A method for quantitatively evaluating casing lowerability risk by considering wellbore quality uncertainty

Abstract

The present application belongs to the technical field of oil and gas drilling, and particularly relates to a casing lowerability risk quantitative evaluation method considering wellbore quality uncertainty. The present application uses Monte Carlo simulation and multi-distribution random sampling to realize the probability evaluation of casing lowerability friction. The core idea is: taking the uncertainty of wellbore quality parameters such as hole diameter and dogleg severity as the starting point, through the process of "probability modeling -> related sampling -> smoothing constraint -> friction calculation -> risk evaluation", the accuracy and decision-making scientificity of casing lowerability evaluation are improved. The method can systematically represent the uncertainty and spatial distribution characteristics of key wellbore quality parameters such as hole diameter and dogleg severity; generate a large number of random wellbore quality parameter sequences conforming to actual geological and engineering laws; on this basis, Monte Carlo simulation is carried out to calculate the probability distribution of casing lowerability friction; finally, the risk of casing lowerability is quantified in the form of probability, providing intuitive probability basis for engineering decision-making.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of oil and gas drilling, and particularly relates to a casing lowerability risk quantitative evaluation method considering wellbore quality uncertainty. BACKGROUND

[0002] In oil and gas well drilling operations, whether the casing can be safely and smoothly lowered to the designed depth is the key to determine the success of well completion. The casing lowerability is directly dependent on the balance between the casing floatation weight and the wellbore-casing friction: when the casing lowerability is greater than the floatation weight, the casing cannot be lowered to the designed depth, which may lead to operation failure or economic loss.

[0003] The traditional casing lowerability calculation model uses a single, fixed wellbore trajectory parameter for friction calculation, and the influence of the drilling wellbore quality on the friction is not considered in the calculation. This has obvious defects: in the actual drilling process, due to the influence of many factors such as formation heterogeneity, drilling assembly, drilling fluid performance and operating parameters, the wellbore quality parameters such as hole diameter and dogleg are not fixed values, but random variables fluctuating within a certain range. Therefore, it cannot truly reflect the inherent uncertainty of the actual wellbore quality, leading to an idealized evaluation result. At the same time, the existing casing lowerability calculation model only gives a certain friction value, and cannot answer the question of "what is the probability that the friction exceeds the casing floatation weight under the condition of wellbore quality uncertainty?", resulting in a lack of probability basis to evaluate the casing lowerability.

[0004] Chinese patent document CN111444637A (202010467593.8) discloses a safety evaluation method and system for casing lowering of long section horizontal well of shale gas, but it is still a deterministic method in essence. It finally outputs a deterministic friction coefficient, maximum well depth and risk level through means such as adjacent well data comparison and critical value analysis, and the output result is a single risk level and maximum well depth. The decision maker only knows that the risk is high, but does not know how high it is and what the probability of exceeding the designed capacity is. Although the above scheme also considers the influence of wellbore irregularity (hole diameter variation coefficient) and dogleg cumulative value, the processing method is rough. It finds the "critical value" by "comparison" with adjacent wells, which is essentially a boundary correction of the deterministic model using historical experience data. The "wellbore cleanliness" correction is also a fixed proportion adjustment based on subjective qualitative judgment.

[0005] Therefore, there is an urgent need for a casing lowerability evaluation method that can consider wellbore quality uncertainty and quantify the random fluctuation of wellbore quality parameters, in order to improve the accuracy of casing lowering operation risk evaluation and the scientificity of decision making. SUMMARY

[0006] To solve the above technical problems, the application provides a casing lowerability risk quantitative evaluation method considering wellbore quality uncertainty, and the application overcomes the defects of traditional deterministic methods and realizes probability evaluation of casing lowerability friction by using Monte Carlo simulation and multi-distribution random sampling.

[0007] The technical problems to be solved by the application are solved by the following technical solutions: a casing lowerability risk quantitative evaluation method considering wellbore quality uncertainty, and the specific steps are as follows:

[0008] S1, multi-source data integration and probability distribution model establishment:

[0009] S101, integrating multi-source data of casing lowerability friction;

[0010] The multi-source data includes wellbore structure data, casing string design data and formation data division.

