Casing tripping risk quantitative evaluation method considering well bore quality uncertainty

Abstract

The invention belongs to the technical field of oil and gas drilling, and particularly relates to a casing tripping-in risk quantitative evaluation method considering well bore quality uncertainty, which realizes probability evaluation of casing tripping-in friction resistance by utilizing Monte Carlo simulation and multi-distribution random sampling. The core thought of the method is as follows: the uncertainty of well diameter and dog-leg-degree well bore quality parameters is taken as an entry point, and the accuracy and decision scientificity of casing tripping-in performance evaluation are improved through the process of'probability modeling-related sampling-smooth constraint-friction resistance calculation-risk evaluation '. According to the method, uncertainty and spatial distribution characteristics of key well bore quality parameters such as the well diameter and the dogleg degree can be systematically represented; a large number of random borehole quality parameter sequences conforming to actual geology and engineering rules are generated; on the basis, Monte Carlo simulation is carried out, and probability distribution of casing running friction resistance is calculated; and finally, the risk that the casing can be put down is quantified in a probability form, and a visual probability basis is provided for engineering decision making.

Description

Technical Field

[0001] This invention belongs to the field of oil and gas drilling technology, and specifically relates to a quantitative evaluation method for casing run-in risk considering the uncertainty of wellbore quality. Background Technology

[0002] In oil and gas well drilling operations, the safe and smooth running of the casing to the designed depth is crucial to the success or failure of well completion. Casing run-in capability directly depends on the balance between the casing's buoyancy and the wellbore-casing friction: when the casing's friction exceeds its buoyancy, the casing cannot be run to the designed depth, potentially leading to operational failure or economic loss.

[0003] Traditional casing running friction calculation models all use single, fixed wellbore trajectory parameters for friction calculation, failing to consider the influence of wellbore mass on friction. This has a significant drawback: in actual drilling, due to various factors such as formation heterogeneity, drill string assembly, drilling fluid properties, and operating parameters, wellbore mass parameters such as wellbore diameter and dogleg are not fixed values ​​but rather random variables fluctuating within a certain range. Therefore, they cannot accurately reflect the inherent uncertainty of actual wellbore mass, leading to overly idealized evaluation results. Furthermore, existing casing running friction calculation models only provide a definite friction value, failing to answer questions such as "What is the probability that the friction will exceed the casing buoyancy under conditions of wellbore mass uncertainty?" This results in a lack of probabilistic basis for evaluating casing running feasibility.

[0004] Chinese patent document CN111444637A (202010467593.8) discloses a safety assessment method and system for running casing in long horizontal wells for shale gas, but it is essentially a deterministic method. It uses methods such as comparing data from adjacent wells and critical value analysis to ultimately output a deterministic friction coefficient, maximum well depth, and risk level, resulting in a single risk level and maximum well depth. Decision-makers only know that the risk is "high," but not "how high," or "how likely it is to exceed design capacity." Although the above scheme also considers the impact of wellbore irregularity (well diameter variation coefficient) and cumulative dogleg degree, the processing method is crude. It finds the "critical value" by "comparing" with adjacent wells, essentially using historical experience data to perform boundary correction on a deterministic model. Its "wellbore cleanliness" correction is also based on a fixed proportional adjustment of subjective qualitative judgment.

[0005] Therefore, there is an urgent need for a casing run-in evaluation method that can take into account the uncertainty of wellbore quality and quantify the random fluctuations of wellbore quality parameters, so as to improve the accuracy of casing run-in operation risk assessment and the scientific nature of decision-making. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a quantitative assessment method for casing run-in risk considering wellbore quality uncertainties. This invention overcomes the shortcomings of traditional deterministic methods by utilizing Monte Carlo simulation and multi-distribution random sampling to achieve probabilistic assessment of casing run-in friction. Its core idea is to use the uncertainty of wellbore quality parameters (wellbore diameter, dogleg degree) as a starting point, and improve the accuracy and scientific basis of casing run-in feasibility assessment through a process of "probabilistic modeling → relevant sampling → smoothing constraints → friction calculation → risk assessment." This method can systematically characterize the uncertainty and spatial distribution characteristics of key wellbore quality parameters such as wellbore diameter and dogleg degree; generate a large number of random wellbore quality parameter sequences that conform to actual geological and engineering laws; perform Monte Carlo simulations on this basis to calculate the probability distribution of casing run-in friction; and finally quantify the risk of casing run-in in probabilistic form, providing an intuitive probabilistic basis for engineering decisions.

[0007] The technical problem to be solved by this invention is achieved by the following technical solution: a method for quantitatively assessing the risk of casing run-in considering the uncertainty of wellbore quality, the specific steps of which are as follows: S1. Multi-source data integration and probability distribution model establishment: S101, Multi-source data on friction during casing insertion; The multi-source data includes: wellbore structure data, casing string design data, and formation data division. Based on the formation data, each sounding point is set at equal intervals according to a preset distance for the generation of wellbore trajectory; S102. Define the probability distribution model for wellbore diameter and dogleg degree; By analyzing and statistically analyzing the wellbore quality data of adjacent wells, probability distribution models for well diameter and dogleg degree are defined for each formation. Based on the distribution parameters corresponding to the distribution type, functions are called to establish a mapping relationship between "formation-parameter-distribution". In this invention, the function call is based on Series / DataFrame of pandas software to obtain distribution statistics; pandas is just a data processing tool and not a necessary condition for Monte Carlo simulation; the core idea of ​​Monte Carlo simulation is random sampling and statistics, which can be implemented in any programming language, such as Python's NumPy, C++, and Java. The purpose of establishing the "strata-parameter-distribution" mapping relationship is to differentiate and model the uncertainties of different strata, so that the generated random sequences have both spatial correlation and conformity to the statistical laws of the strata. As shown in Table 1, due to differences in lithology, hardness, cementation degree, etc., different strata have different wellbore enlargement laws and dogleg variation characteristics. The mapping relationship determines the probability distribution model for each stratum, thereby more realistically depicting this difference. Therefore, when generating the random parameter sequence in step S2, each sounding point calls the corresponding distribution model for sampling according to its stratum. The distribution parameters (such as mean, standard deviation, range) define the statistical tendency and reasonable interval of parameter values, providing a probabilistic framework for random sampling. However, this is not a strict hard limit, and subsequent engineering constraints (step S3) will further impose safety boundaries. Assuming a sounding point is located at 730m (belonging to formation 1), step S2 (if using the Gaussian process method) will query the mapping relationship and find that the well diameter of this point should follow N(0.558, 0.1) and the dogleg degree should follow U(0.01, 2.19). Based on this distribution, and combined with the algorithm of step S2 (such as the covariance function of the Gaussian process), a random value for this point is generated to ensure that the value not only conforms to the statistical characteristics of the formation, but also maintains reasonable continuity with neighboring points. Table 1. Probability Distribution Types and Parameter Definitions

