CN107514251A - SAGD horizontal well concentric tube steam injection heat-transferring methods - Google Patents
SAGD horizontal well concentric tube steam injection heat-transferring methods Download PDFInfo
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- E—FIXED CONSTRUCTIONS
- E21—EARTH DRILLING; MINING
- E21B—EARTH DRILLING, e.g. DEEP DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- E21B43/00—Methods or apparatus for obtaining oil, gas, water, soluble or meltable materials or a slurry of minerals from wells
- E21B43/16—Enhanced recovery methods for obtaining hydrocarbons
- E21B43/24—Enhanced recovery methods for obtaining hydrocarbons using heat, e.g. steam injection
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- E—FIXED CONSTRUCTIONS
- E21—EARTH DRILLING; MINING
- E21B—EARTH DRILLING, e.g. DEEP DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- E21B36/00—Heating, cooling, insulating arrangements for boreholes or wells, e.g. for use in permafrost zones
Abstract
The invention provides a kind of SAGD horizontal wells concentric tube steam injection Heat Transfer Calculation, SAGD horizontal wells concentric tube includes long tube, short tube, screen casing and the sleeve pipe being arranged concentrically, wherein, long tube includes vertical section and the horizontal segment being connected with vertical section；Short tube is set in the periphery of vertical section and is arranged at intervals with long tube；Sleeve pipe is set in the periphery of short tube and is arranged at intervals with short tube；Screen casing is connected to the end of sleeve pipe and is set in the periphery of horizontal segment, and screen casing is arranged at intervals with horizontal segment；SAGD horizontal well concentric tube steam injection heat-transferring methods include：Step S1：Determine the heat loss in the heat loss and short tube in the long tube at vertical section；Step S2：Determine the heat loss of the heat loss and screen casing in the long tube at horizontal segment.According to SAGD horizontal well concentric tube steam injection heat-transferring methods of the invention, the steam heat that can determine from the vertical section injection of long tube passes loss, circulates the optimization of pre-heating technique for SAGD horizontal wells and raising development effectiveness provides foundation.
Description
Technical Field
The invention relates to the field of oil exploitation, in particular to a concentric pipe steam injection and heat transfer method for an SAGD horizontal well.
Background
In some oil fields, the viscosity of the super-thick oil in the oil field is high, the conventional thermal recovery technology is difficult to realize economic and effective development, and the double-horizontal-well SAGD process is adopted for development by referring to the development experience of the foreign super-thick oil. SAGD development is divided into a circulating preheating stage and a production stage, steam is injected into a production well and a steam injection well at the same time in the circulating preheating stage, and the purpose is to realize uniform heating of oil layers in the shortest possible time, so that oil reservoirs with poor initial fluidity or no flow among wells are uniformly heated and communicated.
The steam injection circulation mode is adopted for circularly preheating the SAGD horizontal well in the oil field at present, steam is injected from a long oil pipe of an injection and production well into a parallel double-pipe structure adopted in a shaft of most of the injection and production wells, enters a horizontal section sieve pipe, then exchanges heat with an oil layer, and then returns to the ground through a short oil pipe. Lijing ling et al establishes an analytical model of double-horizontal-well SAGD parallel double-pipe circulation preheating in document SAGD circulation preheating heat transfer calculation and influence factor analysis, and performs cyclic preheatingThe heating condition of the oil layer in the ring preheating process is calculated and analyzed. Parallel double-tube structure and single-tube structure in the pit shaft conduct heat differently, and the heat exchange mode in the vertical section annular space is as follows: and heat transfer is carried out between the long pipe and the short pipe as well as between the annular wall surfaces through natural convection, heat conduction and radiation. Unlike single tubes, because steam is led between single tube annuluses and belongs to forced convection, the influence of radiation heat transfer does not need to be considered in the single tube annuluses, and the forced convection heat transfer coefficient is much larger than that of the radiation heat transfer. For the double-tube annular structure, because no steam flows in the annular structure, the heat exchange coefficient of natural convection heating conduction (about 10W/m) 2 K) is comparable to the radiative heat transfer coefficient, so the effect of radiative heat transfer needs to be considered. The wall temperature of the main pipe, the secondary pipe and the annular wall of the parallel double pipes should be taken for radiation heat exchange, but for the main pipe and the secondary pipe, the forced convection heat exchange of water vapor is carried out in the pipes, so that the heat exchange coefficient is very large, and the temperature of the pipe walls of the main pipe and the secondary pipe can be approximately considered to be equal to the temperature of fluid in the pipes.
Adopt parallel double-barrelled structure, under the higher condition of steam injection volume, the steam injection rubs and hinders and increase, and well head steam injection pressure improves, and adopts concentric tubular column structure, under the same steam injection volume condition, the steam injection rubs and well head pressure is little, and the steam injection height after getting into SAGD production stage is favorable to accelerating SAGD steam chamber development, increases production.
