基于物理约束和傅里叶神经算子的压裂水平井产量智能预测新模型

doi:10.3969/j.issn.2096-1693.2025.03.025

摘要/Abstract

摘要：

页岩油井受页岩储层特征及特殊渗流机制影响，常使用压裂水平井开发，产量预测是其压裂方案优化与经济指标评价的重要前提，然而，目前常用的产量预测方法还不够完善。因此，针对上述问题提出一种基于物理约束和傅里叶神经算子(FNO)的压裂水平井压后智能产量预测方法：首先，建立压裂水平井渗流数学模型，求得瞬时产量典型解后，利用商业软件的不稳定产量分析方法(RTA)模块验证，结果显示两者瞬时产量典型解高度一致，再基于该渗流模型生成不同参数范围下的产量数据作为FNO网络数据集；其次，构建FNO网络并进行训练，训练结果显示，在训练集与验证集中，预测值与真实值的决定系数R²均超过0.99，表明网络具备优异的泛化能力；最后，以古龙页岩油H1井为实例，对其未来两年产量进行预测，具体步骤有：(1)收集该井实际生产资料、地质资料、压裂施工资料，结合试井解释得到输入参数；(2)分别采用RTA与FNO方法对H1井日产油量进行预测；(3)对比两种预测方法，发现FNO网络预测结果与RTA预测结果具有高度一致性(离散点决定系数R²为0.95)，证明了FNO网络预测结果的准确性与可靠性，并且FNO网络速度远快于RTA(FNO：1-2s，RTA：600s)。此外，对不同产量智能预测模型展开评估，对比了FNO与Bi-LSTM、LSTM、CNN模型在同一数据集上的训练误差，结果显示，FNO模型在验证集上误差最小，泛化能力最强。因此，基于FNO网络的压裂水平井压后产量预测方法有望为页岩油井压裂优化和经济评价提供理论支撑，助力油气藏高效开发。

关键词: 人工智能, 压裂水平井, 产量预测, 傅里叶神经算子, 试井解释

Abstract:

Due to the influence of shale reservoir characteristics and special seepage mechanisms, hydraulically fractured horizontal wells are commonly used for shale oil development. Production prediction is an important prerequisite for the optimization of fracturing schemes and the evaluation of economic indicators. However, commonly used production prediction methods still have limitations. Therefore, an intelligent post-fracturing production prediction method for fractured horizontal wells based on physical constraints and Fourier Neural Operator (FNO) is proposed to address the above issues. First, a mathematical model for fluid flow in fractured horizontal wells was established to derive typical solution of transient production rate. Validation using the Unsteady Production Analysis (RTA) module within commercial software confirmed high consistency between the model-generated and RTA transient production data. Subsequently, production data across diverse parameter ranges, generated from this validated seepage model, served as the FNO training dataset. Second, an FNO network was constructed and trained. Results demonstrate exceptional generalization ability, with coefficients of determination (R²) exceeding 0.99 for both training and validation sets. Finally, taking Well H1 in the Gulong shale oilfield as an example, the prediction of its oil production for the next two years was conducted.The specific steps are as follows: (1) The actual production data, geological data, and fracturing construction data of the well were collected, and the input parameters were obtained combined with well test interpretation; (2) The daily oil production of Well H1 was predicted using RTA and FNO methods respectively; (3) The two prediction methods were compared, and it was found that the prediction results of the FNO network are highly consistent with those of RTA (the coefficient of determination R² of discrete points is 0.95), which proves the accuracy and reliability of the FNO network prediction results. Moreover, the FNO network is more efficient and much faster in speed than RTA (FNO: 1-2 seconds, RTA: 600 seconds). In addition, we evaluated different intelligent production prediction models and compared the training errors of the FNO model with those of the Bi-LSTM, LSTM, and CNN models on the same dataset. The results show that the FNO model has the smallest error on the validation set and the strongest generalization ability. Therefore, the post-fracturing production prediction method for fractured horizontal wells based on the FNO network is expected to provide theoretical support for the optimization of hydraulically fractured shale oil wells and economic evaluation contributing to the efficient development of oil and gas reservoirs.

Key words: artificial intelligence, fractured horizontal wells, production prediction, FNO, well test interpretation

中图分类号:

高欣, 陈志明, 朱海锋, 宋海强. 基于物理约束和傅里叶神经算子的压裂水平井产量智能预测新模型[J]. 石油科学通报, 2025, 10(6): 1301-1317.

