For water-wet reservoirs, several expressions may be used to correlate capillary pressure, or height above the free water level, with the water saturation. These correlations all feature a vertical asymptote at the residual water saturation where the capillary pressure goes to plus infinity.We have developed a general capillary pressure correlation that covers primary drainage, imbibition, secondary drainage, and hysteresis scanning loops. The graph exhibits an asymptote at the residual saturation of water and of oil where the capillary pressure goes to plus and minus infinity, respectively. The shape of the correlation is simple yet flexible as a sum of two terms, each with two adjustable parameters and is verified by laboratory experiments and well-log data. An associated hysteresis scheme is also verified by experimental data.The correlation can be used to make representative capillary pressure curves for numerical simulation of reservoirs with varying wettability and to model and interpret flooding processes.
Copyrfght 1998, Society of Petroleum Engineers, Inc. 7Ms paw was wepared fw preaentaficm al ffw 1998 SPE India Oil and Gas Ccaference and Exhibition held h New DelhL India, 17-19 Rebmary 1998. This paper was selactad for prasantation by an SPE Program Commmee following review of information contained in an abstract submittad by the author(s), Contents of tha papar, as Presentd, have not b-n reviewed by tha Society of Patroleum Engineers and are subjecl to rnrractfon by the author(s). l%e material, as presented, doss not necessarily reflect any position of the Scciety of Petroleum Engineers, its officers, or mambers. Papers presented at SPE meetings are subject 10 pubkdion rew-ew by Editorial Committees of tha Society of Petroleum Engineers. Efactmnlc reprciducticm, distribution, or storage of any pert of this paper for commercial purposes wifhoul fhe WiNen consent of the Society of Petrolaum Engineers IS prohibited. Permission 10 reproduce in print is restricted fo an abstract of no! more than 300 words; iflusbations may not be copied. 7he abstract must contein conspicuous acknowledgment of Mere and by whom the papar was presantad. Write Librarian, SPE, P.O. Etox 833836, Richardson, TX 75063-3336, USA, fax 01.972-952-9435. AbstractFor waterwet reservoirs, several expressions may be used to correlate capillary pressure, or height above the free water level, with the water saturation. These correlations all feature a vertical asymptote at the residual water saturation where the capillary pressure goes to plus infinity. We k developed a general capillary pressure correlation that covers primary drainage, imbibition, secondary drainage, and hysteresis scanning loops. The graph exhibits an asymptote at the residual saturation of water and of oil where the capillary pressure goes to plus and minus infinity, respectively. The shape of the correlation is simple yet flexible as a sum of two terms, each with two adjustable parameters and is verified by laboratory experiments and well-log data. An associated hysteresis scheme is also verified by experimental data.The correlation can be used to make representative capillary pressure curves for numerical simulation of reservoirs with varying nettability and to model and interpret flooding processes.
Summary In the coarse-scale simulation of heterogeneous reservoirs, effective or upscaled flow functions (e.g., oil and water relative permeability and capillary pressure) can be used to represent heterogeneities at subgrid scales. The effective relative permeability is typically upscaled along with absolute permeability from a geocellular model. However, if no subgeocellular-scale information is included, the potentially important effects of smaller-scale heterogeneities (on the centimeter to meter scale) in both capillarity and absolute permeability will not be captured by this approach. In this paper, we present a two-stage upscaling procedure for two-phase flow. In the first stage, we upscale from the core (fine) scale to the geocellular (intermediate) scale, while in the second stage we upscale from the geocellular scale to the simulation (coarse) scale. The computational procedure includes numerical solution of the finite-difference equations describing steady-state flow over the local region to be upscaled, using either constant pressure or periodic boundary conditions. In contrast to most of the earlier investigations in this area, we first apply an iterative rate-dependent upscaling (iteration ensures that the properties are computed at the appropriate pressure gradient) rather than assume viscous or capillary dominance and, second, assess the accuracy of the two-stage upscaling procedure through comparison of flow results for the coarsened models against those of the finest-scale model. The two-stage method is applied to synthetic 2D reservoir models with strong variation in capillarity on the fine scale. Accurate reproduction of the fine-grid solutions (simulated on 500'500 grids) is achieved on coarse grids of 10'10 for different flow scenarios. It is shown that, although capillary forces are important on the fine scale, the assumption of capillary dominance in the first stage of upscaling is not always appropriate, and that the computation of rate-dependent effective properties in the upscaling can significantly improve the accuracy of the coarse-scale model. The assumption of viscous dominance in the second upscaling stage is found to be appropriate in all of the cases considered. Introduction Because of computational costs, field-simulation models may have very coarse cells with sizes up to 100 to 200 m in horizontal directions. The cells are typically populated with effective properties (porosity, absolute permeability, relative permeabilities, and capillary pressure) upscaled from a geocellular (or geostatistical) model. In this way, the effects of heterogeneity on the geocellular scale will be included in the large-scale flow calculations. The cell sizes in geocellular models may be on the order of 20 to 50 m in horizontal directions. However, heterogeneities on much smaller scales (cm- to m- scale) may have a significant influence on the reservoir flow (Coll et al. 2001; Honarpour et al. 1994), and this potential effect cannot be captured if the upscaling starts at the geocellular scale.
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.