CN117332513A - Annular trap pressure prediction method and system based on transient temperature method - Google Patents

Annular trap pressure prediction method and system based on transient temperature method Download PDF

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CN117332513A
CN117332513A CN202210718385.XA CN202210718385A CN117332513A CN 117332513 A CN117332513 A CN 117332513A CN 202210718385 A CN202210718385 A CN 202210718385A CN 117332513 A CN117332513 A CN 117332513A
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唐宜家
李文哲
马天寿
胡锡辉
郭建华
王秋彤
何丹
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Petrochina Co Ltd
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Abstract

The invention discloses an annular trap pressure prediction method and system based on a transient temperature method, comprising the following steps: dividing units according to the well structure; establishing a production string fluid heat transfer control equation, a production string heat transfer control equation and a heat transfer control equation of a near-well wall control unit; converting the heat transfer control equation into a general format of a finite volume method; dispersing transient items, convection items, diffusion items and source items in the previous step; adopting finite difference processing to the convection item in the last step; establishing a convection diffusion equation discrete equation; solving a discrete equation by adopting an under-relaxation iteration method to obtain a wellbore temperature distribution model which changes with time; and solving the well bore temperature distribution model by adopting an annular trap pressure method to obtain annular trap pressure. The method overcomes the defect of poor precision of the annular entrapment pressure model in the early production stage, and has important significance for the design of annular entrapment pressure prevention and treatment schemes.

Description

Annular trap pressure prediction method and system based on transient temperature method
Technical Field
The invention relates to the technical field of drilling shaft pressure control, in particular to an annular trap pressure prediction method and system based on a transient temperature method.
Background
With the continuously growing oil and gas demands, the acquisition of oil and gas resources is advanced from shallow layers to deep layers. Deep well mining faces numerous engineering problems, wherein annular trap pressure rise is one of the main problems affecting safe and efficient deep hydrocarbon mining. The annular trap pressure rising refers to the phenomenon that high-temperature fluid mined in an oil pipe radially transfers heat to a stratum through a multilayer pipe wall, an annular space and cement in the production test process, so that the annular space fluid is heated and expanded to cause the pressure rising of a closed annular space, and the annular space pressure rising is a main form of annular space pressure. In fields such as Brazil, western Africa, and the gulf of Mexico, the increase in annulus trap pressure may cause casing collapse or bursting, compromising wellbore safety. Because of the low formation fracture pressure and narrow safety window, the well cementing design generally does not return the cement slurry up to the wellhead, creating a longer free casing (annulus filled with fluid). Meanwhile, the annular trap pressure is increased due to the temperature difference between the high-temperature fluid at the bottom of the well and the free-section fluid in the annular space. While some high sulfur gas wells have a risk of annular entrapment pressure rise in the free annulus due to high downhole temperatures and poor cementing quality. Considering that temperature is the main factor causing the annular trap pressure to rise, research on the high temperature and high pressure well bore temperature field is necessary. And an annular trap pressure treatment scheme is further formed and is implemented before well cementation so as to ensure the safety of a shaft.
Currently, methods of well bore temperature research are classified into quasi-steady state methods and transient methods based on whether time is considered in modeling. The quasi-steady state method is a method of solving the temperature of a well bore by conservation of energy, wherein heat transfer in the well bore is regarded as steady state, and heat transfer in a stratum is regarded as transient state. Ramey first proposes a wellbore temperature semi-steady state calculation method based on simplified energy balance. Willhite describes in detail the calculation of heat transfer coefficients for steam and hot water injection wells. Based on the research of Ramey and Willhite, the quasi-steady-state method is widely applied to the well bore temperature research of steam injection wells, two-phase flow wells and oil and gas production test wells. The quasi-steady state method has the characteristics of rapidness and simplicity, is applied to the prediction of annular trap pressure, and shows a good prediction effect. But this method has a large error in the initial production time. In addition, a number of assumptions and parameters obtained by empirical formulas, such as total heat transfer coefficients, dimensionless time, joule-Thompson coefficients, are used in the calculation process, and these coefficients are difficult to accurately obtain.
Disclosure of Invention
The technical problems to be solved by the invention are as follows: the method and the system for predicting the annular entrapment pressure based on the transient temperature method solve the problems, make up the defect of poor precision of the annular entrapment pressure model in the initial stage of production, and have important significance for the design of an annular entrapment pressure prevention and treatment scheme.
