Computation of dynamic seismic responses to viscous fluid of digitized three-dimensional Berea sandstones with a coupled finite-difference method.

The seismic response of saturated porous rocks is studied numerically using microtomographic images of three-dimensional digitized Berea sandstones. A stress-strain calculation is employed to compute the velocities and attenuations of rock samples whose sizes are much smaller than the seismic wavelength of interest. To compensate for the contributions of small cracks lost in the imaging process to the total velocity and attenuation, a hybrid method is developed to recover the crack distribution, in which the differential effective medium theory, the Kuster-Toksöz model, and a modified squirt-flow model are utilized in a two-step Monte Carlo inversion. In the inversion, the velocities of P- and S-waves measured for the dry and water-saturated cases, and the measured attenuation of P-waves for different fluids are used. By using such a hybrid method, both the velocities of saturated porous rocks and the attenuations are predicted accurately when compared to laboratory data. The hybrid method is a practical way to model numerically the seismic properties of saturated porous rocks until very high resolution digital data are available. Cracks lost in the imaging process are critical for accurately predicting velocities and attenuations of saturated porous rocks.

A finite difference method for a coupled model of wave propagation in poroelastic materials.

A computational method for time-domain multi-physics simulation of wave propagation in a poroelastic medium is presented. The medium is composed of an elastic matrix saturated with a Newtonian fluid, and the method operates on a digital representation of the medium where a distinct material phase and properties are specified at each volume cell. The dynamic response to an acoustic excitation is modeled mathematically with a coupled system of equations: elastic wave equation in the solid matrix and linearized Navier-Stokes equation in the fluid. Implementation of the solution is simplified by introducing a common numerical form for both solid and fluid cells and using a rotated-staggered-grid which allows stable solutions without explicitly handling the fluid-solid boundary conditions. A stability analysis is presented which can be used to select gridding and time step size as a function of material properties. The numerical results are shown to agree with the analytical solution for an idealized porous medium of periodically alternating solid and fluid layers.

Impact of enhanced geothermal systems on US energy supply in the twenty-first century.

Recent national focus on the value of increasing US supplies of indigenous renewable energy underscores the need for re-evaluating all alternatives, particularly those that are large and well distributed nationally. A panel was assembled in September 2005 to evaluate the technical and economic feasibility of geothermal becoming a major supplier of primary energy for US base-load generation capacity by 2050. Primary energy produced from both conventional hydrothermal and enhanced (or engineered) geothermal systems (EGS) was considered on a national scale. This paper summarizes the work of the panel which appears in complete form in a 2006 MIT report, 'The future of geothermal energy' parts 1 and 2. In the analysis, a comprehensive national assessment of US geothermal resources, evaluation of drilling and reservoir technologies and economic modelling was carried out. The methodologies employed to estimate geologic heat flow for a range of geothermal resources were utilized to provide detailed quantitative projections of the EGS resource base for the USA. Thirty years of field testing worldwide was evaluated to identify the remaining technology needs with respect to drilling and completing wells, stimulating EGS reservoirs and converting geothermal heat to electricity in surface power and energy recovery systems. Economic modelling was used to develop long-term projections of EGS in the USA for supplying electricity and thermal energy. Sensitivities to capital costs for drilling, stimulation and power plant construction, and financial factors, learning curve estimates, and uncertainties and risks were considered.