Field Scale Characterization of Geological Formations Using Percolation Theory

Abstract

The connectivity of high conductivity pathways in geological formations depend on the spatial distribution of geological heterogeneities that may appear on various length scales. Appropriate modeling of this is crucial within in hydrology and petroleum systems. The approach taken in this study is to use percolation theory to quantify the connectivity, hydraulic conductivity, and breakthrough time behavior between an injector and a producer within such systems. In particular, a three-dimensional overlapping sandbody model is considered which assumes that the geological formation can be split into either conductive flow units (i.e., good sands) or non-conductive units (i.e., poor sands). The results are the master curves for the formation connectivity as well as the hydraulic conductivity and breakthrough time. The percolation approach is then validated against Burgan offshore reservoir dataset which reveal good matches when compared with the results obtained from computationally expensive conventional methods.

Effect of Pore‐Scale Heterogeneity on Scale‐Dependent Permeability: Pore‐Network Simulation and Finite‐Size Scaling Analysis

“…Similar results were reported by Sadeghnejad et al. (2012) for field characterizations of conductivity in geologic formations.…”

“…They utilized, however, the original form of the finite-size scaling analysis, Equation 4, to illustrate the collapse of their data. Similar results were reported by Sadeghnejad et al (2012) for field characterizations of conductivity in geologic formations.…”

Flow, Transport, and Reaction in Porous Media: Percolation Scaling, Critical‐Path Analysis, and Effective Medium Approximation

“…They investigated the appropriate scaling plots to determine the scaling functions by computer simulations. Sadeghnejad et al () did the same to study the hydraulic conductivity K . Their analysis utilized the method described above, namely, plotting K L μ / ν versus ( p − p c ) L 1/ ν , in order to compute the scaling function for K .…”

“…The two basic approaches can be divided according to the nature of the problem to be solved. When the focus is flow and transport in porous media that are essentially binary mixtures, such as sand or gravel within mud (Kolterman & Gorelick, ; Ramanathan et al, ; Sadeghnejad et al, ), then the scaling formulations of percolation are preferred (Lee et al, ; Makse et al, , ; Masihi et al, ; Sadeghnejad et al, ). In such more traditional subjects of percolation research, the scaling relationships describe the topology of the fluid‐carrying part of a porous medium.…”

“…An important goal of hydrogeology and, more generally, any discipline that has to do with fluid flow and transport in porous media is developing theoretical models to predict the hydraulic conductivity K and to be able to provide a range of likely values of K describing the uncertainty in the predictions (Dagan & Neuman, ; Dagan, ; de Marsily et al, ; Freeze, ; Gelhar & Axness, ; King et al, ; Makse et al, ; Masihi & King, ; Matheron, ; Rubin, ; Sadeghnejad et al, ; Winter et al, ). A significant portion of such efforts has been devoted to the characterization of porous media (Bear, ; Dullien, ; Journel & Huijbregts, ; Rubin, ; Sahimi, , , , ).…”