Calculation method for wellbore pressure under temperature-pressure coupling low shear rate

Abstract

The invention provides a method and a system for calculating wellbore pressure at a temperature-pressure coupling low shear rate, and belongs to the technical field of drilling engineering. According to the method, the rheological parameters of the fluid at the low shear rate are obtained by fitting in combination with the test data of the fluid at the low shear rate; and on the basis, a calculation model of the fluid rheological parameters under the temperature and pressure conditions is established in combination with the influence of the fluid temperature and pressure on the fluid rheological parameters, and a wellbore circulation friction calculation model of the fluid at the low return speed is obtained according to a fluid circulation friction pressure drop calculation equation. According to the method, a key reference method is provided for accurate calculation of the wellbore pressure of fluid under the condition of low return speed under deep well temperature-pressure coupling, and finally, the occurrence of complex conditions such as leakage and overflow in the drilling and completion process of a deep narrow safe density window stratum is reduced.

Description

Technical Field

[0001] The invention relates to the technical field of drilling engineering, and in particular to a method and system for calculating wellbore pressure under temperature-pressure coupling and low shear rate. Background Art

[0002] With the continuous improvement of the exploration and development of medium and shallow oil and gas, the difficulty of oil and gas discovery is increasing. Deep and even ultra-deep oil and gas resources have become an important part of the energy structure. Therefore, effective drilling and production of deep oil and gas resources can alleviate the existing oil and gas shortage problem to a large extent. Effective drilling and production of deep oil and gas resources can alleviate the existing oil and gas shortage problem to a large extent. However, the geological environment of deep oil and gas is complex during drilling and production, and leakage and overflow phenomena occur frequently, resulting in a long drilling and completion cycle for a single well and high well construction costs. Accurate prediction and control of wellbore pressure during drilling and completion is a prerequisite for solving complex problems. During drilling, 127mm drill pipe is often used to transmit torque and drilling pressure to break the rock and continuously deepen the wellbore. When drilling into the designed well depth, casing and cementing operations are usually required to ensure the long-term integrity of the wellbore. During the drilling process, the outer diameter of the drill pipe is small, the annular space formed with the well wall is large, and the flow friction formed is also small; after the casing is lowered, the casing size is large, and the annular space gap formed with the well wall is also small, which makes the flow friction formed larger. The annular circulation friction is proportional to the flow velocity. The greater the flow velocity, the greater the circulation friction. In order to reduce the excessive circulation pressure in the deep well cementing wellbore caused by formation leakage, the accurate calculation technology of the wellbore pressure of the fluid under low return rate conditions under the deep well temperature and pressure coupling needs to be tackled urgently.

[0003] The existing technology has at least the following deficiencies:

[0004] 1. The return velocity of deep well cementing fluid is low, which means that the shear stress received by the fluid when it is stirred is small. The rheological parameters of the fluid fitted by the existing conventional 6-speed rotary viscometer result in a large error in the calculated cyclic friction resistance.

[0005] 2. The significant effect of temperature on fluid rheology is not considered. Summary of the invention

[0006] In order to solve the problems existing in the prior art, the purpose of the present invention is to determine the critical shear rate of the fluid in the wellbore in combination with the wellbore size, construction displacement and fluid performance. The present invention combines the test data of the fluid under low shear rate conditions to fit the rheological parameters of the fluid under low shear rate; on this basis, combined with the influence of fluid temperature and pressure on the rheological parameters of the fluid, a calculation model of the rheological parameters of the fluid under temperature and pressure conditions is established, and according to the fluid circulation friction pressure drop calculation equation, a calculation model of the wellbore circulation friction of the fluid under low return rate is obtained. The present invention provides a key reference method for the accurate calculation of the wellbore pressure of the fluid under low return rate conditions under deep well temperature and pressure coupling, and ultimately reduces the occurrence of complex situations such as leakage and overflow during drilling and completion of deep narrow safety density window formations.

[0007] The present invention provides a method for calculating wellbore pressure under temperature-pressure coupling and low shear rate, comprising the following steps:

[0008] Initially assigning the wellbore fluidity value based on the wellbore parameters;

[0009] Calculate the maximum critical shear rate of the annular fluid;

[0010] Fit the shear rate and shear stress relationship model below the maximum critical shear rate to obtain the fluid rheological parameters at low shear rates;

[0011] Based on the energy conservation principle, a calculation model of the wellbore temperature field during fluid circulation is established; the low shear rate is a shear rate with a Reynolds number less than 800;

[0012] Solve the calculation model of the wellbore temperature field during fluid circulation, obtain the annular temperature distribution characteristics, and establish a model of the relationship between fluid rheological parameters and temperature and pressure under low shear rate;

[0013] Calculate the Reynolds number and friction coefficient of the annular fluid;

[0014] A method for calculating wellbore pressure under low shear rate conditions of forming fluids.

