A method for dynamically predicting the weight loss of cement slurry under long slanting straight well sections

Abstract

This invention provides a method for dynamic prediction of cement slurry weight loss in long inclined vertical well sections. The method includes: calculating the effective bottom hole pressure P during the cement slurry weight loss process. b Effective pressure at the bottom of the well, P b The calculation formula is: P b = P0 + P1; where P0 is the liquid column pressure at the top of the cement slurry; P1 is the effective pressure of the cement slurry; the calculation of the effective pressure P1 of the cement slurry includes determining the remaining pressure P after the cement slurry gels and loses weight, taking into account the eccentricity of the tailpipe and the downhole temperature and pressure. sy The residual pressure P after the cementation and weight loss of the mud obtained by this invention sy The calculations are more consistent with the gelation and weight loss characteristics of cement slurry under complex downhole conditions, effectively ensuring the accuracy of dynamic prediction of cement slurry weight loss.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of tail pipe cementing engineering, and particularly relates to a cement slurry loss dynamic prediction method under a long slant 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 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 continuously during the solidification process, 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 during the waiting period, thereby reducing the pressure on the formation. When the pressure of the annular liquid column on the ground 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 loss of weight during the waiting period is the key to achieving pressure stabilization and prevention of channeling.

[0003] At present, many scholars at home and abroad have conducted 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 conducted researches on the loss law of cement slurry in high-deviation wells, and proposed the settlement loss theory and the settlement loss pressure formula, which calculates the loss value according to the pressure reduction of the cement slurry liquid column to the equal-height water column pressure at the initial setting time; both of these two theoretical calculation methods belong to semi-empirical formula, and do not consider the influence of well temperature, pressure and casing eccentricity 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 cannot accurately reflect the loss law of cement slurry under complex conditions in the well. SUMMARY

[0004] In view of the shortcomings of the above prior art, the purpose of the present application is to provide a cement slurry loss dynamic prediction method under a long slant straight well section, which can more accurately predict the bottom hole effective pressure during the waiting period loss of cement slurry under a long slant straight well section on the basis of considering the tail pipe eccentricity, well temperature and pressure, provide theoretical guidance for accurate application of annulus compensation pressure during the waiting period, and has important significance for preventing annulus channeling.

[0005] To achieve the above-mentioned purpose and other related purposes, the present application provides a cement slurry loss dynamic prediction method under a long slant straight well section, which comprises the following steps:

[0006] calculating the bottom-hole effective pressure P of the cement slurry during weight loss b ; the calculation formula of the bottom-hole effective pressure P of the cement slurry is P = P0+P1; wherein P0 is the liquid column pressure at the top end of the cement slurry; and P1 is the effective pressure of the cement slurry b b

[0007] The calculation of the effective pressure P1 of the cement slurry includes: determining the residual pressure P sy of the cement slurry after gelling weight loss on the basis of considering the eccentricity of the tail pipe and the downhole temperature and pressure, wherein the residual pressure P sy of the cement slurry after gelling weight loss is:

[0008]

[0009] In the formula, ρ cem is the density of the cement slurry;

[0010] g is the acceleration of gravity;

[0011] β is the inclination angle of the long deviated well section;

[0012] n is the number of spans obtained by splitting the tail pipe at each stabilizer when the tail pipe is regarded as a continuous beam;

[0013] L i is the length of the i-th span;

[0014] y i (x) is the total deflection of the tail pipe at the i-th span;

[0015] x is the moment distance of each span;

[0016] T i is the temperature of the cement slurry at the i-th span;

[0017] P i is the pressure of the cement slurry at the i-th span;

[0018] Q(T i , P i , t) is the cumulative heat release of the cement slurry at temperature T i , pressure P i , and time t;

[0019] Q max is the maximum heat release of the cement slurry;

[0020] τ ∞ is the static gel strength limit value of the cement slurry;

[0021] D sw is the outer diameter of the stabilizer;

[0022] D​​co This refers to the outer diameter of the tailpipe.

[0023] Preferably, the residual pressure P after the cement slurry gels and loses weight is... sy The methods for obtaining it include:

[0024] The tailpipe with multiple stabilizers in the long inclined vertical well section is regarded as a multi-support continuous beam, and the total deflection y of the tailpipe at each span of the beam is determined according to the longitudinal and transverse bending beam theory. i (x);

[0025] Stress analysis was performed on the cement grout micro-element to determine the rate of change of residual pressure after the cement grout 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:

[0026]

[0027] In the formula: ΔP is the pressure drop of the cement slurry micro-element in the wellbore direction;

[0028] ΔH is the length of the cement slurry micro-element in the wellbore direction;

[0029] τ is the static cementitious strength of the cement paste, which satisfies...

[0030] Calculate the residual pressure P after cement grout sets and loses weight. sy The residual pressure P after the cement slurry gels and loses weight sy Determined by the following formula:

[0031]

[0032] Preferably, the calculation of the effective pressure P1 of the cement slurry includes determining the pressure loss ΔP due to water loss in the cement slurry. fl The water loss pressure ΔP of the cement slurry fl The calculation formula is:

[0033]

[0034] In the formula, P i The pressure of the cement grout at the i-th span;

[0035] P pro This represents formation pressure, obtained through actual drilling data.

[0036] ΔP r For reference pressure difference;

[0037] C cem The compression coefficient of cement paste is taken as 2.85 × 10⁻⁶. -5 MPa -1 ;

[0038] E is the activation energy of the cement paste;

[0039] R is the gas constant;

[0040] T r is the reference temperature;

[0041] T i is the temperature of the cement paste at the i-th span;

[0042] V FLmax (T r , ΔP r ) is the maximum water loss per unit volume of cement paste at the reference temperature T r and the reference pressure difference ΔP r ;

[0043] b is the first fitting parameter.

