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Abstract Numerical models for naturally fractured reservoirs are generally divided into two types. The first is the double-porosity, single-permeability (dual porosity) model. The second is the double-porosity, double-permeability (dual permeability) model. The difference between the two models is basically that the second type considers matrix block-to-block flow while the first does not. The present work is focused on the dual porosity model, which also requires a transfer function calculation between matrix and fracture. Therefore, proper calculation of mass transfer from matrix to fracture plays an important role in generating good simulation results. In a gas-oil system when the gas with low viscosity and nonwetting characteristics reaches the fractures, it moves rapidly, leaving the wetting fluid (oil) preferentially in the matrix. This paper determines methods of scaling dimensionless variables to simplify the analysis and thus identify the main parameters controlling the gas-oil gravity drainage process in naturally fractured reservoirs. This work is based on a simplified model matched to published lab data and information of a fractured reservoir. The differences between this paper and others are the following:an analysis to simplify a complex problem by neglecting gas viscous pressure drop,a comparison of oil transfer function models from matrix to fracture flow represented in a simple integral equation,an analysis of matrix-fracture flow in all directions with gravity drainage using fine grid simulation, andnumerical simulation of a stack of matrix blocks separated by fractures which compares gas-oil gravity drainage in matrix to fracture flow. The information in this paper has time saving application in history matching and stochastic simulation. Considering gas-oil systems with gravity drainage in stacked matrix blocks, the main technical contributions of this paper are as follows:flow is only in the vertical direction and there is minimal or no flow to lateral fractures;there is maximum oil flux from matrix to fracture which is a function of matrix permeability, oil relative permeability, oil viscosity, and difference of density between oil and gas phases; andthe detailed comparison of dual porosity models. Introduction In naturally fractured reservoirs, as in non-fractured reservoirs, when multiple fluids exist, gravity segregation is present to some degree. Segregation is driven by the difference in density between fluids. The larger the difference in density, the more important is gravity segregation. This paper first presents a literature review, covering important topics in fractured reservoirs and a review of matrix-fracture transfer functions used in numerical simulators; a model is then developed to simulate gravity-capillary phenomena in the vertical direction. This paper also discusses gravity drainage with no capillary pressure and a procedure to generate pseudo oil relative permeability with gravity drainage. A comparison of different transfer functions for dual porosity models is done to determine the differences between them. This work also addresses a methodology to generate pseudo capillary pressure with gravity drainage. Then, this paper reviews 3D flow from matrix to fracture to determine the effects with lateral flow and no liquid saturation in the fracture. Finally a procedure is established to represent matrix-fracture transfer with gravity drainage, which also presents a comparative case between a dual porosity model in a commercial simulator with gravity drainage and a gridded system of a stack of matrix blocks separated by fractures.

Abstract This study was part of a comprehensive program of quantitative characterization of heterogeneity in fluvial-deltaic reservoirs, using the Ferron, Utah outcrop as an analog reservoir. A suite of petrophysical properties were measured simultaneously in the laboratory for over sixty specimens, representing different geologic facies, flow units, and barriers. Properties included porosity, permeability, electrical conductivity, shear and compressional wave velocities, and quasi-static moduli, measured under simulated reservoir conditions during two-phase steady-state flow of gas and brine, in both drainage and imbibition. Petrographic data on each sample were also gathered, including quantification of detrital and authigenic phases, thin-section porosity, textural and grain-size distribution analyses. Centrifuge capillary pressures on plugs from the laboratory test specimens were also measured. Minipermeameter determinations of test specimen air permeabilities were conducted in companion studies. Statistical studies were conducted to relate petrophysical data to petrographic information in an attempt to examine the correlation of petrophysical data with geologic genesis and diagenesis. Reasonable correlations were obtained for most of the data, that may be of use in other similar fluvial-deltaic environments. These types of correlations may also be of use in discerning expected statistical distributions of petrophysical data other than permeability. Introduction Starting in 1989 the Texas Bureau