Evaluation of Capillary Pressure Methods via Digital Rock Simulations

Abstract

Capillary pressure measurements are an important part of the characterization of petroleum-bearing reservoirs. Three commonly used laboratory techniques, namely the porous plate (PP), centrifuge multi-speed experiment (CM), and mercury intrusion (MICP) methods, often provide nonidentical capillary pressure curves. We use high-resolution μ-CT images of Fontainebleau and Bentheimer sandstones to derive saturation profiles numerically in 3D at the pore scale through morphological distance transforms to simulate the above experiments. In the invasion simulation, the capillary pressure is realized by using as structural element a ball-whose diameter is a function of a local pressure potential, which in turn is a function of radial distance in centrifuge experiment and constant throughout the sample in MICP and porous plate measurements. To assess the effect on heterogeneous rock samples, we compare the computed saturation profiles of the relatively homogeneous sandstones to a highly heterogeneous numerical model of rock generated by a mixture of a Gaussian random field approach for the large-scale features and two Poisson particle processes at the small scale. The comparison of the image-based pore-scale numerical interpretation to capillary drainage experiments reveals their match and demonstrates the influence of boundary conditions and heterogeneity on the resulting saturation profiles and capillary pressure curves. Simulated centrifuge experiments may assist in estimation of experimental equilibrium times and provide a useful tool in speed schedule design.

An Experimental and Numerical Study of Relative Permeability Estimates Using Spatially Resolved $$T_1$$-z NMR

“…Fully saturated state is simulated by assigning to the whole void space and a specified fraction of the intermediate phase physical properties of a fluid. The distributions of fluids are simulated using morphological transforms with appropriate boundary conditions to mimic one of a capillary drainage technique (Shikhov and Arns 2015 …”

“…This implies that Corey's model ignores contributions to flow of pore-throat sizes significantly different from the mode of a distribution. We used common capillary pressure techniques (MICP and centrifuge) to validate digitised rock representations by comparing capillary pressure simulations on μ-CT images to experiments (Shikhov and Arns 2015). We then fit the capillary pressure data with Corey's power-law model to obtain estimates of relative permeability curves following the Burdine-Corey model.…”

“…The spherical shape of the structuring element (or ball) corresponds to perfect wetting conditions (180 • contact angle), and the size of a ball (capillary radius) is determined by a local pressure potential, which in turn is a function of radial distance in centrifuge experiment (equation in the caption of Table 3) and constant throughout the sample in MICP measurements. The simulation procedure is described in detail in Shikhov and Arns (2015).…”

“…We compare saturation profiles of centrifuged cores simulated on μ-CT images of three sandstone rocks following Shikhov and Arns (2015) to experimental profiles obtained using two 1D NMR imaging techniques. The first is frequency encode (or constant gradient) 1D NMR spin-density imaging.…”

“…CM-NMR-T 1 relative permeability curves of three sandstone rocks were simulated numerically and validated by T 1 -z experiments. Simulations of a centrifuge capillary drainage are performed by applying morphological transforms on high-resolution 3D tomograms following (Arns et al 2005b;Shikhov and Arns 2015). T 1 responses along the sample are simulated using the random walk technique on μ-CT images (Arns et al 2011).…”