[0044] Preferably, the calculation of the effective pressure P1of the cement paste comprises determining the shrinkage pressure loss ΔP chsh of the cement paste; the calculation formula of the shrinkage pressure loss ΔP chsh of the cement paste is:

[0045]

[0046] wherein K r is the second fitting parameter;

[0047] E is the activation energy of the cement paste;

[0048] R is the gas constant;

[0049] T r is the reference temperature;

[0050] P r is the reference pressure;

[0051] T i is the temperature of the cement paste at the i-th span;

[0052] c r is the third fitting parameter;

[0053] ΔV is the activation volume;

[0054] t is the time;

[0055] is the water-cement ratio;

[0056] C cem is the compressibility of the cement paste, taken as 2.85 x 10 -5 MPa -1 .

[0057] Preferably, the limiting value τ of the static adhesive strength of the cement grout is... ∞ The method for determining it is as follows:

[0058] At reference temperature T r Reference pressure P r An isothermal exothermic test of cement slurry was conducted to determine the cumulative heat release Q(T) of the cement slurry at a preset time t0. r ,P r The maximum heat release of cement slurry (t0) and Q max ;

[0059] pass Determine the ultimate static cementitious strength τ of cement grout ∞ ;wherein, τ(T) r ,P r ,t0) represents the cement slurry at the reference temperature T r Reference pressure P r The static cementitious strength of the cement slurry at the preset time t0.

[0060] Preferably, the τ(T) r ,P r ,t0) is determined in the following way:

[0061] At reference temperature T r Reference pressure P r Rheological tests were conducted on cement slurry samples to determine the shear stress τ of the cement slurry samples at different shear rates γ at a preset time t0. q To obtain multiple sets (γ, τ) q );

[0062] Using Bingham rheological model equation τ q =τ y +γ×η p For multiple groups (γ, τ) q The fitting was performed to obtain the cement slurry at the reference temperature T. r Reference pressure P r Yield stress τ y The yield stress τ y That is, the cement slurry at the reference temperature T r Reference pressure P r The static cementitious strength τ(T) of the cement paste at the preset time t0 r ,P r ,t0); where η p It is a plastic viscosity.

[0063] Preferably, the first fitting parameter b and the unit volume of cement slurry at a reference temperature T r Compared with the reference pressure difference ΔP r Maximum water loss VFLmax (T r ,ΔP r The method for determining ) is as follows;

[0064] At reference temperature T r Compared with the reference pressure difference ΔP r Static filtration loss tests were conducted on a unit volume of cement slurry to obtain multiple sets of filtration loss test data (t, V). FL (T r ,ΔP r ,t)), where V FL (T r ,ΔP r ,t) represents the volume of cement slurry per unit volume at a reference temperature T r Reference pressure difference ΔP r The cumulative water loss at time t;

[0065] Using the first fitting equation V FL (T r ,ΔP r ,t)=V FLmax (T r ,ΔP r )×(1-e -bt ) for multiple filtration loss test data sets (t, V FL (T r ,ΔP r The fitting process is performed to obtain the first fitting parameter b and the unit volume of cement slurry at the reference temperature T. r Compared with the reference pressure difference ΔP r Maximum water loss V FLmax (T r ,ΔP r ).

[0066] Preferably, the method for determining the activation energy E of cement slurry is as follows:

[0067] 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 reference time t were recorded. r The cumulative water loss V FL (T,ΔP,t r ), to obtain multiple sets (T, V) FL (T,ΔP,t r ));

[0068] Using the second fitting equation For multiple groups (T, V) FL (T,ΔP,t r The activation energy E of the cement slurry was obtained by fitting the data.

[0069] Preferably, the activation volume ΔV is determined as follows:

[0070] Multiple cement slurry samples were subjected to isothermal exothermic tests at the same temperature but different pressures. The test temperature T, the test pressure P of each cement slurry sample, and the cumulative heat release Q reaching the reference value were recorded. r At time t, multiple sets of (P, t) are obtained;

[0071] The cumulative heat release Q of any cement slurry sample is reached. r Time t as equivalent age t e The sample pressure P of the corresponding cement slurry sample is taken as the equivalent pressure P. e Then, the multiple sets of (P, t) are transformed into multiple sets of

[0072] Using the third fitting equation For multiple groups The activation volume ΔV is obtained by fitting the data.

[0073] Preferably, the second fitting parameter K r and the third fitting parameter c r The method for determining it is as follows;

[0074] At reference temperature T r Reference pressure P r An isothermal exothermic test was conducted on cement slurry to obtain multiple sets of exothermic test data (t, Q(T)). r ,P r ,t));

[0075] Using the fourth fitting equation InQ(T) r ,P r ,t)=InK r +c r ×Int represents multiple sets of exothermic experimental data (t, Q(T)). r ,P r Fitting the data using the given parameters ,t) yields the second fitting parameter K. r and the third fitting parameter c r .

[0076] As described above, the method for dynamic prediction of cement slurry weight loss in long inclined vertical well sections of the present invention has the following beneficial effects:

[0077] The method for dynamic prediction of cement slurry weight loss in long inclined vertical well sections of the present invention calculates the residual pressure P after cement slurry gelation weight loss. sy The design fully considered the effects of tailpipe eccentricity, well temperature at different depths, and well pressure, ensuring that the residual pressure P after the cement slurry gels and loses weight is minimized. syThe calculation is more consistent with the cement slurry gel loss characteristics under the complex conditions of downhole, effectively improving the accuracy of the cement slurry loss dynamic prediction; in addition, when the cement slurry loss dynamic prediction is carried out, the pressure loss caused by the cement slurry loss and hydration is taken into account, further improving the accuracy of the cement slurry loss dynamic prediction, providing theoretical guidance for the accurate application of annular compensation pressure during the cement setting process, and having important significance for preventing annular channeling. BRIEF DESCRIPTION OF DRAWINGS

[0078] Figure 1 The remaining pressure P of the cement slurry after gel loss sy The calculation flowchart.

[0079] Figure 2 The schematic diagram of the equivalent multi-pivot continuous beam of the tailpipe combination at the long and inclined straight well section.

[0080] Figure 3 The stress analysis diagram of the first span beam.

[0081] Figure 4 The stress analysis diagram of any span beam except the first span beam.

