A level set method for simulating capillary‐controlled displacements at the pore scale with nonzero contact angles
A level set method for simulating capillary‐controlled displacements at the pore scale with nonzero contact angles
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DOI：
10.1002/wrcr.20334
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发表时间：
2013-08
影响因子：
5.4
通讯作者：
E. Jettestuen;J. O. Helland;M. Prodanović
中科院分区：
文献类型：
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作者：
E. Jettestuen;J. O. Helland;M. Prodanović
我们提出了一种水平集方法来模拟多孔介质中具有非零接触角的毛细管控排量。该方法的主要特点是水平集演化速度在孔隙空间和固相中是不同的。这在标准水平集方程中增加了额外的项，使得在稳态时，接触角在固相中被强制，而毛细和界面力在孔隙空间中是平衡的。利用该方法模拟了几种不同孔道几何形状下不同接触角的准静态排水和渗吸过程，并计算了每种情况下的毛管压力和液液比界面面积曲线。我们通过比较在理想的二维几何结构和三维(3-D)直管中计算的稳定流体构型与已知的解析解来验证该方法。在三维砂岩图像子集上进行的模拟表明，所开发的方法解释了众所周知的孔隙尺度机制，如活塞式入侵、海恩斯跳跃、界面合并、润湿膜的回缩、膨胀和折断。接触角由流体/流体界面和孔洞/固体边界的交点形成。因此，用至少与用于近似水平集导数的数值模板的大小相同的网格点来离散孔隙空间周围的固体基质。
We present a level set method for simulating capillary‐controlled displacements with nonzero contact angles in porous media. The main feature of the method is a level set evolution velocity which is different in the pore space and solid phase. This augments the standard level set equation with an extra term such that, at steady state, the contact angle is enforced in the solid phase, whereas capillary and interfacial forces are balanced in the pore space. We employ the method to simulate quasistatic drainage and imbibition processes for different contact angles in several pore geometries, and to compute capillary pressure and fluid/fluid specific interfacial area curves in each case. We validate the method by comparing stable fluid configurations computed in idealized two‐dimensional geometries and three‐dimensional (3‐D) straight tubes with known analytical solutions. Simulations performed in a subset of a 3‐D sandstone image show that the developed method accounts for well‐known pore‐scale mechanisms such as piston‐like invasion, Haines jump, interface coalescence, and retraction, swelling of wetting films and snap‐off. The contact angle is formed by an intersection of the fluid/fluid interface and the void/solid boundary. Therefore, the solid matrix surrounding the pore space is discretized with at least an equal number of grid points as the size of the numerical stencil used to approximate the level set derivatives.