[0011] Each depth point is set at equal intervals according to a preset distance based on the formation data division, for generation of a wellbore trajectory;

[0012] S102, defining a probability distribution model of hole diameter and dogleg severity;

[0013] By analyzing and statistically processing wellbore quality data of adjacent drilled wells, a probability distribution model of hole diameter and dogleg severity is defined for each formation, a function is called based on distribution parameters corresponding to the distribution type, and a mapping relationship of “formation-parameter-distribution” is established;

[0014] The function is obtained based on Series / DataFrame of pandas software in the application; pandas is only a data processing tool and is not a necessary condition for Monte Carlo simulation; the core idea of Monte Carlo simulation is random sampling and statistics, and it can be realized by using any programming language, such as Python's numpy, C++ and Java.

[0015] The purpose of establishing the mapping relationship of "formation-parameter-distribution" is to distinguish the uncertainty of different formations and model the generated random sequence with spatial correlation and in accordance with the statistical law of the formation; as shown in Table 1, different formations have different well diameter expansion laws and dogleg severity variation characteristics due to differences in lithology, hardness, and cementation degree; the mapping relationship determines the probability distribution model for each formation, thereby more truly depicting the difference; when generating the random parameter sequence in step S2, each depth point calls the corresponding distribution model for sampling according to the formation where it is located; the distribution parameters (such as mean, standard deviation, and range) define the statistical tendency and reasonable interval of parameter values, and provide a probability framework for random sampling; however, this is not a strict hard limit, and subsequent engineering constraints (step S3) will further impose a safety boundary;

[0016] Suppose a depth point is located at 730m (belongs to formation 1), step S2 (such as using the Gaussian process method) will query the mapping relationship, and find that the well diameter of the point should follow N(0.558, 0.1), and the dogleg severity should follow U(0.01, 2.19); based on this distribution, the random value of the point is generated in combination with the algorithm of step S2 (such as the covariance function of the Gaussian process), to ensure that the value not only conforms to the statistical characteristics of the formation, but also maintains reasonable continuity with adjacent points;

[0017] Table 1: Probability distribution type and parameter definition

[0018]

[0019] The probability distribution model establishment process is to select the distribution type for well diameter and dogleg severity for each formation (such as formation 1: 0~790m, formation 2: 790~1860m) respectively (by statistical analysis of the wellbore quality data of the drilled wells in the block, i.e. well diameter and dogleg severity);

[0020] S2, related random parameter sequence generation;

[0021] The spatial correlation of the corresponding parameters of the depth point along the well depth direction is simulated by an algorithm, and according to the formation corresponding to each depth point, the well diameter and dogleg severity wellbore quality sequence continuously changing along the well depth is generated by using the random sampling method according to the probability distribution model of the corresponding formation determined in step S1, to obtain the well trajectory parameter sequence composed of the well diameter and dogleg severity wellbore quality sequence;

[0022] Smooth transition at formation boundary:

[0023] To avoid parameter mutation at the formation boundary, the parameters of the 50m before and after the boundary are smoothed;

[0024] Step S2 is the key of the invention distinguishing from traditional methods, since the change of well trajectory parameters along the well depth is not completely independent, the parameters between adjacent survey points usually have spatial correlation, to avoid generating physically unrealistic, jumping random parameters, the invention provides an algorithm to generate well diameter and dogleg severity parameter sequence (along the well depth direction) with spatial correlation; the algorithm will consider the values of its adjacent points md i , md i-1 , md i-2 … (according to the correlation rules of different algorithms) when generating the value of md

[0025] Step S2 extracts the corresponding well diameter and dogleg severity parameters based on the survey points, the mean value indicates where the "central tendency" of this formation parameter should be around; for example, the mean value of the well diameter of a certain formation is 0.3 meters, then no matter which method is used to generate the sequence by limiting the correlation of the parameters corresponding to the survey points along the well depth direction, its overall average level should be close to 0.3 meters; the standard deviation / distribution range defines the reasonable amplitude of parameter fluctuation; the discrete degree of the values generated by the sampling method in step S2 must meet this range; for example, the uniform distribution [0.28, 0.32] explicitly prohibits the sampling method from generating well diameter values less than 0.28 or greater than 0.32; the distribution form determines the preference of the value; the triangular distribution will make the "most likely value" be sampled more; the exponential distribution will make the probability of small values much greater than that of large values; the sampling method in step S2 needs to call the distribution parameters corresponding to each formation to generate a sequence that meets the corresponding form;

