Evaluation of intrinsic velocity-pressure trends from low-pressure P-wave velocity measurements in rocks containing microcracks

摘要

Dependent on the ‘intrinsic’ effects on the crystal lattice of the rock constituents and the diminishing ‘extrinsic’ effects of pores and microcracks, elastic wave velocity versus pressure trends in cracked rocks are characterized by non-linear velocity increase at low pressure. At high pressure the ‘extrinsic’ influence vanishes and the velocity increase becomes approximately linear. Usually, the transition between non-linear and linear behaviour, the ‘crack closure pressure’, is not accessible in an experiment, because actual equipment is limited to lower pressure. For this reason, several model functions for describing velocity—pressure trends were proposed in the literature to extrapolate low-pressure P-wave velocity measurements to high pressures and, in part, to evaluate the ‘intrinsic’ velocity—pressure trend from low-pressure data. Knowing the ‘intrinsic’ velocity trend is of particular importance for the quantification of the crack influence at low pressure, at high pressure, the ‘intrinsic’ trend describes the velocity trend as a whole sufficiently well. Checking frequently used model functions for suitability led to the conclusion that all relations are unsuitable for the extrapolation and, if applicable, the estimation of the ‘intrinsic’ velocity trend. However, it can be shown that the ‘intrinsic’ parameters determined by means of a suitable model function, the zero pressure velocity and the pressure gradient depend on maximum experimental pressure in a non-linear way. Our approach intends to obtain better estimates of particular parameters from observed non-linear behaviour. A converging exponential function is used to approximate particular trends, assuming that the point of convergence of the function represents a better estimate of the zero pressure velocity and the pressure gradient, respectively. Whether the refined ‘intrinsic’ velocity trend meets the ‘true intrinsic’ velocity trend within acceptable errors cannot be proven directly due to missing experimental data at very high pressure. We, therefore, conclude that our approach cannot ensure absolutely certain ‘intrinsic’ velocity trends, however, it can be shown that the optimized trends approximate the ‘true intrinsic’ velocity trend better as all the other relations do.