DEVELOPMENT OF DIGITAL INTELLIGENCE FLUID DYNAMICS AND APPLICATIONS IN THE OIL & GAS SEEPAGE FIELDS
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摘要: 大数据及人工智能技术的崛起推动了数智流体力学的快速发展. 数智流体力学是将流体力学、大数据和人工智能相结合, 以流体力学场景需求为导向, 形成以“数”为基础, 以“智”为核心, 以算力为支撑的新研究范式. 核心内涵是要以数据驱动为主, 融合物理信息、专家经验等先验知识, 利用智能化手段构建“数据 + 物理”双驱动的数智模型, 解决场景需求问题. 数智流体力学在建模灵活性、运算效率、计算精度方面具有十分明显的优势, 其应用潜力已经在多尺度流动、多场耦合以及流场建模等方面得到验证. 数智流体力学研究范式包括数据治理和智能算法构建, 其中数据治理工作尤为重要, 治理后的数据质量是智能算法能否发挥其价值的关键. 智能算法中“数据 + 物理”协同驱动主要存在四种引入机制, 分别是基于输入数据的嵌入机制、基于模型架构的嵌入机制、基于损失函数的嵌入机制和基于模型优化的嵌入机制. 以油气领域应用为例, 介绍了数智流体力学在储层物性参数预测、压裂效果评价以及注采参数优化等方面的一系列研究进展. 数智流体力学是流体力学未来的重要发展方向之一, 以场景需求为导向、深度融合物理信息等先验知识的新一代智能理论与方法是数智流体力学发展的必然趋势, 能够从崭新的角度攻克诸多复杂多变的流体力学关键问题.Abstract: The growth of big data and artificial intelligence technologies has driven the rapid development of digital intelligence fluid mechanics. Digital intelligence fluid mechanics combines fluid mechanics, big data and artificial intelligence, to establish a new research paradigm oriented to specific scenarios of fluid mechanics, with "data" as the basis, "intelligence" as the core, and arithmetic power as the support. Its connotation is to establish a "data + physics" co-driven digital intelligence model, which is mainly data-driven and incorporates prior knowledge such as physical information and expert experience, to solve practical problems in different scenarios. Digital intelligence fluid dynamics has very obvious advantages in modeling flexibility, computing efficiency, and computational accuracy, whose application potential has been proven in multi-scale flow, multi-field coupling, and flow field modeling. In terms of the construction of digital intelligence models, data governance is indispensable since the data quality improved by governance enables intelligent algorithms to perform preferably. There are four main mechanisms for introducing "data + physics" co-driving in intelligent algorithms, which are input data-based embedding mechanism, model architecture-based embedding mechanism, loss function-based embedding mechanism and model optimization-based embedding mechanism. Taking oil & gas field applications as an example, a series of research advances in the prediction of physical parameters, evaluation of fracturing effects and optimization of injection parameters by digital intelligence fluid dynamics are introduced. Future diversified research models can take advantage of the efficient and rapid modeling of digital intelligence fluid dynamics, but also ensure physical interpretability and extrapolation in both classical and computational fluid dynamics. Therefore, digital intelligence fluid mechanics is an inevitable trend in the future development of fluid mechanics, and it is necessary to take the scenario demand as the guide, deeply integrate physical information and prior knowledge, actively explore new intelligent theories and methods, and attack the complex and changing scientific problems in fluid mechanics.
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引 言
流体力学作为一门重要的基础学科之一, 从经典流体力学理论的探索, 到计算流体力学理论的发展, 为人们提供了一系列高效快速的研究方法, 可以应对实际工程中的复杂科学问题[1-2]. 自21世纪以来, 大数据以及人工智能技术的崛起推动了各行各业朝着数字化及智能化发展[3-4], 流体力学与大数据、人工智能的结合提供了一个全新的探索模式, 相比于经典流体力学理论, 数智流体力学无需建立复杂的非线性方程组以及依赖大量的假设条件, 通过数据驱动的方式构建可以自主学习的智能化模型, 解决流体力学中复杂的多相流动、多尺度建模及多场耦合等问题, 与计算流体力学相比, 数智流体力学所构建的智能模型具有更好的灵活性, 无需进行大量的调参以及不确定参数的估计, 更重要的是在运算效率和计算精度方面具有十分明显的优势. 除此之外, 经典流体力学以及计算流体力学可以为数智流体力学提供物理指导以及数据支撑, 同时, 数智流体力学也可以加速他们的参数优化以及进行误差修正等. 因此数智流体力学已经成为了流体力学未来发展的必然趋势, 其与经典流体力学、计算流体力学相辅相成推动流体力学迈向新的台阶.
数智流体力学是以数据为基础, 通过数据处理和人工智能算法, 明确物理参数之间的映射关系, 以数据驱动的方式对流体力学问题进行分析. 数智流体力学的内涵包括两方面重要内容: “数”和“智”. “数”是指来源于实验、模拟以及实际监测的大量的数据, 如何将大量的多源异构数据体形成高质量的数据集尤为关键, 现如今很多国内外的学者都专注于智能算法的研究而忽略了数据本身的重要性, 而数据治理是“数”的核心之一, 通过数据的清洗、关联及融合来提升数据质量, 能够为后续面向场景的智能模型构建奠定基础. “智”是指智能化模型, 不同于经典流体力学和计算流体力学中基于物理的建模形式, 智能化模型的本质是通过数据驱动的方法构建自训练模型, 能够自动捕获和学习在各种复杂条件下物性参数之间隐含的映射关系, 主要分为纯数据驱动的智能模型以及“数据 + 物理”协同驱动的基于物理信息的智能算法. 因此, 数智流体力学是要以流体力学中具体问题为导向, 形成以“数”为基础, 以“智”为核心, 以大数据算力为支撑的新的探索模式, 尤其适用于在复杂的多场耦合以及不确定条件下探究流体流动规律等.
1. 数智流体力学交叉理念
近年来, 大数据和人工智能技术在各个领域的深度融合敲开了数智时代的大门[5-8]. 这两项技术的强强联手解决了面向海量数据时“如何存储处理”以及“如何关联分析”两大难题. 自2003年以来谷歌先后发表三篇论文[9-11], 详细揭示了分布式存储和计算框架, 拉开了大数据时代的帷幕. Doug Cutting成功开发了Hadoop[12]以及Spark[13]等系统相继出现使得大数据技术真正站在了时代的舞台. 与大数据技术不同, 人工智能的概念[14]早在1956年美国达特茅斯会议上就被首次提出. 然而, 由于缺乏常识性知识、推理手段单一以及兼容性等问题导致人工智能的发展很快陷入了低谷. 直至1997年, 由IBM公司开发的超级计算机Deep Blue在国际象棋大赛中力克世界冠军卡斯帕洛夫[15], 重燃了学者们对于人工智能的热情. 人工智能历史性的转折及蓬勃发展出现在2010年之后, LeCun等[16]于2015年在世界顶尖期刊Nature上发表文章Deep learning; 2016年, 由谷歌研发的AlphaGo战胜世界围棋冠军李世石[17], 引发了超过千万人的关注, 具有划时代的意义. 流体力学作为力学的一个分支, 自17世纪开始建立起完善的理论体系, 从纳米尺度的分子动力学[18-19], 到介观尺度的蒙特卡洛模拟[20-21]和格子玻尔兹曼理论[22-23], 再到宏观尺度的计算流体力学模拟[24-26], 各国的物理学家开发了一系列技术手段研究多尺度多场耦合等复杂的流体力学问题, 人工智能以及大数据技术的崛起也推动了数智流体力学的发展, 提供了一种全新的探索模式更好地完善了流体力学理论体系.
