A method for calculating the minimum bottom hole residual pressure in a long slanting straight well section during cement slurry loss

Abstract

This invention provides a method for calculating the minimum bottom hole residual pressure P during the weight loss process of cement slurry in a long inclined vertical well section. b The ultimate pressure loss ΔP caused by the liquid column pressure P0 at the top of the cement slurry and the reduction in the volume of the cement slurry. ss The ultimate residual pressure P after cement slurry sets and loses weight sy It is determined that it satisfies P. b =P0+P sy -ΔP ss The present invention takes into account the effects of tailpipe eccentricity and cement slurry hydration when calculating the minimum bottom hole residual pressure, which effectively improves the accuracy of the calculation of the minimum bottom hole residual pressure.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of tail pipe cementing engineering, and particularly relates to a calculation method of minimum bottom hole residual pressure in a cement slurry loss process of a long deviated straight well section. BACKGROUND

[0002] Tail pipe cementing is an important link in the process of oil and gas well drilling. The main steps of cementing are as follows: a tail pipe is lowered into a well, and a cement slurry is injected into an annular space between the tail pipe and the well wall, so that the tail pipe and the well wall are cemented together. In the early stage, the injected cement slurry is in a liquid state, at this time, the pressure of the liquid in the annulus on the formation is the sum of the static liquid pressures of each slurry column above the action point; because the cement slurry has a large density, it can play a role in pressing the formation. However, with the passage of time, the cement slurry gradually solidifies, and the connection force between the cement slurry and the well wall and the tail pipe increases, so that the weight of the cement slurry column is suspended on the casing and the well wall; that is, the cement slurry will lose weight in the setting process, thereby reducing the pressure on the formation. When the pressure of the annular liquid column on the formation is less than the formation pressure, the formation fluid will invade the annulus and flow to the wellhead, not only causing waste of oil and gas resources, but also polluting the surrounding environment, causing waste of resources and environmental pollution. Therefore, accurately predicting the minimum bottom hole residual pressure in the setting process is the key to pressure stabilization and channeling prevention.

[0003] At present, many scholars at home and abroad have carried out theoretical and experimental researches on the loss of cement slurry; for example, foreign scholars such as Sabins proposed the gelation loss theory and the gelation suspension loss pressure formula, which calculates the maximum loss of cement slurry according to the gel strength of 48 Pa; domestic scholars such as Guo Xiaoyang studied the loss law of cement slurry in high-deviated wells, and proposed the settlement loss theory and the settlement loss pressure formula, which calculates the loss value according to the pressure drop of the cement slurry liquid column to the pressure of the equal-height water column at the initial setting time; both of these two theoretical calculation methods belong to semi-empirical formula, and do not consider the influence of casing eccentricity and cement slurry hydration on the loss of cement slurry. In addition, the existing cement slurry loss measuring device can only test the loss state of cement slurry under a single condition, and a large number of repetitive experimental operations are needed during testing, and the minimum bottom hole residual pressure in the setting loss process of the cement slurry is predicted based on the experimental data, which not only increases the difficulty of predicting the minimum bottom hole residual pressure, but also cannot accurately reflect the minimum bottom hole residual pressure when the cement slurry reaches the limit loss under the complex conditions in the well, affecting the accurate prevention of annular channeling. SUMMARY

[0004] In view of the shortcomings of the prior art, the purpose of this invention is to provide a method for calculating the minimum bottom hole residual pressure during the weight loss process of cement slurry in a long inclined vertical well section. Based on the consideration of tailpipe eccentricity and cement slurry hydration, this method can more accurately predict the minimum bottom hole residual pressure during the weight loss process of cement slurry in a long inclined vertical well section, providing theoretical guidance for the precise application of annular compensation pressure during the weight loss process, and is of great significance for preventing annular crossflow.

[0005] To achieve the above and other related objectives, this invention provides a method for calculating the minimum bottom hole residual pressure P during the weight loss process of cement slurry in a long inclined vertical well section. b The ultimate pressure loss ΔP caused by the liquid column pressure P0 at the top of the cement slurry and the reduction in the volume of the cement slurry. ss The ultimate residual pressure P after cement slurry sets and loses weight sy It is determined that it satisfies P. b =P0+P sy -ΔP ss The ultimate residual pressure P after the cement slurry has gelled and lost weight sy Determined by the following formula:

[0006]

[0007] In the formula: ρ cem The density of the cement paste;

[0008] g is the acceleration due to gravity;

[0009] β is the inclination angle of the long inclined vertical well section;

[0010] n is the number of span beams obtained by splitting the tailpipe at each stabilizer when the tailpipe is regarded as a continuous beam.

