With the recent interest in shale gas, an understanding of the flow mechanisms at the pore scale and beyond is necessary, which has attracted a lot of interest from both industry and academia. One of the suggested algorithms to help understand flow in such reservoirs is the Lattice Boltzmann Method (LBM). The primary advantage of LBM is its ability to approximate complicated geometries with simple algorithmic modificatoins. In this work, we use LBM to simulate the flow in a porous medium. More specifically, we use LBM to simulate a Brinkman type flow. The Brinkman law allows us to integrate fast free-flow and slow-flow porous regions. However, due to the many scales involved and complex heterogeneities of the rock microstructure, the simulation times can be long, even with the speed advantage of using an explicit time stepping method. The problem is two-fold, the computational grid must be able to resolve all scales and the calculation requires a steady state solution implying a large number of timesteps. To help reduce the computational complexity and total simulation times, we use model reduction techniques to reduce the dimension of the system. In this approach, we are able to describe the dynamics of the flow by using a lower dimensional subspace. In this work, we utilize the Proper Orthogonal Decomposition (POD) technique, to compute the dominant modes of the flow and project the solution onto them (a lower dimensional subspace) to arrive at an approximation of the full system at a lowered computational cost. We present a few proof-of-concept examples of the flow field and the corresponding reduced model flow field.


Understanding the flow mechanics of petroleum reservoirs is critical to economic evaluation of recoverable resources and reservoir decelopment planning. Laboratory mesurements can be very expensive and may be limited in scope of scales that can be explored due to inability to accurately describe in-situ conditions. A key tool in understanding flow on both the pore and reservoirs scales is simulation methods. In reservoir conditions, there are many complex muli-physical processes that need to be modeled and, complicating issues further, there are a great number of uncertainties in subsurface parameters. These uncertainties require fast and accurate forward models to update parameters. Finally, due to the scale disparities involved, simulation of these reservoirs is often very computational expensive. With the recent boom in Shale gas, understanding fracture modeling and pore-scale flow mechanics has become critical. Computational tools and techniques must be developed in these areas to reduce simulation cost and time.

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