drop process, and form solidifying oil reservoir, think that this solidifying oil reservoir is to increase with the concentric mode of pipeline; (3) latent heat of phase change adopts the temperature variant form of specific heat capacity to be characterized on the impact of temperature drop process; (4) introduce stagnant point, to distinguish natural convection region and the thermal conductivity region of pipe interior;

By above-mentioned hypothesis, stopping transportation operating mode can be reduced to simple Heat Conduction Problems processing:

The heat conduction equation of pipe flow medium is: $\mathrm{\ρC}\frac{\∂T}{\∂r}=\frac{1}{r}\frac{\∂}{\∂r}\left(\mathrm{\λr}\frac{\∂T}{\∂r}\right)+\frac{1}{r}\frac{\∂}{\∂\mathrm{\θ}}\left(\frac{\mathrm{\λ}}{r}\frac{\∂T}{\∂\mathrm{\θ}}\right);$

In stopping transportation operating mode, if there is natural convection in medium in pipe, coefficient of heat conductivity λ should adopt the equivalent heat conductivity that formula 2.12 calculates; If medium is in viscous flow state in pipe, coefficient of heat conductivity λ can adopt actual value:

${\mathrm{\λ}}_{\mathrm{eff}}=\frac{{-\mathrm{\α}}_y(\mathrm{Ty}-\mathrm{Tw})}{{\left(\frac{\mathrm{\δTy}}{\mathrm{\δr}}\right)}_w};$ It is formula 2.12;

Described tube wall, anticorrosive coat heat conduction equation and thermal conduction of soil equation are still continued to use formula 2.5 and formula 2.6.

Preferably, the mathematical model of safety evaluation is restarted in described foundation, specifically comprises the steps:

It should be noted that: the mathematical model of restarting safety evaluation

When medium in pipe be pure material liquid (as water) or shutdown time more in short-term, the waterpower of restart procedure with heating power governing equation with normally conveying is identical;

When having waxy crude oil in pipe flow medium, and shutdown time is longer, while making part or all of crude oil show thixotropy, needs employing formula 2.13 to replace original equation of momentum:

$\frac{\∂V}{\∂\mathrm{\τ}}+V\frac{\∂V}{\∂z}+\frac{1}{\mathrm{\ρ}}\frac{\∂p}{\∂z}+g\sin \mathrm{\α}+\frac{{4\mathrm{\τ}}_w}{\mathrm{\ρD}}=0;$ It is formula 2.13;

In above formula, τ _wthixotroping model shown in employing formula 2.14 and formula 2.15 calculates, and described thixotroping model can reflect the structure power of material under a certain state by the variation of structural parameters:

$\mathrm{\τ}={\mathrm{\τ}}_{y0}+\mathrm{\λ}{\mathrm{\τ}}_{y1}+(K+\mathrm{\λ\ΔK}){\stackrel{\·}{\mathrm{\γ}}}^n;$ It is formula 2.14;

$\frac{\mathrm{d\λ}}{\mathrm{dt}}=a(1-\mathrm{\λ})-\mathrm{b\λ}{\stackrel{\·}{\mathrm{\γ}}}^m;$ It is formula 2.15;

Wherein, τ is shear stress, Pa; τ _y0yield stress during for the abundant cracking of structure, Pa; τ _y1yield stress while foundation completely for structure, Pa; K is consistency index, Pas; Δ K is thixotropy consistency index, Pas; for shearing rate, s ^-1; N is flow behaviour index; λ is structural parameters; A, b, m are textural constant.

Preferably, adopt different grid systems to carry out discrete to the physical model under described normal conveying operating mode, mathematical model under stopping transportation operating mode and the mathematical model of restarting safety evaluation respectively, application Finite Volume Method for Air and method of finite difference obtain discrete governing equation, specifically comprise the steps:

Adopt unstructured quadrilateral mesh to carry out discrete to pipeline soil heating power range of influence;

Adopt polar grid discrete to steel pipe walls, anticorrosive coat;

In described pipe medium stopping transportation condition model and described in restart in the Calculation of Heat Transfer of Model for Safety Evaluation, adopt polar grid carry out discrete;

Carry under operating mode normal, the medial temperature of a calculation medium, adopts uniform Mesh Grid to carry out discrete.

Compared with prior art, the advantage of the embodiment of the present invention is:

The computing method of a kind of crude oil pipeline preheating operation thermal procession provided by the invention, on the thermodynamic property variation, thermal parameter impact, preheating scheme comparison, the accident stopping transportation that relate in crude oil pipeline preheating operation process and restart, and the problem such as the energy consumption of whole process is launched research and can be applied in engineering reality to the part achievement obtaining.

Brief description of the drawings

The basic procedure schematic diagram of the computing method of the crude oil pipeline preheating operation thermal procession that Fig. 1 provides for the embodiment of the present invention one;

Fig. 2 is that the crude oil pipeline preheating operation thermal procession that the embodiment of the present invention one relates to relates to variable relation schematic diagram;

Fig. 3 a is the pipeline schematic perspective view of the pipeline zoning that relates to of the embodiment of the present invention one;

Fig. 3 b is the conduit section schematic diagram of the pipeline zoning that relates to of the embodiment of the present invention one;

Fig. 4 a is the soil heating power range of influence grid schematic diagram that the embodiment of the present invention one relates to;

Fig. 4 b is the composite grid schematic diagram of the Near Pipelines that relates to of the embodiment of the present invention one;

Fig. 5 is that in the normal conveying time pipe that relates to of the embodiment of the present invention one, medium grid is divided schematic diagram;

Fig. 6 a is the unstructured quadrilateral mesh schematic diagram that the embodiment of the present invention one relates to;

Fig. 6 b is the polar grid schematic diagram that the embodiment of the present invention one relates to.