由于大数据技术、人工智能与流体力学的交叉融合, 流体力学的研究方法可以拓展为以下四种, 包括实验研究、理论求解、数值模拟、数智分析, 如图1所示. 实验研究是最基础也是最可靠的研究方法, 可以直接从流动现象探索流动规律, 许多经典的流体力学理论都是通过实验得来的, 如牛顿的黏性定律、雷诺的层流和湍流发现、普朗特的边界层理论等. 理论求解和数值模拟都是建立在经典流体力学理论的基础之上, 面向具体的流动场景, 根据质量守恒方程、运动方程、状态方程等构建物理模型, 依赖少量的基础数据如初始条件、边界条件等, 通过解析求解如分离变量、拉普拉斯变换等, 以及数值求解如分子动力学、蒙特卡洛模拟、有限差分及有限元[27-29]等求解物理模型, 计算得到相应的流量、流速以及压力等关键流动参数. 基于物理的流动建模方法核心在于理论建模以及求解, 少量的基础数据以及可以随着时间进行流场演化是其主要优势, 然而这个建模体系往往建立在一些假设条件的基础之上, 物理模型中一些重要的物性参数也很难直接获取, 在面向纳米尺度数量庞大的分子模拟以及宏观尺度数以万计的网格划分时, 不但会存在较大的迭代误差, 呈现出过于理想化的结果, 而且消耗大量的计算资源和时间成本. 不同于基于物理的方法, 数智分析方法的核心是依靠大量的实际数据, 以数据驱动的方式训练智能化的模型替代物理的偏微分方程组和繁琐的求解过程. 因此, 该方法所构建的数智模型无需考虑理论方程以及多相多尺度流动、多场耦合等复杂交互机制, 建立从现象到规律的直接映射关系, 实现流体力学的数智化建模[30-32]. 值得一提的是, 计算流体力学和经典流体力学可以为数智流体力学提供数据支撑以及物理指导[33-40], 从而实现更加精准的流动预测以及流场建模. 数智流体力学也可以通过对参数优化以及误差修正[41-47]来加速计算流体力学的模拟过程以及提高运算效率. 如Kochkov等[48]基于端到端的深度学习方法改进计算流体力学中的近似值, 实现了对二维湍流的建模, 对于湍流的直接数值模拟和大涡模拟而言, 使得空间维度的分辨率提高8 ~ 10倍, 计算速度提升了40 ~ 80倍.
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图 1 流体力学四种研究方法的数据流形式图Figure 1. Data flow in four types of research method for fluid mechanics随着流体力学与大数据技术、人工智能方法不断深入结合, 纯数据驱动的数智模型已经无法满足人们对于计算精度的要求, 而且在实际应用时收集到的数据样本不足以及模型内在的可解释性差成为了数智模型的主要制约. 因此, 一些学者将物理信息引入到机器学习的模型中, 通过已有的物理认知规律利用直接的或者间接的方式指导机器学习模型的自主训练, 可以在降低样本数量的同时保证模型的鲁棒性及预测精度, 构建“数据 + 物理”的协同驱动的数智模型. 本文结合了流体力学、大数据技术和人工智能方法提出了数智流体力学概念, 详细阐述了在多相流动、多尺度建模、及多场耦合等方面数智模型的构建方法, 更进一步地总结了将物理信息引入机器学习模型的嵌入机制, 完善流体力学理论体系并促进数智流体力学在相关领域的数智化发展. 以油气领域为例, 据世界权威的油气数据库(美国石油工程协会OnePetro)统计, 如图2所示, 截止2022年9月, 大数据、人工智能和油气领域结合的期刊、会议论文正在飞速增长, 说明了数智流体力学正迅速推动着智慧油气的发展, 孕育全新的油气革命.
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图 2 大数据、人工智能和石油领域结合的论文数量统计(OnePetro数据库)Figure 2. Statistics of papers combining big data, artificial intelligence and petroleum industry (OnePetro database)2. 数智流体力学的理论内容
数智流体力学主要涵盖了两方面的理论内容: “数”和“智”. “数”是指流体力学中通过实验、模拟以及监测等手段获得的多源异构数据本身, 对于真实的实验以及监测数据, 由于实验设计、监测仪器和人为因素等干扰, 往往存在数据的缺失、异常以及冗余等问题. 因此需要利用仅数据特征的治理手段以及含物理约束的治理方法全方位地进行数据的采集、清洗、关联及融合, 面向多尺度的流体力学场景, 需要制定统一的数据标准, 构建多角度的数据治理体系, 最终形成满足完整性、规范性、唯一性、准确性以及一致性的高质量数据集. “智”是指智能算法, 也是数智流体力学所构建数智模型的核心, 包括了纯数据驱动的机器学习方法以及引入了物理信息的“数据 + 物理”协同驱动的机器学习算法两方面内容, 通过构建智能模型来自主学习和挖掘物性参数之间的非线性映射特征和隐含关系, 进而解决流体力学领域中涉及的多相流动、多尺度建模、及多场耦合等问题. 数智流体力学的框架、方法及特点如图3和表1所示.
表 1 数智流体力学方法及特点Table 1. Digital intelligence fluid dynamics methods and featuresCategory Method Feature digital intelligence
fluid mechanicsdata governance data feature-based many applications, suitable for big data stream processing with physical constraints more professional, suitable for data in professional fields artificial intelligence data-driven supervised learning relatively easy, many theoretical and practical applications unsupervised learning relatively easy, mainly for clustering and dimensionality reduction semi-supervised learning relatively easy, used for insufficient sample data, few applications reinforcement learning relatively easy, few applications, mainly for theoretical research physics-informed machine learning input data-based embedding mechanism low difficulty, rely on empirical guidance, many theoretical and practical applications model architecture-based embedding mechanism moderate difficulty, requires lots of trials and empirical guidance loss function-based embedding mechanism high difficulty, high data quality, many theoretical researches and few applications model optimization-based embedding mechanism moderate difficulty, some theoretical researches and few applications 2.1 数据治理
2.1.1 仅数据特征的数据治理
一般而言, 在流体力学领域, 实验以及实际监测的数据由于实验设计、监测仪器和人为因素等干扰都会存在数据缺失、数据异常等问题. 仅数据特征的数据治理是仅依赖数据自身的特征信息, 利用统计学或者机器学习算法对数据进行补全、异常检测以及标准化处理等, 无需考虑数据的物理特性以及专家经验. 当数据存在部分缺失问题, 可以利用多项式插值、克里金插值、函数拟合、K-means聚类等方法[49-56]实现数据的补全. 当数据存在异常值的问题, 可以利用有监督学习算法比如基于二分类器以及多分类器方法, 也可以利用无监督学习算法如基于相关性检测、基于密度检测以及基于距离的检测等手段[57-61]. 除此之外, 面向流体力学各个场景时, 不同物性参数的量纲或者量级存在明显的差异性, 当他们作为输入参数直接导入到数智模型时, 这种差异性会导致模型容易出现欠拟合的情况, 影响预测精度, 因此数据的标准化处理也是极为重要的, 主要包括最小最大归一化、z-score规范化、对数函数转换法等. 如基于克里金模型对稳态空气动力学进行建模[62]. Kashefi等[63]通过归一化对模拟数据进行了预处理并用于在不规则域中进行流场预测[63].
