Summary Reservoir simulations are limited to large scale grid blocks due to prohibitive computational costs of fine grid simulations. Rock properties, such as permeability, are measured on smaller scale than coarse scale simulation grid blocks. Therefore, the properties defined on a smaller scale are upscaled to a coarser scale. Few prior studies on permeability upscaling paid special attention to the problem of the radial flow in the vicinity of a wellbore. This study presents an analytical method to calculate effective permeability for a coarse-grid well-block from fine-grid permeabilities. The method utilizes serial and parallel averaging procedures modified for radial flow. The method is validated with numerical simulations of primary and secondary recovery processes involving 2- and 3-D systems. The results of coarse grid simulations with the permeabilities upscaled through the new well-block approach agree well with the results of the fine grid simulations with initial permeability distributions. Introduction Reservoir heterogeneity can be described on a fine scale by using current stochastic models. In spite of the recent developments in computational speed, it is still not feasible to flow simulate reservoirs with stochastic grid blocks. Coarsened grid-block scheme, therefore, is required to ease the computational burden. Rock properties for coarse scale grid blocks are obtained by utilizing a proper upscaling procedure. Permeability, by far, is the most important property that affects flow performance. Therefore, unlike porosity, permeability upscaling requires a robust upscaling procedure. Several authors have discussed methods to upscale permeability, but few have addressed the problem of upscaling in the vicinity of wellbore although the well performance is more affected by the permeability of this region than by any permeability away from it. The large portion of pressure drop in a reservoir is realized in the near-wellbore region. White and Horne proposed a method to calculate well-block transmissibility. Their method was based on running simulations with fine scale grid blocks for different boundary conditions. The pressures and fluxes from fine scale simulations were averaged and summed to obtain pressures and fluxes on a coarse scale. The least square method is utilized to convert the coarse scale pressures and fluxes into a block transmissibility. Palagi et al. presented an upscaling procedure for the permeability at the interface of Voronoi grid blocks. They used the power law averaging to calculate homogenized permeability. To find the optimum value for the power law coefficient, the simulation results of the initial permeability distribution were compared with the results of various upscaled distributions obtained with various values of . The that minimizes the difference between the fine grid and coarse grid results is accepted as the optimum . Ding presented an upscaling procedure to calculate the equivalent coarse grid transmissibility based on the results of fine grid simulation. To account for a well in a coarse grid block, the numerical productivity index for a coarse grid block was defined. The methods discussed above are based on the fine-grid numerical simulations. Numerical simulations are to be repeated for all coarse grid blocks and require a preprocessing task that usually take up several man-hours. To avoid lengthy numerical simulations, this study presents an analytical method to calculate upscaled well-block effective permeability. The method is based on the understanding that the effective permeability should preserve the ratio of the fluid flux and the potential drop realized across the fine grid blocks with the heterogeneous permeabilities. The method can be applied to either 2- or 3-D flow simulations. It is based on the incomplete-layers concept and the radial flow averaging laws that are applied to a Cartesian grid scheme.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractIt is a common observation that well test permeability values do not match with thickness weighted core permeability averages. This is not a surprise because of the differences in the measurement scales where, unlike well test measurements, core samples represent a very small portion of the reservoir around the well bore. In addition, the presence of fractures and/or high permeability channels will further enhance the difference between the two sources of data. Therefore, reservoir descriptions based on core measurements alone cannot honor well test results. They need to be modified properly without violating the underlying geological and geostatistical information.In this paper, we present a methodology to properly enhance permeability fields that also accounts for fracture distribution in the reservoir. The basic idea is that radial upscaling around a wellbore within a given investigation radius should match the permeability obtained from well tests. The enhancement is caused by two factors: microfractures, which cannot be explicitly represented in the reservoir description, and macro-fractures, which can be interpreted using 3-D seismic data. To account for these two different types of fractures, we calculate two different enhancement factors, one for the base level (microfractures) and one for the higher level (macro-fractures). The base level, after appropriate interpolation, is applied across the entire reservoir, whereas the higher level is applied only to locations where macro-fractures are interpreted from 3-D seismic data.The technique was successfully applied to a Middle Eastern carbonate reservoir. A significant correlation is observed between the enhancement required to match the well test data and the fracture density (macro-fractures obtained from 3-D seismic data) within a given investigation area. A correlation function is then obtained between the enhancement factor and the fracture density for a given grid block, which in turn is used to apply enhancement to interwell locations. Thus, the resulting permeability field did not only honor the well test results but also the fracture distribution and the underlying geological and geostatistical descriptions. In a later stage, a tensorial approach was used to upscale permeability to account for the anisotropy in permeability distribution. Using this approach, a proper anisotropy of permeability distribution, matching the fracture orientation, has been obtained.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractThis paper presents the result of fully 3D integrated reservoir description and flow simulation study of a giant oil field in Middle East using the state of the art technology. The overall goal is to develop a representative reservoir model to form the basis for reservoir management and longterm development planning. This is done by generating alternate reservoir descriptions, based on stochastic models, to quantify uncertainties in the future performance. The data that were integrated include well cores and logs, geological interpretation (stratigraphy, rock type, depositional model), seismic (structure, curvature analysis and inversion-derived porosity), well test, SCAL, production data and fracture distribution.The 3D multiple realizations were generated by considering rock type and petrophysical properties at well location, obtained from well logs and cores, and simultaneously constrained by seismic derived porosity. The simulations of properties were generated using simultaneous sequential Gaussian simulation where the seismic constraint was introduced via Bayesian Updating procedure. Special consideration was given to the spatial modeling of data where soft information was derived both from hard data and depositional environment. Fracture distribution, derived from seismic curvature analysis, was used in the integration process to match the core-based derived permeability with well test permeability. This distribution was used to obtain permeability anisotropy distribution using newly developed tensorial approach.A total of forty-eight realizations were generated considering four major types of uncertainties: structure, spatial model, petrophysical properties and simulation path. The results have been used as the basis for fluid in place (STOIIP) calculation using Monte Carlo simulation technique. These realizations are then ranked based on the sweep efficiency, obtained from multiphase streamline simulations, and the STOIIP. Three realizations, representing medium, low and high realizations, were selected and upscaled. An optimum vertical upscaling level was determined using streamline simulator and developing quantitative criterion. This ensures that the representative heterogeneity of the reservoir was maintained during the upscaling process.Comprehensive history matching was done for the three selected realizations for the entire nineteen years of production history using objective criterion so that the quality of the three matches is similar. The observed data matched include water cuts and measured pressures. The parameters used to match the history are restricted to the parameters that have not been accounted for in the static model. Using probabilistic concepts, uncertainties in future performance were quantified for various scenarios.

This paper was prepared for presentation at the 1999 SPE Mid-Continent Operations Symposium held in Oklahoma City, Oklahoma, 28-31 March 1999.