[0015] Preferably, the wellbore fluidity is initially assigned a value based on the actual wellbore structure, pipe string combination, construction displacement and fluid rheological parameters.

[0016] Preferably, based on the maximum critical shear rate of the annular fluid, a shear rate and shear stress relationship model below the maximum critical shear rate is fitted, specifically including:

[0017] Based on the flow velocity of the fluid in the annulus, the wellbore diameter and the string diameter, combined with the flow velocity and the fluid flow index, the shear rate under the maximum flow velocity condition is obtained, which is the maximum critical shear rate of the annular fluid;

[0018] The relationship between shear rate and shear stress was obtained by a six-speed rotational viscometer;

[0019] Combined with the calculated maximum critical shear rate, a relationship model between shear stress and shear rate below the maximum critical shear rate is fitted.

[0020] Preferably, the annular shear rate formula is used to calculate the maximum critical shear rate of the annular fluid:

[0021]

[0022] in,

[0023] n is the fluidity index;

[0024] γ is the annular shear rate, s -1 ;

[0025] v is the velocity of the fluid in the annulus, m / s;

[0026] D w is the borehole diameter, m;

[0027] D o is the diameter of the pipe, m.

[0028] Preferably, the maximum shear rate under the same wellbore size condition is determined according to the shear rate and shear stress relationship model below the maximum critical shear rate, and then the fluid rheological parameters below the critical shear rate are obtained.

[0029] Preferably, based on the energy conservation principle, establishing a wellbore temperature field calculation model during fluid circulation specifically includes:

[0030] The total heat flux transferred from the remote formation to the wellbore is:

[0031]

[0032] The heat flow rate exchanged between the wellbore wall and the annulus fluid is:

[0033]

[0034] Combining equations (2) and (3) above, we can obtain the calculation model of the wellbore temperature field during fluid circulation. a The transformed form is expressed as:

[0035]

[0036] Where:

[0037]

[0038] q f is the heat transferred from the distant formation to the wellbore, J;

[0039] ρm is the fluid density, kg / m 3 ;

[0040] λ f is the formation thermal conductivity, W (m·℃);

[0041] T i is the original formation temperature, °C;

[0042] T w is the well wall temperature, °C;

[0043] T a is the annulus fluid temperature, ℃.

[0044] T D is the dimensionless time temperature;

[0045] q a is the heat transferred from the distant formation to the wellbore, J;

[0046] Q is the fluid flow rate, m 3 s;

[0047] r w is the wellbore radius, m;

[0048] U a is the comprehensive heat transfer coefficient between the fluid in the annulus and the formation during fluid circulation, J (h·℃·m);

[0049] dz represents the differential unit in the axial direction;

[0050] C m is the specific heat capacity of the fluid, J / (Kg.℃);

[0051] Among them, the far distance refers to the position that is more than 2m away from the well wall;

[0052] Similarly, the heat exchange expression between the fluid in the drill string and the annular drilling fluid is:

[0053]

[0054] Where:

[0055]

[0056] q p is the heat exchange between the fluid in the drill string and the annulus fluid, J;

[0057] T p is the drilling fluid temperature in the pipe, °C;

[0058] Based on the energy conservation principle of the fluid in the string and the annulus in the differential unit, the following annulus and pipe temperature model is obtained:

[0059]

[0060]

[0061] Formulas (6) and (7) are solved jointly to obtain the differential equation of the fluid temperature model in the tubing string. This fluid differential equation is the calculation model of the wellbore temperature field during fluid circulation, which is expressed as follows:

[0062]

[0063] Where:

[0064] T fp is the temperature difference caused by the change of flow pressure drop per unit length of the fluid in the column, °C;

[0065] T fa is the temperature difference caused by the change of flow pressure drop per unit length of the annulus fluid, °C;

[0066] T mf =AT fa +(A+B)T fp +T in +T s ;

[0067] T in is the drilling fluid inlet temperature, °C;

[0068] T s is the surface temperature, °C;

[0069] G t is the formation temperature gradient, °Cm;

[0070] z is the well depth, m;

[0071] The established calculation model expression of the wellbore temperature field during fluid circulation is as follows:

[0072]

[0073]

[0074] Where:

[0075]

[0076]

[0077] β1 is the coefficient of the wellbore temperature field calculation model expression during fluid circulation;

[0078] β2 is the coefficient of the wellbore temperature field calculation model expression during fluid circulation.