[0026] Formation boundary smoothing transition is to solve the problem of discontinuity between formations, eliminate the boundary mutation caused by different formation statistical parameters, and has locality, only in the narrow transition zone near the formation interface (such as 50 meters before and after). The smoothing processing of step S3 is to eliminate noise and high-frequency fluctuations, so that the parameter curve is more consistent with the smooth wellbore shape drilled in practice, and has globality, which smoothes all survey points of the entire well section. The purposes, ranges and methods of the two are different, but they work together to ensure that the well quality sequence finally used for Monte Carlo simulation is both geologically realistic and engineering reasonable;

[0027] The smoothing weight function of formation boundary smoothing:

[0028] (12)

[0029] In the formula, md is the depth value of the current survey point, is the smoothing weight, Z b is the formation boundary depth, that is, the depth of the interface between the two formations in md Figure 1 , md mdmuch less than Z b (i.e. far above the boundary), ( md - Z b ) is a large negative number, exp(...) is close to 0, so w ( md ) ≈ 1. When md is much greater than Z b (i.e. far below the boundary), ( md - Z b ) is a large positive number, exp(...) is very large, so w ( md ) ≈ 0. When md is equal to Z b (just at the boundary), ( w ( md ) = 0.5. Specifically, w ( md ) ≈ 1, the parameter value at this point preserves the original generated value (from the overlying formation model); w ( md ) = 0.5, the parameter value at this point is a weighted average of the generated values from the upper and lower formations, each with a weight of one half, achieving a natural connection at the center point; w ( md ) ≈ 0, the parameter value at this point adopts the generated value from the lower formation model.

[0030] Parameter smoothing calculation:

[0031] (13)

[0032] In the formula: x ( md ) is the original parameter value, which refers to the initial hole diameter or dogleg value generated by step S2 at the depth of the survey point md ; is the average value of the parameter within 50m before and after the boundary. x s ( md ) represents the parameter value (hole diameter or dogleg) after smoothing treatment across the formation boundary at the depth of the survey point md . It is a weighted combination of the original generated value x ( md ) and the average value of the parameters in the boundary transition zone , with the weight controlled by the smoothing weight function w ( md ).

[0033] The purpose of the smoothing calculation is to solve the problem of artificial discontinuity caused by the switching of the formation model.

[0034] The specific steps of the stratum boundary smoothing are as follows: first, taking each stratum boundary depth as the center, extending 50 meters upward and downward as a smoothing transition zone; second, calculating the average value of the original parameters of all sounding points in the transition zone; then, calculating the smoothing weight of each sounding point in the transition zone by using the weight function shown in formula (12); finally, calculating the smoothed parameter value of each sounding point according to formula (13). Z b md w md x s md

[0035] S3, trajectory smoothing and engineering constraint checking;

[0036] The random parameter sequence generated in step S2 is further smoothed by using Fourier transform or cubic spline interpolation algorithm to eliminate high-frequency noise, so that the generated wellbore trajectory is more consistent with the actual drilled wellbore shape;

[0037] The smoothed parameter sequence is checked for engineering constraints to ensure that the hole diameter and dogleg severity meet the engineering limit requirements;

[0038] For samples that do not meet the constraints, iterative smoothing or regeneration is performed until the requirements are met;

[0039] The purpose of step S2 is to ensure that the generated random parameter sequence has physical reality and spatial continuity; the constraint in step S3 is the specific engineering requirement standard for well quality in the drilling process, which is used to check the smoothed wellbore trajectory, which can ensure that the generated wellbore trajectory meets both the physical reality and the engineering requirements;

[0040] S4, Monte Carlo simulation and friction calculation;

[0041] Set the number of Monte Carlo simulations, repeat steps S2 and S3, and generate a new set of random wellbore quality parameter sequences that meet the constraints each time;

[0042] For each simulation, call the friction calculation core engine, which calculates the total friction of the casing from the wellhead to the target depth based on the soft rod model;

[0043] ​​​​​​​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.

[0044] 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;

[0045] S5. Probabilistic Results Analysis and Visualization

[0046] 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.

[0047] 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";

[0048] (1) Characteristics of friction distribution:

[0049] Probability density distribution: Normalized using histograms of 50 intervals, as shown in the following formula:

[0050] (18)

[0051] 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".

[0052] 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:

[0053] (19)

[0054] 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;

[0055] (2) The probability of running in and evaluation criteria:

[0056] The probability of running in is defined as the ratio of the total float weight of the casing to the drag.

[0057] (20)

[0058] Formula (20) is used to explain the reading of the probability of running in, P s is the probability of running in, W b is the float weight; CDF( W b ) is the cumulative distribution function of W b .

