Mohammad Karimi-Fard

From outcrop to flow simulation: Constructing discrete fracture models from a LIDAR survey

Terrestrial light detection and ranging (LIDAR) surveys offer potential enrichment of outcrop-based research efforts to characterize fracture networks and assess their impact on subsurface fluid flow. Here, we explore two methods to extract the three-dimensional (3-D) positions of natural fractures from a LIDAR survey collected at a roadcut through the Cretaceous Austin Chalk: (1) a manual method using the University of California, Davis, Keck Center for Active Visualization in the Earth Sciences and (2) a semiautomated method based on mean normal and Gaussian curvature surface classification. Each extraction method captures the characteristic frequencies and orientations of the primary fracture sets that we identified in the field, yet they extract secondary fracture sets with varying ability. After making assumptions regarding fracture lengths and apertures, the extracted fractures served as a basis to construct a discrete fracture network (DFN) that agrees with field observations and a priori knowledge of fracture network systems. Using this DFN, we performed flow simulations for two hypothetical scenarios: with and without secondary fracture sets. The results of these two scenarios indicate that for this particular fracture network, secondary fracture sets marginally impact (10% change) the breakthrough time of water injected into an oil-filled reservoir. Our work provides a prototype workflow that links outcrop fracture observations to 3-D DFN model flow simulations using LIDAR data, an approach that offers some improvement over traditional field-based DFN constructions. In addition, the techniques we used to extract fractures may prove applicable to other outcrop studies with different research goals.

Discrete fracture model for coupled flow and geomechanics

We present a fully implicit formulation of coupled flow and geomechanics for fractured three-dimensional subsurface formations. The Reservoir Characterization Model (RCM) consists of a computational grid, in which the fractures are represented explicitly. The Discrete Fracture Model (DFM) has been widely used to model the flow and transport in natural geological porous formations. Here, we extend the DFM approach to model deformation. The flow equations are discretized using a finite-volume method, and the poroelasticity equations are discretized using a Galerkin finite-element approximation. The two discretizations—flow and mechanics—share the same three-dimensional unstructured grid. The mechanical behavior of the fractures is modeled as a contact problem between two computational planes. The set of fully coupled nonlinear equations is solved implicitly. The implementation is validated for two problems with analytical solutions. The methodology is then applied to a shale-gas production scenario where a synthetic reservoir with 100 natural fractures is produced using a hydraulically fractured horizontal well.

Fluid flow through porous sandstone with overprinting and intersecting geological structures of various types

Abstract It is well established that compaction bands (CBs), joints and faults are often present in the same rock volume in the Jurassic aeolian Aztec Sandstone, exposed in the Valley of Fire State Park, Nevada, USA. Because the permeability of CBs can be one or more orders of magnitude less than the matrix permeability, and joint permeability, depending on its aperture, can be several orders of magnitude greater than matrix permeability, the combined effect of these structures on subsurface flow can be complex and substantial. In this study, we investigate the effects of a variety of intersecting geological structures on fluid flow. This is accomplished by performing two- (2D) and three-dimensional (3D) permeability upscaling and waterflood simulations over areas/volumes populated by hydraulically interacting geological features. The regions considered are approximately the size of typical grid blocks used for reservoir or aquifer flow simulations, so the results are of practical interest. The systems studied include models with two sets of vertical CBs intersecting at various angles, an inclined CB set intersecting a vertical CB set, a joint set intersecting a CB set at various angles, and a small fault and its damage zone overprinting a CB set. Our numerical results quantify the impact of these composite structures on subsurface flow and show, for example, that the intersection angle of two sets of structures can have a considerable effect on the upscaled directional permeability. In addition, waterflood simulations demonstrate that the efficiency of oil recovery can be significantly impacted by the direction of flow relative to the orientation of intersecting geological structures.

Fluid-flow effects of compartmentalized distribution of compaction bands in an aeolian sandstone in three dimensions

