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

2021 ◽  
Author(s):  
Mehdi Teymouri ◽  
◽  
Zoya Heidari ◽  
Keyword(s):  
Mechanical Properties ◽  
Spatial Distribution ◽  
Pore Structure ◽  
Pore Pressure ◽  
Elastic Properties ◽  
Hydraulic Properties ◽  
Effective Medium ◽  
Pore Scale ◽  
Micro Scale ◽  
Effective Medium Models

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

Geophysics ◽  
2020 ◽  
Vol 85 (6) ◽  
pp. MR341-MR349
Author(s):  
Tongcheng Han ◽  
Zhoutuo Wei ◽  
Li-Yun Fu
Keyword(s):  
Elastic Properties ◽  
Geophysical Methods ◽  
Effective Medium ◽  
Geometric Factor ◽  
Rock Properties ◽  
Modeling Approaches ◽  
The Earth ◽  
Elastic Rock ◽  
Effective Medium Models ◽  
Electromagnetic Surveys

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.

Pore-Scale Joint Evaluation of Dielectric Permittivity and Electrical Resistivity for Assessment of Hydrocarbon Saturation Using Numerical Simulations

SPE Journal ◽  
2016 ◽  
Vol 21 (06) ◽  
pp. 1930-1942 ◽  
Author(s):  
Huangye Chen ◽  
Zoya Heidari
Keyword(s):  
Electrical Resistivity ◽  
Spatial Distribution ◽  
Dielectric Permittivity ◽  
Pore Structure ◽  
Maximum Error ◽  
New Method ◽  
Pore Scale ◽  
Resistivity Measurements ◽  
Hydrocarbon Saturation ◽  
Permittivity Measurements

Summary Complex pore geometry and composition, as well as anisotropic behavior and heterogeneity, can affect physical properties of rocks such as electrical resistivity and dielectric permittivity. The aforementioned physical properties are used to estimate in-situ petrophysical properties of the formation such as hydrocarbon saturation. In the application of conventional methods for interpretation of electrical-resistivity (e.g., Archie's equation and the dual-water model) and dielectric-permittivity measurements [e.g., complex refractive index model (CRIM)], the impacts of complex pore structure (e.g., kerogen porosity and intergranular pores), pyrite, and conductive mature kerogen have not been taken into account. These limitations cause significant uncertainty in estimates of water saturation. In this paper, we introduce a new method that combines interpretation of dielectric-permittivity and electrical-resistivity measurements to improve assessment of hydrocarbon saturation. The combined interpretation of dielectric-permittivity and electrical-resistivity measurements enables assimilating spatial distribution of rock components (e.g., pore, kerogen, and pyrite networks) in conventional models. We start with pore-scale numerical simulations of electrical resistivity and dielectric permittivity of fluid-bearing porous media to investigate the structure of pore and matrix constituents in these measurements. The inputs to these simulators are 3D pore-scale images. We then introduce an analytical model that combines resistivity and permittivity measurements to assess water-filled porosity and hydrocarbon saturation. We apply the new method to actual digital sandstones and synthetic digital organic-rich mudrock samples. The relative errors (compared with actual values estimated from image processing) in the estimate of water-filled porosity through our new method are all within the 10% range. In the case of digital sandstone samples, CRIM provided reasonable estimates of water-filled porosity, with only four out of twenty-one estimates beyond 10% relative error, with the maximum error of 30%. However, in the case of synthetic digital organic-rich mudrocks, six out of ten estimates for water-filled porosity were beyond 10% with CRIM, with the maximum error of 40%. Therefore, the improvement was more significant in the case of organic-rich mudrocks with complex pore structure. In the case of synthetic digital organic-rich mudrock samples, our simulation results confirm that not only the pore structure but also spatial distribution and tortuosity of water, kerogen, and pyrite networks affect the measurements of dielectric permittivity and electrical resistivity. Taking into account these parameters through the joint interpretation of dielectric-permittivity and electrical-resistivity measurements significantly improves assessment of hydrocarbon saturation.

