STUDY ON TWO-PHASE DISPLACEMENT FLOW BEHAVIOR THROUGH ROUGH-WALLED FRACTURES USING LBM SIMULATION
-
摘要: 岩体粗糙裂隙两相驱替渗流普遍存在于许多工程应用中, 而裂隙开度分布特征与壁面润湿性是影响两相驱替特性的关键因素. 基于分形理论生成三维粗糙裂隙面并分别构建开度分布一致的均质模型和不一致的非均质模型, 通过LBM伪势模型模拟粗糙裂隙准静态排水过程, 研究了裂隙开度分布特征与壁面润湿性对两相驱替渗流特性的影响规律及细观机制. 研究结果表明: 均质模型驱替前缘基本保持平稳推进, 而非均质模型出现优先驱替阻力较小的大开度区域的优势驱替路径现象, 润湿性增强可加剧该现象致使驱替前缘更快突破, 对均质模型无明显作用; 残余捕获可分为孤立的“圈闭”模式和吸附在裂隙壁面的“水膜”模式, 非均质模型中圈闭捕获明显多于均质模型, 强润湿性有利于水膜捕获增多; 当驱替压力增大至进入压力后, 非均质模型中部分小开度区域润湿相被逐步排驱, 而均质模型大多数润湿相被快速驱替, 因此非均质模型Pc-Sw曲线比均质模型更加平缓, 润湿性增强使得两种裂隙模型驱替开始发生时的进入压力更大, 施加相同驱替压力时驱替效率更低.
-
关键词:
- 粗糙裂隙 /
- 两相驱替 /
- 开度分布 /
- 润湿性 /
- 格子Boltzmann方法
Abstract: Two-phase displacement flow in rough rock fractures is prevalent in many engineering applications, and aperture distribution characteristics and wettability of rough-walled rock fractures are the two significant factors that affect two-phase displacement flow behavior. Three-dimensional rough surfaces of fracture were generated based on fractal theory and the homogenous model with homogenous aperture distribution and heterogeneous model with heterogeneous aperture distribution were established respectively. Quasi-static drainage process through rough fractures was simulated using LBM pseudo-potential model, accordingly the effect of aperture distribution and wettability of fracture and its microscopic mechanism on two-phase displacement flow behavior were studied. The displacement front of homogenous model basically maintained stable movement, while the phenomenon of dominant displacement path that preferentially invading larger-aperture area with smaller displacement resistance occurred in heterogeneous model. Enhanced wettability can exacerbate this phenomenon, leading to faster breakthrough of the displacement front, which has no significant effect on the homogenous model. Residual capture can be divided into isolated “trapped” pattern and “water-film” mode that adsorbed on the fracture wall, heterogeneous model obviously had more trapped capture than homogenous model, and strong wettability was beneficial for increasing water-film capture. When the displacement pressure increases to the entry pressure, some wetting phases in small-aperture regions of heterogeneous model are gradually displaced, while most of wetting phases in homogenous model are rapidly invaded, thus the Pc-Sw relation curves of heterogeneous model were gentler than that of homogenous model, and increasing wettability resulted in higher entry pressure at the beginning of displacement for both two fracture models and lower displacement efficiency when the same displacement pressure was imposed. -
引 言
岩体裂隙两相驱替渗流广泛存在于众多实际工程中, 如CO2地质封存[1-2]、油气开采[3-4]、核废料处理[5]和地下水污染物迁移与修复等[6]. 受不混溶流体的流体性质(界面张力和黏滞系数)、裂隙几何特征(粗糙度和开度分布)、壁面润湿性和流动条件等因素的影响, 裂隙两相驱替渗流往往呈现出复杂的驱替模式和细观流动结构, 进一步导致驱替进入压力、驱替效率和残余捕获特征等宏观规律难以捉摸. 因此, 裂隙介质两相驱替渗流特性及其细观机制一直是亟待解决的关键科学问题.
裂隙几何特征和壁面润湿性是影响两相驱替渗流特性的两个重要因素, 国内外学者对此做了大量研究. Karpyn等[7]运用微观CT扫描直接观测到砂岩粗糙裂隙驱替过程中液相捕获、优势驱替通道以及非润湿相的指进折断等现象, 认为裂隙开度分布是控制两相流体分布的主要因素. Al-Housseiny等[8]通过在开度有变化梯度的平行板裂隙中的气-油驱替试验, 发现裂隙张开度变大时, 即使是小黏度流体驱替高黏度流体, 驱替相界面仍呈现逐渐失稳的趋势. Chen等[9]采用透明树脂复刻真实粗糙裂隙, 开展油-水非稳定驱替试验(高黏度流体驱替小黏度流体), 驱替过程中驱替前缘出现失稳现象, 认为裂隙几何特征的非均质性是失稳的主要原因. Hu等[10]通过同样方法制作透明粗糙裂隙, 在不同粗糙度的裂隙中进行排水试验, 结果表明相对粗糙度增大使得驱替前缘更加不稳定, 驱替过程中能量耗散更多. 最近, 李博等[11]结合3D打印和PIV测速技术观测透明粗糙裂隙中注浆驱水试验过程, 发现残余水分布与裂隙开度分布密切相关, 主要集中在开度大小发生突变的小孔隙区域. 胡冉等[12]研究了开度变化对两相流流动结构与有效渗透率的影响, 结果表明开度的增加使得非润湿相流动通道的分支减少, 两相流体的有效渗透率增大. 以上两相驱替试验研究充分表明裂隙开度分布特征与驱替渗流特性密切相关, 但未考虑裂隙壁面润湿性的作用.
除了驱替试验外, 数值模拟也是研究裂隙内两相驱替特性的有效方式. Wang等[13]通过连续模型模拟超临界二氧化碳驱替卤水过程, 发现裂隙大开度区域更容易侵入, 当裂隙开度标准差较大时, 由于裂隙开度分布范围更广, Pc-Sw曲线更加平缓. Yang等[14]采用修正逾渗模型模拟非均质裂隙中两相驱替过程, 结果表明突破时刻非润湿相饱和度与润湿相残余饱和度均随开度非均质性增大而减小. 盛建龙等[15]基于类似方法研究分形粗糙裂隙中水-气驱替过程, 结果显示当分形维数越小, 裂隙开度分布的空间相关性越大时, 两相可以共同流动的饱和度范围越大. 然而, 以上数值模拟研究, 基于平行板假设, 将粗糙裂隙概化为平面模型, 因此研究成果对于复杂的三维粗糙裂隙内两相驱替过程的适用性尚不明确.
目前, 关于壁面润湿性研究, 在多孔介质中, 许多学者采用微观孔隙模型进行二维多孔介质内两相驱替可视化试验, 并取得了相当丰硕的成果[16-17]. 他们的研究显示壁面润湿性变化改变了流体与壁面接触特性, 显著影响两相驱替模式和驱替效率[18-19]. 然而, 由于粗糙裂隙壁面润湿性难以控制, 现有的裂隙介质润湿性对两相驱替渗流特性影响试验研究很少. Bergslien等[20]通过透明环氧树脂复刻真实的裂隙表面, 再采用聚苯乙烯和低温等离子体对裂隙面分别进行疏水与亲水处理, 试验结果表明不同壁面润湿性导致了显著不同的两相流行为和残余分布特征, 入侵流体更容易在疏水裂隙中形成连通通道, 而在亲水裂隙中被限制在较大孔径区域而没有稳定的流动路径. Lee等[21]研究了平行板裂隙改变润湿性的3个条件(暴露时间、饱和条件和水流速度), 认为润湿性变化是影响岩体裂隙地下水和两相污染物流动的重要因素. Qiu等[22]通过在微型粗糙裂隙模型中进行水-油驱替试验, 发现由不同粗糙度引起的各种驱替模式使得裂隙表面薄膜对润湿性影响程度不同, 进而导致残余流体分布模式不同. 然而, 他们有限的试验研究, 不足以充分揭示壁面润湿性对两相驱替特性的影响规律, 因此两者的关系仍有待进一步研究.