[0082] Figure 5 The stress analysis diagram of the cement slurry microelement.

[0083] Figure 6 The fitting straight line diagram obtained by using the second fitting equation.

[0084] Figure 7 The fitting straight line diagram obtained by using the third fitting equation.

[0085] Figure 8 The fitting straight line diagram obtained by using the fourth fitting equation. DETAILED DESCRIPTION

[0086] The following illustrates the embodiments of the present application by specific examples, and those skilled in the art can easily understand other advantages and effects of the present application from the content disclosed in the specification.

[0087] Please refer to Figures 1 to 8It is to be understood that the structures, proportions, sizes, etc. shown in the drawings accompanying the present specification are merely intended to cooperate with the content disclosed in the present specification for the understanding and reading of those skilled in the art, and are not intended to limit the defined conditions under which the present application can be implemented, and therefore do not have technical significance. Any modification of the structure, change of the proportional relationship, or adjustment of the size, without affecting the effects and purposes that can be achieved by the present application, should still fall within the scope of the technology disclosed by the present application.

[0088] Embodiment one

[0089] The embodiment of the present application provides a cement slurry weight loss dynamic prediction method under a long deviated straight well section, and the method comprises the following steps:

[0090] calculating the bottom hole effective pressure P b during the cement slurry weight loss process b , which is determined by the liquid column pressure P0 at the top of the cement slurry and the effective pressure P1 of the cement slurry, and satisfies P b =P0+P1(1); wherein the liquid column pressure P0 at the top of the cement slurry is a known value, which satisfies P0=ρ0gH0; wherein ρ0 is the drilling fluid density; H0 is the cement return depth, which can be measured and obtained; and the effective pressure P1 of the cement slurry is the residual pressure P sy of the cement slurry after considering the eccentricity of the tail pipe and the downhole temperature and pressure.

[0091] Specifically, the determination method of the residual pressure P sy of the cement slurry after the cement slurry weight loss is as shown in Figure 1 , which comprises

[0092] A1, the tail pipe with multiple stabilizers at the long deviated 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;

[0093] In the present application, the multiple stabilizers comprise a tail pipe hanger at the top of the tail pipe and each centralizer which is spaced and sleeved on the tail pipe, and the centralizer of the tail pipe at the long deviated straight well section preferably adopts a rigid centralizer; the tail pipe is suspended at the long deviated straight well section of the extended reach well through the tail pipe hanger at the top of the tail pipe.

[0094] Because the tail pipe will be longitudinally and transversely bent to cause the tail pipe to be eccentrically arranged relative to the wellbore after the tail pipe is lowered to the bottom of the well, the eccentrically arranged tail pipe will cause the generation of the eccentric annular space gap, and the weightlessness velocity at the wide gap of the eccentric annular space gap is different from that at the narrow gap. Therefore, the accuracy of the weightlessness pressure prediction can be effectively improved by considering the tail pipe eccentricity in the weightlessness pressure prediction.

[0095] Based on this, when the weightlessness pressure prediction is performed by considering the tail pipe eccentricity, the narrow annular space gap needs to be determined first, and the narrow annular space gap is closely related to the deformation of the tail pipe. When the deformation of the tail pipe is obtained, the tail pipe with n stabilizers can be regarded as a multi-joint continuous beam subjected to longitudinal and transverse bending, and the stabilizers are regarded as supports. The structure of the multi-joint continuous beam is shown in Figure 2 , which is divided at each joint (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.

[0096] By using the longitudinal and transverse beam bending theory, the total deflection y i (x) and the total rotation θ i (x) of each span beam can be obtained. 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 .

[0097] As shown in Figure 3 , the first span beam is a cantilever beam, and the stress analysis of the first span beam can obtain formula (2).

[0098]

[0099] Wherein, N1 is the support reaction force at the first stabilizer;

[0100] q is the unit length floating weight of the tail pipe.

[0101] L1 is the length of the first span beam;

[0102] β is the inclination angle of the long and inclined well section;

[0103] T1 is the axial tension at the first stabilizer;

[0104] f is the friction coefficient between the stabilizer and the well wall.

[0105] The moment at x can be obtained by formula (3):

[0106]

[0107] Wherein, M1 is the bending moment at the first stabilizer;

[0108] x is the x-axis distance from the moment taking position to the first stabilizer.

[0109] Based on the approximate differential equation of the torsion curve y"=M(x) / EI(4), formula (3) is transformed into formula (5).

[0110]

[0111] Where E is the elastic modulus of the tailpipe;

[0112] I is the moment of inertia of the tailpipe, which satisfies Among them, D co D ci These are the outer diameter and inner diameter of the tailpipe, respectively.

[0113] Since formula (5) is a second-order non-homogeneous linear differential equation with constant coefficients, its integral solution yields formula (6).

[0114]

[0115] Taking the first derivative of formula (6) yields formula (7).

[0116]

[0117] Taking the first derivative of formula (7) yields formula (8).

[0118]

[0119] From the boundary conditions: y1(0)=0, y1"(L1)=0, we can solve for:

[0120]

[0121] Will Substituting k1=2u1 / L1 into equations (6) and (7), we can obtain the total deflection y1(x) and rotation angle θ1(x) of the first span beam.

[0122] Since all beams except the first span are simply supported, the force analysis diagrams for the remaining beams (i.e., beams i = 2, 3, ..., n) are as follows: Figure 4 As shown. By performing a force analysis, we can obtain formula (9):

[0123]

[0124] Where, N i N i-1 These are the support reactions at the i-th and (i-1)-th stabilizers, respectively;

[0125] T i T i-1axial tension at the i-th and i-1-th stabilizer, respectively;

[0126] q is the unit length buoyant weight of the tail pipe.

[0127] L i is the length of the i-th span beam;

[0128] β is the inclination angle of the long slanting straight well section;

[0129] f is the friction coefficient between the stabilizer and the well wall.

