H13C-1386
A Fracture-Only Reservoir Simulator
We present a fracture-only reservoir simulator for multiphase flow: the fracture geometry is modeled explicitly, while fluid movement between fracture and matrix is accommodated using empirical transfer functions. This is a hybrid between discrete fracture modeling where both the fracture and matrix are gridded, and dual porosity or dual permeability simulation where both fracture and matrix continua are upscaled. The advantage of this approach is that the complex fracture geometry that controls the main flow paths is retained. The use of transfer functions, however, makes the simulation method considerably more efficient than conventional discrete fracture models. The transfer functions used accommodate capillary and gravity-mediated flow between fracture and matrix and have shown to be accurate for simple fracture geometries, capturing both the early and late-time average behavior. We validate our simulator by comparing our predictions with simulation results where the fracture and matrix are explicitly modeled. We then show the utility of the approach by simulating multiphase flow in a geologically realistic fracture network. We demonstrate that both the fracture geometry and capillary forces in the matrix govern the overall transport. http://csmp.ese.imperial.ac.uk/wiki/Home
H13C-1387
Comparison of Deterministic and Stochastic Fractures in Water Flooding Numerical Simulations
ABSTRACT Determining fracture attributes including fracture number, number of fractures sets, their length distribution, orientation, spacing and aperture in reservoirs is a challenge. One way of doing this is by studying outcrop analogues that have the same geological history and show comparable petrophysical properties and incorporate into our reservoir model building and simulation. Vein networks that were once barren fractures (fossil fractures) which were later filled with minerals are used in this work. We accept the differences between veins and fractures proposed in the literature (e.g. Peacock 2004) who argued that veins and joints should be analysed separately. In this article we assume that the geometrical properties of both veins and joints can be analysed using the same approach. We have used calcite vein attributes determined from eight scan lines (to simulate boreholes) and window samples on well-exposed Liassic carbonate platforms on the southern margin of the Bristol Channel Basin. The vein attributes determined from each scan line were used to condition stochastic generation of fractures using the Discrete Fracture Network (DFN) code, FracMan. Water breakthrough time, comparison of storage capacity of fractures and matrix, total fracture surface area, fracture surface area per volume, fracture volume and fracture volume per volume of the model were then determined by applying a constant pressure gradient for each realisation to simulate water flooding numerical simulations using combined finite element – finite volume. This was then compared with water flooding numerical simulation for real fracture networks. The results indicate that, depending on the variability of the above attributes, fluid flow in the system can vary from pervasive type where the fractures play subordinate role to a highly localised flow where most of the flow occurs either through single or connected networks of fractures. The results of this work have profound impact for predicting oil recovery and water breakthrough time based on limited information from boreholes. Key words: fractures, fluid flow, water flooding, numerical simulations
H13C-1388
Dependence of Upscaled Effective Permeability Upon Fracture Orientation and Connectivity in Naturally Fractured Reservoirs
Although geologically informed models of hydrocarbon reservoirs are available at relatively high resolution, i.e. the pore scale, numerical reservoir simulators require descriptions at a larger scale, i.e. the grid-block scale, in order to produce exploitable information about the reservoir. This process, known as upscaling, is especially complicated, yet relevant, in the case of naturally fractured reservoirs which contain over half of the global hydrocarbon reserves, and are extremely heterogeneous, exhibiting complicated multiphase flow behaviour at all scales. In this work we study the effect of discrete fracture networks upon the upscaled effective permeability of the system, using a sophisticated numerical pressure-solver method based upon a finite element-finite volume scheme. We begin by examining an idealized scenario consisting of a single discrete fracture in two dimensions, and show how the upscaled effective permeability is a non-additive property. This investigation is extended to real fracture networks using outcrop data, where we find the upscaled effective permeability to be dependent upon the orientation and connectivity of the fracture network. Finally, we present our ideas for examining the influence of three dimensional fractures upon upscaled reservoir parameters.
