A method of hydrodynamic analysis of a pingen fluid in a wellbore eccentric annulus

Abstract

The application discloses a kind of fluid dynamics analysis methods of Bingham fluid in wellbore eccentric annulus, it is related to oil and gas well technical field.The application constructs extended reach well model according to the design parameter of extended reach well, Bingham fluid flows in the eccentric annulus of extended reach well model, determines the shearless plug position of Bingham fluid, obtains the shear stress and velocity distribution of Bingham fluid in eccentric annulus, determines the dimensionless volume flow of Bingham fluid in eccentric annulus, based on the frictional pressure drop gradient of Bingham fluid in concentric annulus in extended reach well model, using numerical simulation software, calculates the frictional pressure drop gradient ratio of Bingham fluid, determines the frictional pressure drop gradient of Bingham fluid in eccentric annulus, completes the fluid dynamics analysis of Bingham fluid in wellbore eccentric annulus.The method of the application combines eccentric annulus dynamics and hydraulics numerical analysis, accurately obtains the frictional pressure drop gradient ratio of Bingham fluid, and lays a foundation for guiding the drilling operation of extended reach well.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of oil and gas wells, and particularly relates to a method for fluid dynamics analysis of Bingham fluid in an eccentric annulus of a wellbore. BACKGROUND

[0002] In the process of extended reach well drilling operation, accurately predicting the fluid dynamics and hydraulic characteristics of drilling fluid in the annular space of the wellbore under the yield Bingham mode is the theoretical basis for accurately evaluating the real-time equivalent circulating density (ECD for short), and is crucial for the determination and effective management of wellbore pressure. Theoretical and experimental studies have shown that the pressure loss and fluid velocity distribution in the annular space of the wellbore are significantly affected by the fluid rheological properties, wellbore eccentricity and annular geometry.

[0003] The research on the eccentric annulus flow of non-Newtonian fluid has evolved from analytical exploration to multi-method cooperation. Early research mainly focused on Newtonian fluid, using the bipolar coordinate system analytical method, but it is difficult to extend to non-Newtonian fluid due to its complexity. After 1980, with the simplified model becoming the mainstream method, some scholars proposed using the slit model to equivalent the eccentric annulus to a variable height slit, and solving the power-law fluid flow by integrating the motion equation; another part of the scholars proposed the concentric annulus superposition method, which discretizes the eccentric annulus into infinite concentric ring elements, and obtains the analytical solution of power-law and Bingham fluid by combining geometric equivalence and rheological equation integration.

[0004] With the improvement of computing power, since 2000, the research on the eccentric annulus flow of non-Newtonian fluid has gradually adopted the analysis method combining numerical simulation and experiment. However, the existing theoretical model and analysis method mostly focus on the analysis of the dimensionless shear stress, shear rate and volume flow of the eccentric annulus relative to the concentric annulus, and a systematic method for fluid dynamics analysis of Bingham fluid in the eccentric annulus of the wellbore has not been established, especially the analysis method of the friction pressure drop gradient in the eccentric annulus. Therefore, it is urgent to propose a method for fluid dynamics analysis of Bingham fluid in the eccentric annulus of the wellbore, which can provide a basis for quantitatively obtaining the drilling hydraulic parameters of the extended reach well and guiding the drilling operation of the extended reach well. SUMMARY

[0005] The application aims to solve the problems of the prior art, and proposes a method for fluid dynamics analysis of Bingham fluid in the eccentric annulus of the wellbore, which combines the numerical analysis method of eccentric annulus dynamics and hydraulics, realizes the accurate acquisition of the friction pressure drop gradient of Bingham fluid in the eccentric annulus, and can quantitatively obtain the distribution of shear stress, shear rate and flow rate of Bingham fluid in the eccentric annulus, thereby providing a theoretical basis and technical support for guiding the drilling operation of the extended reach well.

[0006] The application specifically adopts the following technical scheme:

[0007] A method for fluid dynamics analysis of a Bingham fluid in an eccentric annulus of a wellbore, comprising the following steps:

[0008] Step 1, constructing a large displacement well model with an eccentric annulus inside according to design parameters of the large displacement well;

[0009] Step 2, setting the drilling fluid in the large displacement well model as a Bingham fluid, and determining the shear-free plug position of the Bingham fluid in the large displacement well model;

[0010] Step 3, obtaining the shear stress and velocity distribution of the Bingham fluid in the eccentric annulus;

[0011] Step 4, determining the dimensionless volume flow rate of the Bingham fluid in the eccentric annulus;

[0012] Step 5, based on the frictional pressure drop gradient of the Bingham fluid in the concentric annulus of the large displacement well model, using numerical simulation software to calculate the frictional pressure drop gradient ratio of the Bingham fluid, determine the frictional pressure drop gradient of the Bingham fluid in the eccentric annulus, and complete the fluid dynamics analysis of the Bingham fluid in the eccentric annulus of the wellbore.

[0013] Preferably, in the step 1, the large displacement well model is constructed according to the design parameters of the large displacement well;

[0014] The large displacement well model comprises a drill string model and a wellbore model, the drill string model is eccentrically arranged in the wellbore model, and the annular space between the outer wall of the drill string model and the inner wall of the wellbore model is the eccentric annulus;

[0015] A polar coordinate system is constructed in the large displacement well model, and the center position of the drill string model is taken as the origin of the polar coordinate system , the positive direction of the polar axis in the polar coordinate system points to the widest direction of the eccentric annulus, and the polar angle corresponding to the positive direction of the polar axis is 0°, and the polar angle increases in the counterclockwise direction;

[0016] The vertical distance between the center of the wellbore model and the center of the drill string model is the eccentricity , and the eccentricity is used to determine the eccentricity of the drill string model :

[0017] ;

[0018] In the formula, D is the outer diameter of the drill string model; is the inner diameter of the wellbore model;

[0019] The polar coordinate equation of the wellbore model is: ​

[0020] ;

[0021] wherein, is the polar radius, used to represent the polar coordinate system origin is the distance between the inner wall of the wellbore model;

[0022] is the annular gap between the drill string model and the wellbore model is:

[0023] ;

[0024] wherein, is the annular gap, used to represent the distance between the outer wall of the drill string model and the inner wall of the wellbore model on the polar azimuth line.

[0025] Preferably, in step 2, the drilling fluid in the extended reach well model is set as a Bingham fluid, and the fluid parameters of the Bingham fluid are set according to the fluid properties of the Bingham fluid;

[0026] The Bingham fluid flowing in the eccentric annulus in the extended reach well model forms a shear-free plug flow region, the plug flow region is located in the middle region of the eccentric annulus, the width of the plug flow region is independent of the annular gap, and the shear-free plug position of the Bingham fluid in the eccentric annulus is determined according to the width of the plug flow region;

[0027] The calculation formula of the plug flow region width is:

[0028] ;

[0029] wherein,

[0030] ;

[0031] ;

[0032] wherein, is the width of the plug flow region; is the upper boundary of the plug flow region; is the lower boundary of the plug flow region; is the natural logarithm; is the dynamic shear force of the Bingham fluid; is the eccentric annulus friction pressure drop gradient of the Bingham fluid.

