Downhole ECD accurate determination method based on field multi-point cycle test

Abstract

The invention provides a well bottom ECD accurate determination method based on a field multi-point cycle test, and belongs to the technical field of petroleum and natural gas drilling engineering. Comprising the following steps: selecting at least three different-depth test points on a casing section, and synchronously obtaining pump pressure, drilling fluid rheological parameters and borehole-drill rod geometric data; preprocessing the data; calculating annulus pressure loss, drill rod pressure loss and drill bit pressure loss of each test point based on an API standard formula; establishing a pumping pressure-pressure consumption associated linear equation set and solving annulus and drill rod pressure consumption correction coefficients; and outputting a shaft bottom ECD for eliminating naked eye interference in combination with the real-time drilling parameters and the inversion coefficient. According to the method, the multi-point cycle test and the dynamic inversion model are combined, the deviation between the theoretical model and the actual working condition is quantified through the correction coefficient, the weighted least square and the matrix condition number pre-judgment technology are combined, the problem of ECD calculation misalignment of a traditional method is solved, and the pressure control precision and safety in a complex drilling scene are remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of oil and gas drilling engineering technology, and in particular to a method for accurately determining the bottom hole ECD based on on-site multi-point cyclic testing. Background Technology

[0002] In oil and gas drilling operations, bottomhole equivalent circulating density (ECD) is a core parameter for maintaining wellbore pressure balance and preventing well kicks, lost circulation, and formation damage. Accurate ECD calculation relies on the accurate prediction of annular pressure loss, which is influenced by multiple factors, including drilling fluid rheology, wellbore geometry, drill string movement, and cuttings bed distribution. Traditional ECD calculation methods are mainly based on the following technical approaches, but they still have significant limitations:

[0003] 1. Theoretical Model Dependence: Existing technologies (such as the API RP 13D standard) calculate annular pressure loss using Newtonian / non-Newtonian fluid dynamics formulas, assuming a regular cylindrical wellbore and homogeneous steady-state drilling fluid flow. However, in actual open-hole sections, the annular cross-section is often irregular due to formation collapse, erosion, or cuttings accumulation, leading to a deviation of 15% to 30% between theoretical model calculations and actual results.

[0004] 2. The local pressure loss generated by drill bits and downhole tools (such as motors and shock absorbers) is usually simplified to a fixed empirical coefficient, ignoring its dynamic characteristics as a function of drilling speed and displacement.

[0005] 3. Single-point test correction: Some improved methods use downhole pressure while drilling (PWD) data to perform single-point correction of ECD. However, PWD equipment is expensive and easily affected by vibration, high temperature and high pressure environment, and cannot cover real-time monitoring of the entire well section.

[0006] 4. Single-point data makes it difficult to distinguish the contributions of annular pressure loss and drill string pressure loss, leading to over-coupling of correction coefficients and failure under complex working conditions.

[0007] 5. Neglecting the impact of cuttings beds: Cuttings bed accumulation significantly alters the effective flow area and velocity distribution in the annulus. Existing technologies mostly use empirical models based on cuttings transport ratio (CTR) to estimate cuttings concentration, but CTR models do not quantify the dynamic impact of cuttings beds on pressure loss, especially in horizontal and extended reach wells where errors are amplified.

[0008] 6. Insufficient adaptability to dynamic operating conditions: The rheological properties of drilling fluid (such as viscosity and yield value) change in real time with temperature and shear rate. Traditional methods use fixed rheological parameters (such as Bingham model) to calculate pressure loss, which leads to ECD prediction deviation in high-temperature deep wells.

[0009] 7. Existing inversion methods (such as closed-loop control based on pump pressure) often fail to accurately decouple the correction coefficients of annular, drill pipe and drill string pressure loss due to insufficient number of test points or overly strong linear assumptions in the model.

[0010] The aforementioned issues lead to insufficient accuracy in ECD calculations, potentially causing significant risks such as wellbore pressure runaway (e.g., well kick, lost circulation), stuck pipe, or formation fracturing. Especially in complex scenarios such as deepwater drilling and shale gas horizontal wells, there is an urgent need for a high-precision ECD determination method that can dynamically adapt to changes in open-hole annular morphology, cuttings bed distribution, and fluctuations in drilling fluid rheological properties. Summary of the Invention

[0011] In view of this, the present invention proposes a method for accurate determination of bottom hole ECD based on field multi-point cyclic testing, which aims to solve the problem of insufficient accuracy in traditional ECD calculation caused by factors such as irregular shape of open hole annulus and rock cuttings accumulation. Through multi-point cyclic testing and dynamic correction coefficient inversion model, it can break through the theoretical assumptions of traditional methods and realize dynamic high-precision inversion and accurate real-time calculation of bottom hole equivalent cyclic density.

