CN115370322B - Well-shaft-integrity-based prediction method for annular space pressure - Google Patents
Well-shaft-integrity-based prediction method for annular space pressure 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
- E21B17/00—Drilling rods or pipes; Flexible drill strings; Kellies; Drill collars; Sucker rods; Cables; Casings; Tubings
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/28—Design optimisation, verification or simulation using fluid dynamics, e.g. using Navier-Stokes equations or computational fluid dynamics [CFD]
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2113/00—Details relating to the application field
- G06F2113/08—Fluids
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
Abstract
The application provides a prediction method for annular space belt pressure caused by temperature and oil well pressure release under the condition of good well integrity; the method comprises the following steps: 1) According to the on-site production condition, defining the temperature distribution and variation value of each annulus; 2) Initially determining the initial PVT of the annular fluid; 3) Solving the change of annular sleeve volume along with annular temperature and pressure by considering the temperature of adjacent sleeves and the thermal property change of materials; 4) Solving the change of the annular fluid volume along with the annular temperature and pressure by considering the thermal property change of the fluid; 5) According to the closed loop air, the fluid and the sleeve change volume are equal, and an annular pressure rise prediction model is established; 6) Solving the annular pressure of the corresponding condition; 7) Determining the annular fluid change volume under the state, and if the annular fluid is not limited to the temperature rise change volume; 8) Determining the volume of fluid in the annulus that is restricted (pressure relief release volume); 9) And determining the residual volume (namely the initial volume) of the annular fluid, and further obtaining the annular pressure caused by the temperature after each pressure relief.
Description
Technical Field
The application relates to a prediction method, in particular to a prediction method for annular space with pressure caused by temperature and oil well pressure release under the condition of good well integrity.
Background
The annular pressure is the phenomenon that the annular pressure at the wellhead is restored to the pressure level before pressure relief after pressure relief, and the problem of continuous annular pressure is solved at present, the safety of a shaft is ensured by mainly adopting a method of releasing the annular pressure when the annular pressure reaches a set safety value, but frequent pressure release can cause the influence of alternating load on a pipe column and a cement sheath, so that the pipe column and the cement sheath can be subjected to fatigue damage, and the integrity of the shaft is invalid.
The method has the advantages that the annular pressure calculation is accurately predicted and calculated, the method has guiding significance for evaluation and control of the integrity of a high-temperature high-pressure gas well shaft, the existing annular pressure calculation model only analyzes the annular pressure calculation problem in a single time process of initial annular pressure rising, in the subsequent pressure change process of pressure relief-pressure rising, because the quality, components and other factors of annular fluid can generate certain change after each pressure relief, the change trend of annular pressure after each pressure relief is different, no corresponding calculation prediction method exists in the annular pressure dynamic change in the current pressure relief pressure rising process, and corresponding guidance can not be provided for preventing and controlling the annular pressure on site.
Disclosure of Invention
Aiming at the problems, the application aims to provide a prediction method for annular space with pressure caused by temperature and oil well pressure release under the condition of good well integrity, which can provide support for designing a casing string of a high-temperature high-pressure oil-gas well and formulating a trap pressure prevention and control scheme.
In order to achieve the above purpose, the present application adopts the following technical scheme: a prediction method for annular space with pressure caused by temperature and oil well pressure release based on the condition of good well integrity comprises the following steps; 1) According to the on-site production condition, defining the temperature distribution and variation value of each annulus; 2) Initially determining the initial PVT of the annular fluid; 3) Solving the change of annular sleeve volume along with annular temperature and pressure by considering the temperature of adjacent sleeves and the thermal property change of materials; 4) Solving the change of the annular fluid volume along with the annular temperature and pressure by considering the thermal property change of the fluid; 5) According to the closed loop air, the fluid and the sleeve change volume are equal, and an annular pressure rise prediction model is established; 6) Solving the annular pressure of the corresponding condition; 7) Determining the annular fluid change volume under the state, and if the annular fluid is not limited to the temperature rise change volume; 8) Determining the limited volume of the annular fluid, namely the release volume of the annular fluid in the annular pressure release process; 9) And determining the residual volume of the annular fluid, namely, the initial volume parameter when the annular pressure is solved for the next cycle, and further solving the annular pressure caused by the temperature after each pressure relief.