[0079] Preferably, the coefficient calculation method of the wellbore temperature field calculation model expressions (9) and (10) during fluid circulation is obtained by combining the model boundary conditions and initial conditions, as follows:

[0080] The initial conditions of the fluid at the wellhead and the function of the wellbore temperature changing with the depth are given as follows:

[0081]

[0082] Substituting equation (11) into equation (9) and equation (10), we obtain... The coefficients of model expressions (9) and (10) are as follows:

[0083]

[0084]

[0085] In the formula,

[0086] H is the well depth, m;

[0087] T b is the temperature generated by the hydraulic pressure drop of the drill bit, °C;

[0088]

[0089] Preferably, according to the annular temperature distribution characteristics, a model of the relationship between the rheological parameters of the low-return fluid and the temperature and pressure when the temperature and pressure are coupled at a low shear rate is established;

[0090] Fluid dynamic shear force τ:

[0091] τ=2.6142exp(-0.0117(T-60)+0.0071(p-0.1)-7.6842×10 -7 (T-60) 2 ) (15)

[0092] Fluid flow index n:

[0093] n=0.938exp(0.0024(T-60)-0.0014(p-0.1)-1.3691×10 -5 (T-60) 2 ) (16)

[0094] Fluid viscosity coefficient K:

[0095] K=0.0435exp(-0.0316(T-60)+0.0175(p-0.1)+1.2362×10 -4 (T-60) 2 ) (17)

[0096] In the formula,

[0097] T is the fluid temperature, °C;

[0098] p is the fluid pressure, MPa.

[0099] Preferably, the Reynolds number of the fluid in the annulus is calculated based on the flow velocity and rheological parameters at low shear rate using the following formula:

[0100]

[0101] In the formula,

[0102] τ0 is the dynamic shear force of the fluid, Pa;

[0103] v o is the flow velocity, m / s;

[0104] D hy is the equivalent hydraulic diameter, m;

[0105] Re a is the Reynolds number of the annular flow;

[0106] ρ is the fluid density, kg / m3.

[0107] Preferably, the annular fluid friction coefficient is calculated using the following formula:

[0108] Laminar flow conditions:

[0109] f l =24Re a (19)

[0110] Turbulent flow conditions:

[0111]

[0112] Where:

[0113] f l is the laminar friction coefficient;

[0114] f t is the turbulent friction coefficient;

[0115] Re g is the Reynolds number calculated under turbulent flow.

[0116] Preferably, the annular circulation pressure drop is calculated based on the annular fluid friction coefficient using the following formula:

[0117]

[0118] In the formula,

[0119] f is the friction coefficient;

[0120] is the friction pressure drop per unit length, Pa / m.

[0121] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0122] 1. The present invention combines the obtained low shear rate and shear stress fitting fluid rheological parameters, considers the influence of temperature, and then fits to obtain a fluid rheological parameter calculation model under temperature conditions, and the calculated cyclic friction error is small.

[0123] 2. The present invention combines the rheological parameter calculation model under temperature conditions and considers the calculation method of fluid circulation friction, and then can obtain the circulation pressure drop calculation method considering the temperature influence at low return rate, which provides support for the accurate prediction of wellbore pressure during drilling and completion, and accurately predicts the wellbore pressure under the combined effect of fluid temperature and low shear rate, providing the prerequisite for solving various complex situations underground, ensuring the safety of underground operations, and greatly shortening the operation cycle. BRIEF DESCRIPTION OF THE DRAWINGS

[0124] Figure 1 A flow chart of a method for calculating wellbore pressure under temperature-pressure coupling and low shear rate according to an embodiment of the present invention;

[0125] Figure 2 A cloud diagram showing the relationship between annular temperature and time during a period of low fluid velocity according to an embodiment of the present invention;

[0126] Figure 3 This is a cross-sectional diagram of temperature distribution of the fluid in the tube and the fluid in the annulus at 261 min when the fluid has a low flow rate according to an embodiment of the present invention;

[0127] Figure 4 A cloud diagram showing the relationship between the flow index of a fluid at a low flow rate and time according to an embodiment of the present invention;

[0128] Figure 5 A cloud diagram showing the relationship between the annular circulation pressure and time when the fluid has a low flow rate according to an embodiment of the present invention;

[0129] Figure 6 This is a graph showing the relationship between the total circulating pressure at the bottom of the well and time distribution under the conditions of considering temperature-pressure coupling and low shear rate and not considering such conditions in one embodiment of the present invention. DETAILED DESCRIPTION

[0130] The specific implementation modes of the present invention are described in detail below in conjunction with the accompanying drawings.

