Predicting Carbonate Rock Properties Using NMR Data and Generalized Interpolation-Based Techniques

Abstract

This paper describes an application of the radial basis function (RBF) method, a generalized interpolation method, for predicting petrophysical parameters of complex carbonate formation rocks from NMR measurements. The predictions are refined using a forward-selection algorithm. To develop and validate the petrophysical models based on RBF methods, 103 core-plug measurements, including porosity, permeability, NMR relaxation times, capillary pressure, and thin-section images are used. The forward-selection algorithm is used to improve the robustness of the RBF methods for predicting the permeability, the Thomeer parameters of the capillary pressure function, and the pore-throat-size distribution. It is demonstrated that for heterogeneous carbonate rocks, the generalized interpolation method is better than a closed-form expression to correlate NMR measurements with petrophysical variables. Furthermore, the comparison of four approaches of applying the RBF technique for permeability prediction is presented together with recommended methods for practical use.

Introduction

In many carbonates, the biological origin and diagenetic processes that occurred at the post-depositional stage resulted in highly complex pore systems and large variations of the pore structures from depth to depth. The heterogeneity occurs at all scales (Nurmi et al., 1990). This complexity makes it difficult, if not impossible, to describe well-logging measurements with the key porous media properties, such as pore connectivity, pore type, capillary pressure, or permeability, in analytical or empirical expressions. A typical approach for developing a petrophysical interpretation model for heterogeneous reservoirs uses a large number of core samples; this approach recognizes that a small number of samples cannot adequately represent the reservoir rock system. The use of a larger number of samples, it is hoped, will enable the capture of all variations. However, it is often found that a larger sample base only points to a larger spreading, or uncertainty, associated with fitting to a correlation equation. To reduce the uncertainty, additional conditions or constraints are often applied to decrease the application window of a correlation, as a means of narrowing the heterogeneity range. Consequently, multiple correlations are often required; determining their application window is often not straightforward. This type of model is difficult to implement if logging measurements respond to multiple formation attributes in a nonlinear fashion, which is often the case for carbonate formations.