[0011] L i Let be the length of the i-th span of the beam;

[0012] y i (x) represents the total deflection of the tailpipe at the i-th span beam;

[0013] x represents the moment distance of each span of the beam;

[0014] τ L The critical static adhesive strength value at which cement grout has complete anti-gas channeling capability is determined empirically.

[0015] D sw The outer diameter of the stabilizer;

[0016] D co The outer diameter of the tailpipe;

[0017] The ultimate pressure loss ΔP caused by the reduction in the volume of the cement slurry ssThe shrinkage pressure loss ΔP of the cement slurry under the limit hydration chsh The shrinkage pressure loss ΔP of the cement slurry under the limit hydration chsh is calculated by the following formula:

[0018]

[0019] In the formula, is the water-cement ratio;

[0020] C cem is the compression coefficient of the cement slurry, and is 2.85×10 -5 MPa -1 .

[0021] Preferably, the limit residual pressure P sy of the cement slurry after the cementing weight loss is determined by the following method:

[0022] S1, the tail pipe with multiple stabilizers at the long and oblique straight well section is regarded as a multi-pivot continuous beam, and the total deflection y i (x) of the tail pipe at each span beam is determined according to the longitudinal and transverse curved beam theory;

[0023] S2, stress analysis is performed on the cement slurry microelement, and the residual pressure change rate of the cement slurry after the cementing weight loss at each span beam is determined The residual pressure change rate of the cement slurry after the cementing weight loss is calculated by the following formula:

[0024]

[0025] In the formula, ΔP is the pressure drop of the cement slurry microelement in the wellbore direction;

[0026] ΔH is the length of the cement slurry microelement in the wellbore direction;

[0027] ρ cem is the density of the cement slurry;

[0028] g is the acceleration of gravity;

[0029] β is the inclination angle of the long and oblique straight well section;

[0030] τ is the static cementing strength of the cement slurry;

[0031] y i (x) is the total deflection of the tail pipe at the i-th span beam;

[0032] x is the moment distance of each span beam;

[0033] D sw is the outer diameter of the stabilizer;

[0034] D coThe outer diameter of the tail pipe;

[0035] S3, calculating the limit residual pressure P of the cement slurry after gel loss sy The limit residual pressure P of the cement slurry after gel loss sy Determined by the following formula:

[0036]

[0037] In the formula, n is the number of span beams obtained by splitting the tail pipe at each stabilizer when the tail pipe is regarded as a continuous beam;

[0038] L i is the length of the i-th span beam;

[0039] τ L is the critical static gel strength value of the cement slurry with complete gas channeling prevention capability, determined by experience.

[0040] Preferably, the limit pressure loss ΔP of the cement slurry caused by volume reduction ss includes the limit pressure loss ΔP of the cement slurry caused by water loss fl The limit pressure loss ΔP of the cement slurry caused by water loss fl The calculation formula is:

[0041]

[0042] In the formula, P i is the pressure of the cement slurry at the i-th span beam;

[0043] P pro is the formation pressure, obtained by actual drilling data;

[0044] ΔP r is the reference pressure difference;

[0045] C cem is the compression coefficient of the cement slurry, taken as 2.85×10 -5 MPa -1 ;

[0046] E is the activation energy of the cement slurry;

[0047] R is the gas constant;

[0048] T r is the reference temperature;

[0049] T i is the temperature of the cement slurry at the i-th span beam;

[0050] V FLmax (T r ,ΔP r ) is the volume of the cement slurry per unit volume at the reference temperature Tr The maximum fluid loss of the cement slurry under the reference pressure difference ΔP r .

[0051] Preferably, the cement slurry activation energy E is determined by the following method: r The maximum fluid loss of the cement slurry under the reference pressure difference ΔP r . FLmax (T r ,ΔP r ) is obtained by static filtration test of the unit volume of cement slurry.