[0130] For the convenience of calculation, the force of the i-th span beam (i = 2, 3, …, n) can be decomposed into the following three combinations: the self weight and the axial tension, the right end bending moment and the axial tension, and the left end bending moment and the axial tension. The deflection and the rotation angle of the i-th span beam (i = 2, 3, …, n) under the action of different combined forces are respectively solved, and then the total deflection y i (x) and the total rotation angle θ i (x) of the i-th span beam (i = 2, 3, …, n) are obtained by linear superposition. i (x) is formula (10):

[0131]

[0132] In the formula, L i is the length of the i-th span beam, i is a positive integer, and i = 2, 3, …, n;

[0133] q is the unit length buoyant weight of the tail pipe.

[0134] β is the inclination angle of the long slanting straight well section.

[0135] E is the elastic modulus of the tail pipe.

[0136] I is the moment of inertia of the tail pipe, and satisfies where D co and D ci are the outer diameter and the inner diameter of the tail pipe, respectively.

[0137] u i is the stabilization parameter of the i-th span beam, u i = k i L i / 2, and where T i is the axial tension at the i-th stabilizer.

[0138] M i-1 and M i are the bending moments at the i-1-th stabilizer and the i-th stabilizer, respectively.

[0139] It can be understood that the unit length floating weight q of the tail pipe can be calculated by using various existing casing line floating weight methods such as domestic buoyancy coefficient method and foreign buoyancy coefficient method, and the unit length floating weight q of the tail pipe in the embodiment is preferably calculated by using the foreign buoyancy coefficient method, at this time, the calculation formula of the unit length floating weight q of the tail pipe is formula (11):

[0140]

[0141] 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 the tail pipe outer diameter respectively.

[0142] The total angle θ i of the i-th span beam (i = 2, 3, …, n) is formula (12), which can be obtained by first-order derivation of formula (10), and formula (12) is:

[0143]

[0144] Since the continuous beam has equal angles at both sides of each support point, θ i (L i ) = - θ i+1 (0) is satisfied, wherein i is a positive integer, and i = 1, 2, …, n-1; in addition, since the tail pipe is small elastic deformation, the angle at the stabilizer is very small, and thus the angle at the tail pipe hanger (i.e. the last stabilizer) can be calculated as 0, at this time, M n = 0 is satisfied; on this basis, the bending moment equation group is established, and the bending moment equation group is formula (13):

[0145]

[0146] The bending moment equation group of formula (13) is solved by using a solving software such as VB software, and thus the values of M1, M2, …, M n are determined, and thus the total deflection y i (x) of the entire tail pipe at each span beam is determined, wherein i is a positive integer, and i = 2, 3, …, n.

[0147] A2, stress analysis of the cement slurry microelement is performed 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):

[0148]

[0149] wherein ΔP is the pressure drop of the cement slurry microelement in the wellbore direction;

[0150] ΔH is the length of the cement slurry microelement in the wellbore direction;

[0151] ρ cem is the density of the cement slurry;

[0152] g is the acceleration of gravity;

[0153] β is the inclination angle of the long deviated well section;

[0154] τ is the static gel strength of the cement slurry;

[0155] D sw is the outer diameter of the stabilizer;

[0156] D co is the outer diameter of the tail pipe;

[0157] y i (x) is the total deflection of the tail pipe at the ith span, i is a positive integer, and i = 2, 3, …, n.

[0158] Specifically, the residual pressure change rate of the cement slurry after gel loss under each span is determined in the following manner:

[0159] 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. By analyzing the force of the cement slurry microelement, formula (15) can be obtained.

[0160] (P2S-P1S)cosβ=mg-2τcosβΔH=ρ cem gSΔH-2τcosβΔH (15) wherein P1 and P2 are the forces acting on the upper and lower ends of the microelement cement slurry;

[0161] S is the narrow edge annular space gap,

[0162] Substitute ΔP = P2-P1 into formula (15) and rearrange to obtain formula (14).

[0163] A3, calculating the residual pressure P of the cement slurry after gel loss sy , the residual pressure P of the cement slurry after gel loss sy is determined by formula (16):

[0164]

[0165] Since the static gel strength τ of the cement slurry is affected by temperature, pressure and time, the relationship between the static gel strength τ(T, P, t) of the cement slurry and the cumulative heat release Q(T, P, t) at any temperature T, any pressure P and any time t can be determined by the hydration degree equation; the hydration degree equation is shown in formula (17).

[0166]

[0167] In the formula, α(T, P, t) is the hydration degree of the cement slurry at any temperature T, any pressure P and any time t;

[0168] Q max is the maximum heat release of the cement slurry;

[0169] τ ∞ is the limit value of the static gel strength of the cement slurry.

[0170] Since the wellbore has different well temperatures and well pressures at different depths, in order to improve the calculation accuracy of the residual pressure P sy of the cement slurry after gelation weight loss, formula (16) can be optimized based on formula (17) to optimize the calculation formula of the residual pressure P sy of the cement slurry after gelation weight loss on the basis of considering the changes of well temperature and well pressure, and the optimized calculation formula is formula (18).

[0171]

[0172] In the formula, T i is the temperature of the cement slurry at the i-th span beam;

[0173] P i is the pressure of the cement slurry at the i-th span beam;

[0174] Q(T i , P i , t) is the cumulative heat release of the cement slurry at temperature T i , pressure P i and time t.

[0175] The limit value τ ∞ of the static gel strength of the cement slurry can be determined by the following method:

[0176] 1) Perform an isothermal heat release test of the cement slurry at a reference temperature T r and a reference pressure P r to determine the cumulative heat release Q(T r , P r , t0) of the cement slurry at a preset time t0 and the maximum heat release Q max of the cement slurry; the reference temperature T r and the reference pressure P rYou can determine this yourself; generally, the reference temperature T is... r At room temperature (293K), the reference pressure is P. r At atmospheric pressure (i.e., 0.1 MPa);

[0177] 2) Through Determine the ultimate static cementitious strength τ of cement grout ∞ ;wherein, τ(T) r ,P r ,t0) represents the cement slurry at the reference temperature T r Reference pressure P r The static cementitious strength of the cement slurry at the preset time t0.

