Specific interfacial area: The missing state variable in two‐phase flow equations?
Specific interfacial area: The missing state variable in two‐phase flow equations?
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DOI：
10.1029/2010wr009291
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发表时间：
2011-05
影响因子：
5.4
通讯作者：
V. Joekar‐Niasar;S. Hassanizadeh
中科院分区：
文献类型：
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作者：
V. Joekar‐Niasar;S. Hassanizadeh
经典的多相流达西方程假设重力和流体压力梯度是唯一的驱动力，流动阻力由（相对）渗透率作为饱和度的函数来参数化。可以想象，在多相流中，还可能存在其他驱动力。这意味着这种非平衡效应可以集中到渗透率系数中。事实上，许多研究表明，相对渗透率系数通常不仅取决于饱和度，还取决于系统的动力学。通过合理热力学的应用，建立了两相流理论，其中界面区域作为单独的热力学实体引入，并明确地包括了它们的宏观效应。这一理论包含了新的驱动力，其意义尚待确定。为了研究理论中的新术语，我们采用了一种称为DYPOSIT的动态孔隙网络模型。形成一个长孔隙网络（由几个具有代表性的基本体串联而成），代表一维多孔介质柱。该模型提供了局部相压力、毛管压力、界面面积、饱和度和流量的孔隙尺度分布，并对其进行平均，得到这些变量的宏观尺度分布。我们的分析表明，模拟结果与描述瞬态行为的经典方程存在差异，特别是对非润湿相瞬态渗透率的描述。对扩展方程中的系数进行了量化和参数化。尽管在Dirichlet边界条件下，流量变化明显，但有一个明显的趋势表明，系数与饱和度有关，与动态条件无关。此外，使用新的系数，可以解释瞬态或稳态流动形式，这是一个新的成就。
Classical Darcy's equation for multiphase flow assumes that gravity and the gradient in fluid pressure are the only driving forces and resistance to the flow is parameterized by (relative) permeability as a function of saturation. It is conceivable that, in multiphase flow, other driving forces may also exist. This would mean that such nonequilibrium effects are lumped into a permeability coefficient. Indeed, many studies have shown that the relative permeability coefficient generally depends not only on saturation but also on dynamics of the system. Through the application of rational thermodynamics, a theory of two‐phase flow had been developed in which interfacial areas were introduced as separate thermodynamic entities and their macroscale effects were explicitly included. This theory includes new driving forces whose significance needs still to be established. To study new terms in the theory, we employ a dynamic pore network model called DYPOSIT. A long pore network (several representative elementary volumes connected in series) is generated, which represents as a one‐dimensional porous medium column. This model provides pore scale distribution of local phase pressures, capillary pressure, interfacial area, saturation, and flow rate, which are averaged to obtain the macroscale distributions of these variables. Our analysis shows that there are discrepancies between the simulation results and the classical equations to describe the transient behavior, especially for the nonwetting phase transient permeability. The coefficients in the extended equations are quantified and parameterized. Although under the applied Dirichlet boundary conditions, flow varies significantly, there is a clear trend illustrating dependency of coefficients on saturation, independent of dynamic conditions. Furthermore, using the new coefficients, it is possible to explain either transient or steady state flow regimes, which is a new achievement.