A method for determining transient flow fluctuation pressure of drilling fluid during tripping in high-temperature and high-pressure wells

Abstract

The present invention discloses a method for determining the transient flow fluctuation pressure of drilling fluid during tripping in a high-temperature and high-pressure well, comprising the following steps: S1: establishing a physical model of the transient flow fluctuation pressure in the wellbore during tripping, and establishing hypothetical conditions for calculating the transient flow fluctuation pressure in the wellbore; S2: establishing a physical property equation for drilling fluid under high-temperature and high-pressure conditions; S3: establishing a set of control equations for the transient flow fluctuation pressure in the wellbore taking into account constant steady-state friction and non-constant transient friction based on the laws of conservation of mass, conservation of momentum, and conservation of energy; S4: establishing a set of characteristic line equations based on the set of control equations for the transient flow fluctuation pressure in the wellbore; S5: establishing an initial boundary, and solving the transient flow fluctuation pressure equation in the wellbore in combination with solving the characteristic line equations to obtain the transient flow fluctuation pressure in the wellbore. The present invention can obtain a more realistic transient flow fluctuation pressure of drilling fluid during tripping in a high-temperature and high-pressure well, providing technical support for oil and gas drilling.

Description

Technical Field

[0001] The present invention relates to the technical field of drilling, and in particular to a method for determining the transient flow fluctuation pressure of drilling fluid during tripping of a high-temperature and high-pressure well. Background Art

[0002] The surge pressure during tripping refers to the temporary additional pressure generated when the drilling fluid in the annulus flows due to the speed of the drill string moving up and down in the well. With the frequent occurrence of complex drilling accidents during the transient flow of drilling fluid in high-temperature and high-pressure drilling conditions, the continuous development and improvement of technologies such as the automated control of transient surge pressure and controlled pressure drilling have led to increasingly higher requirements for the transient flow pressure value and its variation law. Therefore, a more accurate transient flow model is urgently needed to accurately and realistically simulate the pressure fluctuations in the wellbore when transient flow actually occurs, so as to meet the requirements of refined drilling operations and pressure control, and ensure the safety of tripping and drilling in high-temperature and high-pressure wells with narrow pressure window formations. Summary of the Invention

[0003] In view of the above problems, the present invention aims to provide a method for determining the transient flow fluctuation pressure of drilling fluid during tripping in a high-temperature and high-pressure well.

[0004] The technical solutions of the present invention are as follows:

[0005] A method for determining transient flow fluctuation pressure of drilling fluid during tripping of a high-temperature and high-pressure well comprises the following steps:

[0006] S1: Establish a physical model of transient flow fluctuation pressure in the wellbore during drilling, and establish the assumptions for calculating the transient flow fluctuation pressure in the wellbore;

[0007] S2: Establish the physical property equation of drilling fluid under high temperature and high pressure conditions;

[0008] S3: Based on the laws of conservation of mass, momentum, and energy, a set of governing equations for transient flow fluctuation pressure in the wellbore is established, taking into account constant steady-state friction and non-constant transient friction;

[0009] S4: establishing a set of equations for solving characteristic lines based on the set of equations for transient flow fluctuation pressure in the wellbore;

[0010] S5: Establishing an initial boundary, solving the transient flow fluctuation pressure equation in the wellbore in combination with the solution of the characteristic line equation group, and obtaining the transient flow fluctuation pressure in the wellbore.

[0011] Preferably, in step S1, the assumptions for calculating the transient flow fluctuation pressure in the wellbore include:

[0012] (1) The formation, wellbore and tubing are all elastic, and the bottom of the well is a rigid body;

[0013] (2) Ignore the influence of cement and formation around the casing on the elasticity of the casing;

[0014] (3) The fluid in the wellbore is compressible;

[0015] (4) Ignoring the effect of drill string eccentricity on fluid flow in the wellbore;

[0016] (5) The fluid in the wellbore flows transiently and is pure liquid drilling fluid;

[0017] (6) Considering wellbore heat transfer, fluid properties are functions of temperature and pressure;

[0018] (7) Consider the non-steady transient friction during transient flow.

[0019] Preferably, in step S2, the physical property equation of the drilling fluid under high temperature and high pressure conditions includes:

[0020] (1) Function of the relationship between drilling fluid density, temperature and pressure

[0021] ρ(T,p)=ρ(T0,p0)·exp(γ1(p-p0)+γ2(T-T0)+γ3(T-T0) 2 ) (1)

[0022] Where: ρ(T, p) is the density of drilling fluid at temperature T and pressure p, kg / m 3 ; ρ(T0, p0) is the density of drilling fluid at temperature T0 and pressure p0, kg / m 3 ; γ1, γ2, γ3 are characteristic coefficients in the drilling fluid density function; p is pressure, MPa; p0 is reference pressure, MPa; T is temperature, °C; T0 is reference temperature, °C;

[0023] (2) a function of the relationship between the rheological parameters of the drilling fluid and temperature and pressure, wherein the rheological parameters include any one or more of yield value, consistency coefficient and flow index;

[0024] The function of the relationship between the yield value of drilling fluid and temperature and pressure is:

[0025] τ0(T,P)=τ0(T0,p0)·exp[η1(T-T0)+η2(p-p0)+η3(T-T0) 2 ] (2)

[0026] The function of the relationship between drilling fluid viscosity coefficient, temperature and pressure is:

[0027] K(T,P)=K(T0,p0)·exp[eta4(T-T0)+eta5(p-p0)+eta6(T-T0) 2] (3)

[0028] The function of the relationship between drilling fluid fluidity index, temperature and pressure is:

[0029] n(T,P)=n(T0,p0)·exp[eta7(T-T0)+eta8(p-p0)+eta9(T-T0) 2 ] (4)

[0030] Where: τ0(T, p) is the yield value of the drilling fluid at temperature T and pressure p, Pa; K(T, p) is the viscosity coefficient of the drilling fluid at temperature T and pressure p, Pa·s n ; n(T, p) is the drilling fluid fluidity index at temperature T and pressure p, dimensionless; τ0(T0, p0) is the drilling fluid yield value at temperature T0 and pressure p0, Pa; K(T0, p0) is the drilling fluid viscosity coefficient at temperature T0 and pressure p0, Pa·s n ; n(T0, p0) is the drilling fluid fluidity index under the conditions of temperature T0 and pressure p0, which is dimensionless; η1, η2, η3, η4, η5, η6, η7, η8, and η9 are all characteristic coefficients in the drilling fluid rheological parameter function.