[0012] To achieve the above objectives, the technical solution of the present invention is as follows: a method for accurate determination of bottom hole ECD based on field multi-point cyclic testing, comprising the following steps:

[0013] Step S1, Data Acquisition: Select at least three different depths in the casing section as cyclic test points to collect on-site pump pressure data, drilling fluid rheological parameters, wellbore geometry and drill pipe structural parameters;

[0014] Step S2, Preprocessing: Perform quality checks on the collected data, remove outliers, filter and denoise the data, correct missing values, and integrate, correct, and standardize the data according to the test points and time sequence.

[0015] Step S3, Preliminary assessment: Calculate the estimated values ​​of theoretical drill pipe internal pressure loss, casing drill pipe annular pressure loss, and drill bit pressure loss at each test point based on the API formula;

[0016] Step S4, Model Construction: Based on the difference between the measured pump pressure and the theoretical pressure loss prediction, construct a system of linear equations;

[0017] Step S5, coefficient inversion: Solve the system of equations simultaneously to invert the annular pressure loss correction coefficient, the drill pipe internal pressure loss correction coefficient, and the total pressure loss of the drill bit and drill string;

[0018] Step S6, ECD calculation: Combining measured parameters with inversion, dynamically correct pressure loss, and calculate the bottom hole equivalent circulating density to eliminate the influence of open hole annulus shape and cuttings accumulation.

[0019] Furthermore, in step S1, all the test points selected at different depths are located within the casing section of the well, covering the upper, middle, and lower parts of the well section. At the same time, the depth spacing between the uppermost and lowermost test points meets the requirement of 30% to 50% of the total length of the casing section, and all test point positions avoid the casing couplings.

[0020] Furthermore, in step S2, outliers are removed using box plot outlier detection, noise reduction is performed using moving mean filtering, and missing values ​​are corrected using linear interpolation. At the same time, the data is integrated and corrected according to the test points and time sequence.

[0021] Integration calibration refers to time alignment and displacement and temperature consistency processing of pump pressure, density and rheological parameters collected from different test points to eliminate system deviations caused by differences in collection timing and operating conditions.

[0022] Time alignment includes: aligning the pump pressure P at each test point. i (t), flow Q i (t), drilling fluid density ρ i (t) These data are interpolated according to the sampling timestamp so that the data of different test points correspond to the same time node, in order to ensure the synchronization of the input matrix data;

[0023] Displacement and temperature standardization processing includes: addressing the impact of displacement or temperature fluctuations during different test periods, and adjusting the discharge rate according to the reference displacement Q. ref With reference temperature T ref After normalization correction, the pump pressure is adjusted by integrating and correcting factors such as displacement and temperature. for:

[0024]

[0025] Among them, P i For actual pump pressure, MPa; Q i For the displacement corresponding to the test period, m 3 / s;μ(T i ) represents the drilling fluid viscosity at temperature, in mPa·s; μ(T) represents the drilling fluid viscosity at temperature. ref () represents the drilling fluid viscosity at the reference temperature, in mPa·s;

[0026] Data with different parameters are standardized using the Z-score method.

[0027] Furthermore, in step S3, the estimated value of the theoretical internal pressure loss of the drill pipe is calculated using the API standard formula, as shown below:

[0028]

[0029]

[0030] Among them, Pf 环空 The calculated value of the annular pressure loss of the theoretical casing drill pipe is given in MPa; Pf 钻杆 The estimated value of internal pressure loss in the theoretical drill pipe is given in MPa and Pf. 钻具+钻头 The theoretical bottom hole pressure loss is estimated in MPa; f is the fluid friction correction factor; ρ is the drilling fluid density in g / cm³. 3 v is the flow velocity, m / s; d h d represents the wellbore diameter in meters (m). p d is the outer diameter of the drill pipe (m); d is the depth of the test point (m); L is the length of the corresponding section (m); C is the flow coefficient of the drill bit nozzle (v). jet The nozzle flow rate is in m / s. Calculated; Q is the drilling fluid displacement, m 3 / s;A nozzle The total cross-sectional area of ​​the drill bit nozzle is m 2 .

[0031] Furthermore, in step S4, the linear equation system is constructed based on the difference between the measured pump pressure and the theoretical pressure loss estimate, and includes three variables: the annular pressure loss correction coefficient, the drill pipe internal pressure loss correction coefficient, and the total pressure loss of the drill bit and drill string. The calculation formula is shown below:

[0032]

[0033] Where f1 is the annular pressure loss correction coefficient, f2 is the drill pipe internal pressure loss correction coefficient, and Pf 钻具+钻头 This represents the total pressure loss of the drilling tools and drill bit, in MPa.