[0059] Preferably, in step S101, the well structure data includes the well depth and the borehole size of each drilling;

[0060] The casing string design data includes the length, outer diameter, inner diameter and steel grade of each casing section;

[0061] The formation data division includes the formation data from top to bottom, and the top depth and bottom depth of each formation are clear;

[0062] In step S102, the supported probability distribution types include normal distribution, uniform distribution, triangular distribution, lognormal distribution, exponential distribution and gamma distribution.

[0063] Preferably, in step S2, the algorithm adopts Gaussian process simulation, and the specific method is:

[0064] The parameter change along the well depth is regarded as a Gaussian process, and by defining the mean function and the covariance function, a random field that is smooth and consistent with the statistical characteristics of the formation is generated, that is, a probability model of the wellbore quality parameters (hole diameter, dogleg) continuously changing along the well depth direction and having spatial correlation is generated.

[0065] Sampling: call the multivariate normal distribution sampling function to generate the final sequence.

[0066] The core formula is:

[0067] Covariance function k ( md i , md j ) is:

[0068] (1)

[0069] In the formula: mdi , md j These are the i-th and j-th sounding points, respectively. md , It is a length scale.

[0070] Covariance matrix K i，j for:

[0071] (2)

[0072] In the formula: δ i，j This is the Kronecker function (1 when i=j, 0 otherwise). ε For noise (default 0.01).

[0073] Mean vector μ ( md i ) for:

[0074] (3)

[0075] 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.

[0076] Sampling formula:

[0077] (4)

[0078] 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 .

[0079] Formula (3) defines the mean function, while formulas (1) and (2) together define the covariance function.

[0080] Equation (1) is a square exponential kernel, which introduces a control parameter length scale l The covariance (i.e. similarity) of two sounding points md i and md j is determined jointly by their distance md i - md j and the length scale l . The larger the length scale l , the slower the correlation decays with distance, and the smoother the resulting curve.

[0081] Equation (2) constructs the total covariance matrix and adds noise, applies the pair-wise relationship defined by equation (1) to all sounding points, and constructs 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, avoiding numerical calculation problems.

[0082] Equation (3) specifies the expected value (mean) of each sounding point, mathematically represents geological knowledge, and ensures that the generated random curve will fluctuate around a baseline (mean vector μ ) that conforms to the trend of the stratum.

[0083] Equation (4) extracts a specific random sample x that meets all the aforementioned definitions.

[0084] Specifically, in the software, input: step S1 defines the sounding points, stratum division, and mean of each stratum; length scale l of equation (1), noise ε of equation (2). Then calculate μ ( md i ) : according to equation (3), the mean vector μ ( md i ) is obtained by cyclic calculation. Calculate K: according to equations (1) and (2), the covariance matrix K i,j is obtained by double cyclic calculation.

[0085] Preferably, the algorithm in step S2 uses Markov chain simulation, and the specific method is: this method is based on the Markov property that "the next state is only related to the current state", controls the influence degree of the corresponding value of the current sounding point on the corresponding value of the next sounding point through the state transition coefficient, and combines the mean value of the stratum distribution determined in step S1 to generate a parameter sequence with local continuity. This method has high calculation efficiency and is suitable for parameters with obvious local changes.

[0086] The core formula is:

[0087] State transition formula:

[0088] (5)

[0089] 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.

[0090] Sample generation formula:

[0091] (6)

[0092] 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 the base. The amplitude of the perturbation is... β (Maximum step size factor) and formation standard deviation σ k Joint control.

[0093] 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.

[0094] Physical range truncation:

[0095] (7)

[0096] where: max k , min k are the physical maximum / minimum values of the current formation parameter. x i The initial value of " is obtained by directly random sampling from the probability distribution of the formation where it locates.

[0097] Input in software: S1 defines the depth points, formation division and the average value of each formation; the state transition coefficient of formula (5) α (suggested range 0.6-0.95), the maximum step of formula (6) β . α The larger, the smoother the sequence, the stronger the continuity; α The smaller, the closer the sequence to the formation average value. β The larger, the more dramatic local changes; β The smaller, the smoother the sequence.

[0098] Parameter generation:

[0099] For the first depth point, directly random sampling from the probability distribution of the formation where it locates;

[0100] For the i-th depth point (i≥2), calculate the trend value according to formula (5), calculate the parameter value according to formula (6), and perform physical range truncation according to formula (7).

