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Summary The discrete feature network (DFN) approach offers many key advantages over conventional dual porosity (DP) approaches, particularly when issues of connectivity dominate recovery and reservoir stimulation in fractured and heterogeneous reservoirs. DP models have been developed for complex multiphase and thermal effects, and have been implemented for basin scale modeling. However, DP models address only the dual porosity nature of fractured reservoirs, generally simplifying connectivity and scale-dependent heterogeneity issues which are modeled efficiently and more accurately by the DFN approach. This paper describes the development of techniques to integrate DFN and DP approaches. These techniques allow the analyst to maintain many of the advantages of the DP simulator approach without losing the realism of complex fracture system geometry and connectivity, as captured by DFN models. The techniques described are currently used within a DOE funded research project for linking a DFN and a DP thermal simulation model for the Yates field, Texas. The paper describes some of the geological and engineering aspects of the Yates field and gives two examples of how DP parameters for the thermal simulation can be derived using DFN modeling techniques. Introduction Reservoir simulation can be significantly more challenging for fractured reservoirs than it is for conventional clastic reservoirs. The dual porosity (DP) approach for the simulation of fractured reservoirs adds a second interacting continuum to reflect storage and permeability characteristics but does not adequately address connectivity issues. These effects, which play a key role in fractured reservoirs, are generally better addressed by discrete feature network (DFN) models.1 Another advantage of DFN models is that they are generally implemented as stochastic models, in which multiple realizations provide a quantitative measure for uncertainty and variability. Despite the significant simplifications made regarding the geometry of the fracture network in equivalent porous medium DP models (Fig. 1) and the recent progress made in developing powerful DFN modeling software, DP models still offer advantages regarding the level of sophistication of available multiphase flow solvers. In many cases, DP models also offer advantages regarding model size and speed. As a result, there is a need to link DP and DFN models to be able to take maximum advantage of each approach. This paper presents a series of techniques, which can be used to develop DP models that more accurately reflect the anisotropy, heterogeneity, and most important, the scale-dependent connectivity structure of fractured reservoirs. These techniques will allow the DP approach to take advantage of some of the features of the DFN approach. The approach adopted is to derive grid cell and well parameters through DFN models. The first section of this paper discusses which fracture porosity parameters can be derived for DP models from DFN models and how they are derived. The second section describes different techniques that can be used to link DP and DFN models. At the end of the paper two examples are given based on data from the Yates field, Texas. DP Input Parameter from DFN Modeling Fracture System Porosity. The fracture system porosity fF can be directly calculated as the product of the fracture intensity expressed as fracture area per unit volume (P32) and the storage aperture of the fractures (e):… Because the fracture system porosity depends on the number of fractures per unit volume, the fracture size distribution and the fracture aperture distribution, a different porosity needs to be calculated for every portion of the continuum model where these parameters vary. Using a full field DFN model, the fracture system porosity can be calculated separately for each grid cell. The primary issue in definition of fracture porosity from fracture intensity P32 is the selection of an appropriate measure for storage aperture e. Possible measures include:aperture derived from transient hydraulic response,mechanical aperture,aperture derived from fracture permeability or transmissivity ("cubic law"),aperture derived from geophysical measurements (gamma density, matrix porosity), andcorrelations to fracture size and orientation. Directional Fracture System Permeability. The permeability of the fracture system depends on the fracture intensity, the connectivity of the fracture network, and the distribution of fracture transmissivities. Approaches for calculation of approximate measures of grid cell effective directional permeability include the tensor approach of Oda,2 and the use of DFN simulations with a range of orientations for a unit gradient. Oda's2 method begins by considering the orientation of fractures in a grid cell, expressed as a unit normal vector n. Integrating the fractures over all of the unit normals N, Oda obtained the mass moment of inertia of fracture normals distributed over a unit sphere: ….For a specific grid cell with known fracture areas Ak and transmissivities Tk obtained from the DFN model, an empirical fracture tensor can be calculated by adding the individual fractures weighted by their area and transmissivity:…. Oda's permeability tensor is derived from Fij by assuming that Fij expresses fracture flow as a vector along the fracture's unit normal. Assuming that fractures are impermeable in a direction parallel to their unit normal, Fij must be rotated into the planes of permeability ….

This dissertation presents the development of a method for quantitative integration of seismic (elastic) anisotropy attributes with reservoir performance data as an aid in characterization of systems of natural fractures in hydrocarbon reservoirs. This new method incorporates stochastic Discrete Feature Network (DFN) fracture modeling techniques, DFN model based fracture system hydraulic property and elastic anisotropy modeling, and non-linear inversion techniques, to achieve numerical integration of production data and seismic attributes for iterative refinement of initial trend and fracture intensity estimates. Although DFN modeling, flow simulation, and elastic anisotropy modeling are in themselves not new technologies, this dissertation represents the first known attempt to integrate advanced models for production performance and elastic anisotropy in fractured reservoirs using a rigorous mathematical inversion. The following new developments are presented:• Forward modeling and sensitivity analysis of the upscaled hydraulic properties of realistic DFN fracture models through use of effective permeability modeling techniques. iv• Forward modeling and sensitivity analysis of azimuthally variant seismic attributes based on the same DFN models.• Development of a combined production and seismic data objective function and computation of sensitivity coefficients.• Iterative model-based non-linear inversion of DFN fracture model trend and intensity through minimization of the combined objective function.This new technique is demonstrated on synthetic models with single and multiple fracture sets as well as differing background (host) reservoir hydraulic and elastic properties. Results on these synthetic control models show that, given a well conditioned initial DFN model and good quality field production and seismic observations, the integration procedure results in convergence of both fracture trend and intensity in models with both single and multiple fracture sets. Tests show that for a single fracture set convergence is accelerated when the combined objective function is used as compared to a similar technique using only production data in the objective function.Tests performed on multiple fracture sets show that, without the addition of seismic anisotropy, the model fails to converge. These tests validate the importance of the new process for use in more realistic reservoir models.

The discrete feature network (DFN) approach offers many key advantages over conventional dual porosity (DP) approaches, particularly when issues of connectivity dominate recovery and reservoir stimulation in fractured and heterogeneous reservoirs. DP models have been developed for complex multiphase and thermal effects, and have been implemented for basin scale modeling. However, DP models address only the dual porosity nature of fractured reservoirs, generally simplifying connectivity and scale-dependent heterogeneity issues which are modeled efficiently and more accurately by the DFN approach. This paper describes the development of techniques to integrate DFN and DP approaches. These techniques allow the analyst to maintain many of the advantages of the DP simulator approach without losing the realism of complex fracture system geometry and connectivity, as captured by DFN models. The techniques described are currently used within a DOE funded research project for linking a DFN and a DP thermal simulation model for the Yates Field, Texas. The paper describes some of the geological and engineering aspects of the Yates Field and gives two examples how DP parameters for the thermal simulation can be derived using DFN modeling techniques. P. 351

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