[0034] Furthermore, in step S5, the inversion of the linear equation system is performed numerically using the least squares method to obtain the optimal solution. The linear equation system from step S4 is transformed into matrix form A·X=B, where: the coefficient matrix A is derived from the theoretical annular pressure loss at each test point. Drill pipe pressure loss It consists of the constant term 1, as shown below:

[0035]

[0036] Variable matrix X = [f1, f2, Pf] 钻具+钻头 ] T ;

[0037] Observation matrix B = [P 泵压 ,d1,P 泵压 ,d2,P 泵压 ,d3] T ;

[0038] An ill-conditioned prediction mechanism is introduced: before matrix inversion, the condition number cond(A) of matrix A is calculated; if cond(A) > 10... 3 Then, redundant data rows with pump pressure differences of less than 5% from adjacent test points are removed, the A matrix is ​​reconstructed, and the condition number is verified again until cond(A) ≤ 10. 3 ;

[0039] Introducing a weight matrix W, with diagonal elements w i The accuracy is determined jointly by pump pressure measurement and well depth to suppress the influence of abnormal test points. The formula is as follows:

[0040]

[0041] Where, σ 泵压,i Let d be the standard deviation of the pump pressure measurement at the i-th test point. max For the maximum test depth, m; d min To minimize the test depth, assign higher weights to deeper test points, m;

[0042] Solving the equation yields the final solution:

[0043] X = (A T ·W·A) -1 ·A T ·W·B (8)

[0044] Calculate the residual R = ||A·XB||2. If the residual exceeds the preset threshold, trigger the data review process, re-execute steps S2 to S4, and output f1, f2, and Pf that satisfy the residual and constraint conditions. 钻具+钻头 , which serves as the dynamic correction input parameter for step S6.

[0045] Furthermore, in step S6, the correction coefficients f1, f2, and Pf obtained from the inversion in step S5 are... 钻具+钻头 Combined with real-time collected drilling fluid density ρ 实时 Drilling fluid temperature T 实时 The dynamic correction formulas for annular pressure loss and drill pipe pressure loss are shown below:

[0046]

[0047] Where, μ 基准 The reference drilling fluid viscosity is given in mPa·s; μ 实时 The real-time drilling fluid viscosity is given in mPa·s; ΔT = T 实时 -T 基准 ,℃; β is the coefficient of thermal expansion; The annular pressure loss at depth d after temperature and viscosity correction, in MPa; The internal pressure loss of the drill pipe at depth d after temperature and viscosity correction, in MPa;

[0048] Calculate the volume concentration C of annular rock fragments 岩屑 And correct the annular pressure loss:

[0049]

[0050] Wherein, ΔP 岩屑沉降 =0.021·C 岩屑 ·d represents the additional hydrostatic pressure drop caused by rock cuttings settling;

[0051] We can obtain:

[0052]

[0053] The calculated bottom hole pressure is:

[0054]

[0055] The bottom-hole ECD value is calculated using the following formula:

[0056]

[0057] Among them, ΔECD 振动补偿 =0.05·σ 振动 , σ 振动 The standard deviation of the downhole vibration sensor measurement is used to compensate for pressure fluctuations caused by vibration.

[0058] Compared with existing technologies, the method for accurate determination of bottom hole ECD based on field multi-point cyclic testing described in this invention has the following advantages: This invention combines multi-point cyclic testing with a dynamic inversion model, quantifies the deviation between the theoretical model and the actual working conditions by correcting coefficients, and combines weighted least squares and matrix condition number prediction technology to overcome the problem of inaccurate ECD calculation caused by the uncertainty of annular morphology and dynamic changes in cuttings bed in traditional methods, and significantly improves the pressure control accuracy and safety in complex drilling scenarios.

[0059] (1) Improved ECD calculation accuracy: This invention selects multiple test points in the casing section, combines the actual pump pressure measurement with the theoretical pressure loss to establish a linear equation system, and dynamically corrects the model through coefficient inversion. This effectively overcomes the problem of pressure loss calculation deviation caused by the irregularity of the wellbore and the accumulation of cuttings in the traditional method, and significantly reduces the calculation error of the bottom hole equivalent circulating density (ECD).

[0060] (2) Enhanced adaptability to complex working conditions: By adopting real-time parameters and rheological dynamic correction mechanism, combined with temperature-viscosity relationship and rock cuttings deposition effect, it can adapt to ECD calculation under various working conditions such as high temperature deep well, complex well section and formation heterogeneity, and ensure the timeliness and reliability of pressure control.

[0061] (3) A highly robust correction coefficient inversion method was implemented: By identifying the ill-conditioned nature of the matrix condition number, eliminating redundant points, and introducing a weight matrix to suppress measurement errors, the stability and reliability of the inversion model in a high-noise environment were improved, avoiding the risk of failure of the traditional linear assumption model under actual drilling conditions.

[0062] (4) Reduced dependence on high-cost downhole instruments: Unlike single-point correction methods that rely on test-and-drill (PWD) equipment, this invention uses measurable parameters on the ground to complete the correction of the entire well section, reducing dependence on high-cost and complex-to-install downhole tools, and has good engineering scalability and economic efficiency.

