Predicting Static Data Using Dynamic Data and Quantitative Sample Characterization

We have analyzed static and dynamic data along a triaxial stress path with the goal of better understanding the mechanisms controlling each response and their relationship to the correlation between large strain and small strain measurements. “Static data” large strain (10−4) measurements were performed on both unloading and reloading along a multistage triaxial stress path. Simultaneous “dynamic data” (10−6) strain were acquired using standard pitch and catch acoustic velocity measurement techniques. The samples were measured “dry” i.e. equilibrated to ambient conditions. Young’s modulus was calculated from the acoustic data and compared to the measured static Young’s modulus. A quadratic fit has been applied to the static unloading and reloading data. This allows us to characterize the elastic data in terms of linear and nonlinear elastic terms, with coefficients M1, and M2 respectively. The quadratic fit for the elastic data is subtracted from the total strain response during each reload cycle to obtain the “induced plastic strains”. The value of M1 is found to be equal to the measured dynamic modulus within experimental error. It was therefore interpreted to be dominated by the physics of the grain contacts. M2, the nonlinear elastic term, is interpreted to be due to the opening and closing of induced micro-cracks. This is based on the correlation observed between M2 and the measured irrecoverable strains. A network model is developed to fit the observed plastic strain data as a function of mean and deviatoric stress. Application of this model allows prediction of the sample stiffness (the slope of a triaxial test along the initial loading curve), at any confining stress. This is a key component of wellbore stability models, and allows for more robust model developments for wellbore stability, sand control etc. Future work will include the extension of the model to include nonlinearities for the prediction of failure. Thin section analysis to predict the plastic and nonlinear elastic parameters in combination with velocity data is also planned.