[0008] The process of establishing the probability distribution model is as follows: for each formation (e.g., formation 1: 0~790m, formation 2: 790~1860m), the distribution type is selected for well diameter and dogleg degree respectively (selected by statistical analysis of the well quality data of the drilled wells in the block, i.e. well diameter and dogleg degree). S2, Generation of relevant random parameter sequences; The algorithm simulates the spatial correlation of parameters corresponding to sounding points along the well depth direction. Based on the formation corresponding to each sounding point, and according to the probability distribution model of the corresponding formation determined in step S1, a random sampling method is used to generate a wellbore mass sequence of continuously varying diameter and dogleg wellbore mass along the well depth, thus obtaining a wellbore trajectory parameter sequence composed of the wellbore mass sequence of diameter and dogleg wellbore mass. Smooth transition of stratigraphic boundaries: To avoid abrupt parameter changes at the stratigraphic boundary, the parameters within 50m before and after the boundary are smoothed. Step S2 is the key difference between this invention and traditional methods. Since the wellbore trajectory parameters do not vary completely independently along the well depth, the parameters between adjacent sounding points usually exhibit spatial correlation. To avoid generating physically unrealistic and abruptly random parameters, this invention provides an algorithm to generate a spatially correlated sequence of wellbore diameter and dogleg parameters (along the well depth direction). The algorithm generates md... i When calculating the value of a point, its neighboring points md will be considered. i-1,md i-2 The value of … (based on the relevant rules of different algorithms) is measured and realized by the relative distance (Δmd) between sounding points; Step S2 extracts the corresponding wellbore diameter and dogleg parameters based on sounding points. The mean value indicates where the "central tendency" of this formation parameter should be centered. For example, if the mean wellbore diameter of a formation is 0.3 meters, then regardless of the method used to limit the correlation of the parameters corresponding to the sounding points along the well depth direction, the overall average level should be close to 0.3 meters. The standard deviation / distribution range defines the reasonable range of parameter fluctuations. The dispersion of the values ​​generated by the sampling method in step S2 must conform to this range. For example, a uniform distribution [0.28, 0.32] explicitly prohibits the sampling method from generating wellbore values ​​less than 0.28 or greater than 0.32. The distribution shape determines the preference of the values. A triangular distribution will result in more sampling near the "most likely value." An exponential distribution will result in a much higher probability of small values ​​than large values. The sampling method in step S2 needs to call the distribution parameters corresponding to each formation to generate a sequence that conforms to the corresponding shape. Formation boundary smoothing addresses discontinuities between formations, eliminating abrupt boundary changes caused by differences in formation statistical parameters. It is localized, occurring only within a narrow transition zone near the formation interface (e.g., within 50 meters before and after). Step S3, smoothing, eliminates noise and high-frequency fluctuations, making the parameter curves more closely resemble the actual smooth wellbore shape. It is global, smoothing all sounding points throughout the entire well section. While their purposes, scope, and methods differ, they work together to ensure that the final wellbore quality sequence used in Monte Carlo simulations is both geologically accurate and engineeringally sound. Smoothing weight function for formation boundary smoothing: (12) In the formula, md This represents the current depth value of the sounding point. To smooth out the weights, Z b The depth of the stratigraphic boundary, i.e. Figure 1 The depth at the boundary between the two strata, when md much smaller Z b (i.e., far above the border) md - Z b Since ) is a large negative number, exp(...) is close to 0, therefore w ( md )≈1. When md is much greater than Z b (i.e., far below the boundary) md - Z bIf ) is a large positive number, exp(...) is very large, therefore w ( md )≈0. When md equal Z b (When it is exactly at the boundary) w ( md =0.5. Specifically, w ( md When )≈1, the parameter value at that point retains the original generated value (from the overlying strata model). w ( md When )=0.5, the parameter value at this point is a weighted average of the generated values ​​of the upper and lower strata, each accounting for half of the weight, thus achieving a natural connection at the center point; w ( md When )≈0, the parameter value at this point is the generated value from the lower stratum model.

[0009] Parameter smoothing calculation: (13) In the formula: x ( md The original parameter value refers to the value obtained from step S2 at the sounding point. md The initial wellbore or dogleg value generated at the location; The average parameter values ​​are taken 50m before and after the boundary. x s ( md ) indicates the depth at the sounding point md The parameter values ​​(wellbore diameter or dogleg) after formation boundary smoothing. These are the original generated values. x ( md ) and the average value of boundary transition zone parameters The weighted combination, with weights determined by a smoothing weight function. w ( md )control.

[0010] The purpose of performing smoothing calculations is to address the artificial discontinuities caused by switching formation models.

