海上浅层井眼稳定性的人工神经网络预测+考虑井眼稳定性的定向井轨迹优化受地质力学参数的影响

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海上浅层井眼稳定性的人工神经网络预测

（关键词：井筒稳定性；井筒失稳；人工神经网络；近海浅层地层；渤海湾盆地）

文献信息：

Wu J, Liu W, Li J, et al. Artificial neural network prediction of wellbore stability in offshore shallow formations[J]. Geoenergy Science and Engineering, 2024, 243: 213322. DOI:10.1016/j.geoen.2024.213322.

摘要译文：

井壁失稳是钻井过程中的关键难题，会导致卡钻、扭矩增大和钻井液漏失等复杂问题，延误钻井进度，增加钻井成本。海上浅层地层胶结弱、强度低，井壁失稳现象频发。传统的井壁稳定物理模型旨在预测在给定钻井液密度下井壁失稳的风险，为安全钻进提供最优钻井液密度。然而，这些模型通常包含大量经验系数，而其确定在很大程度上依赖于工程师的现场经验，因此预测结果可能因人而异。为了降低预测主观性，并将邻井的钻井情况动态映射到预测结果中，本研究建立了一种用于井壁稳定性预测的人工神经网络（ANN）模型。基于当前常用的井壁稳定物理模型，确定了11个可能影响井壁稳定性的因素作为ANN模型的输入参数，而井眼扩大率（WER）作为量化井壁稳定性能的输出参数。本模型使用渤海湾盆地近海浅层5口井的钻井数据进行训练，然后用于预测同一地区另一口井的井眼扩大率。结果表明，模型的平均预测误差为6.113%，且预测的井径与实测值的偏差最大不超过5%。将ANN模型与其他机器学习模型（包括随机森林模型、决策树模型、线性回归模型）进行了比较，结果表明ANN模型在预测井径剖面方面效果最佳。最后，通过准确预测不同泥浆比重下的井径剖面，验证了该模型在优化钻井液密度中的潜在应用。本文提出的方法兼具物理性和数据驱动性质，可为井壁稳定性分析提供新思路。

摘要原文：

Wellbore instability is one of the most critical challenges during drilling, which may result in complex problems such as stuck pipe, high torque and mud loss, impeding the drilling progress and increasing the cost of drilling operations. Offshore shallow formations are characterized by weak consolidation and low strength, causing serious wellbore collapse frequently. The traditional physics-based wellbore instability models attempt to predict the risk of failure of the wellbore for given drilling fluid densities and provide optimal fluid density for safe drilling. However, these models generally involve quite a few empirical coefficients, determination of which heavily rely on the field experiences of the engineers, and thus the results may vary greatly from person to person. In this study, an artificial neural network (ANN) model has been established for wellbore stability prediction, aiming to reduce the subjectivity while mapping the drilling performance of neighboring wells into the predicted results. Eleven factors that may affect wellbore stability have been identified from the prevailing physics-based model and used as the input of the ANN model, while the wellbore enlargement rate (WER) is used as the output to quantify the wellbore stability performance. The model has been trained using data from 5 wells drilled in the offshore shallow formations of the Bohai Bay Basin in east China and then used to predict the WER of another well in the same region. The results show that the mean absolute percentage error is 6.113%, and at most well depths the predicted wellbore diameter deviate from the measured values not more than 5%. Comparison of the ANN model and some other machine learning models, including random forest model, decision trees model, linear regression model, was conducted, which demonstrated the best performance of the ANN model in terms of the predicted wellbore diameter profile. Finally, the potential application of the ANN model in optimizing mud weight has been illustrated through the predicted wellbore diameter profiles for different mud weights. It is worth noting that the method presented in this paper is of physics and data-driven nature and provides a new research insight for wellbore stability analysis.

图1 渤中凹陷周边典型浅层油气田分布(a)与综合地层柱(b)测井数据（c）

测井时每0.1m采集一组数据，X-1~X-6 6口井的测井数据共获得78985组数据（图1(c)）

图2 数据集的静态分析

图3 WER与各因素的相关系数。

图3给出了6口井11个影响因素与WER的相关关系。结果表明，CN、Dogleg和DT与WER的相关性最强，相关系数分别为0.60、0.59和0.53。其他因素均与WER表现出不同程度的相关性。

