MODELLING OF NONLINEAR VISCOELASTIC PROPERTIES OF TERRIGENOUS-CALCAREOUS SANDSTONES

The studies of terrigenous-calcareous sandstones core were carried out in order to determine the structure of fractured and porous void space, petrophysical properties of samples and to conduct the further statistical analysis of the obtained data. The equipment of petrophysical laboratory of the Institute of Geology was used to carry out the experiments in the variable external pressure conditions in order to verify the hypothesis concerning substantially nonlinear properties of porous sandstone which depends on the amplitude and direction of the external pressure. Previous investigations related to the modeling of properties of the fluid-saturated porous sandstones and to the prediction of their physical and mechanical properties were analyzed. A model of the nonlinear viscoelastic porous medium of the Bio type as the basic version for the further development was chosen. Presence of the viscous fluid substantially affects the reaction of medium for both gradual and periodic pressure changes. The previous papers of authors concerning the studied problem were used and the defining equations of the state with fractional-exponential functions of the creep and relaxation were applied. The microstructural approach to the analysis of equivalent properties of the mass transfer in the isotropic viscoelastic medium was proposed in order to estimate the permeability parameters of the calcareous sandstones. The key moment was the application of integral Laplace-Carson transform during the studies of viscous effects, and Fourier transform during the analysis of complex, multilevel microstructure. The analytical expressions to predict the viscoelastic functions of creep and relaxation were obtained and the algorithm of solution that includes numerical analysis as an important component in case of multicomponent medium with complex microstructure was presented.