GAO Xin, CHEN Zhiming, ZHU Haifeng, SONG Haiqiang, WEI Yu. A new intelligent prediction model for production of fractured horizontal wells based on physical constraints and fourier neural operator[J]. Petroleum Science Bulletin, 2025, 10(6): 1301-1317.

https://sykxtb.cup.edu.cn/CN/Y2025/V10/I6/1301

图/表 25

图1 压裂水平井物理模型及裂缝离散示意图

Fig. 1 Schematic of the fractured horizontal well physical model

表1 模型输入参数表

Table 1 Model input parameters

参数名称	参数
初始压力/MPa	25
井底流压/MPa	20
原油黏度/(mPa·s)	0.65
孔隙度	0.1
综合压缩系数/MPa^-1	0.001 33
改造区渗透率/mD	1
体积系数/(m³/ m³)	1.03
储层厚度/m	10
裂缝导流能力/(mD·m)	1200
裂缝半长/m	80
裂缝间距/m	40
裂缝倾角/°	90
裂缝条数	10
井筒半径/m	0.09
表皮系数	1
井筒储集系数/(m³·MPa^-1)	0.2

图2 典型产量曲线验证

Fig. 2 Validation of typical production curves

表2 数据集参数范围

Table 2 Dataset parameter ranges

参数名称	参数范围
无量纲井储系数	[0.0001,10]
表皮系数	[0,10]
无量纲导流能力	[1,300]
裂缝半长/m	[30,280]
缝间距/m	[10,100]
裂缝条数/条	[5,50]

图3 产量数据示意图

Fig. 3 Typical production curves of samples

图4 傅里叶神经算子网络结构示意图

Fig. 4 Schematic diagram of the Fourier neural operator architecture

表3 FNO网络参数

Table 3 FNO network parameters

模块	层	尺寸
输入	Input	32×138×7
全连接	Fc1	7×128
傅里叶模块1	Fourier1d	128×128×32
傅里叶模块1	Conv1d	128×128×1
傅里叶模块2	Fourier1d	128×128×32
傅里叶模块2	Conv1d	128×128×1
傅里叶模块3	Fourier1d	128×128×32
傅里叶模块3	Conv1d	128×128×1
傅里叶模块4	Fourier1d	128×128×32
傅里叶模块4	Conv1d	128×128×1
全连接	Fc2	128×64
输出	Output	64×1

图5 损失函数曲线

Fig. 5 Loss function curve

图6 箱式误差图

Fig. 6 Box error plot

图7 预测结果散点图

Fig. 7 Scatter plot of prediction results

图8 随机产量数据网络预测效果图

Fig. 8 FNO prediction effect diagram of random production data

图9 实例应用流程图

Fig. 9 Example application flowchart

表4 H1井基础参数表

Table 4 Basic parameter table of well H1

参数名称	参数
原始地层压力/MPa	42.2
井底流压/MPa	20.5
储层厚度/m	17.8
原油黏度/(mPa·s)	0.32
孔隙度	0.1
综合压缩系数/MPa^-1	0.002 855
原油体积系数/(m³/m³)	1.756
井长/m	2003
裂缝段数	37
缝间距/m	55.64

图11 生产动态资料解释效果图

Fig. 11 Interpretation effect diagram of production dynamic data

表5 试井解释参数表

Table 5 Well test interpretation parameter table

参数名称	参数
井筒储集系数/(m³·MPa^-1)	0.2
表皮系数	0.022
裂缝导流能力/(mD·m)	20
裂缝半长/m	40
储层渗透率/mD	0.005

图12 FNO、RTA预测H1井产量对比图

Fig. 12 H1 well production forecast comparison: FNO versus RTA

表6 误差分析参数表 Tabe 6 Error analysis parameter table

参数类型	计算结果
MAE	2.8714
RMSE	3.7603
R²	0.8163

图13 真实值与预测值相对误差图

Fig. 13 Plot of relative error between actual and predicted values

表7 离散点数据表

Table 7 Sampling points data table

采样点	RTA预测产量/(m³/d)	FNO预测产量/(m³/d)	误差/%
采样点1	14.64	14.8	1.09
采样点2	12.53	12.3	1.84
采样点3	11.06	11.55	4.43
采样点4	10.37	10.84	4.53
采样点5	9.72	10.18	4.73

图10 松辽盆地构造单元分区与古龙页岩油层位分布^[45]

Fig. 10 Tectonic unit division of the Songliao Basin and horizon distribution of the Gulong shale oil layer^[45]

表8 预测速度对比

Table 8 Comparison of prediction speed among RTA and FNO methods

方法	耗时
RTA模拟	10 min
FNO网络	1~2 s

图14 不同模型损失变化图

Fig. 14 Variation of loss among different models

表9 超参数取值

Table 9 Hyperparameter values

模型超参数	取值
模态数	(10，16，32，64)
通道宽度	(16，32，64，128，256)
学习率	(0.0005，0.001，0.005，0.01，0.05)
Batch size	(10，20，32，50，100)

表10 超参数优选结果

Table 10 Hyperparameter optimization results

模型超参数	大小
模态数	32
通道宽度	128
学习率	0.001
Batch size	32

图15 超参数优化误差曲线

Fig. 15 Error curve of hyperparameter optimization

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