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 a 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 cause significant uncertainties in geomechanical evaluations. The objective of this paper is to develop a numerical method to enhance the 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 microscale 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 microscale 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 microscale 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 the spatial distribution of petrophysical, mechanical, and hydraulic properties of inclusions, pore structure and natural microfractures, dynamic fluid flow, 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 35% 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 microfractures 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.

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Mehdi Teymouri, Zoya Heidari
The University of Texas at Austin