相比驱替试验, 数值模拟方法可以更好地研究裂隙壁面润湿性对两相驱替特性的影响. 近30年, 介观数值方法-格子波尔兹曼方法(LBM)由于特殊的边界处理方式和高效的计算性能[23-25], 被广泛运用到复杂介质单相流[26-28]和多相流[29-31]模拟研究中. 研究人员运用LBM多相流模型, 通过改变壁面与流体间作用参数模拟接触角变化来控制流体润湿性, 从而实现裂隙壁面润湿性影响研究[32]. Dou等[33]通过LBM研究了粗糙裂隙润湿性对排水过程驱替特性影响, 结果表明当润湿性越强(接触角较小), 润湿相饱和度相同时毛管力更大, 最终残余捕获更多. Guiltinan等[34]通过LBM模拟动态驱替过程, 研究显示驱替过程主要由裂隙非均匀润湿性和粗糙度控制, 润湿性非均匀程度越大, 残余捕获水饱和度越大. Yi等[35]采用LBM研究了二维粗糙裂隙壁面润湿性对两相流特性的影响, 结果表明润湿性与细观流体分布相关, 进一步影响裂隙表观粗糙度和相对渗透率曲线. 然而, 他们的研究对于三维粗糙裂隙内准静态驱替过程的饱和度演变规律未详细讨论, 且没有考虑裂隙开度分布对裂隙两相驱替渗流特性的影响.
在众多LBM多相流模型中, 由于多组分伪势模型具有自动追踪相界面、处理壁面润湿性和简单高效等特点[36-38], 因此选择采用LBM多组分伪势模型. 针对以上问题, 本文基于分形理论生成三维粗糙裂隙面, 经过平移处理建立开度分布不同的裂隙模型, 通过LBM多组分伪势模型模拟粗糙裂隙准静态排水过程, 研究裂隙开度分布特征与壁面润湿性对两相驱替渗流特性的影响规律及细观机制, 重点关注驱替过程中两相饱和度演化规律和残余捕获模式, 进而阐明毛管力与驱替效率的关系, 以期为油气开采, CO2埋存和地下水污染物迁移与修复等工程技术领域提供参考依据.
1. 分形裂隙模型
研究表明, 岩体粗糙裂隙面具有自相仿性[39-41], 其不规则表面形态可由分形理论表征, 通过单值连续的随机函数Z(x)描述裂隙面高程, 任意相邻间距为$ \varDelta $的裂隙面高程服从正态分布$ N\left( {0, {\delta ^2}} \right) $
$$\qquad\qquad \delta _\varDelta ^2 = \left\langle {{{\left[ {Z\left( x \right) - Z\left( {x + \varDelta } \right)} \right]}^2}} \right\rangle $$ (1) $$\qquad\qquad \delta _{r\varDelta }^2 = \left\langle {{{\left[ {Z\left( x \right) - Z\left( {x + r\varDelta } \right)} \right]}^2}} \right\rangle $$ (2) $$\qquad\qquad \left\langle {Z\left( x \right) - Z\left( {x + r\varDelta } \right)} \right\rangle = 0 $$ (3) 式中, $ \langle \cdot \rangle $表示数学期望, x为坐标分量, $ r $为常数; $ \delta _\varDelta ^2 $与$ \delta _{r\varDelta }^2 $分别为间距$ \varDelta $与$ r\varDelta $裂隙面高程增量的方差, 结合式(1)和式(2)可得
$$ \delta _{r\varDelta }^2 = {r^{2(3 - D)}}\delta _\varDelta ^2 \Rightarrow \delta _{r\varDelta }^{} = {r^{3 - D}}\delta _\varDelta ^{} $$ (4) 式中, D为分形维数, 三维裂隙面D在2 ~ 3之间.
本文通过逐次随机累加法生成三维裂隙面, 如图1所示, 先给正方形裂隙面的4个顶点(标记1)定义初始高程为满足$ N\left( {0, \delta _0^2} \right) $的随机值; 正方形中心点和边线中点(标记2)的高程分别取4个顶点和各边线两个端点的平均值; 再给标记1和2的高程增加满足$ N\left( {0, \delta _1^2} \right) $的随机值; 然后对所有新生成的小正方形区域重复上述步骤生成新标记3, 各标记点继续增加服从$ N\left( {0, \delta _n^2} \right) $的随机值, 直至生成$ {2^n} \times {2^n} $个子域, 其中$ \delta _n^2 = \delta _0^2\left( {1 - {2^{2(3 - D){{-}}2}}} \right)/{\left( {{2^{2(3 - D)}}} \right)^n} $, δ0, δ1, ···, δn分别为第1次, 第2次, ···, 第n + 1次各小正方形区域顶点高程增加的随机值的标准差. 由前人研究结果可知, 天然真实粗糙裂隙分形维数D处于2. 0 ~ 2. 6之间[39, 42-43], 因此选择具有代表性的中间值2. 3, 最后生成长宽为500 mm × 500 mm、D = 2. 3时裂隙面形貌如图2所示.
2. LBM数值模拟
2.1 多组分伪势模型
多组分伪势模型由Shan等[44]提出, 又称Shan-Chen模型. 与传统的数值方法不同, LBM采用自下而上的计算模式, 通过粒子分布函数$ {f_i}(x, t) $表征微观粒子团在计算域中的分布概率, 粒子团的迁移、碰撞过程由Boltzmann方程控制, 可避免求解复杂的N-S方程. 将连续Boltzmann方程离散为格子节点形式, 引入单松弛BGK (Bhatnagar-Gross-Krook)碰撞算子, 每个组分$ {f_i}(x, t) $演化均满足格子Boltzmann方程
$$ \begin{split} & f_i^\alpha ({\boldsymbol{x}}, t) - f_i^\alpha ({\boldsymbol{x}} + {{\boldsymbol{c}}_i}\varDelta t, t + \varDelta t)= \\ & \qquad \frac{{\varDelta t}}{{{\tau ^\alpha }}}\left[ {f_i^\alpha ({\boldsymbol{x}}, t) - f_i^{\alpha (eq)}({\boldsymbol{x}}, t)} \right]\end{split}$$ (5) 式中, 上标α代表流体组分; 下标i为离散速度的方向(如图3所示), $ f_i^\alpha ({\boldsymbol{x}}, t) $代表t时刻α组分在x位置的i方向的粒子分布函数; $ {\tau ^\alpha } $是组分α的松弛时间, 代表平衡过程的平均时间; 流体运动黏度$ {\nu ^\alpha } = c_s^2({\tau ^\alpha } - 1/2) $, 声速$ {c_s} = c/\sqrt 3 $; 时间步长$ \varDelta t $和各方向格子速度$ {{\boldsymbol{c}}_i} $分量大小为简便计算均取1
$$ \begin{split} & \left[ {{\boldsymbol{c}}_0}, {{\boldsymbol{c}}_1}, {{\boldsymbol{c}}_2}, {{\boldsymbol{c}}_3}, {{\boldsymbol{c}}_4}, {{\boldsymbol{c}}_5}, {{\boldsymbol{c}}_6}, {{\boldsymbol{c}}_7}, {{\boldsymbol{c}}_8}, {{\boldsymbol{c}}_9}, {{\boldsymbol{c}}_{10}}, {{\boldsymbol{c}}_{11}}, {{\boldsymbol{c}}_{12}}, {{\boldsymbol{c}}_{13}},\right. \\ & \left.{{\boldsymbol{c}}_{14}}, {{\boldsymbol{c}}_{15}}, {{\boldsymbol{c}}_{16}}, {{\boldsymbol{c}}_{17}}, {{\boldsymbol{c}}_{18}} \right]=\\ & c\left[ \begin{array}{ccccccccccccccccccc} 0 & -1 & 1 & 0 & 0 & 0 & 0 & 1 & -1 & 0 & 0 & -1 & 1 & -1 & 1 & 0 & 0 & 1 & -1 & \\ 0 & 0 & 0 & -1 & 1 & 0 & 0 & 1 & -1 & -1 & 1 & 0 & 0 & 1 & - 1 & 1 & - 1 & 0 & 0 & \\ 0 & 0 & 0 & 0 & 0 & 1 & - 1 & 0 & 0 & 1 & - 1 & 1 & - 1 & 0 & 0 & 1 & - 1 & 1 & - 1 \\ \end{array} \right]\end{split} $$ (6) 每个组分α的平衡分布函数$ f_i^{\alpha (eq)}({\boldsymbol{x}}, t) $为
$$ f_i^{\alpha (eq)}({\boldsymbol{x}}, t) = {w_i}{\rho ^\alpha }\left[ {1 + \frac{{{\boldsymbol{u}} \cdot {{\boldsymbol{c}}_i}}}{{c_s^2}} + \frac{{{{({\boldsymbol{u}} \cdot {{\boldsymbol{c}}_i})}^2}}}{{2c_s^4}} - \frac{{{{\boldsymbol{u}}^2}}}{{2c_s^2}}} \right] $$ (7) 式中, $ {\boldsymbol{u}} = {{\boldsymbol{u}}^{\alpha (eq)}} $和$ {\rho ^\alpha } $分别是α组分平衡态时流体宏观速度和密度, $ {w_i} $是特定方向速度$ {{\boldsymbol{c}}_i} $的权重. 本文采用D3Q19模型, 如图3所示, 除中间0方向外有18个速度方向与相邻节点相互迁移粒子, 相应的速度权重为wi = 1/3 (i = 0), wi = 1/18 (i = 1 ~ 6), wi = 1/36 (i = 7 ~ 18).