2.1.2 含物理约束的数据治理
仅数据特征的数据治理方法是从数据自身的角度出发, 对数据中存在的缺失值以及异常值进行补充及检测, 然而当面对物性参数完全缺失时, 这种治理方法很难发挥其价值. 在这种情况下更多依靠的是含物理约束的数据治理模式, 即利用与目标参数相关性高的其他参数, 通过物理规律或者先验信息进行数值计算, 间接地获得全部的目标参数信息. Yao等[64]提出了一种基于离散经验的插值方法, 可以从机翼表面的稀疏测量数据中获得气动载荷以及流动细节. 对于油、气、水三相渗流的油田开发领域, 如图4所示, 井底流压(BHFP)是关键的物性参数, 对于油气田的产量预测以及生产优化都具有重要的影响. 受限于复杂的地质条件以及开发措施, 井底流压的监测较为困难. 相比而言, 井头压力(WHFP)由于离地面近, 监测起来较为简单, 然而由于人为以及环境因素等干扰, 会存在监测点的压力不连续的问题. 为了获取完整的有效的井底压力数据, 首先利用函数拟合的方法得到连续的随时间变化的拟合曲线, 为尽可能保证数据的真实性, 用真实监测点的数据代替拟合曲线上的数据, 构建出连续的井头压力. 然后基于伯努利方程
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图 4 井底流压的数据治理方法 (1 psi = 6.895 kPa)Figure 4. Data governance of bottom hole fluid pressure (1 psi = 6.895 kPa)$$ \qquad\qquad{P_B} = {P_H} + {\rho _F}gH $$ (1) $$\qquad\qquad {\rho _F} = \frac{{\displaystyle\sum\nolimits_{j = 1}^J {{\rho _j}{V_j}} }}{{\displaystyle\sum\nolimits_{j = 1}^J {{V_j}} }},J \in {N^ * } $$ (2) 其中, PB和PH分别为井底流压和井头压力, ρF为流体的密度, ρj和Vj分别为流体的密度和体积, 这里J包括油、气、水三相. 基于上述函数拟合以及物理规律, 可以计算出完整的井底流压. 因此, 含物理约束的数据治理模式在面向流体力学具体的应用场景时, 往往发挥了更为重要的作用.
针对油气领域开发过程中动态数据常见的缺失、异常以及冗余问题, 如表2所示, 需要根据场景的数据特征、物理背景和专家经验研究制定针对不同数据类型的清洗规则, 将仅数据特征的治理方法和含物理约束的治理手段相互结合, 最终形成一套完善且高效的治理体系. 值得注意的是, 真实的油藏开发过程中, 数据的治理极为关键, 往往占用超过一半以上的开发周期, 也决定了智能模型性能上限.
表 2 油气数据存在的问题及解决方法示例Table 2. Examples of oil & gas data problems and solutionsData Description Problems Solutions Features production production is not 0, choke size is 0 abnormal depending on the choke size, the production is defaulted to 0 data +
experiencemultiple sets of records at the same
timeredundant subject to the first record data +
experienceinjection well has no injection volume but pressure abnormal depending on injection volume, the pressure is defaulted to 0 data +
experienceproduction record error abnormal complemented by differential methods relying on adjacent records data +
experiencepressure days of wellhead pressure monitoring are far less than the days of drainage missing based on function fitting and machine learning algorithms based on well head pressure data days of bottom hole pressure monitoring are far less than the days of drainage missing calculated from the wellhead pressure based on the Bernoulli equation, or complemented by distance interpolation based on the average pressure of surrounding wells data +
physics +
experiencepressure is completely missing missing based on the bottom pressure of each single well and considering the frictional resistance, set the outer boundary pressure constraint and use kriging interpolation to complete data +
physicssaturation days of saturation monitoring are far less than the days of drainage missing calculated by combining the classic seepage equation and relative permeability curve, or complemented by distance interpolation according to known saturation and injection conditions data +
physics +
experiencesaturation is completely missing missing based on the saturation data of each single well, set saturation constraints and use kriging interpolation to complete data +
physics2.2 智能算法
2.2.1 纯数据驱动的机器学习算法
纯数据驱动的机器学习算法简单而言就是面向不同场景时机器学习模型的直接应用, 主要解决流体力学中涉及的分类、回归、聚类以及降维等问题, 主要分为监督学习、无监督学习以及强化学习[65]. 在数智流体力学中, 监督学习是最主要的建模算法. Gholizadeh等[66]基于温度、体积分数、纳米颗粒尺度以及颗粒密度等参数利用随机森林算法准确地估计了纳米流体的黏度. Li等[67]用极限梯度提升算法来检测湍流区域. Song等[68-69]结合数值模拟技术并利用卷积神经网络(CNN)对储层渗透率进行预测, 实现了井间连通性的评价以及纵向非均质性的标定. 一种融合了计算流体力学以及反向传播网络的粒子群优化算法被用于预测和优化空气质量[70]. Sekar等[71]以数据驱动的方式, 利用深度神经网络预测机翼上不可压缩层流稳定流场. Han等[72]和Bukka等[73]探讨了基于深度学习的非定常流动预测. 一些机器学习方法也被用于涡旋尾流的分类[74]以及检测边界层中的湍流[75]及圆柱绕流等问题[67].
除了监督学习, 无监督学习算法在流体力学领域中也取得了很好的应用效果[76-77]. Huang等[78]提出了一种用于喷墨打印中液滴演化预测的无监督学习算法. Aulakh等[79]使用离散损失函数在计算流体力学中进行无监督学习并建立了数据恢复的通用框架. Kim等[80]开发了不同雷诺数下湍流的无监督学习算法. Zhang等[81]成功实现了无监督学习算法在低渗透油藏采油预测中的应用. Brunton等[82]通过非线性动力系统的稀疏识别从数据中发现控制方程.
强化学习也被广泛运用于流体力学相关的控制策略中[83-85]. Colabrese等[86]利用强化学习来训练智能惯性粒子以针对具有高涡量的特定流动区域. Guéniat等[87]也基于强化学习讨论了利用稀缺和流数据的复杂系统闭环控制策略. 深度强化学习为开发能够利用复杂流动环境的机器人设备提供了一个有前途的框架[88].
2.2.2 基于物理信息的机器学习算法
基于物理信息的机器学习算法是指将物理信息通过多种方式引入到机器学习模型中, 直接或者间接指导AI模型的训练, 使其具有更加强大的自适应能力. 广义而言, 将物理信息引入到智能模型的主流方式可以分为以下四种嵌入机制: 基于输入数据、基于模型架构、基于损失函数以及基于模型优化的嵌入机制, 如图5所示. 基于物理先验信息的机器学习算法不但具备了机器学习强大的自学习能力, 而且融合了物理背景使得模型具有更高的精度和可解释性.
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图 5 物理信息引入机器学习的四种嵌入机制Figure 5. Four embedding mechanisms of physics-informed machine learning(1) 基于输入数据的嵌入机制
基于输入数据的嵌入模式主要涵盖了: 数据筛选、数据融合以及注意力机制. 机器学习模型是由数据驱动的, 输入数据对于模型的训练而言至关重要. 因此, 基于输入数据的物理信息嵌入机制是较为灵活且有效的引入手段.