The invention is realized by the following technical scheme:
an annular trap pressure prediction method based on a transient temperature method comprises the following steps:
s1, dividing units according to a well structure;
s2, establishing a production string fluid heat transfer control equation according to an energy conservation principle;
s3, establishing a production string heat transfer control equation;
s4, establishing a heat transfer control equation of the near-well wall control unit; the near-well wall control unit comprises a casing, annular fluid, a cement sheath and a stratum;
s5, converting the heat transfer control equation from the step S2 to the step S4 into a general format of a finite volume method;
s6, dispersing the transient item, the convection item, the diffusion item and the source item in the step S5;
s7, adopting finite difference processing to the convection item in the step S6;
s8, establishing a discrete equation of a convection diffusion equation;
s9, solving a discrete equation in the step S8 by adopting an under-relaxation iteration method to obtain a wellbore temperature distribution model which changes with time;
s10, solving a well bore temperature distribution model by adopting an annular space trap pressure method to obtain annular space trap pressure.
Further optionally, in step S2, the production string fluid heat transfer control equation is:
wherein ρ is 1 To produce a liquid-tight degree of kg/m 3 ；T 1 The temperature of the produced liquid is DEG C; t (T) 2 Producing a column wall temperature, DEG C; c p1 J/(kg. DEG C.) for specific heat of produced liquid; h is a 1 W/(m) is the convection heat exchange coefficient of the inner surface of the drill string 2 ·℃)；r ti To drill the inside diameter, m; v 1 For the flow rate of the produced stream, m/s; t is time, s; z is the well depth, m.
Further optionally, in step S3, the production string heat transfer control equation is:
where r is the radial distance from the borehole axis to the formation, m; ρ 2 To produce column density, kg/m 3 ；c p2 J/(kg. DEG C.) for producing the specific heat capacity of the column; t (T) 2 Is the temperature of the fluid in the annulus, DEG C; r is (r) to The outer diameter of the production string column, m; k (k) tub For the production column thermal conductivity, W/(m.degree.C.).
Further alternatively, in step S4, the heat transfer control equation of the near-wellbore wall control unit is:
wherein ρ is j For the j-th layer unit density, kg/m 3 ；T j The temperature of the unit of the j layer is the temperature of the unit of the j layer; c pj The specific heat capacity of the J-th layer unit is J/(kg. DEG C.).
Further alternatively, in step S5, the general format of the finite volume method is:
namely:
wherein,is a generalized variable; Γ is corresponding to +.>Is a generalized diffusion coefficient of (2); s is equal to->A corresponding generalized source item;
ρ is density, kg/m 3 The method comprises the steps of carrying out a first treatment on the surface of the t is; x isThe x-direction of the control unit; u is the flow velocity in the x direction, m/s; v is the flow velocity in the y direction, m/s; y is the y direction of the control unit;vector velocity, m/s.
Further alternatively, in step S6,
discrete transient terms, assuming physical quantitiesHas the same value +.>The transient term becomes:
wherein the superscript 0 indicates the value of the physical quantity at time t, the subscript P indicates the value of the physical quantity at the control volume P, and Δv is the volume of the control volume;
for discrete convection terms, as known from the Gauss divergence theorem, the volume integral can be converted to a surface integral, and then the convection term can be expressed as:
wherein A is the area of the control volume interface, m 3 ；
For dispersion terms, the Gauss dispersion theorem is also adopted to convert volume integral into surface integral, and then the dispersion terms can be expressed as follows:
wherein A is the area of the control unit in different directions; subscript e is the eastern face of the control unit; subscript w is the western face of the control unit; subscript n is the north face of the control unit; the subscript s is the south of the control unit. Discrete source items, the source items are expressed as:
wherein S is a control unit heat source, subscript c is an intermediate control unit, and subscript p is a control node midpoint.
Further alternatively, in step S7, the convection item in step S adopts a second order windward format.
When the flow is in the positive direction, u w >0,u e >At 0, there is:
when the flow is in the opposite direction, u w <0,u e <At 0, there is:
wherein,and->The heat flows in the east, west, north and south directions on the interface of the control unit respectively; the heat flows from the middle, north, south, west, north, south and east of the control unit nodes respectively.