各组分根据式(5)左半部分进行迁移过程后, 组分α的流体密度和速度分别为
$$ \qquad\qquad\qquad {\rho ^\alpha } = \sum\limits_i {f_i^\alpha } $$ (8) $$\qquad\qquad\qquad {\rho ^\alpha }{{\boldsymbol{u}}^\alpha } = \sum\nolimits_i {f_i^\alpha {{\boldsymbol{c}}_i}} $$ (9) 所有组分的共同平均速度$ {{\boldsymbol{u}}{'}} $为
$$ {{\boldsymbol{u}}{'}} = \frac{{\displaystyle\sum\nolimits_\alpha {{\rho ^\alpha }{{\boldsymbol{u}}^\alpha }/{\tau ^\alpha }} }}{{\displaystyle\sum\nolimits_\alpha {{\rho ^\alpha }/{\tau ^\alpha }} }} $$ (10) 在伪势模型中, 假设各组分流体粒子之间存在相互作用力为
$$ {\boldsymbol{F}}_c^\alpha \left( {{\boldsymbol{x}}, t} \right) = - {G_c}{\rho ^\alpha }\left( {{\boldsymbol{x}}, t} \right)\sum\nolimits_i {{w_i}{\rho ^{\bar \alpha }}\left( {{\boldsymbol{x}} + {{\boldsymbol{c}}_i}\varDelta t, t} \right){{\boldsymbol{c}}_i}} $$ (11) 式中, $ \alpha $与$ \bar \alpha $分别代表润湿相与非润湿相, 系数Gc控制两相流体间相互作用强度. 定义各组分流体与固体表面的作用力为
$$ {\boldsymbol{F}}_s^\alpha \left( {{\boldsymbol{x}}, t} \right) = - G_s^\alpha {\rho ^\alpha }\left( {{\boldsymbol{x}}, t} \right)\sum\nolimits_i {{w_i}s\left( {{\boldsymbol{x}} + {{\boldsymbol{c}}_i}\varDelta t, t} \right){{\boldsymbol{c}}_i}} $$ (12) 式中, $ G_s^\alpha $是控制α组分流体与固体相互作用强度的系数, $ s\left( {{\boldsymbol{x}} + {{\boldsymbol{c}}_i}\varDelta t, t} \right) $是布尔函数, 固体节点取1, 流体节点取0. 当无外力作用下, 合力$ {{\boldsymbol{F}}^\alpha } = {\boldsymbol{F}}_c^\alpha + {\boldsymbol{F}}_s^\alpha $提供各组分流体加速度, 组分α平衡态时流体宏观速度$ {{\boldsymbol{u}}^{\alpha (eq)}} $为
$$ {{\boldsymbol{u}}^{\alpha (eq)}} = {{\boldsymbol{u}}{'}} + {\tau ^\alpha }{{\boldsymbol{F}}^\alpha }/{\rho ^\alpha } $$ (13) 组分α的$ {{\boldsymbol{u}}^{\alpha (eq)}} $求出后可进一步通过式(7)确定平衡分布函数$ f_i^{\alpha (eq)}({\boldsymbol{x}}, t) $, 最后由式(5)右半部分完成碰撞过程, 重复上述步骤直至模拟收敛. 各时间步每个格子的混合流体速度和压力为
$$\qquad\qquad\qquad {\boldsymbol{v}} = {{\boldsymbol{u}}{'}} + \frac{{\displaystyle\sum\nolimits_\alpha {{{\boldsymbol{F}}^\alpha }} }}{{2\displaystyle\sum\nolimits_\alpha {{\rho ^\alpha }} }} $$ (14) $$\qquad\qquad\qquad P = c_s^2{\sum\nolimits_\alpha \rho ^\alpha } + \frac{{{G_c}}}{3}{\rho ^\alpha }{\rho ^{\bar \alpha }} $$ (15) 2.2 接触角验证
由于壁面润湿性强弱可采用接触角大小直接表征, 为保证润湿性研究结果可靠, 有必要验证多组分伪势模型模拟接触角的有效性. 根据Huang等[32]提出的通过改变流体与固体之间相互作用大小实现不同大小的接触角
$$ \cos \theta = \frac{{{G_{s, 1}} - {G_{s, 2}}}}{{{G_c}({\rho _1} - {\rho _2})/2}} $$ (16) 式中, $ {G_{s, 1}} $和$ {G_{s, 2}} $分别为润湿相和非润湿相流体与固体之间相互作用强度, 设置为Gs,2 = −Gs,1, $ {G_c} $为两相流体间相互作用强度, 取0. 9, $ {\rho _1} $和$ {\rho _2} $分别代表平衡态时主要组分密度和溶解密度, 取值为2和0.06, 两相的松弛时间$ \tau $均为1, 因此动力黏度υ为0.1667, 表面张力为0.15. 模拟结果如图4所示, θ随Gs,1增大而减小, 模拟结果与式(16)预测曲线基本一致, 说明LBM多组分伪势模型能够很好地模拟不同润湿性条件下的接触角变化. 由于本文研究关注粗糙裂隙内准静态排水过程, 因此控制被驱替相与裂隙壁面的接触角θ在0° ~ 90°之间, θ越小表示壁面润湿性越强. 为方便叙述, 后续分析采用理论值区分不同润湿性.
2.3 计算模型设置
本文采用图2中大小为500Lu × 500Lu (Lu为lattice unite, 格子单位)和D = 2. 3的分形裂隙面, 通过复制并向上平移10Lu构建上、下裂隙面相互匹配的均质模型; 再将上、下裂隙面分别同时向x和y坐标轴的相反方向平移50Lu, 形成非匹配的非均质模型, 这与天然岩体节理、裂隙在剪切、错动位移作用下, 上、下节理面由初始的基本吻合状态逐渐向非吻合状态演变正好分别对应. 为独立研究裂隙开度是否均匀分布对驱替特性的影响, 保证两种裂隙模型开度均值都为10Lu. 为节约计算成本, 最终计算区域选取裂隙模型的中间200Lu × 200Lu区域, 非均质模型开度分布情况如图5所示. 可以看出, 非均质模型裂隙开度呈现较强的非均匀性, 上、下两端的开度相对较小, 中间部分开度较大.