In the step 3), the change of the annular sleeve volume along with the annular temperature and pressure is solved by considering the temperature of adjacent sleeves and the thermophysical property change of materials, and the method comprises the following steps:
(1) measuring the elastic modulus and the thermal expansion coefficient of the sleeve under different temperature pressures, and performing experimental statistics fitting to determine the elastic modulus and the thermal expansion coefficient of the sleeve under different temperature pressures;
(2) considering the influence of the thermal stress change caused by the temperature of adjacent casings on the expansion volume of annular fluid, deriving a radial displacement equation generated by the thermal expansion of the inner casing, wherein the radial displacement derivation equation is as follows:
(3) the displacement of the sleeve due to pressure change is determined by referring to the following formula:
(4) the change of the casing volume under different temperature pressures is determined by referring to the following formula:
ΔV 1 ＝π[b 2 -(b+u b1 -u b2 ) 2 ]Δx
wherein u is b1 The displacement caused by the heating of the sleeve is m; alpha is the thermal expansion coefficient of steel and is 1/°c; mu is the poisson ratio of the steel; r is the distance from any point on the oil layer sleeve body to the circle center, and m; a is the inner radius of the inner sleeve, m; delta T 1 Is the temperature variation quantity in the inner sleeve and is at the temperature of DEG C; delta T 2 Is the external temperature variation of the inner sleeve, and is at the temperature of DEG C; b is the outer radius of the inner sleeve, m; u (u) b2 The sleeve displacement is caused by pressure change, m; deltaV 1 Variable quantity, m, of casing volume under different temperature pressures 3 The method comprises the steps of carrying out a first treatment on the surface of the Δx is the infinitesimal length of the sleeve in the suspended section, m; e is the elastic modulus of steel and MPa; Δp is the annular pressure variation, MPa.
In the step 4), the change of the annular fluid volume along with the annular temperature and pressure is solved by considering the change of the thermophysical properties of the fluid, and the process is as follows:
(1) measuring the density change of annular fluid under different temperature and pressure, and performing experimental parameter fitting;
(2) solving a change equation of the thermal expansion coefficient and the compression coefficient of the fluid along with the temperature and pressure by solving the fitting density equation in the step (1), wherein the deduction equation is as follows:
(3) and (3) obtaining an equation of the annular fluid volume according to the temperature and the pressure according to the equation obtained in the step (2), wherein the equation is as follows:
ΔT 2 ＝ΔT
(4) and (3) obtaining an annular fluid volume total change equation under the state that the annular space is full of liquid according to the equation obtained in the step (3), wherein the equation is as follows:
ΔV 4 ＝ΔV 2 -ΔV 3
wherein a is 1 Is the inner diameter of the outer sleeve, m 3 The method comprises the steps of carrying out a first treatment on the surface of the ρ is the mud density, kg/m 3 ；α c Is the expansion coefficient of the slurry body, 1/DEGC; e (E) c Is the volume elastic coefficient of slurry and MPa; deltaV 2 For the variation of annular fluid volume caused by temperature variation, m 3 ；ΔV 3 For the change quantity, m, caused by the pressure change of annular fluid volume 3 ；ΔV 4 For total change in annular fluid volume, m 3 The method comprises the steps of carrying out a first treatment on the surface of the Delta T is the temperature variation of annular liquid and is in DEG C; Δx is the infinitesimal length of the sleeve in the suspended section, m;
(5) if the annulus is not full of liquid containing gas, the equation for the total volume of annulus fluid is as follows:
ΔV 4 ＝ΔV 2 -ΔV 3 -|ΔV 5 |
wherein p is N Is the initial pressure of the annular gas, MPa; v (V) Ni For an initial volume of annular gas,m 3 the method comprises the steps of carrying out a first treatment on the surface of the The initial temperature of the annular gas T and K; delta p annular gas pressure increment, MPa; deltaV 5 Volume change of annular gas, m 3 ；ΔT g The temperature variation of the annular gas, K.
In the step 5), according to the closed loop air, the fluid and the change volume of the sleeve are equal, and an annular pressure rise prediction model is established, wherein the process is as follows:
(1) according to the difference of the volume increment values of the components in the closed container being zero, the corresponding equation is as follows:
ΔV 1 -ΔV 4 ＝0
ΔV 1 variable quantity, m, of casing volume under different temperature pressures 3 ；ΔV 4 Volume change amount, m of annular fluid under different temperature and pressure 3 。
In the step 6), the annular pressure corresponding to the condition is solved, and the process is as follows:
(1) the Newton iteration method is adopted in the solving process, and the second-order convergence is high in convergence speed and faster in solving.