[0178] Wherein, τ(T) r ,P r The determination of t0) can be made in ways including but not limited to the following two methods:

[0179] Method 1: Directly measure the cement paste at the reference temperature T using a static cementitious strength analyzer. r Reference pressure P r The static cementitious strength of the cement slurry at the preset time t0.

[0180] Method 2: First at the reference temperature T r Reference pressure P r Rheological tests were conducted on cement slurry samples to determine the shear stress τ of the cement slurry samples at different shear rates γ at a preset time t0. p To obtain multiple sets (γ, τ) p Then, using the Bingham rheological model equation τ q =τ y +γ×η p For multiple groups (γ, τ) p The fitting was performed to obtain the cement slurry at the reference temperature T. r Reference pressure P r Yield stress τ y The yield stress τ y That is, the cement slurry at the reference temperature T r Reference pressure P r The static cementitious strength τ(T) of the cement paste at the preset time t0 r ,P r ,t0); where η p It is a plastic viscosity.

[0181] Furthermore, in order to reduce Q(T) i P i The calculation difficulty of t) can be reduced by determining the cumulative heat release Q(T, P, t) of cement slurry at any temperature T, any pressure P, and any time t based on the principle of equivalent age, which satisfies formula (19).

[0182]

[0183] wherein K r is a second fitting parameter;

[0184] E is the activation energy of the cement slurry;

[0185] R is the gas constant, taking 8.314 J / (mol·K);

[0186] T r is a reference temperature;

[0187] c r is a third fitting parameter;

[0188] ΔV is the activation volume;

[0189] t is the time;

[0190] is the water-cement ratio.

[0191] Substituting equation (19) into equation (18), the calculation formula of the residual pressure P sy of the cement slurry after the cementation weight loss is updated to equation (20).

[0192]

[0193] wherein the determination method of the activation energy E of the cement slurry is as follows:

[0194] 1) Perform the static filtration test of the cement slurry of multiple unit volumes 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 cumulative water loss V r of each cement slurry sample at the reference time t FL (T,ΔP,t r ), to obtain multiple groups of (T, V FL (T,ΔP,t r ));

[0195] 2) Use the second fitting equation to fit the multiple groups of (T, V FL (T,ΔP,t r )), to obtain a fitting line; wherein ΔP r is a reference pressure difference, generally 3 MPa; V FLmax (T r ,ΔP r ) is the cumulative water loss of the cement slurry at the reference temperature T r and the reference pressure difference ΔP rThe maximum water loss per unit volume of cement paste is a constant; b is a first fitting parameter, which is a constant. According to the second fitting equation, InV FL (T, ΔP, t r ) is linearly related to , thus, the obtained fitting line is a fitting straight line as shown in Figure 6 , and the value of can be determined by the slope of the fitting straight line; since the gas constant R is known, the value of the cement paste activation energy E can be determined.

[0196] The determination method of the activation volume ΔV is as follows:

[0197] 1) Perform cement paste isothermal exothermic tests on multiple cement paste samples under the same temperature and different pressures, and record the test temperature T, the test pressure P of each cement paste sample, and the time t at which the reference cumulative heat Q r is reached, to obtain multiple groups of (P, t);

[0198] 2) Take the time t at which the reference cumulative heat Q r is reached by any one of the cement paste samples as the equivalent age t e , and take the sample pressure P of the corresponding cement paste sample as the equivalent pressure P e ; then convert the multiple groups of (P, t) into multiple groups of ; the reference cumulative heat Q r is given by the user;

[0199] 3) use the third fitting equation to fit the multiple groups of , to obtain a fitting line; since P e , T and R are all fixed values, is linearly related to P. Thus, the obtained fitting line is a fitting straight line as shown in Figure 7 , and the value of can be determined by the slope of the fitting straight line; since the gas constant R and the test temperature T are known, the value of the activation volume ΔV can be determined.

[0200] The determination method of the second fitting parameter K r and the third fitting parameter c r is as follows:

[0201] 1) Perform a cement paste isothermal exothermic test at a reference temperature T r and a reference pressure P r , to obtain multiple exothermic test data groups (t, Q(T r , P r , t));

[0202] use the fourth fitting equation InQ(T r , Pr ,t)=InK r +c r ×Int represents multiple sets of exothermic experimental data (t, Q(T)). r ,P r Fitting is performed using ,t)) to obtain the fitted line; since InQ(T) r ,P r ,t) is linearly correlated with Int. Therefore, the obtained fitted line is as follows: Figure 8 The third fitting parameter c can be determined by the slope of the fitted line shown. r InK can be determined by fitting the intercept of the straight line. r Thus, K was determined. r The value of .

[0203] Example 2

[0204] The only difference between this embodiment and Embodiment 1 is the method of calculating the effective pressure P1 of the cement slurry.

[0205] In this embodiment, the effective pressure P1 of the cement slurry is the residual pressure P after the cement slurry has gelled and lost weight. sy The water loss pressure ΔP of cement grout fl It is determined that it satisfies P1 = P sy -ΔP fl (21); where P is the residual pressure after the cement slurry gels and loses weight. sy The method for determining the residual pressure P after the cement slurry gels and loses weight in Example 1 is the same as that for the cement slurry gels and loses weight. sy The methods for determining them are completely identical.

[0206] Due to hydration reactions and water loss during the cement slurry setting process, the volume of the cement slurry shrinks; and a closed hydraulic system can be formed between the well wall and the tailpipe. Based on the principle that the volume shrinkage of the cement slurry in a closed hydraulic system causes a decrease in system pressure, the volume shrinkage caused by cement slurry loss and hydration leads to a rapid drop in the hydrostatic pressure of the cement slurry column. Therefore, the pressure loss ΔP caused by the volume shrinkage of the cement slurry is significant. ss satisfy: Where, ΔV ss V is the shrinkage volume of the cement grout; a C represents the total volume of cement slurry. cem The compression coefficient of cement paste is taken as 2.85 × 10⁻⁶. -5 MPa -1 .

[0207] Based on formula (22), the pressure loss ΔP caused by water loss of cement slurry can be determined. fl It satisfies formula (23).

