A unified effective medium model is developed to incorporate the endpoints of perfectly smooth and infinitely rough sphere components and to allow partitioning between rough and smooth grains. We incorporate the unified model into the framework for gas hydrates in unconsolidated sediments using pore-fluid and rock-matrix configurations for grain placement, while reviewing other developments that have taken place in the past four decades. The unified rock-matrix model is validated with data available from the 2002 Mallik gas hydrates project well 5L-38. Gas-hydrate saturation and neutron-porosity logs from this well are used to generate synthetic P- and S-wave velocity models for several values of the friction coefficient. First, we overlaid crossplots of P- versus S-wave velocities for synthetic and measured velocities, and we compared the match until a good choice was found for the friction coefficient. Second, we plotted the synthetic velocities as separate logs of P- and S-wave velocities for each friction coefficient; the synthetic velocity logs were then overlaid on the measured velocities calculated from the sonic logs. Results of a direct comparison of the synthetic and measured velocity logs provide valuable insights into the validation of the unified effective medium model. Recognizing the significance of the Hertz-Mindlin-type effective medium models for gas hydrates in unconsolidated sediments, we incorporate the previous efforts into a single “unified” model and define a common nomenclature. Although we attempt to assign a single friction coefficient value to each hydrate window, it is not surprising that in a real and heterogeneous environment, the value might vary with depth, as it does here at the larger spatial scales. We determine and quantitatively estimate that gas hydrates in sediments are well-predicted with a friction coefficient closer to a smooth sphere model than a rough sphere model.
Intrinsic viscosity and friction coefficient of polymer molecules in solution: Porous sphere model