The difference between the concentric tube and the parallel double tubes is that heat exchange exists between the main tube and the auxiliary tube of the parallel double tubes and the annulus at the inclined and straight well section, and heat exchange does not exist between the long tube (inner tube) of the concentric tube and the annulus at the inclined and straight well section. Meanwhile, the long pipe of the concentric pipe inclined straight well section adopts a heat insulation oil pipe, heat exchange between the long pipe and the short pipe is less, more heat is used for heating a horizontal section oil layer, and the utilization rate of steam is improved.
At present, SAGD of an oil field adopts concentric tube steam injection to enter a test stage, an analytical model about concentric tube circulation preheating is not established, and no related article introduction exists in China, so that calculation and analysis are necessary for a heat transfer process of a concentric tube circulation preheating stage, operation parameters of the circulation preheating stage are optimized, operation cost is saved, and a basis is provided for optimization of an SAGD circulation preheating process and improvement of development effects.
Disclosure of Invention
The invention mainly aims to provide a SAGD horizontal well concentric pipe steam injection heat transfer method, which provides a basis for optimization of an SAGD circulating preheating process.
In order to achieve the purpose, the invention provides a SAGD horizontal well concentric tube steam injection heat transfer calculation method, the SAGD horizontal well concentric tube comprises a long tube, a short tube, a sieve tube and a sleeve which are concentrically arranged, wherein the long tube comprises a vertical section and a horizontal section connected with the vertical section; the short pipe is sleeved on the periphery of the vertical section and is arranged at intervals with the long pipe; the sleeve is sleeved on the periphery of the short pipe and is arranged at intervals with the short pipe; the sieve tube is connected to the end part of the sleeve and sleeved on the periphery of the horizontal section, and the sieve tube and the horizontal section are arranged at intervals; the SAGD horizontal well concentric tube steam injection heat transfer method comprises the following steps: step S1: determining heat loss in the long tube and heat loss in the short tube at the vertical section; step S2: heat loss in the long pipe and heat loss of the screen at the horizontal section are determined.
Further, in step S1, the heat loss a within the long tube is determined using the following formula:
A＝K 1 πd 1 (T 2 -T 1 )
in the formula: d 1 Is the inner diameter of a long pipe, and the unit is m; t is a unit of 1 The temperature of steam in a long pipe is shown in unit of ℃; t is 2 The temperature of steam in the short pipe is expressed in unit; k is 1 Is the heat transfer coefficient between the long pipe and the short pipe, and has the unit of W/(m) 2 ·℃)。
Further, the long pipe comprises an inner pipe sleeve, an outer pipe sleeve and a heat insulation layer arranged between the inner pipe sleeve and the outer pipe sleeve, and the heat transfer coefficient K between the long pipe and the short pipe 1 Determined by the following equation:
in the formula: h is 1 For steam in long tubes to long tubesThe convective heat transfer coefficient of the inner wall surface has the unit of W/(m) 2 ·℃)；h 2 The convective heat transfer coefficient of the fluid in the short pipe to the outer wall surface of the vertical section of the long pipe is W/(m) 2 ·℃)；d 2 Is the outer diameter of the inner pipe sleeve, and the unit is m; d is a radical of 3 The inner diameter of the outer pipe sleeve is m; d is a radical of 4 The outer diameter of the outer pipe sleeve is m; lambda [ alpha ] tb The thermal conductivity coefficient of the inner pipe sleeve is expressed as W/(m DEG C); lambda in The thermal conductivity of the outer jacket is expressed in W/(m.DEG C.).
Further, the outer circumference of the casing is fitted with a cement sheath, and in step S1, the heat loss B in the short pipe is determined using the following formula:
B＝K 1 πd 1 (T 1 -T 2 )+K 2 πd 5 (T h -T 2 )
in the formula: t is 1 The temperature of steam in a long pipe is measured in unit; t is a unit of 2 The temperature of steam in the short pipe is expressed in unit; d 5 The outer diameter of the short pipe is measured in unit; t is h The temperature of the outer edge of the cement sheath is expressed in unit; k 2 Is the total heat transfer coefficient between the short pipe and the stratum and has the unit of W/(m) 2 ·℃)。
Further, the overall heat transfer coefficient K between the short pipe and the formation 2 Determined by the following equation:
in the formula: h is 3 The convection heat transfer coefficient of steam in the short pipe to the inner wall of the short pipe is W/(m) 2 DEG C.); r5 is to consider fouling resistance; lambda [ alpha ] stb The thermal conductivity coefficient of the wall of the short pipe is expressed in W/(m DEG C); d 6 Is the outer diameter of the short pipe, and the unit is m; h is c3 Is the convective heat transfer coefficient in the sleeve, and has the unit of W/(m) 2 ·℃)；h r3 Is the heat radiation heat exchange coefficient in the sleeve with the unit of W/(m) 2 ·℃)；d 7 Is the inner diameter of the casing, and the unit is m; lambda [ alpha ] ct The thermal conductivity of the sleeve is expressed in W/(m DEG C); lambda sn The thermal conductivity coefficient of the cement sheath is expressed as W/(m DEG C); d is a radical of 8 Is the outer diameter of the sleeve, and the unit is m; d 9 Is the outer diameter of the cement sheath and has the unit of m.
