Pore network modeling of the Non-Darcy flows in shale and tight formations
Pore network modeling of the Non-Darcy flows in shale and tight formations
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DOI：
10.1016/j.petrol.2018.01.021
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发表时间：
2018-04
影响因子：
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通讯作者：
Xiukun Wang;J. Sheng
中科院分区：
文献类型：
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作者：
Xiukun Wang;J. Sheng
孔隙网络建模是模拟多孔介质中多相流动的有力工具。本文采用准静态模型，模拟了排水置换过程。在页岩和致密地层中，提出了气体非达西流动和液体低速非达西流动的非达西流动机理。页岩和致密地层中的气体流动通常根据努森数值分为滑移流和过渡流。本研究中气体非达西流动采用BK模型（Beskok和Karniadakis，1999），液体低速非达西流动主要基于我们以前的工作（Wang和Sheng，2017 a，B）。这两种效应分别纳入我们的孔隙网络模型。对于气水两相流，气体为非润湿相，气体为非达西流，水为润湿相，达西流。对于油水两相流，考虑了水相和油相的低速非达西渗流。然后，我们的模型被应用在3种情况下。案例1是Berea砂岩（Valvatne，2004），它是常规孔隙网络建模的基准。在这种情况下，在我们的孔隙网络模型中没有考虑非达西流，它完全是达西流。绝对渗透率和相对渗透率均与实验数据相吻合。情况2是Bossier致密气砂岩（Rushing等人，2003年）。在实验中，测量了不同含水饱和度下的气体视渗透率与压力的关系。从而验证了两相条件下气体的非达西流动。案例3是巴内特页岩（Moghills和Jamiolahmady，2016），这是我们的主要关注点。在这种情况下，这两种类型的非达西流的研究和进一步讨论。当压力梯度为10 MPa时，气体非达西渗流使气体渗透率提高了2.66倍，而当压力梯度为0.1MPa/m时，液体低速非达西渗流使液体渗透率降低了40%。在这项研究中提出了两种类型的相对渗透率（KR）的定义：达西渗透率为基础的KR和归一化KR的非达西渗透率作为基础渗透率。结果表明，两种非达西渗流条件下，归一化的相对渗透率变化不大，这意味着在处理非达西渗流机制时，可以假定相对渗透率不变，只考虑对绝对渗透率的影响。
Pore network modeling is a powerful tool to simulate multiphase flow in porous media. Quasi-static model is used in this work and the drainage displacement process is simulated. In shale and tight formations, there are proposed non-Darcy flow mechanisms: gas non-Darcy flow and liquid low velocity non-Darcy flow. The gas flow in shale and tight formations is generally classified in slip flow and transitional flow regimes according to the Knudsen number values. The BK model (Beskok and Karniadakis, 1999) is used for gas non-Darcy flow in this study and the liquid low velocity non-Darcy flow is mainly based on our previous work (Wang and Sheng, 2017a, b). Both effects are incorporated into our pore network model separately. For gas-water flow, gas is the non-wetting phase with gas non-Darcy flow and water is the wetting phase with Darcy flow. For oil-water flow, the low velocity non-Darcy flow is considered for both water and oil phases. Then our model is applied in 3 cases. Case 1 is the Berea sandstone (Valvatne, 2004), which is the benchmark for conventional pore network modeling. In this case, no non-Darcy flows is considered in our pore network model and it is totally Darcy flow. The absolute permeability and relative permeability are both matched with the experimental data. Case 2 is the Bossier tight gas sandstone (Rushing et al., 2003). Gas apparent permeability vs. pressure was measured at different water saturations in their experiments. In this way, the gas non-Darcy flow in two-phase conditions are verified. Case 3 is the Barnett shale (Moghaddam and Jamiolahmady, 2016), which is our major focus. The two types of non-Darcy flows are studied and further discussed in this case. Specifically, the effect of gas non-Darcy flow enhances the gas permeability 2.66 times of the Darcy permeability when pressure is 10 MPa, while the effect of liquid low velocity non-Darcy flow decreases the liquid permeability to 40% of the Darcy permeability when pressure gradient is 0.1 MPa/m. Two types of relative permeability (k r) definition are presented in this study: Darcy permeability based k r and normalized k r where non-Darcy permeability is used as the base permeability. In the results, the normalized relative permeability doesn't change much for both non-Darcy flows, which implies that we can probably assume the relative permeability unchanged and just consider the effect on absolute permeability, when we deal with these non-Darcy flow mechanisms.