INTERPRETATION OF MULTI-FREQUENCY DIELECTRIC PERMITTIVITY MEASUREMENTS FOR ASSESSMENT OF WATER SATURATION IN CARBONATE FORMATIONS WITH COMPLEX PORE STRUCTURE

2021 ◽  
Author(s):  
Zulkuf Azizoglu ◽  
◽  
Zoya Heidari ◽  
Keyword(s):  
Spatial Distribution ◽  
Dielectric Permittivity ◽  
Pore Structure ◽  
Carbonate Rock ◽  
Water Saturation ◽  
Dielectric Dispersion ◽  
Pore Scale ◽  
Rock Samples ◽  
Wide Range ◽  
Permittivity Measurements

Broadband relative dielectric dispersion measurements are considered interesting options for assessment of water-filled pore volume. Conventional models such as Complex Refractive Index Model (CRIM) and Maxwell Garnett (MG), often overlook or oversimplify the complexity of pore structure, geometrical distribution of the constituting fluids, and spatial distribution of minerals. This yields to significant errors in assessment of water saturation especially in rocks with complex pore structure. Therefore, it becomes important to quantify the impacts of pore structure and spatial distribution of minerals on broadband relative dielectric dispersion measurements to be able to make decisions about reliability of water saturation estimates from these measurements in a given formation. The objectives of this paper are (a) to quantify the impacts of pore structure and spatial distribution of minerals on relative dielectric permittivity measurements in a wide range of frequencies, (b) to propose a new simple and physically meaningful workflow, which honors pore geometry and spatial distribution of minerals to enhance fluid saturation assessment using relative dielectric permittivity measurements, (c) to verify the reliability of the introduced model in the pore-scale domain. First, we perform numerical simulations of relative dielectric dispersion measurements in the frequency range of 20 MHz to 1 GHz in the pore-scale domain. The input to the numerical simulator includes pore-scale images of actual complex carbonate rock samples. We use a physically meaningful model which honors spatial distribution of the rock constituents for the multi-frequency interpretation of relative dielectric response. To verify the reliability of the model in multiple frequencies, we apply the model to the results of relative dielectric simulations in the pore-scale domain on 3D computed tomography scan (CT-scan) images of carbonate rock samples, which are synthetically saturated to obtain a wide range of water saturation. We successfully verified the reliability of the introduced model in the pore-scale domain using carbonate rock samples with multi-modal pore-size distribution. Estimated water saturations from the results of simulations at 1 GHz resulted in an average relative error of less than 4%. We observed measurable improvements in fluid saturation estimates compared to the cases which CRIM or MG models are used. Results demonstrated that application of conventional models to estimate water saturation from relative dielectric response is not reliable in frequencies below 1 GHz.

ANISOTROPY QUANTIFICATION USING HIGH-RESOLUTION WHOLE-CORE CT-SCAN IMAGES

2021 ◽  
Author(s):  
Andres Gonzalez ◽  
◽  
Mehdi Teymouri ◽  
Zoya Heidari ◽  
Olivier Lopez ◽  
...  
Keyword(s):  
Spatial Distribution ◽  
Ct Scan ◽  
Elastic Properties ◽  
Image Data ◽  
Core Material ◽  
3D Ct ◽  
Pore Scale ◽  
Formation Evaluation ◽  
3D Ct Scan ◽  
Rock Anisotropy

