This paper was prepared for presentation at the 1999 SPE Reservoir Simulation Symposium held in Houston, Texas, 14-17 February.
We describe a hierarchical approach for modeling fluid flow in a naturally fractured reservoir with multiple length-scale fractures. Based on fracture length (lf) relative to the finite-difference grid size (lg), fractures are classified as belonging to one of three groups:short disconnected fractures (lf << lg),medium-length fractures (lf ~ lg), andlong fractures (lf >> lg). Effective grid-block permeabilities, associated with the short and medium length fractures, are used as input to a finite-difference simulator. We also present a separate transport equation for flow through long fractures to capture effects of large-scale high permeability pathways. Our new approach provides an improved means to include realistic and explicit fracture descriptions. Previously, Lough et al. (1997, 1998) developed a numerical method to compute the effective permeability of simulation grid-blocks with realistic fracture characterizations. Although this method handles generalized fracture geometries, it is numerically inefficient for the case where many small fractures exist. The method can also underestimate the flow contribution from long fractures. Assuming a linear potential gradient along the short fractures, we derive an analytical solution for the permeability contribution from short fractures. The solution becomes more accurate as fractures become randomly distributed and asymptotically small in length. The permeabilities from this analytical solution are used as the effective matrix permeability in computing a combined effective grid-block permeability that includes medium-length fractures. The method of Lough et al. is used for this computation. This hierarchical approach takes into account coupled flow between the rock matrix, short fractures and medium-length fractures. Long fractures are modeled explicitly in the reservoir simulator, using a transport equation that describes flow between long fractures and surrounding simulation grid-blocks. Simulation results from our new hierarchical approach are compared with those from the conventional dual porosity/permeability model. Numerical efficiency and accuracy are also examined.
The gridblock permeabilities used in reservoir simulation are commonly determined through the upscaling of a fine scale geostatistical reservoir description. Though it is well established that permeabilities computed in this manner are, in general, full tensor quantities, most finite difference reservoir simulators still treat permeability as a diagonal tensor. In this paper, we implement a capability to handle full tensor permeabilities in a general purpose finite difference simulator and apply this capability to the modeling of several complex geological systems. We formulate a flux continuous approach for the pressure equation by use of a method analogous to that of previous researchers (Edwards and Rogers 1 ; Aavatsmark et al. 2 ), consider methods for upwinding in multiphase flow problems, and additionally discuss some relevant implementation and reservoir characterization issues. The accuracy of the finite difference formulation, assessed through comparisons to an accurate finite element approach, is shown to be generally good, particularly for immiscible displacements in heterogeneous systems. The formulation is then applied to the simulation of upscaled descriptions of several geologically complex reservoirs involving crossbedding and extensive fracturing. The method performs quite well for these systems and is shown to capture the effects of the underlying geology accurately. Finally, the significant errors that can be incurred through inaccurate representation of the full permeability tensor are demonstrated for several cases.
Many carbonate rocks have pore features that are large at the core plug scale. Laboratory assessment of recovery behavior in these carbonates can be unreliable. Pore network modeling offers an approach to improve our analysis of complex flows in such heterogeneous rocks. We have discussed earlier our experimental data on a heterogeneous dolomite, the calibration methodology to link pore model inputs and laboratory data, and our initial attempts to use pore network models to match the experiments. This paper reports new results on our attempts to match the coreflood data. We analyze spatial correlation in our core sample using thin section and Computed Tomography (CT) data. We also investigate further the derivation of throat sizes using mercury injection data. Finally, we compare pore network model predictions to coreflood data. Introduction Carbonate rocks often display heterogeneities significant at the core plug scale. Conventional analysis is likely to be inadequate, and it is not surprising that the literature contains few references to multiphase flow studies on such rocks. A review of studies on carbonate systems by Espie et al. shows a wide range of process efficiency. They find that the residual oil saturation to water flood varies from 28 to 80% oip and that to tertiary miscible flood varies from 0 to 50% oip. Pore network (PN) models (figure 1) attempt to relate macroscopic behavior of porous media to simplified representations of the flow physics and pore structure. The general PN models consider capillary, viscous, and gravitational forces. They are useful for understanding multiphase flow mechanisms and the effects of pore scale heterogeneity. However, except for a few cases, pore network models have not been linked directly to data on real rocks. Technological advances in computing and flow visualization are now allowing us to connect laboratory tests and network models more closely. For example, we can now run 500 000 node models to recreate fine scale CT flow images. Experimental Data on Carbonate Sample In an earlier paper, we have discussed our experimental data on a dolomite rock from the Beaverhill Lake formation, Canada (k=300md, =14%, L=4.9 Cm, d=3.8cm). Figure 2 is the CT derived porosity distribution along a cross-section parallel to flow. It shows that the porosity is heterogeneously distributed. The thin section picture in figure 3 displays millimeter size pore features. Figure 4 is a CT image of a unit mobility, equal density miscible flood and it reveals that the flow channeled along a connected high porosity path. Figure 5 contains cross-sectional images of water saturation obtained at Swi, and at the end of different rate water floods. These images correspond closely to the porosity image in figure 2. At the flow rate of 0.5 feet/day, the water mostly invades the high porosity, high permeability channel. High oil saturation of 67% PV remains in large unswept areas. Completely new channels are invaded as the flow rate is increased and the residual oil saturation at the flow rate of 120 feet/day has decreased to 37% PV. This waterflood is a drainage process and new channels are invaded as the flow rate increases. We were unsuccessful in using conventional analysis to extract meaningful information from this data. P. 359^
The coning of water can impact well productivity and increase water treatment requirements. Coning correlations are often used to model water-breakthrough time and water cut due to coning. Most existing coning correlations are based on a steady state approximation so that the prediction of water-breakthrough time and initial water cut development are generally unreliable. By first determining the key reservoir, production, and well completion parameters through a theoretical analysis, improved correlations were developed. They have been extensively compared with numerical simulation results to validate their general applicability. The correlations simplify the procedure in the study of the effects of production rate, vertical and horizontal permeabilities, well completion location, physical properties of fluids, relative permeabilities, aquifer thickness, completion interval size, and drainage radius on coning dynamics.The new correlations can be used in a stand-alone program or in reservoir simulation. In field-scale reservoir simulation, correlations are often employed to model sub-scale flow behavior near a well. Hence, technical issues in implementing correlations into a finite difference simulator are also discussed. In addition, the new correlations are extended to multi-layered, nonhomogeneous reservoir models.
TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractThe upscaling of geostatistical models characterized by oriented layering is considered. Such models are representative of a broad class of geologically complex reservoir characterizations as they display full tensor permeabilities on both the fine and coarse scales. The significant errors that result from the improper numerical treatment of the full tensor permeability are demonstrated. The application of existing upscaling approaches to these oriented systems is shown to lead to coarse models of lower accuracy, for both flow and displacement calculations, than in the case of models with horizontal layers. Two alternate upscaling procedures are presented in an attempt to improve the accuracy of these coarse scale reservoir descriptions. The first technique involves the use of a border or "skin" region, while the second approach entails the use of a rotation procedure, in which the gridblock permeability is computed in a coordinate system approximately aligned with the principal directions of the upscaled permeability tensor. Both methods are shown to generally result in improved accuracy in displacement calculations, though the rotation procedure appears to be the more accurate overall. The approaches presented here can be used in conjunction with sophisticated gridding techniques to achieve more accurate and robust coarse scale models.
In multiblock reservoir simulation techniques, the reservoir model is divided into a number of subdomains or blocks. In our current implementation, these blocks are locally structured but globally unstructured. This representation enables the modeling of geometrically complex reservoir features such as fault surfaces and nonconventional wells while avoiding many of the complications of fully unstructured formulations. In this paper, we present several important developments within this framework. These include the extension of a previous two phase flow finite volume formulation to the general black oil case, the implementation of techniques for treating systems in which grid lines do not match between adjacent subdomains, and the application of a near-well radial upscaling technique to the multiblock paradigm. Simulation results illustrating the accuracy and efficiency of these new capabilities are presented. These include a black oil simulation for a local well study, flow through a realistic reservoir with several wells and faults, flow through a fault surface represented by nonmatching grid lines, and a two phase flow simulation demonstrating the applicability of the near-well upscaling procedure to multiblock models. With the new developments presented in this paper, the finite volume based multiblock simulator can be applied to a variety of problems of practical interest. TX 75083-3836, U.S.A., fax 01-972-952-9435.
The grid block permeabilities used in reservoir simulation are commonly determined via the upscaling of a fine scale geostatistical reservoir description. Though it is well established that permeabilities computed in this manner are in general full tensor quantities, most finite difference reservoir simulators still treat permeability as a diagonal tensor. In this paper, we implement a capability to handle full tensor permeabilities in a general purpose finite difference simulator and apply this capability to the modeling of several complex geological systems. We formulate a flux continuous approach for the pressure equation using a method analogous to that of previous researchers (Edwards and Rogers; Aavatsmark et al.), consider methods for upwinding in multiphase flow problems, and additionally discuss some relevant implementation and reservoir characterization issues. The accuracy of the finite difference formulation, assessed through comparisons to an accurate finite element approach, is shown to be generally good, particularly for immiscible displacements in heterogeneous systems. The formulation is then applied to the simulation of upscaled descriptions of several geologically complex reservoirs involving crossbedding and extensive fracturing. The method performs quite well for these systems and is shown to accurately capture the effects of the underlying geology. Finally, the significant errors which can be incurred through inaccurate representation of the full permeability tensor are demonstrated for several cases. Introduction Recent advances in reservoir characterization permit the construction of realistic, highly detailed, heterogeneous reservoir descriptions. Such models typically contain far too many grid blocks to simulate directly and therefore require some type of upscaling before they can be used for reservoir simulation. The most important of the upscaled rock properties, for purposes of flow simulation, is the absolute permeability. Accurate procedures for the scale up of permeability generate full tensor permeabilities on the coarse scale, even in cases where the underlying fine scale permeability description is isotropic. Therefore, simulation models generated through scale up of complex reservoir descriptions will in general be characterized by full tensor permeabilities. For many models, however, the off-diagonal components of the effective (or equivalent grid block) permeability tensors can be expected to be small relative to the diagonal components and can generally be ignored. This will typically be the case, for example, when the fine scale permeability is correlated along the coordinate directions (e.g., strictly layered systems) or is correlated nearly isotropically. However, for other types of systems the cross terms of the permeability tensor can be expected to be quite significant. These include formations containing complex crossbedding, dipping layers not aligned with the coordinate system, or extensive fracturing. In these cases the upscaled simulation model will contain full tensor permeabilities with significant off-diagonal terms, which must be accommodated by the simulator if reservoir performance is to be predicted accurately. Our intent here is to develop an approach for the modeling of complex geological systems using a general purpose reservoir simulator. Toward that end, we first develop and implement a formulation for full tensor permeability models, applicable for curvilinear grids, into a general purpose finite difference reservoir simulator. Second, we apply this formulation to the simulation of flow through a variety of upscaled geologic descriptions. P. 253^
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.