Streamlines have been used for reservoir modeling and flow visualization in the petroleum industry and in computational fluid dynamics. When applied to the calculation of volumetric sweep and the identification of by-passed hydrocarbons for improved oil recovery, it is important that the velocity models that are used to trace trajectories across the cells of a grid are flux conservative. As such, the requirements on their tracing may be more stringent than in other disciplines. Flux conservation is also important at faults, at locally refined or coarsened embedded grid boundaries, and within unstructured grids, where the modeling of flow within a cell may not be consistent with the connection fluxes from adjacent cells. In such cases, additional degrees of freedom must be introduced to satisfy flux conservation. In this study, we introduce a flux conservative conforming cell face local boundary layer construction to resolve these inconsistencies. In contrast, solutions that rely upon spatial continuity of streamlines between elements are shown to not be flux conservative when these inconsistencies are present. The use of flux conservative conforming elements also allows the solution to be developed in local isoparametric coordinates, without explicit reference to cell or connection geometry. The solution has been implemented for both 3D corner point and for 2.5D PEBI grids. In all cases we utilize the lowest order Raviart–Thomas zeroth order velocity model, for which the trajectories and transit times may be obtained analytically. The results are demonstrated on a sequence of increasingly complex type, sector and full-field model applications.

流线已用于石油工业和计算流体动力学中的储层建模和流动可视化。当应用于体积扫描计算和旁通烃识别以提高采收率时，用于跟踪网格单元中轨迹的速度模型是通量保守的，这一点很重要。因此，对其追踪的要求可能比其他学科更严格。通量守恒在断层、局部细化或粗化的嵌入网格边界以及非结构化网格中也很重要，其中单元内的流动建模可能与来自相邻单元的连接通量不一致。在这种情况下，必须引入额外的自由度以满足通量守恒。在这项研究中，我们引入了通量保守一致的单元面局部边界层构造来解决这些不一致问题。相比之下，当存在这些不一致时，依赖于元素之间流线空间连续性的解决方案被证明不是通量保守的。使用通量保守一致元素还允许在局部等参坐标中开发解决方案，而无需明确参考单元或连接几何。该解决方案已针对 3D 角点和 2.5D PEBI 网格实施。在所有情况下，我们都使用最低阶 Raviart-Thomas 零阶速度模型，可以通过分析获得轨迹和渡越时间。结果在一系列日益复杂的类型、部门和全领域模型应用程序中得到证明。