The mathematical model of stress sensitivities on tight reservoirs of different sedimentary rocks and its application

In this paper, five types of sedimentary rocks (the Turbidite, the Beach bar sand, the Glutenite and the two outcrop cores) with permeability (k，10−3μm2) grades (k < 0.1, 0.1＜k ≤ 0.3, 0.3＜k ≤ 0.5, 0.5＜k ≤ 1.0, 1.0＜k ≤ 3.0) are studied for the building of the model. The uniaxial compression tests, the stress sensitivity tests, and the CT structure scanning have been done, then the data and the curves obtained from the lab are carefully analyzed and examined. Studies on the grain sizes, the components ratios of the different grains, and the original pore structures are conducted in order to get the stress sensitivities of the rocks. Those of the Glutenite, the Turbidite and the Beach bar sand with the same permeability level (k ≤ 0.1 × 10−3μm2) are found having the order of stress sensitivity from high to low, and the maximum drops of permeability is range from 20.8% to 30.7%. Based on the experiment results, combined with the unequal diameter tortuous capillary bundle model and the contact deformation theory of Hertz, a mathematical model on stress sensitivities of tight reservoirs is established, which takes the characteristic parameters (Young's moduli, Poisson's ratios) of the reservoir rock materials, the pore structure parameters (the pore radii, the throat radii), and the macro physical parameters (the original permeability values) into account. The calculation error of the model is 2.6%. Finally, taking the actual data of the tight reservoirs in Jiyang Depression of Bohai Bay Basin as an example, this model is introduced into productivity equation to predict the production under the different formation pressures. It is suggested that the formation energy retention rate of the Glutenite reservoir to be above 0.9, the Turbidite reservoir above 0.85, and the Beach bar sand reservoir above 0.78. © 2020 Elsevier B.V.