[0101] Formation statistical parameters μ k , σ k Ensure that the overall statistical characteristics of the generated sequence meet the geological understanding, while min k , max k imposes the engineering safety boundary.

[0102] Preferably, the algorithm in step S2 of the present application adopts overall constraints based on the wellbore trajectory: when generating the hole diameter and dogleg severity parameters, engineering and physical constraints are introduced. For example, limit the maximum change rate of dogleg severity between adjacent measuring points to ensure that the generated dogleg severity sequence is coordinated with the overall trend and smoothness of the wellbore trajectory, and prevent unreasonable dramatic fluctuations.

[0103] Suppose the distance between adjacent depth points is 30 meters, and the maximum change rate of dogleg severity between adjacent measuring points is set to r m =0.2° / 30m, and the current formation dogleg severity distribution is N(0.98, 0.3) / 30m, if the dogleg severity of the previous point is x i-1= 0.95° / 30m.

[0104] determining x i The allowable range (0.95-0.2, 0.95+0.2) combined with the stratum range (0.01, 2.06) results in the sampling value being limited to (0.75, 1.15).

[0105] The method is suitable for well sections with high continuity requirements for dogleg severity (such as extended reach wells and horizontal wells).

[0106] The main task of step S2 is to generate a parameter sequence, and the task of step S3 is constraint checking and smoothing. The two steps are logically separated, but the method integrates constraints in the generation stage. The Gaussian process simulation, spatial correlation coefficient matrix method and Markov chain simulation other three methods mainly focus on spatial correlation in the parameter generation stage, and do not actively impose engineering constraints. Engineering constraints are implemented in step S3.

[0107] Preferably, the algorithm in step S2 adopts the spatial correlation coefficient matrix method, specifically: the statistical correlation between the hole diameter and the dogleg severity is explicitly defined through a 2x2 correlation coefficient matrix. Each depth point corresponds to a generated hole diameter value and a dogleg severity value. Through Cholesky decomposition technology, hole diameter and dogleg severity samples with specified correlation at any depth point are generated, thereby simulating the coupling effect between parameters, i.e. generating curves with continuity, smoothness or conforming to specific variation rules, thereby simulating the wellbore shape formed by real drilling.

[0108] The core formula is:

[0109] Correlation coefficient matrix (2x2 matrix, only considering hole diameter and dogleg severity):

[0110] (8)

[0111] In the formula: ρ is the hole diameter-dogleg severity correlation coefficient, representing the linear correlation degree between hole diameter and dogleg severity, with a value range of [-1, 1]. : Positive correlation, hole diameter expansion often accompanied by dogleg severity increase (common in soft and easy-to-collapse formations). : Negative correlation, hole diameter expansion accompanied by dogleg severity decrease (less common). : No correlation, both change independently. ρ The value of should be based on geological engineering understanding or statistical analysis of historical data in the block to analyze the linear correlation degree between hole diameter and dogleg severity.

[0112] The covariance matrix Σ is (combined with the standard deviation of each parameter):

[0113] (9)

[0114] 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.

[0115] Positive definiteness processing (ensuring the matrix is ​​sampleable):

[0116] If Σ is not positive definite (eigenvalue ≤ 0), it is corrected by eigenvalue:

[0117] (10)

[0118] 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.

[0119] Multivariate normal sampling:

[0120] (11)

[0121] 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.

[0122] 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.

[0123] Lk Obtained through Cholesky decomposition Lower triangular matrix, satisfying ,in Let be the covariance matrix of the current stratum as defined by formula (9).

[0124] Let be a two-dimensional standard normal random vector, where , Independent and identically distributed according to the standard normal distribution .

[0125] Formula (8) defines the basic correlation framework between wellbore diameter (D) and dogleg degree (K).

[0126] Equation (9) combines the abstract correlation framework R with the statistical properties of the specific formation to form an executable covariance matrix.

[0127] Equation (10) numerically guarantees the step, ensuring that the covariance matrix is strictly positive definite, so that subsequent calculations such as Cholesky decomposition can be performed.

[0128] Equation (11) is the final generation step, which extracts a pair of correlated hole diameter and dogleg values from the defined bivariate normal distribution. Equation (11) defines a linear transformation method for extracting random samples from a bivariate normal distribution with specified mean μ k and covariance structure Σ k The software implementation steps are as follows:

[0129] Determine the formation at the current depth point i k ; call an independent standard normal random number generator to generate two independent random numbers ξ i1 , ξ i2 to form a vector ξ i2 ; obtain the mean vector μ k and the Cholesky decomposition matrix L k of the formation; perform matrix operation equation (11) to obtain a pair of hole diameter values and dogleg values with specified correlation.