[0208]

[0209] In the formula, ΔV FL_i V represents the volume of water loss from the cement grout at the i-th span of the beam; i V represents the total volume of cement grout at the i-th span of the beam; FL_i (T i ,ΔP i ,t) represents the temperature T of a unit volume of cement slurry at the i-th span of the beam. i Pressure difference ΔP at the i-th span of the beam i The cumulative water loss at time t.

[0210] Among them, the cumulative water loss V per unit volume of cement slurry at any temperature T, any pressure difference ΔP, and any time t. FL (T,ΔP,t) is determined in the following way:

[0211] 1) According to GB / T 19139-2012 "Test Methods for Cement in Oil Wells", at a reference temperature T r and reference pressure difference ΔP r A static filtration loss test was conducted on a unit volume of cement slurry, and the cumulative water loss V of a unit volume of cement slurry at each time point t was recorded. FL For each time t and the corresponding cumulative water loss V FL By performing a fitting operation, the cumulative water loss V per unit volume of cement slurry is obtained. FL The first fitting relationship between (t) and time t is: V FL (t)=V FLmax (T r ,ΔP r )·(1-e -bt (24), where V FLmax (T r ,ΔP r (T is the reference temperature) r Reference pressure difference ΔP r The maximum water loss per unit volume of cement slurry; b is the first fitting parameter; by taking the first derivative of the first fitting equation, the instantaneous water loss rate can be obtained. The calculation formula is:

[0212] 2) If the cement slurry flow is regarded as a steady-state planar radial flow, then the cement slurry seepage velocity v satisfies formula (26).

[0213]

[0214] In the formula, K is the permeability; η is the pressure gradient; r is the radial distance; η is the viscosity of the cement slurry; ΔP is the pressure difference.

[0215] From formula (26), the cement slurry filtration rate v fl (T, ΔP) satisfies formula (27).

[0216]

[0217] wherein v fl (T r , ΔP r ) is the cement slurry filtration rate at the reference temperature T r and the reference pressure difference ΔP r ; η r is the cement slurry viscosity at the reference temperature T r ; and η is the cement slurry viscosity at any temperature T.

[0218] 3) A second relationship between the cement slurry viscosity η and the temperature T at any temperature T is established by the Arrhenius equation, which satisfies formula (28).

[0219]

[0220] wherein η r is the cement slurry viscosity at the reference temperature T r ; and E is the cement slurry activation energy.

[0221] E is the cement slurry activation energy.

[0222] R is the gas constant.

[0223] T and T r are absolute temperature and reference temperature, respectively, in K.

[0224] 4) The cement slurry filtration rate v fl (T, ΔP, t) at any temperature T, any pressure difference ΔP, and any time t is obtained by formula (25), formula (27), and formula (28), which satisfies formula (29).

[0225]

[0226] 5) The integral of formula (29) is obtained, and combined with formula (24), the cumulative filtration volume V FL (T, ΔP, t) of the cement slurry per unit volume at any temperature T, any pressure difference ΔP, and any time t is obtained, which satisfies formula (30).

[0227]

[0228] Based on formula (30), the filtration pressure loss ΔP fl caused by the cement slurry filtration can be converted from formula (23) to formula (31).

[0229]

[0230] In the formula, P i The pressure of the cement grout at the i-th span;

[0231] P pro This represents formation pressure, obtained through actual drilling data.

[0232] ΔP r The reference pressure difference can be determined as needed, and is generally 3 MPa.

[0233] C cem —The compressibility coefficient of cement paste is taken as 2.85×10. -5 MPa -1 ;

[0234] E is the activation energy of cement slurry, and its determination method is the same as that used in Example 1.

[0235] R is the gas constant;

[0236] T r For reference temperature;

[0237] T i The temperature of the cement grout at the i-th span of the beam;

[0238] V FLmax (T r ,ΔP r (T is the reference temperature) r Compared with the reference pressure difference ΔP r The maximum water loss per unit volume of cement slurry.

[0239] Example 3

[0240] The only difference between this embodiment and Embodiment 1 is the method of calculating the effective pressure P1 of the cement slurry.

[0241] In this embodiment, the effective pressure P1 of the cement slurry is the residual pressure P after the cement slurry has gelled and lost weight. sy Shrinkage pressure loss ΔP caused by cement slurry hydration chsh It is determined that it satisfies P1 = P sy -ΔP chsh (32); where P is the residual pressure after the cement slurry has gelled and lost weight. sy The method for determining the residual pressure P after the cement slurry gels and loses weight in Example 1 is the same as that for the cement slurry gels and loses weight. sy The methods for determining them are completely identical.

[0242] The volume of the cement slurry will shrink due to the hydration reaction and filtration loss during the setting process of the cement slurry, 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 slurry in the closed hydraulic system causes the pressure of the system to decrease, the volume shrinkage caused by the loss and hydration of the cement slurry will cause the static liquid column pressure of the cement slurry to decrease rapidly. Therefore, the pressure loss ΔP ss of the cement slurry caused by the volume shrinkage of the cement slurry satisfies formula (22). Where ΔV ss is the shrinkage volume of the cement slurry; V a is the total volume of the cement slurry; C cem is the compressibility of the cement slurry, which is 2.85×10 -5 MPa -1 .

[0243] Based on formula (22), the shrinkage pressure loss ΔP chsh satisfying formula (32) can be determined by the hydration of the cement slurry.

[0244]

[0245] Where ΔV chsh_i is the shrinkage volume of the cement slurry at the ith span; V i is the total volume of the cement slurry at the ith span; v chsh_i (α) is the hydration volume shrinkage rate of the cement slurry at the ith span at an arbitrary hydration degree α; α(T i ,P i ,t) is the hydration degree of the cement slurry at the ith span at the temperature T i at the ith span, the pressure P i at the ith span, and the time t; is the water-cement ratio.

