Brinell indentation tests were performed on Montney siltstone, and the results were compared with discrete element indentation simulations that use the micro-parameters calibrated using compression test data from the same siltstone samples. The simulated proppant indentation into the rock surface can be 15% less than the laboratory measurements. A lower effective particle–particle modulus and thus a lower Young’s modulus are needed in discrete element models for proper simulation of indentation. An equation to find the appropriate value of Young’s modulus for indentation simulation is proposed using Brinell indentation tests including 198 laboratory tests and 32 discrete element simulations. This equation can improve the prediction of Young’s modulus and thus the particle–particle effective modulus for indentation simulations to match the measured force–indentation depth curve in the laboratory. Using the improved micro-parameters, a parametric analysis of the influence of rock Young’s modulus and proppant particle size on proppant embedment was performed. An equation to estimate Brinell hardness as a function of Young’s modulus and closure stress was derived. A practical procedure was developed to predict proppant embedment from the estimated hardness. The predictions agree with the laboratory measurements in a case study on the Montney Formation.
Physical geography is a basic research subject of natural sciences.Its research object is the natural environment which is closely related to human living and development,and China's natural environment is complex and diverse.According to national needs and regional development,physical geographers have achieved remarkable achievements in applied basis and applied research,which also has substantially contributed to the planning of national economic growth and social development,the protection of macro ecosystems and resources,and sustainable regional development.This study summarized the practice and application of physical geography in China over the past 70 years in the following fields:regional differences in natural environments and physical regionalization;land use and land cover changes;natural hazards and risk reduction;process and prevention of desertification;upgrading of medium-and low-yield fields in the Huang-Huai-Hai region;engineering construction in permafrost areas; geochemical element anomalies and the prevention and control of endemic diseases;positioning and observation of hysical geographical elements;and identification of geospatial differentiation and geographical detectors. Furthermore, we have proposed the future direction of applied research in the field of physical geography. 相似文献