[0011] The specific steps for smoothing stratigraphic boundaries are as follows: First, based on the depth of each stratigraphic boundary... Z b Centered on a point, extend 50 meters upwards and downwards to form a smooth transition zone; secondly, calculate the average original parameters of all sounding points within the transition zone. Then, the weighting function shown in formula (12) is used to calculate the depth of each sounding point in the transition zone. md Smoothing weights w ( md Finally, the smoothed parameter values ​​for each sounding point are calculated according to formula (13). xs ( md ).

[0012] S3, Trajectory smoothing and engineering constraint check; The random parameter sequence generated in step S2 is further smoothed using Fourier transform or cubic spline interpolation algorithm to eliminate high-frequency noise and make the generated wellbore trajectory more consistent with the actual drilled wellbore shape. The smoothed parameter sequence is subjected to engineering constraint checks to ensure that the well diameter and dogleg degree meet the engineering limitations. For samples that do not meet the constraints, perform iterative smoothing or regeneration until the requirements are met; The purpose of step S2 is to ensure that the generated random parameter sequence has physical authenticity and spatial continuity; the constraints in step S3 are the engineering requirements standards for wellbore quality during the specific drilling process, which are used to check the smoothed wellbore trajectory. This can ensure that the generated wellbore trajectory conforms to both physical reality and engineering requirements. S4, Monte Carlo simulation and friction calculation; Set the number of Monte Carlo simulations, repeat steps S2 and S3, and generate a completely new set of random wellbore quality parameters that meet the constraints each time; For each simulation, the friction calculation core engine is invoked, which calculates the total friction of the casing from the wellhead to the target depth based on the soft rod model; Monte Carlo simulation is the core method for quantifying the impact of wellbore quality uncertainty on casing run-inability. Its core logic is to transform deterministic friction calculation into a probability distribution problem through a large number of repeated random experiments (simulation times). The Monte Carlo simulation of this method is not a simple random sampling superposition, but a systematic process that integrates the generation of relevant random parameter sequences in step S2 and the trajectory smoothing and engineering constraint checking in step S3. Generally, steps S2 and S3 need to be repeated thousands to tens of thousands of times, each time generating a completely new set of random wellbore quality parameters that meet the constraints; S5. Probabilistic Results Analysis and Visualization The friction results for all simulations are statistically analyzed to form the probability density distribution of friction, and the cumulative probability distribution curve of friction is calculated and plotted. The total buoyant weight of the casing in the drilling fluid is marked on the cumulative probability distribution chart to obtain the probability value of "friction less than buoyant weight"; (1) Friction distribution characteristics: Probability density distribution: Normalized using histograms of 50 intervals, as shown in the following formula: (18) In the formula: p (F ( ) is friction F The probability density function value, N Let Δ be an interval number. N Δ is the number of samples within the interval. F The interval width is given by formula (18). Formula (18) is used to explain the method of drawing the friction probability density distribution diagram. "Interval" refers to several equal-width sub-ranges into which a continuous range of friction values ​​is divided in statistical analysis for the purpose of drawing a histogram. It is also called "group interval". Cumulative probability distribution: Calculated using the trapezoidal integral, reflecting the probability that the frictional resistance is less than or equal to the given value. The formula is as follows: (19) Formula (19) is used to explain the method of drawing the cumulative probability distribution diagram of friction. P ( F ≤ F 0) is the cumulative probability distribution function in F The value at point 0, that is, the friction resistance is less than or equal to a certain specific value. F The total probability of 0; (2) Probability of entry and evaluation criteria: The probability of being able to enter is defined as the proportion of samples where "the total buoyancy of the casing is greater than the frictional resistance".

[0013] (20) Formula (20) is used to explain the reading of the probability of being able to enter. P s Let be the probability of being able to enter. W b For buoyancy; CDF ( W b )for W b The cumulative distribution function.

[0014] Preferably, in step S101 of this invention, the wellbore structure data includes the well depth and wellbore size for each opening. The casing string design data includes the length, outer diameter, inner diameter, and steel grade of each casing section; Stratigraphic data division includes top-down stratigraphic data, clearly defining the top and bottom depths of each stratum; In step S102, the supported probability distribution types include normal distribution, uniform distribution, triangular distribution, log-normal distribution, exponential distribution, and gamma distribution.

[0015] Preferably, in this invention, the algorithm in step S2 employs Gaussian process simulation, specifically as follows: The parameter variation along the well depth is regarded as a Gaussian process. By defining the mean function and covariance function, a smooth random field that conforms to the statistical characteristics of the formation is generated. That is, a probabilistic model is generated in which the well quality parameters (well diameter, dogleg degree) vary continuously along the well depth direction and have spatial correlation.

[0016] Sampling: Call the multivariate normal distribution sampling function to generate the final sequence.

[0017] The core formula is: covariance function k ( md i , md j )for: (1) In the formula: md i , md j These are the i-th and j-th sounding points, respectively. md , It is a length scale.

[0018] Covariance matrix K i，j for: (2) In the formula: δ i，j This is the Kronecker function (1 when i=j, 0 otherwise). ε For noise (default 0.01).

[0019] Mean vector μ ( md i ) for: (3) In the formula: M The total number of strata. μ k strata k The average wellbore quality parameters, derived from statistical data of drilled wells in the block; Z t，k Z b，k Strata k The top depth and bottom depth; For indicator functions, if md i Located in the strata k Inside, i.e., Z t，k ≤ md i ≤Z b，k , It is 1 if it is true, otherwise it is 0.

[0020] Sampling formula: (4) In the formula: x is the generated parameter sample sequence (well diameter or dogleg degree). μ Mean vector μ ( md i ) K is the covariance matrix K i，j .

[0021] Formula (3) defines the mean function, while formulas (1) and (2) together define the covariance function.