In the step 7), the annular fluid change volume and the annular fluid temperature rise change volume which are not limited in the state before pressure relief are determined, and the process is as follows:
(1) according to the volume compatibility principle of the closed container, an annular fluid change volume equation before pressure release under the state that the annular is full of liquid can be deduced, and the equation is as follows:
Δv ki ＝πΔx[((b+u b1 ) 2 -(b+u b1 -u b2 ) 2 )]-πΔx[(b+u b1 ) 2 -b]
(2) if the annulus is not full of liquid and contains gas, the equation of the volume of the annulus fluid change in the state before the pressure release of the annulus can be deduced according to the volume compatibility principle of the closed container, and the equation is as follows:
Δv ki ＝πΔx[((b+u b1 ) 2 -(b+u b1 -u b2 ) 2 )]-πΔx[(b+u b1 ) 2 -b]-ΔV 5
(3) the equation of the volume of the annular fluid, if not limited, can be derived from the saturated vapor pressure measurement method as follows:
Δv ni ＝α c × Δ T×V m(i-1) -k×V m(i-1) ×p ni
V m0 ＝V 0
wherein u is b1 The displacement caused by the heating of the sleeve is m; u (u) b2 The sleeve displacement is caused by pressure change, m; b is the outer radius of the inner sleeve, m; Δx is the infinitesimal length of the sleeve in the suspended section, m; deltaV 5 For volume change of annular gas, m 3 ；α c Is the expansion coefficient of the slurry body, 1/DEGC; v (V) m0 For annular fluid volume at pressure relief, m 3 The method comprises the steps of carrying out a first treatment on the surface of the Delta T is the temperature variation of annular liquid and is in DEG C; k is the volume compression coefficient of annular fluid and MPa -1 ；p ni The saturation vapor pressure corresponding to the annular temperature in the ith pressure relief is MPa; deltav ni Volume changeable of annular liquid under the condition of unlimited volume at annular temperature of ith circulation, m 3 ；Δv ki The volume of the annular liquid which is changed under the annular limit at the annular temperature of the ith circulation, m 3 ；V m(i-1) For the residual volume of the annular liquid in the annular space at the ith-1 st pressure relief, m 3 ；V 0 Is annular volume, m 3 。
Step 8), determining the limited volume of the annular fluid, namely the release volume of the annular fluid in the annular pressure release process, wherein the process is as follows:
(1) according to the pressurized principle of the closed container, the volume equation of the fluid in the annular space can be deduced, and the equation is as follows:
Δv ji ＝Δv ni -Δv ki
wherein Deltav ni Volume changeable of annular liquid under the condition of unlimited volume at annular temperature of ith circulation, m 3 ；Δv ki The volume of the annular liquid which is changed under the annular limit at the annular temperature of the ith circulation, m 3 ；Δv ji The volume of the annular liquid limited by the annular limitation at the annular temperature of the ith cycle, namely the initial volume parameter when the annular pressure is solved for the (i+1) th cycle,m 3 。
step 9), determining the residual volume of the annular fluid, namely, the initial volume parameter when the annular pressure is solved for the next cycle, and further solving the annular pressure caused by the temperature after each pressure relief, wherein the process is as follows:
(1) according to the actual pressure relief requirement on site and the pressure relief volume formula obtained in the step 8), an annulus initial volume formula after the pressure relief of the annulus in a state of being full of liquid can be obtained, wherein the formula is as follows:
V mi ＝V m(i-1) -ΔV j(i-1)
(2) according to the actual pressure relief requirement on site and the pressure relief volume formula obtained in the step 8), an annulus initial volume formula after the annular pressure relief in the gas-containing state can be obtained, wherein the formula is as follows:
V mi ＝V m(i-1) -ΔV j(i-1)
V Ni ＝V N(i-1) +ΔV j(i-1)
wherein V is mi For the residual volume of the annular liquid in the annular space at the ith pressure relief, m 3 ；V m(i-1) For the residual volume of the annular liquid in the annular space at the ith-1 st pressure relief, m 3 ；Δv j(i-1) The volume of the annular liquid limited by the annular liquid at the annular temperature of the ith-1 th circulation, namely the release volume of the annular liquid in the annular pressure release process, m 3 ；V Ni For the residual volume of the annular ring air body in the ith pressure relief, m 3 ；V N(i-1) The residual volume of the annular ring air body in the ith-1 st pressure relief, m 3 ；
(3) According to the annular initial volume in the step (1) and the step (2), the annular pressure value after the pressure relief can be obtained by combining the casing temperature distribution, and finally, the pressure value of the annular pressure caused by the temperature and the pressure relief in the whole production process of the oil well can be obtained in the steps 1) to 9) in the technical scheme of circulation in sequence.
The application adopts the technical proposal, and has the following advantages: according to the method, the influence of temperature distribution on two sides of the sleeve on the sleeve thermal expansion is considered when the sleeve thermal expansion is calculated, so that a predicted expansion value is more in line with the actual production condition, meanwhile, the change of thermal physical properties of annular fluid and sleeve materials along with time is considered in the calculation process, and then a release volume formula of pressure relief after annular pressurization is deduced according to the principle of a saturated vapor pressure measuring method and the pressurizing principle of a closed container, so that the annular pressure, temperature and pressure relief frequency relation, namely the temperature induced annular pressure value can be obtained.