[0033] Preferably, in step 3, the flow domain of the Bingham fluid at any polar azimuth in the eccentric annulus is divided into three sub-regions, namely an inner sub-region, a plug flow sub-region and an outer sub-region, wherein the flow domain range of the inner sub-region is , the flow domain range of the plug flow sub-region is , and the flow domain range of the outer sub-region is , wherein, is a radial coordinate of the Bingham fluid in the eccentric annulus, used to represent the radial position of the Bingham fluid in the eccentric annulus;

[0034] is the flow rate of the Bingham fluid in the inner sub-domain increases, the flow rate of the Bingham fluid at the outer diameter of the drill string model is 0; the flow rate of the Bingham fluid in the plug sub-domain is constant, , is the maximum flow rate of the Bingham fluid; the flow rate of the Bingham fluid in the outer sub-domain decreases as the polar radius increases, the flow rate of the Bingham fluid at the polar radius is 0.

[0035] Preferably, the shear stress and the flow rate of the Bingham fluid in the inner sub-domain, the plug sub-domain and the outer sub-domain are different;

[0036] The momentum conservation equation in the inner sub-domain is:

[0037] ;

[0038] In the formula, is the shear stress of the Bingham fluid;

[0039] The rheological model of the Bingham fluid in the inner sub-domain is:

[0040] ;

[0041] In the formula, is the plastic viscosity of the Bingham fluid;

[0042] The shear rate equation of the Bingham fluid in the inner sub-domain is obtained by combining the momentum conservation equation in the inner sub-domain with the rheological model of the Bingham fluid:

[0043] ;

[0044] The flow rate equation of the Bingham fluid in the inner sub-domain is obtained by integrating the boundary conditions of the inner sub-domain:

[0045] ;

[0046] In the plug sub-domain, at the lower boundary of the plug sub-domain , at the upper boundary of the plug sub-domain , the shear rate equation of the Bingham fluid in the plug sub-domain is determined as:

[0047] ​​​;

[0048] The momentum conservation equation in the outer sub-domain is:

[0049] ;

[0050] The rheological model of the Bingham fluid in the outer sub-domain is:

[0051] ;

[0052] The shear rate equation of the Bingham fluid in the outer sub-domain is obtained by combining the momentum conservation equation in the outer sub-domain with the rheological model of the Bingham fluid:

[0053] ;

[0054] The flow velocity equation of the Bingham fluid in the outer sub-domain is obtained by separating variables and integrating the boundary conditions of the outer sub-domain:

[0055] ;

[0056] The velocity distribution of the Bingham fluid in the eccentric annulus is determined according to the flow velocity equations of the Bingham fluid in the inner sub-domain, the plug flow sub-domain and the outer sub-domain.

[0057] Preferably, in step 4, based on the symmetry of the eccentric annulus, the eccentric annulus frictional pressure drop gradient when the Bingham fluid flows in the eccentric annulus is determined as:

[0058] ;

[0059] wherein,

[0060] ;

[0061] ;

[0062] wherein, is the eccentric annulus frictional pressure drop gradient of the Bingham fluid; is the dimensionless discharge of the Bingham fluid in the eccentric annulus; is the volume flow rate of the Bingham fluid in the eccentric annulus;

[0063] The dimensionless discharge of the Bingham fluid in the eccentric annulus is calculated by using the numerical integration method The integral calculation is performed in the integral interval [0, ] to obtain:

[0064] ;

[0065] The expression of the dimensionless discharge of the Bingham fluid in the eccentric annulus is simplified by setting an intermediate quantity, and the expression of the dimensionless discharge of the Bingham fluid in the eccentric annulus is simplified as:

[0066] ;

[0067] wherein,

[0068] ;

[0069] wherein, is an intermediate quantity;

[0070] The numerical integration is performed by using the composite Simpson rule. According to the preset angle, the number of segments is set, and after the integral interval is equally divided into a plurality of sub-intervals, the intermediate quantity is obtained according to the Simpson formula expansion, and the calculation formula of the intermediate quantity is as follows:

[0071] ;

[0072] wherein,

[0073] ;

[0074] wherein, is a sub-interval serial number, is a total number of sub-intervals; is a weight coefficient of the i-th sub-interval; is an integral function; According to the integral function value at each angle and according to the weight coefficient weighted summation, multiplied by the coefficient

[0075] is substituted into the volume flow calculation formula of the Bingham fluid in the eccentric annulus, and the dimensionless displacement of the Bingham fluid in the eccentric annulus is calculated.

[0076] Preferably, in step 5, when the eccentricity of the drill string model in the extended reach well model is 0, at this time, the center of the drill string model is coincided with the center of the wellbore model, and the annular space between the outer wall of the drill string model and the inner wall of the wellbore model changes into a concentric annulus.

[0077] When the Bingham fluid flows in the concentric annulus, the concentric annulus friction pressure drop gradient of the Bingham fluid is expressed as:

[0078] ;

[0079] wherein, is the concentric annulus friction pressure drop gradient of the Bingham fluid; is the dynamic shear force of the Bingham fluid; is the average flow velocity of the annulus;

[0080] ​​​​​Based on the dimensionless displacement of the Bingham fluid in the concentric annulus, the simplified expression for the frictional pressure drop gradient in the concentric annulus is:

[0081] ;

[0082] in,

[0083] ;

[0084] ;

[0085] ;

[0086] In the formula, For the dimensionless displacement of Bingham fluid in concentric annular spaces; The radial coordinates of the inner boundary of the concentric annular slug flow region; The right boundary radial coordinates of the concentric annular slug flow region;

[0087] Calculate the ratio between the eccentric annular frictional pressure drop gradient and the concentric annular frictional pressure drop gradient of Bingham fluid under the same displacement, and determine the frictional pressure drop gradient ratio of Bingham fluid as:

[0088] ;

[0089] In the formula, The Bingham fluid frictional pressure drop gradient ratio;

[0090] Combining the simplified expression for the dimensionless displacement of the Bingham fluid in the eccentric annulus and the simplified expression for the pressure drop gradient of the frictional resistance in the concentric annulus, we obtain:

[0091] ;

[0092] Substituting the dimensionless displacement of the eccentric annular air Bingham fluid From the calculation formula, the implicit function of the Bingham fluid friction pressure drop gradient ratio is obtained as:

[0093] ;

[0094] Due to intermediate quantity Width of the middle flow region and upper boundary All are variables, and the width of the choke region and upper boundary All are eccentric annular frictional resistance voltage drop gradients The function yields the width of the slug flow region. and upper boundary Regarding the pressure drop gradient ratio of Bingham fluid frictional resistance The expression is:

[0095] ;

[0096] ;

[0097] The implicit function of the Bingham fluid friction pressure drop gradient ratio is iteratively solved, a Bingham fluid eccentric annulus friction pressure drop gradient ratio calculation equation is constructed, and the following is obtained:

[0098] ;

[0099] In the formula, is a calculation function of the eccentric annulus friction pressure drop gradient ratio;

[0100] The Bingham fluid friction pressure drop gradient ratio is the root of the Bingham fluid eccentric annulus friction pressure drop gradient ratio calculation equation, and is obtained by Taylor expansion linear approximation using the Newton-Raphson method:

[0101] ;

[0102] In the formula, is the number of iterations; is the derivative of the eccentric annulus friction pressure drop gradient ratio in the iteration calculation;

[0103] The derivative of the eccentric annulus friction pressure drop gradient calculation function is solved by using a numerical differentiation method, and the following is obtained:

[0104] ;

[0105] In the formula, is the difference between the Bingham fluid friction pressure drop gradient ratios before and after updating.