Embodiment

Also by reference to the accompanying drawings the present invention is described in further detail below by specific embodiment.

Embodiment mono-

Referring to Fig. 1, the embodiment of the present invention one provides a kind of computing method of crude oil pipeline preheating operation thermal procession, comprises the steps:

Step S100, crude oil pipeline preheating operation process is carried out to Rational Simplification, set up the physical model of medium and pipeline soil heat exchange in the normal description pipe of carrying under operating mode; Derive governing equation according to described physical model, and definite zoning and boundary condition;

Step S200, set up the mathematical model under stopping transportation operating mode and restart the mathematical model of safety evaluation;

Step S300, to adopt different grid systems respectively the physical model under described normal conveying operating mode, mathematical model under stopping transportation operating mode and the mathematical model of restarting safety evaluation to be carried out discrete, and application Finite Volume Method for Air and method of finite difference obtain discrete governing equation;

Step S400, described discrete governing equation is carried out to iterative Output rusults.

Preferably, in described pipe, medium comprises pre-thermal medium, pumped (conveying) medium.

It should be noted that, buried heated pipeline is in preheating operation process, and pipeline and surrounding soil temperature field are all the time in transient state, and any accident or planned shutdown all can increase solidifying manage-style danger during this time.Proceed to normal production run for making pipe safety, need to accurately describe the thermal procession relating in warm.Meanwhile, also inquire into the Changing Pattern of managing interior medium temperature and the outer Soil Temperature Field of pipe and amount of stored heat in crude oil pipeline preheating operation process, and then analyzed soil thermal conductivity, ground temperature, out-station temperature and pipeline throughput rate to managing the impact of interior medium and the outer Soil Temperature Field thermodynamic property of pipe, and the pre-heat effect of different preheating methods is carried out to comparing research.

In sum, preheating operation plant is than selecting and evaluating three aspects:

(1) crude oil pipeline preheating operation process is carried out to Rational Simplification, set up the physical model of describing the interior medium (comprising pre-thermal medium and pumped (conveying) medium) of pipe and pipeline soil heat exchange; Derive governing equation according to physical model, determine zoning, boundary condition; Adopt unstructured quadrilateral mesh and polar grid to carry out to soil region and tube wall and anticorrosive coat philosophy discrete, apply Finite Volume Method for Air and method of finite difference simultaneously and obtain discrete governing equation; It should be noted that, obtain the method for discrete: employing radially be finite volume method, axial employing be finite difference method.

(2) for certain definite pipeline, the Changing Pattern of the interior medium temperature of pipe and the Changing Pattern of the outer Soil Temperature Field of pipe and amount of stored heat in analysis conduit preheating operation process; For certain definite operation mode, inquire into soil thermal conductivity, operation ground temperature, medium out-station temperature and pipeline throughput rate to managing the impact of interior medium and the outer Soil Temperature Field thermodynamic property of pipe;

(3) adopt multiple evaluation criterion to carry out than choosing the pre-heat effect of different preheating methods; Calculate the energy consumption of different preheating methods; Contrast the maximum safety margin of pipeline shut down of pipeline under different preheating methods.

The numerical simulation study of the computing method by above-mentioned crude oil pipeline preheating operation thermal procession, mainly can obtain drawing a conclusion:

(1), in different pipeline preheating methods, in pipe, medium co-exists in forced convertion, natural convection and three kinds of heat transfer modes of heat conduction in the diabatic process of soil.Forward preheating, oppositely preheating, forward and reverse preheating and anyway mainly rely on forced convertion to preheating, therefore heat-transfer effect is better; And " vexed pipe " process has natural convection and two kinds of modes of heat conduction concurrently, the utilization ratio of energy is higher;

(2) soil thermal conductivity is a responsive variable of buried heated pipeline operation thermal procession, and the accuracy of its numerical value is larger on the impact of result of calculation, for the pipeline in spanning of river or marsh, the soil thermal conductivity of through section should be set separately; Ground temperature is not fairly obvious on the impact of pipeline warm, if but conditions permit also should select the period that ground temperature is higher to carry out the preheating operation of pipeline; Pipeline throughput rate is larger on the impact of pre-heat effect, should be preferably in warm and appropriateness increase throughput rate; The pre-heat effect difference that out-station temperature difference is brought can progressively be weakened along with the increase of station spacing, for improving energy utilization efficiency, out-station temperature should be rationally set; The in the situation that, energy consumption certain at heating furnace power being identical: the pipeline of longer distance should adopt the mode preheating of low out-station temperature, large discharge capacity; More short-range pipeline should adopt the mode preheating of high out-station temperature, small displacement;

(3) research between single station is shown, forward preheating, oppositely preheating, forward and reverse preheating, anyway in preheating and " vexed pipe " five kinds of preheating methods, the pre-heat effect of forward preheating is best, and the capacity usage ratio of " vexed pipe " is the highest, and economy is best; But for the pipeline between multiple heat stations, its preheating scheme determine the supply/demand that also needs to consider as a whole the pre-thermal medium of upstream and downstream and pumped (conveying) medium, and in conjunction with the actual conditions of pipeline analyze with than choosing, determine the optimum preheating operation mode of this pipeline;

(4) in pipeline preheating operation process, because pipeline Soil Temperature Field along the line is always in unstable state changes, the inlet temperature of pipeline can not be served as the basis for estimation of weighing conduit running state, more can not serve as criterion and the foundation of establishment preheating scheme, should be using pipeline stopping transportation restart the successfully core principles as the design of pipeline preheating operation plant under bad working environments, and take into account on this basis the economy of preheating scheme.