Drawings
FIG. 1 is a schematic overall flow chart of the present application
Detailed Description
The present application will be described in detail with reference to the accompanying drawings and examples.
As shown in fig. 1, the application provides a prediction method for annular space with pressure caused by temperature and oil well pressure release under the condition of good well bore integrity, which comprises the following steps:
1) Determining the temperature distribution and variation value of each annulus according to the on-site production condition
In the high-temperature high-pressure oil-gas well exploitation process, heat carried by fluid in stratum in the process of flowing from a well pipe to a wellhead can be transferred to surrounding casings and casing annuluses, annulus temperatures at the same positions are different along with different exploitation depths, exploitation times and yields, and therefore, an oil well annulus model can be built through a corresponding mathematical model so as to calculate annulus temperature distribution at different positions and temperature change values under different working conditions.
2) Preliminary determination of annulus fluid initial PVT
The initial pressure, temperature and volume of the annular fluid are further defined according to the actual production working conditions of the oil-gas well in the high-temperature and high-pressure area.
3) Solving annular casing volume change along with annular temperature-pressure change by considering adjacent casing temperature and material thermophysical property change
In the annular sleeve temperature rising expansion process, the thermal expansion coefficient and the elastic modulus of the sleeve material change along with the temperature and pressure change, so that statistics is required to be carried out on the thermal expansion coefficient and the elastic modulus change of the corresponding material under corresponding different temperature and pressure, the thermal expansion coefficient and the elastic modulus under corresponding temperature and pressure are put into corresponding equations in the calculation process, and meanwhile, the influence of the temperature difference between the inner side and the outer side of the sleeve on the thermal expansion of the sleeve is considered in the calculation process of the thermal expansion of the annular sleeve; the specific process is as follows:
(1) measuring the elastic modulus and the thermal expansion coefficient of the sleeve under different temperature pressures, and performing experimental statistics fitting to determine the elastic modulus and the thermal expansion coefficient of the sleeve under different temperature pressures;
(2) considering the influence of the thermal stress change caused by the temperature of adjacent casings on the expansion volume of annular fluid, deriving a radial displacement equation generated by the thermal expansion of the inner casing, wherein the radial displacement derivation equation is as follows:
(3) the displacement of the sleeve due to pressure change is determined by referring to the following formula:
(4) the change of the casing volume under different temperature pressures is determined by referring to the following formula:
ΔV 1 ＝π[b 2 -(b+u b1 -u b2 ) 2 ]Δx
wherein u is b1 The displacement caused by the heating of the sleeve is m; alpha is the thermal expansion coefficient of steel and is 1/°c; mu is the poisson ratio of the steel; r is the distance from any point on the oil layer sleeve body to the circle center, and m; a is the inner radius of the inner sleeve, m; delta T 1 Is the temperature variation quantity in the inner sleeve and is at the temperature of DEG C; delta T 2 Is the external temperature variation of the inner sleeve, and is at the temperature of DEG C; b is the outer radius of the inner sleeve, m; u (u) b2 The sleeve displacement is caused by pressure change, m; deltaV 1 Variable quantity, m, of casing volume under different temperature pressures 3 The method comprises the steps of carrying out a first treatment on the surface of the Δx is the infinitesimal length of the sleeve in the suspended section, m; e is the elastic modulus of steel and MPa; Δp is the annular pressure variation, MPa.
4) Solving annular fluid volume along with annular temperature-pressure change by considering fluid thermophysical property change
In the process of annular fluid heating expansion, the thermal expansion coefficient and the compression coefficient of the casing fluid change along with the temperature and pressure change, so that the data of the thermal expansion coefficient and the elastic modulus change of the corresponding fluid under different temperature and pressure are subjected to statistical fitting, and the thermal expansion coefficient and the compression coefficient under the corresponding temperature and pressure are put into corresponding equations in the calculation process;
the specific process for solving the annular fluid volume along with the annular temperature and pressure change is as follows:
(1) measuring the density change of annular fluid under different temperature and pressure, and performing experimental parameter fitting;
(2) solving a change equation of the thermal expansion coefficient and the compression coefficient of the fluid along with the temperature and pressure by solving the fitting density equation in the step (1), wherein the deduction equation is as follows:
(3) and (3) obtaining an equation of the annular fluid volume according to the temperature and the pressure according to the equation obtained in the step (2), wherein the equation is as follows:
ΔT 2 ＝ΔT
(4) and (3) obtaining an annular fluid volume total change equation under the state that the annular space is full of liquid according to the equation obtained in the step (3), wherein the equation is as follows:
ΔV 4 ＝ΔV 2 -ΔV 3
wherein a is 1 Is the inner diameter of the outer sleeve, m 3 The method comprises the steps of carrying out a first treatment on the surface of the ρ is the mud density, kg/m 3 ，α c Is the expansion coefficient of the slurry body, 1/DEGC; e (E) c Is the volume elastic coefficient of slurry and MPa; deltaV 2 For the variation of annular fluid volume caused by temperature variation, m 3 ；ΔV 3 For the change quantity, m, caused by the pressure change of annular fluid volume 3 ；ΔV 4 For total change in annular fluid volume, m 3 The method comprises the steps of carrying out a first treatment on the surface of the Delta T is the temperature variation of annular liquid and is in DEG C; Δx is the infinitesimal length of the sleeve in the suspended section, m;
(5) if the annulus is not full of liquid containing gas, the equation for the total volume of annulus fluid is as follows:
ΔV 4 ＝ΔV 2 -ΔV 3 -|ΔV 5 |
wherein p is N Is the initial pressure of the annular gas, MPa; v (V) Ni For the initial volume of annular gas, m 3 The method comprises the steps of carrying out a first treatment on the surface of the T is the initial temperature of annular gas, K; Δp is the pressure increment of the annular gas, MPa; deltaV 5 For volume change of annular gas, m 3 ；ΔT g The temperature variation of the annular gas, K.