![]()
图 6 三维粗糙裂隙LBM计算模型Figure 6. LBM computational model of three-dimensional rough fracture获得上下裂隙面后, 通过自编Python程序将裂隙模型三值化处理并添加进出口边界, 结果如图6所示, 黄色部分代表岩体基质, 中间蓝色部分为可流动的裂隙区域, 两端各预留4Lu长度的进、出口区域以减小数值波动性. 本文采用进、出口压力边界条件, 裂隙模型四周采用反弹格式的非滑移边界[45-46], 根据润湿性条件调整裂隙两端施加的驱替压差. 为实现准静态排水过程, 开始时裂隙由润湿相完全饱和, 非润湿相从裂隙进口进入, 通过保持进口边界压力不变、逐渐降低出口压力, 从而实现不断增大的驱替压差[33, 47]. 也就是说, 当较小的驱替压差不足以使得非润湿相继续驱动润湿相时, 则逐级增大驱替压差, 直到驱替过程达到完全稳定状态. 由于本文研究重点是壁面润湿性, 而对于影响驱替特性的其他流体性质如流体密度和黏度等未考虑, 因此设置两相密度均为2, 动力黏度为0.1667, 类似于密度和黏度相近的水-油系统; 另外两相流体间相互作用强度Gc = 0.9, 表面张力为0.15, 溶解密度为0.06, 两相流体与固体之间相互作用强度Gs,1 = −Gs,2 = 0.1, 0.2, 0.3, 0.4, 对应的接触角理论值分别为76.8°, 62.7°, 46.6°, 23.6°. 以上物理量均为LBM格子单位, 可由实际物理量与格子单位量的比值确定特征长度L0、特征时间T0和特征质量M0, 其他物理量实际值均可根据表1中关系式求出. 所有模拟计算在Linux平台使用开源程序Palabos (https: //palabos.unige.ch/)[48]完成, 综合考虑模拟精度和计算时间, 认为经过1000次迭代后的相对能量差小于1.0 × 10−4时模拟收敛[49]. 完成两种裂隙模型、4种润湿性共计8次模拟, 在双核Intel CPU i7-12700F的台式机上需要计算时间约15 d.
表 1 格子单位与物理单位的转换关系Table 1. The transformational relationship between lattice unit and physical unitParameters Physical unit Lattice unit Relationship length L/m Lb Lb = L/L0 dynamic viscosity υ/(m2·s−1) υb υb = υT0/L02 density ρ/(kg·m−3) ρb ρb = ρL03/M0 surface tension σ/(kg·m−2) σb σb = σT02/M0 time T/s Tb Tb = T/T0 velocity u/(m·s−1) ub ub = uT0/L0 pressure P/(kg·(m·s2)−1) Pb Pb = PL0T02/M0 3. 结果与分析
3.1 准静态驱替过程
图7和图8分别为均质模型和非均质模型不同润湿性条件下准静态驱替过程图, 橙黄色部分代表非润湿相, 剩余白色部分为润湿相(为方便观察, 未用颜色显示), 灰色为裂隙壁面. 可以看出, 由于不均匀开度分布, 非均质模型驱替路径比均质模型更加曲折且不规则, 出现明显的优势驱替通道; 而开度一致的均质模型驱替路径相对较平稳且规则. 结合非均质模型开度分布图(图5(a)), 发现非润湿相优先入侵非均质模型裂隙开度较大的中间区域, 再逐渐向两侧小开度区域扩展, 直至达到稳定状态. 由于裂隙两端施加的驱替压力无法克服较大的毛管阻力, 部分开度极小区域的润湿相始终未能被驱替, 形成一些被非润湿相包围的和孤立的“圈闭”捕获. 根据Young-Laplace公式[13-14]: Pc = 2σcosθ/b, 式中Pc为毛管力, σ为表面张力, θ为接触角, b为局部裂隙开度, 说明表面张力和接触角相同时, 大开度区域毛管阻力更小, 因此更容易优先被非润湿相驱替.
对比两种裂隙模型的不同润湿性条件下驱替过程, 可以发现, 较强的润湿性使得驱替过程更加趋于不稳定, 相界面更加弯曲, 这种现象对于开度不均匀分布的非均质模型更加明显. 非均质模型中润湿性较强(θ = 23.6°)时, 优势驱替路径现象更加明显, 表现出更细长的驱替路径.
为进一步定量表征驱替过程相界面特征, 定义界面相对长度l为相界面实际长度与裂隙模型宽度的比值, 驱替相对时间T*为当前驱替时刻与总时间的比值. 如图9所示, 随着驱替过程的进行, 均质模型相界面相对长度l在很小范围内变化, 而非均质模型l有明显增大的趋势, 整体上比均质模型大得多, 说明非均质模型驱替过程中相界面更加曲折, 而均质模型相界面相对较平稳. 对于非均质模型, 润湿性增强时, 相界面相对长度l增长越快, 更早地达到第一个峰值, 说明润湿性越强相界面演变越快.
图10给出了驱替过程润湿相饱和度随驱替前缘位置的演变关系, 可以看出, 随着驱替前缘的推进, 润湿相饱和度逐渐降低, 当前缘位置到达裂隙出口时即突破时刻, 前缘位置不再增大, 而饱和度继续下降至残余饱和度, 此时驱替达到稳定状态. 驱替过程中, 在突破时刻之前, 均质模型饱和度下降幅度比非均质模型更大, 说明更加平稳的驱替前缘导致突破时驱替效率更大.
![]()
图 10 驱替最前缘位置与润湿相饱和度关系图Figure 10. Relationship between the foremost location of interface and saturation of wetting phase对比两种裂隙模型的不同润湿性结果, 驱替前缘位置相同时, 润湿相饱和度基本上随润湿性增强而增大, 说明强润湿性使得驱替过程中润湿相更难被驱替, 导致残余捕获更多. 值得注意的是, 到达突破时刻之前, 两种裂隙模型均出现驱替前缘位置几乎不变而饱和度跳跃式下降的“阶梯状”现象, 说明驱替过程中, 驱替最前缘位置除了向前推进, 有时候也会等待其他驱替前缘追赶, 出现横向发展现象, 在Chen等[9]和魏鹳举等[17]的驱替试验中有类似的发现.
3.2 局部残余捕获模式
表2给出了突破与稳定时刻的润湿相饱和度数据, 对应于图10中突破后饱和度垂直下降段. 可以看出, 非均质模型中明显的优势驱替路径现象(图8), 致使非均质模型两个时刻的饱和度差值显著大于均质模型. 由于不同润湿性条件下裂隙两端施加的驱替压力不同, 最终润湿相孤立的残余分布各不相同, 因此非均质模型稳定时刻饱和度无明显规律. 然而, 稳定时刻均质模型基本没有孤立的“圈闭”捕获(图7), 润湿相残余饱和度随润湿性增强而增大, 最大可达15%, 说明除了图7中可见的捕获模式外, 还存在一种未展现的捕获模式有待进一步发掘.
表 2 不同润湿性条件下突破与稳定时刻润湿相饱和度Table 2. The saturation of wetting phase at breakthrough time and steady state under different wetting conditionsSaturation Sw Homogeneous model Heterogeneous model 76.8° 62.7° 46.6° 23.6° 76.8° 62.7° 46.6° 23.6° breakthrough time Tb 0.071 0.141 0.128 0.184 0.327 0.406 0.410 0.505 steady state Ts 0.015 0.030 0.077 0.150 0.155 0.113 0.151 0.166 difference 0.056 0.111 0.051 0.034 0.172 0.293 0.259 0.339 为详细分析驱替过程中残余捕获模式, 图11以非均质模型θ = 23.6°驱替达到稳定状态时为例, 截取X = 104处截面展现两相局部分布特征, 截面图中两条蓝色曲线为上、下粗糙裂隙壁面, 中间深红色部分代表非润湿相, 其余浅色部分为润湿相. 可以看出, 残余的润湿相主要有两种捕获模式, 第1种是黑色圈出部分(标记1), 该部分润湿相或赋存于小开度区域, 或被小开度区域包围, 导致驱替阻力较大, 非润湿相只能绕过这部分润湿相流体, 形成孤立的“圈闭”捕获区域. 从图7和图8可见, 该捕获模式在均质模型中很少, 而非均质模型中较多, 因此裂隙开度的非均匀分布有利于第一种捕获模式发生.