[0106] Preferably, in step 5, the Bingham fluid friction pressure drop gradient ratio is calculated using numerical simulation software, specifically including the following steps:

[0107] Step 5.1, input calculation parameters;

[0108] The calculation parameters include the outer diameter of the drill string model , the inner diameter of the wellbore model , the eccentricity of the drill string model , the volume flow rate of the Bingham fluid in the eccentric annulus , the dynamic shear force , and the plastic viscosity ;

[0109] Step 5.2, calculate the concentric annulus friction pressure drop gradient of the Bingham fluid ;

[0110] Step 5.3, calculate the inner boundary radial coordinate of the plug flow region in the concentric annulus and right boundary radial coordinates ;

[0111] Step 5.4, based on the outer diameter of the drill string model , the inner diameter of the wellbore model and the radial coordinates of the inner boundary of the concentric annular slug flow region and right boundary radial coordinates Calculate the dimensionless displacement of Bingham fluid in concentric annular spaces. ;

[0112] Step 5.5, set the frictional voltage drop gradient ratio initial value and convergence threshold ;

[0113] Step 5.6, iteratively update the calculated frictional pressure drop gradient ratio ;

[0114] Calculate the width of the slug region Then, based on the polar coordinate equation of the wellbore model and the upper boundary of the plug flow region... The expression for the Bingham fluid frictional pressure drop gradient ratio is used to obtain the extreme diameter at each preset orientation. and the upper boundary of the choke flow region Determine the integrand at each preset orientation. Then, by performing numerical integration on the integrand at each preset orientation, the intermediate quantity is determined. Calculate the calculated value and derivative of the current Bingham fluid eccentric annular friction pressure drop gradient ratio. Then, based on the calculation equation of the Bingham fluid eccentric annular friction pressure drop gradient ratio, obtain the calculated value of the Bingham fluid eccentric annular friction pressure drop gradient ratio and update the Bingham fluid friction pressure drop gradient ratio.

[0115] Step 5.7: Obtain the updated Bingham fluid friction pressure drop gradient ratio Calculate the difference in the Bingham fluid friction pressure drop gradient ratio before and after the update. ;

[0116] Step 5.8: Perform a convergence check by updating the difference between the Bingham fluid friction pressure drop gradient ratio before and after the update. With the preset convergence threshold Compare the differences in the Bingham fluid friction pressure drop gradient ratio before and after the update. Exceeding the preset convergence threshold If the updated Bingham fluid friction pressure drop gradient ratio is set as the initial value of the Bingham fluid friction pressure drop gradient ratio, return to step 5.6 and continue iterative updates; otherwise, end the iteration.

[0117] Step 5.9: Output the frictional pressure drop gradient ratio of Bingham fluid.

[0118] The beneficial technical effects brought by the present application are:

[0119] The present application provides a kind of fluid dynamics analysis method of Bingham fluid in wellbore eccentric annulus, based on the design parameters of large displacement well, the large displacement well model is constructed, the shear plug position of Bingham fluid in eccentric annulus is determined by using large displacement well model, shear stress and velocity distribution, the dimensionless volume flow of Bingham fluid in eccentric annulus is obtained, and based on the frictional pressure drop gradient of Bingham fluid in concentric annulus in large displacement well model, the frictional pressure drop gradient ratio of Bingham fluid is accurately calculated by using numerical simulation software, the frictional pressure drop gradient of Bingham fluid in eccentric annulus is determined, which provides technical support for accurately obtaining the distribution of shear stress, shear rate and flow rate of Bingham fluid in eccentric annulus, and lays a foundation for fluid dynamics analysis of Bingham fluid in wellbore eccentric annulus.

[0120] The present application provides a kind of fluid dynamics analysis method of Bingham fluid in wellbore eccentric annulus, which makes up for the lack of method for systematically analyzing the flow properties of Bingham fluid in eccentric annulus at present, and the method is based on the variable-diameter concentric annulus superposition thinking, combines eccentric annulus dynamics analysis and hydrodynamic numerical simulation, realizes the quantitative cognition of large displacement well drilling hydrodynamic engineering parameters, and provides a basis for guiding the drilling operation of large displacement well. BRIEF DESCRIPTION OF DRAWINGS

[0121] Figure 1 It is the flow chart of the present application, a kind of fluid dynamics analysis method of Bingham fluid in wellbore eccentric annulus.

[0122] Figure 2 It is the schematic diagram of large displacement well model.

[0123] Figure 3 It is annular gap with the variation curve of polar angle .

[0124] Figure 4 It is the calculation flow chart of Bingham fluid frictional pressure drop gradient ratio.

[0125] In the figure, it is the origin of polar coordinate system, it is polar angle, it is the outer diameter of drill string model, it is the inner diameter of wellbore model, it is annular gap, it is eccentric distance, it is the upper boundary of plug flow region, it is the lower boundary of plug flow region, it is the width of plug flow region. DETAILED DESCRIPTION

[0126] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0127] Example 1

[0128] This invention proposes a fluid dynamics analysis method for Bingham fluid in the air of an eccentric annulus of a wellbore, such as... Figure 1 As shown, the specific steps include:

[0129] Step 1: Based on the design parameters of the extended reach well, construct a model of the extended reach well with an eccentric annulus inside.

[0130] In step 1, a large-displacement well model is constructed based on the design parameters of the large-displacement well. This model includes a drill string model and a wellbore model, such as... Figure 2 As shown, the drill string model is eccentrically positioned inside the wellbore model, and the annular space between the outer wall of the drill string model and the inner wall of the wellbore model is an eccentric annulus.

[0131] A polar coordinate system is constructed in the large-displacement well model, with the center position of the drill string model as the origin of the polar coordinate system. In the polar coordinate system, the positive polar axis points to the widest point of the eccentric annulus, and the polar angle corresponding to the positive polar axis direction is... 0°, polar angle Increase in a counter-clockwise direction.