[0031] Preferably, in step S3, the transient flow fluctuation pressure control equations in the wellbore include:

[0032]

[0033]

[0034]

[0035] in:

[0036]

[0037] Where: h is the wellbore depth, m; ρ is the drilling fluid density, kg / m 3 ; v is flow velocity, m / s; t is time, s; F T is the transient flow friction and pressure gradient in the wellbore, Pa / m; g is the acceleration of gravity, m / s 2 ; θ is the well inclination angle, rad; c is the pressure wave velocity, m / s; T f is the drilling fluid temperature, °C; w is the drilling fluid mass flow rate, kg / s; c p is the specific heat capacity of drilling fluid at constant pressure, J / (kg·℃); L R is the relaxation distance, m -1 ; m is the mass of the fluid per unit length, kg / m; C T is the heat storage coefficient, dimensionless; Tei is the initial formation temperature, °C; φ is a lumped parameter, dimensionless; α is the fluid compressibility, Pa -1 ; β is the wellbore flow channel compression coefficient, Pa -1 .

[0038] As a preference, the drilling fluid temperature T f Calculate using the following formula:

[0039]

[0040] in:

[0041]

[0042]

[0043]

[0044] Where: e is the natural base, dimensionless; L is the well depth, m; g G is the geothermal gradient, ℃ / m; r ti is the wellbore radius, m; U t is the total heat transfer coefficient, W / (m 2 ℃); k e is the formation thermal conductivity, W / (m·℃); T D is the dimensionless temperature and has no dimensions.

[0045] As a preference, the transient flow friction pressure gradient F in the wellbore is T From the constant steady-state friction F S and non-steady transient friction F U The composition is expressed as:

[0046]

[0047] in:

[0048]

[0049] Where: f is the constant steady-state Fanning friction coefficient, dimensionless; D hy is the equivalent diameter, m; k is the attenuation coefficient of non-constant transient friction, dimensionless; sign(v) is the sign function, dimensionless;

[0050] Substituting formula (13) into formula (5), the motion equation in the transient flow fluctuation pressure control equation group in the wellbore becomes:

[0051]

[0052] As an example, in step S4, the characteristic line equations include the forward characteristic line equation C + and the negative characteristic line equation C - ;

[0053] (1) When the sign function sign(v)=1:

[0054] The forward characteristic line equation C + for:

[0055]

[0056] The negative characteristic line equation C - for:

[0057]

[0058] (2) When the sign function sign(v) = -1:

[0059] The forward characteristic line equation C + for:

[0060]

[0061] The negative characteristic line equation C - for:

[0062]

[0063] Preferably, in step S5, the initial boundary includes:

[0064] (1) Initial conditions:

[0065]

[0066] Where: v1(h,0), v2(h,0), v3(h,0) are the flow velocities at each node of the empty wellbore flow channel, annulus flow channel, and inner tube flow channel, respectively, m / s; Q m is the drilling pump flow rate, m 3 / s; A2(h) and A3(h) are the cross-sectional areas of each node of the annular flow channel and the inner tube flow channel, respectively, m 2 ; p1(h,0), p2(h,0), p3(h,0) are the pressures of each node of the empty wellbore flow channel, annulus flow channel and circular pipe flow channel, Pa; F T2 、F T3 are the flow friction and pressure gradients of the annular flow channel and the flow channel in the circular tube, Pa / m; l2 is the initial well depth at the bottom of the drill string, m;

[0067] (2) Boundary conditions:

[0068]

[0069] Where: v N (l1) is the flow velocity at the bottom of the well, m / s; p N (l2) is the pressure at the wellhead node, Pa; N is the flow channel number, dimensionless;

[0070] (3) Intersection point constraints:

[0071] The intersection of the drill string bottom, the annulus, and the empty wellbore is the intersection point. When the drilling pump is turned on, the constraint conditions at the intersection point are:

[0072]

[0073] When the drilling pump is in the off state, the constraint condition at the intersection is:

[0074]

[0075] Where: v1(0,t), v2(0,t), v3(0,t), v s (t) are the flow velocities of the empty wellbore flow channel, annular flow channel, and inner tube flow channel at each moment, as well as the movement speed of the drill string at each moment, m / s; A0, A i A1, A2, and A3 are the cross-sectional areas of the flow channel outside the string, inside the string, empty wellbore, annulus, and inside the circular pipe, respectively. 2 ; p1(0, t), p2(0, t), p3(0, t) are the pressures at each moment in the empty wellbore flow channel, annulus flow channel, and inner tube flow channel, respectively, in Pa; k' is the nozzle discharge coefficient, dimensionless;

[0076] (4) Connection point constraints:

[0077]

[0078] Where: q is the flow channel section number of the connection point, dimensionless; l3 is the distance between the flow channel connection point and the origin, m; A is the flow channel cross-sectional area, m 2 ; ΔA is the difference in cross-sectional area of ​​the flow channel at the connection point, m 2 .

[0079] Preferably, in step S5, when solving the transient flow fluctuation pressure equation in the wellbore, a finite difference method or a finite volume method is used for solving.

[0080] Preferably, when the finite difference method is used for solving:

[0081] First, the finite difference method is used to discretize the well depth and time. The well depth is divided into M1 segments, each with a spatial length of Δh, and the time is divided into M2 segments, each with a time step of Δt, to obtain the characteristic line finite difference grid.