[0063] (5) Improved ability to identify and respond to abnormal working conditions: The residual threshold judgment mechanism is introduced. When the inversion result exceeds the confidence interval, the data verification process is automatically triggered, which effectively avoids the transmission of erroneous parameters to the ECD calculation module and provides intelligent early warning and safety guarantee for the drilling process. Attached Figure Description

[0064] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. Obviously, the drawings described below are merely some embodiments herein, and those skilled in the art can obtain other drawings based on these drawings without creative effort. In the drawings:

[0065] Figure 1 A flowchart of a method for accurate determination of bottom hole ECD based on field multi-point cyclic testing;

[0066] Figure 2 This is a schematic diagram showing the layout of the well section and test points;

[0067] Figure 3 This is a pump pressure curve.

[0068] Figure 4 This is a diagram showing the distribution of the inverted residuals.

[0069] Figure 5 Diagram showing the impact of rock cuttings beds;

[0070] Figure 6 This is a comparison chart of ECD values ​​from well B1. Detailed Implementation

[0071] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0072] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0073] like Figure 1 As shown, this invention is a method for accurately determining the bottom hole ECD based on on-site multi-point cyclic testing, comprising the following steps:

[0074] Step S1, Data Acquisition: Select at least three different depths in the casing section as cyclic test points to collect on-site pump pressure data, drilling fluid rheological parameters, wellbore geometry and drill pipe structural parameters;

[0075] All selected test points at different depths are located within the casing section of the well, covering the upper, middle, and lower parts of the well section. The depth spacing between the uppermost and lowermost test points meets the requirement of 30% to 50% of the total length of the casing section, and all test point locations avoid the casing couplings to ensure the representativeness of the depth distribution of the pump pressure data.

[0076] Step S2, Preprocessing: Perform quality checks on the collected data, remove outliers, filter and denoise the data, correct missing values, and integrate, correct, and standardize the data according to the test points and time sequence.

[0077] Specifically, outliers were removed using box plot outlier detection, noise was removed using moving mean filtering, and missing values ​​were corrected using linear interpolation. At the same time, the data were integrated and corrected according to the test points and time sequence, and the data were standardized.

[0078] Step S3, Preliminary assessment: Calculate the estimated values ​​of theoretical drill pipe internal pressure loss, casing drill pipe annular pressure loss, and drill bit pressure loss at each test point based on the API formula;

[0079] Step S4, Model Construction: Based on the difference between the measured pump pressure and the theoretical pressure loss prediction, construct a system of linear equations;

[0080] Step S5, coefficient inversion: Solve the system of equations simultaneously to invert the annular pressure loss correction coefficient, the drill pipe internal pressure loss correction coefficient, and the total pressure loss of the drill bit and drill string;

[0081] Step S6, ECD calculation: Combining measured parameters with inversion, dynamically correct pressure loss, and calculate the bottom hole equivalent circulating density (ECD) to eliminate the influence of open hole annulus shape and cuttings accumulation.

[0082] In step S2, integration and calibration refers to time alignment and displacement and temperature consistency processing of the pump pressure, density and rheological parameters collected from different test points to eliminate system deviations caused by differences in collection timing and operating conditions.

[0083] Time alignment includes: aligning the pump pressure P at each test point. i (t), flow Q i (t), drilling fluid density ρ i(t) These data are interpolated according to the sampling timestamp so that the data of different test points correspond to the same time node, in order to ensure the synchronization of the input matrix data;

[0084] Displacement and temperature standardization processing includes: addressing the impact of displacement or temperature fluctuations during different test periods, and adjusting the discharge rate according to the reference displacement Q. ref With reference temperature T ref After normalization correction, the pump pressure is adjusted by integrating and correcting factors such as displacement and temperature. for:

[0085]

[0086] Among them, P i For actual pump pressure, MPa; Q i For the displacement corresponding to the test period, m 3 / s;μ(T i ) represents the drilling fluid viscosity at temperature, in mPa·s; μ(T) represents the drilling fluid viscosity at temperature. ref () represents the drilling fluid viscosity at the reference temperature, in mPa·s;

[0087] The dimensions of different parameters (such as pump pressure, density, and viscosity) vary greatly, so the data of different parameters are standardized using the Z-score method.

[0088] In step S3, the estimated value of the theoretical internal pressure loss of the drill pipe is calculated using the API standard formula, as shown below:

[0089]

[0090] Among them, Pf 环空 The calculated value of the annular pressure loss of the theoretical casing drill pipe is given in MPa; Pf 钻杆 The estimated value of internal pressure loss in the theoretical drill pipe is given in MPa and Pf. 钻具+钻头 The theoretical bottom hole pressure loss is estimated in MPa; f is the fluid friction correction factor; ρ is the drilling fluid density in g / cm³. 3 v is the flow velocity, m / s; d h d represents the wellbore diameter in meters (m). p d is the outer diameter of the drill pipe (m); d is the depth of the test point (m); L is the length of the corresponding section (m); C is the flow coefficient of the drill bit nozzle (v). jet The nozzle flow rate is in m / s. Calculated; Q is the drilling fluid displacement, m 3 / s;A nozzle The total cross-sectional area of ​​the drill bit nozzle is m 2 .