[0246] Where the hydration degree α(T, P, t) of the cement slurry at an arbitrary temperature T, an arbitrary pressure P, and an arbitrary time t is determined in the following manner:

[0247] 1) Based on the equivalent age principle and the scaling factor model, the hydration degree α(T, P, t) of the cement slurry at an arbitrary temperature T, an arbitrary pressure P, and an arbitrary time t is obtained, which satisfies formula (33).

[0248]

[0249] Where α(T r ,P r ,t) is the hydration degree of the cement slurry at the reference temperature T r , the reference pressure P r , and the equivalent time t e .

[0250] k(T, P) is the hydration reaction rate of the cement paste at any temperature T and any pressure P;

[0251] k(T r , P r ) is the hydration reaction rate of the cement paste at the reference temperature T r and the reference pressure P r ;

[0252] E is the activation energy of the cement paste, which is determined in the same way as the activation energy E of the cement paste in Example 1.

[0253] ΔV is the activation volume, which is determined in the same way as the activation volume ΔV in Example 1.

[0254] R is the gas constant.

[0255] 2) A mathematical fitting model of hydration heat is established based on a power function, and the mathematical fitting model of hydration heat is (34); wherein K r is a second fitting parameter; c r is a third fitting parameter.

[0256] Specifically, the determination method of the second fitting parameter K r and the third fitting parameter c r is:

[0257] a) converting formula (34) into a linear function, and the linear function is a fourth fitting equation: InQ(T r , P r , t) = InK r + c r x Int formula (35);

[0258] b) performing an isothermal heat release test of the cement paste at the reference temperature T r and the reference pressure P r , and recording the cumulative heat release Q(T r , P r , t) of the cement paste at each time t; using the fourth fitting equation to fit each time t and the corresponding cumulative heat release Q(T r , P r , t), the second fitting parameter K r and the third fitting parameter c r are obtained.

[0259] 3) Based on formula (33) and formula (34), the cumulative heat release Q(T, P, t) of the cement paste at any temperature T, any pressure P and any time t is determined, which satisfies formula (35).

[0260]

[0261] 5) Based on formula (17) and formula (35), the hydration degree α of the cement slurry at any temperature T, any pressure P and any time t is determined T,P (t) which satisfies formula (36).

[0262]

[0263] Based on formula (36), the shrinkage pressure loss ΔP caused by hydration of the cement slurry chsh can be converted into formula (37) by formula (32).

[0264]

[0265] It can be understood that the hydration heat mathematical fitting model can also be established based on other common thermodynamic curve fitting functions such as hyperbolic function, exponential function, logarithmic function, etc.

[0266] Example Four

[0267] The difference between this embodiment and example one is only in the calculation method of the effective pressure P1 of the cement slurry.

[0268] In this embodiment, the effective pressure P1 of the cement slurry is determined by the residual pressure P sy of the cement slurry after cementation weight loss, the water loss pressure loss ΔP fl of the cement slurry and the shrinkage pressure loss ΔP chsh caused by hydration of the cement slurry, which satisfies P1=P sy -ΔP fl -ΔP chsh (38); wherein the determination method of the residual pressure P sy of the cement slurry after cementation weight loss is completely consistent with the determination method of the residual pressure P sy of the cement slurry after cementation weight loss in example one; the determination method of the water loss pressure loss ΔP fl of the cement slurry is completely consistent with the determination method of the water loss pressure loss ΔP fl of the cement slurry in example two; the determination method of the shrinkage pressure loss ΔP chsh caused by hydration of the cement slurry is completely consistent with the determination method of the shrinkage pressure loss ΔP chsh caused by hydration of the cement slurry in example three.

[0269] In summary, the residual pressure P syThe dynamic change rule basically accords with the actual weight loss characteristics of the cement slurry under complex conditions in the well, effectively ensures the accuracy of the dynamic prediction of the cement slurry weight loss, provides a theoretical guidance for the accurate application of the annular compensation pressure in the waiting-on-cement process, and has important significance for preventing the annular channeling.

[0270] 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 dynamic prediction of cement slurry weight loss in long inclined vertical well sections, characterized in that, The method includes: Calculate the effective bottom-hole pressure P during the weight loss process of cement slurry. b The effective pressure P at the bottom of the well b The calculation formula is: P b =P0+P1; where P0 is the liquid column pressure at the top of the cement slurry; P1 is the effective pressure of the cement slurry; The calculation of the effective pressure P1 of the cement slurry includes: determining the residual pressure P after the cement slurry gels and loses weight, taking into account tailpipe eccentricity and downhole temperature and pressure. sy The residual pressure P after the cement slurry gels and loses weight sy for: In the formula, ρ cem The density of the cement paste; g is the acceleration due to gravity; β is the inclination angle of the long inclined vertical well section; n is the number of span beams obtained by splitting the tailpipe at each stabilizer when the tailpipe is regarded as a continuous beam. L i Let be the length of the i-th span of the beam; y i (x) represents the total deflection of the tailpipe at the i-th span beam; x represents the moment distance of each span of the beam; T i The temperature of the cement grout at the i-th span of the beam; P i The pressure of the cement grout at the i-th span; Q(T i P i ,t) represents the cement slurry at temperature T i Pressure P i The cumulative heat released at time t; Q max This represents the maximum heat release of the cement slurry. τ ∞ This refers to the ultimate static strength of the cement grout. D sw The outer diameter of the stabilizer; D co This refers to the outer diameter of the tailpipe.

