Ultra-deep well drilling wellbore pressure inversion correction method

Abstract

The invention discloses an ultra-deep well drilling wellbore pressure inversion correction method, and aims to improve pressure prediction precision and well control safety in an ultra-deep well drilling process. The method mainly comprises the following two parts: firstly, establishing a wellbore pressure calculation model, fully considering the change of drilling fluid density along with temperature and pressure based on a mass and momentum conservation equation in a drill rod and an annulus, performing discrete solution on the established control equation by adopting a finite difference method, and performing iterative calculation from a well bottom to a well mouth and from the well mouth to the well bottom, so as to obtain a well pressure calculation model; and acquiring pressure and physical property parameters of each node. Secondly, on the basis of model output, a friction correction factor is introduced, a nonlinear state space model is constructed, an unscented Kalman filter (UKF) algorithm is used for conducting dynamic estimation on the friction correction factor, and online self-adaptive correction on the wellbore pressure model is achieved; according to the method, the accuracy of wellbore pressure calculation is effectively improved, and reliable technical support is provided for ultra-deep well operation.

Description

Technical Field

[0001] The present invention belongs to the field of fluid dynamics and control technology in a drilling process, and in particular relates to an inversion correction method for ultra-deep well drilling wellbore pressure. Background Art

[0002] In deep and ultra-deep drilling operations, accurate calculation of wellbore pressure is crucial for ensuring safety and improving operational efficiency. Existing technologies involve a variety of wellbore pressure calculation methods and real-time correction models, but these methods generally have limitations and struggle to provide accurate pressure descriptions under complex underground conditions.

[0003] Regarding fluid rheological properties, patent CN202310967351.9 proposes a temperature-pressure coupled wellbore pressure calculation method. This method aims to establish a calculation model for the rheological parameters of the fluid under different temperature and pressure conditions, thereby obtaining a calculation model for the wellbore's circulatory friction. However, this technology primarily focuses on the properties of fluids at low shear rates and cannot guarantee its accuracy for rheological behavior under high shear rate conditions. Therefore, in practical applications, this may lead to deviations in the pressure calculation results.

[0004] Regarding real-time correction, patent CN201510567464.5 has developed a method that utilizes basic wellbore pressure parameters and managed pressure drilling boundary conditions to adjust pressure parameters such as bottomhole pressure, annular pressure loss, and wellhead backpressure in real time. While this method effectively corrects for pressure loss within the annular space, it does not address pressure loss within the drill pipe. Therefore, its correction effect remains insufficient when dealing with complex wellbore systems.

[0005] In addition, the method proposed in the literature for calculating the transient fluctuation pressure in the wellbore annulus (Zhao Yanlong, 2022) uses the characteristic line method for numerical solution. Although multiple influencing factors are considered, the model still has room for improvement in parameter selection and the accuracy of the description of daytime operating conditions, which may lead to a large error between the predicted results and the actual wellbore pressure. Similarly, Xia Shunlei (2022) introduced an unscented Kalman filter algorithm to achieve real-time correction of wellbore friction resistance. However, this model is limited to the correction of annular friction resistance and fails to fully consider the friction resistance factors within the drill pipe. It may not accurately reveal the pressure distribution of the entire wellbore system.

[0006] In summary, while existing technologies offer numerous methods for calculating and correcting wellbore pressure, these approaches still have numerous limitations in the complex geological conditions of deep and ultra-deep formations. To achieve more accurate description and control of wellbore pressure, an improved mechanism and model is urgently needed that comprehensively considers various influencing factors and can simultaneously correct pressure in different parts of the wellbore. This will provide more reliable data support for future safe and efficient drilling. Summary of the Invention

[0007] In order to solve the technical problems existing in the background technology, the present invention aims to provide an ultra-deep wellbore pressure inversion correction method, introduce the fluid flow friction correction factor in the drill pipe, and simultaneously correct the fluid flow friction correction factor in the drill pipe and the annulus through the UKF inversion algorithm to improve the wellbore pressure prediction accuracy.

[0008] In order to solve the technical problem, the technical solution of the present invention is:

[0009] A method for inversion correction of wellbore pressure in ultra-deep well drilling, the method comprising:

[0010] S1: Establishing a wellbore pressure calculation model. First, a steady-state calculation model for wellbore pressure is established based on the mass and momentum conservation equations of the drilling fluid in the drill pipe and annulus. The influence of drilling fluid density changes with temperature and pressure is fully considered, and a friction pressure drop gradient model is constructed. The control equations are discretely solved using the finite difference method. Under known boundary conditions, pressure and velocity are iteratively calculated from the bottomhole to the wellhead (drill pipe) and from the wellhead to the bottomhole (annulus) to obtain the drilling fluid physical properties and pressure distribution at each node.