Further alternatively, in step S8, the discrete equation of the convective diffusion equation is:
when u > 0:
a P φ P ＝a NN φ NN +a N φ N +a W φ W +a S φ S +a E φ E +b (26)；
wherein the method comprises the steps of
a NN ＝-0.5F N (28)；
a N ＝1.5F n +0.5F s +D n (29)；
When u < 0:
a P φ P ＝a SS φ SS +a S φ S +a W φ W +a N φ N +a E φ E +b (18)；
wherein the method comprises the steps of
a SS ＝0.5F S (32)；
a S ＝-1.5F s -0.5F n +D n (33)；
Further alternatively, parameters F and D used in the discrete equation of the convection diffusion equation are closely related to the thermophysical parameters in the heat transfer process and are controlled by four interfaces of north and south, F represents the heat flux of the convection item, and D represents the heat flux of the diffusion item, and the specific calculation process is shown in table 1:
expressions of tables 1F and D
Further optionally, in step S9, the wellbore temperature distribution model that changes with time is obtained by solving:
wherein ω is a relaxation iteration parameter, when ω=1, it is a gauss-seidel iteration; when omega >1, the super relaxation iteration is performed; when 0< ω <1, an under-relaxation iteration is performed.
Further alternatively, the method may comprise, in a further alternative,
the initial conditions refer to: at the initial moment, the initial temperatures of the fluid in the production string, the oil casing string and the fluid in the annulus are the same as the original stratum temperature, so that the initial conditions of the wellbore temperature field calculation model are as follows:
wherein T is blh Is the bottom hole temperature, DEG C; g e Is the ground temperature gradient, DEG C/m;
the boundary conditions are: (1) at the position far away from the well bore, no radial heat flow exists in the stratum, and the stratum temperature is always the initial stratum temperature; (2) there is no heat exchange between the formation and the surface at the wellhead:
T(r＞＝10r wb ,t)＝T blh -g e z (237)；
an annular trap pressure prediction system based on a transient temperature method is used for realizing the annular trap pressure prediction method based on the transient temperature method, and comprises the following steps of
The first module is used for dividing units according to the well structure;
the second module is used for establishing a production string fluid heat transfer control equation according to the energy conservation principle;
a third module for establishing a production string heat transfer control equation;
a fourth module for establishing a heat transfer control equation of the near-wellbore wall control unit; including casing, annular fluid, cement sheath, and formation;
a fifth module for converting the heat transfer control equation into a common format for a finite volume method;
a sixth module for discretizing transient terms, stream terms, diffusion terms, and source terms in the common format;
a seventh module, configured to perform finite difference processing on the convection item;
an eighth module for establishing a discrete equation of the convective diffusion equation;
a ninth module, configured to solve the discrete equation in step S8 by using an under-relaxation iteration method, to obtain a wellbore temperature distribution model that changes with time;
and a tenth module, configured to solve the wellbore temperature distribution model by using an annular trap pressure method, so as to obtain annular trap pressure.
The invention has the following advantages and beneficial effects:
the existing quasi-steady state method has larger error in the initial production time; in addition, a number of assumptions and parameters obtained by empirical formulas, such as total heat transfer coefficients, dimensionless time, joule-Thompson coefficients, are used in the calculation process, and these coefficients are difficult to accurately obtain. According to the annular trap pressure prediction method based on the transient temperature method, the influence of time is considered in the heat transfer process of the shaft temperature in the radial direction and the axial direction, the method is more consistent with the evolution process of the actual temperature in the shaft, the annular trap pressure can be more accurately predicted, the defect that the annular trap pressure model is poor in initial production precision is overcome, and the method has important significance in the research and development of an annular trap pressure management method and a management and control tool.
Drawings
The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiments of the invention. In the drawings:
FIG. 1 is a flow chart of the wellbore temperature calculation of the present invention.
FIG. 2 is a schematic diagram of a typical high temperature, high pressure well bore. In the drawings, the reference numerals and corresponding part names:
1-wellhead, 2-conduit, 3-stratum, 4-surface casing, 5-cement sheath, 6-technical casing, 7-packer, 8-production string, 9-production casing; a-first annulus, B-second annulus, C-third annulus.
FIG. 3 is a graph of temperature versus production for the transient and quasi-steady state methods of example 2.