5) According to the closed loop air, the fluid and the sleeve change volume are equal, and an annular pressure rise prediction model is built
The process of establishing the annulus pressure rise prediction model is as follows:
(1) according to the difference of the volume increment values of the components in the closed container being zero, the corresponding equation is as follows:
ΔV 1 -ΔV 4 ＝0
ΔV 1 for the volume change of the sleeve under different temperature pressures, m 3 ；ΔV 4 For the volume change quantity, m, of annular fluid under different temperature and pressure 3 。
6) Solving the annular pressure corresponding to the condition
The annular pressure process for solving the corresponding condition is as follows
(1) The Newton iteration method is adopted in the solving process, the iteration error is 0.000001, and the second-order convergence is high in convergence speed, so that the solving is faster.
7) Determining the annular fluid change volume and the annular fluid temperature rise change volume before pressure relief
The solution process of the annular fluid change volume and the annular fluid temperature rise change volume without limitation under the state before pressure relief is as follows:
(1) according to the volume compatibility principle of the closed container, an annular fluid change volume equation before pressure release under the state that the annular is full of liquid can be deduced, and the equation is as follows:
Δv ki ＝πΔx[((b+u b1 ) 2 -(b+u b1 -u b2 ) 2 )]-πΔx[(b+u b1 ) 2 -b]
(2) if the annulus is not full of liquid and contains gas, the equation of the volume of the annulus fluid change in the state before the pressure release of the annulus can be deduced according to the volume compatibility principle of the closed container, and the equation is as follows:
Δv ki ＝πΔx[((b+u b1 ) 2 -(b+u b1 -u b2 ) 2 )]-πΔx[(b+u b1 ) 2 -b]-ΔV 5
(3) the equation of the volume of the annular fluid, if not limited, can be derived from the saturated vapor pressure measurement method as follows:
Δv ni ＝α c ×ΔT×V m(i-1) -k×V m(i-1) ×p ni
V m0 ＝V 0
wherein u is b1 The displacement caused by the heating of the sleeve is m; u (u) b2 The sleeve displacement is caused by pressure change, m; b is the outer radius of the inner sleeve, m; Δx is the infinitesimal length of the sleeve in the suspended section, m; deltaV 5 For volume change of annular gas, m 3 ；α c Is the expansion coefficient of the slurry body, 1/DEGC; v (V) m0 For annular fluid volume at pressure relief, m 3 The method comprises the steps of carrying out a first treatment on the surface of the Delta T is the temperature variation of annular liquid and is in DEG C; k is the volume compression coefficient of annular fluid and MPa -1 ；p ni The saturation vapor pressure corresponding to the annular temperature in the ith pressure relief is MPa; deltav ni Volume changeable of annular liquid under the condition of unlimited volume at annular temperature of ith circulation, m 3 ；Δv ki The volume of the annular liquid which is changed under the annular limit at the annular temperature of the ith circulation, m 3 ；V m(i-1) For the residual volume of the annular liquid in the annular space at the ith-1 st pressure relief, m 3 ；V 0 Is annular volume, m 3 。
8) Determining volume of fluid in annulus
Determining the limited volume of the annular fluid, namely the release volume of the annular fluid in the annular pressure release process, wherein the solving process is as follows:
(1) according to the pressurized principle of the closed container, the volume equation of the fluid in the annular space can be deduced, and the equation is as follows:
Δv ji ＝Δv ni -Δv ki
wherein Deltav ni Volume changeable of annular liquid under the condition of unlimited volume at annular temperature of ith circulation, m 3 ；Δv ki The volume of the annular liquid which is changed under the annular limit at the annular temperature of the ith circulation, m 3 ；Δv ji The volume of the annular liquid limited by the annular limitation at the annular temperature of the ith cycle, namely the initial volume parameter when the annular pressure is solved for the (i+1) th cycle, m 3 。
9) Determining the residual volume of the annular fluid, namely, the initial volume parameter when the annular pressure is solved for the next cycle, and further solving the annular pressure caused by the temperature after each pressure relief
The residual volume of the annulus fluid is solved as follows:
(1) according to the actual pressure relief requirement on site and the pressure relief volume formula obtained in the step 8), an annulus initial volume formula after the pressure relief of the annulus in a state of being full of liquid can be obtained, wherein the formula is as follows:
V mi ＝V m(i-1) -ΔV j(i-1)
(2) according to the actual pressure relief requirement on site and the pressure relief volume formula obtained in the step 8), an annulus initial volume formula after the annular pressure relief in the gas-containing state can be obtained, wherein the formula is as follows:
V mi ＝V m(i-1) -ΔV j(i-1)
V Ni ＝V N(i-1) +ΔV j(i-1)
wherein V is mi For the residual volume of the annular liquid in the annular space at the ith pressure relief, m 3 ；V m(i-1) For the residual volume of the annular liquid in the annular space at the ith-1 st pressure relief, m 3 ；Δv j(i-1) The volume of the annular liquid limited by the annular liquid at the annular temperature of the ith-1 th circulation, namely the release volume of the annular liquid in the annular pressure release process, m 3 ；V Ni For the residual volume of the annular ring air body in the ith pressure relief, m 3 ；V N(i-1) The residual volume of the annular ring air body in the ith-1 st pressure relief, m 3 ；
(3) According to the annular initial volumes of the step (1) and the step (2), the annular pressure value after the pressure relief can be obtained by combining the casing temperature distribution, and finally, the pressure value of the annular pressure caused by the temperature and the pressure relief in the whole production process of the oil well can be obtained by sequentially circulating the steps 1) to 9).
In the specific implementation process, the method comprises the steps of solving the deformation of the casing volume in the step 3) and solving the deformation of the annular fluid volume in the step 4), and substituting the deformation into the step 5); meanwhile, combining the parameters of the step 5) and extracting annulus pressure variation delta P by the same type item, adopting a Newton iteration method, selecting 0.000001 for iteration error and 1MPa for initial value, and solving the high-precision value of the annulus pressure after single boosting of the shaft; and simultaneously substituting the solving result of the step 6) into the step 7) and the step 8) to calculate and determine the limited volume of the annular fluid, substituting the result of the step 8) into the step 9) to calculate the annular fluid volume after annular pressure relief, solving the temperature change of the well through a well temperature transfer model, and allowing the initial pressure of the well to enter the next circulation to calculate the annular pressure value after the annular pressure relief.
The foregoing is merely exemplary of the present application and is not intended to limit the present application. Various modifications and variations of the present application will be apparent to those skilled in the art. Any modification, equivalent replacement, improvement, etc. which come within the spirit and principles of the application are to be included in the scope of the claims of the present application.
Claims (8)
1. A method for predicting annular space pressure based on good wellbore integrity, comprising:
1) According to the on-site production condition, defining the temperature distribution and variation value of each annulus; 2) Initially determining the initial PVT of the annular fluid; 3) Solving the change of annular sleeve volume along with annular temperature and pressure by considering the temperature of adjacent sleeves and the thermal property change of materials; 4) Solving the change of the annular fluid volume along with the annular temperature and pressure by considering the thermal property change of the fluid; 5) According to the closed loop air, the fluid and the sleeve change volume are equal, and an annular pressure rise prediction model is established; 6) Solving the annular pressure of the corresponding condition; 7) Determining the annular fluid change volume in the annular pressure increasing state, and if the annular fluid is not limited to the temperature increasing change volume; 8) Determining the limited volume of the annular fluid, namely the release volume of the annular fluid in the annular pressure release process; 9) And determining the residual volume of the annular fluid, namely, the initial volume parameter when the annular pressure is solved for the next cycle, and further solving the annular pressure caused by the temperature after each pressure relief.