[0022] Formula (1) is a squared exponential kernel, which introduces a control parameter length scale. l Two sounding points md i and md j The covariance (i.e., similarity) is determined by their distance | md i - md j |and length scale l A joint decision. l The larger the value, the slower the correlation decays with distance, and the smoother the resulting curve.

[0023] Formula (2) constructs the total covariance matrix and adds noise. The pairwise relationship defined in Formula (1) is applied to all sounding points to construct a complete covariance matrix K. At the same time, a small noise is introduced on the diagonal of the matrix to ensure that the matrix is ​​mathematically positive definite and invertible, thus avoiding numerical calculation problems.

[0024] Formula (3) specifies the expected value (mean) of each sounding point, thus mathematizing geological understanding and ensuring that the generated random curve will revolve around a baseline (mean vector) that conforms to the stratigraphic trend. μ )fluctuation.

[0025] Formula (4) extracts a specific random sample x that meets all the aforementioned constraints.

[0026] Specifically, in the software, input: Step S1 defines the sounding points, stratigraphic division, and mean values ​​of each stratigraphic unit; the length scale of formula (1) l The noise in formula (2) ε Then calculate. μ ( md i ) The mean vector is obtained by iterative calculation according to formula (3). μ ( md i )Calculate K: The covariance matrix K is obtained by double-loop calculation according to formulas (1) and (2). i,j .

[0027] Preferably, the algorithm in step S2 of this invention employs Markov chain simulation. Specifically, this method is based on the Markov property that "the next state is only related to the current state." It controls the influence of the current sounding point's corresponding value on the next sounding point's corresponding value through state transition coefficients, and combines this with the mean of the stratigraphic distribution determined in step S1 to perform a random walk, generating a parameter sequence with local continuity. This method has high computational efficiency and is suitable for parameters with significant local variations.

[0028] The core formula is: State transition formula: (5) In the formula: α These are the state transition coefficients. x i-1 The parameter values ​​are from the previous sounding point. μ k This represents the mean value of the stratum where the current sounding point is located. Markov chain simulation is based on state sequence transitions and does not have absolute requirements on the spacing between sounding points. However, to ensure the rationality of the simulation and the interpretability of the parameters, it is recommended to use an equally spaced sounding sequence. Preferably, in this invention, the spacing between sounding points is set to 30m. μ i Indicates the current depth sounding point i The expected or trend value of the parameters is used to generate specific parameter values. x i The central benchmark. It consists of a two-part weighted average: α·x i-1 This reflects the continuity of the sequence (Markov property), indicating that the current value tends to be close to the value of the previous depth point. (1- α )· μ k It reflects the statistical regularity of stratigraphy, indicating that the current value is attracted by the typical value (mean) of the stratum in which it is located.

[0029] Sample generation formula: (6) In the formula: β This is the maximum step size (default 0.5, which controls the fluctuation range). σ k This represents the standard deviation of the current stratum. Formula (6) indicates that: in the trend value μ i A random perturbation is superimposed on top of this. The amplitude of the perturbation is... β (Maximum step size factor) and formation standard deviation σ kJoint control.

[0030] ζ It is a random number that follows a uniform distribution in the interval [0, 1). (2) ζ -1) physical meaning: to ζ A linear transformation to the interval [-1, 1] represents a random direction and amplitude, with a 50 / 50 probability of being positive or negative.

[0031] Physical range truncation: (7) Where: max k min k These represent the current physical maximum / minimum values ​​of the formation parameters. x i The initial value of is obtained by directly sampling randomly from the probability distribution of the stratum where it is located.

[0032] Input the following into the software: S1 defines the sounding point, stratigraphic division, and mean values ​​of each stratigraphic unit; state transition coefficient of formula (5). α (Recommended range 0.6-0.95), the maximum step size of formula (6) is β . α The larger the value, the smoother the sequence and the stronger its continuity; α The smaller the value, the closer the sequence is to the formation mean. β The larger the value, the more drastic the local changes. β The smaller the value, the flatter the sequence.

[0033] Parameter generation: For the first sounding point, it is generated by direct random sampling from the probability distribution of the stratum where it is located; For the i-th sounding point (i≥2), the trend value is calculated according to formula (5), the parameter value is calculated according to formula (6), and the physical range is truncated according to formula (7).

[0034] Stratigraphic Statistical Parameters μ k , σ k This ensures that the overall statistical properties of the generated sequences conform to geological understanding, while min k ,max k Then an engineering safety boundary was applied.

[0035] Preferably, in this invention, the algorithm in step S2 employs overall constraints based on the wellbore trajectory: engineering physical constraints are introduced when generating the wellbore diameter and dogleg parameters. For example, the maximum rate of change of dogleg between adjacent measuring points is limited to ensure that the generated dogleg sequence is consistent with the overall direction and smoothness of the wellbore trajectory, preventing unreasonable and drastic fluctuations.

[0036] Assuming the distance between adjacent sounding points is 30 meters, and the maximum rate of change of dogleg degree between adjacent sounding points is set as follows: r m =0.2° / 30m, the current formation dogleg distribution is N(0.98, 0.3) / 30m, if the previous point dogleg... x i-1 =0.95° / 30m.

[0037] Sure x i The allowable range is (0.95-0.2, 0.95+0.2), and combined with the stratigraphic range (0.01, 2.06), the sampling value is limited to (0.75, 1.15).

[0038] This method is applicable to well sections where dogleg continuity is required (such as extended reach wells and horizontal wells).

[0039] The main task of step S2 is to generate the parameter sequence, and the task of step S3 is constraint checking and smoothing. These two steps are logically separate, but this method incorporates constraints in the generation stage. The other three methods, Gaussian process simulation, spatial correlation coefficient matrix method, and Markov chain simulation, mainly focus on spatial correlation in the parameter generation stage and do not actively apply engineering constraints. Engineering constraints are implemented in step S3.

