| High permeability sands can be distinguished from low permeability sands by examining slopes on sonic versus porosity crossplots. Sonic-transit-time is plotted against porosity from neutron-density nuclear logs or simply density logs. A best fit line is drawn through the scatter of data; the slope of this best fit line is used in the process of permeability estimation. The slope of this line is steepest in relatively low permeability sands, while a shallow slope is observed in more permeable sands. This variability in slope can be understood in terms of grain size distributions, pore fluids, bulk modulus of the fluids and that of the grains, clay content affecting changes in porosity, permeability, and sonic-transit-time. A physical model, which is a qualitative sand-shale model, and a mathematical model, which is a quantitative model, based on the Biot-Stoll theory, are proposed to substantiate the above mentioned phenomenon.;There are many applications of this technique. First of all, it is obvious from this study, and many previous studies, that sonic-transit-time is a very complicated function of porosity, bulk modulus of fluid and rock, viscosity and density of fluid. Because of the varied functions the sonic-transit-time depends on, there is no universal relationship between sonic-transit-time and porosity as yet, even for one lithology at any one location. The research herein reveals that, the sonic-transit-time versus porosity gradient has a strong correlation with permeability and well productivity. Accordingly, a shallow gradient is observed in high permeability sands, and a steep gradient in low permeability formations. Although absolute magnitude of permeability probably cannot be computed directly, relative contrasts in permeability can be estimated. A second contribution of this research is a physical model that explains the sonic-transit-time versus porosity trends. The third contribution of this research is the use of the Biot-Stoll mathematical model to substantiate observations. Finally, a case study on the limitations of gradient analysis technique demonstrates the need for a well behaved sonic versus porosity relationship for the gradient technique to be applicable. |
