Using rock physics models to validate rock composition from multimineral log analysis

Multimineral log analysis is a quantitative formation evaluation tool for geological and petrophysical reservoir characterization. Rock composition can be estimated by solving equations that relate log measurements to the petrophysical endpoints of minerals and fluids. Due to errors in log data and uncertainties in petrophysical endpoints of constituents, we propose using effective medium models from rock physics as additional independent information to validate or constrain the results. In this paper, we examine the Voigt-Reuss (VR) bound model, self-consistent approximation (SCA), and differential effective medium (DEM). The VR bound model provides the first-order quality control of multimineral results. We first show a conventional carbonate reservoir study with intervals where the predicted effective medium models from multimineral results are inconsistent with the measured elastic properties. We use the VR bound model as an inequality constraint in multimineral analysis for plausible alternative solutions. SCA and DEM models provide good estimates in low porosity intervals and imply geological information for the porous intervals. Then, we show a field case of the Bakken and Three Forks formations. A linear interpolation of the VR bound model helps validate multimineral results and approximate the elastic moduli of clay. There are two major advantages to use our new method (a) rock physics effective medium models provide independent quality control of petrophysical multimineral results, and (b) multimineral information leads to realistic rock physics models.

Optical Properties of Porous Alumina Assisted Niobia Nanostructured Films–Designing 2-D Photonic Crystals Based on Hexagonally Arranged Nanocolumns

Three types of niobia nanostructured films (so-called native, planarized, and column-like) were formed on glass substrates by porous alumina assisted anodizing in a 0.2 M aqueous solution of oxalic acid in a potentiostatic mode at a 53 V and then reanodizing in an electrolyte containing 0.5 M boric acid and 0.05 M sodium tetraborate in a potentiodynamic mode by raising the voltage to 230 V, and chemical post-processing. Anodic behaviors, morphology, and optical properties of the films have been investigated. The interference pattern of native film served as the basis for calculating the effective refractive index which varies within 1.75–1.54 in the wavelength range 190–1100 nm. Refractive index spectral characteristics made it possible to distinguish a number of absorbance bands of the native film. Based on the analysis of literature data, the identified oxide absorbance bands were assigned. The effective refractive index of native film was also calculated using the effective-medium models, and was in the range of 1.63–1.68. The reflectance spectra of all films show peaks in short- and long-wave regions. The presence of these peaks is due to the periodically varying refractive index in the layers of films in two dimensions. FDTD simulation was carried out and the morphology of a potential 2-D photonic crystal with 92% (wavelength 462 nm) reflectance, based on the third type of films, was proposed.

AN ADVANCED PETROPHYSICAL ORIENTED NUMERICAL METHOD FOR RELIABLE ASSESSMENT OF MECHANICAL PROPERTIES IN CARBONATE FORMATIONS AT THE PORE-SCALE DOMAIN