第2种是红色圈出部分(标记2), 这部分润湿相存在于裂隙壁面凸起处, 吸附在裂隙壁面而始终难以被驱替, 形成一层“水膜”. 类似地, 在LBM模拟研究[33-34]和两相流试验[22, 50]中均发现在裂隙壁面上有较多残余润湿相存在. 如前文所述, 对于稳定时刻的均质模型, 润湿相饱和度随润湿性增强而增大(表2), 而第1种捕获模式很少(图7), 因此饱和度变化主要来源于第2种捕获模式, 也就是说“水膜”捕获随润湿性增强而增多, 这是因为强润湿性会导致润湿相对裂隙壁面吸附性更强. 此外, “水膜”现象在细观尺度的多孔介质LBM模拟中被广泛关注, 张晟庭等[51]发现壁面强润湿性使得孔隙壁面上有大量润湿相残余, 滞留的液相回流是导致相界面形成卡断的主要原因; Li等[52-54]认为孔隙介质的水膜残余会改变壁面与流体之间作用形式, 进一步影响页岩对甲烷的吸附能力; Zhang等[55]研究表明水膜使得气体有效流动的孔隙尺寸减小, 导致气体突破时驱替阻力更大. 以上研究结果充分说明水膜现象在两相驱替过程中是普遍存在的, 而且对驱替渗流特性有着重要影响.
3.3 驱替突破与稳定时刻特征规律
图12和图13给出了突破与稳定时刻的非润湿相饱和度分布特征. 如图12, 当驱替突破时, 均质模型前半段由于没有圈闭捕获, 非润湿相饱和度基本保持恒定, 随着润湿性增强, 更多的水膜捕获占据裂隙空间, 非润湿相饱和度降低; 后半段侧边少量润湿相未被驱替, 导致非润湿相饱和度下降. 对于非均质模型, 在裂隙进口附近出现显著的优势驱替现象, 非润湿相饱和度在裂隙范围内有较剧烈波动, 这与局部开度非均匀分布引起的圈闭捕获有关.
![]()
图 12 突破时刻非润湿相饱和度沿X驱替方向分布情况Figure 12. Distribution of non-wetting phase along invading direction X at breakthrough time![]()
图 13 稳定时刻非润湿相饱和度沿X驱替方向分布情况Figure 13. Distribution of non-wetting phase along invading direction X at steady state如图13, 当驱替达到稳定时, 对于均质模型, 非润湿相饱和度始终保持基本恒定, 与突破时刻前半段特征一致. 对于非均质模型, 许多突破时刻暂未被驱替的裂隙两侧的小开度区域逐渐被非润湿相侵入(见图8), 裂隙在0 ~ 50范围内基本由非润湿相占据, 仅有少量的润湿相以水膜形式存在, 特征规律与均质模型相近. 然而, 在其他范围内, 由于有许多随机的圈闭捕获模式, 非润湿相饱和度无明显分布规律.
图14给出了驱替突破时刻与稳定所需时间的比值, 可以看出, 非均质模型比值整体上比均质模型更小, 随着润湿性增强, 均质模型比值无明显变化, 而非均质模型比值逐渐减小. 这是因为均质模型驱替前缘较平稳, 两个时间十分接近, 而非均质模型有明显的优势驱替路径现象, 使得有一部分非润湿相提前到达裂隙出口, 两个时间相差较大; 同时, 润湿相增强会加剧优势驱替路径现象, 导致两个时间相差更大, 比值更小, 而对均质模型中前缘平稳推进过程无明显作用.
3.4 Pc-Sw关系
图15给出了准静态驱替过程毛管力与饱和度的关系, 为方便表达, 毛管力采用格子单位. 图中采用五角星标注突破时刻对应的Pc-Sw状态并以箭头突出显示, 五角星右侧为突破前的毛管力曲线, 左侧则表示突破后的毛管力曲线. 可以看出, 非均质模型Pc-Sw曲线比均质模型更加平缓. 在驱替开始时, 由于施加的驱替压力较小, 润湿相饱和度基本无变化; 随着驱替压力逐渐增大达到进入压力(又叫排驱压力, 为润湿相被非润湿相开始排驱所需的最低压力)时, 两种裂隙模型的润湿相饱和度快速下降. 当驱替压力继续增大, 非均质模型有部分小开度区域可进一步被排驱, 因此润湿相饱和度仍一定程度地降低直至残余饱和度. 然而, 均质模型裂隙开度分布一致, 一旦驱替压力大于进入压力, 除少量水膜捕获外, 大多数润湿相被完全驱排.
![]()
图 15 毛管力与润湿相饱和度的关系Figure 15. Relationship between capillary force and saturation of wetting phase继续增大驱替压力对润湿相饱和度改变无明显作用, 因此均质模型Pc-Sw曲线左边第一个转角比非均质模型更加尖锐. 由于两种裂隙模型的平均开度一致, 相同润湿性时进入压力基本相近. 随润湿性增强, 两种裂隙模型的进入压力均增大, 这是因为排驱过程中毛管力是阻力, 强润湿性导致润湿相有更大的吸附阻力, 因此润湿相开始被排驱的最低压力增大. 值得注意的是, 当施加的驱替压力相同(稍大于进入压力)时, 润湿性增强时润湿相饱和度更大, 说明驱替效率更低, 与文献[16-17, 56]等的研究结论一致. 如前所述, 强润湿性导致吸附在裂隙壁面的水膜捕获更多, 同时优势驱替路径现象更加显著, 均会导致裂隙内更多的残余润湿相, 不同程度地降低驱替效率.
4. 结 论
结合分形裂隙模型和LBM数值模拟方法, 研究了岩体粗糙裂隙开度分布特征和润湿性对两相准静态驱替渗流特性的影响规律, 主要结论如下:
(1)均质模型驱替前缘基本保持平稳推进, 非均质模型出现明显的优势驱替路径现象, 优先驱替阻力较小的大开度区域;
(2)残余捕获可分为两种模式, 第1种是被非润湿相包围的且孤立的“圈闭”捕获, 第2种是吸附在裂隙壁面凸起处的“水膜”捕获, 非均匀开度分布有利于第1种捕获模式发生, 润湿性增强第2种捕获模式增多;
(3)随着润湿性增强, 对于非均质模型, 加剧优势驱替路径现象, 驱替前缘到达裂隙出口更快, 而均质模型无明显差别;
(4)非均质模型Pc-Sw曲线比均质模型更加平缓, 随着润湿性增强, 两种裂隙模型驱替开始发生时的进入压力更大, 当施加相同驱替压力时驱替效率更低.
