Robust Centrifuge Data Processing for Tight and Permeable Rock Samples

Abstract

Capillary pressure measurements are key to reservoir characterization. The centrifuge technique is the most used industrial laboratory method to obtain capillary pressure curves for rock samples. The generated experimental data, however, requires conversion of average saturation into local saturation to get correct capillary pressure curves, which is often complicated by the need of fitting of complex and noisy data. Therefore, the objective of this study is to construct a smooth, stable and physically-consistent data fitting model for complex centrifuge data, in order to deliver accurate local saturations for different capillary pressure curves. Drainage capillary pressure curves were generated by centrifugation. Isoparaffinic oil was used to displace brine from core samples at elevated capillary pressure steps. Average water saturation was determined at each capillary pressure step after attaining production stability. Hassler-Brunner and Forbes’s second approximate solutions were used to convert the acquired average water saturations into local saturations. For these two solutions, three analytical fitting techniques were compared on different sets of experimental data. These are power law, global polynomial and cubic spline fitting methods. Two carbonate samples of (96 md) and (0.7 md) permeability were evaluated to represent two distinct cases of a capillary pressure curves. Initially, the power law was used to fit the centrifuge data. For both permeable and tight samples, the resulting capillary pressure curves were found strongly biased by a choice of non-zero initial pressure point, which makes this technique not suitable for data interpretation. The second approach was to use the polynomial fitting method, which found unable to properly fit the tight sample data. It was, however, capable to fit the raw data of the permeable sample. The generated corrected capillary pressure curve, however, was unphysical at low water saturation ranges. Therefore, the raw data of the both samples required application of more complex fitting approach, i.e. the spline method. From the results, the spline function showed high degree of fitting and could account for irregularities of the experimental data. However, non-physical oscillations may occur during the data processing. Therefore, additional constraints of monotonicity of the fit and of the derived Forbes solutions were imposed on the optimal fitting spline. This approach was implemented using cubic splines and verified by equally good results obtained in processing experimental data sets for tight and permeable samples. Robust interpretation workflow to reconstruct capillary pressure curves from centrifuge experiment was built and verified on two limiting cases of tight and permeable samples. The approach is based on fitting of noisy experimental data with cubic spline, constructed using constrained optimization procedure to ensure monotonicity of the derived solutions. The latter physical consistency of the constructed spline fit returns correct capillary pressure curves required for accurate prediction of oil recovery and reservoir fluid distribution.