[0131] The present invention provides a method for calculating wellbore pressure under temperature-pressure coupling and low shear rate, comprising the following steps:

[0132] Initially assigning the wellbore fluidity value based on the wellbore parameters;

[0133] Calculate the maximum critical shear rate of the annular fluid;

[0134] Fit the shear rate and shear stress relationship model below the maximum critical shear rate to obtain the fluid rheological parameters at low shear rates;

[0135] Based on the energy conservation principle, a calculation model of the wellbore temperature field during fluid circulation is established; the low shear rate is a shear rate with a Reynolds number less than 800;

[0136] Solve the calculation model of the wellbore temperature field during fluid circulation, obtain the annular temperature distribution characteristics, and establish a model of the relationship between fluid rheological parameters and temperature and pressure under low shear rate;

[0137] Calculate the Reynolds number and friction coefficient of the annular fluid;

[0138] A method for calculating wellbore pressure under low shear rate conditions of forming fluids.

[0139] According to a specific implementation of the present invention, an initial value is assigned to the wellbore fluidity in combination with the wellbore structure, pipe string combination, construction displacement and fluid rheological parameters of an actual well.

[0140] According to a specific embodiment of the present invention, based on the maximum critical shear rate of the annular fluid, a shear rate and shear stress relationship model below the maximum critical shear rate is fitted, specifically including:

[0141] Based on the flow velocity of the fluid in the annulus, the wellbore diameter and the string diameter, combined with the flow velocity and the fluid flow index, the shear rate under the maximum flow velocity condition is obtained, which is the maximum critical shear rate of the annular fluid;

[0142] The relationship between shear rate and shear stress was obtained by a six-speed rotational viscometer;

[0143] Combined with the calculated maximum critical shear rate, a relationship model between shear stress and shear rate below the maximum critical shear rate is fitted.

[0144] According to a specific embodiment of the present invention, the following annular shear rate formula is used to calculate the maximum critical shear rate of the annular fluid:

[0145]

[0146] in,

[0147] n is the fluidity index;

[0148] γ is the annular shear rate, s -1 ;

[0149] v is the velocity of the fluid in the annulus, m / s;

[0150] Dw is the borehole diameter, m;

[0151] D o is the diameter of the pipe, m.

[0152] According to a specific embodiment of the present invention, the maximum shear rate under the same wellbore size conditions is determined based on the shear rate and shear stress relationship model below the maximum critical shear rate, and then the fluid rheological parameters below the critical shear rate are obtained.

[0153] According to a specific embodiment of the present invention, based on the principle of energy conservation, establishing a wellbore temperature field calculation model during fluid circulation specifically includes:

[0154] The total heat flux transferred from the remote formation to the wellbore is:

[0155]

[0156] The heat flow rate exchanged between the wellbore wall and the annulus fluid is:

[0157]

[0158] Combining equations (2) and (3) above, we can obtain the calculation model of the wellbore temperature field during fluid circulation. a The transformed form is expressed as:

[0159]

[0160] Where:

[0161]

[0162] q f is the heat transferred from the distant formation to the wellbore, J;

[0163] ρ m is the fluid density, kg / m 3 ;

[0164] λ f is the formation thermal conductivity, W (m·℃);

[0165] T i is the original formation temperature, °C;

[0166] T w is the well wall temperature, °C;

[0167] T a is the annulus fluid temperature, ℃.

[0168] T D is the dimensionless time temperature;

[0169] qa is the heat transferred from the distant formation to the wellbore, J;

[0170] Q is the fluid flow rate, m 3 / s;

[0171] r w is the wellbore radius, m;

[0172] U a is the comprehensive heat transfer coefficient between the fluid in the annulus and the formation during fluid circulation, J (h·℃·m);

[0173] dz represents the differential unit in the axial direction;

[0174] C m is the specific heat capacity of the fluid, J / (Kg.℃);

[0175] Among them, the far distance refers to the position that is more than 2m away from the well wall;

[0176] Similarly, the heat exchange expression between the fluid in the drill string and the annular drilling fluid is:

[0177]

[0178] Where:

[0179]

[0180] q p is the heat exchange between the fluid in the drill string and the annulus fluid, J;

[0181] T p is the drilling fluid temperature in the pipe, °C;

[0182] Based on the energy conservation principle of the fluid in the string and the annulus in the differential unit, the following annulus and pipe temperature model is obtained:

[0183]

[0184]

[0185] Formulas (6) and (7) are solved jointly to obtain the differential equation of the fluid temperature model in the tubing string. This fluid differential equation is the calculation model of the wellbore temperature field during fluid circulation, which is expressed as follows:

[0186]

[0187] Where:

[0188] T fp is the temperature difference caused by the change of flow pressure drop per unit length of the fluid in the column, °C;

[0189] Tfa is the temperature difference caused by the change of flow pressure drop per unit length of the annulus fluid, °C;

[0190] T mf =AT fa +(A+B)T fp +T in +T s ;

[0191] T in is the drilling fluid inlet temperature, °C;

[0192] T s is the surface temperature, °C;

[0193] G t is the formation temperature gradient, °C / m;

[0194] z is the well depth, m;

[0195] The established calculation model expression of the wellbore temperature field during fluid circulation is as follows:

[0196]

[0197]

[0198] Where:

[0199]

[0200]

[0201] β1 is the coefficient of the wellbore temperature field calculation model expression during fluid circulation;

[0202] β2 is the coefficient of the wellbore temperature field calculation model expression during fluid circulation.