of Economic Geology and the University of Texas Department of Petroleum Engineering conducted a Gas Research Institute (GRI) sponsored study to develop methods to quantify styles and scales of sandstone reservoir petrophysical property heterogeneity by combining outcrop studies, laboratory petrographic and petrophysical analyses, and geostatistical analysis. Because it is virtually impossible to determine detailed spatial distributions of petrophysical properties in the subsurface, outcrop studies are increasingly being used to provide data on sand-body geometry, positions and continuity of bounding elements between major sand bodies, the internal architecture of sandstones, and the distribution of permeability (and other petrophysical property) values within and between strata are reported elsewhere (Tyler, et al.). The Ferron Sandstone, in central Utah, is ideal for such an outcrop study because it was deposited in environments similar to those of sandstone reservoirs in the Texas Gulf Coast, is well exposed both parallel and perpendicular to sediment transport direction by a series of bifurcating canyons, and the sequence stratigraphic setting is well documented. The results of a comprehensive geologic outcrop characterization of the outcrop. In this paper we report on measurements of a large number of complex petrophysical properties of their material under two-phase flow conditions, and efforts to find ways to utilize a large, but limited, number of measurements to predict the distributions of these properties within different flow units and bounding elements. On the basis of field observations and field air permeability values, approximately sixty samples were taken that would appear to act as flow units, baffles, and barriers in a gas reservoir. Suites of detailed petrophysical property measurements were made on these samples, including, porosity, air permeability, brine permeability, relative permeability curves, capillary pressure curves, formation factor, saturation exponent, and shear and compressional wave velocities under dynamic and quasi-static conditions. P. 757^

SPE Members Abstract The stability of three-dimensional condensable gas (steam) displacements in porous media is investigated by precise simulation using a recently developed three-dimensional front tracking model. This model uses a finite element method with an adaptive grid redistribution scheme that accurately represents the front as a moving discontinuity. Frontal displacement is evaluated by precise calculation of the velocity field around the front. Abrupt changes in volumetric flux across the front is a consequence of conservation of mass and energy, which enhances stability. Model results show excellent agreement with data in the literature. Displacement patterns and sweep efficiency correlations are shown for selective flooding patterns using steam. Introduction Injection processes of all kinds, and thermal processes in particular, tend to develop fairly distinct fronts that move through the reservoir. Although diffusion, dispersion, heat conduction, etc. tend to smear these interfaces, they generally propagate in-tact. It is important to describe mass and energy transfer in regions between these fronts; however, production of oil is in large part governed by the location and movement of the fronts themselves (Myhill and Stegemeir, Vogel).Calculation of convection-dominated flow on fixed meshes using conventional simulation techniques tend to yield numerical solutions that oscillate, especially in regions where the solution changes rapidly, especially if the characteristic thickness of the front is much smaller than the mesh size used. Numerical dispersion and oscillations can be decreased if the mesh is sufficiently fine and well graded. However, this means higher cost of computer storage and time such that full-field simulations may not be practical. Therefore, although conventional reservoir simulators can model physical phenomena very accurately, they do not always adequately model hydrodynamic movement of sharp fronts. Even with vector-processing supercomputers, application of thermal simulation models can usually be made only on small fractions of field projects, or must utilize such large grid cells that spatial definition is inadequate. There are computational methods that take into account the highly convective nature of the problem. Some physical processes, such as diffusion occurring around the front, although important to overall behavior of a process, do not greatly affect overall frontal movement. Their effect can be sometimes de-coupled from the hydrodynamic part of the problem. On the other hand, other phenomena such as condensation, combustion, and gravity and mobility changes are actually part of the hydrodynamic problem and must be included in the hydrodynamic solution. For problems in which local physical phenomena can be de-coupled from the hydrodynamic movement of the front, one approach is to model hydrodynamic movement of the front first by only incorporating important physical phenomena that have a strong effect and later superimposing important other physical phenomena over the movement of the front. P. 19^