Fig. 4 is a discrete view of a typical high temperature high pressure well unit. The ring a void represents the first annulus in fig. 2 and the ring B void represents the second annulus in fig. 2.
FIG. 5 is a schematic diagram of a well bore of example 3. In the drawings, the reference numerals and corresponding part names:
1-wellhead, 2-mud line, 3-surface casing, 4-cement ring, 5-technical casing, 6-production casing, 7-oil pipe and 8-packer; a-first annulus, B-second annulus, C-third annulus, D-production flow fluid, E-sea level, F-sea water, G-formation.
FIG. 6 is a graph comparing example 3 well transient simulation results with steady state simulation results. The a-ring void represents the first annulus in fig. 5, the B-ring void represents the second annulus in fig. 5, and the C-ring void represents the third annulus in fig. 5.
Detailed Description
For the purpose of making apparent the objects, technical solutions and advantages of the present invention, the present invention will be further described in detail with reference to the following examples and the accompanying drawings, wherein the exemplary embodiments of the present invention and the descriptions thereof are for illustrating the present invention only and are not to be construed as limiting the present invention.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. However, it will be apparent to one of ordinary skill in the art that: no such specific details are necessary to practice the invention. In other instances, well-known structures, circuits, or methods have not been described in detail so as not to obscure the invention.
Throughout the specification, references to "one embodiment," "an embodiment," "one example," or "an example" mean: a particular feature, structure, or characteristic described in connection with the embodiment or example is included within at least one embodiment of the invention. Thus, the appearances of the phrases "in one embodiment," "in an example," or "in an example" in various places throughout this specification are not necessarily all referring to the same embodiment or example. Furthermore, the particular features, structures, or characteristics may be combined in any suitable combination and/or sub-combination in one or more embodiments or examples. Moreover, those of ordinary skill in the art will appreciate that the illustrations provided herein are for illustrative purposes and that the illustrations are not necessarily drawn to scale. The term "and/or" as used herein includes any and all combinations of one or more of the associated listed items.
Example 1
The embodiment provides an annular trap pressure prediction method based on a transient temperature method, which comprises the following specific steps:
step 1: and according to the well structure, carrying out unit division.
Step 2: and establishing a production string fluid heat transfer control equation according to an energy conservation principle.
The energy transfer involved in the production process of the production string fluid includes: (1) the net heat carried by the upward flowing liquid is axially generated; (2) heat generated by convective heat exchange between the inner wall of the production string and the production string in the radial direction. The law of conservation of energy indicates that the work done by the outside on the control unit is equal to the variable quantity in the control unit, and the fluid heat transfer equation in the production string can be obtained as follows:
wherein ρ is 1 To produce a liquid-tight degree of kg/m 3 ；T 1 The temperature of the produced liquid is DEG C; t (T) 2 Producing a column wall temperature, DEG C; c p1 J/(kg. DEG C.) for specific heat of produced liquid; h is a 1 W/(m) is the convection heat exchange coefficient of the inner surface of the drill string 2 ·℃)；r ti To drill the inside diameter, m; v is the flow rate of the produced stream, m/s.
Step 3: and establishing a production string heat transfer control equation.
The wall temperature of the production pipe column is related to the convection heat exchange of a flow unit of the produced liquid in the production pipe column, the pipe body infinitesimal of the production pipe column is taken as a control unit, and the energy transfer process comprises the following steps: (1) heat generated by the conduction of the production string in the axial direction; (2) producing heat generated by convective heat exchange between the column wall and the fluid in the pipe in the radial direction; (3) producing heat generated by heat conduction between the tubular column wall and the fluid in the annulus in the radial direction; and (3) establishing a heat transfer equation for producing the tubular column wall according to the law of conservation of energy without considering the work done by the outside on the control body:
wherein ρ is 2 To produce column density, kg/m 3 ；c p2 J/(kg. DEG C.) for producing the specific heat capacity of the column; t (T) 2 Is the temperature of the fluid in the annulus, DEG C; r is (r) to The outer diameter of the production string column, m; k (k) tub For the production column thermal conductivity, W/(m.degree.C.).
Step 4: establishing a heat transfer control equation of the near-well wall control unit; the near wall control unit comprises a casing, annular fluid, a cement sheath and a stratum.