[0052] Preferably, the cement slurry activation energy E is determined by the following method:

[0053] A plurality of unit volumes of cement slurry samples are subjected to static filtration test of the cement slurry under the same pressure difference and different temperatures, and the test pressure difference ΔP, the test temperature T of each cement slurry sample and the maximum fluid loss V FLmax (T,ΔP) of each cement slurry sample are recorded, and a plurality of groups of (T, V FLmax (T,ΔP)) are obtained.

[0054] The first fitting equation is used to fit the plurality of groups of (T, V FLmax (T,ΔP)), and the cement slurry activation energy E is obtained.

[0055] As described above, the method for calculating the minimum bottom hole residual pressure of the cement slurry in the long deviated well section of the present application has the following beneficial effects:

[0056] The present application fully considers the influence of the eccentricity of the tail pipe and the limit hydration of the cement slurry when calculating the minimum bottom hole residual pressure, so that the calculation of the minimum bottom hole residual pressure is more simple and accurate. In addition, when calculating the minimum bottom hole residual pressure, the pressure loss caused by the fluid loss of the cement slurry under the influence of temperature and pressure is taken into account, which further improves the accuracy of the calculation of the minimum bottom hole residual pressure and has important significance for preventing annular channeling. BRIEF DESCRIPTION OF DRAWINGS

[0057] Figure 1 The flow chart for calculating the residual pressure P sy of the cement slurry after gelation and fluid loss.

[0058] Figure 2 The schematic diagram of the tail pipe combination equivalent to a multi-pivot continuous beam at the long deviated well section.

[0059] Figure 3 The force analysis diagram of the first span beam.

[0060] Figure 4 The force analysis diagram of any span beam except the first span beam.

[0061] Figure 5Force analysis diagram of cement slurry microelement.

[0062] Figure 6 Fitting the obtained fitting straight line graph by using the first fitting equation. DETAILED DESCRIPTION

[0063] The embodiments of the present application are illustrated by specific working examples below, and other advantages and effects of the present application can be easily understood by those skilled in the art from the content disclosed in the specification.

[0064] Please refer to Figures 1 to 6 . It should be understood that the structures, proportions, sizes, etc. shown in the drawings attached to the specification are only used to cooperate with the content disclosed in the specification for understanding and reading by those skilled in the art, and are not used to limit the defined conditions under which the present application can be implemented, so they do not have technical significance. Any modification of the structure, change of the proportional relationship or adjustment of the size, without affecting the effects that can be produced by the present application and the purposes that can be achieved, should still fall within the scope covered by the disclosed technical content of the present application. At the same time, the terms such as "upper", "lower", "left", "right", "middle" and "one" used in the specification are only for the convenience of clear description, and are not used to limit the scope in which the present application can be implemented, and the change or adjustment of the relative relationship, without substantially changing the technical content, is also considered as the scope in which the present application can be implemented.

[0065] Example 1

[0066] The embodiment of the present application provides a calculation method of the minimum bottom hole residual pressure in the weight loss process of cement slurry, which comprises:

[0067] The minimum bottom hole residual pressure P in the weight loss process of cement slurry is calculated b The minimum bottom hole residual pressure P b The limit pressure loss ΔP caused by the volume reduction of cement slurry ss and the limit residual pressure P after the weight loss of cement slurry gelation sy is determined, which satisfies P b =P0+P sy -ΔP ss (1); the liquid column pressure P0 at the top of the cement slurry is a known value, which satisfies P0=ρ0gH0; wherein ρ0 is the density of drilling fluid; H0 is the cement return depth, which can be measured and obtained; the limit pressure loss ΔP caused by the volume reduction of cement slurry includes the shrinkage pressure loss ΔP under the limit hydration of cement slurry ss . chsh

[0068] The determination method of the limit residual pressure P after the weight loss of cement slurry gelation sy is shown in Figure 1 , which comprises​

[0069] S1, the tail pipe at the long and oblique straight well section with multiple stabilizers is regarded as a multi-pivot continuous beam, and the total deflection y of the tail pipe at each span beam is determined according to the longitudinal and transverse bending beam theory i (x);

[0070] In the present application, the multiple stabilizers include a tail pipe hanger at the top end of the tail pipe and each centralizer which is sleeved on the tail pipe, and the centralizer of the tail pipe at the long and oblique straight well section preferably adopts a rigid centralizer; the tail pipe is suspended at the long and oblique straight well section of the large displacement well through the tail pipe hanger at the top end thereof.