[0130] Preferably, in step S3, the parameter sequence is converted to the frequency domain by Fourier transform, the high-frequency noise corresponding to the parameter mutation is filtered out, and then inverse transformed back to the time domain. Specifically, the entire wellbore parameter sequence (such as hole diameter) is regarded as a signal fluctuating on the “depth axis”, and through global frequency analysis and filtering, high-frequency noise representing non-physical mutations is removed, thereby obtaining a smoother and continuous parameter curve that is more consistent with the actual drilling formation. The smoothing strength parameter is adjusted by controlling the cutoff frequency f c to adjust the degree of smoothing, and the cutoff frequency f c can be set by inputting the value of the smoothing strength.

[0131] The core formula is:

[0132] Fourier transform:

[0133] (14)

[0134] 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.

[0135] High-frequency filtering:

[0136] (15)

[0137] 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.

[0138] Inverse Fourier Transform:

[0139] (16)

[0140] 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.

[0141] Wellbore trajectory parameter smoothing process based on Fourier transform:

[0142] 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.

[0143] 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.

[0144] 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.

[0145] Cubic spline interpolation is an existing technique in numerical analysis, and its core formula is:

[0146] For depth sounding interval spline function S i (md) for:

[0147] (17)

[0148] 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);

[0149] b i For spline functions in The first derivative at that point represents the instantaneous rate of change at that point;

[0150] 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;

[0151] 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.

[0152] 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.

[0153] The basic physical and engineering constraints in step S3 are:

[0154] Minimum hole diameter constraint: the generated hole diameter is greater than the casing outer diameter multiplied by a safety factor (e.g. 1.05) to ensure sufficient annular clearance;

[0155] Maximum dogleg severity constraint: the generated dogleg severity should not exceed the maximum value allowed by engineering.

[0156] The application preferably further comprises step S6, grade evaluation:

[0157] The probability value of "friction less than float weight" is defined as the run-in probability P;

[0158] When P≥95%, it indicates that it can be safely run in without adjustment, and the original design is executed;

[0159] When 80%≤P<95%, it indicates that it can be run in but needs to pay attention to the risk, and it is suggested to optimize the drilling fluid performance or adjust the casing steel grade;

[0160] When P<80%, it indicates that the risk of running in is high, and it is suggested to redesign the well profile or use auxiliary running-in tools.

[0161] The application is to generate a large number of wellbore trajectories that meet the physical reality by statistically analyzing the well profile quality data of the drilled wells in the region, using Monte Carlo simulation as a tool, considering the uncertainty of well profile quality, and performing casing friction calculation. It evaluates whether the designed well profile structure will encounter resistance risk during casing operation and gives the probability basis before drilling, so as to adjust the well profile structure design in time.

[0162] Table 2 Run-in evaluation standard

[0163]

[0164] The key quantile of output friction (such as P1, P5, P50, P90, P95, P99) provides data support for decision-making with different risk preferences. For example, the P90 friction value indicates that 90% of the sample friction is less than or equal to this value. It provides a set of friction risk values at different confidence levels for engineering decision-makers, so that they can choose the corresponding friction design value or evaluation standard according to their own risk acceptance level; Table 2 is the conclusion obtained by evaluating a large number of drilled wells during casing operation by this method; for various situations in engineering practice, such as not wanting to use this conclusion, those skilled in the art can determine the corresponding evaluation standard according to the key quantile and their own risk acceptance level.

[0165] In the present application, the Monte Carlo simulation is performed by repeatedly performing (step S4 defines the number of simulations) the parameter sequence generation of step S2, the smoothing constraint of step S3, and the friction calculation of step S4, accumulates a large number of friction results, and performs statistical analysis on them in step S5. Therefore, the Monte Carlo simulation in the present application is similar to a framework.

[0166] Monte Carlo simulation is a general, probability-based numerical calculation method. In specific implementation, it can be implemented by any tool with random number generation and numerical calculation capability, such as using Python (NumPy, SciPy for random sampling and calculation).

