An Embedded Grid-Free Approach for Near Wellbore Streamline Simulation
Authors: Wang Bin , Du Juan , Feng Yin , Wang Yihui , Wang Sijie , Yang Ruiyue 
Published: February 2017

Abstract
Reactive transport phenomenon, such as CO2 sequestration and Microbial EOR, has been of interest in streamline-based simulations. Tracing streamlines launched from a wellbore is important especially for time-sensitive transport behaviors. However, gridblocks containing wells are usually too large compared to wellbore radius. Field-scale simulations with local-grid-refinement (LGR) models are often consume huge computational time. An embedded grid-free approach is developed to account for the transport along streamlines in the vicinity of wellbore.
An embedded semi-analytical approach to integrate near wellbore transport behaviors into field-scale streamline simulation is developed, which consists of two-stage of development: tracing streamlines in a local gridblock (containing wells) and coupling with neighboring grids. The velocity field in a local gridblock is produced based on boundary element method, and then streamlines are numerically traced with TOF along each streamline based on the velocity field. This local streamline system is then coupled with Pollock-algorithm-based system at the interface between the local gridblock and its neighbors. Finally, the coupling result is verified by matching boundary conditions and transport equations are solved along streamlines.
The presented algorithm for solving near-wellbore streamlines is verified by both commercial finite element simulator and Pollock-algorithm-based 3D streamline simulator. Simulation results (including velocity field, time-of-flight (TOF), streamline pattern and concentration pattern) produced by different approaches are analyzed. Results show that the presented method can accurately perform the near-wellbore streamline simulation in a time-effective manner. The algorithm can easily extend to one grid containing multiple wells to account for the effect of interactions between wells on the overall flow pattern. Two and three-dimensional synthetic field-scale cases are investigated considering advection-reaction transport and multiple-well modeling. The streamline pattern and distribution of TOF within the gridblock containing wells are highly dependent on well location and number of wells. Assuming streamlines are evenly launched from the gridblock boundary and ignoring transport in the local gridblock containing wells are not always reasonable and may lead to overestimating the concentration front (up to 21.3% error).
Two algorithms are introduced in this work. One is referred to as Virtual-Boundary Element Method that is used to generate near wellbore streamlines. And the other one is an embedded semi-analytical approach to solve and integrate near wellbore transport behaviors into field-scale streamline simulation. This study provides a simple and grid-free solution, but is capable of capturing the flow field accurately near the wellbore with significant accuracy and computational efficiency. The method is promising for streamline-based reservoir simulation with time-sensitive transport, and other simulations which require an accurate assessment of interactions between wells in one particular gridblock.