[1] To elucidate the geological processes associated with hydrate formation and dissociation in the marine environment under a wide range of conditions, we have developed a one-dimensional numerical computer model (simulator). The numerical model can be used to simulate the following aspects of hydrate formation, decomposition, reformation, and distribution: (1) burial history of deep marine sediments and associated phenomena (e.g., sediment compaction and consequent reduction in sediment porosity and permeability, fluid expulsion, time evolution of temperature and pressure, heat flux), (2) in situ generation of biogenic methane from buried organic carbon and methane solubility in formation brine, (3) methane hydrate formation, decomposition, reformation, and distribution in response to changes in gas concentration, pressure, temperature and fluid salinity (the hydrate formation and decomposition are treated as equilibrium processes), (4) influence of sulfate reduction zone under the seafloor on hydrate formation, (5) possible presence of a free gas zone beneath the gas hydrate stability zone, and (6) multiphase (i.e., liquid brine with dissolved gas, free gas, gas hydrate) flow through a deformable porous matrix. The model provides for a reduction/ increase in permeability due to the formation/decomposition of the gas hydrate. Initial applications of the model to study hydrate distribution at the Blake Ridge (site 997) and Hydrate Ridge (site 1249) are described. Model results are compared with chlorinity, sulfate, and hydrate distribution data.

Reflection and transmission of compressional waves by a stratification with discontinuities in density and/or sound speedConcepts from the theory of interacting continua are employed to develop constitutive relations for liquid and/or gas saturated elastic porous media. The model is formulated by defining intrinsic stress tensors and densities in terms of the partial stress tensors, partial densities, and actual volume fractions occupied by each component. It is assumed that the constitutive law for each component as a single continuum relates intrinsic pressure to intrinsic deformation. Relative motion between the constituents is allowed through simple Darcy-type expressions. The governing equations together with the constitutive relations are used to investigate the propagation of both harmonic and transient pulses. In general three modes of wave propagation exist. In the case of a transient pulse, these modes lead to a three-wave structure. Laplace transform techniques are used to derive closed-form solutions for transient loading for two limiting values of viscous coupling (Le., weak viscous coupling, strong viscous coupling). Strong viscous coupling results in the coalescence of the three wave fronts into a single front. Solutions for the genera] case of transient loading are obtained by numerical inversion of the Laplace transforms.

Governing equations for the motion of gas-fluidized beds are derived within the framework of the theory of interacting continua. Steady-state solutions for two simple cases (incompressible fluid, isothermal ideal gas) are outlined in detail. The stability of these steady-state solutions is examined by conventional linear hydrodynamic stability analysis. Finally, some numerical results illustrating the effects of various physical parameters are presented.

This article discusses the propagation of compressional waves in fluid-saturated elastic porous media. Both harmonic and transient pulses are considered. In general, two modes of wave propagation exist. In the case of a transient pulse, these modes lead to a two-wave structure. It is not possible to obtain closed-form solutions for the general case of transient loading, but considerable insight may be obtained from certain limiting cases (e.g., no viscous coupling, large viscous coupling) for which analytical solutions are derived by means of Laplace transform techniques. Strong viscous coupling leads to the coalescence of the two wave fronts into a single front; in this case the material behaves like a single continuum with internal dissipation. Solutions for the general case are obtained both by numerical inversion of the Laplace transforms and by direct finite-difference methods.

In their paper, Brownell et al. [1977] have demonstrated unusual insight in the development of governing equations for geothermal reservoirs. However, before applying their equations to a physical geothermal reservoir underground, it is appropriate to ask some fundamental conceptual questions which are neither raised nor answered in their paper. GENERAL PROBLEMTheir balance equations (1)-(10) for mass, momentum, and energy form the backbone of their paper. All these balance equations, as expressed in the paper, may not be applicable to a single arbitrarily specified surface or volume element.Equations (1) and (2) express the conservation of solid mass and liquid mass for an element of interest. The local derivatives in (1) and (2) imply that the authors are considering particles (solid and liquid) which are passing a surface fixed in space. Hence porosity ½ in (1) and (2) is applicable to a bulk surface or an elemental volume, or is associated some way with a center of mass located at a point P0 fixed in space.As pointed out by the authors, the expression (O/Ot + rs' V) in (3) and (9) refers to the material derivative Ds/Dt that appears in (7). This implies that the corresponding balance of momentum and energy is associated with an element that moves with the solid phase. Similarly, porosity ½ in (3), (7), and (9) is applicable to a bulk surface or an elemental volume, or in some way is associated with a center of mass located at a point Ps that is fixed in the solid matrix.Once again, as pointed out by the authors, the expression (O/Ot + vt'V) in (4) and (10) refers to the material derivative Dt/Dt that appears in their (8). This implies that the corresponding balance of momentum and energy is associated with an element that moves with the liquid phase. Hence porosity ½ in (4), (8), and (10) is applicable to a bulk surface or an elemental volume, or in some way is associated with a center of mass located at a point Pt that moves with the liquid phase.Let us assume at an initial time, to, that some fluid and solid material of interest lies within and completely fills a specified saturated bulk volume. Let us specify that the centers of fluid mass and solid mass within this element both initially lie at a point P0, fixed in space. For subsequent time (t > to) let the solid particles of interest move at an average rate v8 and the liquid particles of interest move at an average rate of vt. For t > to we find there is no longer one bulk volume; there are three: 1. One bulk volume is specified at to by the solid and liquid material of interest and remains fixed in space centered at P0. Hence for t > to new solid and liquid material occupies and fills this bulk volume whose average porosity ½0 is free to change with time.2. Another bulk volume is defined by the solid particles of interest specified at tn and remains fixed in the solid matrix. Although the solid particles within this elemental volume do not change with time, liquid particles within this elemental volume are free to change. The average porosity ½8 of th...