Geostatistical Modeling of Gridblock Permeabilities for 3D Reservoir Simulators

Abstract

Summary A geostatistical method is presented to determine the absolute horizontal and vertical effective permeabilities at the reservoir block scale from coresupport-scale values required for 3D reservoir flow simulations. The key element of the geostatistical model is the definition of block support-scale permeabilities as the spatial power average of core-support values permeabilities as the spatial power average of core-support values over the volume of a reservoir gridblock. Block support-scale permeabilities are then found to be a function of the permeability permeabilities are then found to be a function of the permeability variogram, the averaging volume, and a power-averaging constant, which is derived separately for horizontal and vertical flow with a numerical approach. The application of the proposed method requires that core-support values be available within each reservoir block. These values are generated with the technique of conditional simulation. This technique provides simulated values reproducing the actual core data at sampled locations and their statistical properties. The approach developed for the determination of permeability input to full-field simulators is demonstrated by an application to the Crystal Viking field "H" pool in Alberta. Introduction The understanding, prediction, and history matching of reservoir performance during production and optimization of hydrocarbon performance during production and optimization of hydrocarbon recovery are based on reservoir flow simulation studies. In these studies, the reservoir is represented by a large grid of rectangular blocks. Effective reservoir rock properties (e.g., permeability, porosity, and fluid saturations) are assigned to permeability, porosity, and fluid saturations) are assigned to these blocks. The assignment of representative values of these variables to the gridblocks of the discrete reservoir model is of critical significance for reservoir simulation results. This assignment of values is a problem of interpolation and simultaneous change of scale on the basis of measurements from a limited number of core samples, geophysical logs, and geological characterization of the reservoir. Permeability is one of the most significant reservoir properties affecting reservoir fluid flow and one of the most challenging to estimate. The nonadditive character of permeability does not permit direct estimation of effective block equivalents from the available core measurements; thus, specialized techniques are required. To date, considerable effort has been devoted to the calculation of permeability in heterogeneous geological formations. These efforts include numerical methods based on Monte Carlo simulations, 4–8 streamtube methods based on the geometry of discontinuous shales in sand/shale sequences, and analytical methods based on either a self-consistent approach or perturbation methods. The different approaches have contributed significantly to the understanding of the factors controlling permeability. All these methods, however, have limitations. Numerical methods, although more general, are approximate and tedious, and their accuracy depends on the relative lengths of the discretization grid and the correlation scale of permeability. Streamtube methods are suitable for only a limited number of simple shale configurations and low shale factors. Analytical methods are restricted by assumptions of isotropy, by limits in the distribution and shape of the correlation of permeability, and most important, by field size. Nevertheless, it is possible to expand the existing techniques and to extend their applicability, thus significantly improving current practices. practices. The goal of this paper is to develop a new practical approach to the problem of assigning permeability values to the large grid-blocks of full-field flow simulators. The approach is developed within the framework of geostatistics, where permeability values represent the outcome of a spatial stationary and ergodic random function. Consequently, spatial variations of core-sample permeabilities in a reservoir are characterized by the probability permeabilities in a reservoir are characterized by the probability distribution function and the spatial covariance (or variogram) of the random function, estimated from the available core measurements. Basic geostatistical concepts and definitions for modeling transmissibility for 2D reservoir studies have already been presented, with block support-scale transmissibility defined as presented, with block support-scale transmissibility defined as the spatial geometric average of point support-scale data. The present paper expands that approach to the 3Dcase. Absolute block present paper expands that approach to the 3D case. Absolute block support-scale permeability is defined here as a spatial power average of point support-scale values over a reservoir block. This differs from point support-scale values over a reservoir block. This differs from previous work on power averaging in sand/shale sequences, not previous work on power averaging in sand/shale sequences, not only in the definition of blocksupport-scale permeability, but also in that the effective permeability is not considered to follow a discrete binary-type distribution. Rather, it is assumed to be continuous and to follow a log-normal distribution, a frequent observation with permeability data. Theoretical concepts are illustrated in an example from the Crystal Viking reservoir "H" pool in south-central Alberta.