It should be noted that, the computing method of the crude oil pipeline preheating operation thermal procession that the embodiment of the present invention provides are on the thermodynamic property variation, thermal parameter impact, preheating scheme comparison, the accident stopping transportation that relate in crude oil pipeline preheating operation process and restart, and the problem such as the energy consumption of whole process is launched research, and develop software, can be applied in engineering reality to the part achievement obtaining.

From the angle of thermal conduction study, forward preheating is in five kinds of preheating methods, and pre-heat effect is best.In order to verify the ubiquity of this result, also contrast pipeline end point temperature and the pipeline average oil temperature along the line of different station spacings, different soils coefficient of heat conductivity, different ground temperature, different medium out-station temperature and the lower five kinds of preheating methods of different preheating throughput rates herein.Result proves, in five kinds of preheating methods, the pre-heat effect of forward preheating is best, and the pre-heat effect of other four kinds of preheating methods can be slightly variant along with the variation of parameter.This is because different preheating methods, in warm, manage the body position difference that interior medium conducts heat to pipeline soil, and the net heat that forward preheating is transmitted to pipeline soil are maximum.

The concrete technology contents of computing method of a kind of crude oil pipeline preheating operation the thermal procession below embodiment of the present invention being provided does detailed explanation:

First,, according to the difference of preheating medium transport mode, the preheating method of crude oil pipeline can be divided into forward preheating, oppositely preheating, forward and reverse preheating, anyway to preheating and " vexed pipe " five kinds of different modes.Wherein, " vexed pipe " refer to first before the pre-thermal medium certain hour of a certain conveying in four kinds of preheating methods, then stopping transportation completely, makes heat in pre-thermal medium be delivered to the preheating method of inner-walls of duct with the form of natural convection.

A complete preheating operation process is made up of preheating and medium displacement two parts.Except normal conveying operating mode, in preheating and medium replacement process, also may there is planned shutdown (as " vexed pipe " process) or accident stopping transportation.After stopping transportation finishes, also need pipeline to restart, thereby make pipeline return to gradually normal feed status.Because pipeline and Soil Temperature Field in preheating operation process are all the time in transient state, the standard as measurement conduit running state by the security of restarting using pipeline herein.Normally carry operating mode, stopping transportation operating mode and restart thermodynamic model used in safety evaluation and method for solving describing in detail in crude oil pipeline preheating operation process below.

2.1 mathematical description

2.1.1 research object

Crude oil pipeline is in preheating operation process, along with the continuous flow further downstream of pre-thermal medium, in ground temperature along the line, pipe, medium physical property and soil physical property are all in continuous variation, by solving managing this pair of coupled problem of interior media flow and heat transfer and media for heat exchange and thermal conduction of soil, just can obtain along the situation of medium temperature in spool and Soil Temperature Field variation.Under planned shutdown or accident stopping transportation operating mode, in pipe, medium can be by natural convection or heat conduction continuation and inner-walls of duct heat exchange, until restart procedure starts.The relation of whole solution procedure unknown variable and known variables as shown in Figure 2.

2.1.2 normally carry the mathematical model of operating mode

For above-mentioned two coupled problems, set up the mathematical model of media flow and heat transfer according to the relation between media for heat exchange amount and thermal conduction of soil amount in pipe.For simplifying computation process, make following basic assumption:

(1) normally carry in operating mode and think that managing medium temperature, pressure, flow velocity and density on interior same cross section is uniformly, thinks that these variablees are the function of time and pipeline axial position;

(2) pipeline soil is considered as to uniform dielectric, thinks that its physical property is respectively to identical;

(3) because soil is along the thermograde of pipeline axial much smaller than along pipeline thermograde radially, ignoring the heat conduction between adjacent soil cross section, is two-dimension unsteady state heat conduction by problem reduction;

(4) do not consider that pre-thermal medium and pumped (conveying) medium (water and crude oil, crude oil of low-coagulation and crude oil with high solidifying point etc.) in the blending of interface, think " piston-type " displacement;

(5) think that the rectangular area of the vertical center line of the pipeline wide 10m in left and right, dark 10m is the soil heating power zone of influence, as shown in Fig. 3 a and Fig. 3 b.

Based on above hypothesis and simplification, consider influencing each other between medium on cross-section of pipeline, tube wall, anticorrosive coat, soil (the pipeline heating power zone of influence) and atmosphere, can obtain following mathematical model.

Continuity equation, the equation of momentum and the energy equation of medium in pipe:

$\frac{\∂}{\∂\mathrm{\τ}}\left(\mathrm{\ρA}\right)+\frac{\∂}{\∂z}\left(\mathrm{\ρVA}\right)=0---\left(2.1\right)$

$\frac{\∂V}{\∂\mathrm{\τ}}+V\frac{\∂V}{\∂z}=-g\sin \mathrm{\α}-\frac{1}{\mathrm{\ρ}}\frac{\∂p}{\∂z}-\frac{f}{D}\frac{V^2}{2}---\left(2.2\right)$

$\frac{\∂}{\∂\mathrm{\τ}}\left[\left(\mathrm{\ρA}\right)(u+\frac{V^2}{2}+\mathrm{gs})\right]+\frac{\∂}{\∂z}\left[\left(\mathrm{\ρVA}\right)(h+\frac{V^2}{2}+\mathrm{gs})\right]=-\mathrm{\πDq}---\left(2.3\right)$

Obtained the heat exchange equation of pipe flow medium and tube wall by above three equations:

