Novel permeability upscaling method using Fast Marching Method

Abstract

Despite computational advances, geo-cellular models are routinely upscaled for reservoir simulation purposes. Geo-cellular models typically incorporate small scale variations obtained from static data; whereas, simulation models capture dynamic data obtained from production of the field. The process of reducing the number of grid blocks in the geological model so that the simulation model can be run efficiently is called the process of upscaling. Upscaling requires combining the small grid blocks from geological model to make a larger grid block, as well as assigning reservoir properties on the coarse scale. Among the physical properties that need to be assigned, the assignment of permeability is the most challenging. Unlike porosity (or saturation), permeability is a dynamic property and capturing the fine scale dynamic displacement requires a non-linear upscaling of fine scale permeability values.The two types of methods used for permeability upscaling can be broadly categorized as static upscaling and dynamic upscaling. Static upscaling methods average fine scale values to calculate an upscaled value. These methods are efficient but may not capture the dynamic behavior. The dynamic upscaling methods are computationally expensive and may be dependent on boundary conditions. In this paper, we propose a new dynamic method for areal upscaling based on the fast marching algorithm. The Fast Marching Method (FMM) accurately captures the propagating pressure front as a function of time. We define the objective function as the difference in the propagation time between fine scale and coarse scale models. By minimizing the objective function, we calculate the permeability of the upscaled model.The Fast Marching Method is an extremely efficient method for calculating the pressure front propagation time based on reservoir properties. This method is based on solving the Eikonal equation using an upwind finite difference approximation. The advantage of this method is that, without running any flow simulation, we can calculate the pressure front location (radius of investigation) as a function of time. In this paper, using 2D and 3D models, we demonstrate that the calculated effective permeability using the new method can reproduce the dynamic behavior of the fine scale model.