[0091] In step S4, the linear equation system is constructed based on the difference between the measured pump pressure and the theoretical pressure loss estimate, and includes three variables: annular pressure loss correction coefficient, drill pipe internal pressure loss correction coefficient, and total pressure loss of the drill bit and drill string. The calculation formula is shown below:

[0092]

[0093] Where f1 is the annular pressure loss correction coefficient, f2 is the drill pipe internal pressure loss correction coefficient, and Pf 钻具+钻头 This represents the total pressure loss of the drilling tools and drill bit, in MPa.

[0094] In step S5, the inversion of the linear equation system is performed numerically using the least squares method to obtain the optimal solution. The linear equation system from step S4 is then transformed into matrix form A·X=B, where: the coefficient matrix A is derived from the theoretical annular pressure loss at each test point. Drill pipe pressure loss It consists of the constant term 1, as shown below:

[0095]

[0096] Variable matrix X = [f1, f2, Pf] 钻具+钻头 ] T ;

[0097] Observation matrix B = [P 泵压 ,d1,P 泵压 ,d2,P 泵压 ,d3] T ;

[0098] An ill-conditioned prediction mechanism is introduced: before matrix inversion, the condition number cond(A) of matrix A is calculated; if cond(A) > 10... 3 Then, redundant data rows with pump pressure differences of less than 5% from adjacent test points are removed, the A matrix is ​​reconstructed, and the condition number is verified again until cond(A) ≤ 10. 3 ;

[0099] Introducing a weight matrix W, with diagonal elements w i The accuracy is determined jointly by pump pressure measurement and well depth to suppress the influence of abnormal test points. The formula is as follows:

[0100]

[0101] Where, σ 泵压,i Let d be the standard deviation of the pump pressure measurement at the i-th test point. max For the maximum test depth, m; d min To minimize the test depth, assign higher weights to deeper test points, m;

[0102] Solving the equation yields the final solution:

[0103] X = (A T ·W·A) -1 ·A T ·W·B (8)

[0104] Calculate the residual R = ||A·XB||2. If the residual exceeds the preset threshold, trigger the data review process, re-execute steps S2 to S4, and output f1, f2, and Pf that satisfy the residual and constraint conditions. 钻具+钻头 , which serves as the dynamic correction input parameter for step S6.

[0105] In step S6, the correction coefficients f1, f2, and Pf are inverted based on step S5. 钻具+钻头 Combined with real-time collected drilling fluid density ρ 实时 Drilling fluid temperature T 实时 The dynamic correction formulas for annular pressure loss and drill pipe pressure loss are shown below:

[0106]

[0107] Where, μ 基准 The reference drilling fluid viscosity is given in mPa·s; μ 实时 The real-time drilling fluid viscosity is given in mPa·s; ΔT = T 实时 -T 基准 ,℃; β is the coefficient of thermal expansion; The annular pressure loss at depth d after temperature and viscosity correction, in MPa; The internal pressure loss of the drill pipe at depth d after temperature and viscosity correction, in MPa;

[0108] Calculate the volume concentration C of annular rock fragments 岩屑 And correct the annular pressure loss:

[0109]

[0110] Wherein, ΔP 岩屑沉降 =0.021·C 岩屑 ·d represents the additional hydrostatic pressure drop caused by rock cuttings settling;

[0111] We can obtain:

[0112]

[0113] The calculated bottom hole pressure is:

[0114]

[0115] The bottom-hole ECD value is calculated using the following formula:

[0116]

[0117] Among them, ΔECD 振动补偿 =0.05·σ 振动 , σ 振动 The standard deviation of the downhole vibration sensor measurement is used to compensate for pressure fluctuations caused by vibration.

[0118] Example 1

[0119] According to the present invention, a method for accurately determining the bottom-hole ECD based on multi-point cyclic testing in the field is used to accurately determine the bottom-hole ECD of horizontal well B1 in the XX block of an oilfield in eastern China. The details are as follows:

[0120] 1. In this embodiment, the XX block of an oilfield in eastern China is controlled by a strike-slip fault, with a formation dip angle of 15° to 25°, and multiple pressure systems exist (the normal pressure in the shallow part is 1.05 g / cm³). 3 ~1.10g / cm 3 Deep overpressure 2.0 g / cm 3 ~2.2g / cm 3 The geothermal gradient is 4.2℃ / 100m, with a bottom-hole temperature reaching 182℃ (well depth 4500m). The drilling fluid exhibits significant high-temperature aging (viscosity decreased from 42 mPa·s at 60℃ to 28 mPa·s at 180℃). The open-hole section encountered formations of mudstone and shale (prone to hydration and expansion) and siltstone (permeability 15mD~30mD), with a wellbore enlargement rate of 18%~35% and a cuttings bed concentration of 8%~25%. The B1 wellbore structure is shown in Table 1.