[0011] S2: Inversion correction modeling. Based on the output of step S1, the error between the model and the actual measurement is considered, and a friction correction factor is further introduced to construct an inversion correction model for wellbore pressure. The friction correction factors in the drill pipe and annulus are used as state variables, and the drill pipe wellhead pressure is used as the observation variable to construct a nonlinear state space model. The friction correction factor is dynamically estimated using the unscented Kalman filter algorithm to achieve online adaptive correction of the wellbore pressure model.

[0012] Furthermore, the step S1, establishing a steady-state calculation model for wellbore pressure, specifically includes:

[0013] Based on the conservation equations of mass and momentum of drilling fluid in the drill pipe and annulus, a steady-state calculation model for wellbore pressure is established;

[0014] The conservation equation of drilling fluid mass in the drill pipe is:

[0015]

[0016] ρ d is the density of drilling fluid in the drill pipe, kg / m 3 ;v d is the drilling fluid velocity in the drill pipe, m / s; A d is the inner cross-sectional area of the drill pipe, m 2 ; z is the well depth, m; subscript d represents the drill pipe;

[0017] The momentum conservation equation of drilling fluid in the drill pipe is:

[0018]

[0019] p d is the drilling fluid pressure in the drill pipe, Pa; g is the acceleration due to gravity, m / s 2 ; F f,d is the friction pressure drop per unit length of drilling fluid in the drill string, that is, the friction pressure drop gradient in the drill pipe, Pa / m;

[0020] The conservation equation of drilling fluid mass in the annulus is:

[0021]

[0022] ρ a is the density of drilling fluid in the annulus, kg / m 3 ;v a is the drilling fluid velocity in the annulus, m / s; A a is the cross-sectional area of the annulus, m 2 ;Subscript a represents annulus;

[0023] The conservation equation of drilling fluid momentum in the annulus is:

[0024]

[0025] p a is the drilling fluid pressure in the annulus, Pa; F f,a is the friction pressure drop per unit length of drilling fluid in the annulus, that is, the friction pressure drop gradient in the annulus, Pa / m;

[0026] During the drilling process, the density of drilling fluid is greatly affected by temperature and pressure. The calculation model of drilling fluid density is as follows:

[0027]

[0028] Where: ρ is the drilling fluid density at target temperature and pressure, kg / m 3 ; ρ0 is the drilling fluid density at the test temperature and pressure, kg / m3; T0 is the test temperature, ℃; P0 is the test pressure, Pa; T is the target temperature, ℃; P is the target pressure, Pa; A1 and A2 are fitting parameters.

[0029] Furthermore, the step S1, constructing a friction pressure drop gradient model, specifically includes:

[0030] Friction pressure drop gradient inside the drill pipe:

[0031]

[0032] D d,i is the inner diameter of the drill pipe, m; v d is the drilling fluid velocity in the drill pipe, m / s; f dis the Fanning friction factor of the drilling fluid in the drill pipe;

[0033] Friction pressure drop gradient in the annulus:

[0034]

[0035] D w is the inner diameter of the wellbore, m; D d,o is the outer diameter of the drill pipe, m; v a is the drilling fluid velocity in the annulus, m / s; f a is the Fanning friction factor of the drilling fluid in the annulus.

[0036] Furthermore, the step S1 uses the finite difference method to discretely solve the control equation, which specifically includes:

[0037] The wellbore with a measured depth of L is evenly divided into N grid units with a step size of △h. Then there are Nx (Nx = N + 1) storage nodes. The bottom of the well and the wellhead are marked as Nx and 1 respectively. △z(i) represents the vertical distance between adjacent storage nodes, m.

[0038] The annular outlet pressure is a known boundary, so the annular pressure is calculated from the wellhead to the bottomhole; the drill pipe pressure is calculated from the bottomhole to the wellhead. That is, in the annular space, the data of the i-1th storage node is used to solve the data of the i-th storage node, while in the drill pipe, the data of the i+1th storage node is used to solve the data of the i-th storage node.

