A modeling solution for predicting (a) dry rock bulk modulus, rigidity modulus and (b) seismic velocities and reflection coefficients in porous, fluid-filled rocks with applications to laboratory rock samples and well logs

摘要

The velocity of sound in porous, fluid-saturated rocks can be predicted using the Biot-Geertsma-Gassmann (BGG) and shear-wave velocity equations. However, two of the needed input parameters, the bulk modulus (K_b) of the empty, porous rock and the shear modulus (#mu#) of the rock are very difficult to obtain in situ. In the past, these values were typically chosen a priori and input into the BGG and shear-wave equations in a forward modeling mode. In addition to K_b and #mu#, it is also essential to input rock-matrix and fluid parameters that reflect in situ conditions. In this paper, the BGG and shear-wave equations are inverted to generate values for K_b and #mu#, respectively, by using available velocity and porosity data obtained from well logs and/or cores for water/brine-saturated rocks. These values of K_b and #mu# along with reasonable in situ estimates of rock-matrix and fluid parameters generated from the Batzle-Wang [Batzle, M., Wang,Z., 1992. Seismic properties of pore fluids. Geophysics 57, 1396-1408.] formulation, are then used to predict compressional and shear-wave velocities, compressional-shear wave ratios, and reflection coefficients at the interfaces between host rocks and fluid-saturated rocks, either fully or partially saturated with hydrocarbons, as a function of depth and/or porosity. Although generally similar to the approach of Murphy et al. [Murphy, W.F., Reischer, A., Hsu, K., 1993. Modulus decomposition of compressional and shear velocities in sand bodies. Geophysics 58, 227-239.], our method of inversion to determine K_b and #mu#, coupled with our input of in situ estimates of rock-matrix and fluid parameters as a function of depth from the Batzle-Wang formulation, forms a novel solution for predicting in situ velocities. A modeling program has been developed to perform these calculations and plot the velocity and reflection coefficient information as a function of depth, porosity, and water saturation. The resulting relationships between porous rock parameters provide valuable information for imaging and interpreting seismic data, interpreting well log data, aiding in the direct detection of subsurface fluids, and in developing reasonable models of the subsurface geology to assist with exploration and exploitation decisions. When our modeling program is applied to water-saturated reservoir rocks (sandstones and limestones) under controlled laboratory conditions, the percentage error between velocities predicted by our modeling program and values measured in the laboratory are topically less than 10% for both sandstone and limestone samples. When applied to well logs to predict sonic travel times and/or velocities for hydrocarbon-saturated rocks in the uninvaded formation, the predictions correlate with interpretations from other well logs and with hydrocarbon production from zones of interest.