H13C-1389
A Practical Methodology To Estimate The Fracture Spacing In A Dual-porosity Model From Discrete Fracture Networks
The dual-porosity model and discrete fracture network (DFN) model are two common approaches used to simulate field scale multiphase flow in naturally fractured reservoirs. While the DFN approach has several advantages, for example, it can explicitly take into account the geometry, conductivity and connectivity of fracture networks, it is seldom used in field scale multiphase flow simulation due to the difficulties in describing the flow exchange between the matrix and fractures and also due to the requirements of an excessive number of elements in spatial discretization. As an alternative, many researchers have sought to use the DFN model to upscale geological information into the dual porosity model to simulate multiphase flow (Bourbiaux et.al., 1999 and 2005; Dershowitz et.al., 2000). Fracture spacing is widely used to estimate input parameters (for example, shape factor) in a dual-porosity multiphase flow model. Based on the assumption that the conditions in rock matrix are controlled primarily by the distance from the fractures, a function called the "proximity function" can be defined in a certain volume of subdomain as the total fraction of matrix volume within a distance from fracture faces (Pruss, 1985). A practical way is proposed to compute the proximity function for a 3D subdomain characterized by a DFN with the help of Monte Carlo simulation. For a subdomain described by an ideal dual porosity model, the proximity function is a function of unknown fracture spacing which can be written analytically. Based on the computed proximity function of DFN subdomain, an optimization problem to minimize the difference between two proximity functions is set up. Solving this optimization problem, unknown fracture spacing that is appropriate for the dual porosity model can be estimated.
H13C-1390
Characterization of Fracture Capillary Pressure from Geo-statistical Analysis of Rough Fracture Structures
The importance of the effect of fracture morphology on the flows of fluids through fractures has been extensively recognized. Nevertheless, understanding of the correlation between geostatistical parameters of fractures and macroscopic transport properties remains limited. The aim of this contribution is to examine the effect of geostatistical characteristics of fractures on the capillary pressure curves. The study model implements a modified invasion percolation (MIP) approach for modeling primary drainage which had been conducted in the previous experiment. MIP is the invasion percolation including normal and in-plane curvature terms of the fluid interface for calculating the local capillary pressure which indicates the least resistant path for invading fluid to flow through. The lattice model for the simulation is constructed from geometric structure of the fracture which was measured using a high resolution Computed Tomography (CT). The simulation results concur with 70% match of CT images of fluid distribution maps. A satisfactory agreement with the experimental results enables us to further study the characterization of capillary pressure for a wide range of the fracture structures having different geostatistical characteristics. The generation of fracture replicas is based on a matrix decomposition technique. Mean, spatial correlation length and variance of the aperture distribution are the geostatistical parameters used in the generator to characterize the replicas. The results show that the connectivity of the fractures strongly influences on the shape of the capillary pressure curve, and the connectivity can be quantified from the calculation of aperture variance and spatial correlation length.
H13C-1391
New capillary interface conditions for three-phase flow in fractured rock masses
Discrete fracture models are a very promising tool to simulate multiphase fluid flow in fractured reservoirs realistically because they retain the natural geometry of the fracture network and calculate the contribution of fluid flow from each individual fracture accurately. However, discrete fracture models are currently limited to two-phase flow simulations only. Recently, the first Black-Oil three-phase discrete fracture model has been introduced (Geiger et al., 2007). This model cannot yet simulate capillary pressure effects between fracture and matrix because it lacks an appropriate capillary interface condition for the three phases, oil, gas, and water, at nodes that are shared by the matrix as well as the fracture. In this work we present a new fracture-matrix capillary pressure interface condition that can be used in generic three-phase discrete fracture simulations. We have extended the two-phase Brooks-Corey and the van Genuchten capillary pressure-saturation relations to the three-phase case. We have determined the conditions when capillary pressures are continuous and discontinuous. This allows us to calculate the saturations at each side of the interface. Our theoretical models have been compared to numerical simulations, which match the theoretical predictions. Geiger S, Matthai SK, Niessner J, Helimg R, 2007. Black-Oil simulations for three-component - three-phase flow in fractured porous media. SPE Paper 107485, 2007.