[0039] The finite difference method is used to discretize the mass conservation equation of the drilling fluid in the drill pipe, and the following is obtained:

[0040]

[0041] Where, subscript i represents the i-th storage node;

[0042] According to the drilling fluid density, drilling fluid velocity and flow area of the i+1th storage node, the drilling fluid velocity of the i-th storage node is calculated:

[0043]

[0044] The finite difference method is used to discretize the momentum conservation equation of the drilling fluid in the drill pipe, and the following is obtained:

[0045]

[0046] Calculate the drilling fluid pressure at the i-th storage node based on the drilling fluid pressure, density, velocity, and friction pressure drop gradient at the i+1-th storage node, as well as the density, velocity, and friction pressure drop gradient at the i-th storage node:

[0047]

[0048] The finite difference method is used to discretize the drilling fluid mass conservation equation in the annulus, and the following is obtained:

[0049]

[0050] According to the drilling fluid density, drilling fluid velocity and flow area of the i-1th storage node, the drilling fluid velocity of the i-th storage node is calculated:

[0051]

[0052] The finite difference method is used to discretize the drilling fluid momentum conservation equation in the annulus, and the equation is obtained:

[0053]

[0054] Calculate the pressure of the i-th storage node based on the drilling fluid pressure, density, velocity, and friction pressure drop gradient of the i-1th storage node and the density, velocity, and friction pressure drop gradient of the i-th storage node:

[0055]

[0056] Furthermore, the step S2 specifically includes:

[0057] A friction correction factor is introduced into the friction pressure drop gradient calculation model of the drill pipe and annulus;

[0058] Drill pipe:

[0059]

[0060] C d is the annular internal friction correction factor;

[0061] Annulus:

[0062]

[0063] C a is the annular internal friction correction factor;

[0064] Combined with the UKF algorithm, the friction correction factors in the annulus and drill pipe are used as state values, and the annulus outlet pressure is used as the observation value. The state variable (X) and observation variable (Z) in the inversion model are expressed as follows:

[0065] X(k)=[C a (k),C d (k)] T (18)

[0066] Z(k)=p d,0(k) (19)

[0067] The state model for formation parameter inversion using the unscented Kalman filter (UKF) algorithm is expressed as:

[0068] X(k)=X(k-1)+W(k) (20).

[0069] Compared with the prior art, the advantages of the present invention are:

[0070] The present invention establishes an inversion correction model for ultra-deep wellbore pressure, introduces a fluid flow friction correction factor within the drill pipe, and uses the UKF inversion algorithm to simultaneously correct the fluid flow friction correction factor within the drill pipe and the annulus, thereby improving the accuracy of wellbore pressure prediction. Compared with CN202310967351.9, the present invention can simultaneously ensure the accuracy of friction pressure drop calculation under low and high shear rate conditions through UKF correction. Compared with CN201510567464.5, in addition to bottomhole pressure, annular pressure loss, and wellhead back pressure, the present invention can also calculate and correct the pressure within the drill pipe, improving on-site understanding of downhole pressure distribution. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 , schematic diagram of wellbore grid division;

[0072] Figure 2 , Wellbore pressure inversion flow chart;

[0073] Figure 3 , the inversion calculation result diagram of wellbore injection pressure;

[0074] Figure 4 , relative error comparison chart. DETAILED DESCRIPTION

[0075] The specific implementation of the present invention is described below in conjunction with examples:

[0076] It should be noted that the structures, proportions, sizes, etc. shown in this specification are only used to match the contents disclosed in the specification for people familiar with this technology to understand and read, and are not used to limit the conditions under which the present invention can be implemented. Any structural modification, change in proportional relationship or adjustment of size should still fall within the scope of the technical content disclosed in the present invention without affecting the efficacy and purpose that can be achieved by the present invention.

[0077] At the same time, the terms such as "upper", "lower", "left", "right", "middle" and "one" quoted in this specification are only for the convenience of description and are not used to limit the scope of implementation of the present invention. Changes or adjustments to their relative relationships should be regarded as the scope of implementation of the present invention without substantially changing the technical content.

[0078] Example 1:

[0079] The present invention provides an ultra-deep wellbore pressure inversion correction method, the main steps of which include:

[0080] 1. Establish a wellbore pressure calculation model

[0081] (1) Based on the conservation equations of mass and momentum of drilling fluid in the drill pipe and annulus, a steady-state calculation model for wellbore pressure is established.

[0082] The mass conservation equation of drilling fluid in the drill pipe is:

[0083]

[0084] ρ d is the density of drilling fluid in the drill pipe, kg / m 3 ;v d is the drilling fluid velocity in the drill pipe, m / s; A d is the inner cross-sectional area of the drill pipe, m 2 ; z is the well depth, m; subscript d represents the drill pipe.