方式一为数据筛选, 即从多维的参数中筛选出与场景的关联性强、切合度好且质量高的参数作为模型的输入, 如基于物理规律以及专家经验选取适合的物性参数, 此类主要依赖领域专家经验估计的筛选方式简单易行且应用范围广泛, 但当参数数量较多, 这种方式的筛选效率低、可靠性差. 如Zimmermann等[89]将集成的空气动力学系数数据与流动模式融合, 用于稳定流动重建. 在湍流机器学习中引入伽利略不变量[90-91]湍流模型系数校准[47]. 另外, 某些由专家经验筛选出来的物性参数虽然具有重要的物理意义, 但是由于监测手段等因素干扰导致数据被污染严重, 大大降低此类数据的实际价值. 因此, 一些自动化的特征筛选方法也被提出, 主要分为过滤法、包装法以及嵌入法. 过滤法是通过计算参数之间的相关性作为特征筛选的依据, 是一种可以独立的预处理方法, 主要包括卡方检验、t检验、皮尔森相关系数等[92-96]. 包装法需要依赖学习算法作为性能评估的基模型, 通过搜索策略来对输入参数的敏感性进行分析, 如递归特征消除、置换检验等[97-101]. 嵌入法是将特征选择的过程和机器学习算法相互嵌入, 在训练过程中同步实现特征筛选, 如重要性分析、Lasso回归、岭回归等[102-107].
方式二为数据融合, 为了在模型准确性和数据生成成本之间保持良好的平衡, 以数据融合为动力的数据驱动建模越来越受到关注. 尽管其定义在不同的科学界有所不同, 但数据融合通常是指将来自多个来源的数据和信息进行组合的过程以实现对于数据更深层次的挖掘利用. 如自动编码器用于空气动力学优化中的几何降维[108]. Xie等[109]开发了物理感知的数据增强步骤, 结合对抗生成网络解决了流体流动的超分辨率问题. Dobuis等[110]利用正交分解等数据降维方式来提取主导空间方向, 进而实现非定常流体流场的重建.
方式三为注意力机制, 从命名上可以看出, 该机制借鉴了人类视觉注意力机制. 当人眼对全局图像进行扫描时, 大脑特有的信号处理机制会对重要的信息区域投入更多的注意力, 从而忽略一些无用的信息, 通过有限的注意力资源从庞大的数据中筛选出关键信息, 提升数据处理的准确性和效率. 因此, 注意力机制的引入可以使得模型在训练过程中聚焦于关键的输入数据, 抑制一些噪声数据带来的影响, 进而提升模型的预测精度和效率[111-113]. Wu等[114]提出了具有自注意力机制的卷积自动编码器的新型降阶模型, 提高了网络对于输入数据的特征提取能力, 并在圆柱绕流中得到验证. 基于注意力机制的增强网络模型被用于学习高雷诺数湍流独特的流动特征[115], 注意模块通过自动调整不同区域的权重来捕获湍流的非平衡性. 其主要结构如图6所示:
注意力模块包括了三个子模块: 查询矩阵(Wf)、键矩阵(Wg)和值矩阵(Wh). 基于三个子模块去计算出通道注意力Mc以及空间注意力Ms如下
$$ \left.\begin{split} &{\boldsymbol{Mc}} = {{\boldsymbol{W}}_h}{{\boldsymbol{v}}_t}\left( x \right)\\ &{\boldsymbol{Ms}} = \frac{{\exp \left( {{{\boldsymbol{s}}_{ij}}} \right)}}{{\displaystyle\sum\nolimits_{i = 1}^N {\exp \left( {{{\boldsymbol{s}}_{ij}}} \right)} }}\\ &{{\boldsymbol{s}}_{ij}} = {\left( {{{\boldsymbol{W}}_f}{{\boldsymbol{v}}_t}\left( {{x_i}} \right)} \right)^{\rm{T}}}\left( {{{\boldsymbol{W}}_g}{{\boldsymbol{v}}_t}\left( {{x_j}} \right)} \right)\end{split}\right\} $$ (3) 可以得到新的基于注意力机制的特征如下
$$ {{\boldsymbol{v}}_t}{\left( x \right)^\prime } = {\boldsymbol{Ms}} \cdot {\boldsymbol{Mc}} $$ (4) 将傅里叶神经网络(FNO)和注意力机制相融合构建的注意力增强网络, 可以更好地预测不同雷诺数下湍流的涡旋.
(2) 基于模型架构的嵌入机制
在面向具体的流体力学应用场景时, 数据维度的严重不平衡以及物性参数的重要程度都会影响数智模型的准确性, 比如随时间变化的压力、流量等动态数据高达几千个, 但是静态数据如孔隙度、渗透率等仅有几个, 当他们同时作为输入数据导入到机器学习模型中时, 这种数据维度的差异性会使得具有重要物理意义的静态数据被忽视. 因此, 很多学者通过改变机器学习模型的架构来解决这类问题[116-122], 如图7所示. 一种常见的方式是可以将具有重要价值的物性参数放到更加深层的神经网络结构中, 以此来增大这些参数在模型训练过程中的影响力. 另一种是建立组合式的模型, 针对不同机器学习模型所擅长的能力, 比如将善于提取图片数据特征的卷积神经网络和善于对时间序列数据进行预测的长短时记忆网络(LSTM)组合, 构建了组合式的ConvLSTM模型, 这种结合架构更适合处理对于整个流场随时间的演化问题. Fukami等[123]利用混合卷积神经网络模型对湍流数据进行超分辨率分析并重建高分辨率流场. Hou等[124]结合了循环神经网络和卷积网络以表面压力作为输入实现了对临界参数的智能预测. Lin 等[125]建立了DeepONet网络结构用于多速率气泡增长问题的宏观和微尺度建模. 多保真神经网络框架被开发, 可以根据组成成分成功预测该流体的稳态剪切黏度[126]. Tang等[127]利用ConvLSTM方法可以对现实中地下流动问题的数据同化进行改进和评估. 这种混合的神经网络模型也在流速预测、降阶建模、流动模拟等方面广泛应用[128-131].
(3) 基于损失函数的嵌入机制
基于损失函数的嵌入机制一般又称为物理信息的神经网络(PINN), 该思想来源于美国布朗大学Raissi等[132]所提出的基于物理的深度学习框架, 其有效性和可行性通过解决了在流体、量子力学以及反应扩散系统等遇到的一系列经典流体力学问题得以证明. 神经网络模型得以自主训练的关键就是在于其可以根据损失函数计算的误差, 利用反向传播算法不断地自主更新模型中的权重和阈值, 因此损失函数参与并指导了神经网络中每一次的迭代训练. 基于损失函数的物理嵌入机制主要聚焦于流体力学中偏微分方程的正、反解问题[133-137].