[0082] The characteristic line equation is integrated along the positive and negative characteristic lines on the characteristic line finite difference grid. The solution of the characteristic line equation can be obtained by using the first-order approximation method. The flow velocity and pressure at time i and node j can be obtained by simultaneous solution:

[0083]

[0084]

[0085] in:

[0086]

[0087]

[0088] (1) When the sign function sign(v)=1:

[0089]

[0090]

[0091]

[0092]

[0093] (2) When the sign function sign(v) = -1:

[0094]

[0095]

[0096]

[0097]

[0098] Where: v i,j is the flow velocity at time i and node j, m / s; p i,j is the pressure at node j at time i, Pa; p i-1,j+1 is the pressure at node j+1 at time i-1, Pa; p i-1,j-1 is the pressure at the j-1 node at the i-1 moment, Pa; v i-1,j+1 is the flow velocity at time i-1 and node j+1, m / s; v i-1,j-1 is the flow velocity at time i-1 and node j-1, m / s; k i-1,j+1k is the attenuation coefficient of the non-steady transient friction at the node j+1 at time i-1, dimensionless; i-1,j-1 is the attenuation coefficient of the non-steady transient friction at the i-1 moment and the j-1 node, dimensionless.

[0099] The beneficial effects of the present invention are:

[0100] The present invention considers not only the influence of the physical properties of the drilling fluid on the fluctuating pressure, but also the influence of constant steady-state friction and non-constant transient friction on the fluctuating pressure. The fluctuating pressure model obtained by such coupling can improve the prediction accuracy of the fluctuating pressure, make the prediction results more consistent with the actual working conditions, and ensure the safety of tripping and drilling in the narrow pressure window formation of high-temperature and high-pressure wells. BRIEF DESCRIPTION OF THE DRAWINGS

[0101] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0102] Figure 1 Schematic diagram of a flow chart of a method for determining transient flow fluctuation pressure of drilling fluid during tripping of a high-temperature and high-pressure well according to the present invention;

[0103] Figure 2 This is a schematic diagram of the results of the physical model of transient flow fluctuation pressure in the wellbore during drilling;

[0104] Figure 3 for Figure 2 Schematic diagram of the simplified motion model results;

[0105] Figure 4 This is a schematic diagram of the characteristic line finite difference grid results;

[0106] Figure 5 Schematic diagram of the distribution of wellbore annulus temperature and pressure along the well depth in the embodiment.

[0107] Figure 6 This is a schematic diagram of the variation of bottom hole pressure fluctuations over time during tripping in the embodiment;

[0108] Figure 7 Schematic diagram of the variation of the fluctuating pressure over time when drilling at different well depths in the embodiment;

[0109] Figure 8 Schematic diagram of the variation of bottom hole pressure fluctuation with time at different tripping speeds under stopped circulation conditions in the embodiment;

[0110] Figure 9Schematic diagram of the variation of bottom hole pressure fluctuation with time at different tripping speeds under circulation conditions in the embodiment. DETAILED DESCRIPTION

[0111] The present invention is further described below with reference to the accompanying drawings and examples. It should be noted that, in the absence of conflict, the embodiments in this application and the technical features in the embodiments can be combined with each other. It should be noted that, unless otherwise specified, all technical and scientific terms used in this application have the same meanings as those commonly understood by those of ordinary skill in the art to which this application belongs. The use of similar words such as "include" or "comprising" in the present invention means that the elements or objects appearing before the word cover the elements or objects listed after the word and their equivalents, without excluding other elements or objects.

[0112] like Figure 1 As shown, the present invention provides a method for determining the transient flow fluctuation pressure of drilling fluid during tripping in a high-temperature and high-pressure well, comprising the following steps:

[0113] S1: Establish a physical model of transient flow fluctuation pressure in the wellbore during drilling and establish the assumptions for calculating the transient flow fluctuation pressure in the wellbore;

[0114] In a specific embodiment, the physical model of transient flow fluctuation pressure in the wellbore during drilling is as follows: Figure 2 As shown, it can be simplified to Figure 3 In the simplified motion model shown, Ⅰ represents the empty wellbore flow path, Ⅱ represents the annular flow path, and Ⅲ represents the flow path within the circular tube. When tripping in a wellbore filled with drilling fluid, the movement of the drill string causes the drilling fluid to flow, resulting in changes in the drilling fluid flow rate within the wellbore. This causes oscillations in the wellbore pressure, leading to water hammer. This is due to the inertia and compressibility of the fluid. Inertia attempts to maintain the fluid's original motion state, so changes in flow velocity cause transient fluctuations in the wellbore pressure.

[0115] The actual pressure of a stable wellbore is composed of the static pressure of the wellbore and the fluctuating pressure during the tripping process. The total pressure in the wellbore during tripping must be between the formation pressure and the fracture pressure. This is especially important for high-temperature and high-pressure wells with a narrow safety pressure window to ensure safe drilling. Therefore, the following assumptions are established:

[0116] (1) The formation, wellbore and tubing are all elastic, and the bottom of the well is a rigid body;

[0117] (2) Ignore the influence of cement and formation around the casing on the elasticity of the casing;

[0118] (3) The fluid in the wellbore is compressible;

[0119] (4) Ignoring the effect of drill string eccentricity on fluid flow in the wellbore;

[0120] (5) The fluid in the wellbore flows transiently and is pure liquid drilling fluid;

[0121] (6) Considering wellbore heat transfer, fluid properties are functions of temperature and pressure;

[0122] (7) Consider the non-steady transient friction during transient flow.

[0123] S2: Establishing a physical property equation of drilling fluid under high temperature and high pressure conditions; the physical property equation of drilling fluid under high temperature and high pressure conditions includes:

[0124] (1) Function of the relationship between drilling fluid density, temperature and pressure

[0125] ρ(T,p)=ρ(T0,p0)·exp(γ1(p-p0)+γ2(T-T0)+γ3(T-T0) 2 ) (1)

[0126] Where: ρ(T, p) is the density of drilling fluid at temperature T and pressure p, kg / m 3 ; ρ(T0, p0) is the density of drilling fluid at temperature T0 and pressure p0, kg / m 3 ; γ1, γ2, γ3 are characteristic coefficients in the drilling fluid density function; p is pressure, MPa; p0 is reference pressure, MPa; T is temperature, °C; T0 is reference temperature, °C;

[0127] The reference pressure and the reference temperature refer to the pressure and temperature under initial experimental conditions, generally referring to the pressure and temperature under standard atmospheric pressure.

