There are currently two types of relative permeability models that are used to model gas production from hydrate-bearing sediments: fully empirical parameter-fitting models [such as the University of Tokyo model (Masuda et al. 1997) and the Brooks and Corey model (Brooks and Corey 1964)] and partially empirical models [such as the Kozeny and Carman model (Wyllie and Gardner 1958) and capillary-tube-based models that assume only a single phase]. This study proposes an analytical model to estimate relative permeability of gas and water in a hydrate-bearing porous medium without curve fitting or use of any empirical parameters. The model is derived by conserving the momentum balance with the steady-state form of the Navier-Stokes equation for gas/water flow in a hydrate-bearing porous medium. The model is validated against a number of laboratory studies and is shown to perform better than most empirical models over a full range of experimental data. The proposed model is an analytical function of rock properties (average pore size and shape, porosity, irreducible water saturation, and saturation of hydrate), fluid properties (gas/water saturations and viscosities), and the hydrate-growth pattern [pore filling (PF), wall coating (WC), and a combination of PF and WC]. The benefits of the proposed model include sensitivity analysis of relevant physical parameters on relative permeability and estimation of rock parameters (such as porosity, pore size, and residual water saturation) using inverse modeling. The model can also be used to estimate two-phase permeability in a permeable medium without hydrates.
The proposed model was used to analyze the effects of pore shapes, the hydrate-growth pattern, variable gas saturation, and wettability on relative permeability. The sensitivity results produced by the proposed model were verified using observations from other studies that investigated similar problems using either experiments or computationally expensive pore-scale simulations.