H13C-1392
Pore-scale modelling of two-phase and three-phase fracture-matrix interface conditions
A key assumption of multi-phase discrete fracture model simulations is that the capillary pressure is constant and continuous at nodes that are shared by the fracture as well as by the matrix. In this work, we study the fundamental flow physics at the fracture-matrix interface using a 3D pore-scale network model. The conceptual model represents the pores of the matrix and fracture for the situation where the fluid flow is perpendicular to the interface plane, hence mimicking counter-current imbibition. We could not validate the general assumption that the capillary pressure at the interface is continuous directly. Instead it was inferred from the study of the flow pattern across it. By determining the capillary pressure curves individually for the fracture and matrix individually and comparing it with the capillary pressure of the heterogeneous fracture-matrix interface, we were able to develop a qualitative understanding of the trapping behaviour and the residual phase saturations. In general, our simulations show how the wetting phase fills preferentially the smallest pores while the non-wetting phase fills the largest pores. However, the heterogeneity at the fracture-matrix interface gives rise to complex new capillary pressure curves that cannot be modeled by classical Brooks-Corey or van Genuchten curves. We observed that hysteresis effects increase with increasingly more heterogeneous the media. This implies that two different capillary pressure curves should be used for drainage and imbibition.
H13C-1393
Monodisperse and polydisperse colloid transport in water saturated fractures with various orientations: Gravity effects
Numerical experiments are conducted to examine the effect of gravity on monodisperse and polydisperse colloid transport in water-saturated fractures with uniform aperture. Dense colloids travel in water-saturated fractures by advection and diffusion while subject to the influence of gravity. Colloids are assumed to neither attach onto the fracture walls nor penetrate the rock matrix based on the assumption that they are inert and their size is larger than the pore size of the surrounding solid matrix. Both the size distribution of a colloid plume and colloid density are shown to be significant factors impacting their transport when gravitational forces are important. A constant- spatial-step particle-tracking code simulates colloid plumes with increasing densities transporting in water- saturated fractures while accounting for three forces acting on each particle: a deterministic advective force due to the Poiseuille flow field within the fracture, a random force caused by Brownian diffusion, and gravitational force. Integer angles of fracture orientation with respect to the horizontal ranging from -90 to +90 degrees are considered, and three log-normally distributed colloid plumes with mean particle size of 1 μm and standard deviation of 0.6, 1.2, and 1.8 μm are examined. Colloid plumes are assigned densities of 1.25, 1.5, 1.75, and 2.0 g/cm3. The first four spatial moments and the first two temporal moments are estimated as functions of fracture orientation angle and colloid density. Several snapshots of colloid plumes in fractures of different orientations are presented. Results are strongly dependent upon fracture orientation angle. In all cases, larger particles tend to spread over wider sections of the fracture in the flow direction, but smaller particles can travel faster or slower than larger particles depending on fracture orientation angle. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
H13C-1394
Application of a hydro-ecological model (RHESSys) for up-scaling of plot and flux tower measurements to MODIS GPP and evapotranspiration
Interest in quantifying carbon and water flux over large geographical areas has increased in recent years. Since water and carbon cycles in terrestrial ecosystem are strongly linked with each other, simultaneous evaluation can give us more insight on characteristics of and interactions between the cycles. In this study, we examined the flux of carbon and water by using a eco-hydrological model, Regional Hydro-Ecologic Simulation System (RHESSys), and examined suitability of applying parameters determined at a specific watershed to other watershed for broad-scale RHESSys application. RHESSys has been developed for applications in local hydrological investigations, forest productivity, and large scale water and carbon budgets for terrestrial ecosystems. In addition, we used felid data of streamflow, transpiration, Soil Water Content (SWC) and Wood Biomass Product (WBP). We used tree-ring data from 1978 to 1997 to estimate WBP. Transpiration was measured by using sap flow measurement, Thermal Diccipation Probe (TDP), first proposed by Granier (1985). The study sites were the Gwangneng National Arboretum (GN), Mt. Jumbong and Mt. Gyebang in Kangwon Province, Korea. The simulation results of GN generally agreed well with observation. RHESSys reasonably reproduced daily and yearly patterns of streamflow, transpiration, SWC, and WBP. The parameters identified at GN were applied to Mt. Jumbong and Mt. Gyebang. Simulation results of Mt. Jumbong and Mt. Gyebang were a reasonably reproduced daily data of transpiration and SWC. The GPP and evapotranspiration estimated by RHESSys simulation were utilized to test reliability of MODIS (Moderate Resolution Imaging Spectroradiometer) products. Our initial effort for multi-watershed application of RHESSys and up-scaling of field measurements showed promising results for broad-scale model application in Korea but for evaluating reliability of MODIS products.