图4 具有一个隐藏层的人工神经网络模型结构

在模型训练过程中，模型中每个神经元的值会不断更新。在计算当前神经元的值之前，它接受前一层神经元传输的输出值作为输入，并对权重和偏置进行线性叠加运算，如图4所示。

图5 5口用于训练的井径：(a)X-1井；(b)X-3井；(c)X-4井；(d)X-5井；(e)井X-6

我们将X-2井分配用于模型预测，其余5口井的数据用于模型训练。这5口井的井径如图5所示，一般在井深小于1000m处表现为严重的扩径。

图6 X-2井在(a)500-1000米、(b)1000.1-1500米、(c)1500.1-2021米深度的预测和实际井筒直径

图6显示了模型训练过程中的训练损失和验证损失。可以发现，损失在200个epoch时基本停止变化。

图7 不同模型的绝对百分比误差分布。

在图7中，绝对百分比误差低于20%时，频率在每个量程组中的分布更为均匀。这一观察结果表明，在评估的模型中，人工神经网络模型表现出最好的性能。

图8 不同泥浆密度下的井眼直径预测

结果表明，泥浆比重为1.1 g/cm³时，预测井筒直径更大，更接近实际值。随着泥浆比重的增加，预测井眼直径逐渐减小增加。预测结果与经验知识一致，即适当增加泥浆比重可以防止井筒坍塌，表明人工神经网络模型具有优化泥浆比重的能力。当钻井液密度为1.3g/cm³时，井径最接近钻头尺寸。

考虑地质力学参数非独立性和不确定性影响下井壁稳定性的定向井轨迹优化

（关键词：参数相关性；不确定性分析；井壁失稳风险定量评估；Nataf转换；蒙特卡罗法）

文献信息：

Fuzhi Chen, Jiajia Gao, Yutian Feng, et al. Optimizing the wellbore trajectory of directional wells considering wellbore stability Subjected to the non-independence and uncertainty of geomechanical parameters[J]. Geoenergy Science and Engineering, 2024, 241:213085. DOI:10.1016/j.geoen.2024.213085.

摘要译文：

在复杂深层油气资源勘探过程中，有效分析定向井井壁稳定性至关重要。井壁稳定性评价模型旨在确定与坍塌压力和破裂压力相关的井壁失稳压力，其控制着井眼轨迹优化，并与地质力学参数（包括力学参数、强度参数、原地应力和孔隙压力）密切相关。然而，在获取地质力学参数过程中存在的测量误差和固有模糊性引入了不确定性特征，进而导致井壁失稳压力在一定范围内呈现概率分布。此外，水平原地应力和强度参数的确定也与包括弹性模量和泊松比在内的力学参数相关。因此，井壁失稳风险评估的有效手段是根据适当的分布函数和地质力学参数的相关性，将不确定性量化引入井壁稳定性评估模型。。本文提出了一种考虑地质力学参数不确定性和相关性的井壁失稳风险分析方法。首先，通过地质力学参数的数据采样，利用Kolmogorov-Smirnov（K-S）检验和Pearson线性相关系数量化不确定性特征和参数相关性。然后，结合蒙特卡洛方法和Nataf变换，使随机生成的样本能够恢复参数自身的不确定性和相关性特征。最后，将样本代入优化模型，实现参数不确定性和非独立性条件下的井壁失稳风险分析和目标地层的参数敏感性评价。主要研究结果表明，采用新提出的方法分析井壁失稳风险，可以显著降低坍塌压力和破裂压力预测结果的不确定性。此外，井眼轨迹优化结果表明，原地应力的不确定性可能导致地层岩石经历应力状态的改变，例如正断层应力转变为走滑断层应力，这对井壁稳定性评价和井眼轨迹优化方案的选择产生显著影响。无论参数是否独立，坍塌压力预测的不确定性范围均大于破裂压力，但破裂压力与坍塌压力的整体比值受井眼轨迹的显著影响。同时，考虑单一因素的直接影响时，原地应力对井壁失稳风险评估有很大影响，尤其是最小水平原地应力对破裂压力的影响最为明显。弹性模量、泊松比、内聚力、内摩擦角和抗拉强度等地质力学参数对井壁失稳的影响相对较弱。然而，上述变化忽略了参数自身的相关性特征。当考虑到相关性特征，弹性模量、泊松比和孔隙压力等弱参数与原地应力具有较强的相关性，从而对井壁失稳产生间接影响。