Further, in step S2, the heat loss C within the long tube is determined using the following formula:
C＝K 11 πd 11 (T s -T 11 )；
in the formula: k is 11 Is the heat transfer coefficient between the inner walls of the long-tube sieve tube at the horizontal section, and the unit is W/(m) 2 ·℃)；d 11 Is the inner diameter of the long tube at the horizontal section, and the unit is m; t is s The temperature between the outer wall surface of the sieve tube at the horizontal section and the inner wall of the sieve tube is measured in units of; t is a unit of 11 Is the vapor temperature in the long tube at the horizontal section in degrees centigrade.
Further, the heat transfer coefficient K between the long pipe and the inner wall of the sieve tube 11 Determined by the following equation:
in the formula: h is 11 The heat transfer coefficient of steam in the long pipe to the inner wall surface of the long pipe is W/(m) 2 ·℃)；d 11 The inner diameter of a long pipe at the horizontal section is m; h is a total of 21 The heat transfer coefficient of steam between the outer wall of the sieve tube and the inner wall of the sieve tube to the outer wall surface of the long tube is W/(m) 2 ·℃)；d 21 The diameter of the outer wall of the long pipe at the horizontal section is m; r is a radical of hydrogen 11 The radius of the inner wall of a long pipe at the horizontal section is m; r is 21 The radius of the outer wall of the long pipe at the horizontal section is m; lambda [ alpha ] tb1 The heat conductivity coefficient of the long pipe at the horizontal section is W/(m DEG C).
Further, in step S2, the heat loss of the screen at the horizontal section is determined by the following formula:
in the formula:T x the temperature of a certain point in an oil layer is measured in units of ℃; t is s Is the temperature in the sieve tube, in units of ℃; r is a radical of hydrogen s The radius of the inner wall of the sieve tube is m; λ is the time of 1 day, in units of s; t is the number of days of heating in units of d; alpha is the thermal diffusion coefficient of the oil layer, unit m 2 /s；λ e The thermal conductivity of the oil layer is expressed in W/(m.K).
Further, when the steam injection time satisfies gamma/t <0.01 and the steam injection temperature is constant:
by applying the technical scheme, the steam injection and heat transfer method for the concentric tubes of the SAGD horizontal well can determine the heat transfer loss of steam injected from the vertical section of the long tube, and provide a basis for optimizing the circulating preheating process of the SAGD horizontal well and improving the development effect.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit the invention. In the drawings:
FIG. 1 schematically illustrates a front view of a SAGD horizontal well concentric tube of the present invention;
FIG. 2 schematically illustrates a half-sectional view of a SAGD horizontal well concentric tube vertical section of the present invention; and
figure 3 schematically shows a half-section view of a horizontal section of concentric tubes of a SAGD horizontal well of the present invention.
Wherein the figures include the following reference numerals:
10. a long tube; 11. a vertical section; 12. a horizontal segment; 13. an inner pipe sleeve; 14. a thermal insulation layer; 15. an outer pipe sleeve; 20. a short pipe; 30. a screen pipe; 40. a sleeve; 50. a cement sheath; 60. the earth formation.
Detailed Description
It should be noted that, in the present application, the embodiments and features of the embodiments may be combined with each other without conflict. The present invention will be described in detail below with reference to the embodiments with reference to the attached drawings.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an", and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
It should be noted that the terms "first," "second," and the like in the description and claims of this application and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used may be interchanged under appropriate circumstances such that, for example, embodiments of the application described herein may be implemented in sequences other than those illustrated or described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
Referring to fig. 1 to 3, according to an embodiment of the present invention, a calculation method for SAGD horizontal well concentric tube steam injection heat transfer is provided.
As shown in fig. 1, the SAGD horizontal well concentric pipe in the embodiment includes a long pipe 10, a short pipe 20, a screen 30 and a sleeve 40 which are concentrically arranged, wherein the long pipe 10 includes a vertical section 11 and a horizontal section 12 connected to the vertical section 11; the short pipe 20 is sleeved on the periphery of the vertical section 11 and is arranged at intervals with the long pipe 10; the sleeve 40 is sleeved on the periphery of the short pipe 20 and is arranged at intervals with the short pipe 20; the screen 30 is connected to the end of the casing 40 and sleeved on the outer periphery of the horizontal section 12, and the screen 30 and the horizontal section 12 are arranged at intervals.
As shown in fig. 2, the long pipe 10 in this embodiment includes an inner jacket 13, an outer jacket 15, and a thermal insulation layer 14 disposed between the inner jacket 13 and the outer jacket 15.