正问题是指根据自然顺序探究事物的演化过程, 比如不同场景中流场演化, 动态参数的变化等. 因此正问题的求解具有更加广阔的发展潜力, 同时也适用于更多的物理应用场景. 以Wang等[138]构建的理论指导的神经网络(TgNN)模型预测地下流动中水头演化为例, 饱和均质多孔介质中地下流动应满足控制方程为
$$ {S_s}\frac{{\partial h}}{{\partial t}} = K\frac{{{\partial ^2}h}}{{\partial {x^2}}} + K\frac{{{\partial ^2}h}}{{\partial {y^2}}} $$ (5) 其中K为水力传导系数, h为水头. 边界条件以及初始条件可以分别表示为
$$ h\left( {{x_{BC}},{y_{BC}}} \right) = {h_{BC}},\begin{array}{*{20}{c}} {}&{}&{h\left( {{t_{IC}}} \right)} = {h_{IC}}\end{array} $$ (6) 此外, 在某些特定的边界和初始条件时, 水头值可能落在某个范围或者小于某个值, 因此一些工程控制以及专家经验也能有效指导模型的构建, 可以分别表示为
$$ EC\left( {t,x,y} \right) \leqslant 0,\begin{array}{*{20}{c}} {}&{}&{EK\left( {t,x,y} \right) \leqslant 0} \end{array} $$ (7) 常规的基于数据驱动的损失函数可以表示为
$$ MS{E_{{\rm{DATA}}}} = \frac{1}{N}{\sum\nolimits_{i = 1}^N {\left| {N{N_h}\left( {x,y,t;\theta } \right) - H} \right|} ^2} $$ (8) 为了更好地预测水头的演化, 可以将控制方程、初始条件、边界条件、工程控制以及专家经验等物理信息引入到损失函数中, 进而更好地指导深度学习模型的训练. 以控制方程为例, 首先构建基于控制方程的残差函数为
$$ \begin{split} &f = {S_s}\frac{{\partial N{N_h}\left( {x,y,t;\theta } \right)}}{{\partial t}} - K\frac{{{\partial ^2}N{N_h}\left( {x,y,t;\theta } \right)}}{{\partial {x^2}}} - \\ &\qquad K\frac{{{\partial ^2}N{N_h}\left( {x,y,t;\theta } \right)}}{{\partial {y^2}}}\end{split} $$ (9) 其中θ表示神经网络中的权重和阈值, NN表示神经网络的预测, 这些偏导数通过自动微分对网络应用链式法则很容易求取. 因此, 对于控制方程的损失函数项可以表示为
$$ {MSE_{{\rm{PDE}}}} = \frac{1}{{{N_f}}}{\sum\nolimits_{i = 1}^{{N_f}} {\left| {f\left( {{x_i},{y_i},{t_i}} \right)} \right|} ^2} $$ (10) 同理, 对于其他的边界条件、初始条件等都可以构建相应的损失函数项, 最终形成的总的损失函数被表示为
$$ \begin{split} &L\left( \theta \right) = {\lambda _1}{MSE_{{\rm{DATA}}}} + {\lambda _2}{MSE_{{\rm{PDE}}}} + {\lambda _3}{MSE_{IC}} + \\ &\qquad {\lambda _4}{MSE_{BC}} + {\lambda _5}{MSE_{EC}} + {\lambda _6}{MSE_{EK}}\end{split} $$ (11) 其中L为总的损失函数,
$\lambda $ 为各项权重的控制系数, MSEDATA和MSEPDE分别为数据驱动项损失以及控制方程项损失, MSEIC和MSEBC分别为初始条件和边界条件项损失, MSEEC和MSEEK分别为工程控制以及专家经验项损失. 基于理论指导的神经网络架构如图8所示.如图9所示, 以在第50个时间步对于水头的预测结果为例, 图9(a)为实际的参考值, 图9(b)是引入了理论指导的神经网络模型预测结果, 图9(c)是常规的深度神经网络模型(DNN)预测结果. 由图可得, 引入了物理信息的神经网络具有更高的预测精度, 证明了构成先验知识的理论如控制方程等约束条件可用于指导神经网络的训练, 减少神经网络模型对于数据本身的依赖性.
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反问题的求解指的是通过事物的演化结果及可观测现象, 探索事物的内在规律. 以Navier-Stokes方程描述的不可压缩流体流动为例, 完整和简化形式的 Navier-Stokes 方程有助于模拟天气、洋流、飞机和汽车的设计、血液流动、污染物扩散分析等许多应用. 具体的二维Navier-Stokes 方程[139]可以被描述为
$$ {u_t} + {\lambda _1}\left( {u{u_x} + v{u_y}} \right) = - {p_x} + {\lambda _2}\left( {{u_{xx}} + {u_{yy}}} \right) $$ (12) $$ {v_t} + {\lambda _1}\left( {u{v_x} + v{v_y}} \right) = - {p_y} + {\lambda _2}\left( {{v_{xx}} + {v_{yy}}} \right) $$ (13) 其中u和v分别表示速度的x分量和y分量, p为压力, λ1和λ2为系数(参考值为λ1 = 1, λ2 = 0.01). 所构建的残差函数为
$$ f = {u_t} + {\lambda _1}\left( {u{u_x} + v{u_y}} \right) + {p_x} - {\lambda _2}\left( {{u_{xx}} + {u_{yy}}} \right) $$ (14) $$ g = {v_t} + {\lambda _1}\left( {u{v_x} + v{v_y}} \right) + {p_y} - {\lambda _2}\left( {{v_{xx}} + {v_{yy}}} \right) $$ (15) 总的损失函数可以表示为
$$ \begin{split} &Loss = \frac{1}{N}\sum\nolimits_{i = 1}^N {\left[ {{{\left( {u\left( {{t_i},{x_i},{y_i}} \right) - {u_i}} \right)}^2} + {{\left( {v\left( {{t_i},{x_i},{y_i}} \right) - {v_i}} \right)}^2}} \right]} +\\ &\qquad \frac{1}{N}\sum\nolimits_{i = 1}^N {\left( {f_i^2 + g_i^2} \right)}\\[-12pt]\end{split} $$ (16) 值得注意的是, 正问题的核心是通过数智模型学习以前的流速场, 对未来流速场的演化进行预测, 即u和v. 反问题的核心是利用数智模型对于流速场的学习来调整关键系数
$ \lambda $ , 使其在自训练过程中得到最优的$ \lambda $ 值. 对于Navier-Stokes方程不可压缩流体圆柱绕流而言, 首先初始化一组λ1.0和λ2.0, 图10中展示了数智模型在训练过程中, 系数$ \lambda $ 随着迭代次数进行的动态调整[140], 可以看到, 尽管设置了不同的初始值, 但是在数智模型自学习过程中, 系数λ可以自动调整到期待的参考值, 这也证明了基于损失函数的物理嵌入方法所构建的数智模型具有对于反问题求解的能力.除此之外, 很多学者基于PINN的思想提出了改进算法去更好地解决多相流以及流场建模等问题. Almajid等[141]利用引入了物理信息的神经网络模型对多孔介质中流体流动进行有效预测. 金晓威等[142]提出了一种物理增强的流场深度学习建模集模拟方法. Cheng等[143]提出了结合Resnet模块的神经网络模型求解流体流动, 实现了对速度场和压力场的有效预测. He等[144]开发了MPINN模型对地下传输问题中的参数和状态进行估计. Kissas等[145]利用机器学习方法对心血管血液流动建模并成功预测动脉血压. Chiu等[146]采用了数值微分与自动微分相耦合定义损失函数, 建立了can-PINN框架在面对流体流动模拟时表现出了更好的性能. 董彬等[147]探讨了深度学习在偏微分方程中的反问题求解. Pang等[148]使用分数阶微积分中的数值微分公式来表示分数算子以及利用自动微分来表示整数阶算子, 构建了fPINN框架实现偏微分方程求解. Kharazmi等建立[149]了hp-VPINN求解框架可以有效定位网络参数并进行参数优化, 在节约训练成本方面具有很大优势. 更多的基于PINN的衍生框架如XPINN和cPINN被提出用于多尺度和多物理问题的求解[150-151].
(4) 基于模型优化的嵌入机制
基于模型优化的嵌入机制是指通过引入优化算法来加强机器学习模型对于物性信息的学习能力, 进而提高模型的预测精度以及计算效率. 优化算法的嵌入一方面可以优化机器学习模型的超参数[152-155], 超参数是指模型预设的参数, 例如对于深度神经网络而言, 隐含层的层数以及神经元的个数等都是重要的超参数, 层数过少会导致模型学习物性参数之间的非线性映射关系的能力变差, 层数过多会出现过拟合等问题, 这些超参数可以影响模型的结构. 还有一些超参数不会直接改变模型的结构, 但是会影响模型的学习效率, 比如学习率、优化器等. 传统的优化算法包括网格搜索以及随机搜索, 网格搜索通过遍历整个参数范围达到寻优目的, 当参数过多或者范围过大时, 往往需要大量的计算时间, 随机搜索虽然一定程度缓解了网格搜索的局限性, 但是容易陷入局部最优解中. 因此, 一些启发式的优化算法被用于和机器学习模型相结合去更加高效地进行模型优化, 如粒子群算法、模拟退火算法以及遗传算法等[156-163].