Spatial anisotropy and heterogeneity in petrophysical properties can significantly affect formation evaluation of hydrocarbon bearing formations. A common example is permeability anisotropy, which is a consequence of the depositional mechanisms of sediments. Additionally, the variation in spatial distribution of rock components and the effect of post-depositional processes on the physical and chemical structure of the rock constituents can strongly impact the directional dependency of petrophysical, electrical, and elastic properties. Therefore, image-based quantification of spatial distribution of rock constituents can be used for anisotropy evaluation. Assessment of anisotropy has been previously accomplished through use of pore-scale images. However, the discrete nature of this images gives a narrow picture of anisotropy in larger scales. Whole-core computed tomography (CT) scan images, despite revealing the distribution of rock components at a coarser scale, provide a continuous medium for anisotropy estimation. Assessment of anisotropy using three-dimensional (3D) CT-scan data and incorporation of that information in well-log-based formation evaluation is, however, not widely studied or practiced in the petroleum industry. The objectives of this paper are (a) to develop a method to quantify anisotropy utilizing whole-core 3D CT-scan image stacks, (b) to provide a semi-continuous measure of rock anisotropy, and (c) to show the value of the proposed method by means of estimation of directional-dependent elastic properties. First, we pre-process the raw whole-core CT-scan images to remove undesired image artifacts and to generate an image containing pixels representing only the recovered core material. Then, we segment each whole-core CT-scan image stack into distinctive phases. Then, we conduct numerical simulations of electric potential distribution in conjunction with streamline tracing techniques to quantify the electrical tortuosity of the continuous phase in each cartesian direction. We employed the tortuosity distribution values in each direction as a measure of rock anisotropy. Finally, we use a simulation model to estimate direction-dependent elastic properties. We applied the introduced method to dual energy whole-core CT-scan image stacks acquired in a siliciclastic depth interval. Estimates of rock anisotropy obtained using the proposed method agreed with the observed visual distribution of the segmented phase and the observed heterogeneity in available slabbed whole-core photos and 2D CT-scan images. Additionally, estimation of directional-dependent elastic properties demonstrated the value of the proposed method. Anisotropy results coincided with directional-dependent estimation of elastic properties. We observed measurable anisotropy in the 3D CT-scan image stacks, which is important to be quantitatively taken into account in petrophysical/ mechanical evaluation of this formation. A unique contribution of the proposed workflow is the use of core-scale image data for anisotropy estimation and the continuous nature of the anisotropy estimates when compared with workflows employing only pore-scale image data. It should also be noted that the proposed method can potentially be employed to identify the optimum locations to acquire core plugs for further assessment of rock anisotropy.

Using a pore-scale model to quantify the effect of particle re-arrangement on pore structure and hydraulic properties

2007 ◽  
Vol 21 (8) ◽  
pp. 989-997 ◽  
Author(s):  
Oagile Dikinya ◽  
Peter Lehmann ◽  
Christoph Hinz ◽  
Graham Aylmore
Keyword(s):  
Pore Structure ◽  
Hydraulic Properties ◽  
Scale Model ◽  
Pore Scale ◽  
Pore Scale Model

Macroprobe Mode for the Study of Segregation in Steels

1990 ◽  
Vol 48 (2) ◽  
pp. 260-261
Author(s):  
Auclair Gilles ◽  
Benoit Danièle
Keyword(s):  
Mechanical Properties ◽  
Spatial Distribution ◽  
High Performance ◽  
Volume Fraction ◽  
Sheet Steel ◽  
Acquisition Time ◽  
Chemical Information ◽  
X Ray ◽  
Accurate Quantitative Analysis ◽  
Optical Micrographs

During these last 10 years, high performance correction procedures have been developed for classical EPMA, and it is nowadays possible to obtain accurate quantitative analysis even for soft X-ray radiations. It is also possible to perform EPMA by adapting this accurate quantitative procedures to unusual applications such as the measurement of the segregation on wide areas in as-cast and sheet steel products.The main objection for analysis of segregation in steel by means of a line-scan mode is that it requires a very heavy sampling plan to make sure that the most significant points are analyzed. Moreover only local chemical information is obtained whereas mechanical properties are also dependant on the volume fraction and the spatial distribution of highly segregated zones. For these reasons we have chosen to systematically acquire X-ray calibrated mappings which give pictures similar to optical micrographs. Although mapping requires lengthy acquisition time there is a corresponding increase in the information given by image anlysis.

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