Assessment of effective mechanical properties such as elastic properties and brittleness can be challenging in the presence of complex rock composition, pore structure, and spatial distribution of minerals, especially in the absence of acoustic measurements. Conventional methods such as effective medium modeling, are not reliable for assessments of mechanical properties in complex formations such as carbonates, because solid skeleton of carbonates does not consist of granular minerals with ideal shapes. The effective medium models also overlook both the spatial distribution of petrophysical properties, and the coupled hydraulic and mechanical (HM) processes, which causes significant uncertainties in geomechanical evaluations. The objective of this paper is to develop a numerical method to enhance assessment of effective mechanical properties of anisotropic and heterogenous carbonate formations by modeling the variation of effective stress and the evolution of corresponding strain. The developed method takes into account the coupled HM processes, the realistic spatial distribution of rock inclusions (i.e., rock fabrics), dynamic fluid flow, pore pressure, and pore structure. To achieve this objective, we develop a pore-scale numerical simulator by satisfying conservation equations and considering the coupling among relevant HM phenomena. We adopt peridynamic theory to discretize the micro-scale medium. The inputs to our numerical modeling include pore-scale images of rock samples as well as mechanical and hydraulic properties of each rock inclusion. We perform image processing on micro-CT scan images of rock samples to obtain a realistic micro-scale structure of both rock matrix (i.e., concentration, spatial distribution, and shape of rock constituents) and pore space. We then assign realistic mechanical and hydraulic properties to each rock constituent within the pore-scale medium. The outcomes of numerical modeling include the variation of effective stress and the evolution of corresponding strain by honoring the variability in mechanical/hydraulic properties of rock inclusions caused by their spatial distribution, pore pressure, pore structure, natural fractures, and dynamic fluid flow at the micro-scale domain. We then compare the outcomes of numerical models with the mechanical properties estimated based on effective medium models. We performed sensitivity analyses to quantify the effects of concentration and spatial distribution of rock constituents, divergence in spatial distribution of petrophysical, mechanical, and hydraulic properties of inclusions, pore structure and natural micro-fractures, and pore pressure on variations in effective elastic properties of rock samples. We estimated the elastic properties from the stress/strain curves obtained from numerical simulations. We observed significant errors (more than 30.6% relative error depending on the content and distribution of rock constituents) in estimated effective elastic properties by the effective medium models. These errors are due to overlooking the coupled HM analysis, the spatial distribution, actual shape and size of inclusions, pore-structure, and natural micro-fractures by such effective medium models. The presented advanced pore-scale numerical analysis will (a) enhance reliable assessments of effective elastic/mechanical properties of carbonates or any other rock type in the presence of pore pressure and dynamic flow, and (b) assist upscaling techniques for reliable geomechanical evaluation and assessment of fracture propagation in these formations at larger scales.

Cementation exponent as a geometric factor for the elastic properties of granular rocks

A geometric factor properly describing the microstructure of a rock is compulsory for effective medium models to accurately predict the elastic and electrical rock properties, which, in turn, are of great importance for interpreting data acquired by seismic and electromagnetic surveys, two of the most important geophysical methods for understanding the earth. Despite the applications of cementation exponent for the successful modeling of electrical rock properties, however, there has been no demonstration of cementation exponent as the geometric factor for the elastic rock properties. We have developed a workflow to model the elastic properties of clean and normal granular rocks through the combination of effective medium modeling approaches using cementation exponent as the geometric factor. Based on the dedicated modeling approaches, we find that cementation exponent can be adequately used as a geometric factor for the elastic properties of granular rocks. Further results highlight the effects of cementation exponent on the elastic and joint elastic-electrical properties of granular rocks. The results illustrate the promise of cementation exponent as a geometric link for the joint elastic-electrical modeling to better characterize the earth through integrated seismic and electromagnetic surveys.

A scale-consistent method for imaging porosity and micrite in dual-porosity carbonate rocks

Unlike many other clastic rocks, relating velocity and permeability to porosity for micrite-bearing carbonate rocks has been largely unsuccessful. Recent studies have shown that additional parameters, most notably the distribution and/or proportion of micrite, can be used to parameterize the velocity and permeability behavior. However, there is currently no scale-consistent, 3D methodology for differentiating macroporosity and microporosity from the total porosity measured on bench-top laboratory equipment. Previous studies estimated microporosity and micrite content by combining total porosity measurements conducted on whole 50 mm cores with measurements of phase volumes on 1 mm digital rocks (i.e., scale-inconsistent). As a step forward from those, we imaged dual-porosity carbonate rocks using X-ray microcomputed tomography and then leveraged a recently developed, optimization-based technique, called data-constrained modeling, to map the macroporosity and microporosity distribution of our samples. We evaluate the volumetric proportions of macropores, micropores, and coarse-grained calcite as a function of micrite content — with their respective uncertainties — all measured on the same digital rock and with the same method. Finally, we determine how measurements of the volumetric phase proportions could be extended using standard effective medium models to predict reservoir physical properties. The sensitivity of these models to the proportion of micrite and microporosity within the micrite is evidence that the nonuniqueness among permeability, velocity, and porosity that is commonly observed of micrite-bearing carbonate rocks can be explained by a variation of micrite content and microporosity at a similar porosity.