[0040] Preferably, the algorithm in step S2 of this invention employs the spatial correlation coefficient matrix method. Specifically, a 2x2 correlation coefficient matrix is ​​used to explicitly define the statistical correlation between the two parameters, well diameter and dogleg score. Each sounding point corresponds to a generated well diameter value and a dogleg score value. Through Cholesky decomposition, well diameter and dogleg score samples with a specified correlation at any sounding point are generated, thereby simulating the coupling effect between parameters, i.e., generating curves with continuous, smooth, or specific variation patterns, thus simulating the wellbore morphology formed by actual drilling.

[0041] The core formula is: Correlation coefficient matrix (2×2 matrix, considering only well diameter and dogleg degree): (8) In the formula: ρ The wellbore-dogleg correlation coefficient represents the degree of linear correlation between wellbore diameter and dogleg, and its value ranges from [-1, 1]. Positive correlation: Increased well diameter is often accompanied by increased dogleg (common in soft and easily collapsible formations). Negative correlation: well diameter enlargement is accompanied by a decrease in dogleg degree (rare). : No relation, the two change independently. ρThe value should be based on geological engineering understanding or statistical analysis of historical data of the block, and the degree of linear correlation between well diameter and dogleg degree should be analyzed.

[0042] The covariance matrix Σ is (combined with the standard deviation of each parameter): (9) In the formula: These are the standard deviations of the well diameter and dogleg of the stratum where the current sounding point is located, respectively, derived from the probability distribution defined in step S1.

[0043] Positive definiteness processing (ensuring the matrix is ​​sampleable): If Σ is not positive definite (eigenvalue ≤ 0), it is corrected by eigenvalue: (10) In the formula: the `diag` function is a matrix operation function in programming environments such as MATLAB and FreeMat, mainly used to construct diagonal matrices or return the diagonal elements of a matrix in vector form; V is the eigenvector matrix. λ i For eigenvalues, Ò For the minimum value, T is the transpose of the eigenvector matrix V.

[0044] Multivariate normal sampling: (11) In the formula, In the first A two-dimensional parameter vector generated from each sounding point, where Indicates the well diameter value. This indicates the degree of sycophancy.

[0045] The current depth sounding point is located at the [number]th [position]. The mean vector of each stratum, where These are the mean values ​​of well diameter and dogleg degree for the formation, respectively, derived from the probability distribution defined in step S1.

[0046] Lk Obtained through Cholesky decomposition Lower triangular matrix, satisfying ,in Let be the covariance matrix of the current stratum as defined by formula (9).

[0047] Let be a two-dimensional standard normal random vector, where , Independent and identically distributed according to the standard normal distribution .

[0048] Formula (8) defines the basic correlation framework between wellbore diameter (D) and dogleg degree (K).

[0049] Formula (9) combines the abstract correlation framework R with the statistical characteristics of specific strata to form an executable covariance matrix.

[0050] Formula (10) provides a numerical guarantee step to ensure that the covariance matrix is ​​strictly positive definite, thus enabling subsequent calculations such as Cholesky decomposition.

[0051] The final generation step of formula (11) involves extracting a pair of associated wellbore diameter and dogleg values ​​from a predefined bivariate normal distribution. Formula (11) defines the extraction of a pair of associated wellbore diameter and dogleg values ​​from a bivariate normal distribution with a specified mean. μ k Covariance Structure Σ k A linear transformation method for drawing random samples from a bivariate normal distribution. The software implementation steps are as follows: Determine the stratum where the current sounding point i is located. k Call a separate standard normal random number generator to generate two independent random numbers. ξ i1 , ξ i2 , forming a vector ξ i2 Obtain the mean vector of this stratum. μ k Cholesky decomposition matrix L k ; Execute matrix operation formula (11) to obtain a pair of well diameter values ​​and dogleg values ​​with specified correlation.

[0052] In a preferred embodiment of this invention, in step S3, the parameter sequence is transformed to the frequency domain using Fourier transform to filter out high-frequency noise corresponding to parameter abrupt changes, and then inversely transformed back to the time domain. Specifically, the entire wellbore parameter sequence (such as well diameter) is considered as a signal fluctuating on the "depth-sounding axis." Through global frequency analysis and filtering, high-frequency noise representing non-physical abrupt changes is eliminated, thereby obtaining a smoother and more continuous parameter curve that better reflects actual drilling. The smoothing intensity parameter is controlled by the cutoff frequency. f The 'c' option adjusts the smoothing level; the cutoff frequency can be set by inputting the smoothing intensity value. f c.

[0053] The core formula is: Fourier transform: (14) In the formula: Frequency represents the number of times a parameter fluctuates within a unit depth (e.g., every 30 meters). High frequencies correspond to drastic changes (e.g., sudden changes, noise) over short distances, while low frequencies correspond to trend changes over long distances. t For depth measurement, is the independent variable, and the unit is meters (m). x(t) The parameter sequence to be smoothed is the dependent variable, i.e., the wellbore quality parameters that need to be smoothed.

[0054] High-frequency filtering: (15) In the formula: The cutoff frequency is determined by the smoothing intensity. The lower the value, the more high-frequency components are filtered out, and the stronger the smoothing effect. I As an indicator function, it performs "clipping" in the frequency domain, when the frequency... f ≤ f c hour, I =1, retain that frequency component, when the frequency... f > f c hour, I =0, filter out this frequency component.

[0055] Inverse Fourier Transform: (16) In the formula, x s The smoothed parameter sequence is the final output, which is the new parameter value corresponding to the original sounding point, after eliminating high-frequency abrupt changes.