[0203] According to a specific embodiment of the present invention, the coefficient calculation method of the wellbore temperature field calculation model expressions (9) and (10) during fluid circulation is obtained by combining the model boundary conditions and initial conditions, as follows:

[0204] The initial conditions of the fluid at the wellhead and the function of the wellbore temperature changing with the depth are given as follows:

[0205]

[0206] Substituting equation (11) into equation (9) and equation (10), we obtain... The coefficients of model expressions (9) and (10) are as follows:

[0207]

[0208]

[0209] In the formula,

[0210] H is the well depth, m;

[0211] T b is the temperature generated by the hydraulic pressure drop of the drill bit, °C;

[0212]

[0213] According to a specific embodiment of the present invention, a model of the relationship between rheological parameters and temperature and pressure of a low-return fluid during temperature-pressure coupling at a low shear rate is established based on the annular temperature distribution characteristics;

[0214] Fluid dynamic shear force τ:

[0215] τ=2.6142exp(-0.0117(T-60)+0.0071(p-0.1)-7.6842×10 -7 (T-60) 2 ) (15)

[0216] Fluid flow index n:

[0217] n=0.938exp(0.0024(T-60)-0.0014(p-0.1)-1.3691×10 -5 (T-60) 2 ) (16)

[0218] Fluid viscosity coefficient K:

[0219] K=0.0435exp(-0.0316(T-60)+0.0175(p-0.1)+1.2362×10 -4 (T-60) 2 ) (17)

[0220] In the formula,

[0221] T is the fluid temperature, °C;

[0222] p is the fluid pressure, MPa.

[0223] According to a specific embodiment of the present invention, based on the flow rate and rheological parameters at low shear rate, the Reynolds number of the fluid in the annulus is calculated using the following formula:

[0224]

[0225] In the formula,

[0226] τ0 is the dynamic shear force of the fluid, Pa;

[0227] v ois the flow velocity, m / s;

[0228] D hy is the equivalent hydraulic diameter, m;

[0229] Re a is the Reynolds number of the annular flow;

[0230] ρ is the fluid density, kg / m3.

[0231] According to a specific embodiment of the present invention, the annular fluid friction coefficient is calculated using the following formula:

[0232] Laminar flow conditions:

[0233] f l =24 / Re a (19)

[0234] Turbulent flow conditions:

[0235]

[0236] Where:

[0237] f l is the laminar friction coefficient;

[0238] f t is the turbulent friction coefficient;

[0239] Re g is the Reynolds number calculated under turbulent flow.

[0240] According to a specific embodiment of the present invention, the annular circulation pressure drop is calculated based on the annular fluid friction coefficient using the following formula:

[0241]

[0242] In the formula,

[0243] f is the friction coefficient;

[0244] is the friction pressure drop per unit length, Pa / m.

[0245] Example 1

[0246] According to a specific embodiment of the present invention, the calculation method of the wellbore pressure under the temperature-pressure coupling low shear rate of the present invention is described in detail below.

[0247] The present invention provides a method for calculating wellbore pressure under temperature-pressure coupling and low shear rate, comprising the following steps:

[0248] Initially assigning the wellbore fluidity value based on the wellbore parameters;

[0249] Calculate the maximum critical shear rate of the annular fluid;

[0250] Fit the shear rate and shear stress relationship model below the maximum critical shear rate to obtain the fluid rheological parameters at low shear rates;

[0251] Based on the energy conservation principle, a calculation model of the wellbore temperature field during fluid circulation is established; the low shear rate is a shear rate with a Reynolds number less than 800;

[0252] Solve the calculation model of the wellbore temperature field during fluid circulation, obtain the annular temperature distribution characteristics, and establish a model of the relationship between fluid rheological parameters and temperature and pressure under low shear rate;

[0253] Calculate the Reynolds number and friction coefficient of the annular fluid;

[0254] A method for calculating wellbore pressure under low shear rate conditions of forming fluids.

[0255] Among them, the wellbore fluidity is initially assigned based on the actual wellbore structure, pipe string combination, construction displacement and fluid rheological parameters.

[0256] Among them, based on the maximum critical shear rate of the annular fluid, the shear rate and shear stress relationship model below the maximum critical shear rate is fitted, specifically including:

[0257] Based on the flow velocity of the fluid in the annulus, the wellbore diameter and the string diameter, combined with the flow velocity and the fluid flow index, the shear rate under the maximum flow velocity condition is obtained, which is the maximum critical shear rate of the annular fluid;

[0258] The relationship between shear rate and shear stress was obtained by a six-speed rotational viscometer;

[0259] Combined with the calculated maximum critical shear rate, a relationship model between shear stress and shear rate below the maximum critical shear rate is fitted.