In operation, the periphery of the SAGD horizontal concentric pipe of the present embodiment is filled with a cement sheath 50, and the periphery of the cement sheath 50 is a formation 60. In the circulation preheating process, steam is injected from the vertical section 11 of the long pipe 10, flows out from the toe end of the SAGD horizontal well, exchanges heat with an oil layer in the sieve pipe 30 at the horizontal section 12, and then returns out of the SAGD horizontal well from the short pipe 20.
Specifically, the SAGD horizontal well concentric tube steam injection heat transfer method in the embodiment includes step S1 and step S2.
Wherein the purpose of step S1 is to determine the heat loss in the long pipe 10 and the heat loss in the short pipe 20 at the vertical section 11; the purpose of step S2 is to determine the heat loss in the long pipe 10 and the heat loss of the screen 30 at the horizontal section 12. According to the SAGD horizontal well concentric tube steam injection heat transfer method, the heat transfer loss of steam injected from the vertical section 11 of the long tube 10 can be determined, and a basis is provided for optimization of the SAGD horizontal well circulating preheating process and improvement of development effects.
The SAGD horizontal well concentric tube steam injection heat transfer method of the embodiment is specifically described as follows:
during calculation, it is assumed that no steam flows into the oil layer during the cyclic preheating process, and the heating mode of the oil layer is heat conduction.
During the steam injection cycle, the high temperature steam in the SAGD horizontal well concentric tubes has heat and spontaneously transfers to the formation 60. Heat is transferred through 9 links: the steam injected into the long pipe 10 and the inner wall of the inner pipe sleeve 13 have the links of forced convection heat transfer of phase change, heat conduction of the inner pipe sleeve 13, heat conduction of the heat insulation layer 14, heat conduction of the outer pipe sleeve 15, convection heat transfer of fluid in a gap between the outer wall of the long pipe 10 and the short pipe 20 and the outer wall of the long pipe 10, heat conduction of the pipe wall of the short pipe 20, convection heat transfer between fluid in a gap between the outer wall of the short pipe 20 and the inner wall of the sleeve 40 and the outer wall of the short pipe 20, heat conduction of the pipe wall of the sleeve 40, heat conduction of the cement ring 50 and the like, and the heat resistances are radially connected in series to form heat transfer in a 'shaft'.
With reference to fig. 2, according to the above-mentioned link affecting heat transfer, the SAGD horizontal well concentric tube steam injection heat transfer method includes the following steps:
a small section dz is taken along the length of the long tube 10 at the vertical section 11 for analysis, see figure 2.
(1) Determining the heat loss A in the long tube 10 at the vertical section 11
In the formula: d 1 Is the inner diameter of a long pipe, and the unit is m;
T 1 the steam temperature in a long pipe is expressed in unit;
T 2 the steam temperature in the short pipe is expressed in unit;
K 1 is the heat transfer coefficient between the long pipe and the short pipe, W/(m) 2 ·℃)。
Wherein the solving process of K1 is as follows:
1) The forced convection heat exchange phenomenon accompanied with phase change between the steam injected into the long pipe 10 and the inner wall of the inner pipe sleeve 13 is set as q heat flow 1 The heat formula is:
in the formula: h is 1 The convective heat transfer coefficient of steam in the long pipe 10 to the inner wall surface of the long pipe 10 is W/(m) 2 ·℃)；
T 1 Is the temperature of the steam in the long tube 10, and the unit is;
T c1 the temperature of the inner wall surface of the long tube 10 is measured in DEG C；
d 1 The inner diameter of the inner tube of the long tube 10 is m; a. The 1 Is the area of the inner wall surface of the long pipe 10, and the unit is m 2 ；
l is the length of the vertical section of the long tube 10 in m.
2) The heat of the inner wall of the inner pipe sleeve 13 is transferred to the outer wall of the inner pipe sleeve 13 in a heat conduction mode, and the heat flow is set to be q 2 From the heat transfer rate equation for a single cylindrical wall:
in the formula: lambda tb The thermal conductivity of the inner pipe sleeve 13 is expressed as W/(m DEG C);
T c2 the temperature of the outer wall surface of the inner pipe sleeve 13 is measured in units of ℃;
d 2 is the outer diameter of the inner jacket 13 in m.
3) The heat is mainly considered to be the heat insulation effect of the heat insulation layer 14 when the heat is spread in the heat insulation layer 14, and the heat process in the heat insulation layer 14 comprises three modes of heat conduction, convection and radiation. The SY/T5324-94 (prestressed insulated tubing) standard provides a concept of 'apparent thermal conductivity', the heat transferred in three ways of heat conduction, convection and radiation in the heat insulation layer 14 of the long tube 10 is regarded as the heat transferred in a pure heat conduction way by an 'imaginary solid' with the same heat insulation thickness, the heat conductivity of the 'imaginary solid' is called as 'apparent thermal conductivity', and the heat flow is set as q 3 The heat transfer process is a visual heat transfer process:
in the formula: lambda in Is the apparent thermal conductivity coefficient of the long tube 10 at the vertical section 11, and is given in units of W/(m DEG C);
T c3 is the temperature of the inner wall surface of the outer jacket 15, and the unit is;
is the inner diameter of the outer jacket 15 in m.