[0056] Wellbore trajectory parameter smoothing process based on Fourier transform: The wellbore trajectory parameter sequence to be smoothed (such as well diameter and dogleg) and its corresponding equally spaced sounding sequence are used as input. A Fourier transform is performed on the entire parameter sequence to transform it from the sounding domain to the frequency domain, obtaining the original spectrum containing different frequency components. Low-frequency components represent long-term trend changes in the parameters, while high-frequency components represent local abrupt changes and noise. Based on a set smoothing intensity (cutoff frequency), a low-pass filter is applied to the original spectrum. High-frequency components above the cutoff frequency are filtered out, retaining only the low-frequency components representing the macroscopic trend, resulting in the filtered spectrum. An inverse Fourier transform is performed on the filtered spectrum to transform it back from the frequency domain to the sounding domain, obtaining the smoothed parameter sequence at the original sounding point location.

[0057] This process uses global frequency analysis to eliminate high-frequency noise representing non-physical abrupt changes, while retaining and enhancing low-frequency components that represent real geological and engineering trends, thereby generating a smoother, more realistic wellbore trajectory parameter curve.

[0058] In a preferred embodiment of the present invention, in step S3, the parameter sequence is fitted using a cubic spline function, and additional depth sounding points are added at equal intervals between adjacent depth sounding points. Then, resampling is performed on these additional depth sounding points to eliminate local abrupt changes. The additional depth sounding points are a series of new depth points with smaller intervals inserted between the original depth sounding points using mathematical methods. For example, the interval becomes 1 meter. Resampling involves inserting additional depth points between the original depth sounding points using cubic spline interpolation and calculating new values. These newly generated smooth sequences are then used to replace or map the original depth sounding point sequence, thereby eliminating local abrupt changes in the data.

[0059] Cubic spline interpolation is an existing technique in numerical analysis, and its core formula is: For depth sounding interval spline function S i (md) for: (17) In the formula, a i For the spline function in the th Starting point of each interval The function value at that point, i.e. The corresponding parameter value at that point (such as well diameter or dogleg); b i For spline functions in The first derivative at that point represents the instantaneous rate of change at that point; c i For spline functions in The value of the second derivative at that point is half of the value of the curve's curvature; d i For spline functions in One-sixth of the third derivative value at a given point describes the rate of change of the second derivative.

[0060] The spline function described above satisfies the continuity of the second derivative. A cubic spline function is constructed for the generated wellbore trajectory. Throughout the entire interval, the curve itself, as well as its first and second derivatives, are continuous.

[0061] Preferably, in step S3 of this invention, the basic physical and engineering limitations are as follows: Minimum wellbore constraint: The generated wellbore diameter is greater than the outer diameter of the casing multiplied by a safety factor (e.g., 1.05) to ensure sufficient annular clearance; Maximum dogleg degree constraint: The generated dogleg degree must not exceed the maximum value allowed by the project.

[0062] Preferably, the present invention further includes step S6, grade evaluation: The probability value of "frictional resistance is less than buoyancy" is defined as the probability of being able to descend, P. When P≥95%, it indicates that it is safe to proceed without adjusting the plan; proceed according to the original design. When 80%≤P<95%, it indicates that drilling can be carried out, but risks need to be monitored. It is recommended to optimize drilling fluid performance or adjust casing steel grade. When P < 80%, it indicates a high risk of well sinking, and it is recommended to redesign the wellbore structure or use auxiliary sinking tools.

[0063] This invention uses statistical analysis of wellbore quality data from drilled wells in the region, Monte Carlo simulation as a tool, and considers the uncertainty of wellbore quality to generate a large number of wellbore trajectories that conform to physical reality. It also performs casing friction calculations to evaluate whether the designed wellbore structure will encounter obstacles during casing operation before drilling and provides a probability basis so as to adjust the wellbore structure design in a timely manner.

[0064] Table 2 Accessibility Evaluation Criteria

[0065] The key quantiles of friction resistance (e.g., P1, P5, P50, P90, P95, P99) are output to provide data support for decisions based on different risk preferences. For example, a P90 friction resistance value indicates that 90% of the sample friction resistance is less than or equal to this value. This provides engineering decision-makers with a set of friction resistance risk values ​​at different confidence levels, allowing them to select appropriate friction resistance design values ​​or evaluation criteria based on their risk tolerance. Table 2 shows the conclusions drawn from evaluating a large number of drilled well casing operations using this method. For various situations in actual engineering, if the conclusions are not used, those skilled in the art can determine appropriate evaluation criteria based on these key quantiles and their own risk tolerance.

[0066] In this invention, Monte Carlo simulation involves repeatedly executing step S2 (where step S4 defines the number of simulations) to generate the parameter sequence, step S3 to apply smoothing constraints, and step S4 to calculate friction, accumulating a large number of friction results, which are then statistically analyzed in step S5. Therefore, Monte Carlo simulation serves as a framework in this invention.

[0067] Monte Carlo simulation is a general-purpose numerical computation method based on probability and statistics. In practice, it can be implemented using any tool with random number generation and numerical computation capabilities, such as Python (NumPy, SciPy for random sampling and computation).

[0068] Compared with the prior art, the beneficial effects of the present invention are: 1. Based on the uncertainty of wellbore quality, this invention upgrades the traditional deterministic analysis to probabilistic risk analysis by introducing probability distribution and Monte Carlo simulation, which fully considers the uncertainty of wellbore quality in actual engineering and makes the evaluation results closer to the actual engineering situation.

[0069] 2. This invention uses an algorithm to simulate the spatial correlation of parameters corresponding to sounding points along the well depth direction, which can ensure that the simulated wellbore trajectory parameter sequence has real physical continuity, avoid non-physical random jumps, and improve the scientific nature of the model.

[0070] 3. The method of this invention integrates trajectory smoothing and multiple engineering constraint checks, ensuring that all random scenarios used for calculation are within a reasonable engineering range, thereby enhancing the practicality and reliability of the method.