-
![]()
图 6 三维粗糙裂隙LBM计算模型
Figure 6. LBM computational model of three-dimensional rough fracture
![]()
图 10 驱替最前缘位置与润湿相饱和度关系图
Figure 10. Relationship between the foremost location of interface and saturation of wetting phase
![]()
图 12 突破时刻非润湿相饱和度沿X驱替方向分布情况
Figure 12. Distribution of non-wetting phase along invading direction X at breakthrough time
![]()
图 13 稳定时刻非润湿相饱和度沿X驱替方向分布情况
Figure 13. Distribution of non-wetting phase along invading direction X at steady state
![]()
图 15 毛管力与润湿相饱和度的关系
Figure 15. Relationship between capillary force and saturation of wetting phase
表 1 格子单位与物理单位的转换关系
Table 1 The transformational relationship between lattice unit and physical unit
Parameters Physical unit Lattice unit Relationship length L/m Lb Lb = L/L0 dynamic viscosity υ/(m2·s−1) υb υb = υT0/L02 density ρ/(kg·m−3) ρb ρb = ρL03/M0 surface tension σ/(kg·m−2) σb σb = σT02/M0 time T/s Tb Tb = T/T0 velocity u/(m·s−1) ub ub = uT0/L0 pressure P/(kg·(m·s2)−1) Pb Pb = PL0T02/M0 
下载: 导出CSV
表 2 不同润湿性条件下突破与稳定时刻润湿相饱和度
Table 2 The saturation of wetting phase at breakthrough time and steady state under different wetting conditions
Saturation Sw Homogeneous model Heterogeneous model 76.8° 62.7° 46.6° 23.6° 76.8° 62.7° 46.6° 23.6° breakthrough time Tb 0.071 0.141 0.128 0.184 0.327 0.406 0.410 0.505 steady state Ts 0.015 0.030 0.077 0.150 0.155 0.113 0.151 0.166 difference 0.056 0.111 0.051 0.034 0.172 0.293 0.259 0.339
下载: 导出CSV
-
[1] 于恩毅, 邸元, 吴辉等. CO2 地质封存风险分析的多场耦合数值模拟技术综述. 力学学报, 2023, 55(9): 2075-2090 (Yu Enyi, Di Yuan, Wu Hui, et al. Numerical simulation on risk analysis of CO2 geological storage under multi-field coupling: A review. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(9): 2075-2090 (in Chinese) Yu Enyi, Di Yuan, Wu Hui, et al. Numerical simulation on risk analysis of CO2 geological storage under multi-field coupling: A review. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(9): 2075-2090 (in Chinese)
[2] Wei B, Wang B, Li X, et al. CO2 storage in depleted oil and gas reservoirs: A review. Advances in Geo-Energy Research, 2023, 9(2): 76-93 doi: 10.46690/ager.2023.08.02
[3] 刘文超, 乔成成, 汪萍等. 页岩气井压裂液返排与生产阶段的压裂裂缝特征差异研究. 力学学报, 2023, 55(6): 1382-1393 (Liu Wenchao, Qiao Chengcheng, Wang Ping, et al. Study on fracture characteristics difference between fracturing fluid flowback and gas production stages of shale gas wells. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(6): 1382-1393 (in Chinese) Liu Wenchao, Qiao Chengcheng, Wang Ping, et al. Study on fracture characteristics difference between fracturing fluid flowback and gas production stages of shale gas wells. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(6): 1382-1393 (in Chinese)
[4] Shen W, Ma T, Zuo L, et al. Advances and prospects of supercritical CO2 for shale gas extraction and geological sequestration in gas shale reservoirs. Energy & Fuels, 2024, 38(2): 789-805
[5] 于洪丹, 崔景川, 陈卫忠等. 核废料地下储库围岩长期水力响应特征. 岩石力学与工程学报, 2022, 41(S1): 2639-2648 (Yu Hongdan, Cui Jingchuan, Chen Weizhong, et al. Characterization of the long-term hydro-mechanical response in the host rock of a potential nuclear waste disposal repository. Chinese Journal of Rock Mechanics and Engineering, 2022, 41(S1): 2639-2648 (in Chinese) Yu Hongdan, Cui Jingchuan, Chen Weizhong, et al. Characterization of the long-term hydro-mechanical response in the host rock of a potential nuclear waste disposal repository. Chinese Journal of Rock Mechanics and Engineering, 2022, 41(S1): 2639-2648 (in Chinese)
[6] 张烨, 施小清, 邓亚平等. 结合蒸汽和空气注入修复多孔介质中DNAPL污染物的多目标多相流模拟优化. 水文地质工程地质, 2015, 42(5): 140-148 (Zhang Ye, Shi Xiaoqing, Deng Yaping, et al. Multi-objective multi-phase optimization with steam and air co-injection for DNAPL contaminant remediation in porous media. Hydogeology & Engineering Geology, 2015, 42(5): 140-148 (in Chinese) Zhang Ye, Shi Xiaoqing, Deng Yaping, et al. Multi-objective multi-phase optimization with steam and air co-injection for DNAPL contaminant remediation in porous media. Hydogeology & Engineering Geology, 2015, 42(5): 140-148 (in Chinese)
[7] Karpyn ZT, Grader AS, Halleck PM. Visualization of fluid occupancy in a rough fracture using micro-tomography. Journal of Colloid and Interface Science, 2007, 307(1): 181-187 doi: 10.1016/j.jcis.2006.10.082
[8] Al-Housseiny TT, Tsai PA, Stone HA. Control of interfacial instabilities using flow geometry. Nature Physics, 2012, 8(10): 747-750 doi: 10.1038/nphys2396
[9] Chen YF, Wu DS, Fang S, et al. Experimental study on two-phase flow in rough fracture: Phase diagram and localized flow channel. International Journal of Heat and Mass Transfer, 2018, 122: 1298-1307 doi: 10.1016/j.ijheatmasstransfer.2018.02.031
[10] Hu R, Zhou CX, Wu DS, et al. Roughness control on multiphase flow in rock fractures. Geophysical Research Letters, 2019, 46(21): 12002-12011 doi: 10.1029/2019GL084762
[11] 李博, 王晔, 邹良超等. 岩石裂隙内浆液-水两相流可视化试验与驱替规律研究. 岩土工程学报, 2022, , 44(9): 1608-1616, 2-3 (Li Bo, Wang Ye, Zou Liangchao, et al. Displacement laws of grout-water two-phase flow in a rough-walled rock fracture through visualization tests. Chinese Journal of Geotechnical Engineering, 2022, 44(9): 1608-1616, 2-3 (in Chinese) Li Bo, Wang Ye, Zou Liangchao, et al. Displacement laws of grout-water two-phase flow in a rough-walled rock fracture through visualization tests. Chinese Journal of Geotechnical Engineering, 2022, 44(9): 1608-1616, 2-3 (in Chinese)
[12] 胡冉, 钟翰贤, 陈益峰. 变开度岩体裂隙多相渗流实验与有效渗透率模型. 力学学报, 2023, 55(2): 543-553 (Hu Ran, Zhong Hanxian, Chen Yifeng. Experiments and effective permeability model for multiphase flow in rock fractures with variable apertures. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(2): 543-553 (in Chinese) Hu Ran, Zhong Hanxian, Chen Yifeng. Experiments and effective permeability model for multiphase flow in rock fractures with variable apertures. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(2): 543-553 (in Chinese)
[13] Wang LC, Cardenas MB. Connecting pressure-saturation and relative permeability models to fracture properties: The case of capillary-dominated flow of supercritical CO2 and brine. Water Resources Research, 2018, 54(9): 6965-6982 doi: 10.1029/2018WR023526
[14] Yang ZB, Li DQ, Xue S, et al. Effect of aperture field anisotropy on two-phase flow in rough fractures. Advances in Water Resources, 2019, 132: 103390 doi: 10.1016/j.advwatres.2019.103390
