This paper presents a study of the relationship between permeability and effective stress in tight petroleum reservoir formations. Specifically, a quantitative method is developed to describe the correlation between permeability and effective stress, a method based on the original in situ reservoir effective stress rather than on decreased effective stress during development. The experimental results show that the relationship between intrinsic permeability and effective stress in reservoirs in general follows a quadratic polynomial functional form, found to best capture how effective stress influences formation permeability. In addition, this experimental study reveals that changes in formation permeability, caused by both elastic and plastic deformation, are permanent and irreversible. Related pore-deformation tests using electronic microscope scanning and constant-rate mercury injection techniques show that while stress variation generally has small impact on rock porosity, the size and shape of pore throats have a significant impact on permeability-stress sensitivity. Based on the test results and theoretical analyses, we believe that there exists a cone of pressure depression in the area near production within such stress-sensitive tight reservoirs, leading to a low-permeability zone, and that well production will decrease under the influence of stress sensitivity. IntroductionWithin the petroleum literature, there are many studies on the sensitivity of permeability to stress fields in tight reservoirs [1][2][3][4][5][6][7][8]. However, most of these studies are carried out in conditions under the low range of effective stress (e.g., generally no more than 7 MPa) as reference stress. Therefore, the extent of "damage" caused by stress or stress sensitivity is found to be very high from such studies. As a result, these studies indicate that low-permeability tight oil reservoirs are inadvisable to be developed under large pressure gradients, because of the formation's high sensitivity to change in effective stress. In fact, during well drilling and core sampling the state of stress within core samples will vary from the initial in situ state of stress, to a mud-hydrostatic-pressure state inside wellbores and to atmospheric conditions on the surface with stress release. If laboratory experimental conditions are not set approximately to actual in situ stress level of reservoirs, experimental results often show substantial changes in core pore-throat structures with changes in effective stress. The resulting stress sensitivity or formation deformation results cannot in general reflect the actual situation in formations. It has been shown in many experiments [9][10][11] that studies using stress fields lower than those for reservoir conditions overestimate the effects of stress on formation deformation (e.g., the results from laboratory experiments using conventional cores under low effective stress conditions fail to predict realistic changes in pore throats and structures). This paper presents results an...

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Unsuitable locations of bus stops which provide feeder transportation connecting subways near urban intersections usually lead to the low efficiency of public transport and level of passenger service. A multiobjective optimization model to distribute such stop locations is proposed to attain the shortest total walk distance of passengers and minimum delay time of cars through intersections and travel time of buses. The Pareto frontier and optimal solutions for the proposed model are given by the distance-based and enumerative methods. The Xizhimen bus stop is selected to implement case studies for verifying the validity of the proposed model. The analysis of sensitivity on possible solutions is also carried out in the case studies. The results show that the proposed model is capable of optimizing the locations of bus stops connecting subways near intersections and helpful to improve the level of passengers service and operational efficiency of public transportation.