Improved granular medium model for unconsolidated sands using coordination number, porosity, and pressure relations

We have developed a recipe for using closed-form expressions of effective-medium models to predict velocities in unconsolidated sandstones. The commonly used Hertz-Mindlin effective-medium model for granular media often predicts elastic wave velocities that are higher, and [Formula: see text] ratios that are lower, than those observed in laboratory and well log measurements in unconsolidated sediments. We use the extended Walton model, which introduces a parameter [Formula: see text] to represent the fraction of grain contacts that are perfectly adhered. Using the extended Walton model with [Formula: see text] ranging from 0.3 to 1, we obtain new empirical relations between the coordination number (C), porosity, and pressure for P- and S-wave velocities by inverting dynamic measurements on dry, unconsolidated sands. We propose using the extended Walton model [Formula: see text] along with these new C-porosity and C-pressure relations to study the mechanical compaction of unconsolidated sandstones. The model has been tested on two experimental data sets. It provides a reasonable fit to observed P- and S-wave velocities and specifically improves shear-wave predictions.

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A unified effective medium model for gas hydrates in sediments

Geophysics ◽

10.1190/geo2017-0513.1 ◽

2018 ◽

Vol 83 (6) ◽

pp. MR317-MR332 ◽

Cited By ~ 2

Author(s):

Darrell A. Terry ◽

Camelia C. Knapp

Keyword(s):

Friction Coefficient ◽

Gas Hydrates ◽

Effective Medium ◽

Unconsolidated Sediments ◽

Sphere Model ◽

S Wave ◽

Wave Velocities ◽

Effective Medium Model ◽

Medium Model ◽

Rough Sphere

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.

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An effective-medium model for P-wave velocities of saturated, unconsolidated saline permafrost

Geophysics ◽

10.1190/geo2016-0474.1 ◽

2017 ◽

Vol 82 (3) ◽

pp. EN33-EN50 ◽

Cited By ~ 10

Author(s):

Shan Dou ◽

Seiji Nakagawa ◽

Douglas Dreger ◽

Jonathan Ajo-Franklin

Keyword(s):

Laboratory Data ◽

Parameter Tuning ◽

Effective Medium ◽

P Wave ◽

Mixing Ratios ◽

Wave Velocities ◽

Effective Medium Model ◽

Medium Model ◽

P Wave Velocities ◽

Ice Content

To better understand the relationship between P-wave velocities and ice content in saturated, unconsolidated saline permafrost, we constructed an effective-medium model based upon ultrasonic P-wave data that were obtained from earlier laboratory studies. The model uses a two-end-member mixing approach in which an ice-filled, fully frozen end member and a water-filled, fully unfrozen end member are mixed together to form the effective medium of partially frozen sediments. This mixing approach has two key advantages: (1) It does not require parameter tuning of the mixing ratios, and (2) it inherently assumes mixed pore-scale distributions of ice that consist of frame-strengthening (i.e., cementing and/or load-bearing) ice and pore-filling ice. The model-predicted P-wave velocities agree well with our laboratory data, demonstrating the effectiveness of the model for quantitatively inferring ice content from P-wave velocities. The modeling workflow is simple and is largely free of calibration parameters — attributes that ease its application in interpreting field data sets.

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