4) The heat of the inner wall of the outer sleeve 15 is transferred to the outer wall of the outer sleeve 15 in a heat conduction mode, and the heat flow is set to be q 4 ：
In the formula: t is a unit of c4 The temperature of the outer wall surface of the outer sleeve 15 is measured in units of ℃;
d 4 is the outer diameter of the outer jacket 15 in m.
5) Within the short pipe 20 heat is transferred by convection mainly through the return fluid with the outer wall of the long pipe 10, given a heat flow q 5 ：
In the formula: t is 2 Fluid temperature, deg.C, in the short tube 20;
h 2 is the convective heat transfer coefficient of the fluid in the short pipe 20 to the outer wall surface at the vertical section 11 of the long pipe 10, and has the unit of W/(m) 2 ·℃)；
When the heat transfer is stable, the continuity of the heat transfer indicates that: q. q.s 1 ＝q 2 ＝q 3 ＝q 4 ＝q 5
Definition of phi 1 ＝q 1 ＝q 2 ＝q 3 ＝q 4 ＝q 5
It is possible to obtain:
the overall heat transfer coefficient between the long pipe 10 and the short pipe 20 is defined as:
meanwhile, in the actual heat transfer process, the influence of fouling must be considered, so the influence of heat conduction resistance substituted by the existence of fouling needs to be considered in the actual heat transfer process, that is:
from the above analysis it can be obtained that the heat transfer coefficient between the long pipe 10 and the short pipe 20 is:
in the parameters to be solved, the convection heat transfer coefficient h of the steam in the long pipe 10 to the inner wall surface of the long pipe 10 1 The convective heat transfer coefficient of the fluid in the short pipe 20 needs to be solved by using the convective heat transfer theory in the heat transfer science. The solution theory is as follows:
before discussion, several dimensionless numbers are defined:
reynolds number:where ρ is the density of the fluid, u is the flow velocity, d is the internal diameter of the tube, η the viscosity. Describing the flow conditions of the fluid (laminar, transition, turbulent), in general, for flow problems in tubes, re&=2300, laminar flow; 2300<＝Re&=10000, transition zone; re> =10000, turbulent flow.
Number of knoop shert:wherein h is the convective heat transfer coefficient (to-be-solved quantity), the d pipe diameter and the heat conductivity of lambda fluid; the amount of convective heat transfer is described.
Prandtl number:eta viscosity, lambda fluid thermal conductivity, c p Fluid specific heat capacity; the magnitude of the fluid momentum transfer capability and the heat transfer capability are described.
Three dimensionless relationships:
Nu＝f(Re,Pr)
from this, it can be seen that the convective heat transfer coefficient h is required as long as the nuschelt number Nu can be obtained, but Nu = f (Re, pr) requires the reynolds number Re and the prandtl number Pr, and the reynolds number Re can be obtained by obtaining the velocity from the flow rate of the fluid in the pipe and then by combining the physical parameters of the fluid; the Plantt number Pr can be directly obtained from physical parameters of the fluid; when these two quantities are obtained, the Nu number Nu can be obtained. Thereby obtaining the convective heat transfer coefficient h.
Reynolds number Re
Prandtl number Pr
Nu number of nuschel
a. In laminar flow (Re < = 2300), the formula of Xide and Tate is adopted:
b. transition zone (2300 < = Re < = 10000), using the genilinsky formula:
f＝(1.82log Re-1.64) -2
c. turbulence (Re > = 10000), using the pilder-hough equation:
f＝(1.82log Re-1.64) -2
convective heat transfer coefficient h
(2) Determining heat loss B of the screen 30 at the horizontal section 12
The heat loss B within the short tube 20 is determined using the following equation:
in the formula: t is a unit of h Is the outer edge temperature of the cement sheath 50, in units of deg.C;
K 2 is the total heat transfer coefficient between the short pipe 20 and the stratum 60 and has the unit of W/(m) 2 ·℃)。
Wherein, K 2 The solving process is as follows:
1) The fluid in the short pipe 20 and the inner wall of the short pipe 20 generate convection heat exchange, and the heat flow is set as q:
in the formula: t is d1 The temperature of the inner wall surface of the short pipe 20 is measured in units of;
d 5 is the inner diameter of the short pipe 20, and the unit is m;
h 3 the convective heat transfer coefficient of the steam in the short pipe 20 to the inner wall of the short pipe 20 is W/(m) 2 ·℃)。
2) The inner pipe wall of the short pipe 20 transfers heat to the outer pipe wall in a heat conduction mode, and the heat flow is set as q:
in the formula: lambda stb The thermal conductivity coefficient of the wall of the short pipe 20 is expressed by W/(m DEG C);
T d2 the temperature of the outer wall surface of the short pipe 20 is measured in units of;
d 6 is the outer diameter of the short tube 20 and is expressed in m.