[0085] The momentum conservation equation of drilling fluid in the drill pipe is:

[0086]

[0087] p d is the drilling fluid pressure in the drill pipe, Pa; g is the acceleration due to gravity, m / s 2 ; F f,d It is the friction pressure drop per unit length of drilling fluid in the drill string, that is, the friction pressure drop gradient in the drill pipe, Pa / m.

[0088] The conservation equation of drilling fluid mass in the annulus is:

[0089]

[0090] ρ a is the density of drilling fluid in the annulus, kg / m 3 ;v a is the drilling fluid velocity in the annulus, m / s; A a is the cross-sectional area of the annulus, m 2 ; Subscript a represents annulus.

[0091] The conservation equation of drilling fluid momentum in the annulus is:

[0092]

[0093] p a is the drilling fluid pressure in the annulus, Pa; F f,a It is the friction pressure drop per unit length of drilling fluid in the annulus, that is, the friction pressure drop gradient in the annulus, Pa / m.

[0094] During the drilling process, the density of drilling fluid is greatly affected by temperature and pressure. The calculation model of drilling fluid density is as follows:

[0095]

[0096] Where: ρ is the drilling fluid density at target temperature and pressure, kg / m 3 ; ρ0 is the drilling fluid density at the test temperature and pressure, kg / m3; T0 is the test temperature, ℃; P0 is the test pressure, Pa; T is the target temperature, ℃; P is the target pressure, Pa; A1 and A2 are fitting parameters.

[0097] Friction pressure drop gradient inside the drill pipe:

[0098]

[0099] D d,i is the inner diameter of the drill pipe, m; c d is the drilling fluid velocity in the drill pipe, m / s; f d is the Fanning friction factor of the drilling fluid in the drill pipe.

[0100] Friction pressure drop gradient in the annulus:

[0101]

[0102] D w is the inner diameter of the wellbore, m; D d,o is the outer diameter of the drill pipe, m; v a is the drilling fluid velocity in the annulus, m / s; f a is the Fanning friction factor of the drilling fluid in the annulus.

[0103] (2) Model solution

[0104] The wellbore with a measured depth of L is divided evenly, such as Figure 1 , the step size is △h, and it is divided into N grid units. There are Nx (Nx = N + 1) storage nodes (storing parameters such as pressure, temperature, drilling fluid flow rate, drilling fluid density, wellbore trajectory, wellbore structure, etc.). The bottom of the well and the wellhead are marked as Nx and 1 respectively. △z(i) represents the vertical distance between adjacent storage nodes, m.

[0105] The annular outlet pressure is a known boundary, so the annular pressure is calculated from the wellhead to the bottomhole; the drill pipe pressure is calculated from the bottomhole to the wellhead. That is, in the annular, the data of the i-1th storage node is used to solve the data of the i-th storage node, while in the drill pipe, the data of the i+1th storage node is used to solve the data of the i-th storage node.

[0106] The finite difference method is used to discretize the mass conservation equation of the drilling fluid in the drill pipe, and the following is obtained:

[0107]

[0108] Wherein, the subscript i represents the i-th storage node.

[0109] According to the drilling fluid density, drilling fluid velocity and flow area of the i+1th storage node, the drilling fluid velocity of the i-th storage node is calculated:

[0110]

[0111] The finite difference method is used to discretize the momentum conservation equation of the drilling fluid in the drill pipe, and the following is obtained:

[0112]

[0113] Calculate the drilling fluid pressure at the i-th storage node based on the drilling fluid pressure, density, velocity, and friction pressure drop gradient at the i+1-th storage node, as well as the density, velocity, and friction pressure drop gradient at the i-th storage node:

[0114]

[0115] The finite difference method is used to discretize the drilling fluid mass conservation equation in the annulus, and the following is obtained:

[0116]

[0117] According to the drilling fluid density, drilling fluid velocity and flow area of the i-1th storage node, the drilling fluid velocity of the i-th storage node is calculated:

[0118]

[0119] The finite difference method is used to discretize the drilling fluid momentum conservation equation in the annulus, and the equation is obtained:

[0120]

[0121] Calculate the pressure of the i-th storage node based on the drilling fluid pressure, density, velocity, and friction pressure drop gradient of the i-1th storage node and the density, velocity, and friction pressure drop gradient of the i-th storage node:

[0122]

[0123] 2. Wellbore pressure inversion correction algorithm and modeling

[0124] Introducing friction correction factor into the friction pressure drop gradient calculation model between drill pipe and annulus

[0125] Drill pipe:

[0126]

[0127] C d is the correction factor for the friction in the annulus.