[0071] After the tail pipe is lowered to the bottom of the well, the tail pipe will be longitudinally and transversely bent due to the restriction of the well trajectory and the stabilizers, so that the tail pipe is eccentrically arranged relative to the wellbore; the eccentrically arranged tail pipe will cause the generation of the eccentric annular space gap, and the weightless velocity at the wide gap of the eccentric annular space gap is different from that at the narrow gap. Therefore, the accuracy of the weightless pressure prediction can be effectively improved by considering the eccentricity of the tail pipe.

[0072] Based on this, when the weightless pressure prediction is performed by considering the eccentricity of the tail pipe, the narrow annular space gap needs to be determined first, and the narrow annular space gap is closely related to the deformation condition of the tail pipe. When the deformation condition of the tail pipe is obtained, the tail pipe with n stabilizers can be regarded as a multi-pivot continuous beam which bears longitudinal and transverse bending, and at this time, the stabilizers are regarded as supports. The structure of the multi-pivot continuous beam is shown in Figure 2 , which is divided at each support (i.e. each stabilizer) to obtain n span beams; wherein the first span beam is a cantilever beam, and the remaining span beams are simply supported beams.

[0073] By the longitudinal and transverse beam bending theory, the stress analysis of each span beam can be performed to obtain the total deflection y i (x) and the total rotation angle θ i (x) of each span beam. The stress deformation diagram of the first span beam is shown in Figure 3 , and the stress deformation diagrams of the remaining span beams are shown in Figure 4 .

[0074] As shown in Figure 3 , the first span beam is a cantilever beam, and the stress analysis of the first span beam can be performed to obtain formula (2).

[0075]

[0076] Wherein, N1 is the support reaction force at the first stabilizer;

[0077] q is the unit length floating weight of the tail pipe.

[0078] L1 is the length of the first span beam;

[0079] β is the inclination angle of the long and oblique straight well section;

[0080] T1 is the axial tension at the first stabilizer;

[0081] f is the friction coefficient between the stabilizer and the well wall.

[0082] Taking the moment at x, formula (3) is obtained:

[0083]

[0084] where M1 is the bending moment at the first stabilizer;

[0085] x is the x-direction distance from the position of taking the moment to the first stabilizer.

[0086] According to the approximate differential equation y'' = M(x) / EI (4) of the deflection curve, formula (3) is converted into formula (5).

[0087]

[0088] where E is the elastic modulus of the tail pipe;

[0089] I is the moment of inertia of the tail pipe, satisfying where D co and D ci are the outer diameter and the inner diameter of the tail pipe, respectively.

[0090] Since formula (5) is a second-order constant coefficient non-homogeneous linear differential equation, integrating it to solve can obtain formula (6).

[0091]

[0092] First-order derivation of formula (6) can obtain formula (7).

[0093]

[0094] First-order derivation of formula (7) can obtain formula (8).

[0095]

[0096] From the boundary conditions y1(0) = 0 and y1''(L1) = 0, it can be solved that:

[0097]

[0098] Substituting into formula (6) and formula (7), the total deflection y1(x) and the rotation angle θ1(x) of the first span beam can be obtained.

[0099] Since the rest of the beams are simply supported beams except the first span beam, the stress analysis diagram of the rest of the beams (i.e. the beams of i = 2, 3, …, n) is shown in Fig. 2. Figure 4 The stress analysis of the beams can obtain formula (9):

[0100]

[0101] wherein N i and N i-1 are the support reaction forces at the i-th and i-1-th stabilizers, respectively;

[0102] T i and T i-1 are the axial tension forces at the i-th and i-1-th stabilizers, respectively;

[0103] q is the unit length floating weight of the tail pipe.

[0104] L i is the length of the i-th beam;

[0105] β is the inclination angle of the long deviated well section;

[0106] f is the friction coefficient between the stabilizer and the well wall.