3) Heat is transferred in the casing 40 by natural convection and radiation, and the heat flow is set as q:
in the formula: h is c3 Is the convective heat transfer coefficient in the sleeve 40, and has the unit W/(m) 2 ·℃)；
h r3 Is the heat radiation heat exchange coefficient in the sleeve 40, and the unit is W/(m) 2 ·℃)；
T 3 Is the temperature of the inner wall surface of the sleeve 40, and the unit is;
d 7 is the inner diameter of the sleeve 40 in m.
4) The outer wall of the casing 40 and the cement sheath 50 are thermally conducted, and the heat flow is set as q:
in the formula: lambda ct The thermal conductivity of the sleeve 40 is given in W/(m DEG C);
λ sn is the thermal conductivity coefficient of 50 cement sheath, and the unit is W/(m DEG C);
d 8 is the outer diameter of the sleeve 40 in m;
d 9 is the outer diameter of the cement sheath 5 in m.
5) Wherein the cement sheath 50 is in thermal communication with the formation 60
It varies with time due to unstable heat conduction. Heat loss to the formation 60 begins to be large, but as steam injection progresses, the formation 60 temperature increases and the heat transfer power temperature differential Δ T will decrease, resulting in reduced heat loss. Assuming the heat flow is q, it can be expressed by the formula:
q＝πd 8 λ d (T h -T 4 )/f(t)
in the formula: lambda [ alpha ] d The thermal conductivity of the formation 60 is given in W/(m. DEG C);
T h the temperature of the outer edge of the cement sheath 50 is measured in units of ℃;
T 4 the temperature of the junction between the cement sheath 50 and the stratum 60 is measured in units of ℃;
f (t) is a dimensionless time function.
According to "Wellbore Heat Transmission" published by Ramey H J in 1962 on JPT:
in the formula: alpha (alpha) ("alpha") d Is the formation 60 thermal diffusivity in m 2 /s；
t is time in units of s.
Defined in terms of thermal diffusivity:
in the formula: λ is the thermal conductivity of the rock, and has the unit of W/(m.K);
rho is the equivalent density of the rock in kg/m 3 ；
C P The specific heat capacity of the formation 60 rock is expressed in J/kg.K.
Considering the continuity of heat transfer, knowing that the heat dissipated from the stub pipe to the annulus is equal to the heat dissipated from the annulus to the outer edge of the cement sheath 50, we obtain:
solving to obtain K2 as: (considering fouling resistance r 5)
Considering the continuity of heat transfer, knowing that the amount of heat lost to the outer edge of the cement sheath 50 in the annulus is equal to the amount of heat transferred to the formation at the outer edge of the cement sheath 50, we obtain:
the temperature expression of the outer edge of the cement sheath 50 can be obtained as follows:
in step S1, the heat loss within the long tube 10 at the horizontal segment 12 is determined as follows:
a small section dz is taken along the length of the long tube 10 at the horizontal section 12 for analysis, see figure 3.
The horizontal section 12 has only one smooth oil pipe, and heat is transferred from the long pipe 10 to the annular space of the screen pipe 30 and is transferred to the oil layer through the annular space of the screen pipe 30.
(3) Determining heat loss within long tube 10 at horizontal segment 12
In the formula: k 11 Is the heat transfer coefficient between the long pipe 10 and the inner wall of the sieve tube 30, and has the unit of W/(m) 2 ·℃)；
d 11 The inner diameter of the long tube 10 at the horizontal section 12 is m;
T s the temperature in the annulus of the sieve tube at the horizontal section is expressed in degrees centigrade.
T 11 The steam temperature in a long pipe at the horizontal section is expressed in unit;
the heat dissipated between the long pipe 10 and the inner wall of the sieve pipe 30 is phi 1 (considering fouling resistance):
in the formula: h is 11 The heat transfer coefficient of the steam in the long pipe 10 to the inner wall surface of the long pipe 10 is W/(m) 2 ·℃)；
h 21 The heat transfer coefficient of the steam between the outer wall of the sieve tube 30 and the inner wall of the sieve tube 30 to the outer wall of the long pipe 10 is W/(m) 2 ·℃)；
d 11 The inner diameter of the long tube 10 at the horizontal section 12 is m;
T s the temperature of the sieve tube 30 at the horizontal section 12 is measured in units of ℃;
T 11 is the steam temperature in the horizontal section 12 of the long tube 10, and the unit is ℃.
