Study of heterogeneity loss in upscaling of geological maps by introducing a cluster-based heterogeneity number

• An indicator is introduced to quantify the heterogeneity in geological models.
• The heterogeneity loss due to upscaling is described by heterogeneity number.
• The heterogeneity loss vs. flow behavior accuracy shows a logarithmic relation.

The prediction of flow behavior in porous media can provide useful insights into the mechanisms involved in CO22 sequestration, petroleum engineering and hydrology. The multi-phase flow is usually simulated by solving the governing equations over an efficient model. The geostatistical (or fine grid) models are rarely used for simulation purposes because they have too many cells. A common approach is to coarsen a fine gird realization by an upscaling method. Although upscaling can speed up the flow simulation, it neglects the fine scale heterogeneity. The heterogeneity loss reduces the accuracy of simulation results.In this paper, the relation between heterogeneity loss during upscaling and accuracy of flow simulation is studied. A realization is divided into some clusters. Every cluster consists of a number of neighboring cells whose permeability values belong to a pre-known interval. The concept of coefficient of variation is applied to define the intra-cluster and inter-cluster heterogeneity numbers. These numbers are then calculated for some fine grid and corresponding upscaled models. The heterogeneous fine grid models are generated by the process of fractional Brownian motion. After simulating water–oil displacement in both fine and coarse models, the relation between flow performance error and heterogeneity loss is investigated. An upper limit for the degree of coarsening is also suggested according to this relation.