[0071] 4. The final output of this invention is a risk indicator in the form of probability (such as success probability, quantile), rather than a single numerical value, which enables engineering decision-makers to clearly understand the risk level and make more scientific and evidence-based decisions. Attached Figure Description

[0072] Figure 1 This is a schematic diagram of the formation division of an oil well in a block of Xinjiang Oilfield, as described in an embodiment of the present invention. Figure 2 This is an example of a friction probability density distribution diagram in an embodiment of the present invention; Figure 3 This is an example of a cumulative friction probability distribution diagram in an embodiment of the present invention; Figure 4 This is a flowchart of the present invention. Detailed Implementation

[0073] The technical solutions in the embodiments of the present invention will now be clearly and completely described in conjunction with the accompanying drawings.

[0074] like Figure 1 As shown in this embodiment, the casing run-in capability of a production well in a certain block of Xinjiang Oilfield is evaluated. The well has completed the first casing run-in. During the second casing run-in, the well encountered resistance. However, conventional methods using existing friction calculation software Landmark show that the casing can be run normally. The method of this invention is now used to evaluate the casing run-in capability of this well during the second run-in.

[0075] like Figure 4 The flowchart below shows the method of the present invention. The casing run-in evaluation method based on wellbore quality uncertainty includes the following steps: S1. Multi-source data integration and probability distribution model establishment Based on the on-site data, the basic parameters for calculation were determined.

[0076] Wellbore structure data, including the depth and borehole dimensions of the second opening; casing string design data, including the length, outer diameter, inner diameter, and steel grade of each casing section; formation division, including data for the three formations from top to bottom, clearly defining the top and bottom depths of each formation; drilling fluid, friction coefficient, and other relevant parameters for friction calculation.

[0077] Based on the formation data, each sounding point is set at a preset distance with equal intervals for the generation of wellbore trajectory. Since the unit of dogleg degree is ° / 30m, the sounding interval between adjacent sounding points is set to 30 meters, that is, the original sounding points are (0, 30, 60, 90...).

[0078] like Figure 1 As shown, the second drilling of this well is located in formations 1, 2 and 3. By analyzing and statistically analyzing the wellbore quality data of adjacent wells, the probability distribution types and parameters of well diameter and dogleg in each formation are determined as shown in Table 3 below.

[0079] Table 3. Types of Wellbore Quality Probability Distribution

[0080] S2, Generation of relevant random parameter sequences The sampling method selected is the Gaussian process method, with a length scale of l=50m and noise ε=0.01. Based on the formation corresponding to each sounding point, and according to the probability distribution model of the corresponding formation determined in step S1, a random sampling method is used to generate a wellbore mass sequence that continuously varies along the well depth in terms of well diameter and dogleg, resulting in a wellbore trajectory parameter sequence composed of the well diameter and dogleg wellbore mass sequences. Smooth transition of stratigraphic boundaries: To avoid abrupt parameter changes at the stratigraphic boundary, the parameters within 50m before and after the boundary are smoothed.

[0081] S3, Trajectory Smoothing and Engineering Constraint Check Fourier transform was selected for trajectory smoothing, with a smoothing intensity of γ=0.15. Engineering constraint checks were performed, and samples that did not meet the constraints were iterated again. Samples that still did not meet the constraints after 10 iterations were marked as "warning samples".

[0082] S4, Monte Carlo simulation and friction calculation The Monte Carlo simulation was set to 10,000 times. The friction calculation of this invention is based on a soft rod model, and the friction of the sleeve is calculated for effective samples.

[0083] The core formula is: Annular space clearance calculation: well diameter Directly affects the clearance between the casing and the wellbore. The smaller the well diameter, the smaller the clearance, the tighter the contact between the casing and the well wall, and the greater the friction.

[0084] (100) In the formula: The annular space gap is m; For the first The well diameter value at each sounding point, in meters; OD is the outer diameter of the casing, in meters.

[0085] Dogleg to Curvature Conversion: Converting commonly used engineering units of dogleg degree (° / 30m) to radians of curvature. (rad / m), used for mechanical calculations.

[0086] (200) In the formula: For the first Dogleg value of each sounding point, ° / 30m.

[0087] Lateral force calculation (maximum value from both mechanisms): Bending effect lateral force F L1,i for: (300) In the formula: This refers to the bending stiffness of the casing.

[0088] Axial force effect lateral force F L2,i for: (400) In the formula: F a,i In the first The axial tensile force borne by the lower end of the casing at each calculation point (sounding point). To calculate the unit length, 1m is usually taken (after interpolation).

[0089] Combined lateral forces F L,i for: (500) Unit friction F f,i Calculation: The friction of the i-th unit is the product of the lateral force and the coefficient of friction.

[0090] (600) In the formula: is the coefficient of friction.

[0091] Total friction F t Calculation: Frictional resistance is the sum of the frictional resistances of all units.

[0092] (700) S5. Probabilistic Results Analysis and Visualization Based on the results of the Monte Carlo simulation, the ingress risk was quantified through statistical analysis. The output results are shown below. Figure 2 and Figure 3 .

[0093] Table 4 Evaluation Conclusions on the Ability to Run the Casing

[0094] from Figure 3 The reading in the middle indicates the buoyancy of the casing ( Figure 3 Figure 3 The value at the red line (middle section) is 2440.6 kN, and the cumulative probability curve value at this point is 30.43%. After considering the uncertainty of wellbore mass, the probability that the casing friction is less than its own buoyancy is 30.43%, that is, the success probability of casing installation is 30.43%. Based on the installation feasibility evaluation criteria in Table 4 above, it can be seen that the casing could not be installed normally during the casing installation operation in this instance.

[0095] The results show that this method takes into account the uncertainty of the actual wellbore quality and generates probabilistic casing run-in evaluation results, which improves the accuracy of casing run-in operation risk assessment and the scientific nature of decision-making.