摘要原文：

Effectively analyzing the wellbore stability risk in directional wells is important in exploring oil and gas resources in complex deep formations. An evaluation model of wellbore stability prefers to determine the wellbore instability pressures related to collapse pressure and fracture pressure that controls the optimized wellbore trajectory and is strongly related to the characteristics of geomechanical parameters, including the mechanical and strength parameters, in-situ stresses, and pore pressure, However, the measured errors and inherent fuzziness during the obtaining of geomechanical parameters introduce the uncertainty characteristics and further produce a probability distribution within a certain range of the wellbore instability pressures. Besides, the determination of horizontal in-situ stresses and the strength parameters also are correlated with the mechanical parameters including elastic modulus and Poisson’s ratio. Therefore, an effective means of risk assessment of wellbore instability resorts to introducing uncertainty quantification, depending on the appropriate distribution function, and correlations of geomechanical parameters into the evaluation model of wellbore stability. This work proposes a risk analysis method for wellbore instability considering the uncertainty and correlation of geomechanical parameters. Firstly, the uncertainty characteristics and parameter correlations are quantified by Kolmogorov-Smirnov (K–S) test and Pearson linear coefficient through data sampling of geomechanical parameters. Then, the Monte Carlo method and the Nataf transform are combined to make the randomly generated samples restore the uncertainty and correlation characteristics of the parameters themselves. Finally, the sample is brought into the optimal model to realize the risk analysis of wellbore instability and parameter sensitivity evaluation of the target formation under parameter uncertainty and non-independent conditions. The main research shows that the uncertainty of the prediction results of collapse pressure and fracture pressure is significantly reduced by using the newly proposed method to analyze the risk of wellbore instability. In addition, the results of wellbore trajectory optimization indicate that the uncertainty of in-situ stress makes it possible for the formation rock to experience a changing type of stress state, for example, normal stress faulting changing to the strike-slip one, which significantly affects the evaluation of wellbore stability and the selection of wellbore trajectory optimization. The uncertainty range of collapse pressure prediction is greater than that of fracture pressure regardless of whether the parameters are independent or not. However, the overall value of the fracture pressure compared to the collapse pressure is significantly affected by the wellbore trajectory. Meanwhile, considering the direct effect of a single factor, the in-situ stress has a great influence on the risk analysis of wellbore instability, especially the minimum horizontal in-situ stress has the most obvious influence on the fracture pressure. The influence of geomechanical parameters such as elastic modulus, Poisson’s ratio, cohesion, internal friction angle, and tensile strength on wellbore instability is relatively weak. However, the aforementioned variation ignores the correlation characteristics of the parameters themselves. With the correlation characteristics considered, weak parameters such as elastic modulus, Poisson’s ratio, and pore pressure have a strong correlation with in-situ stress, and thus exert the indirect effect on wellbore instability.

图1 不同坐标系之间的转换（ICS、GCS和BCS分别表示地应力坐标系、全球坐标系和钻孔坐标系）

一般来说，任意斜度井周围的应力分布通常涉及四个坐标系之间的转换。即全局坐标系、地应力坐标系、井筒坐标系、井筒柱坐标系。得到各坐标系的转换关系如图1所示。

图2 基于蒙特卡罗方法和Nataf变换的相关地质力学参数定量处理

取样本数据的函数，拟合优度较高的函数作为参数的边缘分布函数。其次，对参数相关矩阵进行Nataf变换，实现地质力学参数非正态分布空间到独立正态分布空间的转换；然后在随机空间中进行蒙特卡罗随机抽样，通过Nataf变换的相关系数矩阵映射回原始分布空间。进而得到与样本数据具有一定一致分布特征的随机数。最后，将随机数与评价模型相结合，可以达到定量评价井筒失稳风险的目的。

图3 基于地质力学参数均值的定向井坍塌和破裂压力变化

井筒稳定性评价的主要目标预测涉及两种类型的有效应力，包括确定坍塌压力和破裂压力。因此，首先考虑地质力学参数的不确定性满足石油工程领域中常用的一种特殊情况，即均值条件，然后根据崩塌和破裂压力的结果确定哪种有效应力定义更适合于评价井筒稳定性。地层应力状态为走滑断裂，相应的定向井坍塌压力和破裂压力变化如图3所示。

图4 坍塌压力和破裂压力等效密度散点图和累积分布曲线

在不考虑参数相关性的情况下，坍塌压力与破裂压力形成的散点图与失稳压力轴线平行线正交。也就是说，坍塌压力和破裂压力是近似独立的。然而，在参数相关性的约束下，图的左偏使得坍塌压力与破裂压力存在一定程度的负相关关系。在三种钻井轨迹下，考虑参数相关性的井筒稳定性可靠度曲线斜率绝对值大于不考虑情况的斜率绝对值，不确定性范围相对较小。同时，不确定性范围在平均值附近扩大，裂缝压力随井筒轨迹的变化明显大于坍塌压力。

图5 不同断裂状态下井筒轨迹参数敏感性变化

本文控制地质力学参数相对变化率±10%，分析了正、走滑、逆断裂三种断裂机制下不同井眼轨迹的参数敏感性变化。从结果可以看出：井眼轨迹对上覆岩压力和水平原地应力的敏感性有显著影响，而其他地质力学参数并未显示出敏感程度发生显著变化。值得注意的是，垂直井眼中的上覆岩压力对井壁稳定性没有影响，而水平原地应力是影响井壁坍塌压力和破裂压力的最重要参数。