We used electrical resistance tomography (ERT) to map the subsurface distribution of a steam flood as a function of time as part of a prototype environmental restoration process performed by the Dynamic Underground Stripping Project. We evaluated the capability of ERT to monitor changes in the soil resistivity during the steam injection process using a dipole-dipole measurement technique to measure the bulk electrical resistivity distribution in the soil mass. The injected steam caused changes in the soil's resistivity because the steam displaced some of the native pore water, increased the pore water and soil temperatures and changed the ionic content of the pore water. We could detect the effects of steam invasion by mapping changes in the soil resistivity as a function of space and time. The ERT tomographs are compared with induction well logs, formation temperature logs and lithologic logs. These comparisons suggest that the ERT tomographs mapped the formation regions invaded by the steam flood. The data also suggest that steam invasion was limited in vertical extent to a gravel horizon at depth of approximately 43 m. The tomographs show that with time, the steam invasion zone extended laterally to all areas monitored by the ERT technique. us understand the heterogeneous subsurface environment, the factors controlling steam movement in situ, and the steam flow behavior induced by the process. An accurate understanding of the interaction between the steam process and the geologic environment is needed to assess the remediation effectiveness. This underground imaging technique substantially reduces the need for the number of boreholes that would otherwise be required to monitor the process. DESCRIPTION OF ERTTo image the resistivity distribution between two boreholes, we placed a number of electrodes in electrical contact with the soil in each borehole (Figure 1). Using an automatic data collection and switching system (shown schematically in Figure 2), we then applied a known current to any two electrodes and measured the resulting voltage difference between other pairs of electrodes. Each ratio of measured voltage and current is a transfer resistance. Next, we switched to two other electrodes, applied current between two other electrodes and again measured the voltage differences using electrode pairs not being used for the source current. We repeated this process until many combinations were measured which completely encircled the target area. For n electrodes there are n (n -3)/2 linearly independent transfer resistances. A complete set of linearly independent data contains the maximum information content about the target; any additional measurements collected are redundant. This formula does not count reciprocal measurements because a measurement and its reciprocal contain the same information and therefore are only counted as one by the formula. The reciprocal to any original transmitter-receiver pair is one where the original transmitter dipole becomes the receiver dipole and where the original receiver ...

We consider an M×N periodic system of hard squares each of which prohibits the occupation of its nearest-neighbor sites by the other squares. An appropriate unitary transformation factors the matrix required in evaluating the grand canonical partition function into a direct sum of submatrices. Each submatrix belongs to a distinct irreducible representation of the dihedral group of order 2M. For an M×∞ system, only the submatrix belonging to the one-dimensional symmetric representation A1 must be considered. To investigate the possible existence of an order—disorder transition for a system infinite in both dimensions, detailed calculations are carried out with the M×∞ systems (M=2, 4, 6, ···, 18). All eigenvalues λi+ and eigenvectors of the submatrix are evaluated with eight-digit accuracy, and the various thermodynamic variables are expressed exactly in terms of the eigenvalues and eigenvectors. The result indicates that an order—disorder transition takes place continuously without any sharp break in a density (ρ)- vs-activity (z) plot, or a pressure (P)- vs-ρ plot. The transition point is characterized by the following set of numbers: zt=3.7966±0.0003, ρt/ρ0=0.73552±0.00001 (ρ0≡the close-packed density), and Pt/kT=0.7916±0.0001. Within numerical accuracy of the data, Pt/kT is equal to zt/(1+zt). The compressibility ρ−1dρ/dP appears to become infinite at the transition point, while the ratio λ1+/λ2+ of the two largest eigenvalues of the submatrix becomes unity. For a semi-infinite system in the neighborhood of zt, these two quantities exhibit, respectively, a maximum and a minimum given for large M by [(kTρ/ρ0)dρ/dP]max≃(0.0798±0.0001) lnM+(0.0910±0.0009) and [λ1+/λ2+]min≈exp[(6.25±0.04)/M]. We find that the activity z at [λ1+/λ2+]min converges rapidly to zt, thus providing a good means of locating the transition point. From the study of the eigenvalue spectrum over all densities, it appears that the transition point zt, the ordered (z>zt), and the disordered (z<zt) phases are, respectively, characterized by asymptotic degeneracy of order ∞, 2, and 0 in the modulus of the largest eigenvalue. The ordering of the hard-square lattice is investigated by introducing a radial distribution function g(l, ρ) (l is lattice spacing). The calculations of g(l, ρ) are carried out for the 4×4, 8×8, and 8×∞ systems. A long-range order parameter L(ρ) {≡liml→∞[g(l, ρ) −1], l: even} is introduced. For a two-dimensionally infinite system, all coefficients in the low-density expansion of L(ρ) vanish identically, while the first five terms of the high-density expansion of L(ρ) are computed. Therefore, the transition to an ordered state presumably takes place at density between 0 and ρ0.

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impact of matrix imbibition on episodic nonequilibrium fracture-man'ix flow and transport for the eight major hydmstratigraphic units in the unsaturated zone at Yucca Mom'_tain.