[0260] The following annular shear rate formula is used to calculate the maximum critical shear rate of the annular fluid:

[0261]

[0262] in,

[0263] n is the fluidity index;

[0264] γ is the annular shear rate, s -1 ;

[0265] v is the velocity of the fluid in the annulus, m / s;

[0266] D w is the borehole diameter, m;

[0267] D o is the diameter of the pipe, m.

[0268] Among them, according to the shear rate and shear stress relationship model below the maximum critical shear rate, the maximum shear rate under the same wellbore size conditions is determined, and then the fluid rheological parameters below the critical shear rate are obtained.

[0269] Among them, based on the principle of energy conservation, the calculation model of the wellbore temperature field during fluid circulation is established, which specifically includes:

[0270] The total heat flux transferred from the remote formation to the wellbore is:

[0271]

[0272] The heat flow rate exchanged between the wellbore wall and the annulus fluid is:

[0273]

[0274] Combining equations (2) and (3) above, we can obtain the calculation model of the wellbore temperature field during fluid circulation. a The transformed form is expressed as:

[0275]

[0276] Where:

[0277]

[0278] q f is the heat transferred from the distant formation to the wellbore, J;

[0279] ρ m is the fluid density, kg / m 3 ;

[0280] λ f is the formation thermal conductivity, W / (m·℃);

[0281] T i is the original formation temperature, °C;

[0282] T w is the well wall temperature, °C;

[0283] T a is the annulus fluid temperature, ℃.

[0284] T D is the dimensionless time temperature;

[0285] q a is the heat transferred from the distant formation to the wellbore, J;

[0286] Q is the fluid flow rate, m3 / s;

[0287] r w is the wellbore radius, m;

[0288] U a is the comprehensive heat transfer coefficient between the fluid in the annulus and the formation during fluid circulation, J (h·℃·m);

[0289] dz represents the differential unit in the axial direction;

[0290] C m is the specific heat capacity of the fluid, J / (Kg.℃);

[0291] Among them, the far distance refers to the position that is more than 2m away from the well wall;

[0292] Similarly, the heat exchange expression between the fluid in the drill string and the annular drilling fluid is:

[0293]

[0294] Where:

[0295]

[0296] q p is the heat exchange between the fluid in the drill string and the annulus fluid, J;

[0297] T p is the drilling fluid temperature in the pipe, °C;

[0298] Based on the energy conservation principle of the fluid in the string and the annulus in the differential unit, the following annulus and pipe temperature model is obtained:

[0299]

[0300]

[0301] Formulas (6) and (7) are solved jointly to obtain the differential equation of the fluid temperature model in the tubing string. This fluid differential equation is the calculation model of the wellbore temperature field during fluid circulation, which is expressed as follows:

[0302]

[0303] Where:

[0304] T fp is the temperature difference caused by the change of flow pressure drop per unit length of the fluid in the column, °C;

[0305] T fa is the temperature difference caused by the change of flow pressure drop per unit length of the annulus fluid, °C;

[0306] Tmf =AT fa +(A+B)T fp +T in +T s ;

[0307] T in is the drilling fluid inlet temperature, °C;

[0308] T s is the surface temperature, °C;

[0309] G t is the formation temperature gradient, °C / m;

[0310] z is the well depth, m;

[0311] The established calculation model expression of the wellbore temperature field during fluid circulation is as follows:

[0312]

[0313]

[0314] Where:

[0315]

[0316]

[0317] β1 is the coefficient of the wellbore temperature field calculation model expression during fluid circulation;

[0318] β2 is the coefficient of the wellbore temperature field calculation model expression during fluid circulation.

[0319] Among them, the coefficient calculation method of the wellbore temperature field calculation model expressions (9) and (10) during fluid circulation is obtained by combining the model boundary conditions and initial conditions, as follows:

[0320] The initial conditions of the fluid at the wellhead and the function of the wellbore temperature changing with the depth are given as follows:

[0321]

[0322] Substituting equation (11) into equation (9) and equation (10), we obtain... The coefficients of model expressions (9) and (10) are as follows:

[0323]

[0324]

[0325] In the formula,

[0326] H is the well depth, m;

[0327] T b is the temperature generated by the hydraulic pressure drop of the drill bit, °C;

[0328]

[0329] Among them, according to the annular temperature distribution characteristics, a model of the relationship between the rheological parameters of low-return fluid and temperature and pressure during temperature-pressure coupling at low shear rate is established;

[0330] Fluid dynamic shear force τ:

[0331] τ=2.6142exp(-0.0117(T-60)+0.0071(p-0.1)-7.6842×10 -7 (T-60) 2 ) (15)

[0332] Fluid flow index n:

[0333] n=0.938exp(0.0024(T-60)-0.0014(p-0.1)-1.3691×10 -5 (T-60) 2 ) (16)

[0334] Fluid viscosity coefficient K:

[0335] K=0.0435exp(-0.0316(T-60)+0.0175(p-0.1)+1.2362×10 -4 (T-60) 2 ) (17)

[0336] In the formula,

[0337] T is the fluid temperature, °C;

[0338] p is the fluid pressure, MPa.