[15] 盛建龙, 韩云飞, 叶祖洋等. 粗糙裂隙水、气两相流相对渗透系数模型与数值分析. 岩土力学, 2020, 41(3): 1048-1055 (Sheng Jianglong, Han Yunfei, Ye Zuyang, et al. The relative permeability model for water-air two-phase flow in rough-walled fractures of rock and numerical analysis. Rock and Soil Mechanics, 2020, 41(3): 1048-1055 (in Chinese) Sheng Jianglong, Han Yunfei, Ye Zuyang, et al. The relative permeability model for water-air two-phase flow in rough-walled fractures of rock and numerical analysis. Rock and Soil Mechanics, 2020, 41(3): 1048-1055 (in Chinese)
[16] Zhao B, MacMinn CW, Juanes R. Wettability control on multiphase flow in patterned microfluidics. Proceedings of the National Academy of Sciences, 2016, 113(37): 10251-10256 doi: 10.1073/pnas.1603387113
[17] 魏鹳举, 胡冉, 廖震等. 湿润性对孔隙介质两相渗流驱替效率的影响. 力学学报, 2021, 53(4): 1008-1017 (Wei Guanju, Hu Ran, Liao Zhen, et al. Effects of wettability on displacement effciency of two-phase flow in porous media. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(4): 1008-1017 (in Chinese) Wei Guanju, Hu Ran, Liao Zhen, et al. Effects of wettability on displacement effciency of two-phase flow in porous media. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(4): 1008-1017 (in Chinese)
[18] Trojer M, Szulczewski ML, Juanes R. Stabilizing fluid-fluid displacements in porous media through wettability alteration. Physical Review Applied, 2015, 3(5): 054008 doi: 10.1103/PhysRevApplied.3.054008
[19] Holtzman R, Segre E. Wettability stabilizes fluid invasion into porous media via nonlocal, cooperative pore filling. Physical Review Letters, 2015, 115(16): 164501 doi: 10.1103/PhysRevLett.115.164501
[20] Bergslien E, Fountain J. The effect of changes in surface wettability on two-phase saturated flow in horizontal replicas of single natural fractures. Journal of Contaminant Hydrology, 2006, 88(3-4): 153-180 doi: 10.1016/j.jconhyd.2006.06.009
[21] Lee HB, Kim BW. Effect of NAPL exposure on the wettability and two-phase flow in a single rock fracture. Hydrological Processes, 2015, 29(23): 4919-4931 doi: 10.1002/hyp.10543
[22] Qiu Y, Xu K, Pahlavan AA, et al. Wetting transition and fluid trapping in a microfluidic fracture. Proceedings of the National Academy of Sciences, 2023, 120(22): e2303515120 doi: 10.1073/pnas.2303515120
[23] Chen S, Doolen GD. Lattice Boltzmann method for fluid flows. Annual Review of Fluid Mechanics, 1998, 30(1): 329-364 doi: 10.1146/annurev.fluid.30.1.329
[24] Aidun CK, Clausen JR. Lattice-Boltzmann method for complex flows. Annual Review of Fluid Mechanics, 2010, 42: 439-472 doi: 10.1146/annurev-fluid-121108-145519
[25] Qian YH, d'Humières D, Lallemand P. Lattice BGK models for Navier-Stokes equation. Europhysics Letters, 1992, 17(6): 479 doi: 10.1209/0295-5075/17/6/001
[26] 申林方, 曾叶, 王志良等. 考虑几何形貌特征的粗糙岩体裂隙渗流特性研究. 岩石力学与工程学报, 2019, 38(S1): 2704-2711 (Shen Linfang, Zeng Ye, Wang Zhiliang, et al. Research on seepage properties of rough fracture considering geometrical morphology. Chinese Journal of Rock Mechanics and Engineering, 2019, 38(S1): 2704-2711 (in Chinese) Shen Linfang, Zeng Ye, Wang Zhiliang, et al. Research on seepage properties of rough fracture considering geometrical morphology. Chinese Journal of Rock Mechanics and Engineering, 2019, 38(S1): 2704-2711 (in Chinese)
[27] 张戈, 田园, 李英骏. 不同JRC粗糙单裂隙的渗流机理数值模拟研究. 中国科学: 物理学, 力学, 天文学, 2019, 49(1): 30-39 (Zhang Ge, Tian Yuan, Li Yingjun. Numerical study on the mechanism of fluid flow through single rough fractures with different JRC. Science China : Physics, Mechanics & Astronomy, 2019, 49(1): 30-39 (in Chinese) Zhang Ge, Tian Yuan, Li Yingjun. Numerical study on the mechanism of fluid flow through single rough fractures with different JRC. Science China: Physics, Mechanics & Astronomy, 2019, 49(1): 30-39 (in Chinese)
[28] 王登科, 田晓瑞, 魏建平等. 基于工业CT扫描和LBM方法的含瓦斯煤裂隙演化与渗流特性. 采矿与安全工程学报, 2021, 39(2): 387-396 (Wang Dengke, Tian Xiaorui, Wei Jianping, et al. Fracture evolution and permeability characteristics in gas-bearing coal based on industrial CT scanning and LBM method. Journal of Mining & Safety Engineering, 2021, 39(2): 387-396 (in Chinese) Wang Dengke, Tian Xiaorui, Wei Jianping, et al. Fracture evolution and permeability characteristics in gas-bearing coal based on industrial CT scanning and LBM method. Journal of Mining & Safety Engineering, 2021, 39(2): 387-396 (in Chinese)
[29] Liu Y, Berg S, Ju Y, et al. Systematic investigation of corner flow impact in forced imbibition. Water Resources Research, 2022, 58(10): e2022WR032402 doi: 10.1029/2022WR032402
[30] Wang H, Cai J, Su Y, et al. Imbibition behaviors in shale nanoporous media from pore-scale perspectives. Capillarity, 2023, 9(2): 32-44 doi: 10.46690/capi.2023.11.02
[31] 张晟庭, 李靖, 陈掌星等. 基于改进LBM的气液自发渗吸过程中动态润湿效应模拟. 力学学报, 2023, 55(2): 355-368 (Zhang Shengting, Li Jing, Chen Zhangxing, et al. Simulation of dynamic wetting effect during gas-liquid spontaneous imbibition based on modified LBM. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(2): 355-368 (in Chinese) doi: 10.6052/0459-1879-22-409 Zhang Shengting, Li Jing, Chen Zhangxing, et al. Simulation of dynamic wetting effect during gas-liquid spontaneous imbibition based on modified LBM. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(2): 355-368 (in Chinese) doi: 10.6052/0459-1879-22-409
[32] Huang H, Thorne Jr DT, Schaap MG, et al. Proposed approximation for contact angles in Shan-and-Chen-type multicomponent multiphase lattice Boltzmann models. Physical Review E, 2007, 76(6): 066701 doi: 10.1103/PhysRevE.76.066701
[33] Dou Z, Zhou Z, Sleep BE. Influence of wettability on interfacial area during immiscible liquid invasion into a 3D self-affine rough fracture: Lattice Boltzmann simulations. Advances in Water Resources, 2013, 61: 1-11 doi: 10.1016/j.advwatres.2013.08.007
[34] Guiltinan EJ, Santos JE, Cardenas MB, et al. Two-phase fluid flow properties of rough fractures with heterogeneous wettability: Analysis with lattice Boltzmann simulations. Water Resources Research, 2021, 57(1): e2020WR027943 doi: 10.1029/2020WR027943
[35] Yi J, Liu L, Xia Z, et al. Effects of wettability on relative permeability of rough-walled fracture at pore-scale: A lattice Boltzmann analysis. Applied Thermal Engineering, 2021, 194: 117100 doi: 10.1016/j.applthermaleng.2021.117100
[36] 张春华, 刘卫东, 苟斐斐. 基于格子玻尔兹曼的润湿性对降压效果的研究. 西南石油大学学报(自然科学版), 2017, 39(3): 111-120 (Zhang Chunhua, Liu Weidong, Gou Feifei. Simulation study on the effects of wettability on depressurization based on lattice boltzmann model. Journal of Southwest Petroleum University (Science & Technology Edition), 2017, 39(3): 111-120 (in Chinese) Zhang Chunhua, Liu Weidong, Gou Feifei. Simulation study on the effects of wettability on depressurization based on lattice boltzmann model. Journal of Southwest Petroleum University (Science & Technology Edition), 2017, 39(3): 111-120 (in Chinese)