[0132] The vertical distance between the center of the wellbore model and the center of the drill string model is the eccentricity. According to eccentricity Determine the eccentricity of the drill string model for:

[0133] ;

[0134] In the formula, The outer diameter of the drill string model; This is the inner diameter of the wellbore model.

[0135] The polar coordinate equation of the wellbore model is:

[0136] ;

[0137] In the formula, The polar radius is used to represent the origin of the polar coordinate system. The distance between the wellbore model and the inner wall.

[0138] The annular space between the drill string model and the wellbore model for:

[0139] ;

[0140] In the formula, is the annular clearance, used to represent the distance between the outer wall of the drill string model and the inner wall of the wellbore model on the polar azimuth line, and in the embodiment, the annular clearance varies with the polar angle as shown in the curve. Figure 3

[0141] Step 2, set the drilling fluid in the extended reach well model as Bingham fluid, and determine the shear-free plug position of the Bingham fluid in the extended reach well model.

[0142] In the embodiment, the drilling fluid in the extended reach well model is set as Bingham fluid, and the fluid parameters of the Bingham fluid are set according to the fluid properties of the Bingham fluid.

[0143] The Bingham fluid flows in the eccentric annulus in the extended reach well model to form a shear-free plug flow region, in which the flow rate of the Bingham fluid is the same everywhere and the shear rate is 0, the upper boundary of the plug flow region is , the lower boundary is , and the width is , The plug flow region is located in the middle region of the eccentric annulus, the width of the plug flow region is independent of the annular clearance, and the shear-free plug position of the Bingham fluid in the eccentric annulus is determined according to the width of the plug flow region.

[0144] The calculation formula of the width of the plug flow region is:

[0145] ;

[0146] wherein,

[0147] ;

[0148] ;

[0149] In the formula, is the width of the plug flow region, in units of cm; is the upper boundary of the plug flow region, specifically the distance between the top end of the plug flow region and the horizontal plane where the origin is located; is the lower boundary of the plug flow region, specifically the distance between the bottom end of the plug flow region and the horizontal plane where the origin is located; is the natural logarithm; is the dynamic shear force of the Bingham fluid, in units of ; is the eccentric annulus friction pressure drop gradient of the Bingham fluid, in units of .

[0150] When the eccentricity of the drill string model is ​When the value is 0, that is, the center of the drill string model coincides with the center of the wellbore model, and the annular space between the outer wall of the drill string model and the inner wall of the wellbore model changes to a concentric annulus. The calculation formula for the shearless plug characteristic parameter of the slug flow region in the concentric annulus is the same as the calculation formula for the shearless plug characteristic parameter of the slug flow region in the eccentric annulus.

[0151] Step 3: Obtain the shear stress and velocity distribution of the Bingham fluid in the eccentric annular space.

[0152] In this embodiment, the flow domain of the Bingham fluid at any polar angle in the eccentric annulus is divided into three sub-regions: the inner sub-domain, the sluice sub-domain, and the outer sub-domain. The flow domain of the inner sub-domain is [missing information]. The catchment area of ​​the sluice sub-domain is The watershed range of the outer subdomain is ,in, The radial coordinates of the Bingham fluid in the eccentric annular space are used to represent the radial position of the Bingham fluid in the eccentric annular space.

[0153] The flow velocity of the Bingham fluid in the inner subdomain. With the polar diameter The outer diameter of the drill string model increases with the increase of the size of the drill string. The flow rate of Bingham fluid The velocity is 0; in the slug subdomain, the velocity of the Bingham fluid is... Constant and unchanging, , The maximum flow velocity of the Bingham fluid; the flow velocity of the Bingham fluid in the outer subdomain. With polar diameter The value decreases as the radius increases. The flow rate of Bingham fluid It is 0.

[0154] The shear stress and velocity characteristics of Bingham fluid differ in the inner subdomain, slug subdomain, and outer subdomain; that is, the shear rate and shear stress of Bingham fluid exhibit different characteristics in the inner subdomain, slug subdomain, and outer subdomain.

[0155] The momentum conservation equation in the inner subdomain is:

[0156] ;

[0157] In the formula, For Bingham fluid, the shear stress is denoted as .

[0158] The rheological mode of the Bingham fluid in the inner subdomain is as follows:

[0159] ;

[0160] In the formula, The plastic viscosity of Bingham fluid is given by units of 1000 ppm. .

[0161] By combining the momentum conservation equation in the inner subdomain with the Bingham fluid rheological model, the shear rate equation for the Bingham fluid in the inner subdomain is obtained as follows:

[0162] ;

[0163] Integrating the boundary conditions of the inner subdomain, the velocity equation for the Bingham fluid in the inner subdomain is obtained as follows:

[0164] .

[0165] In the plug subdomain, at the lower boundary of the plug subdomain At the upper boundary of the plug subdomain That is, in the plug subdomain place, , Place, Thus, the shear rate equation for the Bingham fluid in the plug subdomain is determined as follows:

[0166] ;

[0167] The momentum conservation equation in the outer subdomain is:

[0168] .

[0169] The rheological mode of the Bingham fluid in the outer subdomain is as follows:

[0170] .

[0171] By combining the momentum conservation equation in the outer subdomain with the Bingham fluid rheological model, the shear rate equation for the Bingham fluid in the outer subdomain is obtained as follows:

[0172] .

[0173] By separating variables and integrating the boundary conditions of the outer subdomain, the velocity equation for the Bingham fluid in the outer subdomain is obtained as follows:

[0174] .

[0175] Based on the flow velocity equations of Bingham fluid in the inner subdomain, plug subdomain, and outer subdomain, the velocity distribution of Bingham fluid in the eccentric annulus is determined.

[0176] Step 4: Determine the dimensionless volumetric flow rate of the Bingham fluid in the eccentric annulus.

[0177] In step 4, based on the symmetry of the eccentric annulus, the non-dimensional volumetric flow rate expression of Bingham fluid flowing in the concentric annulus is imitated to determine the eccentric annulus frictional pressure drop gradient of Bingham fluid flowing in the eccentric annulus as follows:

[0178] ;

[0179] wherein,

[0180] ;

[0181] ;

[0182] in the formula, is the eccentric annulus frictional pressure drop gradient of Bingham fluid; is the non-dimensional displacement of Bingham fluid in the eccentric annulus; is the volumetric flow rate of Bingham fluid in the eccentric annulus.

[0183] Since the integral interval of the non-dimensional volumetric flow rate expression of Bingham fluid in the eccentric annulus is [0, ], the integrand and depend on the polar angle , contain multiple nonlinear terms and power function terms, and it is difficult to obtain a rigorous analytical solution, so the numerical integral method is used to perform integral calculation on the non-dimensional volumetric flow rate of Bingham fluid in the eccentric annulus.

[0184] The non-dimensional displacement of Bingham fluid in the eccentric annulus is calculated by using the numerical integral method, and the following is obtained:

[0185] .