[0339] Among them, based on the flow velocity and rheological parameters at low shear rate, the Reynolds number of the fluid in the annulus is calculated using the following formula:

[0340]

[0341] In the formula,

[0342] τ0 is the dynamic shear force of the fluid, Pa;

[0343] v o is the flow velocity, m / s;

[0344] D hy is the equivalent hydraulic diameter, m;

[0345] Re ais the Reynolds number of the annular flow;

[0346] ρ is the fluid density, kg / m3.

[0347] The following formula is used to calculate the annular fluid friction coefficient:

[0348] Laminar flow conditions:

[0349] f l =24 / Re a (19)

[0350] Turbulent flow conditions:

[0351]

[0352] Where:

[0353] f l is the laminar friction coefficient;

[0354] f t is the turbulent friction coefficient;

[0355] Re g is the Reynolds number calculated under turbulent flow.

[0356] The annular circulation pressure drop is calculated based on the annular fluid friction coefficient using the following formula:

[0357]

[0358] In the formula,

[0359] f is the friction coefficient;

[0360] is the friction pressure drop per unit length, Pa / m.

[0361] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.

Claims

1. A method for calculating wellbore pressure under temperature-pressure coupling and low shear rate, characterized in that: The steps include: Initially assigning the wellbore fluidity value based on the wellbore parameters; Calculate the maximum critical shear rate of the annular fluid; Fit the shear rate and shear stress relationship model below the maximum critical shear rate to obtain the fluid rheological parameters at low shear rates; Based on the energy conservation principle, a calculation model of the wellbore temperature field during fluid circulation is established; the low shear rate is a shear rate with a Reynolds number less than 800; Solve the calculation model of the wellbore temperature field during fluid circulation, obtain the annular temperature distribution characteristics, and establish a model of the relationship between fluid rheological parameters and temperature and pressure under low shear rate; Calculate the Reynolds number and friction coefficient of the annular fluid; A method for calculating wellbore pressure under low shear rate conditions of forming fluids.

2. The method for calculating wellbore pressure under temperature-pressure coupling and low shear rate according to claim 1, characterized in that: The wellbore fluidity is initially assigned based on the actual wellbore structure, pipe string combination, construction displacement and fluid rheological parameters.

3. The method for calculating wellbore pressure under temperature-pressure coupling and low shear rate according to claim 1, characterized in that: Based on the maximum critical shear rate of the annular fluid, the shear rate and shear stress relationship model below the maximum critical shear rate is fitted, including: Based on the flow velocity of the fluid in the annulus, the wellbore diameter and the string diameter, combined with the flow velocity and the fluid flow index, the shear rate under the maximum flow velocity condition is obtained, which is the maximum critical shear rate of the annular fluid; The relationship between shear rate and shear stress was obtained by a six-speed rotational viscometer; Combined with the calculated maximum critical shear rate, a relationship model between shear stress and shear rate below the maximum critical shear rate is fitted.

4. The method for calculating wellbore pressure under temperature-pressure coupling and low shear rate according to claim 3, characterized in that: The maximum critical shear rate of the annular fluid is calculated using the following annular shear rate formula: in, n is the fluidity index; γ is the annular shear rate, s -1 ; v is the velocity of the fluid in the annulus, m / s; D w is the borehole diameter, m; D o is the diameter of the pipe, m.

5. The method for calculating wellbore pressure under temperature-pressure coupling and low shear rate according to claim 4, characterized in that: According to the shear rate and shear stress relationship model below the maximum critical shear rate, the annular shear rate formula is used to determine the maximum shear rate under the same wellbore size conditions, and then the fluid rheological parameters below the critical shear rate are obtained.