[0128] Annulus:

[0129]

[0130] C a is the correction factor for the friction in the annulus.

[0131] Combined with the UKF algorithm, the friction correction factors in the annulus and drill pipe are used as state values, and the annulus outlet pressure is used as the observation value. The state variable (X) and observation variable (Z) in the inversion model can be expressed as follows:

[0132] X(k)=[C a (k),C d (k) ] T (18)

[0133] Z(k)=p d,0 (k) (19)

[0134] The state model for formation parameter inversion using the UKF algorithm can be expressed as:

[0135] X(k)=X(k-1)+W(k) (20)

[0136] The wellbore pressure inversion correction process is as follows: Figure 2 shown.

[0137] Example 2:

[0138] The calculation is based on data from an actual well, selecting the injection pressure and displacement data from the 4884-5547m section during the third drilling process of the well. The main calculation parameters are as follows:

[0139]

[0140] The initial values of the friction correction factors in the annulus and drill pipe are both 1. The three relevant parameters in the unscented Kalman filter are set to: α = 0.75, β = 2, κ = 0. The standard deviations of the system noise and observation noise are set to 0.05 and 0.0002 respectively. The calculation results are shown in Figure 2. Figure 3 shown.

[0141] The initial values of the friction correction factors in the annulus and drill pipe are both 1. The three relevant parameters in the unscented Kalman filter are set to: α = 0.75, β = 2, κ = 0. The standard deviations of the system noise and observation noise are set to 0.05 and 0.0002 respectively. The calculation results are shown in Figure 2. Figure 3shown.

[0142] After the calculation began, the model-calibrated results quickly approached the measured injection pressure. Excluding the first uncalibrated result, the maximum relative error was 4.57% and the average relative error was 2.05%. The results calculated by the uncalibrated model had a maximum relative error of 15.68% and an average relative error of 12.09%. Figure 4 For relative error comparison.

[0143] It will be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0144] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0145] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0146] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0147] The preferred embodiments of the present invention are described in detail above, but the present invention is not limited to the above embodiments. Various changes can be made within the knowledge of ordinary technicians in this field without departing from the scope of the present invention.

[0148] Many other changes and modifications can be made without departing from the spirit and scope of the present invention. It should be understood that the present invention is not limited to the specific embodiments, and the scope of the present invention is defined by the appended claims.

Claims

1. A method for inversion correction of wellbore pressure in ultra-deep well drilling, characterized in that: The method comprises: S1: Establishing a wellbore pressure calculation model. First, a steady-state calculation model for wellbore pressure is established based on the mass and momentum conservation equations of the drilling fluid in the drill pipe and annulus. The influence of drilling fluid density changes with temperature and pressure is fully considered, and a friction pressure drop gradient model is constructed. The control equations are discretely solved using the finite difference method. Under known boundary conditions, pressure and velocity are iteratively calculated from the bottomhole to the wellhead (drill pipe) and from the wellhead to the bottomhole (annulus) to obtain the drilling fluid physical properties and pressure distribution at each node. S2: Inversion correction modeling. Based on the output of step S1, the error between the model and the actual measurement is considered, and a friction correction factor is further introduced to construct an inversion correction model for wellbore pressure. The friction correction factors in the drill pipe and annulus are used as state variables, and the drill pipe wellhead pressure is used as the observation variable to construct a nonlinear state space model. The friction correction factor is dynamically estimated using the unscented Kalman filter algorithm to achieve online adaptive correction of the wellbore pressure model.