[0186] The intermediate quantity is set to simplify the expression of the non-dimensional displacement of Bingham fluid in the eccentric annulus, and the non-dimensional displacement expression of Bingham fluid in the eccentric annulus is simplified as follows:

[0187] ;

[0188] wherein,

[0189] ;

[0190] in the formula, is the intermediate quantity.

[0191] That is, the integrand in the intermediate quantity is decomposed , , and into four parts in total.

[0192] The numerical integration is performed by using the composite Simpson rule, the number of segments is set according to the preset angle, the integral interval is equally divided into a plurality of sub-intervals, the intermediate quantity is obtained according to the Simpson formula expansion, and the calculation formula of the intermediate quantity is:

[0193]

[0194]

[0195]

[0196] In the formula, i is the sub-interval serial number, and n is the total number of sub-intervals. The weight coefficient of the i-th sub-interval is: The independent variable of the integrand is the polar angle, that is, the integrand is a function of the polar angle, that is, the polar angle is used to determine the and in the integrand.

[0197] In this embodiment, the numerical integration is performed by using the composite Simpson rule, the number of segments is set to 3 according to the preset azimuth, the integral interval is equally divided into 6 equal-length sub-intervals, and an engineering-acceptable calculation result can be obtained. The intermediate quantity is obtained according to the Simpson formula expansion, and the calculation formula of the intermediate quantity is:

[0198]

[0199] In the formula, i is the sub-interval serial number, and n is the total number of sub-intervals. The weight coefficient of the i-th sub-interval is: ​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​the weight coefficient is 2, the weight coefficient is , the weight coefficient is .

[0200] According to the integral function value at each angle and the weighted sum according to the weight coefficient, multiply the coefficient , and then substitute into the simplified expression of the dimensionless displacement of the Bingham fluid in the eccentric annulus, the dimensionless displacement of the Bingham fluid in the eccentric annulus is calculated .

[0201] Step 5, based on the frictional pressure drop gradient of the Bingham fluid in the concentric annulus in the extended reach well model, the frictional pressure drop gradient ratio of the Bingham fluid is calculated by using numerical simulation software, the frictional pressure drop gradient of the Bingham fluid in the eccentric annulus is determined, and the fluid dynamics analysis of the Bingham fluid in the eccentric annulus of the wellbore is completed.

[0202] Since the frictional pressure drop gradient of the Bingham fluid in the eccentric annulus is a function of the dimensionless displacement , and the width of the plug flow region in the dimensionless displacement and the upper boundary depend on the eccentric annulus frictional pressure drop gradient of the Bingham fluid, that is, the frictional pressure drop gradient expression of the Bingham fluid in the eccentric annulus and the dimensionless displacement expression can form a closed equation group, but it is difficult to determine the explicit analytical expression of the Bingham fluid frictional pressure drop gradient. Therefore, in this embodiment, based on the frictional pressure drop gradient ratio of the Bingham fluid in the concentric annulus in the extended reach well model, the expression of the frictional pressure drop gradient of the Bingham fluid in the eccentric annulus is determined.

[0203] In the extended reach well model, when the eccentricity of the drill string model is 0, at this time the center of the drill string model coincides with the center of the wellbore model, the annular space between the outer wall of the drill string model and the inner wall of the wellbore model changes to a concentric annulus, and when the Bingham fluid flows in the concentric annulus, the frictional pressure drop gradient of the Bingham fluid in the concentric annulus is expressed as:

[0204] ;

[0205] In the formula, is the frictional pressure drop gradient of the Bingham fluid in the concentric annulus; is the dynamic shear force of the Bingham fluid; is the average flow velocity of the annulus, in m / s. ​​

[0206] Based on the dimensionless displacement of the Bingham fluid in the concentric annulus, the simplified expression for the frictional pressure drop gradient in the concentric annulus is:

[0207] ;

[0208] in,

[0209] ;

[0210] ;

[0211] ;

[0212] In the formula, For the dimensionless displacement of Bingham fluid in concentric annular spaces; The radial coordinates of the inner boundary of the concentric annular slug flow region; The right boundary radial coordinates of the concentric annular slug flow region.

[0213] Calculate the ratio between the eccentric annular frictional pressure drop gradient and the concentric annular frictional pressure drop gradient of Bingham fluid under the same displacement, and determine the frictional pressure drop gradient ratio of Bingham fluid as:

[0214] ;

[0215] In the formula, This represents the Bingham fluid frictional resistance pressure drop gradient ratio.

[0216] Therefore, the calculation problem of the pressure drop gradient of the eccentric annular fluid friction is transformed into solving the ratio between the pressure drop gradient of the eccentric annular fluid friction and the pressure drop gradient of the concentric annular fluid friction under the same displacement. Combining the simplified expression for the dimensionless displacement of the eccentric annular fluid and the simplified expression for the pressure drop gradient of the concentric annular fluid friction, we obtain:

[0217] .

[0218] Substituting the dimensionless displacement of the eccentric annular air Bingham fluid The calculation formula yields the Bingham fluid friction pressure drop gradient ratio. The implicit function is:

[0219] .

[0220] Due to intermediate quantity Width of the middle flow region and upper boundary All are variables, and the width of the choke region and upper boundary All are eccentric annular frictional resistance voltage drop gradients The function yields the width of the slug flow region. and upper boundary Regarding the Bingham fluid frictional pressure drop gradient ratio The expression is:

[0221] ;

[0222] .

[0223] By iteratively solving the implicit function of the frictional pressure drop gradient ratio of Bingham fluid, the equation for calculating the frictional pressure drop gradient ratio of the eccentric annulus in Bingham fluid is constructed, yielding:

[0224] ;

[0225] In the formula, This is the function for calculating the gradient ratio of the frictional pressure drop of the eccentric annulus.

[0226] The Bingham fluid frictional pressure drop gradient ratio The root of the equation for calculating the pressure drop gradient ratio of the eccentric annular fluid friction is obtained by linear approximation using the Newton-Raphson method through Taylor expansion:

[0227] ;

[0228] In the formula, This represents the number of iterations. For the first The derivative of the gradient ratio of the eccentric ring air friction pressure drop during the next iteration.

[0229] Due to intermediate quantity To describe the Bingham fluid frictional pressure drop gradient ratio The function cannot obtain Since the explicit expression is given, the derivative of the function for calculating the pressure drop gradient of the eccentric ring air friction is solved using the numerical differentiation method, resulting in:

[0230] ;

[0231] In the formula, This is to update the difference in the pressure drop gradient ratio of the Bingham fluid friction before and after.

[0232] In this embodiment, the Bingham fluid friction pressure drop gradient ratio is calculated using numerical simulation software. ,like Figure 4 As shown, the specific steps include:

[0233] Step 5.1: Input calculation parameters, including the outer diameter of the drill string model. , the inner diameter of the wellbore model Eccentricity of the drill string model Volume flow rate of Bingham fluid in eccentric annulus Dynamic shear stress And plastic viscosity .