The energy transfer process of the annular fluid, the casing, the cement sheath and the stratum comprises the following steps: (1) heat generated by heat conduction of the control unit in the axial direction; (2) heat conduction between the control units in the radial direction; as known from the law of conservation of energy, the control equation of the control unit near the well wall is:
wherein ρ is j For the j-th layer unit density, kg/m 3 ；T j The temperature of the unit of the j layer is the temperature of the unit of the j layer; c pj The specific heat capacity of the J-th layer unit is J/(kg. DEG C.).
Step 5: the heat transfer control equation of step 2 to step S4 is converted into a general format of the finite volume method.
The heat transfer control equations in the steps 2 to 4 are discretized by adopting a finite volume method, and for the calculation model of the well bore temperature field, the calculation model can be regarded as a special form of a two-dimensional convection-diffusion equation in terms of the form of the control equation, and the general form of the control equation can be written as:
namely:
in the method, in the process of the invention,is a generalized variable; Γ is corresponding to +.>Is a generalized diffusion coefficient of (2); s is equal to->Corresponding generalized source items.
Step 6: and (5) discretizing the transient term, the convection term, the diffusion term and the source term in the step 5.
For the general form of step 5, equation (4) is a transient term, a convective term, a diffuse term, and a source term in that order from left to right. The transient, convective, diffusive and source terms are discretized by a controlled volume integration method as follows:
(1) Discrete transient terms, assuming physical quantitiesHas the same value +.>The transient term becomes:
wherein the superscript 0 denotes the value of the physical quantity at time t, the subscript P denotes the value of the physical quantity at the control volume P, and Δv is the volume of the control volume.
(2) For discrete convection terms, as known from the Gauss divergence theorem, the volume integral can be converted to a surface integral, and then the convection term can be expressed as:
wherein A is the area of the control volume interface, m 3 。
(3) For dispersion terms, the Gauss dispersion theorem is also adopted to convert volume integral into surface integral, and then the dispersion terms can be expressed as follows:
(4) The source item is discretized into:
step 7: adopting finite difference processing to the convection item in the step 6;
and (3) processing the convection item in the step (6) by adopting finite difference, so that the physical quantity at the interface is represented by the physical quantity at the node, and in order to improve the calculation accuracy, the convection item in the step (6) adopts a second-order windward format.
When the flow is in the positive direction, i.e. u w >0,u e >At 0, there is:
when the flow is in the opposite direction, i.e. u w <0,u e <At 0, there is:
wherein,and->To control the heat flow at the body interface.
Step 8: and establishing a discrete equation of the convection diffusion equation.
With a fully implicit time integration scheme, the convective diffusion equation of step 5 can be expressed as:
when u > 0:
a P φ P ＝a NN φ NN +a N φ N +a W φ W +a S φ S +a E φ E +b (44)；
wherein the method comprises the steps of
a NN ＝-0.5F N (46)；
a N ＝1.5F n +0.5F s +D n (47)；
When u < 0:
a P φ P ＝a SS φ SS +a S φ S +a W φ W +a N φ N +a E φ E +b (18)；
wherein:
a SS ＝0.5F S (20)；
a S ＝-1.5F s -0.5F n +D n (21)；
parameters F and D used in each item in the discrete equation in the step 8 are closely related to the thermophysical parameters in the heat transfer process and are controlled by four interfaces of east, west, south and north, F represents the heat flux of a convection item, D represents the heat flux of a diffusion item, and the specific calculation process is shown in a table 1.
Expressions of tables 1F and D
Step 9: and (3) solving the discrete equation in the step S8 by adopting an under-relaxation iteration method to obtain a wellbore temperature distribution model which changes with time.
The finite volume method is used to discretize the wellbore heat transfer control equation, where the control equation for each unit involves the unknown temperatures of itself and the 5 control units of the southwest, northwest, in the formation and wellbore region. For more accurate calculation results, a second order windward format is used for the flow terms in the heat transfer equation. Each node in the flow area in the middle of the pipe string involves itself, two control units upstream and two control units east and west, for a total of 5 control units. In the flow zone of the annulus, the flow rate is opposite to the flow direction in the middle of the string, and 5 control units of unknown temperature are also involved in each control unit in this zone. The heat transfer control equation discrete format is as follows:
converting all unit control heat transfer equations into a matrix form representation:
in order to improve the solving efficiency and stability, an under-relaxation iteration method is adopted for calculation. The general solution form of its discrete format is:
wherein ω is a relaxation iteration parameter, when ω=1, it is a gauss-seidel iteration; when omega >1, the super relaxation iteration is performed; when 0< ω <1, an under-relaxation iteration is performed.