It is well established that the depositional architecture of dunes (cross-bed orientations and dune boundaries) controls the formation and orientation of compaction bands (CBs) in three dimensions, resulting in a compartmentalized distribution of low-angle bed-parallel CBs and high-angle CBs in the Jurassic aeolian Aztec Sandstone, exposed in the Valley of Fire State Park, Nevada, USA. In this study, we used two idealized configurations to represent the characteristic compartmentalization of CBs in three dimensions and performed flow computations to investigate the fluid-flow effects of these configurations. The results suggest that the upscaled permeability of the compartmentalized compaction-band arrays is influenced significantly by the permeability of the compaction-band sets and their orientations and distributions. In particular, in Configuration A, which represents a combination of both the high-angle and bed-parallel domains, upscaled permeability in the direction normal to the dune trend is controlled primarily by the high-angle CB domain. In contrast, in Configuration B, in which the high-angle CB domain is distributed within a limited portion, upscaled permeability in the direction normal to the dune trend is controlled by both the high-angle CB domain and the bed-parallel CB domain. The upscaled permeability in the direction parallel to the dune trend in Configuration A is controlled by both high-angle CBs and bed-parallel CBs, but in Configuration B it is controlled mainly by bed-parallel CBs. In comparison, in both configurations A and B, upscaled permeability in the vertical direction is controlled primarily by the bed-parallel CB domain. The orientation of the major permeability component in both configurations A and B remains almost unaffected by the variation in permeability of CB sets, presumably because the preferred flow path crosses a minimum number of CBs. In contrast, the plunges of the minor permeability component changes significantly in Configuration A, but remains nearly the same in Configuration B. This suggests that the interplay between the spatial distributions of CB sets and their permeability exerts significant influence on the orientation of the minor permeability component in Configuration A, whereas the permeability of bed-parallel CBs has dominant control on the minor permeability component in Configuration B. The difference between the magnitudes of the major principal permeability component and the minor principal permeability component (permeability anisotropy) is about a factor of 2.5, 2.2 and 1.9 in Configuration A for cases 1, 2 and 3, respectively, and about a factor of 5.1, 3.4 and 1.3 in Configuration B for cases 1, 2 and 3, respectively. The parametric study implies that the range of potential variations in the permeability values in flow models would generally yield similar results for the major permeability component, but may yield different results for the minor permeability component. The results presented in this study clearly demonstrate that the compartmentalized distribution of CBs exerts strong influences on fluid flow through aeolian sandstone.

Coupled Geomechanics and Flow in Fractured Porous Media

The effects of geomechanics on the reservoir response can be important, and this is especially true for naturally fractured formations. Modeling the mechanical deformation of naturally fractured formations poses significant numerical challenges, and accurate coupling between mechanical deformation and flow adds to the challenge. We describe a simulation framework for coupled mechanics and flow based on a Discrete Fracture Model (DFM). An important aspect is that the mechanics and flow problems share the same unstructured DFM grid. The geomechanical model is based on the classical Biot theory. The Barton-Bandis model is used to describe the fracture mechanical response. For the flow problem, we use Darcy’s law and mass conservation for slightly compressible fluids. The fractured formation is discretized using DFM, which leads to complex unstructured grids. Three standard elements (hexahedrons, tetrahedrons and wedges) are used to represent the volumes of the matrix, and the fractures are represented using lower dimensional objects (triangles or quadrangles). The Galerkin finite-element method is used for the mechanics, and a DFM finite-volume method is used the flow equations. Two different coupling strategies are considered: the fully implicit method and the fixed-stress sequential-implicit scheme. Several examples of fractured porous media are used to illustrate our methodology.

A New Global Upscaling Technique for 3D Unstructured Grids

New procedures for unstructured coarse-model generation are presented and applied. The underlying fine-grid model is considered to be unstructured, and the coarse-model cells are defined as groupings of fine-grid cells. The key flow quantity that must be computed for the coarse model is the upscaled transmissibility for each cell-to-cell connection. We introduce a global upscaling procedure for this computation. The method first requires several (minimum of three) global single-phase flow solutions. Appropriately defined linear combinations of these solutions are used to compute each upscaled transmissibility. This approach circumvents some of the limitations of existing (local and global) upscaling procedures. It also enables transmissibility to be quickly computed for a number of different coarse grids without performing any additional pressure solutions. Results are presented for an idealized two-phase flow problem. The fine grid contains nearly 200,000 cells, and coarse models of varying resolution are considered. Accurate results for total injector-producer flow rate are observed for all grid-resolution levels for the three different well configurations considered. Oil rate as a function of time is shown to improve in accuracy with increasing resolution, and is quite accurate for a model of about 10,000 cells.

An Expanded Well Model for Accurate Simulation of Reservoir-well Interactions

We present a new framework for modeling wells in reservoir simulation. This approach is based on an “expanded well model” in which the well region is expanded geometrically to include portions of the reservoir. The well region is then represented as an “equivalent” multi-segmented well defined by a list of connections for all completed segments. This generalizes and simplifies well-reservoir flow modeling by shifting the interface between the well region and the reservoir region. As is the case with standard well models, the well region is linked to the reservoir region through use of well indices. In the case of the expanded well model, these well indices, along with the connections between segments in the equivalent multi-segmented well, are computed by upscaling an underlying fine-scale description of the reservoir and well. The method is applied to model a hydraulically-fractured well and production in a tight-gas reservoir. In both cases, direct application of standard approaches is shown to lead to inaccurate coarse-scale predictions. Use of the expanded well model, by contrast, provides high degrees of accuracy in both cases.