Rate Dependency in Steady-State Upscaling
Rate Dependency in Steady-State Upscaling
复制标题
稳态升级中的速率依赖性
DOI：
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发表时间：
2015
影响因子：
2.7
通讯作者：
A. Rustad
中科院分区：
文献类型：
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作者：
L. Odsæter;C. Berg;A. Rustad
针对一系列储层模型研究了相对渗透率的稳态放大。考虑了速率相关的放大以及毛细管和粘性极限的放大。我们特别研究河流沉积系统，它代表了一类大型且重要的储层。根据之前的工作，数值例子表明稳态放大是速率相关的。在这方面，我们引入了与尺度相关的毛细管数来估计粘性力和毛细管力之间的平衡。极限解之间的差异可能很大，并且我们表明中间流速可以跨越几个数量级。这证实了在一系列流量场景中对速率相关的稳态放大的需求。我们证明了随着流速的增加，稳态放大从毛细管收敛到粘性极限解，并且我们确定了一个简单的合成模型，其中收敛不是单调的。测试了两组不同的边界条件，但对所提出的油藏模型影响很小。最后，我们通过在细尺度和放大模型上在储层尺度上进行动态流动模拟来证明稳态放大的适用性。所考虑的模型对于实际流速来说是粘性主导的，模拟结果表明粘性极限放大是合适的。
Steady-state upscaling of relative permeability is studied for a range of reservoir models. Both rate-dependent upscaling and upscaling in the capillary and viscous limits are considered. In particular, we study fluvial depositional systems, which represent a large and important class of reservoirs. Numerical examples show that steady-state upscaling is rate dependent, in accordance with previous work. In this respect we introduce a scale-dependent capillary number to estimate the balance between viscous and capillary forces. The difference between the limit solutions can be large, and we show that the intermediate flow rates can span several orders of magnitude. This substantiate the need for rate-dependent steady-state upscaling in a range of flow scenarios. We demonstrate that steady-state upscaling converges from the capillary to the viscous limit solution as the flow rate increases, and we identify a simple synthetic model where the convergence fails to be monotone. Two different sets of boundary conditions were tested, but had only minor effects on the presented reservoir models. Finally, we demonstrate the applicability of steady-state upscaling by performing dynamic flow simulation at the reservoir scale, both on fine-scaled and on upscaled models. The considered model is viscous dominated for realistic flow rates, and the simulation results indicate that viscous limit upscaling is appropriate.