[0167] Compared with the prior art, the present application has the following beneficial effects:

[0168] 1. The present application is based on the uncertainty of wellbore quality, and by introducing probability distribution and Monte Carlo simulation, the traditional deterministic analysis is upgraded to probabilistic risk analysis, which fully considers the uncertainty of wellbore quality in actual engineering, so that the evaluation result is closer to the actual engineering.

[0169] 2. The present application simulates the spatial correlation of the corresponding parameters of the depth measuring point along the well depth direction through algorithm, which can ensure that the simulated well trajectory parameter sequence has real physical continuity, avoids non-physical random jumps, and improves the scientificity of the model.

[0170] 3. The present application integrates trajectory smoothing and various engineering constraint checks, which ensures that all random scenes used for calculation are within a reasonable engineering range, and enhances the practicability and reliability of the method.

[0171] 4. The present application finally outputs the risk indicators (such as success probability, quantile) in the form of probability, rather than a single numerical value, so that the engineering decision maker can clearly understand the risk level, and make more scientific and reliable decisions. BRIEF DESCRIPTION OF DRAWINGS

[0172] Figure 1 is a stratigraphic division diagram of an oil production well in a certain block of Xinjiang Oilfield in the embodiment of the present application;

[0173] Figure 2 is a friction probability density distribution diagram example in the embodiment of the present application;

[0174] Figure 3 is a friction cumulative probability distribution diagram example in the embodiment of the present application;

[0175] Figure 4 is a flowchart of the present application. DETAILED DESCRIPTION

[0176] The technical solutions in the embodiments of the present invention will now be clearly and completely described in conjunction with the accompanying drawings.

[0177] 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.

[0178] 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:

[0179] S1. Multi-source data integration and probability distribution model establishment

[0180] Based on the on-site data, the basic parameters for calculation were determined.

[0181] 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.

[0182] 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...).

[0183] 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.

[0184] Table 3. Types of Probability Distribution of Wellbore Quality

[0185]

[0186] S2, Generation of relevant random parameter sequences

[0187] 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.

[0188] Smooth transition of stratigraphic boundaries:

[0189] To avoid abrupt parameter changes at the stratigraphic boundary, the parameters within 50m before and after the boundary are smoothed.

[0190] S3, Trajectory Smoothing and Engineering Constraint Check

[0191] 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".

[0192] S4, Monte Carlo simulation and friction calculation

[0193] 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 underrun is calculated for effective samples.

[0194] The core formula is:

[0195] 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.

[0196] (100)

[0197] 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.

[0198] Dogleg to Curvature Conversion: Converting commonly used engineering units of dogleg degree (° / 30m) to radians of curvature. (rad / m), used for mechanical calculations.

[0199] (200)

[0200] In the formula: For the first Dogleg value of each sounding point, ° / 30m.

[0201] Lateral force calculation (maximum value from both mechanisms):

[0202] Bending effect lateral force F L1,i for:

[0203] (300)

[0204] where: is the casing bending stiffness.

[0205] axial force effect lateral force F L2,i is:

[0206] (400)

[0207] where: F a,i is the axial tension force at the lower end of the casing string at the th calculation point (sounding point). is the calculation unit length, usually taken as 1 m (after interpolation).

[0208] total lateral force F L,i is:

[0209] (500)

[0210] unit friction F f,i Calculation: the friction of the ith unit is the product of the lateral force and the friction coefficient.

[0211] (600)

[0212] where: is the friction coefficient.

[0213] total friction F t Calculation: the friction is the sum of the friction of all units.

[0214] (700)

[0215] S5, probabilistic result analysis and visualization

[0216] Based on the results of Monte Carlo simulation, the downhole risk is quantified by statistical analysis, and the output results are shown in Figure 2 and Figure 3 .

[0217] Table 4 Casing downhole evaluation conclusion

[0218]

[0219] From Figure 3 , it can be read that the casing float weight ( Figure 3 Figure 3The middle red line is 2440.6 kN, and the value of the cumulative probability curve at this point is 30.43%. After considering the uncertainty of the wellbore quality, the probability of the casing running friction being less than its own float weight is 30.43%, that is, the success probability of running is 30.43%. Based on the running evaluation criteria in Table 4, the casing cannot be normally run during the casing running operation of this trip.

[0220] As can be seen from the results, the method considers the uncertainty of the actual wellbore quality, generates a probabilistic casing running evaluation result, and improves the accuracy of the casing running operation risk evaluation and the scientificity of the 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 evaluating 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 assessing the risk of casing run-in considering wellbore quality uncertainty as described in 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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