$C_p\frac{\mathrm{dT}}{\mathrm{d\τ}}-\frac{T}{\mathrm{\ρ}}\mathrm{\β}\frac{\mathrm{dp}}{\mathrm{d\τ}}-\frac{{\mathrm{fV}}^3}{2D}=-\frac{4q}{\mathrm{\ρD}}---\left(2.4\right)$

Wherein, τ is the time, s; Z is the distance apart from pipeline starting point, m; ρ is the average density of the interior medium of pipe at section, kg/m ³; V is the mean speed of pipe flow medium, m/s; A is the sectional area of pipeline, m ²; G is acceleration of gravity, m/s ²; α is the angle of pipeline axial and horizontal direction; P is the mean pressure of medium at section, Pa; F is the darcy coefficient of friction resistance; D is the diameter of the effective flow area of pipeline, m; U is medium specific internal energy in pipe, J/kg; S is the difference of elevation between adjacent cells, m; H is the specific enthalpy of unit mass medium in pipe, J/kg; Q is the tube wall of medium and unit area in the pipe heat exchange amount within the unit interval, W/m ²; C _pfor managing the specific heat at constant pressure of interior medium, J/ (kg DEG C); T is medium temperature in pipe, DEG C; β is the expansion coefficient of medium in pipe, DEG C ^-1.

The heat conduction equation of tube wall and anticorrosive coat:

${\mathrm{\ρ}}_i{C}_i\frac{{\∂T}_i}{\∂\mathrm{\τ}}=\frac{1}{r}\frac{\∂}{\∂r}\left({\mathrm{\λ}}_{i}r\frac{{\∂T}_i}{\∂r}\right)+\frac{1}{r^2}\frac{\∂}{\∂\mathrm{\θ}}\left({\mathrm{\λ}}_i\frac{{\∂T}_i}{\∂\mathrm{\θ}}\right)---\left(2.5\right)$

Wherein, when the newly-built pipeline of preheating, i=1,2, represent respectively tube wall and anticorrosive coat; When preheating in-service pipeline (crude oil of low-coagulation changes defeated crude oil with high solidifying point), i=1,2,3, represent respectively wax deposition layer, tube wall and anticorrosive coat; In two kinds of situations, ρ _ibe the density of i layer, kg/m ³; C _ibe the specific heat capacity of i layer, J/ (kg DEG C); T _ibe the temperature of i layer, DEG C; λ _ibe the coefficient of heat conductivity of i layer, W/ (m DEG C); R is radial position, m; θ is hoop radian.

The heat conduction equation of pipeline soil:

${\mathrm{\ρ}}_s{C}_s\frac{{\∂T}_s}{\∂\mathrm{\τ}}=\frac{\∂}{\∂x}\left({\mathrm{\λ}}_s\frac{{\∂T}_s}{\∂x}\right)+\frac{\∂}{\∂y}\left({\mathrm{\λ}}_s\frac{{\∂T}_s}{\∂y}\right)---\left(2.6\right)$

Wherein, ρ _sfor the density of soil, kg/m ³; C _sfor the specific heat capacity of soil, J/ (kg DEG C); T _sfor the temperature of soil, DEG C; λ _sfor the coefficient of heat conductivity of soil, W/ (m DEG C); X is the lateral separation apart from pipeline center's vertical section, m; Y is the longitudinal degree of depth apart from earth's surface, m.

Consider the symmetry of zoning, only get the right half part (the rectangle heating power influence district of 10m × 10m) of pipeline and study, boundary condition is:

In the time of y=0, ${\mathrm{\λ}}_s\frac{{\mathrm{dT}}_s}{\mathrm{dy}}={\mathrm{\α}}_a(T_a-T_s)---\left(2.7\right)$

Work as x=0, and-(h ₀-R)≤y≤0 or y≤-(h ₀+ R) time,

In the time of y=-H, T _s=T _n(2.9)

In the time of x=L, ${\mathrm{\λ}}_s\frac{{\mathrm{dT}}_s}{\mathrm{dx}}=0---\left(2.10\right)$ Wherein, h ₀for pipeline center's buried depth, m; R is the pipeline radius comprising after anticorrosive coat, m; α _afor the coefficient of heat transfer of earth's surface and atmosphere, W/ (m ²dEG C); T _afor temperature, DEG C; T _nfor the temperature of soil thermostat layer, DEG C; H is longitudinal degree of depth of the pipeline heating power zone of influence, m; L is the half of the transverse width of the pipeline heating power zone of influence, m.

In addition, in pipe, in the diabatic process of medium, tube wall, anticorrosive coat and soil, also should meet the relevant Correlation Criteria shown in table 2.1.

Table 2.1 preheating pipe system heat exchange Correlation Criteria

2.1.3 the mathematical model of stopping transportation operating mode

Crude oil pipeline in preheating operation process, its pipe flow medium may comprise waxy crude oil and pure material liquid (as water) simultaneously, makes the heat transfer characteristic of pipeline and the pipeline of Single Medium different.Because the phase transformation of waxy crude oil (analysing wax) latent heat is just emitted gradually after oil temperature is down to wax precipitation piont, if section temperature lower than wax precipitation piont, crude oil entirety is emitted latent heat of phase change; And water is only emitted latent heat of phase change in process of setting below freezing point temperature, this latent heat is emitted at phase interface place.