2. The method for inversion correction of ultra-deep wellbore pressure according to claim 1, characterized in that: The step S1, establishing a steady-state calculation model for wellbore pressure, specifically includes: Based on the conservation equations of mass and momentum of drilling fluid in the drill pipe and annulus, a steady-state calculation model for wellbore pressure is established; The conservation equation of drilling fluid mass in the drill pipe is: ρ d is the density of drilling fluid in the drill pipe, kg / m 3 ;v d is the drilling fluid velocity in the drill pipe, m / s; A d is the inner cross-sectional area of the drill pipe, m 2 ; z is the well depth, m; subscript d represents the drill pipe; The momentum conservation equation of drilling fluid in the drill pipe is: p d is the drilling fluid pressure in the drill pipe, Pa; g is the acceleration due to gravity, m / s 2 ; F f,d is the friction pressure drop per unit length of drilling fluid in the drill string, that is, the friction pressure drop gradient in the drill pipe, Pa / m; The conservation equation of drilling fluid mass in the annulus is: ρ a is the density of drilling fluid in the annulus, kg / m 3 ;v a is the drilling fluid velocity in the annulus, m / s; A a is the cross-sectional area of the annulus, m 2 ;Subscript a represents annulus; The conservation equation of drilling fluid momentum in the annulus is: p a is the drilling fluid pressure in the annulus, Pa; F f,a is the friction pressure drop per unit length of drilling fluid in the annulus, that is, the friction pressure drop gradient in the annulus, Pa / m; During the drilling process, the density of drilling fluid is greatly affected by temperature and pressure. The calculation model of drilling fluid density is as follows: Where: ρ is the drilling fluid density at target temperature and pressure, kg / m 3 ; ρ0 is the drilling fluid density at the test temperature and pressure, kg / m3; T0 is the test temperature, ℃; P0 is the test pressure, Pa; T is the target temperature, ℃; P is the target pressure, Pa; A1 and A2 are fitting parameters.

3. The method for inversion correction of ultra-deep wellbore pressure according to claim 1, characterized in that: The step S1, constructing a friction pressure drop gradient model, specifically includes: Friction pressure drop gradient inside the drill pipe: D d,i is the inner diameter of the drill pipe, m; v d is the drilling fluid velocity in the drill pipe, m / s; f d is the Fanning friction factor of the drilling fluid in the drill pipe; Friction pressure drop gradient in the annulus: D w is the inner diameter of the wellbore, m; D d,o is the outer diameter of the drill pipe, m; v a is the drilling fluid velocity in the annulus, m / s; f a is the Fanning friction factor of the drilling fluid in the annulus.

4. The method for inversion correction of wellbore pressure in ultra-deep well drilling according to claim 1, characterized in that: The step S1, using the finite difference method to discretely solve the control equation, specifically includes: The wellbore with a measured depth of L is evenly divided into N grid units with a step size of △h. Then there are Nx (Nx = N + 1) storage nodes. The bottom of the well and the wellhead are marked as Nx and 1 respectively. △z(i) represents the vertical distance between adjacent storage nodes, m. The annular outlet pressure is a known boundary, so the annular pressure is calculated from the wellhead to the bottomhole; the drill pipe pressure is calculated from the bottomhole to the wellhead. That is, in the annular space, the data of the i-1th storage node is used to solve the data of the i-th storage node, while in the drill pipe, the data of the i+1th storage node is used to solve the data of the i-th storage node. The finite difference method is used to discretize the mass conservation equation of the drilling fluid in the drill pipe, and the following is obtained: Where, subscript i represents the i-th storage node; According to the drilling fluid density, drilling fluid velocity and flow area of the i+1th storage node, the drilling fluid velocity of the i-th storage node is calculated: The finite difference method is used to discretize the momentum conservation equation of the drilling fluid in the drill pipe, and the following is obtained: Calculate the drilling fluid pressure at the i-th storage node based on the drilling fluid pressure, density, velocity, and friction pressure drop gradient at the i+1-th storage node, as well as the density, velocity, and friction pressure drop gradient at the i-th storage node: The finite difference method is used to discretize the drilling fluid mass conservation equation in the annulus, and the following is obtained: According to the drilling fluid density, drilling fluid velocity and flow area of the i-1th storage node, the drilling fluid velocity of the i-th storage node is calculated: The finite difference method is used to discretize the drilling fluid momentum conservation equation in the annulus, and the equation is obtained: Calculate the pressure of the i-th storage node based on the drilling fluid pressure, density, velocity, and friction pressure drop gradient of the i-1th storage node and the density, velocity, and friction pressure drop gradient of the i-th storage node:

5. The method for inversion correction of ultra-deep wellbore pressure according to claim 1, characterized in that: The step S2 specifically includes: A friction correction factor is introduced into the friction pressure drop gradient calculation model of the drill pipe and annulus; Drill pipe: C d is the annular internal friction correction factor; Annulus: C a is the annular internal friction correction factor; Combined with the UKF algorithm, the friction correction factors in the annulus and drill pipe are used as state values, and the annulus outlet pressure is used as the observation value. The state variable (X) and observation variable (Z) in the inversion model are expressed as follows: X(k)=[C a (k),C d (k) ] T (18) Z(k)=p d,0 (k) (19) The state model for formation parameter inversion using the unscented Kalman filter (UKF) algorithm is expressed as: X(k)=X(k-1)+W(k) (20).

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