另一方面, 优化算法的嵌入可以优化神经网络的权重, 如将贝叶斯算法嵌入到神经网络中开发出贝叶斯网络模型[164-168]. 众所周知, 神经元之间的权重是影响神经网络性能的关键, 常规的网络模型在经历反向传播后, 更新的权重是个固定值, 贝叶斯网络是将权重变为服从均值为μ, 方差为δ的高斯分布, 即贝叶斯网络所优化的实质是不同神经元之间权重的均值和方差. Maulik 等[169]开发了数据驱动的湍流闭合框架, 并结合超参数优化分析用于湍流的亚网格建模. Sun等[170]设计了基于物理约束的贝叶斯优化神经网络模型, 用于在稀疏和噪声数据中重建流体流动. Hirschen等[171]也利用贝叶斯正则化的神经网络优化流体流动过程. Meng等[172]将贝叶斯引入到神经网络中对偏微分方程反问题进行求解. Owoyele等[173]将遗传算法和机器学习相结合优化超参数, 经过和计算流体力学模拟效果验证具有更好的预测性能.
3. 数智流体力学在油气渗流领域的应用
随着油气勘探开发手段的日渐成熟和飞速发展, 油田已经积累了海量的多源异构数据体, 如何将庞大的数据资源有效地转化为数据资产是油田现场面临的主要难题. 对于油气渗流领域而言, 一个核心的科学问题是如何建立面向多场景的油气多源异构数据治理体系, 由于人为环境、地质结构以及流动机理等复杂性, 油田收集到的数据往往存在大量的数据缺失、数据异常以及数据冗余等问题, 因此需要深度结合物理规律以及专家经验, 针对具体场景和数据类型构建完善的数据治理体系, 提高数据质量, 进而为油气数据挖掘打下坚实的基础. 另一个关键的科学问题是如何打造面向油气领域高度智能化自动化的应用生态环境. 针对油气领域生产开发的各个环节, 将先验信息和人工智能相融合, 构建基于“物理 + 数据”双驱动模式的智能模型, 显著提高计算效率和精度, 完成油气多场景的智能化“落地”, 实现降本增效的目的.
目前, 国内外大量学者都致力于智能油气开发的研究中. Liu等[174-175]详细阐述了人工智能在石油勘探领域的应用及发展, 包括岩性识别、测井解释以及参数预测等方面. 李道伦等利用神经网络实现了径向复合油藏试井解释[176]、产量预测[177]以及渗流方程求解[178]. Liu等[179]基于测井数据并结合知识图谱技术实现了油气层智能识别, 并且总结了知识图谱技术在油气上游领域的构建及应用[180]. 张凯等将优化算法和机器学习相结合, 实现了油藏井位优化[181]、实时生产优化[182]、注采优化[183]等. Mousavi等[184]根据地面接收器记录的波形特征, 使用机器学习算法区分深部微震事件和浅层微震事件. Mohaghegh等[185]通过深度学习实时识别钻井异常. Goebel等[186]利用管道旋度、倾角和流速等参数智能预测未来的卡钻. 还有大量的智能算法已经成功应用于油藏勘探、测井、录井、生产、优化等各个方面[187-193].
3.1 面向油气领域的储层剩余油分布智能预测
储层剩余油分布是指储层的含油饱和度, 涉及宏观尺度上流场建模及多物理场耦合问题. 当油田开发步入中后期阶段, 剩余油分布在提高采收率以及油藏二次开发方面起着至关重要的作用. 对于真实的储层而言, 所面临的第一个挑战就是饱和度数据在时间维度和空间维度的严重缺失, 通常饱和度的获取是利用测井解释计算而来[194]. 对于时间维度上饱和度数据不连续的问题, 利用完整的实际监测压力和产量数据, 根据物理规律得到油相相对渗透率, 通过油、水和油、气的相对渗透率曲线获取其含水和含气饱和度, 最后根据饱和度约束条件得到含油饱和度. 具体而言, 水平井中的流动被简化为水平截面的平面径向流动和尾端的球形向心流动. 假设球形向心流的半径远大于井筒半径, 那么水平井的产量公式为
$$ {Q_{{\text{horizontal}}}} = \frac{{2\text{π} {K_p}L\left( {{P_e} - {P_{{\rm{Bottom}}}}} \right)}}{{\mu \ln \left( {{{R} _e}/{{R} _W}} \right)}} + \frac{{2\text{π} {K_p}{{R} _W}\left( {{P_e} - {P_{{\rm{Bottom}}}}} \right)}}{\mu } $$ (17) 其中, Kp为相渗透率, L为水平井长度, Pe为地层压力, Re和RW分别为外边界到井筒的距离以及井筒半径. 对于直井而言, 只发生平面径向流, 因此直井的产量公式为
$$ {Q_{{\text{vertical}}}} = \frac{{2\text{π} {K_p}L\left( {{P_e} - {P_{{\rm{Bottom}}}}} \right)}}{{\mu \ln \left( {{{R} _e}/{{R} _W}} \right)}} $$ (18) 基于上述公式, 可以计算出在不同井型下油相的相对渗透率为
$$ {K_r} = \left\{ {\begin{array}{*{20}{l}} {\dfrac{{\mu {Q_{{\text{horizontal}}}}}}{{2\text{π} {K_a}\left( {{P_e} - {P_{{\rm{Bottom}}}}} \right)\left[ {\dfrac{L}{{\ln \left( {{{R} _e}/{{R} _W}} \right)}} + {{R} _W}} \right]}}},\;{ {{\text{horizontal}}}\;{{\text{well}}} } \\ {\dfrac{{\mu \ln \left( {{{R} _e}/{{R} _W}} \right){Q_{{\text{vertical}}}}}}{{2\text{π} L{K_a}\left( {{P_e} - {P_{{\rm{Bottom}}}}} \right)}},}\;\;{ {{\text{vertical}}}\;{{\text{well}}} } \end{array}} \right. $$ (19) 其中, Ka为绝对渗透率, Kr为相对渗透率. 然后, 结合油、水和油、气的相对渗透率曲线, 可以求得时间上连续的含水和含气饱和度. 最后依据饱和度的物理约束条件得到完整的含油饱和度数据
$$ {S_o} + {S_w} + {S_g} = 1 $$ (20) 其中, So, Sw, Sg分别为含油、含水和含气饱和度. 对于空间维度的不连续问题, 可以利用克里金插值计算得到完整的饱和度场数据体, 值得一提的是研究中该数据的治理占用了超过50%的工作量, 其结果如图11所示.
为了预测随时间变化的饱和度场分布, 输入的样本数据是由在先前时刻下的含油、含水、含气饱和度场以及压力场叠加而成的数据立方体, 输出的是未来时刻的含油、含水、含气饱和度场以及压力场分布. 针对整个场数据的时间序列预测问题, 充分利用卷积神经网络对于空间数据特征的提取能力, 通过卷积核同时提取多个物理场的空间特征, 并且发挥长短时记忆网络对于时间序列数据的记忆特性, 学习各个物理场随时间的变化信息, 构建卷积长短时记忆网络融合模型(ConvLSTM), 实现对于未来含油、含水、含气饱和度分布预测. 基于ConvLSTM模型的训练流程如图12所示.
