Empirical rock physics relationships on carbonate dry-frame elastic properties

Laboratory tests were conducted to analyze the ultrasonic velocity response to the pressure change in dry carbonate rocks from the Weyburn oilfield,Canada.Twenty-four samples are from seven wells with helium porosities ranging from 1%to 29%.Thin-section images,SEM and mercury intrusion porosimetry were performed to show their inner structures and pore throat size distributions.P-and S-wave velocities(V_(p) and V_(s))measurements were first done under hydrostatic loading and then while unloading,with confining pressures varying between 3 and 35 MPa.The results indicate that V_(p) and V_(s) in these samples follow a linear relation independent of the pressure change.The ratio V_(p)/V_(s) is more responsive to pressure change irrespective of the pore volume.One-third of the carbonate samples show abnormal V_(p)/V_(s) reduction with the increase in the effective pressure.The pressure dependence of velocities(PDV)of Weyburn carbonate rocks varies widely even for samples from the same formation with similar sedimentary history.Samples with loosely packed crystals and/or relatively large dominant pore diameter have higher PDV.The exponential empirical model V=A−Ce^(DPe) was tested;therein,V is the elastic wave velocity,Pe is the effective confining pressure,and A,C and D are the best fitting coefficients determined by curve fitting.The model gives good fits for most of the Weyburn carbonate samples.From a statistical point of view,there is no difference between the V_(p)-and V_(s)-derived exponential coefficient D.