[0121] Table 1B1 Well Results Parameters

[0122]

[0123]

[0124] Drill assembly: Drill pipe: S135 steel grade, inner diameter 108.6mm; drill collar: Length 120m; Downhole tools: screw motor (pressure loss coefficient 0.12), drilling rig (pressure loss coefficient 0.08). Drilling fluid properties are shown in Table 2.

[0125] Table 2 Drilling Fluid Performance Parameters

[0126] parameter Design value Real-time measurement (well depth 3000m) density 1.25 1.23~1.27 (fluctuation ±1.6%) Plastic viscosity 42 35 (15% degradation at high temperatures) Dynamic shear force 8.5 6.3 (Shear Dilution) API filter flux ≤4.0 5.2 (mud shale hydration)

[0127] 2. Test point selection: such as Figure 2 As shown, Figure 2A schematic diagram of the well section and test point layout is provided. Location: Three test points were selected within the casing section (700m, 1400m, and 1700m), with spacing of 700m (35%) and 300m (15%), respectively. The total spacing accounts for 50% of the casing section length (700m + 300m = 1000m, accounting for 50% of the 2000m length). Avoidance area: Verified through caliper logging, the test points are located far from the casing coupling. The measured pump pressure, drilling fluid density, viscosity, and displacement parameters for each test point are shown in Table 3.

[0128] Table 3. Monitoring Data of Test Points

[0129] test points Pump pressure Drilling fluid density Viscosity Displacement TP1 24.5 1.25 42 30 TP2 28.1 1.25 42 30 TP3 30.8 1.25 42 30

[0130] 3. Data Preprocessing: Outlier Removal: The original pump pressure at TP3 was 32.5 MPa (exceeding Q3 + 1.5IQR = 31.2) detected by box plot method, and corrected to 30.8 MPa. Filtering: Moving average filtering (window 5s) reduced pump pressure noise from ±0.4 MPa to ±0.1 MPa. Missing Value Correction: Drilling fluid density was missing at TP2, and linear interpolation was used to complete it to 1.25 g / cm³. 3 Simultaneously, the data was integrated and corrected according to the test points and time sequence, and the data was standardized. The pump pressure curve is shown below. Figure 3 As shown, by Figure 3 It can be seen that the fluctuation of the pump pressure curve is significantly reduced after preprocessing, and the data is continuous and smooth, indicating that the outlier removal and filtering steps are effective, and the preprocessing results can meet the accuracy requirements of subsequent inversion calculations.

[0131] 4. Calculate theoretical pressure loss: The estimated theoretical pressure loss is calculated using the API standard formula:

[0132]

[0133]

[0134] Among them, Pf 环空 The calculated value of the annular pressure loss of the theoretical casing drill pipe is given in MPa; Pf 钻杆 The estimated value of internal pressure loss in the theoretical drill pipe is given in MPa and Pf. 钻具+钻头 The theoretical bottom hole pressure loss is estimated in MPa; f is the fluid friction correction factor; ρ is the drilling fluid density in g / cm³. 3 v is the flow velocity, m / s; d h d represents the wellbore diameter in meters (m). p d is the outer diameter of the drill pipe (m); d is the depth of the test point (m); L is the length of the corresponding section (m); C is the flow coefficient of the drill bit nozzle (v). jet The nozzle flow rate is in m / s. Calculated; Q is the drilling fluid displacement, m 3 / s;A nozzle The total cross-sectional area of ​​the drill bit nozzle is m 2 .

[0135] The estimated results of this embodiment are shown in Table 4.

[0136] Table 4. Predicted Results for Test Points

[0137] test points <![CDATA[Pf 环空 ]]> <![CDATA[Pf 钻杆 ]]> <![CDATA[Pf 钻具+钻头 ]]> TP1 1.6 5.1 6.0 TP2 3.2 10.2 6.0 TP3 4.8 15.3 6.0

[0138] 5. Construct a system of equations containing three variables: annular pressure loss correction coefficient, drill pipe internal pressure loss correction coefficient, and total pressure loss coefficient of the drill bit and drill string. The formula is as follows:

[0139]

[0140] Where f1 is the annular pressure loss correction coefficient, f2 is the drill pipe internal pressure loss correction coefficient, and Pf 钻具+钻头 This represents the total pressure loss of the drilling tools and drill bit, in MPa.

[0141] 6. The inversion of the linear equation system is performed numerically using the least squares method to obtain the optimal solution. The condition number cond(A) is calculated to be 1.5 × 10⁻⁶. 3 >10 3 Redundant data was removed. The pump pressure difference was checked; the difference between TP3 and TP2 was (30.8-28.1) / 28.1 = 9.6% > 5%. All data were retained, and the calculation results are shown in Table 5.

