Study On The Stress-dependent Properties Of Low-permeability Rock And 3D Rock Porous Structure Reconstruction

The stress-dependence of hydro-mechanical properties of low-permeability rock has drawn great attentions in a variety of engineering applications, such as dam construction, tunnel excavation, coal mining safety, nuclear waste disposal, fossil fuel exploitation and CO2 geological sequestration. In this paper, the low-permeability sedimentary rock refers to those with permeability less than 0.1 mD(10-16m2) under reservoir or in-situ conditions. These low-permeability sedimentary rock, such as tight sandstone and shale, usually show highly stress-sensitive mechanical and/or hydraulic properties. Knowledge of the dependence of such properties on stress is critical for a series of engineering applications. In dam construction, it is crucial to consider the influences of the dam and impound water to the around rock stability. In tunnel excavation, one has to consider that the stress release will cause the physical/mechanical properties changes of the surrounded rock. Geologic carbon sequestration(GCS) has been considered as one of the promising method for mitigating the global climate change. The permeability evolution with effective stress of the caprock, usually low-permeability formations, is vital for predicting its retarding effects of the upward CO2 migration and thus the safety of the GCS site. Similarly, lowpermeability formations such as clay rocks have long been considered as host rock for the disposal of radioactive nuclear waste. The stress-dependence of porosity and permeability in these formations, especially in an excavation damaged zone(EDZ), is of great importance for the performance assessment of the disposal site.With effective stress increasing, low-permeability rock undergoes fairly small porosity changes, but significant decreases in the permeability which can be up to several orders of magnitude. Empirical relationships based on the fitting of laboratory-measured data, typically the exponential or power laws, have been proposed to describe the stresspermeability, stress-porosity, and permeability-porosity relationships. However, these approximations either yield poor fitting in low effective stress ranges or unreasonable prediction for certain effective stresses. Extremely high exponent in the current power law, for an example, is often needed in the relationship between permeability and porosity, which is largely attributed to the assumption of relating permeability changes to the total porosity changes. In this thesis, we study the hydro-mechanical properties of lowpermeability rock in macroscopic/apparent scale and microscopic/mechanism scale for a better understanding the stress-dependent properties of the rock.In macroscale, we developed a series of theoretical models for the essential relationships among the porosity, permeability and the effective stresses for lowpermeability sedimentary rock, based on the concept of Two-Part Hooke’s Model(TPHM). The TPHM conceptualizes an intact rock into soft-part and hard-part which comply with the natural-strain-based and engineering-strain-based Hooke’s law, respectively. The division of hard and soft parts in THPM provides us with a framework to consider such heterogeneity development of stress-dependent permeability and porosity relationships. Based on this concept, a series of constitutive relations between stress and a variety of hydro-mechanical rock properties were derived, e.g., stressdependent rock bulk compressibility, pore compressibility, rock porosity and fracture aperture. The relationships derived using TPHM are consistent with those revealed from micromechanical point of views, albeit with different physical origins. These relationships based on the TPHM represent the experimental data in the literature very well. In this thesis, we extended to formulate the stress-dependence of permeability based on the concept of TPHM. The derived relationships explain well the permeability stresssensitive phenomena in the low effective stress range. The cornerstone of our development is the recognition of the fact that the porosities from the soft and hard parts have different contributions to the permeability changes with stresses. The derived relationships are validated by the experimental data from literatures. The comparisons show that the theoretical predictions agree well with the experimental results. The softpart, comprising of only a small portion of the pore space, is responsible for the significant permeability reduction in low stress levels. The high stress-sensitivity of permeability is mainly attributed to the micro-crack(soft-part) closure in the intact rock.The overall changes of hydraulic and mechanical properties with stress are contributed from both the hard and soft part. Specially, the large degree deformation of the soft part is the main reason for significant permeability reduction in the low effective stress range. The relationship between the soft part porosity and permeability approximately obeys a “cubic law”, further demonstrating that the soft part is composed of more deformable slot-like micro-cracks. Our theoretically derived equations have the following advantages: 1. it includes the heterogeneities of rock in the derivation. 