Claims

1. A method for quantitatively assessing the risk of casing run-in considering the uncertainty of wellbore quality, characterized in that, The specific steps are as follows: S1. Multi-source data integration and probability distribution model establishment: S101, Multi-source data on friction during casing insertion; The multi-source data includes: wellbore structure data, casing string design data, and formation data division. Based on the formation data, each sounding point is set at equal intervals according to a preset distance for the generation of wellbore trajectory; S102. Define the probability distribution model for wellbore diameter and dogleg degree; By analyzing and statistically analyzing the wellbore quality data of adjacent wells, probability distribution models for well diameter and dogleg degree are defined for each formation. Based on the distribution parameters corresponding to the distribution type, functions are called to establish a mapping relationship between "formation-parameter-distribution". S2, Generation of relevant random parameter sequences; The algorithm simulates the spatial correlation of parameters corresponding to sounding points along the well depth direction. Based on the formation corresponding to each sounding point, and according to the probability distribution model of the corresponding formation determined in step S1, a random sampling method is used to generate a wellbore mass sequence of continuously varying diameter and dogleg wellbore mass along the well depth, thus obtaining a wellbore trajectory parameter sequence composed of the wellbore mass sequence of diameter and dogleg wellbore mass. S3, Trajectory smoothing and engineering constraint check; The random parameter sequence generated in step S2 is further smoothed using Fourier transform or cubic spline interpolation algorithm to eliminate high-frequency noise and make the generated wellbore trajectory more consistent with the actual drilled wellbore shape. The smoothed parameter sequence is subjected to engineering constraint checks to ensure that the well diameter and dogleg degree meet the engineering limitations. For samples that do not meet the constraints, perform iterative smoothing or regeneration until the requirements are met; S4, Monte Carlo simulation and friction calculation; Set the number of Monte Carlo simulations, repeat steps S2 and S3, and generate a completely new set of random wellbore quality parameters that meet the constraints each time; For each simulation, the friction calculation core engine is invoked, which calculates the total friction of the casing from the wellhead to the target depth based on the soft rod model; S5. Probabilistic Results Analysis and Visualization The friction results for all simulations are statistically analyzed to form the probability density distribution of friction, and the cumulative probability distribution curve of friction is calculated and plotted. The total buoyant weight of the casing in the drilling fluid is marked on the cumulative probability distribution chart to obtain the probability value of "friction less than buoyant weight".

2. The method for quantitatively assessing the risk of casing run-in considering wellbore quality uncertainty as described in claim 1, characterized in that: In step S101, the wellbore structure data includes the well depth and wellbore size for each opening; The casing string design data includes the length, outer diameter, inner diameter, and steel grade of each casing section; Stratigraphic data division includes top-down stratigraphic data, clearly defining the top and bottom depths of each stratum; In step S102, the supported probability distribution types include normal distribution, uniform distribution, triangular distribution, log-normal distribution, exponential distribution, and gamma distribution.

3. The method for quantitatively evaluating the risk of casing run-in considering wellbore quality uncertainty as described in claim 1, characterized in that, The algorithm in step S2 uses Gaussian process simulation, specifically as follows: By treating the parameter variation along the well depth as a Gaussian process, a smooth random field that conforms to the statistical characteristics of the formation is generated by defining the mean function and covariance function.

4. The method for quantitatively evaluating the risk of casing run-in considering wellbore quality uncertainty as described in claim 1, characterized in that, The algorithm in step S2 uses Markov chain simulation. Specifically, the influence of the current sounding point value on the next sounding point value is controlled by the state transition coefficient, and a random walk is performed in combination with the mean of the stratum distribution determined in step S1 to generate a parameter sequence with local continuity.

5. The method for quantitatively assessing the risk of casing run-in considering wellbore quality uncertainty as described in claim 1, characterized in that, The algorithm in step S2 adopts an overall constraint based on the wellbore trajectory: engineering physical constraints are introduced when generating wellbore diameter and dogleg parameters.

6. The method for quantitatively evaluating the risk of casing run-in considering wellbore quality uncertainty according to claim 1, characterized in that, The algorithm in step S2 uses the spatial correlation coefficient matrix method. Specifically, a 2x2 correlation coefficient matrix is ​​used to explicitly define the statistical correlation between the two parameters, well diameter and dogleg degree.

7. The method for quantitatively evaluating the risk of casing run-in considering wellbore quality uncertainty as described in claim 1, characterized in that: In step S3, the parameter sequence is transformed to the frequency domain by Fourier transform to filter out high-frequency noise corresponding to parameter abrupt changes, and then inversely transformed back to the time domain.

8. The method for quantitatively assessing the risk of casing run-in considering wellbore quality uncertainty as described in claim 1, characterized in that: In step S3, the parameter sequence is fitted by a cubic spline function, and additional sounding points are added at equal intervals between two adjacent sounding points. Then, the sounding points are resampled to eliminate local abrupt changes.

9. The method for quantitatively evaluating the risk of casing run-in considering wellbore quality uncertainty as described in claim 1, characterized in that, In step S3, the basic physical and engineering constraints are: Minimum wellbore constraint: The generated wellbore diameter is greater than the outer diameter of the casing multiplied by a safety factor to ensure sufficient annular clearance; Maximum dogleg degree constraint: The generated dogleg degree must not exceed the maximum value allowed by the project.

10. The method for quantitatively assessing the risk of casing run-in considering wellbore quality uncertainty according to claim 1, characterized in that, It also includes step S6, rating evaluation: The probability value of "frictional resistance is less than buoyancy" is defined as the probability of being able to descend, P. When P≥95%, it indicates that it is safe to proceed without adjusting the plan; proceed according to the original design. When 80%≤P<95%, it indicates that drilling can be carried out, but risks need to be monitored. It is recommended to optimize drilling fluid performance or adjust casing steel grade. When P < 80%, it indicates a high risk of well sinking, and it is recommended to redesign the wellbore structure or use auxiliary sinking tools.

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