[0142] Table 5 Calculation Parameters for Test Points

[0143] test points σ pump pressure Depth weighting factor Weight TP1 0.3 1.0 11.11 TP2 0.4 0.3 1.88 TP3 0.5 0.0 0.0

[0144] Solving the equation yields the final solution: X = (A T ·W·A) -1 ·A T ·W·B, calculate the residual R = ||A·XB||², = 0.35MPa < threshold 0.5MPa, therefore, the inversion is effective. The distribution of the inversion residual is as follows: Figure 4 As shown.

[0145] 7. Correction coefficients f1, f2 and Pf based on inversion 钻具+钻头 Combined with real-time collected drilling fluid density ρ 实时 Temperature T 实时 Dynamically correct annular pressure loss and drill pipe pressure loss:

[0146]

[0147] Where, μ 基准 The reference drilling fluid viscosity is given in mPa·s; μ 实时The real-time drilling fluid viscosity is given in mPa·s; ΔT = T 实时 -T 基准 ,℃; β is the coefficient of thermal expansion; The annular pressure loss at depth d after temperature and viscosity correction, in MPa; The internal pressure loss of the drill pipe at depth d after temperature and viscosity correction, in MPa;

[0148] Calculate the volume concentration C of annular rock fragments 岩屑 And correct the annular pressure loss:

[0149]

[0150] Wherein, ΔP 岩屑沉降 =0.021·C 岩屑 ·d represents the additional hydrostatic pressure drop caused by rock cuttings settling;

[0151] We can obtain:

[0152]

[0153] The calculated bottom hole pressure is:

[0154]

[0155] The bottom-hole ECD value is calculated using the following formula:

[0156]

[0157] Among them, ΔECD 振动补偿 =0.05·σ 振动 , σ 振动 The standard deviation of the downhole vibration sensor measurements is used to compensate for pressure fluctuations caused by vibration. The influence diagram of the cuttings bed is shown below. Figure 5 As shown.

[0158] The final calculated ECD increment for this implementation is 0.101. The comparison chart of ECD values ​​for well B1 is shown below. Figure 6 As shown in Table 6, a comparison between the method of the present invention and the conventional method is presented.

[0159] Table 6 Comparison of Calculation Results

[0160] index Traditional API computing Method of the present invention Real-world PWD testing while drilling Error Analysis ECD increment 0.082 0.101 0.098 The error decreased from 22.0% to 2.0%. Annular pressure loss 12.3 15.8 15.2 The error decreased from 19.1% to 3.9%.

[0161] As shown in Table 6, the ECD increment calculated by the method of this invention is highly consistent with the measured values ​​while drilling, and the calculation error is significantly reduced compared with the traditional method. The prediction accuracy of annular pressure loss is also significantly improved. This indicates that the present invention can effectively correct the deviation of the theoretical model and improve the reliability and accuracy of bottom hole pressure calculation.

[0162] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for accurately determining the bottom hole ECD based on field multipoint cyclic testing, characterized in that, The method comprises the following steps: Step S1, data collection: selecting at least three different depths in the casing section as the circulation test points, collecting the field pump pressure data, drilling fluid rheological parameters, wellbore geometric dimensions and drill pipe structure parameters; Step S2, pretreatment: performing quality inspection on the collected data, removing abnormal values, filtering and denoising and correcting missing values, and integrating and correcting and standardizing according to the test points and time sequence; Step S3, preliminary evaluation: calculating the estimated values of the theoretical drill pipe internal pressure loss, the casing and drill pipe annular pressure loss and the drill tool bit pressure loss of each test point based on the API formula respectively; Step S4, model construction: constructing a linear equation set based on the difference between the measured pump pressure value and the theoretical pressure loss estimated value; Step S5, coefficient inversion: solving the equation set to invert the annular pressure loss correction coefficient, the drill pipe internal pressure loss correction number and the drill tool bit total pressure loss; Step S6, ECD calculation: combining the measured parameters and the inversion to dynamically correct the pressure loss and calculate the bottom hole equivalent circulating density eliminating the influence of the open hole annular shape and the cuttings accumulation.

2. The method according to claim 1, wherein the method is characterized by: In step S1, all the test points at different depths selected are located in the casing section, cover the upper, middle and lower parts of the well section, the depth interval between the uppermost test point and the lowermost test point satisfies 30% to 50% of the total length of the casing section, and all the test point positions avoid the casing joints.

3. The method of claim 1, wherein: In step S2, the box chart outlier detection method is used to remove abnormal values, the sliding mean filter method is used for filtering and denoising, and the linear interpolation method is used for correcting missing values; meanwhile, the data are integrated and corrected according to the test points and time sequence; The integrated correction refers to time alignment of the pump pressure, density and rheological parameter data collected at different test points and consistent treatment of the displacement and temperature, so as to eliminate the system deviation caused by the time sequence and working condition difference during collection; Time alignment includes: aligning the pump pressure P at each test point. i (t), flow Q i (t), drilling fluid density ρ i (t) These data are interpolated according to the sampling timestamp so that the data of different test points correspond to the same time node, in order to ensure the synchronization of the input matrix data; The displacement, temperature uniformization processing includes: for the influence of displacement or temperature fluctuation of different test periods, according to the reference displacement Q ref The reference temperature T ref The pump pressure after the correction of the factors of displacement and temperature is: ​ wherein P i is the measured pump pressure, MPa; Q i is the displacement for the corresponding test period, m 3 / s; μ(T i ) is the viscosity of the drilling fluid corresponding to the temperature, mPa-s; μ(T ref ) is the viscosity of the drilling fluid corresponding to the reference temperature, mPa-s; The data of different parameters are standardized by using the Z-score method.