Consider the complicacy of above process, suppose as follows under study for action herein: (1) definition equivalent heat conductivity, is converted into Heat Conduction Problems processing by the natural convection after medium stopping transportation in pipe; (2) if when pipeline shutdown, in pipe, in medium, contain waxy crude oil, and have wax partial crystallization to go out in whole temperature drop process, and form solidifying oil reservoir, think that this solidifying oil reservoir is to increase with the concentric mode of pipeline; (3) latent heat of phase change adopts the temperature variant form of specific heat capacity to be characterized on the impact of temperature drop process; (4) introduce stagnant point, to distinguish natural convection region and the thermal conductivity region of pipe interior.By above-mentioned hypothesis, stopping transportation operating mode can be reduced to simple Heat Conduction Problems processing.

The heat conduction equation of pipe flow medium is:

$\mathrm{\ρC}\frac{\∂T}{\∂r}=\frac{1}{r}\frac{\∂}{\∂r}\left(\mathrm{\λr}\frac{\∂T}{\∂r}\right)+\frac{1}{r}\frac{\∂}{\∂\mathrm{\θ}}\left(\frac{\mathrm{\λ}}{r}\frac{\∂T}{\∂\mathrm{\θ}}\right)---\left(2.11\right)$

In stopping transportation operating mode, if there is natural convection, the equivalent heat conductivity that coefficient of heat conductivity λ should adopt formula 2.12 to calculate in medium in pipe; If medium is in viscous flow state in pipe, coefficient of heat conductivity λ can adopt actual value.

${\mathrm{\λ}}_{\mathrm{eff}}=\frac{{-\mathrm{\α}}_y(\mathrm{Ty}-\mathrm{Tw})}{{\left(\frac{\mathrm{\δTy}}{\mathrm{\δr}}\right)}_w}---\left(2.12\right)$

Tube wall, anticorrosive coat heat conduction equation and thermal conduction of soil equation are still continued to use formula 2.5 and formula 2.6.

2.1.4 restart the mathematical model of safety evaluation

When medium in pipe be pure material liquid (as water) or shutdown time more in short-term, the waterpower of restart procedure with heating power governing equation with normally conveying is identical; But when having waxy crude oil in pipe flow medium, and shutdown time is longer, while making part or all of crude oil show thixotropy, needs employing formula 2.13 to replace original equation of momentum:

$\frac{\∂V}{\∂\mathrm{\τ}}+V\frac{\∂V}{\∂z}+\frac{1}{\mathrm{\ρ}}\frac{\∂p}{\∂z}+g\sin \mathrm{\α}+\frac{{4\mathrm{\τ}}_w}{\mathrm{\ρD}}=0---\left(2.13\right)$

In above formula, τ _whouska model shown in employing formula 2.14 and formula 2.15 calculates, and this thixotroping model can reflect the structure power of material under a certain state by the variation of structural parameters.And think, the foundation of structure with destroy in shear history and deposit, structural damage by yield stress and denseness etc. speed cracking embodied.

$\mathrm{\τ}={\mathrm{\τ}}_{y0}+\mathrm{\λ}{\mathrm{\τ}}_{y1}+(K+\mathrm{\λ\ΔK}){\stackrel{\·}{\mathrm{\γ}}}^n---\left(2.14\right)$

$\frac{\mathrm{d\λ}}{\mathrm{dt}}=a(1-\mathrm{\λ})-\mathrm{b\λ}{\stackrel{\·}{\mathrm{\γ}}}^m---\left(2.15\right)$

Wherein, τ is shear stress, Pa; τ _y0yield stress during for the abundant cracking of structure, Pa; τ _y1yield stress while foundation completely for structure, Pa; K is consistency index, Pas; Δ K is thixotropy consistency index, Pas; for shearing rate, s ^-1; N is flow behaviour index; λ is structural parameters; A, b, m are textural constant.

2.2 zonings discrete

In calculating, adopt different grid systems to carry out discrete to different research objects herein.Adopt unstructured quadrilateral mesh to carry out to pipeline soil heating power range of influence discrete, as shown in Fig. 4 a; Adopt polar grid discrete to steel pipe walls, anticorrosive coat (if crude oil of low-coagulation changes the in-service pipeline of defeated crude oil with high solidifying point, also needing to consider wax deposition layer), as shown in Figure 4 b.Manage interior medium in stopping transportation operating mode and restart in the Calculation of Heat Transfer of safety evaluation, also adopting polar grid to carry out discrete; And normally carry under operating mode, the medial temperature of a calculation medium, adopts uniform Mesh Grid as shown in Figure 5.

2.3 governing equations discrete and solving

(1) pipe flow medium and tube wall heat exchange equation is discrete

Adopt method of finite difference to carry out discrete to formula 2.4.Along pipe range direction, pipeline is divided into some sections, as shown in Figure 5.Within the Δ τ time interval, the discrete form of equation is:

$C_p(\frac{T_i-T_i^0}{\mathrm{\Δ\τ}}+\frac{T_i^0-T_{i-1}^0}{\mathrm{\Δz}}{V}_i)-\frac{T_i}{\mathrm{\ρ}}{\mathrm{\β}}_o(\frac{p_i-p_i^0}{\mathrm{\Δ\τ}}+\frac{{p_i}^0-p_{i-1}^0}{\mathrm{\Δz}}{V}_i)-\frac{{\mathrm{\λV}}_i^3}{2D}=-\frac{{4q}_i}{\mathrm{\ρD}}---\left(2.16\right)$

Arrange:

$T_i=\frac{\frac{{\mathrm{\λV}}_i^3}{2D}-\frac{{4q}_i}{\mathrm{\ρD}}-C_p\frac{T_i^0-T_{i-1}^0}{\mathrm{\Δz}}{V}_i+\frac{C_p{T}_i^0}{\mathrm{\Δ\τ}}}{\frac{C_p}{\mathrm{\Δ\τ}}-\frac{{\mathrm{\β}}_o}{\mathrm{\ρ}}(\frac{p_i-p_i^0}{\mathrm{\Δ\τ}}+\frac{p_i-p_{i-1}}{\mathrm{\Δz}}{V}_i)}---\left(2.17\right)$