图13所示为研究中所构建的ConvLSTM模型对于含油、含水以及含气饱和度的预测效果. 根据预测饱和度以及实际饱和度的散点交汇图可知, ConvLSTM模型对于含水饱和度的预测精度最高, R2达到了0.96. 在含气饱和度现场预测方面, 在0 ~ 0.15范围内含气饱和度预测不准确导致整体的预测性能出现了下降, R2也达到了0.96. 对于含油饱和度预测而言, 模型的R2也可以达到0.80. 因此, 基于ConvLSTM建立的饱和度预测模型表现出了较好的预测性能.
3.2 基于数字岩心的物性参数智能预测
利用数智模型直接从数字岩心图像中快速预测渗透率是一种具有巨大潜力的新型孔隙尺度建模方法. 渗透率是地下流动问题中最重要的属性之一, 可以衡量岩石传输流体的能力. 一般地, 渗透率的确定主要是利用实验室测定以及数值模拟两类方法, 无一例外他们都非常耗时. 因此, 大量学者通过开发数智模型并引入物理信息实现了对于渗透率的快速预测[195-196]. 对于二维(2D)的数字岩心图片来说, Wu等[197]利用Voronoi空间分割算法建立了不同孔隙度和渗透率的数字岩心图片, 每张图片尺寸为600 × 600像素. 然后利用格子玻尔兹曼方法(LBM)计算出所有数字岩心图片的渗透率. 接着以2D的数字岩心图片为输入, 以渗透率为输出, 构建了基于物理信息的神经网络模型, 该模型通过将孔隙度和比表面积这两个重要的物性参数引入到深层的网络结构中, 实现了基于模型架构的物理信息嵌入, 其模型结构如图14所示.
结果如图15所示, 横轴表示样本数, 纵轴为渗透率. Kozeny-Carman方程是通过孔隙度以及比表面积计算渗透率的一种传统求解方法, LBM代表了本次研究所参考的真实渗透率, 图15(a)是利用常规的卷积神经网络的预测效果, 图15(b)是引入了物理信息的神经网络模型的预测结果. 可以明显看到, 传统方法计算的渗透率和实际渗透率相差较大, 利用常规的卷积神经网络构建的数智模型明显提升渗透率的预测精度, R2为0.878 6, 表明了数智模型可以更好地学习数字岩心图片和渗透率之间的非线性映射关系. 更进一步地, 将孔隙度和比表面积嵌入到深层神经网络中所建立的模型表现出了更好的预测性能, R2值达到了0.884 6, 证明了物理信息的引入可以增强网络的预测能力.
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除了2D的数字岩心, Tang等[198]更进一步利用3D尺度的数字岩心预测渗透率. 首先利用Joshi-Quiblier-Adler方法来快速重构3D的孔隙结构体, 共计生成了4500个大小为128 × 128 × 128的数字岩心结构, 接着利用LBM方法模拟流体在3D的孔隙结构体中的流动, 从而计算出相应的渗透率. 这次研究中共建立了三种数智模型. 第一个是常规的神经网络模型ResNet, 它是一种较为通用的卷积神经网络结构体, 已经在图像识别、视觉追踪等多个领域取得了理想的应用效果. 第二个是基于模型架构改进的CNN模型, 与一般的 CNN 不同, dense block 中每个卷积层的输入是由之前所有 dense layers 的输出组成,如图16(a). 这种直连式网络结构设计使得特征和梯度的传递更加有效. 第三个模型是在改进的CNN架构基础上, 将孔隙度和迂曲率引入了每个dense block中, 构建了引入物理信息的神经网络模型CNNphys, 如图16(b).
基于3D数字岩心的渗透率预测结果如图17所示, 可以看到传统的Kozeny-Carman方程预测结果的R2只有0.002, 与实际渗透率相比出现了较大的预测偏差, 表明了传统方法在预测3D数字岩心的渗透率时性能较差. 通用的CNNResNet模型预测R2达到了0.954, 说明了数智模型具有很好的预测效果. 进一步地, 改进了模型架构的CNN模型以及引入了孔隙度和迂曲率CNNphys模型可以将预测精度提升到0.985和0.994, 证明了物理信息的引入可以很好地提升数智模型的预测精度.
3.3 考虑物理约束的煤层气压裂效果智能评价
由于煤层气储层的低渗透率, 水力压裂技术已被证实是煤层气开发的必要和有效手段, 它可以加速煤层气的解吸, 从而获得更好的生产性能[199]. 因此, 对于煤层气藏压裂效果评价对于后续的生产优化以及经济效益都至关重要. 传统的微地震技术以及数值模拟方法往往存在造价高昂、开发周期长, 以及预测效果不佳等问题. Song等[200]构建了考虑物理约束的神经网络模型, 建立组合网络结构充分提取动态生产数据、静态地质数据、压裂施工数据的特征, 克服因动态参数维数过多而忽略网络中静态参数特征的问题. 然后, 在损失函数中加入初始条件、工程控制和专家经验, 建立以物理规律为指导的深度神经网络, 可以准确预测压裂后的渗透率和裂缝半长, 有效评价压裂效果. 其模型结构如图18所示.
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对于收集到的煤层气藏动态数据而言, 往往存在数据异常以及缺失等问题, 因此首先利用局部异常因子(LOF)方法对于产量数据中异常值进行检测, 然后通过极限学习机(Xgboost)方法基于压力等数据对产量进行智能反演, 从而补全产量中的缺失值, 构建基于LOF-Xgboost的煤层气动态产量数据治理框架[201]. 如图19所示, 相比于传统One-class SVM和孤岛森林方法, LOF可以更好地检测出原始产量数据中的异常值. 除此之外, 如图20所示, 横轴表示真实的产量, 纵轴为预测值. 基于Xgboost方法构建的产量智能补全模型所形成的交汇点基本汇聚在y = x红色虚线附近, 相比于其他机器学习算法, 该模型展现出了最高的预测精度, 可以很好地实现对于缺失产量的补全.
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实验中将控制方程、初始条件和专家经验结合到损失函数中, 以构建具有物理约束的数据驱动的深度神经网络. 如图21所示, 横坐标为渗透率和裂缝半长, 纵坐标为不同模型预测结果与实际参考值的相对偏差. 图中黑色虚线表示y = 0, 即理想条件下无偏差. 蓝色的点是基于物理信息的神经网络模型的预测值, 可以明显看出, 与普通深度学习模型相比, 物理约束的深度神经网络计算出的散点基本分布在y = 0附近, 无论是渗透率还是裂缝半长, 都明显更加集中. 同时, 以渗透率为例, 具有物理约束的深度学习模型的整体预测偏差与传统深度神经网络相比下降了约 5%.
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图 21 渗透率和裂缝半长的预测结果Figure 21. Predicted results of permeability and fracture half-length3.4 数据驱动的油藏注采参数智能优化
生产优化在油藏闭环管理中很重要[202-204], 对于注气开发的油藏, 产量和气油比(GOR)的优化是井操作优化的关键, 直接影响经济效益和开发风险. 如果气油比较高, 气体容易发生气窜, 导致注采压力系统损坏. 此外, 一些腐蚀性酸性气体会腐蚀管道和基础设施, 造成严重的安全隐患. 低气油比确保储层可以开发更加长久、安全及高效. 因此, 如何在保持低气油比的同时, 调整注采方案尽可能提高产量成为关键问题. 由于在不确定地质构造中多相流的复杂性, 传统的基于物理的数值模拟不仅计算时间长、资源消耗大, 而且迭代误差大. 因此, 一种结合了贝叶斯随机森林和多目标粒子群优化算法的集成框架被开发用于对油藏注采参数进行优化. 首先利用随机森林算法构建注采系统代理模型, 可以通过生产井的生产措施如开关井状态、油嘴大小以及注入井的注入数据如注入量、注入压力等, 实现对生产井动态的产油量、产气量及气油比的精准预测, 同时融合贝叶斯搜索算法对随机森林中的超参数进行优化, 其效果如图22所示.