[0107] For convenience of calculation, the stress of the i-th beam (i = 2, 3, …, n) can be decomposed into the following three combinations: the self weight and the axial tension force, the right end bending moment and the axial tension force, and the left end bending moment and the axial tension force. The deflection and the rotation angle of the i-th beam (i = 2, 3, …, n) under the action of different combined forces are respectively obtained, and then the total deflection y i (x) and the total rotation angle θ i (x) of the i-th beam (i = 2, 3, …, n) can be obtained by linear superposition. The total deflection y i (x) of the i-th beam (i = 2, 3, …, n) is formula (10):

[0108]

[0109] wherein L i is the length of the i-th beam, i is a positive integer, and i = 2, 3, …, n;

[0110] q is the unit length floating weight of the tail pipe;

[0111] β is the inclination angle of the long deviated well section;

[0112] E is the elastic modulus of the tail pipe;

[0113] I is the moment of inertia of the tail pipe, and I = πD wherein D co and D ciTail pipe outer diameter and tail pipe inner diameter, respectively.

[0114] u i Stability parameter of the i-th span, u i = k i L i / 2, and Where T i is the axial tension at the i-th stabilizer;

[0115] M i-1 , M i are the bending moments at the i-1-th stabilizer and the i-th stabilizer, respectively.

[0116] It can be understood that the unit length buoyant weight q of the tail pipe can be calculated by using various existing casing line buoyant weight methods such as the domestic buoyant coefficient method and the foreign buoyant coefficient method, and the unit length buoyant weight q of the tail pipe in the embodiment is preferably calculated by using the foreign buoyant coefficient method, at this time, the calculation formula of the unit length buoyant weight q of the tail pipe is formula (11):

[0117]

[0118] In the formula, W a is the casing line weight; p cem is the cement slurry density; p mud is the drilling fluid density; p ca is the tail pipe density; D ci , D co are the tail pipe inner diameter and tail pipe outer diameter, respectively.

[0119] The total rotation angle θ i (x) of the i-th span (i = 2, 3, …, n) is formula (12), which can be obtained by first-order derivation of formula (10), and formula (12) is:

[0120]

[0121] Since the continuous beam has equal rotation angles at the left and right of each support point, formula (12) satisfies θ i (L i ) = - θ i+1 (0), where i is a positive integer, and i = 1, 2, …, n-1; in addition, since the tail pipe is small elastic deformation, the rotation angle at the stabilizer is very small, so the rotation angle at the tail pipe hanger (i.e. the last stabilizer) can be calculated as 0, at this time, formula (12) satisfies M n = 0; on this basis, the bending moment equation group can be established, and the bending moment equation group is formula (13):

[0122]

[0123] The bending moment equation group of formula (13) is solved by using VB software and other solving software, so that the values of M1, M2, …, M n are determined, thereby determining the total deflection y i (x) of the entire tail pipe at each span beam, wherein i is a positive integer, and i = 2, 3, …, n.

[0124] S2, stress analysis is performed on the cement slurry microelement to determine the remaining pressure change rate of the cement slurry after cementation weight loss under each span beam and further determine the remaining pressure P1 of the cement slurry after cementation weight loss; the remaining pressure change rate of the cement slurry after cementation weight loss under each span beam is formula (14):

[0125]

[0126] wherein ΔP is the pressure drop of the cement slurry microelement in the wellbore direction;

[0127] ΔH is the length of the cement slurry microelement in the wellbore direction;

[0128] ρ cem is the density of the cement slurry;

[0129] g is the acceleration of gravity;

[0130] β is the inclination angle of the long deviated well section;

[0131] τ is the static cementation strength of the cement slurry;

[0132] D sw is the outer diameter of the stabilizer;

[0133] D co is the outer diameter of the tail pipe;

[0134] y i (x) is the total deflection of the tail pipe at the i-th span beam, i is a positive integer, and i = 2, 3, …, n.

[0135] Specifically, the remaining pressure change rate of the cement slurry after cementation weight loss under each span beam is determined in the following manner:

[0136] Figure 5 is a force diagram of a cement slurry microelement with a length of ΔH, a thickness of S, and a width of 1. Stress analysis is performed on the cement slurry microelement to obtain formula (15).

[0137] (P2S-P1S)cosβ=mg-2τcosβΔH=ρ cem gSΔH-2τcosβΔH (15)

[0138] Wherein, P1, P2 are the forces on the upper and lower ends of the microelement cement slurry;

[0139] S is the narrow edge ring space gap,

[0140] Substitute ΔP=P2-P1 into formula (15), and organize it to obtain formula (14).