(2) steel pipe walls, anticorrosive coat heat conduction equation is discrete

Steel pipe walls and anticorrosive coat (if crude oil of low-coagulation changes the in-service pipeline of defeated crude oil with high solidifying point, also needing the to consider wax deposition layer) structured grid under polar coordinate system is as shown in Fig. 6 (b).Adopt Finite Volume Method for Air to carry out heat conduction equation discrete, discrete form, suc as formula shown in 2.18, is applied this equation of Gauss-Seidel iterative.

a _PT _P＝a _ET _E+a _WT _W+a _NT _N+a _ST _S+b

$a_E=\frac{\mathrm{\Δr}}{r_E{\left(\mathrm{\δ\θ}\right)}_E/{\mathrm{\λ}}_E},a_W=\frac{\mathrm{\Δr}}{r_W{\left(\mathrm{\δ\θ}\right)}_W/{\mathrm{\λ}}_W},a_N=\frac{r_N\mathrm{\Δ\θ}}{{\left(\mathrm{\δr}\right)}_N/{\mathrm{\λ}}_N},a_S=\frac{r_S\mathrm{\Δ\θ}}{{\left(\mathrm{\δr}\right)}_S/{\mathrm{\λ}}_S}---\left(2.18\right)$

$a_P^0=\frac{0.5{\left(\mathrm{\ρc}\right)}_P(r_N+r_S)\mathrm{\Δr\Δ\θ}}{\mathrm{\Δ\τ}},a_P=a_E+a_W+a_N+a_S+a_P^0,b=a_P^0{T}_P^0$

(3) thermal conduction of soil equation is discrete

To the soil heating power range of influence shown in Fig. 4 a, Fig. 4 b, application Gambit 2.2.30 software adopts Pave method to generate unstructured quadrilateral mesh, and local refinement is carried out to grid in the region that Near Pipelines thermograde is larger.Taking the grid cell shown in Fig. 6 (a) as example, adopt Finite Volume Method for Air to carry out discrete solving to thermal conduction of soil equation.Discrete form is:

$a_{p_0}{T}_{p_0}=\underset{j=1}{\overset{4}{\mathrm{\Σ}}}{a}_{p_j}{T}_{p_j}+b$

$\begin{array}{ccc}{a}_{p_0}=\underset{j=1}{\overset{4}{\mathrm{\Σ}}}{a}_{p_j}+\frac{A_{P_0}}{\mathrm{\Δ\τ}}& a_{p_j}=\frac{{\mathrm{\λ}}_s}{{\mathrm{\ρ}}_s{c}_s}\frac{d_j\·A_j}{{\left|d_j\right|}^2}& (j=\mathrm{1,2,3,4})\end{array}---\left(2.19\right)$

$b=\frac{T_{p_0}^0{A}_{P_0}}{\mathrm{\Δ\τ}}+\frac{{\mathrm{\λ}}_s}{{\mathrm{\ρ}}_s{c}_s}\underset{j=1}{\overset{4}{\mathrm{\Σ}}}({\mathrm{\ω}}_{P_0}{(\▿T)}_{P_0}+{\mathrm{\ω}}_{P_j}{(\▿T)}_{P_j})(1-\frac{d_j}{\left|d_j\right|}\frac{d_j}{\left|d_j\right|})$

Wherein, for P ₀the control volume of unit; A _jfor controlling the area vector of volume interface in j direction, its positive dirction is consistent with outer normal unit vector; T _pfor the temperature of P node; for P ₀the thermograde of node; d _jfor from P ₀to P _jdirected line segment; with for interpolation factor.

The main diagonal dominance of above discrete equation, can adopt the methods such as Gauss-Seidel iteration, method of conjugate gradient to solve.In the time obtaining with grid independent solutions, can think that the temperature of Nodes can reflect soil Temperature Distribution.

The foregoing is only the preferred embodiments of the present invention, be not limited to the present invention, for a person skilled in the art, the present invention can have various modifications and variations.Within the spirit and principles in the present invention all, any amendment of doing, be equal to replacement, improvement etc., within all should being included in protection scope of the present invention.

Claims (6)

1. computing method for crude oil pipeline preheating operation thermal procession, is characterized in that, comprise the steps:

Crude oil pipeline preheating operation process is carried out to Rational Simplification, set up the physical model of the interior medium of the description pipe of normally carrying under operating mode and pipeline soil heat exchange; Derive governing equation according to described physical model, and definite zoning and boundary condition;

Set up the mathematical model under stopping transportation operating mode and restart the mathematical model of safety evaluation;

Adopt different grid systems respectively to the mathematical model under physical model, described stopping transportation operating mode under described normal conveying operating mode and described in restart safety evaluation mathematical model carry out discretely, application Finite Volume Method for Air and method of finite difference obtain discrete governing equation;

Described discrete governing equation is carried out to iterative Output rusults.

2. the computing method of crude oil pipeline preheating operation thermal procession as claimed in claim 1, is characterized in that,

In described pipe, medium comprises pre-thermal medium, pumped (conveying) medium.