2. The method for predicting annular space pressure based on well bore integrity as set forth in claim 1, wherein: in the step 3), the annular casing volume change along with the annular temperature and pressure is solved by considering the adjacent casing temperature and the material thermophysical property change, and the method comprises the following steps:
(1) measuring the elastic modulus and the thermal expansion coefficient of the sleeve under different temperature pressures, and performing experimental statistics fitting to determine the elastic modulus and the thermal expansion coefficient of the sleeve under different temperature pressures;
(2) considering the influence of the thermal stress change caused by the temperature of adjacent casings on the expansion volume of annular fluid, deriving a radial displacement equation generated by the thermal expansion of the inner casing, wherein the radial displacement derivation equation is as follows:
(3) the displacement of the sleeve due to pressure change is determined by referring to the following formula:
(4) the change of the casing volume under different temperature pressures is determined by referring to the following formula:
ΔV 1 ＝π[b 2 -(b+u b1 -u b2 ) 2 ]Δx
wherein u is b1 The displacement caused by the heating of the sleeve is m; alpha is the thermal expansion coefficient of steel and is 1/°c; mu is the poisson ratio of the steel; r is the distance from any point on the oil layer sleeve body to the circle center, and m; a is the inner radius of the inner sleeve, m; delta T 1 Is the temperature variation quantity in the inner sleeve and is at the temperature of DEG C; delta T 2 Is the external temperature variation of the inner sleeve, and is at the temperature of DEG C; b is the outer radius of the inner sleeve, m; u (u) b2 The sleeve displacement is caused by pressure change, m; deltaV 1 For the volume change of the sleeve under different temperature pressures, m 3 The method comprises the steps of carrying out a first treatment on the surface of the Δx is the infinitesimal length of the sleeve in the suspended section, m; e is the elastic modulus of steel and MPa; Δp is the annular pressure variation, MPa.
3. The method for predicting annular space pressure based on well bore integrity as set forth in claim 1, wherein: in the step 4), the change of the annular fluid volume along with the annular temperature and pressure is solved by considering the change of the thermophysical properties of the fluid, and the process comprises the following steps:
(1) measuring the density change of annular fluid under different temperature and pressure, and performing experimental parameter fitting;
(2) solving a change equation of the thermal expansion coefficient and the compression coefficient of the fluid along with the temperature and pressure by solving the fitting density equation in the step (1), wherein the deduction equation is as follows:
(3) and (3) obtaining an equation of the annular fluid volume according to the temperature and the pressure according to the equation obtained in the step (2), wherein the equation is as follows:
ΔV 2 ＝α c π(a 1 2 -b 2 )ΔTΔx
ΔT 2 ＝ΔT
(4) and (3) obtaining an annular fluid volume total change equation under the state that the annular space is full of liquid according to the equation obtained in the step (3), wherein the equation is as follows:
ΔV 4 ＝ΔV 2 -ΔV 3
wherein a is 1 Is the inner diameter of the outer sleeve, m 3 The method comprises the steps of carrying out a first treatment on the surface of the ρ is the mud density, kg/m 3 ，α c Is the expansion coefficient of the slurry body, 1/DEGC; e (E) c Is the volume elastic coefficient of slurry and MPa; deltaV 2 For the variation of annular fluid volume caused by temperature variation, m 3 ；ΔV 3 For the change quantity, m, caused by the pressure change of annular fluid volume 3 ；ΔV 4 For total change in annular fluid volume, m 3 The method comprises the steps of carrying out a first treatment on the surface of the Delta T is the temperature variation of annular liquid and is in DEG C; Δx is the infinitesimal length of the sleeve in the suspended section, m;
(5) if the annulus is not full of liquid containing gas, the equation for the total volume of annulus fluid is as follows:
ΔV 4 ＝ΔV 2 -ΔV 3 -|ΔV 5 |
wherein p is N For the initial pressure of the annular gas, MPa；V Ni For the initial volume of annular gas, m 3 The method comprises the steps of carrying out a first treatment on the surface of the T is the initial temperature of annular gas, K; Δp is the pressure increment of the annular gas, MPa; deltaV 5 For volume change of annular gas, m 3 ；ΔT g K is the temperature variation of annular gas.
4. The method for predicting annular space pressure based on well bore integrity as set forth in claim 1, wherein: in the step 5), according to the closed loop air, the fluid and the casing change volume are equal, and an annular pressure rise prediction model is built, and the process comprises the following steps:
(1) according to the difference of the volume increment values of the components in the closed container being zero, the corresponding equation is as follows:
ΔV 1 -ΔV 4 ＝0
ΔV 1 for the volume change of the sleeve under different temperature pressures, m 3 ；ΔV 4 For the volume change quantity, m, of annular fluid under different temperature and pressure 3 。
5. The method for predicting annular space pressure based on well bore integrity as set forth in claim 1, wherein: in the step 6), the annular pressure corresponding to the condition is solved, and the process comprises the following steps:
(1) the Newton iteration method is adopted in the solving process, and the second-order convergence is high in convergence speed and faster in solving.