[0128] (2) a function of the relationship between the rheological parameters of the drilling fluid and temperature and pressure, wherein the rheological parameters include any one or more of yield value, consistency coefficient and flow index;

[0129] The function of the relationship between the yield value of drilling fluid and temperature and pressure is:

[0130] τ0(T,P)=τ0(T0,p0)·exp[η1(T-T0)+η2(p-p0)+η3(T-T0) 2 ] (2)

[0131] The function of the relationship between drilling fluid viscosity coefficient, temperature and pressure is:

[0132] K(T,P)=K(T0,p0)·exp[eta4(T-T0)+eta5(p-p0)+eta6(T-T0) 2 ] (3)

[0133] The function of the relationship between drilling fluid fluidity index, temperature and pressure is:

[0134] n(T,P)=n(T0,p0)·exp[eta7(T-T0)+eta8(p-p0)+eta9(T-T0) 2 ] (4)

[0135] Where: τ0(T, p) is the yield value of the drilling fluid at temperature T and pressure p, Pa; K(T, p) is the viscosity coefficient of the drilling fluid at temperature T and pressure p, Pa·s n ; n(T, p) is the drilling fluid fluidity index at temperature T and pressure p, dimensionless; τ0(T0, p0) is the drilling fluid yield value at temperature T0 and pressure p0, Pa; K(T0, p0) is the drilling fluid viscosity coefficient at temperature T0 and pressure p0, Pa·s n ; n(T0, p0) is the drilling fluid fluidity index under the conditions of temperature T0 and pressure p0, which is dimensionless; η1, η2, η3, η4, η5, η6, η7, η8, and η9 are all characteristic coefficients in the drilling fluid rheological parameter function.

[0136] Under high temperature and high pressure conditions, the rheological curve of the drilling fluid is approximately a curve that does not pass through the origin. In the prior art, the Hershel-Bulkley rheological model combines the Power-Law and Bingham rheological models, and can better describe the flow characteristics of the drilling fluid at low, medium, and high shear rates and under high temperature and high pressure conditions. Therefore, in a specific embodiment, the rheological model of the drilling fluid is described using the Hershel-Bulkley model. The Hershel-Bulkley rheological model expression is:

[0137] τ=τ0+Kγ n (37)

[0138] Where: τ0 is the yield value, Pa; K is the consistency coefficient, Pa·s n ; n is the fluidity index, dimensionless.

[0139] When n = 1 and τ0 ≠ 0 in the Hershel-Bulkley rheological model, the Bingham rheological model is used. When τ0 = 0 in the Hershel-Bulkley rheological model, the Power-Law rheological model is used. Therefore, this model is applicable to a wider range of fluids and can be converted to both the Bingham and Power-Law rheological models, making it more versatile. Selecting the corresponding rheological parameters based on the specific rheological model is a well-known technique and will not be elaborated on here.

[0140] S3: Based on the laws of conservation of mass, conservation of momentum, and conservation of energy, a set of control equations for transient flow fluctuation pressure in the wellbore is established, taking into account constant steady-state friction and non-constant transient friction. The set of control equations for transient flow fluctuation pressure in the wellbore includes:

[0141]

[0142]

[0143]

[0144] in:

[0145]

[0146] Where: h is the wellbore depth coordinate, m; ρ is the drilling fluid density, kg / m 3 ; v is flow velocity, m / s; t is time, s; F T is the transient flow friction and pressure gradient in the wellbore, Pa / m; g is the acceleration of gravity, m / s 2 ; θ is the well inclination angle, rad; c is the pressure wave velocity, m / s; T f is the drilling fluid temperature, °C; w is the drilling fluid mass flow rate, kg / s; c p is the specific heat capacity of drilling fluid at constant pressure, J / (kg·℃); L R is the relaxation distance, m -1 ; m is the mass of the fluid per unit length, kg / m; C T is the heat storage coefficient, dimensionless; T ei is the initial formation temperature, °C; φ is a lumped parameter, dimensionless; α is the fluid compressibility, Pa -1 ; β is the wellbore flow channel compression coefficient, Pa - 1 .

[0147] In a specific embodiment, the drilling fluid temperature T f Calculate using the following formula:

[0148]

[0149] in:

[0150]

[0151]

[0152]

[0153] Where: e is the natural base, dimensionless; L is the well depth, m; g Gis the geothermal gradient, ℃ / m; r ti is the wellbore radius, m; U t is the total heat transfer coefficient, W / (m 2 ℃); k e is the formation thermal conductivity, W / (m·℃); T D is the dimensionless temperature and has no dimensions.

[0154] The transient flow friction pressure gradient F in the wellbore T From the constant steady-state friction F S and non-steady transient friction F U The composition is expressed as:

[0155]

[0156] in:

[0157]

[0158] Where: f is the constant steady-state Fanning friction coefficient, dimensionless; D hy is the equivalent diameter, m; k is the attenuation coefficient of the non-constant transient friction, dimensionless; sign(v) is the sign function, dimensionless; the equivalent diameter refers to the inner diameter of the annular flow channel or the circular pipe flow channel.

[0159] Substituting formula (13) into formula (5), the motion equation in the transient flow fluctuation pressure control equation group in the wellbore becomes:

[0160]

[0161] The derivation process of formula (15) is as follows:

[0162] (1) Calculation of constant steady-state friction F S

[0163] During the flow of drilling fluid, the Reynolds number (Re) is used to distinguish the flow states of laminar flow, turbulent flow, and transitional flow. The constant steady-state friction coefficient is calculated according to the flow state, and the friction pressure loss gradient under different flow conditions is obtained.

[0164] (a) Calculate the Reynolds number:

[0165] Flow in pipe:

[0166]

[0167] Annular flow:

[0168]

[0169] Where: Re is the Reynolds number, dimensionless; D is the inner diameter of the pipe string flowing in the pipe, m; τ0 is the yield value of the drilling fluid, Pa; D o is the wellbore diameter of the annular flow, m; D i is the outer diameter of the pipe string for annular flow, m;

[0170] (b) Calculate the critical Reynolds number and determine the flow state of the drilling fluid:

[0171] Critical Reynolds number for laminar flow:

[0172] Re lf =3470-1370n (40)

[0173] Critical Reynolds number for turbulent flow:

[0174] Re tf =5054-1983n (41)

[0175] Where: Re lf is the critical Reynolds number of laminar flow, dimensionless; Re tf is the critical Reynolds number for turbulence, dimensionless;

[0176] When Re≤Re lf When Re lf <Re<Re tf When Re≥Re tf The drilling fluid is in a turbulent state.