The heat transfer coefficient between the long pipe 10 of the horizontal section 12 and the inner wall of the sieve pipe 30 is as follows:
in the formula: r is a radical of hydrogen 11 The radius of the inner wall of the long tube 10 at the horizontal section 12 is m;
r 21 the radius of the outer wall of the long tube 10 at the horizontal section 12 is m;
λ tb1 the heat conductivity coefficient of the long pipe 10 at the horizontal section 12 is W/(m DEG C).
(4) Heat loss calculation for screen 30 at horizontal segment 12
The Horizontal section 12 dissipates heat from the outside formation, and the temperature distribution in the formation may be determined by reference to the "Thermal transfer Analysis Applied to Horizontal Wells" (SPE/PS/CHOA 117435 PS2008-320):
wherein:T x the temperature of a certain point in the oil layer is measured in unit;
T s is the temperature in the sieve tube 30, in units of ℃;
λ e the thermal conductivity of the oil layer, W/(m.K);
r s is the radius of the inner wall of the sieve tube 30, and the unit is m;
alpha is the thermal diffusion coefficient of the oil layer and has the unit of m 2 /s；
λ is the time of 1 day, in units of s;
t is the number of days of heating in d.
Thus, the heat dissipation heat flow density is obtained as follows:
wherein:the series expansion can be expressed as:
when the steam injection time is long (gamma/t is satisfied to be less than 0.01) and the steam injection temperature is constant:
known sievesThe temperature of the steam in the tube 30 is T s The heat dissipation of the sieve tube 30 to the horizontal section 12 can be obtained as follows:
because the oil layer outside the horizontal section of the horizontal well exists in a state of mixing rock, oil, water and the like, according to the document 'Thermal Conductivity Estimation From Temperature Logs' (SPE 21542), the Thermal Conductivity lambda of the oil layer is determined e Can be calculated from the following formula:
wherein a, b, c, d, e are coefficients, S w Is the water saturation (decimal), S o Oil saturation (decimal), phi the oil layer porosity (decimal), and T the temperature (. Degree. C.). The document also provides a set of coefficient values obtained by multiple regression, a =4.318, b =4.883, c =0.474, d =0.987, e =0.0024.
In the actual calculation, the porosity value is 0.25, the oil saturation value is 0.7, the water saturation value is 0.3, and the heat conductivity coefficient of the oil layer is 2.5 w/(m.K).
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (9)
1. A SAGD horizontal well concentric pipe steam injection heat transfer calculation method is characterized in that the SAGD horizontal well concentric pipe comprises a long pipe (10), a short pipe (20), a sieve pipe (30) and a sleeve pipe (40) which are concentrically arranged, wherein,
the long pipe (10) comprises a vertical section (11) and a horizontal section (12) connected with the vertical section (11);
the short pipe (20) is sleeved on the periphery of the vertical section (11) and is arranged at intervals with the long pipe (10);
the sleeve (40) is sleeved on the periphery of the short pipe (20) and is arranged at intervals with the short pipe (20);
the sieve tube (30) is connected to the end part of the sleeve (40) and sleeved on the periphery of the horizontal section (12), and the sieve tube (30) and the horizontal section (12) are arranged at intervals;
the SAGD horizontal well concentric tube steam injection heat transfer method comprises the following steps:
step S1: determining heat losses within the long pipe (10) and within the short pipe (20) at the vertical section (11);
step S2: determining heat loss within the long pipe (10) at the horizontal section (12) and heat loss of the screen (30).
2. The SAGD horizontal well concentric tube steam injection heat transfer calculation method according to claim 1, characterized in that in step S1, heat loss A inside the long tube (10) is determined using the following formula:
A＝K 1 πd 1 (T 2 -T 1 )
in the formula: d 1 Is the inner diameter of the long tube (10) and has the unit of m;
T 1 the temperature of the steam in the long pipe (10) is measured in unit;
T 2 is the temperature of the steam in the short pipe (20) and has the unit of;
K 1 is the heat transfer coefficient between the long pipe (10) and the short pipe (20) and has the unit of W/(m) 2 ·℃)。
3. SAGD horizontal well concentric tube steam injection heat transfer calculation method according to claim 2, characterized in that the long tube (10) comprises an inner tube sleeve (13), an outer tube sleeve (15) and a thermal insulation layer (14) arranged between the inner tube sleeve (13) and the outer tube sleeve (15), the heat transfer coefficient K between the long tube (10) and the short tube (20) being K 1 Determined by the following equation:
in the formula: h is a total of 1 The convective heat transfer coefficient of the steam in the long pipe (10) to the inner wall surface of the long pipe (10) is W/(m) 2 ·℃)；
h 2 The convective heat transfer coefficient of the fluid in the short pipe (20) to the outer wall surface of the vertical section (11) of the long pipe (10) is W/(m) 2 ·℃)；
d 2 Is the outer diameter of the inner pipe sleeve (13) and has the unit of m;
d 3 the inner diameter of the outer pipe sleeve (15) is m;
d 4 the outer diameter of the outer pipe sleeve (15) is m;
λ tb the thermal conductivity coefficient of the inner pipe sleeve (13) is W/(m DEG C);
λ in the thermal conductivity coefficient of the outer pipe sleeve (15) is W/(m DEG C).