Step 10: and solving the well bore temperature distribution model by adopting an annular trap pressure method to obtain annular trap pressure.
The annular trap pressure evolution rule is obtained by adopting the trap pressure calculation method provided by the specific implementation mode of the annular trap pressure prediction method (201611161173.7) of the patent, as shown in the formula 26, and bringing the temperature result of the step 9).
Wherein ΔP is the annular trap pressure rise value, MPa; delta T is annular temperature change ℃; alpha l Thermal expansion coefficient of annular fluid, DEG C -1 ；K T Is the annulus fluid compression coefficient, MPa -1 The method comprises the steps of carrying out a first treatment on the surface of the V annular volume, m 3 The method comprises the steps of carrying out a first treatment on the surface of the DeltaV is the annular volume change, m 3 ；V f Is annular fluid volume, m3; deltaV f For the volume change of annular fluid, m 3 .
Furthermore, the initial conditions refer to: at the initial time, the initial temperatures of the fluid in the production string, the oil casing string and the fluid in the annulus are the same as the original stratum temperature, so that the initial conditions of the wellbore temperature field calculation model are as follows:
wherein T is blh Is the bottom hole temperature, DEG C; g e Is the ground temperature gradient, DEG C/m.
The boundary conditions are: (1) at the position far away from the well bore, no radial heat flow exists in the stratum, and the stratum temperature is always the initial stratum temperature; (2) there is no heat exchange between the formation and the surface at the wellhead, i.e.:
T(r＞＝10r wb ,t)＝T blh -g e z (28)；
example 2
By adopting the annular trap pressure prediction method based on the transient temperature method provided in the embodiment 1, the calculation simulation of the output temperature of the high-temperature high-pressure well is carried out:
example 2 well the well structure of the well is shown in fig. 2, the well depth is 3658 m, and the heat transfer control equation of each layer of units is established according to unit division. The thermophysical parameters of the production fluid, annulus fluid, production string, cement sheath, and formation were entered as shown in table 2. The heat transfer control equation is solved according to the wellbore transient temperature calculation flow of fig. 1, and wellbore temperature distribution at different moments is obtained. And comparing the transient temperature calculation result with the quasi-steady state method and the field actual measurement data, as shown in fig. 3. The comparison result shows that the difference between the calculated result and the actual measurement result of the quasi-steady-state method and the transient-state method is mainly in the initial production stage, the transient-state method is higher in precision in the initial production stage, the quasi-steady-state method is larger in difference between the initial production stage and the actual measurement data, and along with the production, both methods can be well predicted. The phenomenon that the annular trap pressure rises to cause the sleeve to be squeezed or broken often occurs in the initial production stage, so that the transient method has stronger applicability to the prediction of the annular trap pressure.
TABLE 2 West African high temperature high pressure well bore thermophysical parameters
Example 3
The annular trap pressure prediction method based on the transient temperature method provided in the embodiment 1 is adopted to perform the southern sea high-temperature high-pressure well trap pressure prediction simulation.
Example 3 well bore construction of well as shown in fig. 5, heat transfer control equations for each layer of cells were established based on cell division. The thermophysical parameters of the production fluid, annulus fluid, production string, cement sheath, and formation were entered as shown in table 3. The heat transfer control equation is solved according to the wellbore transient temperature calculation flow of fig. 1, and wellbore temperature distribution at different moments is obtained. The calculated results are compared with the results of the quasi-steady state method, and the simulation results are shown in fig. 6. As can be seen from the graph, the errors of the transient method and the quasi-steady state method in the initial stage of production are larger, the annular trap pressure rising problem is gradually stabilized along with the progress of production, and the calculation errors of the transient method and the quasi-steady state method are gradually reduced. Simulation results show that the prediction precision of the quasi-steady state method in the initial production stage is 20.39%, and the precision of the transient state method in the initial production stage can be improved to 2.02%. The transient method overcomes the defect of calculation results of the quasi-steady state method in the initial production stage and is more thought with field data. The established annular trap pressure prediction method based on the transient temperature method has higher annular trap pressure prediction precision, particularly overcomes the defect that the annular trap pressure is insufficient in calculation at the initial stage of production by the traditional quasi-steady state method, and has important significance for the design of annular trap pressure prevention and treatment schemes.