[0141] S3, the limit residual pressure P of the cement slurry after gel loss sy , the limit residual pressure P of the cement slurry after gel loss sy Determined by formula (16):

[0142]

[0143] In the formula, τ L The critical static gel strength value of the cement slurry with complete gas channeling prevention capability is determined by experience, and the value is generally 240 Pa.

[0144] (II) shrinkage pressure loss ΔP chsh of the limit hydration

[0145] Due to the hydration reaction and filtration loss during the cement slurry setting process, the volume of the cement slurry will shrink; and the well wall and the tail pipe can form a closed hydraulic system. According to the principle that the volume shrinkage of the cement slurry in the closed hydraulic system causes the system pressure to decrease, the volume shrinkage caused by the loss and hydration of the cement slurry will cause the rapid decrease of the static liquid column pressure of the cement slurry. Therefore, the cement slurry pressure loss ΔP ss caused by the volume shrinkage of the cement slurry satisfies: Wherein, ΔV ss is the shrinkage volume of the cement slurry; V a is the total volume of the cement slurry; C cem is the compression coefficient of the cement slurry, which is 2.85×10 -5 MPa -1 .

[0146] Based on formula (17), the shrinkage pressure loss ΔP sh caused by the hydration of the cement slurry satisfies formula (18).

[0147]

[0148] In the formula, ΔV sh_i is the shrinkage volume of the cement slurry at the i-th span beam; V i is the total volume of the cement slurry at the i-th span beam; v s h _i (α) is the hydration volume shrinkage rate of the cement slurry at the i-th span beam at any hydration degree α; α(T i , Pi t) is the temperature of the cement paste at the ith span at time t i P is the pressure at the ith span i at time t is the water-cement ratio.

[0149] When α(T i , P i , t) = 1, the hydration volume shrinkage of the cement paste reaches a maximum value, and therefore, the shrinkage pressure loss ΔP chsh of the cement paste under the limit hydration satisfies equation (19).

[0150]

[0151] Example Two

[0152] The difference between this example and Example One is that the limit pressure loss ΔP ss of the cement paste caused by the volume shrinkage of the cement paste also includes the limit pressure loss ΔP fl of the cement paste caused by the water loss of the cement paste.

[0153] During the setting process of the cement paste, the hydration reaction and the water loss by filtration will cause the volume shrinkage of the cement paste, and a closed hydraulic system can be formed between the well wall and the liner. According to the principle that the volume shrinkage of the cement paste in the closed hydraulic system will cause the pressure reduction of the system, the volume shrinkage of the cement paste caused by the water loss and the hydration will cause the rapid reduction of the hydrostatic pressure of the cement paste. Therefore, the pressure loss ΔP ss of the cement paste caused by the volume shrinkage of the cement paste satisfies: where ΔV ss is the shrinkage volume of the cement paste; V a is the total volume of the cement paste; and C cem is the compression coefficient of the cement paste, which is taken as 2.85 x 10 -5 MPa -1 .

[0154] Based on equation (17), the limit water loss pressure loss ΔP fl of the cement paste caused by the water loss of the cement paste satisfies equation (20).

[0155]

[0156] where ΔV FLmax_i is the limit water loss volume of the cement paste at the ith span; V i is the total volume of the cement paste at the ith span; V FLmax_i (T i , ΔP i ) is the temperature T i and the pressure difference ΔP at the ith span per unit volume of the cement paste at the ith span.i the maximum water loss at the current time.

[0157] wherein the maximum water loss V of the cement slurry per unit volume at any temperature T and any pressure difference ΔP FLmax (T,ΔP) is determined by the following way:

[0158] 1) the flow of the cement slurry is regarded as a steady-state planar radial flow, at this time, the seepage velocity v of the cement slurry satisfies formula (21).

[0159]

[0160] wherein K is the permeability; is the pressure gradient; r is the radial distance; η is the viscosity of the cement slurry; and ΔP is the pressure difference.

[0161] According to formula (21), the water loss rate v of the cement slurry at any temperature T and any pressure difference ΔP fl (T,ΔP) satisfies formula (22).

