Stochastic finite element analysis of the diametral compression test of powder compacts and porous materials

This paper presents a stochastic finite element approach for modeling the mechanical behavior of powder compacts and porous materials under diametral compression test conditions. The main goal is assessing the validity of the diametral compression test as an indirect technique to estimate tensile strengths of brittle or quasi-brittle materials exhibiting porosity heterogeneity. Thus, the study seeks to predict the influence of porosity randomness on stress distributions and the spatial location of the highest tensile stress on thin disc-shaped specimens. The proposed formulation uses a stochastic framework that couples a random spatial field to the finite element analysis to include non-deterministic features. Two case studies consider comparable targets for the mean porosity but different coefficients of variations. For each case study, a total of 1000 realizations are conducted under identical loading and boundary conditions. The predicted stress distributions are compared to the ones from homogenous closed-form solutions from the literature. Then, the expected magnitude and location of the maximum tensile stress are evaluated by statistical means. Findings from the stochastic model show that porosity randomness induces stress concentration around less dense volumes and location deviation of the maximum tensile stress from the center of the discs. Likewise, porosity heterogeneity could affect the accuracy of experimental diametral compression tests even for small variance cases; and so, the reliability of the mechanical properties derived from models based exclusively on the classic assumption of material homogeneity.

Reactive Transport Simulation of Cavern Formation along Fractures in Carbonate Rocks

Karst cavities and caves are often present along fractures in limestone reservoirs and are of significance for oil and gas exploration. Understanding the formation and evolution of caves in fractured carbonate rocks will enhance oil and gas exploration and development. Herein, a reactive transport model was established considering both the matrix and fractures. Different factors affecting the dissolution along fractures were considered in the simulation of matrix–fracture carbonate rocks, including the magnitude and characteristic length of the matrix porosity heterogeneity, intersecting fractures, and complex fracture network. The results show that a strong heterogeneity of the matrix porosity significantly affects the cave formation along the fracture and the existence of fractures increases the heterogeneity due to the high permeability as well as the dissolution area. The characteristic length of the matrix porosity heterogeneity affects the cave location and shape. The larger permeability of intersecting fractures or the matrix greatly increases the cave size, leading to the formation of large, connected cave areas. A complex fracture network leads to more developed karst dissolution caves. The topology of the fracture network and preferential flow dominate the distribution of caves and alleviate the effect of the matrix heterogeneity.

Seismic-based characterization of reservoir heterogeneity within the Meramec interval of the STACK play, Central Oklahoma

The Meramec interval within the “STACK” play of the Anadarko Basin in central Oklahoma has been recently at the epicenter of increased exploration and production of oil and gas. It has become one of the top target intervals of the “Mid-Continent” aided by the technological advancements in horizontal drilling and completion techniques. The Meramec interval, mainly composed of argillaceous siliciclastic sediments with varying amounts of carbonate cement, exhibits high porosity heterogeneity, which is theorized to be caused by varying amounts of clay and post-depositional calcite cement. Characterization of the porosity heterogeneity in the Meramec interval will improve our understanding of the wide range in Meramec oil and gas production volumes and reduce the risk associated with drilling and completion techniques. We completed an initial interpretation followed by inversion of 3D seismic data where we generated a detailed characterization of the porosity heterogeneity and overall reservoir quality within the Meramec interval over an area of approximately 150 square kilometers. We then used the 3D seismic volume and available well logs to map the vertical and lateral extents of the Meramec interval and identify possible structural elements that could affect the reservoir quality. A petrophysical analysis of the well logs confirmed porosity heterogeneity and variations in volumetric calculations of clay and carbonate minerals. Finally, we generated a set of porosity volumes using the acoustic impedance from seismic inversion and probabilistic neural network methods. The derived porosity volume helped us identify porous and non-porous intervals within the Meramec throughout the study area. The results improved our understanding of Meramec heterogeneity, further reducing the risk associated with well planning, drilling and completion.

A Research on the Effect of Heterogeneities on Sandstone Matrix Acidizing Performance

Matrix acidizing is one of the common methods to enhance production in sandstone reservoirs. Conventional acidizing designs generally neglected the effect of heterogeneities of mineral and flow field distributions both in areal and vertical directions and assumed that the acid front propagates with a piston-like style. However, sandstone formations inevitably have small-scale heterogeneities of minerals and flow properties that may give rise to acid propagation in a manner much different from what is predicted based on homogeneous assumptions. In this paper, we conduct a research to numerically investigate how the heterogeneities affect acidizing performance under in situ conditions. Firstly, a heterogeneity model is built for mineral and porosity distributions by using the semivariogram model of geological statistics, based on which we generate spatially correlated porosity and mineral distributions. Next, a model of radial acid flooding is developed based on mass balance and the chemical reactions between the acids and minerals occurring during the acidizing process. The model is numerically solved to investigate the permeability response, acid distributions, precipitate distributions, and the effect of the heterogeneities on acidizing. The results show that the heterogeneities both in areal and vertical directions have a significant effect on acidizing. The flow field heterogeneities have a more serious impact than the mineral heterogeneities. In a plane, strong porosity heterogeneity can give rise to acid fingering and even channeling, which make the acid penetration distance longer than the homogeneous cases. The secondary precipitate has a significant effect when fast-reacting mineral content is high. Vertically, several-fold permeability contrast creates the acid break through the high-perm zone leaving the low-perm zone understimulated. Both flow field and mineral heterogeneities make it possible to create high-permeability channels during the acidizing process and to obtain a longer acid penetration distance.

A Full Coupled Thermal–Hydraulic–Chemical Model for Heterogeneity Rock Damage and Its Application in Predicting Water Inrush

A coupled thermal–hydraulic–chemical (THC) model was carried out in this paper to study the influence of rock heterogeneity and the coupling effect of temperature, groundwater, and hydrochemistry on rock damage. Firstly, the hydrochemical and hydraulic erosion equations were established. The equations of the coupled THC model were established by combining the hydrochemical and hydraulic erosion equations, the flow equations, and the heat transfer equations. Weibull distribution was adopted to govern the heterogeneity of initial rock porosity distribution. Secondly, the influence of the hydrochemistry, the temperature and the initial porosity heterogeneity on porosity and fluid velocity change was studied. Then the rock damage rule changed with time at different pH values and temperature was studied. Finally, an actual deep coal mine model was established to apply the THC model to predict water inrush. Results indicate that: (1) The average porosity and average fluid velocity approximately show linear growth and exponential growth with time, respectively, and their growth rates increase with decreasing pH value and increasing temperature in a certain acidity and temperature range. (2) The increase of initial porosity heterogeneity has little influence on porosity change, but it can increase the fluid velocity growth rate. The porosity heterogeneity and fluid velocity heterogeneity approximately show exponential growth with increasing time, and the rock heterogeneity growth contributes to form cracks. The increase of temperature and decrease of pH value have little influence on the porosity heterogeneity, but they can increase the growth rate of the fluid velocity heterogeneity. (3) The rock damage shows linear growth with time, and its growth rate increases with decreasing pH value and increasing temperature in a certain acidity range and temperature range. (4) The increase of rock heterogeneity can increase the possibility of water inrush.