TABLE 3 calculation of parameters related to annular trap pressure of high-temperature and high-pressure well in south China sea
The foregoing description of the embodiments has been provided for the purpose of illustrating the general principles of the invention, and is not meant to limit the scope of the invention, but to limit the invention to the particular embodiments, and any modifications, equivalents, improvements, etc. that fall within the spirit and principles of the invention are intended to be included within the scope of the invention.

Claims (12)

1. The annular trap pressure prediction method based on the transient temperature method is characterized by comprising the following steps of:
s1, dividing units according to a well structure;
s2, establishing a production string fluid heat transfer control equation according to an energy conservation principle;
s3, establishing a production string heat transfer control equation;
s4, establishing a heat transfer control equation of the near-well wall control unit; the near-well wall control unit comprises a casing, annular fluid, a cement sheath and a stratum;
s5, converting the heat transfer control equation from the step S2 to the step S4 into a general format of a finite volume method;
s6, dispersing the transient item, the convection item, the diffusion item and the source item in the step S5;
s7, adopting finite difference processing to the convection item in the step S6;
s8, establishing a discrete equation of a convection diffusion equation;
s9, solving a discrete equation in the step S8 by adopting an under-relaxation iteration method to obtain a wellbore temperature distribution model which changes with time;
s10, solving a well bore temperature distribution model by adopting an annular space trap pressure method to obtain annular space trap pressure.
2. The method for predicting annular trap pressure based on transient temperature method of claim 1, wherein in step S2, the production string fluid heat transfer control equation is:
wherein ρ is 1 To produce a liquid-tight degree of kg/m 3 ；T 1 The temperature of the produced liquid is DEG C; t (T) 2 Producing a column wall temperature, DEG C; c p1 J/(kg. DEG C.) for specific heat of produced liquid; h is a 1 W/(m) is the convection heat exchange coefficient of the inner surface of the drill string 2 ·℃)；r ti To drill the inside diameter, m; v 1 For the flow rate of the produced stream, m/s; t is time, s; z is the well depth, m.
3. The method for predicting annular trap pressure based on transient temperature method of claim 1, wherein in step S3, the production string heat transfer control equation is:
wherein r isA radial distance, m, from the borehole axis to the formation; ρ 2 To produce column density, kg/m 3 ；c p2 J/(kg. DEG C.) for producing the specific heat capacity of the column; t (T) 2 Is the temperature of the fluid in the annulus, DEG C; r is (r) to The outer diameter of the production string column, m; k (k) 2 W/(m.DEG C) is the thermal conductivity of the production column; .
4. The method for predicting annular trap pressure based on transient temperature method of claim 1, wherein in step S4, the heat transfer control equation of the near-wall control unit is:
wherein ρ is j For the j-th layer unit density, kg/m 3 ；T j The temperature of the unit of the j layer is the temperature of the unit of the j layer; c pj The specific heat capacity of the J-th layer unit is J/(kg. DEG C.).
5. The method for predicting annular trap pressure based on transient temperature method of claim 1, wherein in step S5, the general format of the finite volume method is:
namely:
wherein,is a generalized variable; Γ is corresponding to +.>Is a generalized diffusion coefficient of (2); s is equal to->A corresponding generalized source item; ρ is density, kg/m 3 The method comprises the steps of carrying out a first treatment on the surface of the t is; x is the x direction of the control unit; u is the flow velocity in the x direction, m/s; v is the flow velocity in the y direction, m/s; y is the y direction of the control unit; />Vector velocity, m/s.
6. The method for predicting annular trap pressure based on transient temperature method of claim 5, wherein in step S6,
discrete transient terms, assuming physical quantitiesHas the same value +.>The transient term becomes:
wherein the superscript 0 indicates the value of the physical quantity at time t, the subscript P indicates the value of the physical quantity at the control volume P, and Δv is the volume of the control volume;
for discrete convection terms, as known from the Gauss divergence theorem, the volume integral can be converted to a surface integral, and then the convection term can be expressed as:
wherein A is the area of the control volume interface, m 3 ；
For dispersion terms, the Gauss dispersion theorem is also adopted to convert volume integral into surface integral, and then the dispersion terms can be expressed as follows:
wherein A is the area of the control unit in different directions; subscript e is the eastern face of the control unit; subscript w is the western face of the control unit; subscript n is the north face of the control unit; the subscript s is the south of the control unit.
