基于格子玻尔兹曼方法的井筒热流固耦合数值模拟

doi:10.19596/j.cnki.1001-246x.8715

摘要/Abstract

摘要：

基于格子玻尔兹曼方法(LBM)建立一种求解井筒温度分布的模型。该模型可同时求解井筒内流体的温压耦合流动、流体流动中的强制热对流和井筒与地层的流固热交换三种效应的控制方程, 实现井筒内流体域流动场-流体域温度场-固体域温度场三场的耦合求解, 克服了传统模型井筒流速为定值的缺陷, 并且具有更广的适用范围。通过理论分析和对比分析, 验证模型的可靠性和精度。研究结果表明: 井筒内流体流速变化影响流体在井筒中的温度分布, 在产出条件下, 在同一深度处会造成流体中心温度高、流体边界处温度低的分布情况。流体沿井筒轴向的温度的下降趋势会经历缓-稳-缓三个阶段, 且此三个阶段受到流动雷诺数或者流体普朗特数的影响。

关键词: 井筒温度, 井筒压力, 格子玻尔兹曼, 普朗特数, 耦合计算

Abstract:

A model based on lattice Boltzmann method (LBM) is developed to solve the heat transfer problems in the wellbore, which can simultaneously solve the controlling equations of temperature-pressure coupled flow of fluid in the wellbore, forced thermal convection in fluid flow and fluid-solid heat exchange between the wellbore and the formation, so it can realize the coupling solution of fluid flow field, fluid temperature field and wellbore temperature field, and compared with the traditional model, it not only overcomes the defect that the velocity is constant in wellbore, but also has a wider scope of application and higher computational efficiency. The reliability and accuracy of the model have been verified by comparative analysis with previous studies. The results show that the change of fluid velocity in the wellbore affects the temperature distribution of the fluid in the wellbore. Under the production condition, the temperature distribution at the center of the fluid is high and the temperature at the boundary of the fluid is low at the same depth. The downward trend of fluid temperature along the shaft axis will go through three stages: slow, steady and slow, and these three stages are affected by flow Reynolds number or fluid Prandtl number.

Key words: wellbore temperature, wellbore pressure, lattice Boltzmann, Prandtl number, coupling simulation

中图分类号:

TE31

胡春余. 基于格子玻尔兹曼方法的井筒热流固耦合数值模拟[J]. 计算物理, 2024, 41(3): 316-324.

Chunyu HU. Lattice Boltzmann Model for Simulating Heat-fluid-solid Interaction in Wellbore[J]. Chinese Journal of Computational Physics, 2024, 41(3): 316-324.

图/表 12

图1 井筒结构示意图

Fig.1 Wellbore structure diagram

图2 含导热块的方腔自然对流示意图

Fig.2 Square medium containing discrete circular intrusions

表1 左壁面努森数对比

Table 1 Comparison of the Nusselt numbers on the left

λ_s/λ_f	本文	Ref.[25]	Ref.[26]	Ref.[22]
1	1.224	1.233	1.193	1.250
10	2.048	2.030	2.066	2.051
100	2.345	2.313	2.394	2.336

图3 含导热块方腔自然对流温度分布(a) λs/λf=1；(b) λs/λf=10；(c) λs/λf=100

Fig.3 Natural convection temperature distribution in square cavity with thermal conductive block at (a) λs/λf=1; (b) λs/λf=10; (c) λs/λf=100

表2 油田生产参数及准则数范围

Table 2 Typical range of oilfield production parameters and criterion number

油井深度/m	套管直径(外径)/mm	套管内径/mm	油管直径/mm	油管内径/mm	水泥环厚度/mm	Ra
1 000	177.8	159.4	73	62	32	10³~10⁹

油井日产液量	含水率/%	井底温度/℃	井口温度/℃	原油密度/(kg·m^-3)	原油运动黏度/ (m²·s^-1)	Re
1~100	0.1~99	40~60	20~30	800~1 000	50~10 × 10³	0.1~478

表3 准则数及模型参数

Table 3 Criterion number and model parameters

Pr	Ra	Re	下边界温度	上边界温度	径向网格数
1.0, 10, 100	10³, 10⁴, 10⁵	10, 100, 1 000	1.0	0.0	1 000

流体、环空导热系数	油管、套管导热系数	水泥环导热系数	地层导热系数	流体粘度	轴向网格数
1.0	319	4.42	15	0.01	1 000

图4 (a) 温度，(b) 密度和(c) 流速的分布云图

Fig.4 Distribution cloud map of (a) temperature; (b) density; (c) velocity

图5 井筒各部位中心点沿井筒轴向温度分布

Fig.5 Temperature distribution of the midpoint along the axial direction

图6 雷诺数对井筒径向温度分布的影响

Fig.6 Effect of Reynolds number on radial temperature distribution

图7 雷诺数对井筒轴向的流体温度分布的影响

Fig.7 Effect of Reynolds number on axial temperature distribution

图8 普朗特数对井筒径向温度分布的影响

Fig.8 Effect of Prandtl number on radial temperature distribution

图9 普朗特数对井筒轴向温度分布的影响

Fig.9 Effect of Prandtl number on axial temperature distribution

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