[0162]

[0163] wherein v fl (T r ,ΔP r ) is the water loss rate of the cement slurry at the reference temperature T r , the reference pressure difference ΔP r ; η r is the viscosity of the cement slurry at the reference temperature T r ; and η is the viscosity of the cement slurry at any temperature T.

[0164] 2) a second relationship between the viscosity η of the cement slurry at any temperature T and the temperature T is established by the Arrhenius equation, which satisfies formula (23).

[0165]

[0166] wherein η r is the viscosity of the cement slurry at the reference temperature T r ;

[0167] E is the activation energy of the cement slurry;

[0168] R is the gas constant;

[0169] T and T r are absolute temperature and reference temperature, respectively, in K.

[0170] 3) the water loss rate v fl (T,ΔP) of the cement slurry at any temperature T and any pressure difference ΔP is obtained by formula (22) and formula (23), which satisfies formula (24).

[0171]

[0172] 4) Integrate equation (24) to obtain the cumulative water loss of unit volume of cement slurry at any temperature T and any pressure difference ΔP V FL (T, ΔP) that satisfies equation (25).

[0173]

[0174] Based on equation (25), the maximum water loss of unit volume of cement slurry at any temperature T and any pressure difference ΔP V FLmax (T, ΔP) that satisfies equation (26).

[0175]

[0176] Based on equation (26), the limit water loss pressure loss ΔP fl caused by water loss of cement slurry can be converted from equation (20) to equation (27).

[0177]

[0178] In the formula, P i is the pressure of the cement slurry at the i-th span;

[0179] P pro is the formation pressure, which is obtained through actual drilling data;

[0180] ΔP r is the reference pressure difference, which can be determined by oneself according to the needs, and is generally 3 MPa;

[0181] C cem is the compression coefficient of the cement slurry, which is taken as 2.85 × 10 -5 MPa -1 ;

[0182] E is the activation energy of the cement slurry, and its determination method is the same as that of the determination method of the activation energy E of the cement slurry in Example 1;

[0183] R is the gas constant;

[0184] T r is the reference temperature;

[0185] T i is the temperature of the cement slurry at the i-th span;

[0186] V FLm (T r , ΔP r ) is the cumulative water loss of unit volume of cement slurry at the reference temperature T r and the reference pressure difference ΔP rThe maximum water loss of the cement slurry per unit volume can be obtained by a static filtration test of the cement slurry per unit volume.

[0187] The cement slurry activation energy E is determined by:

[0188] 1) Perform the static filtration test of the cement slurry per unit volume under the same pressure difference and different temperatures, and record the test pressure difference ΔP, the test temperature T of each cement slurry sample and the maximum water loss V of each cement slurry sample. FLmax (T,ΔP), and obtain multiple groups of (T, V FLmax (T,ΔP);

[0189] 2) Use the first fitting equation fit the multiple groups of (T, V FLmax (T,ΔP) to obtain the cement slurry activation energy E.

[0190] In summary, the present application calculates the minimum bottom hole residual pressure in the cement slurry weight loss process by fully considering the effects of the eccentricity of the tail pipe, the temperature and pressure at different depths in the well, effectively ensuring the accuracy of the minimum bottom hole residual pressure calculation, and having important significance for preventing annular channeling.

[0191] The above embodiments only exemplarily illustrate the principles and effects of the present application, and are not used to limit the present application. Any person skilled in the art can modify or change the above embodiments without departing from the spirit and scope of the present application. Therefore, all equivalent modifications or changes completed by those skilled in the art without departing from the spirit and technical thought disclosed by the present application should be covered by the claims of the present application.