6. The method for predicting annular space pressure based on well bore integrity as set forth in claim 1, wherein: in the step 7), determining the annular fluid change volume and the annular fluid temperature rise change volume if not limited in the state before pressure release, wherein the process comprises the following steps:
(1) according to the volume compatibility principle of the closed container, an annular fluid change volume equation before pressure release under the state that the annular is full of liquid can be deduced, and the equation is as follows:
Δv ki ＝πΔx[((b+u b1 ) 2 -(b+u b1 -u b2 ) 2 )]-πΔx[(b+u b1 ) 2 -b]
(2) if the annulus is not full of liquid and contains gas, the equation of the volume of the annulus fluid change in the state before the pressure release of the annulus can be deduced according to the volume compatibility principle of the closed container, and the equation is as follows:
Δv ki ＝πΔx[((b+u b1 ) 2 -(b+u b1 -u b2 ) 2 )]-πΔx[(b+u b1 ) 2 -b]-ΔV 5
(3) the equation of the volume of the annular fluid, if not limited, can be derived from the saturated vapor pressure measurement method as follows:
Δv ni ＝α c ×ΔT×V m(i-1) -k×V m(i-1) ×p ni
V m0 ＝V 0
wherein u is b1 The displacement caused by the heating of the sleeve is m; u (u) b2 The sleeve displacement is caused by pressure change, m; b is the outer radius of the inner sleeve, m; Δx is the infinitesimal length of the sleeve in the suspended section, m; deltaV 5 For volume change of annular gas, m 3 ；α c Is the expansion coefficient of the slurry body, 1/DEGC; v (V) m0 For annular fluid volume at pressure relief, m 3 The method comprises the steps of carrying out a first treatment on the surface of the Delta T is the temperature variation of annular liquid and is in DEG C; k is the volume compression coefficient of annular fluid and MPa -1 ；p ni The saturation vapor pressure corresponding to the annular temperature in the ith pressure relief is MPa; deltav ni Volume changeable of annular liquid under the condition of unlimited volume at annular temperature of ith circulation, m 3 ；Δv ki The volume of the annular liquid which is changed under the annular limit at the annular temperature of the ith circulation, m 3 ；V m(i-1) For the residual volume of the annular liquid in the annular space at the ith-1 st pressure relief, m 3 ；V 0 Is annular volume, m 3 。
7. The method for predicting annular space pressure based on well bore integrity as set forth in claim 6, wherein: in the step 8), determining the volume limited by the annular fluid, namely the release volume of the annular fluid in the annular pressure release process, wherein the process comprises the following steps:
(1) according to the pressurized principle of the closed container, the volume equation of the fluid in the annular space can be deduced, and the equation is as follows:
Δv ji ＝Δv ni -Δv ki
wherein Deltav ni Volume changeable of annular liquid under the condition of unlimited volume at annular temperature of ith circulation, m 3 ；Δv ki The volume of the annular liquid which is changed under the annular limit at the annular temperature of the ith circulation, m 3 ；Δv ji The volume of the annular liquid limited by the annular limitation at the annular temperature of the ith cycle, namely the initial volume parameter when the annular pressure is solved for the (i+1) th cycle, m 3 。
8. The method for predicting annular space pressure based on good wellbore integrity of claim 7, wherein: in the step 9), determining the residual volume of the annular fluid, namely, the initial volume parameter when the annular pressure is solved for the next cycle, and further solving the annular pressure caused by the temperature after each pressure relief, wherein the process comprises the following steps:
(1) according to the actual pressure relief requirement on site and the pressure relief volume formula of claim 7, an annulus initial volume formula after the pressure relief of the annulus in a state of being full of liquid can be obtained, wherein the formula is as follows:
V mi ＝V m(i-1) -ΔV j(i-1)
(2) according to the actual pressure relief requirement on site and the pressure relief volume formula of claim 7, an annulus initial volume formula after the annular pressure relief in the gas-containing state can be obtained, wherein the formula is as follows:
V mi ＝V m(i-1) -ΔV j(i-1)
V Ni ＝V N(i-1) +ΔV j(i-1)
wherein V is mi For the residual volume of the annular liquid in the annular space at the ith pressure relief, m 3 ；V m(i-1) For the residual volume of the annular liquid in the annular space at the ith-1 st pressure relief, m 3 ；Δv j(i-1) Annular liquid ring at annular temperature of ith-1 th circulationThe volume of the space limitation, namely the release volume of the annular fluid in the annular pressure release process, m 3 ；V Ni For the residual volume of the annular ring air body in the ith pressure relief, m 3 ；V N(i-1) The residual volume of the annular ring air body in the ith-1 st pressure relief, m 3 ；
(3) According to the annular initial volumes of the step (1) and the step (2), the annular pressure value after the pressure relief can be obtained by combining the casing temperature distribution, and finally, the pressure value of the annular pressure caused by the temperature and the pressure relief in the whole production process of the oil well can be obtained by sequentially circulating the steps 1) to 9).
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