The nearly analytic discrete method(NADM)is a perturbation method originally proposed by Yang et al.(2003)[26]for acoustic and elastic waves in elastic media.This method is based on a truncated Taylor series expansion and interpolation approximations and it can suppress effectively numerical dispersions caused by the discretizating the wave equations when too-coarse grids are used.In the present work,we apply the NADM to simulating acoustic and elastic wave propagations in 2D porous media.Our method enables wave propagation to be simulated in 2D porous isotropic and anisotropic media.Numerical experiments show that the error of the NADM for the porous case is less than those of the conventional finite-difference method(FDM)and the so-called Lax-Wendroff correction(LWC)schemes.The three-component seismic wave fields in the 2D porous isotropic medium are simulated and compared with those obtained by using the LWC method and exact solutions.Several characteristics of wave propagating in porous anisotropic media,computed by the NADM,are also reported in this study.Promising numerical results illustrate that the NADM provides a useful tool for large-scale porous problems and it can suppress effectively numerical dispersions.
Using an approximately analytical formation, we extend the steady state model of the pure methane hydrate system to include the salinity based on the dynamic model of the methane hydrate system. The top and bottom boundaries of the methane hydrate stability zone (MHSZ) and the actual methane hy-drate zone (MHZ), and the top of free gas occurrence are determined by using numerical methods and the new steady state model developed in this paper. Numerical results show that the MHZ thickness becomes thinner with increasing the salinity, and the stability is lowered and the base of the MHSZ is shifted toward the seafloor in the presence of salts. As a result, the thickness of actual hydrate occur-rence becomes thinner compared with that of the pure water case. On the other hand, since lower solubility reduces the amount of gas needed to form methane hydrate, the existence of salts in sea-water can actually promote methane gas hydrate formation in the hydrate stability zone. Numerical modeling also demonstrates that for the salt-water case the presence of methane within the field of methane hydrate stability is not sufficient to ensure the occurrence of gas hydrate, which can only form when the methane concentration dissolved in solution with salts exceeds the local methane solubility in salt water and if the methane flux exceeds a critical value corresponding to the rate of diffusive methane transport. In order to maintain gas hydrate or to form methane gas hydrate in marine sedi-ments, a persistent supplied methane probably from biogenic or thermogenic processes, is required to overcome losses due to diffusion and advection.
YANG DingHui1 & XU WenYue2 1 Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