3. the computing method of crude oil pipeline preheating operation thermal procession as claimed in claim 2, is characterized in that,

Described crude oil pipeline preheating operation process is carried out to Rational Simplification, set up the physical model of medium and pipeline soil heat exchange in the normal description pipe of carrying under operating mode; Derive governing equation according to described physical model, and definite zoning and boundary condition, specifically comprise the steps:

For simplifying computation process, make following basic assumption:

(1) normally carry in operating mode and think that managing medium temperature, pressure, flow velocity and density on interior same cross section is uniformly, thinks that these variablees are the function of time and pipeline axial position; (2) pipeline soil is considered as to uniform dielectric, thinks that its physical property is respectively to identical; (3) because soil is along the thermograde of pipeline axial much smaller than along pipeline thermograde radially, ignoring the heat conduction between adjacent soil cross section, is two-dimension unsteady state heat conduction by problem reduction; (4) do not consider the blending at interface of pre-thermal medium and pumped (conveying) medium, think " piston-type " displacement; (5) think that the rectangular area of the vertical center line of the pipeline wide 10m in left and right, dark 10m is the soil heating power zone of influence;

Based on above hypothesis and simplification, set up following mathematical model:

In described pipe, continuity equation, the equation of momentum and the energy equation of medium are followed successively by:

$\frac{\∂}{\∂\mathrm{\τ}}\left(\mathrm{\ρA}\right)+\frac{\∂}{\∂z}\left(\mathrm{\ρVA}\right)=0;$

$\frac{\∂V}{\∂\mathrm{\τ}}+V\frac{\∂V}{\∂z}=-g\sin \mathrm{\α}-\frac{1}{\mathrm{\ρ}}\frac{\∂p}{\∂z}-\frac{f}{D}\frac{V^2}{2};$

$\frac{\∂}{\∂\mathrm{\τ}}\left[\left(\mathrm{\ρA}\right)(u+\frac{V^2}{2}+\mathrm{gs})\right]+\frac{\∂}{\∂z}\left[\left(\mathrm{\ρVA}\right)(h+\frac{V^2}{2}+\mathrm{gs})\right]=-\mathrm{\πDq};$

Obtained the heat exchange equation of pipe flow medium and tube wall by above three equations:

$C_p\frac{\mathrm{dT}}{\mathrm{d\τ}}-\frac{T}{\mathrm{\ρ}}\mathrm{\β}\frac{\mathrm{dp}}{\mathrm{d\τ}}-\frac{{\mathrm{fV}}^3}{2D}=-\frac{4q}{\mathrm{\ρD}};$ It is formula 2.5;

Wherein, τ is the time, s; Z is the distance apart from pipeline starting point, m; ρ is the average density of the interior medium of pipe at section, kg/m ³; V is the mean speed of pipe flow medium, m/s; A is the sectional area of pipeline, m ²; G is acceleration of gravity, m/s ²; α is the angle of pipeline axial and horizontal direction; P is the mean pressure of medium at section, Pa; F is the darcy coefficient of friction resistance; D is the diameter of the effective flow area of pipeline, m; U is medium specific internal energy in pipe, J/kg; S is the difference of elevation between adjacent cells, m; H is the specific enthalpy of unit mass medium in pipe, J/kg; Q is the tube wall of medium and unit area in the pipe heat exchange amount within the unit interval, W/m ²; C _pfor managing the specific heat at constant pressure of interior medium, J/ (kg DEG C); T is medium temperature in pipe, DEG C; β is the expansion coefficient of medium in pipe, DEG C ^-1;

Determine the heat conduction equation of tube wall and anticorrosive coat:

${\mathrm{\ρ}}_i{C}_i\frac{{\∂T}_i}{\∂\mathrm{\τ}}=\frac{1}{r}\frac{\∂}{\∂r}\left({\mathrm{\λ}}_{i}r\frac{{\∂T}_i}{\∂r}\right)+\frac{1}{r^2}\frac{\∂}{\∂\mathrm{\θ}}\left({\mathrm{\λ}}_i\frac{{\∂T}_i}{\∂\mathrm{\θ}}\right);$ It is formula 2.6;

Wherein, when the newly-built pipeline of preheating, i=1,2, represent respectively tube wall and anticorrosive coat; When preheating in-service pipeline (crude oil of low-coagulation changes defeated crude oil with high solidifying point), i=1,2,3, represent respectively wax deposition layer, tube wall and anticorrosive coat; In two kinds of situations, ρ _ibe the density of i layer, kg/m ³; C _ibe the specific heat capacity of i layer, J/ (kg DEG C); T _ibe the temperature of i layer, DEG C; λ _ibe the coefficient of heat conductivity of i layer, W/ (m DEG C); R is radial position, m; θ is hoop radian;

Determine the heat conduction equation of pipeline soil:

${\mathrm{\ρ}}_s{C}_s\frac{{\∂T}_s}{\∂\mathrm{\τ}}=\frac{\∂}{\∂x}\left({\mathrm{\λ}}_s\frac{{\∂T}_s}{\∂x}\right)+\frac{\∂}{\∂y}\left({\mathrm{\λ}}_s\frac{{\∂T}_s}{\∂y}\right);$

Wherein, ρ _sfor the density of soil, kg/m ³; C _sfor the specific heat capacity of soil, J/ (kg DEG C); T _sfor the temperature of soil, DEG C; λ _sfor the coefficient of heat conductivity of soil, W/ (m DEG C); X is the lateral separation apart from pipeline center's vertical section, m; Y is the longitudinal degree of depth apart from earth's surface, m;

Consider the symmetry of zoning, only get the right half part (the rectangle heating power influence district of 10m × 10m) of pipeline and study, boundary condition is:

In the time of y=0, ${\mathrm{\λ}}_s\frac{{\mathrm{dT}}_s}{\mathrm{dy}}={\mathrm{\α}}_a(T_a-T_s);$

Work as x=0, and-(h ₀-R)≤y≤0 or y≤-(h ₀+ R) time,

In the time of y=-H, T _s=T _n;

In the time of x=L, ${\mathrm{\λ}}_s\frac{{\mathrm{dT}}_s}{\mathrm{dx}}=0;$

Wherein, h ₀for pipeline center's buried depth, m; R is the pipeline radius comprising after anticorrosive coat, m; α _afor the coefficient of heat transfer of earth's surface and atmosphere, W/ (m ²dEG C); T _afor temperature, DEG C; T _nfor the temperature of soil thermostat layer, DEG C; H is longitudinal degree of depth of the pipeline heating power zone of influence, m; L is the half of the transverse width of the pipeline heating power zone of influence, m.