4. The SAGD horizontal well concentric tube steam injection heat transfer calculation method according to claim 1, wherein the outer periphery of the casing (40) is sleeved with a cement sheath (50), and in step S1, the heat loss B in the short tube (20) is determined using the following formula:
B＝K 1 πd 1 (T 1 -T 2 )+K 2 πd 5 (T h -T 2 )
in the formula: t is 1 The temperature of the steam in the long pipe (10) is measured in unit;
T 2 the temperature of the steam in the short pipe (20) is measured in unit;
d 5 the outer diameter of the short pipe (20) is measured in unit;
T h is the outer edge temperature of the cement sheath (50) in units of;
K 2 is the total heat transfer coefficient between the short pipe (20) and the stratum (60) and has the unit of W/(m) 2 ·℃)。
5. The SAGD horizontal well concentric tube steam injection heat transfer calculation method of claim 4, wherein the overall heat transfer coefficient K between the short pipe (20) and the formation (60) is 2 Determined by the following equation:
in the formula: h is a total of 3 The convective heat transfer coefficient of the steam in the short pipe (20) to the inner wall of the short pipe (20) is W/(m) 2 ·℃)；
r5 is to consider fouling resistance;
λ stb the coefficient of heat conductivity of the wall of the short pipe (20) is W/(m DEG C);
d 6 is the outer diameter of the short pipe (20) and has the unit of m;
h c3 is the convective heat transfer coefficient in the sleeve (40) and has the unit of W/(m) 2 ·℃)；
h r3 Is the heat radiation heat exchange coefficient in the sleeve (40) with the unit of W/(m) 2 ·℃)；
d 7 Is the inner diameter of the sleeve (40) in m;
λ ct is the thermal conductivity of the sleeve (40) in W/(m DEG C);
λ sn is the thermal conductivity coefficient of the cement sheath (50) and has the unit of W/(m DEG C);
d 8 is the outer diameter of the sleeve (40) in m;
d 9 is the outer diameter of the cement sheath (50) in m.
6. The SAGD horizontal well concentric tube steam injection heat transfer calculation method according to claim 1, characterized in that in step S2, the heat loss C inside the long tube (10) is determined using the following formula:
C＝K 11 πd 11 (T s -T 11 )；
in the formula: k 11 Is the heat transfer coefficient between the long pipe (10) and the inner wall of the sieve pipe (30) at the horizontal section (12) and has the unit of W/(m) 2 ·℃)；
d 11 Is the inner diameter of the long tube (10) at the horizontal section (12) and has the unit of m;
T s the temperature between the outer wall surface of the sieve tube (30) and the inner wall of the sieve tube (30) at the horizontal section (12) is measured in unit;
T 11 is the steam temperature in the long tube (10) at the horizontal section (12) and has the unit of C.
7. SAGD horizontal well concentric tube steam injection heat transfer calculation method according to claim 1, characterized by heat transfer coefficient K between the long tube (10) and the screen (30) inner wall 11 Determined by the following equation:
in the formula: h is 11 The heat transfer coefficient of the steam in the long pipe (10) to the inner wall surface of the long pipe (10) is W/(m) 2 ·℃)；
d 11 Is the inner diameter of the long pipe (10) at the horizontal section (12) and has the unit of m;
h 21 the heat transfer coefficient of steam in the space between the outer wall of the sieve tube (30) and the inner wall of the sieve tube (30) to the outer wall surface of the long tube (10) is W/(m) 2 ·℃)；
d 21 The diameter of the outer wall of the long pipe (10) at the horizontal section (12) is m;
r 11 the radius of the inner wall of the long pipe (10) at the horizontal section (12) is m;
r 21 the radius of the outer wall of the long pipe (10) at the horizontal section (12) is m;
λ tb1 the unit is W/(m DEG C) which is the heat conductivity coefficient of the long pipe (10) at the horizontal section (12).
8. The SAGD horizontal well concentric tube steam injection heat transfer calculation method of claim 1, wherein in step S2, heat loss of the screen (30) at the horizontal section (12) is determined by the following formula:
in the formula:
T x the temperature of a certain point in the oil layer is measured in unit;
T s the temperature in the sieve tube (30) is measured in units of;
r s the radius of the inner wall of the sieve tube (30) is m;
λ is the time of 1 day, in units of s;
t is the number of days of heating in units of d;
alpha is the thermal diffusion coefficient of the oil layer, unit m 2 /s；
λ e The thermal conductivity of the oil layer is expressed in W/(m.K).
9. The SAGD horizontal well concentric tube steam injection heat transfer calculation method of claim 8, wherein when steam injection time is gamma/t <0.01 and steam injection temperature is constant:
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