2. it can accurately describe the stress-dependent rock hydro-mechanical properties in elastic stage. 3. the porosity act as a bridge linked the stress induced pore deformation and thus the permeability change. 4. parameters in the derived equations have clear physical meaning. 5. the equations have the ability to better describe the stress sensitive permeability changes for the low-permeability rock.The TPHM based stress-dependent permeability equation was incorporated into a COMSOL to study the production decline curve of a shale gas well. One of the distinct characteristics of the shale gas production rate is that it declines sharply in the initial stage and keep a long tail in the production curve, in other words, long production time. In contrast to previous studies, the effect of permeability changes of rock matrix along with the production is considered. However, for the sake of the manageability of the study, the desorption effect, thermal effect, and chemical reactions are not considered. As calculated, the gas pressure in the middle of the reservoir decrease slowly with time mainly because of the low permeability of the reservoir. The production rate decline curves are compared and analyzed using models that consider and not consider the geomechanical effects. The comparison result shows a much more rapid production rate decline and long tail in the production decline curve for the model considering the permeability changing effect. As a result, the geomechanical effect should be included in the shale gas production prediction to ensure better accuracy.From a microscopic point of view, we constructed 3D digital models for accurate describing the porous structures in the low-permeability rock. Natural rock has a large number of discontinuous, multi-scale, geometry-irregular pores, forming a complex porous structure. This porous structure essentially determines the physical and/or mechanical properties of rock, which are of great significance to a variety of applications in the fields of science and engineering. X-ray CT scanning technology has been used to measure the porous microstructures of two rock samples. One is natural sandstone and the other is artificial sandstone. As a supplement to the experimental observation, a reliable reconstruction model of porous structure could provide an effective and economical way to characterize the physical and mechanical properties of a porous rock. We presented a novel method for reconstructing the porous structures of the two models. A fractal descriptor is here proposed for better characterizing the complex pore morphologies. The reconstruction procedure is optimized by integrating the improved simulated annealing algorithm and the fractal system control function. The proposed reconstruction method enables us to represent a large-size 3D porous structure. To verify the accuracy of reconstruction, we have analyzed the statistical, geometrical, fractal, topological, and mechanical properties of the reconstructed porous medium and compared them with those of prototype rock samples. The comparisons show good agreement between the reconstructed model and the real porous structure.We incorporated the conclusion from macroscopic analysis into the construction of the porous—micro-fractures model. Specifically, micro-fractures, which cannot be observed by the current experimental method, were fabricated into the porous model to account for the soft-part pores. As assumed, the porous—micro-fractures model and porous model represent the transport structure in relatively low and high effective stress range, respectively. The hypothesis is made based on the fact that the micro-fractures undergo relatively large deformation with increasing effective stress and closed at relatively high effective stress.The lattice Boltzmann method(LBM) was employed to calculate the fluid flow in the porous—micro-fractures model and the porous model. This method enable us to directly visualize the fluid velocity distribution in the model and thus the structure deformation influences on the permeability. As the simulation results shown, the microcracks provide extra transport channels and connect parts of the previous non-effective pores for the fluid flow. As a result, the porous-micro-fractures model possesses much higher permeability than the porous model, although the micro-fractures only occupies a small portion of the pore volume.In this thesis, we deeply investigated the stress-dependent hydro-mechanical properties of the low-permeability rock from macroscopic and microscopic point of view. A series porosity, permeability and effective stress equations were developed based on the TPHM in macroscopic aspect. In microscopic, we constructed porous and porous—micro-fractures models and analyzed their permeability using LBM method. Based on these analysis, we conclude that the rapidly permeability drop of low-permeability rock with increasing effective stress is caused by the micro-fractures closure.