6. The method for calculating wellbore pressure under temperature-pressure coupling and low shear rate according to claim 1, characterized in that: Based on the principle of energy conservation, the calculation model of the wellbore temperature field during fluid circulation is established, which specifically includes: The total heat flux transferred from the remote formation to the wellbore is: The heat flow rate exchanged between the wellbore wall and the annulus fluid is: Combining equations (2) and (3) above, we can obtain the calculation model of the wellbore temperature field during fluid circulation. a The transformed form is expressed as: Where: q f is the heat transferred from the distant formation to the wellbore, J; ρ m is the fluid density, kg / m 3 ; λ f is the formation thermal conductivity, W / (m·℃); T i is the original formation temperature, °C; T w is the well wall temperature, °C; T a is the annulus fluid temperature, °C; T D is the dimensionless time temperature; q a is the heat transferred from the distant formation to the wellbore, J; Q is the fluid flow rate, m 3 / s; r w is the wellbore radius, m; U a is the comprehensive heat transfer coefficient between the fluid in the annulus and the formation during fluid circulation, J / (h·℃·m); dz represents the differential unit in the axial direction; C m is the specific heat capacity of the fluid, J / (Kg.℃); Among them, the far distance refers to the position that is more than 2m away from the well wall; Similarly, the heat exchange expression between the fluid in the drill string and the annular drilling fluid is: Where: q p is the heat exchange between the fluid in the drill string and the annulus fluid, J; T p is the drilling fluid temperature in the pipe, °C; Based on the energy conservation principle of the fluid in the string and the annulus in the differential unit, the following annulus and pipe temperature model is obtained: Formulas (6) and (7) are solved jointly to obtain the differential equation of the fluid temperature model in the tubing string. This fluid differential equation is the calculation model of the wellbore temperature field during fluid circulation, which is expressed as follows: Where: T fp is the temperature difference caused by the change of flow pressure drop per unit length of the fluid in the column, °C; T fa is the temperature difference caused by the change of flow pressure drop per unit length of the annulus fluid, °C; T mf =AT fa +(A+B)T fp +T in +T s ; T in is the drilling fluid inlet temperature, °C; T s is the surface temperature, °C; G t is the formation temperature gradient, °C / m; z is the well depth, m; The established calculation model expression of the wellbore temperature field during fluid circulation is as follows: Where: β1 is the coefficient of the wellbore temperature field calculation model expression during fluid circulation; β2 is the coefficient of the wellbore temperature field calculation model expression during fluid circulation.

7. The method for calculating wellbore pressure under temperature-pressure coupling and low shear rate according to claim 6, characterized in that: Combining the model boundary conditions and initial conditions, the coefficient calculation method of the wellbore temperature field calculation model expressions (9) and (10) during fluid circulation is obtained as follows: The initial conditions of the fluid at the wellhead and the function of the wellbore temperature changing with the depth are given as follows: Substituting equation (11) into equation (9) and equation (10), the coefficients β1 and β2 of the wellbore temperature field calculation model expressions (9) and (10) during fluid circulation are obtained as follows: In the formula, H is the well depth, m; T b is the temperature generated by the hydraulic pressure drop of the drill bit, °C; 8. The method for calculating wellbore pressure under temperature-pressure coupling and low shear rate according to claim 7, characterized in that: According to the temperature distribution characteristics of the annulus, a model of the relationship between the rheological parameters of the low-return fluid and the temperature and pressure when the temperature and pressure are coupled under low shear rate is established; Fluid dynamic shear force σ: τ=2.6142exp(-0.0117(T-60)+0.0071(p-0.1)-7.6842×10 -7 (T-60) 2 ) (15) Fluid flow index n: n=0.938exp(0.0024(T-60)-0.0014(p-0.1)-1.3691×10 -5 (T-60) 2 ) (16) Fluid viscosity coefficient K: K=0.0435exp(-0.0316(T-60)+0.0175(p-0.1)+1.2362×10 -4 (T-60) 2 ) (17) In the formula, T is the fluid temperature, °C; p is the fluid pressure, MPa.

9. The method for calculating wellbore pressure under temperature-pressure coupling and low shear rate according to claim 8, characterized in that: Based on the flow velocity and rheological parameters at low shear rate, the Reynolds number of the fluid in the annulus is calculated using the following formula: In the formula, τ0 is the dynamic shear force of the fluid, Pa; v o is the flow velocity, m / s; D hy is the equivalent hydraulic diameter, m; Re a is the Reynolds number of the annular flow; ρ is the fluid density, kg / m3.

10. The method for calculating wellbore pressure under temperature-pressure coupling and low shear rate according to claim 9, characterized in that: The annular fluid friction coefficient is calculated using the following formula: Laminar flow conditions: f l =24 / Re a (19) Turbulent flow conditions: Where: f l is the laminar friction coefficient; f t is the turbulent friction coefficient; Re g is the Reynolds number calculated under turbulent flow.

11. The method for calculating wellbore pressure under temperature-pressure coupling and low shear rate according to claim 10, characterized in that: The annular circulation pressure drop is calculated based on the annular fluid friction coefficient using the following formula: In the formula, f is the friction coefficient; is the friction pressure drop per unit length, Pa / m.

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