The Study On Non-Linear Effective Stress For Permeability In Low-Permeability Rocks

Classical effective stress theory holds that non-linear effective stress is of little physical significance and applications. However, the common effect of deformation of microcracks and pores in low-permeability rocks will result in non-linear characteristics of effective stress in the process of oil and gas production. And available linear effective stress theory can't be used to determine how the rock properties (such as permeability, porosity et al.) vary with pore pressure. With regard to this, low-permeability rocks are selected as the study object. Theoretical studies, pore network simulation, laboratory experiment, microstructure observation and numerical simulation are main study methods. And studies of nonlinearity of permeability and effective stress have been carried out. Meanwhile, the exploratory researches about the relationship between non-linear effective stress and microscopic structure & diagenesis sequence have been done, which improves the stress sensitivity evaluation system of reservoir rocks. Besides, the effect of the non-linear coupling interactions of pore pressure and permeability to the single well development index are analyzed with the help of numerical simulator. The main research works are as follows:(1) According to the definition of effective stress and iso-k curves, the differences and relations between linear effective stress and non-linear effective stress are acquired. And then the equation about non-linear effective stress is proposed.(2) The simplified model about fractured rock with clay mineral has been put forward. And the mathematical equation has also been established to describe the relationship between permeability and confining pressure & pore pressure. The iso-k curves are drawn and the effective stress coefficients are calculated. And then the effect of clay minerals and fracture on the iso-k curves and the effective stress coefficients are also discussed. Besides, combining with the previous studies, the relations between the effective stress coefficients and rock deformation characteristics are determined.(3) Based on the different types of pore models, mixed pore network model of the stress sensitivity is built. Meanwhile,3D pore network model is programmed to be used to analyze the effect on non-linear effective stress of micro-pore parameters and the types of different pores combinations.(4) The experimental apparatus and testing methods are improved to achieve the stability of permeability test for a long time under high confining pressure and high pore pressure. The effective stress experiments of permeability are performed and the permeability data under different confining pressures and pore pressures are obtained with steady-state method. The non-linear effective stress coefficients and non-linear effective stress are calculated with new method proposed to determine the non-linear effective stress experimentally. The rationality of the above new computational method is validated with the definition of effective stress. And physical significance and practical applications of the non-linear effective stress have been demonstrated.(5) Based on the analysis of the non-linear effective stress coefficient and its characteristics of variations, the functional relation between confining pressure and pore pressure are explored. The microstructure experiments of the Slice Thin Section, Scanning Electron Micrograph. Laser Scanning Confocal Microscopy, X-inflection and Capillary pressure have been done, by which rock microscopic pore structure and diagenesis sequence are obtained. Combing with experimental factors, we also studied the effective stress coefficient and deformation characteristics of low-permeability rocks and previous studied rocks and their relationships.(6) The empirical model and theoretical model relationship between permeability and effective stress are analyzed comparatively with theoretical and experimental studies. And then values of different stress sensitivity coefficients are calculated while we clearly understand its physical meaning.(7) Analyzing the relationship among different stress sensitivity coefficients, the stress sensitivity coefficients characteristics, and the curves between permeability and effective stress, the division criterion of stress sensitivity is raised and the relationship between empirical models and rocks of different stress sensitivities is determined.(8) The method implementing the coupling interactions of pore pressure and permeability in the numerical simulation is presented. Effects of the coupling interaction on single-well development, with different stress sensitivity models and different effective stress laws, are analyzed by numerical simulator.Based on this study, the physical significance of non-linear effective stress is stated explicitly. And the new method is proposed how to calculate non-linear effective stress. A systematic method, such as, network simulation and numerical simulation, has been established, combing with relevant theories. Besides, practical significance and applications of the non-linear effective stress have been demonstrated, which deepens our knowledge of origination of non-linear effective stress and its changing law, enriches and develops the theory of effective stress, and provides theoretical base to evaluate stress sensitivity and develop oil and gas bearing in low-permeability reservoirs rationally.