[0177] (c) Obtain the constant steady-state friction coefficient f under different flow conditions:

[0178] When the drilling fluid flows in a laminar state:

[0179]

[0180] When the drilling fluid flows in the pipe, a=16, b=1; when the drilling fluid flows in the annulus, a=24, b=1;

[0181] When the drilling fluid flow is in a turbulent state:

[0182]

[0183] in:

[0184]

[0185] Where: f l is the laminar friction coefficient, dimensionless; f t is the laminar friction coefficient, dimensionless; a, b are friction coefficient constants, dimensionless;

[0186] When the drilling fluid flow is in the transitional flow state:

[0187]

[0188] (d) Calculate the constant steady-state friction pressure gradient F S :

[0189] When drilling fluid flows in the pipe:

[0190]

[0191] When drilling fluid flows in the annulus:

[0192]

[0193] (2) Calculation of non-steady transient friction F U :

[0194]

[0195] in:

[0196]

[0197]

[0198] Where: C* is the shear attenuation coefficient, dimensionless.

[0199] Combining formulas (36)-(38), we can obtain the calculation formula for the transient flow friction and pressure loss gradient in the wellbore shown in formula (13).

[0200] S4: According to the transient flow fluctuation pressure control equations in the wellbore, a characteristic line equation group is established; the characteristic line equation group includes the forward characteristic line equation C + and the negative characteristic line equation C - ;

[0201] (1) When the sign function sign(v)=1:

[0202] The forward characteristic line equation C + for:

[0203]

[0204] The negative characteristic line equation C - for:

[0205]

[0206] (2) When the sign function sign(v) = -1:

[0207] The forward characteristic line equation C + for:

[0208]

[0209] The negative characteristic line equation C - for:

[0210]

[0211] S5: Establishing an initial boundary, solving the transient flow fluctuation pressure equation in the wellbore in combination with the solution of the characteristic line equation group, and obtaining the transient flow fluctuation pressure in the wellbore; the initial boundary includes:

[0212] (1) Initial conditions:

[0213]

[0214] Where: v1(h,0), v2(h,0), v3(h,0) are the flow velocities at each node of the empty wellbore flow channel, annulus flow channel, and inner tube flow channel, respectively, m / s; Q m is the drilling pump flow rate, m 3 / s; A2(h) and A3(h) are the cross-sectional areas of each node of the annular flow channel and the inner tube flow channel, respectively, m 2 ; p1(h,0), p2(h,0), p3(h,0) are the pressures of each node of the empty wellbore flow channel, annulus flow channel and circular pipe flow channel, Pa; F T2 、F T3 are the flow friction and pressure gradients of the annular flow channel and the flow channel in the circular tube, Pa / m; l2 is the initial well depth at the bottom of the drill string, m;

[0215] (2) Boundary conditions:

[0216]

[0217] Where: v N (l1) is the flow velocity at the bottom of the well, m / s; p N (l2) is the pressure at the wellhead node, Pa; N is the flow channel number, dimensionless;

[0218] (3) Intersection point constraints:

[0219] The intersection of the drill string bottom, the annulus, and the empty wellbore is the intersection point. When the drilling pump is turned on, the constraint conditions at the intersection point are:

[0220]

[0221] When the drilling pump is in the off state, the constraint condition at the intersection is:

[0222]

[0223] Where: v1(0,t), v2(0,t), v3(0,t), v s (t) are the flow velocities of the empty wellbore flow channel, annular flow channel, and inner tube flow channel at each moment, as well as the movement speed of the drill string at each moment, m / s; A0, A i A1, A2, and A3 are the cross-sectional areas of the flow channel outside the string, inside the string, empty wellbore, annulus, and inside the circular pipe, respectively. 2 ; p1(0, t), p2(0, t), p3(0, t) are the pressures at each moment in the empty wellbore flow channel, annulus flow channel, and inner tube flow channel, respectively, in Pa; k' is the nozzle discharge coefficient, dimensionless;

[0224] (4) Connection point constraints:

[0225]

[0226] Where: q is the flow channel section number of the connection point, dimensionless; l3 is the distance between the flow channel connection point and the origin, m; A is the flow channel cross-sectional area, m 2 ; ΔA is the difference in cross-sectional area of ​​the flow channel at the connection point, m 2 .

[0227] In a specific embodiment, when solving the transient flow fluctuation pressure equation in the wellbore, the finite difference method or the finite volume method is used for solution. When the finite difference method is used for solution:

[0228] First, the finite difference method is used to discretize the well depth and time. The well depth is divided into M1 segments, each with a spatial length of Δh, and the time is divided into M2 segments, each with a time step of Δt. The following equations are obtained: Figure 4 Characteristic line finite difference grid shown;

[0229] The characteristic line equation is integrated along the positive and negative characteristic lines AP and BP on the characteristic line finite difference grid. The solution of the characteristic line equation can be obtained by using the first-order approximation method. The flow velocity and pressure at time i and node j can be obtained by simultaneous solution:

[0230]

[0231]

[0232] in:

[0233]

[0234]

[0235] (1) When the sign function sign(v)=1:

[0236]

[0237]

[0238]

[0239]

[0240] (2) When the sign function sign(v) = -1:

[0241]

[0242]

[0243]

[0244]

[0245] Where: v i,j is the flow velocity at time i and node j, m / s; p i,j is the pressure at node j at time i, Pa; p i-1,j+1 is the pressure at node j+1 at time i-1, Pa; p i-1,j-1 is the pressure at the j-1 node at the i-1 moment, Pa; v i-1,j+1 is the flow velocity at time i-1 and node j+1, m / s; v i-1,j-1 is the flow velocity at time i-1 and node j-1, m / s; k i-1,j+1 k is the attenuation coefficient of the non-steady transient friction at the node j+1 at time i-1, dimensionless; i-1,j-1 is the attenuation coefficient of the non-steady transient friction at the i-1 moment and the j-1 node, dimensionless.