[0234] Step 5.2, calculating the concentric annulus friction pressure drop gradient of Bingham fluid .

[0235] Specifically, the concentric annulus friction pressure drop gradient of Bingham fluid The calculation formula is:

[0236] .

[0237] Step 5.3, calculating the inner boundary radial coordinate and the right boundary radial coordinate of plug flow region in concentric annulus . .

[0238] Specifically, the inner boundary radial coordinate of plug flow region in concentric annulus The calculation formula is:

[0239] ;

[0240] The calculation formula of right boundary radial coordinate is:

[0241] .

[0242] Step 5.4, calculating the dimensionless discharge of Bingham fluid in concentric annulus according to the outer diameter of drill string model , the inner diameter of wellbore model , the inner boundary radial coordinate and the right boundary radial coordinate of plug flow region in concentric annulus . .

[0243] Specifically, the dimensionless discharge of Bingham fluid in concentric annulus The calculation formula is:

[0244] .

[0245] Step 5.5, setting the initial value of friction pressure drop gradient ratio to 1, and setting the convergence threshold to .

[0246] Step 5.6, iteratively updating the calculation of friction pressure drop gradient ratio , the specific process is:

[0247] Calculate the width of plug flow region ​, the calculation formula is:

[0248] .

[0249] According to the polar coordinate equation of the wellbore model and the upper boundary of the plug flow region Regarding the expression of the friction pressure drop gradient ratio of the Bingham fluid, the polar radius of each preset orientation is obtained And the upper boundary of the plug flow region Determine the integral function of each preset orientation According to the numerical integration of the integral function of each preset orientation, the intermediate quantity is calculated .

[0250] Specifically, the polar coordinate equation of the wellbore model is:

[0251] ;

[0252] The upper boundary calculation formula of the plug flow region is:

[0253] ;

[0254] The integral function calculation formula is:

[0255] ;

[0256] The intermediate quantity The calculation formula is:

[0257] .

[0258] According to the intermediate quantity The calculation value and the derivative value of the eccentric annulus friction pressure drop gradient ratio of the Bingham fluid are calculated.

[0259] In the current iteration calculation, according to the calculation equation of the eccentric annulus friction pressure drop gradient ratio of the Bingham fluid, the calculation value of the eccentric annulus friction pressure drop gradient ratio of the Bingham fluid is obtained, and the eccentric annulus friction pressure drop gradient ratio of the Bingham fluid is updated.

[0260] Specifically, the calculation equation of the eccentric annulus friction pressure drop gradient ratio of the Bingham fluid is:

[0261] ;

[0262] The derivative value of the eccentric annulus friction pressure drop gradient ratio of the Bingham fluid is:

[0263] .

[0264] Step 5.7, update the eccentric annulus friction pressure drop gradient ratio of the Bingham fluid , and obtain the updated eccentric annulus friction pressure drop gradient ratio of the Bingham fluid Calculate the ratio of Bingham fluid friction pressure drop gradient before and after the update. The difference.

[0265] Step 5.8: Perform a convergence check by updating the difference between the Bingham fluid friction pressure drop gradient ratio before and after the update. With the preset convergence threshold Comparing the Bingham fluid friction pressure drop gradient before and after the update, The difference Exceeding the preset convergence threshold If the updated value is true, the updated value will be set as the initial value of the Bingham fluid friction pressure drop gradient ratio, and the process will return to step 5.7 to continue iterative updates; otherwise, the iteration will end.

[0266] Step 5.9: Output the frictional pressure drop gradient ratio of Bingham fluid.

[0267] Example 2

[0268] This embodiment takes a large-displacement well as an example. The outer diameter of the drill string is 0.0635m, the inner diameter of the wellbore is 0.108m, and the eccentricity of the drill string in the wellbore is... The value is 0.02m. Using the fluid dynamics analysis method for Bingham fluid in the eccentric annulus of a wellbore as described in Example 1, the frictional pressure drop gradient ratio of the Bingham fluid is determined. Fluid dynamics analysis was performed on Bingham fluid in the eccentric annulus of the wellbore.

[0269] In the large-displacement well model constructed in this embodiment, the outer diameter of the drill string model The inner diameter of the wellbore model is 0.0635m. The Bingham fluid flows in the eccentric annulus between the drill string model and the wellbore model, with an eccentricity of 0.02 m. The volumetric flow rate of the Bingham fluid in the eccentric annulus is 0.108 m. It is 0.03 Dynamic shear force 10 Plastic viscosity It is 0.02 .

[0270] The specific process for calculating the eccentric annular friction pressure drop gradient of the Bingham fluid in the extended reach well model is as follows:

[0271] The average flow velocity in the annulus for:

[0272] ;

[0273] The concentric annular frictional pressure drop gradient of the Bingham fluid for:

[0274] ;

[0275] The inner boundary radial coordinate of the plug flow region in the concentric annulus is:

[0276] ;

[0277] The right boundary radial coordinate of the plug flow region in the concentric annulus is:

[0278] ;

[0279] The dimensionless discharge of the Bingham fluid in the concentric annulus is:

[0280] ;

[0281] After 4 iterations, the convergent solution of the Bingham fluid frictional pressure drop gradient ratio is 0.7927, and the key parameters in each iteration calculation process are shown in Table 1.

[0282] Table 1 Key parameters in the iteration calculation process

[0283] ;

[0284] The eccentric annulus frictional pressure drop gradient of the Bingham fluid is determined as:

[0285] .

[0286] The shear stress in the azimuthal direction is calculated as:

[0287] ;

[0288] ;

[0289] ;

[0290] .

[0291] The range of the inner sub-domain is , the range of the plug flow sub-domain is , and the range of the outer sub-domain is .

[0292] Further, the shear stress in the inner sub-domain is:

[0293] ;

[0294] The shear stress in the plug flow sub-domain is: ​​

[0295] At the, ;

[0296] At the, ;

[0297] The shear stress in the outer subdomain is:

[0298] .

[0299] The shear rate in the azimuthal direction is calculated by:

[0300] The shear rate of the Bingham fluid in the inner subdomain is:

[0301] ;

[0302] That is, ;

[0303] The shear rate of the Bingham fluid in the outer subdomain is:

[0304] ;

[0305] That is, .

[0306] The velocity in the azimuthal direction is calculated by:

[0307] The flow rate of the Bingham fluid in the inner subdomain is:

[0308] ;

[0309] That is, ;

[0310] The flow rate of the Bingham fluid in the outer subdomain is:

[0311] ;

[0312] That is, .

[0313] The shear stress, shear rate and flow rate distribution in the azimuthal direction are calculated by: Select different radial positions, calculate the shear stress, shear rate and flow rate distribution data at each position, as shown in Table 2.