4. the computing method of crude oil pipeline preheating operation thermal procession as claimed in claim 3, is characterized in that,

The described mathematical model of setting up under stopping transportation operating mode, specifically comprises the steps:

Suppose as follows in advance: (1) definition equivalent heat conductivity, is converted into Heat Conduction Problems processing by the natural convection after medium stopping transportation in pipe; (2) if when pipeline shutdown, in pipe, in medium, contain waxy crude oil, and have wax partial crystallization to go out in whole temperature drop process, and form solidifying oil reservoir, think that this solidifying oil reservoir is to increase with the concentric mode of pipeline; (3) latent heat of phase change adopts the temperature variant form of specific heat capacity to be characterized on the impact of temperature drop process; (4) introduce stagnant point, to distinguish natural convection region and the thermal conductivity region of pipe interior;

By above-mentioned hypothesis, stopping transportation operating mode can be reduced to simple Heat Conduction Problems processing:

The heat conduction equation of pipe flow medium is: $\mathrm{\ρC}\frac{\∂T}{\∂r}=\frac{1}{r}\frac{\∂}{\∂r}\left(\mathrm{\λr}\frac{\∂T}{\∂r}\right)+\frac{1}{r}\frac{\∂}{\∂\mathrm{\θ}}\left(\frac{\mathrm{\λ}}{r}\frac{\∂T}{\∂\mathrm{\θ}}\right);$

In stopping transportation operating mode, if there is natural convection in medium in pipe, coefficient of heat conductivity λ should adopt the equivalent heat conductivity that formula 2.12 calculates; If medium is in viscous flow state in pipe, coefficient of heat conductivity λ can adopt actual value:

${\mathrm{\λ}}_{\mathrm{eff}}=\frac{{-\mathrm{\α}}_y(\mathrm{Ty}-\mathrm{Tw})}{{\left(\frac{\mathrm{\δTy}}{\mathrm{\δr}}\right)}_w};$ It is formula 2.12;

Described tube wall, anticorrosive coat heat conduction equation and thermal conduction of soil equation are still continued to use formula 2.5 and formula 2.6.

5. the computing method of crude oil pipeline preheating operation thermal procession as claimed in claim 4, is characterized in that,

The mathematical model of safety evaluation is restarted in described foundation, specifically comprises the steps:

When medium in pipe be pure material liquid or shutdown time more in short-term, the waterpower of restart procedure with heating power governing equation with normally conveying is identical;

When having waxy crude oil in pipe flow medium, and shutdown time is longer, while making part or all of crude oil show thixotropy, needs employing formula 2.13 to replace original equation of momentum:

$\frac{\∂V}{\∂\mathrm{\τ}}+V\frac{\∂V}{\∂z}+\frac{1}{\mathrm{\ρ}}\frac{\∂p}{\∂z}+g\sin \mathrm{\α}+\frac{{4\mathrm{\τ}}_w}{\mathrm{\ρD}}=0;$ It is formula 2.13;

In above formula, τ _wthixotroping model shown in employing formula 2.14 and formula 2.15 calculates, and described thixotroping model can reflect the structure power of material under a certain state by the variation of structural parameters:

$\mathrm{\τ}={\mathrm{\τ}}_{y0}+\mathrm{\λ}{\mathrm{\τ}}_{y1}+(K+\mathrm{\λ\ΔK}){\stackrel{\·}{\mathrm{\γ}}}^n;$ It is formula 2.14;

$\frac{\mathrm{d\λ}}{\mathrm{dt}}=a(1-\mathrm{\λ})-\mathrm{b\λ}{\stackrel{\·}{\mathrm{\γ}}}^m;$ It is formula 2.15;

Wherein, τ is shear stress, Pa; τ _y0yield stress during for the abundant cracking of structure, Pa; τ _y1yield stress while foundation completely for structure, Pa; K is consistency index, Pas; Δ K is thixotropy consistency index, Pas; for shearing rate, s ^-1; N is flow behaviour index; λ is structural parameters; A, b, m are textural constant.

6. the computing method of crude oil pipeline preheating operation thermal procession as claimed in claim 5, is characterized in that,

Adopt different grid systems to carry out discrete to the physical model under described normal conveying operating mode, mathematical model under stopping transportation operating mode and the mathematical model of restarting safety evaluation respectively, application Finite Volume Method for Air and method of finite difference obtain discrete governing equation, specifically comprise the steps:

Adopt unstructured quadrilateral mesh to carry out discrete to pipeline soil heating power range of influence;

Adopt polar grid discrete to steel pipe walls, anticorrosive coat;

In described pipe medium stopping transportation condition model and described in restart in the Calculation of Heat Transfer of Model for Safety Evaluation, adopt polar grid carry out discrete;

Carry under operating mode normal, the medial temperature of a calculation medium, adopts uniform Mesh Grid to carry out discrete.