Iteratively Coupled Fluid Flow & Geomechanics Simulation using Estimated Equivalent Permeability and Porosity by Fractal and Statistical Methods
Authors: Lee Sangyup , Schechter David S. 
Published: September 2015

Abstract
Permeability and porosity are two of the key parameters for reservoir simulation. Porosity is essential for estimating original oil/gas in place and for calculating saturation and permeability. For naturally fractured reservoir (NFR) simulation, when matrix porosity is negligible, it is important to estimate proper fracture porosity and permeability in order to obtain more accurate simulation results. However, it is difficult to measure and estimate these parameters because of numerous factors, such as high heterogeneity of fluid and fracture properties, a scale difference between sampling window and real reservoir domain, and so on.
In a previous study (Kim and Schechter 2009), a fractal discrete fracture network (FDFN) codes were developed to generate discrete fracture network distributions and to calculate fracture porosity based on outcrop map, core sample and/or image log data. Because it was almost impossible to understand reservoir conditions from limited surveying data, fractal theory was adopted to reduce scale discrepancy errors in simulations. Each generated fracture had constant aperture distribution or normal/log-normal aperture distribution. The aperture distribution characteristics could describe natural like aperture properties. The code directly calculated fracture porosity using generated FDFN geometry data.
In this study, we developed codes to estimate the equivalent permeability distributions of large numbers of fractures using a modified Oda's algorithm. A modified Oda's algorithm reflected the heterogeneous nature of fracture networks using the full tensor permeability scheme. Because we used fractal and statistical methods to generate the fracture networks, the generated fracture geometries could have been different, even though same input data were used. Therefore, to generate reliable fracture network results with given input data, we performed FDFN codes 1000 times, using a Monte Carlo simulation. Then, generated fracture numbers and fracture density were calculated. Cumulative distribution function (CDF) of generated fractures was calculated, and P10, P50 and P90 of the fracture networks were estimated. We selected the P50 case as reservoir fracture map. Simulated FDFN data of P50 map were passed to a modified Oda's algorithm, and x and y directional equivalent permeability distributions were calculated. We also developed iteratively coupled fluid flow and geomechanics codes, and simulated the fluid flow in porous media and estimated the interaction effects between two models. With calculated equivalent permeability data, two-phase fluid flow in porous media was first solved by finite difference methods (FDM), and then the calculated pore pressure data were passed to an elasto-plastic geomechanics model to calculate stress/volumetric strain of each element using finite element methods (FEM). The iteration was repeated until the convergence level was below the desired tolerance level and we estimated the interaction effects between fluid flow and geomechanics on reservoir simulation. All codes were written in Matlab.