Discrete source items, the source items are expressed as:
wherein S is a control unit heat source, subscript c is an intermediate control unit, and subscript p is a control node midpoint.
7. The method for predicting annular trap pressure based on transient temperature method of claim 1, wherein in step S7, the convection term in step S7 adopts a second order windward format.
When the flow is in the positive direction, u w >0,u e >At 0, there is:
when the flow is in the opposite direction, u w <0,u e <At 0, there is:
wherein,and->The heat flows in the east, west, north and south directions on the interface of the control unit respectively; /> The heat flows from the middle, north, south, west, north, south and east of the control unit nodes respectively.
8. The method for predicting annular trap pressure based on transient temperature method of claim 1, wherein in step S8, the discrete equation of the convective diffusion equation is:
when u > 0:
a P φ P ＝a NN φ NN +a N φ N +a W φ W +a S φ S +a E φ E +b (7)；
wherein the method comprises the steps of
a NN ＝-0.5F N (9)；
a N ＝1.5F n +0.5F s +D n (10)；
When u < 0:
a P φ P ＝a SS φ SS +a S φ S +a W φ W +a N φ N +a E φ E +b (18)；
wherein the method comprises the steps of
a SS ＝0.5F S (13)；
a S ＝-1.5F s -0.5F n +D n (14)；
9. The method for predicting annular trap pressure based on transient temperature method of claim 8, wherein,
parameters F and D used in discrete equations of the convection diffusion equation are closely related to thermophysical parameters in the heat transfer process and are controlled by four interfaces of east, west, south and north, F represents heat flux of the convection item, D represents heat flux of the diffusion item, and a specific calculation process is shown in table 1:
expressions of tables 1F and D
10. The method for predicting annular trap pressure based on transient temperature method according to claim 1, wherein in step S9, the wellbore temperature distribution model that changes with time is obtained by solving is:
wherein ω is a relaxation iteration parameter, when ω=1, it is a gauss-seidel iteration; when omega >1, the super relaxation iteration is performed; when 0< ω <1, an under-relaxation iteration is performed.
11. The method for predicting annular trap pressure based on transient temperature method of claim 1, wherein the initial condition is: at the initial moment, the initial temperatures of the fluid in the production string, the oil casing string and the fluid in the annulus are the same as the original stratum temperature, so that the initial conditions of the wellbore temperature field calculation model are as follows:
wherein T is blh Is the bottom hole temperature, DEG C; g e Is the ground temperature gradient, DEG C/m;
the boundary conditions are: (1) at the position far away from the well bore, no radial heat flow exists in the stratum, and the stratum temperature is always the initial stratum temperature; (2) there is no heat exchange between the formation and the surface at the wellhead:
T(r＞＝10r wb ,t)＝T blh -g e z(218)；
12. an annular trap pressure prediction system based on a transient temperature method, which is characterized by being used for realizing the annular trap pressure prediction method based on the transient temperature method as claimed in any one of claims 1 to 11, and comprising the following steps of
The first module is used for dividing units according to the well structure;
the second module is used for establishing a production string fluid heat transfer control equation according to the energy conservation principle;
a third module for establishing a production string heat transfer control equation;
a fourth module for establishing a heat transfer control equation of the near-wellbore wall control unit; including casing, annular fluid, cement sheath, and formation;
a fifth module for converting the heat transfer control equation into a common format for a finite volume method;
a sixth module for discretizing transient terms, stream terms, diffusion terms, and source terms in the common format;
a seventh module, configured to perform finite difference processing on the convection item;
an eighth module for establishing a discrete equation of the convective diffusion equation;
a ninth module, configured to solve the discrete equation in step S8 by using an under-relaxation iteration method, to obtain a wellbore temperature distribution model that changes with time;
and a tenth module, configured to solve the wellbore temperature distribution model by using an annular trap pressure method, so as to obtain annular trap pressure.
CN202210718385.XA 2022-06-23 2022-06-23 Annular trap pressure prediction method and system based on transient temperature method Pending CN117332513A (en)

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