Research on the effective stress model in porous media Based on the fractal method

• 1、Key Laboratory of Enhanced Oil & Gas Recovery, Ministry of Education, Daqing Petroleum Institute

Abstract：Terzaghi equation is a classic model that is used to describe the relationship between stresses in porous media.The later scholars have been conducting a lot of researches and established many models. However, the models are based on the basic shallow rock. On the basis of the full study on the chinese and foreign information about the effective stress in porous media in this paper, the 2D and 3D fractal calculation models for the effective stress in deep porous media are respectively established with application of fractal geometry theory. It consideres the rock characteristics of the deep complex structure in petroleum engineering. The models can show the stress relationship in any pore structure rock and are the improvement to the existing model about the effective stress. In order to facilitate the on-site applications, the simplified models are further given for the effective stress fractal models in porous medium. The examples of calculation shows that the culation errors for the simplified models are less than 7% and can meet the requirements of on-site oil field.An effective stress profile can be obtained by the application of the simplified models on the logging data.

Keywords： Porous media Effective stress Terzaghi equation Fractal Geometry Fractal dimension