Claims

1. A method for calculating the minimum bottom hole residual pressure during the weight loss process of cement slurry in a long inclined vertical well section, characterized in that, Minimum bottom hole residual pressure P b Pressure from the liquid column at the top of the cement grout P 0 The ultimate pressure loss Δ caused by the reduction in the volume of cement slurry P ss Ultimate residual pressure after cement grout sets and loses weight P sy It is determined that it satisfies P b = P 0 + P sy ―Δ P ss The ultimate residual pressure after the cement slurry has gelled and lost weight. P sy Determined by the following formula: ； In the formula: The density of the cement paste; g is the acceleration due to gravity; β The inclination angle of the long, straight well section; n When the tailpipe is considered as a continuous beam, the number of span beams obtained by splitting the tailpipe at each stabilizer. L i Let be the length of the i-th span of the beam; For the tailpipe at the first i Total deflection at the span beam; x The moment distance for each span of the beam; The critical static adhesive strength value for which cement grout has complete anti-air channeling capability is determined empirically; D sw The outer diameter of the stabilizer; D co The outer diameter of the tailpipe; The ultimate pressure loss Δ caused by the reduction in the volume of the cement slurry P ss Including shrinkage pressure loss Δ under the ultimate hydration of cement paste P chsh The shrinkage pressure loss Δ under the ultimate hydration of the cement slurry P chsh The calculation formula is: ； In the formula, Water-cement ratio; C cem The compression coefficient of cement paste is taken as 2.85 × 10⁻⁶. -5 MPa -1 .

2. The method for calculating the minimum bottom hole residual pressure during the weight loss process of cement slurry in a long inclined vertical well section according to claim 1, characterized in that, The ultimate residual pressure after the cement slurry gels and loses weight P sy The methods for determining this include: S1. Treat the tailpipe with multiple stabilizers in the long inclined vertical well section as a multi-support continuous beam, and determine the total deflection of the tailpipe at each span of the beam according to the longitudinal and transverse bending beam theory. y i ( x ); S2. Perform stress analysis on the cement grout micro-elements to determine the rate of change of residual pressure after the cement grout has gelled and lost weight at each span of the beam. The rate of change of residual pressure after the cement slurry gels and loses weight Calculated using the following formula: ； In the formula: ΔP is the pressure drop of the cement slurry micro-element in the wellbore direction; ΔH is the length of the cement slurry micro-element in the wellbore direction; The density of the cement paste; g is the acceleration due to gravity; β The inclination angle of the long, straight well section; This refers to the static cementitious strength of the cement grout. For the tailpipe at the first i Total deflection at the span beam; x The moment distance for each span of the beam; D sw The outer diameter of the stabilizer; D co The outer diameter of the tailpipe; S3. Calculate the ultimate residual pressure after the cement paste has set and lost weight. P sy The ultimate residual pressure after the cement slurry has gelled and lost weight. P sy Determined by the following formula: ； In the formula, n When the tailpipe is considered as a continuous beam, the number of span beams obtained by splitting the tailpipe at each stabilizer. L i Let be the length of the i-th span of the beam; The critical static adhesive strength value at which cement grout has complete anti-gas channeling capability is determined empirically.

3. The method for calculating the minimum bottom hole residual pressure during the weight loss process of cement slurry in a long inclined vertical well section according to claim 1 or 2, characterized in that, The ultimate pressure loss Δ caused by the reduction in the volume of the cement slurry P ss Including the ultimate pressure loss caused by water loss in cement grout The ultimate pressure loss caused by the loss of water in the cement slurry The calculation formula is: ； In the formula, P i For the first i Pressure of cement grout at the cross-beam; P pro This represents formation pressure, obtained through actual drilling data. Δ P r For reference pressure difference; C cem Let be the compressibility coefficient of the cement paste, taken as . ; E represents the activation energy of the cement slurry. R is the gas constant; T r For reference temperature; T i For the first i Temperature of cement grout at the cross-beam; For a unit volume of cement slurry at a reference temperature T r Compared with the reference pressure difference Δ P r The maximum water loss.

4. The method for calculating the minimum bottom hole residual pressure during the weight loss process of cement slurry in a long inclined vertical well section according to claim 3, characterized in that, Cement slurry per unit volume at reference temperature T r Compared with the reference pressure difference Δ P r Maximum water loss The result was obtained through a static filtration test of a unit volume of cement slurry.

5. The method for calculating the minimum bottom hole residual pressure during the weight loss process of cement slurry in a long inclined vertical well section according to claim 3, characterized in that, The method for determining the activation energy E of cement slurry is as follows: Multiple unit volume cement slurry samples were subjected to static filtration loss tests under the same pressure differential and different temperatures. The test pressure differential ΔP, the test temperature T of each cement slurry sample, and the maximum water loss of each cement slurry sample were recorded. , obtain multiple sets (T, ); Using the first fitting equation For multiple groups (T, The activation energy E of the cement slurry was obtained by fitting the data.

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