4. The method of claim 1, wherein: In step S3, the estimated value of the theoretical drill pipe internal pressure loss is calculated by using the API standard formula, and the calculation formula is as follows: wherein Pf 环空 is the calculated value of the theoretical casing annular pressure loss, MPa; Pf 钻杆 is the estimated value of the theoretical drill pipe internal pressure loss, MPa; Pf 钻具+钻头 is the estimated value of the theoretical bottom hole assembly and drill bit pressure loss, MPa; f is the fluid friction correction factor; p is the drilling fluid density, g / cm 3 ; v is the flow rate, m / s; d h is the borehole diameter, m; d p is the drill pipe outer diameter, m; d is the test point depth, m; L is the corresponding section length, m; C is the drill bit nozzle flow coefficient, v jet is the nozzle flow rate, m / s, obtained by calculation; Q is the drilling fluid displacement, m 3 / s; A nozzle is the total drill bit nozzle cross-sectional area m 2 .

5. The method of claim 4, wherein: In step S4, the linear equation set is constructed based on the difference between the measured pump pressure value and the theoretical pressure loss estimated value, contains three variables: the annular pressure loss correction coefficient, the drill pipe internal pressure loss correction coefficient and the drill tool bit total pressure loss, and the calculation formula is as follows: Wherein, f1 is annulus pressure loss correction coefficient, f2 is drill pipe internal pressure loss correction coefficient, Pf 钻具+钻头 is the total pressure loss of the drilling tool and drill bit, MPa.

6. The method of claim 5, wherein: In step S5, the inversion of the linear equations is solved numerically using the least squares method to obtain the optimal solution. The linear equations from step S4 are converted to matrix form A · X = B, where the coefficient matrix A is composed of the theoretical annular pressure losses of each test point Drill pipe pressure loss and the constant term 1, as follows: Variable matrix X = [f1, f2, Pf 钻具+钻头 ] T ; Observation matrix B = [P 泵压 , d1, P 泵压 , d2, P 泵压 , d3] T ; The ill-conditioned prediction mechanism is introduced, and the condition number cond(A) of the matrix A is calculated before the matrix inversion. If cond(A) > 10 3 , the redundant data rows with the pump pressure difference less than 5% of the adjacent test points are removed, the A matrix is reconstructed, and the condition number is verified again until cond(A) <= 10 3 . A weight matrix W is introduced, with diagonal elements w i The pump pressure measurement accuracy and the well depth are combined to determine the formula to suppress the influence of abnormal test points: where σ 泵压,i is the standard deviation of the pump pressure measurements at the ith test point; d max is the maximum test depth, m; d min is the minimum test depth, giving higher weight to the deeper test points, m; The final solution is obtained by solving the equation: X = (A T • W • A) -1 • A T • W • B (8) A residual R = ||A X - B||2 is calculated, and if the residual exceeds a preset threshold, a data review process is triggered, and steps S2 to S4 are re-executed to output f1, f2 and Pf that satisfy the residual and the constraint condition as the dynamic correction input parameter of step S6. 钻具+钻头 , as the dynamic correction input parameter of step S6.

7. The method of claim 6, wherein: In step S6, the correction coefficients f1, f2 and Pf inverted in step S5 are used as a basis 钻具+钻头 , in combination with the real-time collected drilling fluid density p 实时 , drilling fluid temperature T 实时 , to dynamically correct the annular pressure loss and the drill pipe pressure loss, and the calculation formula is as shown below: wherein μ 基准 is the reference drilling fluid viscosity, mPa·s; μ 实时 is the real-time drilling fluid viscosity, mPa·s; ΔT = T 实时 -T 基准 , °C; β is the temperature expansion coefficient; is the temperature and viscosity corrected annular pressure loss at depth d, MPa; is the temperature and viscosity corrected drill pipe internal pressure loss at depth d, MPa; Calculating annular cuttings volume concentration C 岩屑 and correcting the annular pressure loss: where ΔP 岩屑沉降 = 0.021 · C 岩屑 · d, is the additional hydrostatic pressure drop due to cuttings settling. The bottom hole pressure is calculated as follows: The bottom hole ECD value is calculated by the following formula: ​ where ΔECD 振动补偿 = 0.05-σ 振动 , σ 振动 is the standard deviation measured by the downhole vibration sensor to compensate for pressure fluctuations due to vibrations.

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