[37] 唐明明, 卢双舫, 辛盈等. 基于格子玻尔兹曼方法的致密砂岩驱替模拟. 中国石油大学学报(自然科学版), 2020, 44(2): 10-19 (Tang Mingming, Lu Shuangfang, Xin Ying, et al. Displacement of tight sandstone based on lattice Boltzmann method. Journal of China University of Petroleum (Edition of Natural Science), 2020, 44(2): 10-19 (in Chinese) Tang Mingming, Lu Shuangfang, Xin Ying, et al. Displacement of tight sandstone based on lattice Boltzmann method. Journal of China University of Petroleum (Edition of Natural Science), 2020, 44(2): 10-19 (in Chinese)
[38] Zhou X, Sheng J, Ye Z. Evaluation of immiscible two-phase quasi-static displacement flow in rough fractures using LBM simulation: Effects of roughness and wettability. Capillarity, 2024, 11(2): 41-52
[39] Brown SR. Fluid flow through rock joints: The effect of surface roughness. Journal of Geophysical Research: Solid Earth, 1987, 92(B2): 1337-1347 doi: 10.1029/JB092iB02p01337
[40] Ye ZY, Liu HH, Jiang QH, et al. Two-phase flow properties in aperture-based fractures under normal deformation conditions: Analytical approach and numerical simulation. Journal of Hydrology, 2017, 545: 72-87 doi: 10.1016/j.jhydrol.2016.12.017
[41] Ye ZY, Liu HH, Jiang QH, et al. Two-phase flow properties of a horizontal fracture: The effect of aperture distribution. Advances in Water Resources, 2015, 76: 43-54 doi: 10.1016/j.advwatres.2014.12.001
[42] 张传庆, 郭宇航, 徐金顺等. 基于功率谱密度的评估岩石节理粗糙度新方法. 岩土力学, 2022, 43(11): 3135-3143 (Zhang Chuanqing, Guo Yuhang, Xu Jinshun, et al. A method for evaluating rock joint roughness based on power spectral density. Rock and Soil Mechanics, 2022, 43(11): 3135-3143 (in Chinese) Zhang Chuanqing, Guo Yuhang, Xu Jinshun, et al. A method for evaluating rock joint roughness based on power spectral density. Rock and Soil Mechanics, 2022, 43(11): 3135-3143 (in Chinese)
[43] 孙辅庭, 佘成学, 万利台. 新的岩石节理粗糙度指标研究. 岩石力学与工程学报, 2013, 32(12): 2513-2519 (Sun Futing, She Chengxue, Wan Litai. Research on a new roughness index of rock joint. Chinese Journal of Rock Mechanics and Engineering, 2013, 32(12): 2513-2519 (in Chinese) Sun Futing, She Chengxue, Wan Litai. Research on a new roughness index of rock joint. Chinese Journal of Rock Mechanics and Engineering, 2013, 32(12): 2513-2519 (in Chinese)
[44] Shan X, Chen H. Lattice Boltzmann model for simulating flows with multiple phases and components. Physical Review E, 1993, 47(3): 1815-1819 doi: 10.1103/PhysRevE.47.1815
[45] Zou Q, He X. On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Physics of Fluids, 1997, 9(6): 1591-1598 doi: 10.1063/1.869307
[46] He X, Zou Q, Luo L S, et al. Analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice Boltzmann BGK model. Journal of Statistical Physics, 1997, 87: 115-136 doi: 10.1007/BF02181482
[47] Yamabe H, Tsuji T, Liang Y, et al. Lattice Boltzmann simulations of supercritical CO2-water drainage displacement in porous media: CO2 saturation and displacement mechanism. Environmental Science & Technology, 2015, 49(1): 537-543
[48] Latt J, Malaspinas O, Kontaxakis D, et al. Palabos: Parallel lattice Boltzmann solver. Computers & Mathematics with Applications, 2021, 81: 334-350
[49] 鞠杨, 王金波, 高峰等. 变形条件下孔隙岩石 CH4 微细观渗流的 Lattice Boltzmann 模拟. 科学通报, 2014, 22: 2127-2136 ((Ju Yang, Wang Jinbo, Gao Feng, et al. Lattice-Boltzmann simulation of microscale CH4 flow in porous rock subject to force-induced deformation. China Science Bulletin, 2014, 22: 2127-2136 (Ju Yang, Wang Jinbo, Gao Feng, et al. Lattice-Boltzmann simulation of microscale CH4 flow in porous rock subject to force-induced deformation. China Science Bulletin, 2014, 22: 2127-2136
[50] Tokunaga TK. Physicochemical controls on adsorbed water film thickness in unsaturated geological media. Water Resources Research, 2011, 47(8): W08514 doi: 10.1029/2011WR010676
[51] 张晟庭, 李靖, 陈掌星等. 气液非混相驱替过程中的卡断机理及模拟研究. 力学学报, 2022, 54(5): 1429-1442 (Zhang Shengting, Li Jing, Chen Zhangxing, et al. Study on snap-off mechanism and simulation during gas-liquid immiscible displacement. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(5): 1429-1442 (in Chinese) Zhang Shengting, Li Jing, Chen Zhangxing, et al. Study on snap-off mechanism and simulation during gas-liquid immiscible displacement. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(5): 1429-1442 (in Chinese)
[52] Li J, Li X, Wang X, et al. Water distribution characteristic and effect on methane adsorption capacity in shale clay. International Journal of Coal Geology, 2016, 159: 135-154 doi: 10.1016/j.coal.2016.03.012
[53] Li J, Li X, Wu K, et al. Thickness and stability of water film confined inside nanoslits and nanocapillaries of shale and clay. International Journal of Coal Geology, 2017, 179: 253-268 doi: 10.1016/j.coal.2017.06.008
[54] 李靖, 李相方, 王香增等. 页岩黏土孔隙含水饱和度分布及其对甲烷吸附的影. 力学学报, 2016, 48(5): 1217-1228 (Li Jing, Li Xiangfang, Wang Xiangzeng, et al. Effect of water distribution on methane adsorption capacity in shale clay. Chinese Journal of Ship Research, 2016, 48(5): 1217-1228 (in Chinese) Li Jing, Li Xiangfang, Wang Xiangzeng, et al. Effect of water distribution on methane adsorption capacity in shale clay. Chinese Journal of Ship Research, 2016, 48(5): 1217-1228 (in Chinese)
[55] Zhang T, Javadpour F, Li J, et al. Pore-scale perspective of gas/water two-phase flow in shale. SPE Journal, 2021, 26(2): 828-846 doi: 10.2118/205019-PA
[56] Chaudhary K, Bayani CM, Wolfe WW, et al. Pore-scale trapping of supercritical CO2 and the role of grain wettability and shape. Geophysical Research Letters, 2013, 40(15): 3878-3882 doi: 10.1002/grl.50658
-
期刊类型引用(8)
1. 宋远翔，杨成鹏，李俊，贾斐. 2D-C/SiC复合材料的偏轴压缩力学行为. 力学学报. 2025(03): 644-657 . 
本站查看
2. 李鑫，李龙，邵红艳，于国强，高希光，陈官峰，张春兰. SiC_f/SiC陶瓷基复合材料T型结构件在弯曲载荷下的失效行为研究. 推进技术. 2023(08): 173-180 . 百度学术
3. 杨成鹏，林江嵘，贾斐，王波. 2D-C/SiC复合材料的高温非线性本构模型. 力学学报. 2023(08): 1721-1731 . 本站查看
4. 金其多，任毅如，胡绚，蒋宏勇. 含黏弹性夹芯FG-GRC后屈曲梁的低速冲击响应. 力学学报. 2021(01): 194-204 . 本站查看
5. 郭晓龙，姚寅，陈少华. 一种预测颗粒增强复合材料界面力学性能的新方法. 力学学报. 2021(05): 1334-1344 . 本站查看
6. 汪佳辉，吴锦武，郭小军，胡晓安，李龙彪，王海涛. 陶瓷基复合材料结构固有频率与内部损伤分析. 失效分析与预防. 2021(03): 177-183 . 百度学术
7. 王晓博，李璐璐，赵波，宋超胜. 陶瓷基复合材料加工技术及其表面亚表面损伤机制研究进展. 表面技术. 2021(12): 17-34 . 百度学术
8. 曹明月，张启，吴建国，葛敬冉，梁军. 缝合式C/SiC复合材料非线性本构关系及断裂行为研究. 力学学报. 2020(04): 1095-1105 . 本站查看
其他类型引用(8)
计量
- 文章访问数: 147
- HTML全文浏览量: 83
- PDF下载量: 56
- 被引次数: 16