[0246] During the solution process, the initial flow velocity and initial pressure value of each node are first solved based on the initial conditions, and then the v of each node in the wellbore at time Δt is calculated in sequence. i,j and p i,jThe calculation is terminated until the maximum solution calculation time is reached. Specifically: the initial pressure distribution of the wellbore is calculated according to formulas (38) to (47), the initial temperature distribution of the wellbore is calculated according to formulas (9) to (12), the drilling fluid density and rheological parameters are calculated according to the above initial temperature and pressure distribution of the wellbore using formulas (1) to (4), and after obtaining the updated drilling fluid density and rheological parameters, the wellbore pressure distribution is calculated again according to formulas (38) to (47), and the wellbore temperature distribution is calculated using formulas (9) to (12). The temperature and pressure distribution at the initial moment after coupling is obtained by continuous iteration; combined with the initial boundary condition formulas (20) to (24), the flow velocity and pressure at the node j at time i are calculated using formulas (25) to (36), and the change law of transient fluctuating pressure with time can be obtained.

[0247] In a specific embodiment, a high-temperature and high-pressure well in the South China Sea is used as an example to determine the transient flow fluctuation pressure of the drilling fluid. The well has a water depth of 90m, a sea surface temperature of 20°C, and a geothermal gradient of 4.0°C / 100m. The well was drilled to 4500m. The casing is 4000m deep and the drilling fluid density is 2.32g / cm 3 , the equivalent density of the formation pore pressure is 2.30 g / cm 3 , the burst pressure equivalent density is 2.37g / cm 3 , the normal circulation displacement is 16L / s, and the drilling tool assembly is: PDC drill bit+ Drill collar × 14 pieces + Heavy drill pipe × 15 pieces + Drill rod, tripping speed is 0.25m / s, tripping acceleration is 0.1m / s 2 The cumulative drilling displacement is 30m, and the drilling operation is carried out.

[0248] Since the temperature distribution of the wellbore annulus is changing, in order to accurately predict the transient pressure fluctuation during tripping, it is necessary to determine the initial temperature and pressure distribution of the wellbore annulus before and after the coupling. When the drilling fluid circulation rate is 16L / s, the initial temperature and pressure distribution of the wellbore annulus is as follows: Figure 5 As shown. Figure 5 It can be seen that as the drilling fluid flows upward along the annulus, the annular temperature will first increase and then decrease, with the highest temperature being 142.26°C at 4320 m. As for the pressure, it will gradually decrease from 101.9 MPa at the bottom of the well to 0.1 MPa at the wellhead.

[0249] The transient pressure fluctuations under the conditions of (1) coupling consideration of the influence of drilling fluid temperature, pressure, physical properties and non-constant transient friction and (2) not considering the influence of drilling fluid temperature, pressure, physical properties and non-constant transient friction are analyzed. The results are as follows: Figure 6As shown. Figure 6 It can be seen that coupling considerations have a significant impact on the magnitude and variation of bottomhole pressure fluctuations. When the coupled considerations are applied to the drilling fluid temperature, pressure, and non-constant transient friction, the peak and stable bottomhole pressure fluctuations are 104.40 MPa and 101.80 MPa, respectively. When the coupled considerations are applied to the drilling fluid temperature, pressure, and non-constant transient friction, the peak and stable bottomhole pressure fluctuations are 105.48 MPa and 102.52 MPa, respectively. The results calculated without coupling considerations are significantly greater than those calculated with coupling considerations. This is because the high temperature, high pressure, and temperature conditions of the drilling wellbore change the density and rheological properties of the drilling fluid, affecting the damping of pressure fluctuations and, in turn, the magnitude and variation of transient pressure fluctuations. Therefore, in high temperature and high pressure wells, the magnitude of bottomhole pressure fluctuations will be severely overestimated when the coupled considerations are applied. The difference in equivalent density between the two can reach 0.025 g / cm 3 , this is only 0.07g / cm 3 The safe density window will have a significant impact on the pressure fluctuation control and safe drilling of high-temperature and high-pressure wells.

[0250] The present invention is used to analyze the change of transient pressure fluctuation with time when drilling at different well depths. The results are as follows: Figure 7 As shown. Figure 7 It can be seen that the fluctuating pressure value also gradually increases. At well depths of 4300m, 4400m, and 4500m, the fluctuating pressure peaks are 99.74MPa, 102.06MPa, and 104.40MPa, respectively. The fluctuating pressure stable values ​​are 97.30MPa, 99.55MPa, and 101.80MPa, respectively. The difference between the fluctuating pressure peaks and stable values ​​is 2.44MPa, 2.51MPa, and 2.60MPa, respectively. In other words, as the well depth increases, the additional pressure generated by tripping also gradually increases.

[0251] The present invention is used to analyze the change of transient pressure fluctuation with time at different tripping speeds under the condition of stopped circulation (pump displacement 0 L / s). The results are as follows Figure 8 As shown. Figure 8 It can be seen that with the increase of the tripping speed, the peak value of the bottom hole pressure fluctuation gradually increases. When the tripping speeds are 0.20m / s, 0.25m / s, 0.30m / s, and 0.35m / s, the peak values ​​of the bottom hole pressure fluctuation are 104.17MPa, 104.40MPa, 104.68MPa, and 104.93MPa, respectively. With the increase of the tripping speed, the bottom hole pressure fluctuation also gradually increases. It is known that the equivalent density of the formation fracture pressure is 2.37g / cm 3, meaning the fracture pressure is 104.62 MPa, and at a tripping speed of 0.30 m / s, the bottomhole surge pressure will exceed the formation fracture pressure, causing a loss of the formation. It is recommended that the tripping speed should not exceed 0.29 m / s under stopped circulation conditions. Therefore, the surge pressure should be effectively reduced by controlling the tripping speed. When tripping in a narrow pressure window, the tripping speed should be strictly controlled and back-calculated to ensure safety.