[0314] Table 2 Shear stress, shear rate and flow rate distribution in the azimuthal direction in the wellbore

[0315]

[0316] ​​​​ ;

[0317] According to the shear stress, shear rate and flow rate distribution data at each position of the wellbore, the distribution of the shear stress, shear rate and flow rate in the wellbore is obtained, and the fluid dynamics analysis of the Bingham fluid in the eccentric annulus of the wellbore is completed, thereby providing a theoretical basis and technical support for guiding the drilling operation of the extended reach well.

[0318] Of course, the above description is not a limitation of the present application, and the present application is not limited to the above examples. Changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present application should also be within the scope of the present application.

Claims

1. A method of fluid dynamic analysis of a pinger fluid in a wellbore eccentric annulus, characterized by, The method comprises the following steps: Step 1, constructing a large displacement well model with an eccentric annulus according to the design parameters of the large displacement well; Step 2, setting the drilling fluid in the large displacement well model as Bingham fluid, and determining the shear-free plug position of the Bingham fluid in the large displacement well model; Step 3, obtaining the shear stress and velocity distribution of the Bingham fluid in the eccentric annulus; Step 4, determining the dimensionless volume flow rate of the Bingham fluid in the eccentric annulus; Step 5, based on the friction pressure drop gradient of the Bingham fluid in the concentric annulus of the large displacement well model, using numerical simulation software to calculate the friction pressure drop gradient ratio of the Bingham fluid, determine the friction pressure drop gradient of the Bingham fluid in the eccentric annulus, and complete the fluid dynamics analysis of the Bingham fluid in the eccentric annulus of the wellbore; In step 5, when the eccentricity of the drill string model in the extended reach well model... When the value is 0, the center of the drill string model coincides with the center of the wellbore model, and the annular space between the outer wall of the drill string model and the inner wall of the wellbore model changes to a concentric annular space. the bingham fluid when flowing in the concentric annulus the expression is ； wherein is the concentric annulus friction pressure drop gradient for a Bingham fluid; is the yield stress of the Bingham fluid; is the average flow rate of the annulus; is the outer diameter of the drill string model; is the inner diameter of the wellbore model; is the plastic viscosity of the Bingham fluid; The simplified expression of the concentric annulus friction pressure drop gradient is combined with the dimensionless discharge of the Bingham fluid in the concentric annulus, and is: ； Wherein, ； ； ； wherein Q* is the dimensionless discharge of the Bingham fluid in the concentric annulus; Ri is the inner boundary radial coordinate of the plug flow region in the concentric annulus; Rr is the right boundary radial coordinate of the plug flow region in the concentric annulus; The ratio between the eccentric annulus friction pressure drop gradient and the concentric annulus friction pressure drop gradient of the Bingham fluid under the same discharge is calculated, and the Bingham fluid friction pressure drop gradient ratio is determined as: ； wherein is the ratio of the Bingham fluid frictional pressure drop gradient; Combined with the simplified expression of the dimensionless discharge of the Bingham fluid in the eccentric annulus and the simplified expression of the concentric annulus friction pressure drop gradient, the following is obtained: ； Substitute the dimensionless discharge of Bingham fluid in eccentric annulus into the calculation formula of the dimensionless discharge of Bingham fluid in eccentric annulus The implicit function of the Bingham fluid frictional pressure drop gradient ratio is obtained as follows: ； Because the intermediate quantity the width of the plug region and the upper boundary are both variables, and the width of the plug region and the upper boundary are both functions of the eccentric annular frictional pressure drop gradient then the width of the plug region and the upper boundary are given by the expression for the ratio of the frictional pressure drop gradients for Bingham fluids ； ； The implicit function of the Bingham fluid friction pressure drop gradient ratio is iteratively solved, the Bingham fluid eccentric annulus friction pressure drop gradient ratio calculation equation is constructed, and the following is obtained: ； wherein is a calculated function of the eccentric annulus friction pressure drop gradient ratio; The Bingham fluid friction pressure drop gradient ratio is the root of the Bingham fluid eccentric annulus friction pressure drop gradient ratio calculation equation, and the Newton-Raphson method is used to obtain the following through Taylor expansion linear approximation: ； wherein is the number of iterations; is the derivative of the eccentric annulus friction pressure drop gradient ratio at the th iteration; The derivative of the eccentric annulus friction pressure drop gradient calculation function is solved by using the numerical differentiation method, and the following is obtained: ； wherein is the difference in the ratio of the pre- and post-update Bingham fluid frictional pressure drop gradients.

2. The method for the hydrodynamic analysis of a Bingham fluid in a wellbore eccentric annulus of claim 1 wherein, In the step 1, the large displacement well model is constructed according to the design parameters of the large displacement well; The large displacement well model comprises a drill string model and a wellbore model, the drill string model is eccentrically arranged in the wellbore model, and the annular space between the outer wall of the drill string model and the inner wall of the wellbore model is the eccentric annulus; A polar coordinate system is constructed in the large displacement well model, with the center position of the drill string model as the origin of the polar coordinate system , the positive direction of the polar axis in the polar coordinate system points to the widest direction of the eccentric annulus, the polar angle corresponding to the positive direction of the polar axis is 0°, and the polar angle increases in the counterclockwise direction; The vertical distance between the wellbore model center and the drill string model center is the eccentricity The eccentricity of the drill string model is determined from the eccentricity :​ ； wherein is the outer diameter of the drill string model; is the inner diameter of the wellbore model; The polar coordinate equation of the wellbore model is: ； wherein r is the polar radius, used to indicate the origin of the polar coordinate system distance between the inner walls of the wellbore model An annular gap between the drill string model and the wellbore model is: ； In the formula, is the annular space for indicating the distance between the outer wall of the drill string model and the inner wall of the wellbore model on the polar azimuth line.

3. The method for the hydrodynamic analysis of a Bingham fluid in a wellbore eccentric annulus of claim 2 wherein, In the step 2, the drilling fluid in the large displacement well model is set as Bingham fluid, and the fluid parameters of the Bingham fluid are set according to the fluid properties of the Bingham fluid; The Bingham fluid flows in the eccentric annulus of the large displacement well model to form a shear-free plug flow region, the plug flow region is located in the middle region of the eccentric annulus, the width of the plug flow region is independent of the annular gap, and the shear-free plug position of the Bingham fluid in the eccentric annulus is determined according to the width of the plug flow region; The calculation formula of the plug flow region width is: ； Wherein, ； ； wherein is the width of the plug region; is the upper boundary of the plug region; is the lower boundary of the plug region; is the natural logarithm; is the dynamic shear stress of the Bingham fluid; is the eccentric annular friction pressure drop gradient of the Bingham fluid.