2. The method for dynamic prediction of cement slurry weight loss in a long inclined vertical well section according to claim 1, characterized in that, The residual pressure P after the cement slurry gels and loses weight sy The methods for obtaining it include: The tailpipe with multiple stabilizers in the long inclined vertical well section is regarded as a multi-support continuous beam, and the total deflection y of the tailpipe at each span of the beam is determined according to the longitudinal and transverse bending beam theory. i (x); Stress analysis was performed on the cement grout micro-element to determine the rate of change of residual pressure after the cement grout 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; τ is the static cementitious strength of the cement paste, which satisfies... Calculate the residual pressure P after cement grout sets and loses weight. sy The residual pressure P after the cement slurry gels and loses weight sy Determined by the following formula:

3. The method for dynamic prediction of cement slurry weight loss in a long inclined vertical well section according to claim 1, characterized in that, The calculation of the effective pressure P1 of the cement slurry includes determining the pressure loss ΔP due to water loss in the cement slurry. fl The water loss pressure ΔP of the cement slurry fl The calculation formula is: In the formula, P i The pressure of the cement grout at the i-th span; P pro This represents formation pressure, obtained through actual drilling data. ΔP r For reference pressure difference; C cem The compression coefficient of cement paste is taken as 2.85 × 10⁻⁶. -5 MPa -1 ; E represents the activation energy of the cement slurry. R is the gas constant; T r For reference temperature; T i The temperature of the cement grout at the i-th span of the beam; V FLmax (T r ,ΔP r () represents the unit volume of cement slurry at a reference temperature T r Compared with the reference pressure difference ΔP r Maximum water loss; b is the first fitting parameter.

4. A method for dynamic prediction of cement slurry weight loss in a long inclined vertical well section according to any one of claims 1 to 3, characterized in that, The calculation of the effective pressure P1 of the cement slurry includes determining the shrinkage pressure loss ΔP of the cement slurry. chsh The shrinkage pressure loss ΔP of the cement slurry chsh The calculation formula is: In the formula, K r These are the second fitting parameters; E represents the activation energy of the cement slurry. R is the gas constant; T r For reference temperature; P r For reference pressure; T i The temperature of the cement grout at the i-th span of the beam; c r The third fitting parameter; ΔV is the activation volume; t is time; Water-cement ratio; C cem —The compressibility coefficient of cement paste is taken as 2.85×10. -5 MPa -1 .

5. The method for dynamic prediction of cement slurry weight loss in a long inclined vertical well section according to claim 1, characterized in that, The ultimate limit value τ of the static adhesive strength of the cement grout ∞ The method for determining it is as follows: At reference temperature T r Reference pressure P r An isothermal exothermic test of cement slurry was conducted to determine the cumulative heat release Q(T) of the cement slurry at a preset time t0. r ,P r The maximum heat release of cement slurry (t0) and Q max ; pass Determine the ultimate static cementitious strength τ of cement grout ∞ ;wherein, τ(T) r ,P r ,t0) represents the cement slurry at the reference temperature T r Reference pressure P r The static cementitious strength of the cement slurry at the preset time t0.

6. The method for dynamic prediction of cement slurry weight loss in a long inclined vertical well section according to claim 5, characterized in that, The τ(T) r ,P r ,t0) is determined in the following way: At reference temperature T r Reference pressure P r Rheological tests were conducted on cement slurry samples to determine the shear stress τ of the cement slurry samples at different shear rates γ at a preset time t0. q To obtain multiple sets (γ, τ) q ); Using Bingham rheological model equation τ q =τ y +γ×η p For multiple groups (γ, τ) q The fitting was performed to obtain the cement slurry at the reference temperature T. r Reference pressure P r Yield stress τ y The yield stress τ y That is, the cement slurry at the reference temperature T r Reference pressure P r The static cementitious strength τ(T) of the cement paste at the preset time t0 r ,P r ,t0); where η p It is a plastic viscosity.

7. The method for dynamic prediction of cement slurry weight loss in a long inclined vertical well section according to claim 3, characterized in that, The first fitting parameter b and the unit volume of cement slurry at the reference temperature T r Compared with the reference pressure difference ΔP r Maximum water loss V FLmax (T r ,ΔP r The method for determining ) is as follows; At reference temperature T r Compared with the reference pressure difference ΔP r Static filtration loss tests were conducted on a unit volume of cement slurry to obtain multiple sets of filtration loss test data (t, V). FL (T r ,ΔP r ,t)), where V FL (T r ,ΔP r ,t) represents the volume of cement slurry per unit volume at a reference temperature T r Reference pressure difference ΔP r The cumulative water loss at time t; Using the first fitting equation V FL (T r ,ΔP r ,t)=V FLmax (T r ,ΔP r )×(1-e -bt ) for multiple filtration loss test data sets (t, V FL (T r ,ΔP r The fitting process is performed to obtain the first fitting parameter b and the unit volume of cement slurry at the reference temperature T. r Compared with the reference pressure difference ΔP r Maximum water loss V FLmax (T r ,ΔP r ).

8. The method for dynamic prediction of cement slurry weight loss 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 reference time t were recorded. r The cumulative water loss V FL (T,ΔP,t r ), to obtain multiple sets (T, V) FL (T,ΔP,t r )); Using the second fitting equation For multiple groups (T, V) FL (T,ΔP,t r The activation energy E of the cement slurry was obtained by fitting the data.

9. The method for dynamic prediction of cement slurry weight loss in a long inclined vertical well section according to claim 4, characterized in that, The method for determining the activation volume ΔV is as follows: Multiple cement slurry samples were subjected to isothermal exothermic tests at the same temperature but different pressures. The test temperature T, the test pressure P of each cement slurry sample, and the cumulative heat release Q reaching the reference value were recorded. r At time t, multiple sets of (P, t) are obtained; The cumulative heat release Q of any cement slurry sample is reached. r Time t as equivalent age t e The sample pressure P of the corresponding cement slurry sample is taken as the equivalent pressure P. e Then, the multiple sets of (P, t) are transformed into multiple sets of Using the third fitting equation For multiple groups The activation volume ΔV is obtained by fitting the data.

10. The method for dynamic prediction of cement slurry weight loss in a long inclined vertical well section according to claim 4, characterized in that, Second fitting parameter K r and the third fitting parameter c r The method for determining it is as follows; At reference temperature T r Reference pressure P r An isothermal exothermic test was conducted on cement slurry to obtain multiple sets of exothermic test data (t, Q(T)). r ,P r ,t)); Using the fourth fitting equation InQ(T) r ,P r ,t)=InK r +c r ×Int represents multiple sets of exothermic experimental data (t, Q(T)). r ,P r By fitting the data to the given parameters, we can obtain the second fitting parameter K. r and the third fitting parameter c r .

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