Summary Steady-state relative permeability experiments are performed by coinjection of two fluids through core plug samples. The relative permeabilities can be calculated using Darcy’s law from the stabilized pressure drop and saturation of the core if capillary end effects and transient effects are negligible. In most cases, such conditions are difficult to obtain. Recent works have presented ways to extrapolate steady-state pressure drop and average saturation measurements affected by capillary end effects collected at different rates to obtain correct relative permeabilities at correct saturations. Both the considered methods are based on linear extrapolations to determine intercepts. Gupta and Maloney (2016) derived their method intuitively and validated it with numerical and experimental data. Andersen (2021a) derived a method from fundamental assumptions and presented an intercept method in a different form where the saturation and relative permeabilities are found directly and uniquely from straightline intercepts. All system parameters, including saturation functions and injection conditions, appear in the model. In this work, the two methods are compared. It is proven theoretically that Gupta and Maloney’s method is correct in that it produces the correct saturation and pressure drops corrected for capillary end effects. Especially, a constant pressure drop was assumed and here proved to exist, as a result of capillary end effects in addition to the Darcy law pressure drop with no end effects. Their method assumes a well-defined end effect region with length xCEE, but this length can be defined almost arbitrarily. This choice has little impact on average saturation and pressure drop, however. They also assumed that for a defined end effect region, the average saturation was constant and equal to the slope in their saturation plot. It is shown that if the region is defined, the average saturation is indeed constant, but not given by the slope. The correct slope is predicted by the Andersen model. We also comment on theoretical misinterpretations of the Gupta and Maloney method. A few works have correctly calculated that the pressure drop over the end effect region is independent of rate, but not accounted for that its length is rate dependent. We show that the combined pressure drop is equal to a constant plus the Darcy pressure drop over the full core. Examples are presented to illustrate the model behaviors. Literature datasets are investigated showing that (a) apparently rate-dependent CO2-brine relative permeability endpoints can be explained by capillary end effects and (b) the intercept methods can be applied to correct shale relative permeabilities.

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毛细管末端效应稳态相对渗透率实验校正截取方法的比较

小结 稳态相对渗透率实验是通过岩心塞样品共注入两种流体来进行的。如果毛细管末端效应和瞬态效应可以忽略不计，则可以使用达西定律从岩心的稳定压降和饱和度计算相对渗透率。在大多数情况下，这样的条件很难获得。最近的工作提出了外推稳态压降和受以不同速率收集的毛细管末端效应影响的平均饱和度测量值的方法，以获得正确饱和度下的正确相对渗透率。两种考虑的方法都基于线性外推来确定截距。Gupta 和 Maloney (2016) 直观地推导出了他们的方法，并用数值和实验数据对其进行了验证。Andersen (2021a) 从基本假设中推导出了一种方法，并提出了一种不同形式的截距方法，其中饱和度和相对渗透率直接且唯一地从直线截距中找到。所有系统参数，包括饱和函数和注入条件，都出现在模型中。在这项工作中，对这两种方法进行了比较。从理论上证明，Gupta 和 Maloney 的方法是正确的，因为它产生了针对毛细管末端效应校正的正确饱和度和压降。特别是，假设存在恒定压降，并在此证明存在，这是由于毛细端效应和达西定律压降而没有端效应。他们的方法假设一个定义明确的末端效应区域，长度为 xCEE，但这个长度几乎可以任意定义。然而，这种选择对平均饱和度和压降几乎没有影响。他们还假设对于定义的末端效应区域，平均饱和度是恒定的并且等于饱和度图中的斜率。结果表明，如果定义了该区域，则平均饱和度确实是恒定的，但不是由斜率给出的。正确的斜率由安徒生模型预测。我们还评论了对 Gupta 和 Maloney 方法的理论误解。一些工作正确计算了末端效应区域上的压降与速率无关，但没有考虑到其长度与速率有关。我们表明，组合压降等于一个常数加上整个核心上的达西压降。举例说明模型的行为。