4. The method for the hydrodynamic analysis of a Bingham fluid in a wellbore eccentric annulus of claim 3 wherein, In step 3, the flow field of the Bingham fluid at any polar angle position in the eccentric annulus is divided into three sub-regions, namely an inner sub-region, a plug flow sub-region and an outer sub-region, wherein the flow field range of the inner sub-region is , the flow field range of the plug flow sub-region is , and the flow field range of the outer sub-region is , wherein is the radial coordinate of the Bingham fluid in the eccentric annulus, used to represent the radial position of the Bingham fluid in the eccentric annulus. The flow velocity of the Bingham fluid in the inner subdomain. With the polar diameter The outer diameter of the drill string model increases with the increase of the size of the drill string. The flow rate of Bingham fluid The velocity is 0; in the slug subdomain, the velocity of the Bingham fluid is... Constant and unchanging, , The maximum flow velocity of the Bingham fluid; the flow velocity of the Bingham fluid in the outer subdomain. With polar diameter The value decreases as the radius increases. The flow rate of Bingham fluid It is 0.

5. The method for the hydrodynamic analysis of a Bingham fluid in a wellbore eccentric annulus of claim 4 wherein, The shear stress and flow velocity of the Bingham fluid in the inner sub-domain, plug flow sub-domain and outer sub-domain are different; The momentum conservation equation in the inner sub-domain is: ； wherein is the shear stress of the Bingham fluid; The rheological model of the Bingham fluid in the inner sub-domain is: ； wherein is the plastic viscosity of the Bingham fluid; The shear rate equation of the Bingham fluid in the inner sub-domain is obtained by combining the momentum conservation equation in the inner sub-domain with the rheological model of the Bingham fluid: ； The flow velocity equation of the Bingham fluid in the inner sub-domain is obtained by integrating the boundary conditions of the inner sub-domain: ； In the plug subdomain, at the plug subdomain lower boundary , at the plug subdomain upper boundary , the shear rate equation of the Bingham fluid in the plug subdomain is determined as ； The momentum conservation equation in the outer sub-domain is: ； The rheological model of the Bingham fluid in the outer sub-domain is: ； The shear rate equation of the Bingham fluid in the outer sub-domain is obtained by combining the momentum conservation equation in the outer sub-domain with the rheological model of the Bingham fluid: ； The flow velocity equation of Bingham fluid in the outer subdomain is obtained by separating variables and integrating the boundary conditions of the outer subdomain. ； According to the flow velocity equations of Bingham fluid in the inner subdomain, the plug flow subdomain and the outer subdomain, the velocity distribution of Bingham fluid in the eccentric annulus is determined.

6. The method for the hydrodynamic analysis of a Bingham fluid in a wellbore eccentric annulus of claim 5 wherein, In step 4, based on the symmetry of the eccentric annulus, the eccentric annulus frictional pressure drop gradient when the Bingham fluid flows in the eccentric annulus is determined as: ； Wherein, ； ； wherein is the eccentric annulus friction pressure drop gradient for a Bingham fluid; is the dimensionless displacement of a Bingham fluid in an eccentric annulus; is the volumetric flow rate of a Bingham fluid in an eccentric annulus; The dimensionless discharge of Bingham fluid in eccentric annulus is calculated by numerical integration method The integral is calculated in the interval [0, ] to obtain: ； The intermediate quantity is set to simplify the expression of the dimensionless discharge of the Bingham fluid in the eccentric annulus, and the dimensionless discharge expression of the Bingham fluid in the eccentric annulus is simplified as: ； Wherein, ； In the formulae, is an intermediate quantity; The numerical integration is performed by using the composite Simpson rule, a preset angle is set to set the number of segments, the integral interval is divided into multiple sub-intervals, the intermediate quantity is obtained by expanding according to the Simpson formula, and the calculation formula of the intermediate quantity is as follows: The calculation formula of the intermediate quantity is as follows: ​ ； Wherein, ； In the formula, is a sub-interval number, is a total number of sub-intervals; is a weight coefficient of the th sub-interval; is an integrand function; The integrand values ​​at each angle are summed according to weighted coefficients and multiplied by a coefficient. Substituting this into the formula for calculating the volumetric flow rate of the Bingham fluid in the eccentric annular space, the dimensionless displacement of the Bingham fluid in the eccentric annular space is calculated. .

7. The method of the fluid dynamics analysis of a Bingham fluid in a wellbore eccentric annulus of claim 1, wherein, In step 5, the numerical simulation software is used to calculate the Bingham fluid frictional pressure drop gradient ratio, which specifically includes the following steps: Step 5.1, input calculation parameters; the outer diameter of the drill string model the inner diameter of the wellbore model the eccentricity of the drill string model the volume flow rate of the Bingham fluid in the eccentric annulus the dynamic shear force and the plastic viscosity ; Step 5.2, calculating the concentric annulus friction pressure drop gradient for Bingham fluids ; Step 5.

3. Calculate the inner boundary radial coordinate of the plug flow region in the concentric annulus and the right boundary radial coordinate ; Step 5.

4. Calculate the outer diameter of the drill string model , the inner diameter of the wellbore model , and the inner and right boundary radial coordinates of the plug flow region in the concentric annulus and , the dimensionless displacement of the Bingham fluid in the concentric annulus ; Step 5.5, setting the frictional pressure drop gradient ratio of the initial value and the convergence threshold value ; Step 5.6, iteratively update the calculated frictional pressure drop gradient ratio ; Calculate the width of the slug region Then, based on the polar coordinate equation of the wellbore model and the upper boundary of the plug flow region... The expression for the Bingham fluid frictional pressure drop gradient ratio is used to obtain the extreme diameter at each preset orientation. and the upper boundary of the choke flow region Determine the integrand at each preset orientation. Then, by performing numerical integration on the integrand at each preset orientation, the intermediate quantity is determined. Calculate the calculated value and derivative of the current Bingham fluid eccentric annular friction pressure drop gradient ratio. Then, based on the calculation equation of the Bingham fluid eccentric annular friction pressure drop gradient ratio, obtain the calculated value of the Bingham fluid eccentric annular friction pressure drop gradient ratio and update the Bingham fluid friction pressure drop gradient ratio. Step 5.7, obtaining the updated Bingham fluid frictional pressure drop gradient ratio , calculating the difference between the Bingham fluid frictional pressure drop gradient ratio before and after the update ; Step 5.8, performing convergence check, comparing the difference of the ratio of the Bingham fluid friction pressure drop gradient before and after the update with a preset convergence threshold Step 5.8, performing convergence check, comparing the difference of the ratio of the Bingham fluid friction pressure drop gradient before and after the update with a preset convergence threshold Step 5.8, performing convergence check, comparing the difference of the ratio of the Bingham fluid friction pressure drop gradient before and after the update with a preset convergence threshold Step 5.8, performing convergence check, comparing the difference of the ratio of the Bingham fluid friction pressure drop gradient before and after the update with a preset convergence threshold Step 5.8, performing convergence check, comparing the difference of the ratio of the Bingham fluid friction pressure drop gradient before and after the update with a preset convergence threshold Step 5.9, output the Bingham fluid frictional pressure drop gradient ratio.

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