[0252] In high-temperature and high-pressure wells, in order to avoid the wellbore temperature from being too high when the circulation is stopped and thus damaging the drilling fluid performance, a low circulation displacement is required during the drilling operation. Therefore, the present invention is used to analyze the change of transient fluctuation pressure over time when drilling under the circulation condition (pump displacement 5L / s) with different pump displacements. The results are as follows: Figure 9 As shown. Figure 9 It can be seen that when the pump displacement is 5L / s and the tripping speed is 0.05m / s, 0.10m / s, 0.15m / s, and 0.20m / s, the bottomhole surge pressure peaks are 104.18MPa, 104.43MPa, 104.66MPa, and 104.89MPa, respectively. It can be seen that at a low circulating displacement of 5L / s, the bottomhole surge pressure peak gradually increases with increasing tripping speed. At a tripping speed of 0.15m / s, the bottomhole surge pressure exceeds the bottomhole formation fracture pressure of 104.62MPa. Therefore, it is recommended that in narrow safe density window intervals in high-temperature and high-pressure wells, the tripping speed should not exceed 0.14m / s when circulating drilling fluid at a low circulating displacement of 5L / s to avoid excessively fast tripping and causing formation loss.

[0253] From the above analysis we can see that:

[0254] (1) For transient fluctuating pressure, the peak value of bottomhole fluctuating pressure and the stable value of bottomhole pressure when coupling the temperature and pressure properties of drilling fluid and non-constant transient friction are significantly lower than the results calculated without coupling. It is necessary to consider coupling in the well section with narrow safety density window of high temperature and high pressure, otherwise it will have a significant impact on the bottomhole fluctuating pressure control and safe drilling during tripping.

[0255] (2) The peak and stable values ​​of the drilling pressure increase gradually with the increase of well depth. At the same time, the additional pressure generated by drilling also increases gradually with the increase of well depth.

[0256] (3) Under the condition of stopped circulation, the peak value of the bottom hole pressure fluctuation increases with the increase of the drilling speed. By reducing the drilling speed, the fluctuation pressure value can be effectively reduced to ensure the safety of drilling operations in formations with narrow pressure windows.

[0257] (4) Under low circulation displacement conditions, the peak value of the bottom hole fluctuation pressure gradually increases with the increase of the drilling speed. The drilling speed is controlled under the constraint of the formation fracture pressure. At this time, the maximum drilling speed will be lower than the controlled drilling speed under the condition of stopped circulation.

[0258] In summary, the present invention can obtain fluctuating pressure that is more in line with actual working conditions, and is a significant improvement compared to the prior art.

[0259] The above description is merely a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any technician familiar with this profession can make some changes or modifications to equivalent embodiments of the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention are still within the scope of the technical solution of the present invention.

Claims

1. A method for determining transient flow fluctuation pressure of drilling fluid during tripping of a high-temperature and high-pressure well, characterized in that: The following steps are involved: S1: Establish a physical model of transient flow fluctuation pressure in the wellbore during drilling, and establish the assumptions for calculating the transient flow fluctuation pressure in the wellbore; S2: Establish the physical property equation of drilling fluid under high temperature and high pressure conditions; S3: Based on the laws of conservation of mass, conservation of momentum, and conservation of energy, a set of control equations for transient flow fluctuation pressure in the wellbore is established, taking into account constant steady-state friction and non-constant transient friction. The set of control equations for transient flow fluctuation pressure in the wellbore includes: in: Where: p is pressure, MPa; h is wellbore depth, m; ρ is drilling fluid density, kg / m 3 ; v is flow velocity, m / s; t is time, s; F T is the transient flow friction and pressure gradient in the wellbore, Pa / m; g is the acceleration of gravity, m / s 2 ; θ is the well inclination angle, rad; c is the pressure wave velocity, m / s; T f is the drilling fluid temperature, °C; w is the drilling fluid mass flow rate, kg / s; c p is the specific heat capacity of drilling fluid at constant pressure, J / (kg·℃); L R is the relaxation distance, m -1 ; m is the mass of the fluid per unit length, kg / m; C T is the heat storage coefficient, dimensionless; T ei is the initial formation temperature, °C; φ is a lumped parameter, dimensionless; α is the fluid compressibility, Pa -1 ; β is the wellbore flow channel compression coefficient, Pa -1 ; Drilling fluid temperature T f Calculate using the following formula: in: Where: e is the natural base, dimensionless; L is the well depth, m; g G is the geothermal gradient, ℃ / m; r ti is the wellbore radius, m; U t is the total heat transfer coefficient, W / (m 2 ℃); k e is the formation thermal conductivity, W / (m·℃); T D is the dimensionless temperature, dimensionless; The transient flow friction pressure gradient F in the wellbore T From the constant steady-state friction F S and non-steady transient friction F U The composition is expressed as: in: Where: f is the constant steady-state Fanning friction coefficient, dimensionless; D hy is the equivalent diameter, m; k is the attenuation coefficient of non-constant transient friction, dimensionless; sign(v) is the sign function, dimensionless; Substituting formula (13) into formula (5), the motion equation in the transient flow fluctuation pressure control equation group in the wellbore becomes: S4: establishing a set of equations for solving characteristic lines based on the set of equations for transient flow fluctuation pressure in the wellbore; S5: Establishing an initial boundary, solving the transient flow fluctuation pressure equation in the wellbore in combination with the solution of the characteristic line equation group, and obtaining the transient flow fluctuation pressure in the wellbore.

2. The method for determining transient flow fluctuation pressure of drilling fluid during tripping of a high-temperature and high-pressure well according to claim 1, characterized in that: In step S1, the assumptions for calculating the transient flow fluctuation pressure in the wellbore include: (1) The formation, wellbore and tubing are all elastic, and the bottom of the well is a rigid body; (2) Ignore the influence of cement and formation around the casing on the elasticity of the casing; (3) The fluid in the wellbore is compressible; (4) Ignoring the effect of drill string eccentricity on fluid flow in the wellbore; (5) The fluid in the wellbore flows transiently and is pure liquid drilling fluid; (6) Considering wellbore heat transfer, fluid properties are functions of temperature and pressure; (7) Consider the non-steady transient friction during transient flow.