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图 22 产油量的预测结果 (1 bbl = 0.159 m3)Figure 22. Prediction results of oil production (1 bbl = 0.159 m3)基于训练好的基于贝叶斯随机森林的注采系统代理模型, 利用多目标粒子群优化算法去寻找最优的注采参数, 包括注入量、注入压力等, 经过了5000次的迭代计算后, 其结果如图23所示, 每个粒子表示一种注入参数的组合, 根据设计的两个优化目标, 即高产油量以及低气油比, 寻找帕累托前沿解, 在该前沿中粒子构成的集合即为最优的注采优化解集. 当以最大产油量为目标时, 按照图中红色圆点粒子所对应的注入方案来进行优化, 通过对于累产量的预测, 发现了优化后的方案可以将累计产油量提高约11.7%, 具有较为明显的优化效果.
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图 23 多目标粒子群算法的优化结果 (1 scf ≈ 0.028 m3)Figure 23. Optimization results of multi-objective particle swarm optimization (1 scf ≈ 0.028 m3)4. 总结与展望
本文阐明了数智流体力学的理论内容以及体系框架. 数智流体力学是将流体力学、大数据和人工智能相结合, 以流体力学场景需求为导向, 形成以“数”为基础, 以“智”为核心, 以算力为支撑的新研究范式. 其核心内涵是要以数据驱动为主, 融合物理规律、专家经验等先验信息, 利用智能化手段构建“数据 + 物理”双驱动的数智模型, 解决场景需求问题. 数智流体力学是流体力学未来发展的必然趋势, 不但要积极探索新的智能理论以及方法, 更要深度融合物理认知及规律, 进而攻克流体力学中复杂多变的科技问题. 本次研究的总结如下:
(1)随着大数据算力及智能算法的快速发展, 流体力学诞生了新的研究范式, 形成四种流体力学研究方法, 即实验研究、理论求解、数值模拟、数智分析;
(2)数智流体力学中数智模型的构建主要是由“数”和“智”组成, 以“数”为基础, 以“智”为核心, 以算力为支撑;
(3)数据治理工作往往要占数智模型构建较大的工作量, 其决定了智能模型性能的上限, 在实际的工程应用当中, 数据质量是智能算法能否发挥其价值的关键;
(4)智能算法中的“数据 + 物理”协同驱动主要存在四种引入机制, 分别是基于输入数据的嵌入机制、基于模型架构的嵌入机制、基于损失函数的嵌入机制和基于模型优化的嵌入机制.
目前, 数智流体力学在油气渗流领域发展尚处在初步阶段, 很多智能化的应用无法实现真正的“落地”. 一方面缺乏统一的油气数据标准以及完善的数据治理体系, 油气的勘探、测井、录井、生产等不同领域各种类型的数据, 需要依赖充足的先验知识提升数据质量; 另一方面是缺乏油气和智能领域的交叉复合型人才, 在实际油田开发过程中, 面向不同场景如何构建“数据 + 物理”协同驱动的智能模型, 可以实现智能模型的“落地”以及快速“迁移”, 也是一个关键问题. 因此, 油气领域智能化发展需要油气公司、科研院所以及高校之间通力协作, 通过数智流体力学在保证数据安全的前提下形成以数据为基础、算法为核心、算力为支撑的油气大数据智能应用平台, 面向各方面人才打造多元化开放式油气应用生态, 最终实现降本增效的目的.
流体力学未来的发展需要经典流体力学、计算流体力学以及智能流体力学的交叉融合和通力协作, 一方面要将经典流体力学、计算流体力学中所含的物理信息更多引入到智能流体力学中, 增强数智模型的物理可解释性; 另一方面也要充分发挥数智流体力学在计算精度和速度方面的优势, 以数据驱动的方式为经典流体力学、计算流体力学提供智能化的误差修正以及参数指导, 最终推动流体力学发展迈向新的台阶.
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图 1 流体力学四种研究方法的数据流形式图
Figure 1. Data flow in four types of research method for fluid mechanics
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图 2 大数据、人工智能和石油领域结合的论文数量统计(OnePetro数据库)
Figure 2. Statistics of papers combining big data, artificial intelligence and petroleum industry (OnePetro database)
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图 4 井底流压的数据治理方法 (1 psi = 6.895 kPa)
Figure 4. Data governance of bottom hole fluid pressure (1 psi = 6.895 kPa)
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图 5 物理信息引入机器学习的四种嵌入机制
Figure 5. Four embedding mechanisms of physics-informed machine learning
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图 21 渗透率和裂缝半长的预测结果
Figure 21. Predicted results of permeability and fracture half-length
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图 22 产油量的预测结果 (1 bbl = 0.159 m3)
Figure 22. Prediction results of oil production (1 bbl = 0.159 m3)
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图 23 多目标粒子群算法的优化结果 (1 scf ≈ 0.028 m3)
Figure 23. Optimization results of multi-objective particle swarm optimization (1 scf ≈ 0.028 m3)
表 1 数智流体力学方法及特点
Table 1 Digital intelligence fluid dynamics methods and features
Category Method Feature digital intelligence
fluid mechanicsdata governance data feature-based many applications, suitable for big data stream processing with physical constraints more professional, suitable for data in professional fields artificial intelligence data-driven supervised learning relatively easy, many theoretical and practical applications unsupervised learning relatively easy, mainly for clustering and dimensionality reduction semi-supervised learning relatively easy, used for insufficient sample data, few applications reinforcement learning relatively easy, few applications, mainly for theoretical research physics-informed machine learning input data-based embedding mechanism low difficulty, rely on empirical guidance, many theoretical and practical applications model architecture-based embedding mechanism moderate difficulty, requires lots of trials and empirical guidance loss function-based embedding mechanism high difficulty, high data quality, many theoretical researches and few applications model optimization-based embedding mechanism moderate difficulty, some theoretical researches and few applications 
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表 2 油气数据存在的问题及解决方法示例
Table 2 Examples of oil & gas data problems and solutions
Data Description Problems Solutions Features production production is not 0, choke size is 0 abnormal depending on the choke size, the production is defaulted to 0 data +
experiencemultiple sets of records at the same
timeredundant subject to the first record data +
experienceinjection well has no injection volume but pressure abnormal depending on injection volume, the pressure is defaulted to 0 data +
experienceproduction record error abnormal complemented by differential methods relying on adjacent records data +
experiencepressure days of wellhead pressure monitoring are far less than the days of drainage missing based on function fitting and machine learning algorithms based on well head pressure data days of bottom hole pressure monitoring are far less than the days of drainage missing calculated from the wellhead pressure based on the Bernoulli equation, or complemented by distance interpolation based on the average pressure of surrounding wells data +
physics +
experiencepressure is completely missing missing based on the bottom pressure of each single well and considering the frictional resistance, set the outer boundary pressure constraint and use kriging interpolation to complete data +
physicssaturation days of saturation monitoring are far less than the days of drainage missing calculated by combining the classic seepage equation and relative permeability curve, or complemented by distance interpolation according to known saturation and injection conditions data +
physics +
experiencesaturation is completely missing missing based on the saturation data of each single well, set saturation constraints and use kriging interpolation to complete data +
physics
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