Thermal effective stress in shales

Abstract

Calculating velocities in shales in thermal production settings is important to refine time-lapse reservoir characterization from seismic. The effective stress concept is attractive to potentially reduce the amount of expensive core calibration data required. We propose a formulation for thermal effective stress in shales based on the idea of balancing undrained pore pressure increments from thermal expansion with an increase in the matrix stress to minimize pore deformation. This formulation is motivated by a desire to simplify forward modeling, reduce the number of dimensions that must be experimentally calibrated through core testing, and to leverage existing velocity-stress relations for thermal applications. The concept was tested on data from a well-known set of experiments consisting of two North Sea Kimmeridge shale core samples, which displayed a linear dependence of velocity on pressure and temperature. These data were found to be consistent with the proposed thermal effective stress model with a constant effective stress coefficient when considering elastic changes but do not prove that the concept is universally valid. Thermal effective stress coefficients were calculated for P- and S-wave velocities from the data and were found to lie from 0.66 to 1.22, demonstrating reasonable scaling for the proposed model.