3. The method for determining transient flow fluctuation pressure of drilling fluid during tripping of a high-temperature and high-pressure well according to claim 2, characterized in that: In step S2, the physical property equation of the drilling fluid under high temperature and high pressure conditions includes: (1) Function of the relationship between drilling fluid density, temperature and pressure ρ(T,p)=ρ(T0,p0)·exp(γ1(p-p0)+γ2(T-T0)+γ3(T-T0) 2 ) (1) Where: ρ(T, p) is the density of drilling fluid at temperature T and pressure p, kg / m 3 ; ρ(T0, p0) is the density of drilling fluid at temperature T0 and pressure p0, kg / m 3 ;γ1,γ2,γ3 are characteristic coefficients in the drilling fluid density function; p0 is the reference pressure, MPa; T is the temperature, ℃; T0 is the reference temperature, ℃; (2) a function of the relationship between the rheological parameters of the drilling fluid and temperature and pressure, wherein the rheological parameters include any one or more of yield value, consistency coefficient and flow index; The function of the relationship between the yield value of drilling fluid and temperature and pressure is: τ0(T,P)=τ0(T0,p0)·exp[η1(T-T0)+η2(p-p0)+η3(T-T0) 2 ] (2) The function of the relationship between drilling fluid viscosity coefficient, temperature and pressure is: K(T,P)=K(T0,p0)·exp[η4(T-T0)+η5(p-p0)+η6(T-T0) 2 ] (3) The function of the relationship between drilling fluid fluidity index, temperature and pressure is: n(T,P)=n(T0,p0)·exp[η7(T-T0)+η8(p-p0)+η9(T-T0) 2 ] (4) Where: τ0(T, p) is the yield value of the drilling fluid at temperature T and pressure p, Pa; K(T, p) is the viscosity coefficient of the drilling fluid at temperature T and pressure p, Pa·s n ; n(T, p) is the drilling fluid fluidity index at temperature T and pressure p, dimensionless; τ0(T0, p0) is the drilling fluid yield value at temperature T0 and pressure p0, Pa; K(T0, p0) is the drilling fluid viscosity coefficient at temperature T0 and pressure p0, Pa·s n ; n(T0, p0) is the drilling fluid fluidity index under the conditions of temperature T0 and pressure p0, which is dimensionless; η1, η2, η3, η4, η5, η6, η7, η8, and η9 are all characteristic coefficients in the drilling fluid rheological parameter function.

4. The method for determining transient flow fluctuation pressure of drilling fluid during tripping of a high-temperature and high-pressure well according to claim 1, characterized in that: In step S4, the characteristic line equations are solved including the forward characteristic line equation C + and the negative characteristic line equation C - ; (1) When the sign function sign(v)=1: The forward characteristic line equation C + for: The negative characteristic line equation C - for: (2) When the sign function sign(v) = -1: The forward characteristic line equation C + for: The negative characteristic line equation C - for:

5. The method for determining transient flow fluctuation pressure of drilling fluid during tripping of a high-temperature and high-pressure well according to claim 4, characterized in that: In step S5, the initial boundary includes: (1) Initial conditions: Where: v1(h,0), v2(h,0), v3(h,0) are the flow velocities at each node of the empty wellbore flow channel, annulus flow channel, and inner tube flow channel, respectively, m / s; Q m is the drilling pump flow rate, m 3 / s; A2(h) and A3(h) are the cross-sectional areas of each node of the annular flow channel and the inner tube flow channel, respectively, m 2 ; p1(h,0), p2(h,0), p3(h,0) are the pressures of each node of the empty wellbore flow channel, annulus flow channel and circular pipe flow channel, Pa; F T2 、F T3 are the flow friction and pressure gradients of the annular flow channel and the flow channel in the circular tube, Pa / m; l2 is the initial well depth at the bottom of the drill string, m; (2) Boundary conditions: Where: v N (l1) is the flow velocity at the bottom of the well, m / s; p N (l2) is the pressure at the wellhead node, Pa; N is the flow channel number, dimensionless; (3) Intersection point constraints: The intersection of the drill string bottom, the annulus, and the empty wellbore is the intersection point. When the drilling pump is turned on, the constraint conditions at the intersection point are: When the drilling pump is in the off state, the constraint condition at the intersection is: Where: v1(0,t), v2(0,t), v3(0,t), v s (t) are the flow velocities of the empty wellbore flow channel, annular flow channel, and inner tube flow channel at each moment, as well as the movement speed of the drill string at each moment, m / s; A0, A i A1, A2, and A3 are the cross-sectional areas of the flow channel outside the string, inside the string, empty wellbore, annulus, and inside the circular pipe, respectively. 2 ; p1(0, t), p2(0, t), p3(0, t) are the pressures at each moment in the empty wellbore flow channel, annulus flow channel, and inner tube flow channel, respectively, in Pa; k' is the nozzle discharge coefficient, dimensionless; (4) Connection point constraints: Where: q is the flow channel section number of the connection point, dimensionless; l3 is the distance between the flow channel connection point and the origin, m; A is the flow channel cross-sectional area, m 2 ; ΔA is the difference in cross-sectional area of ​​the flow channel at the connection point, m 2 .

6. The method for determining transient flow fluctuation pressure of drilling fluid during tripping of a high-temperature and high-pressure well according to claim 5, characterized in that: In step S5, when solving the transient flow fluctuation pressure equation in the wellbore, a finite difference method or a finite volume method is used to solve it.

7. The method for determining transient flow fluctuation pressure of drilling fluid during tripping of a high-temperature and high-pressure well according to claim 6, characterized in that: When solving using the finite difference method: First, the finite difference method is used to discretize the well depth and time. The well depth is divided into M1 segments, each with a spatial length of Δh, and the time is divided into M2 segments, each with a time step of Δt, to obtain the characteristic line finite difference grid. The characteristic line equation is integrated along the positive and negative characteristic lines on the characteristic line finite difference grid, and the solution of the characteristic line equation is obtained by using the first-order approximation method. The flow velocity and pressure at the time i and the node j are obtained by simultaneous solution: in: (1) When the sign function sign(v)=1: (2) When the sign function sign(v) = -1: Where: v i,j is the flow velocity at time i and node j, m / s; p i,j is the pressure at node j at time i, Pa; p i-1,j+1 is the pressure at node j+1 at time i-1, Pa; p i-1,j-1 is the pressure at the j-1 node at the i-1 moment, Pa; v i-1,j+1 is the flow velocity at time i-1 and node j+1, m / s; v i-1,j-1 is the flow velocity at time i-1 and node j-1, m / s; k i-1,j+1 k is the attenuation coefficient of the non-steady transient friction at the node j+1 at time i-1, dimensionless; i-1,j-1 is the attenuation coefficient of the non-steady transient friction at the i-1 moment and the j-1 node, dimensionless.

Images