We apply the above theoretical models to the well log data collected in Northwest Eileen State Well #2, located onshore North Slope of Alaska. The interval 550-830 m was determined to contain three methane gas hydrate bearing sand intervals (discussed in Mathews, 1986). The gamma ray, resistivity, neutron porosity (with sandstone correction, Schlumberger, 1989), and sonic velocity log curves are plotted versus depth in Figures 3a-d. The correlation of high velocity with high resistivity in the sand intervals, along with gas shows in the mud log (Mathews, 1986), is consistent with the presence of gas hydrate in this well.

In order to provide inputs for the models, we assume, for simplicity, that the mineral phase in the well is pure quartz, and the pore fluid is brine with a salinity of 32,000 ppm and average temperature and pore pressure of 10 °C and 7 MPa, respectively. The density and bulk modulus of the brine are calculated according to Batzle and Wang (1992) and do not vary much in our temperature and pressure regions of interest. The values given in Table III are used for the entire section under investigation. We also assume that the gas hydrate-free porosity of the sand (tp) is given by the corrected neutron porosity log. This assumption is based on the fact that the hydrogen density in methane hydrate is essentially the same as that in liquid water (-0.1 mol H/cm3). Therefore, to first order, the neutron tool should not be able to distinguish between gas hydrate and water in the pore space. The effective pressure, 6 to 9 MPa, is calculated as the difference between the lithostatic and hydrostatic pressures where the average rock bulk density is taken as 2.12 g/cm3 and the density of brine as 1.024 g/cm3.

Constituent |
Bulk Modulus (GPa) |
(g/cm3) | |

Quartz |
36.6 |
45.0 |
2.65 |

Clay |
20.9 |
6.85 |
2.58 |

Calcite |
77.8 |
32 |
2.71 |

Methane Hydrate |
7.7 |
3.2 |
0.90 |

Brine (Eileen) |
2.29 |
0 |
1.024 |

Brine (ODP 995) |
2.5 |
0 |
1.032 |

Table III. Input parameters

Table III. Input parameters

30 50 70 Gamma Ray

90 10 100 1000

b Deep Resistivity (Q-m) C

0.3 0.4 0.5 Neutron Porosity

Figure 3. Physical property logs versus depth from Northwest Eileen State Well #2. (a) Gamma ray (b) Deep resistivity, (c) Neutron porosity, (d) Compressional-wave velocity (black) and the baseline model result (gray).

30 50 70 Gamma Ray

90 10 100 1000

b Deep Resistivity (Q-m) C

0.3 0.4 0.5 Neutron Porosity

Figure 3. Physical property logs versus depth from Northwest Eileen State Well #2. (a) Gamma ray (b) Deep resistivity, (c) Neutron porosity, (d) Compressional-wave velocity (black) and the baseline model result (gray).

First, we use these inputs to calculate the baseline velocity in the well, assuming that the pore space is fully saturated with brine and does not contain hydrate. The coordination number is fixed at 8.3 corresponding to an average porosity of 0.4 (Murphy, 1982), which we use as the critical porosity. The calculated baseline velocity (Figure 3d) closely matches the measured background velocity. This justifies our choice of background model and input parameters. Next, to model the effect of hydrate on the sediment, we need an estimate of the amount of gas hydrate in the pore space. We calculate the non-water saturation of the pore space from resistivity using the "quick-look" Archie method (e.g., Collett, 1998), which is based on the equation

where Sw is water saturation of the pore space; Rq is the resistivity of the formation at Sw = 100%; Rt is the formation's true (i.e., measured) resistivity; and n is an empirical constant (about 1.94, Pearson et al., 1986). It is assumed that the R0 versus depth trend is the same as the background trend of the resistivity log. The choice of background trend is subjective. The trend is supposed to follow the data where gas hydrate is presumably absent and thus highlight the resistivity peaks. In Figure 4a, we offer three linear background fits to the data above 700 m and a single linear fit to the rest of the interval. The corresponding non-water saturation is shown in Figure 4b. We assume that all non-water saturation is methane hydrate. Easily seen in Figure 4b is the high estimated gas hydrate saturation in three of the sandy intervals. Also evident is the lack of precision (±20%) inherent in this technique. However, within the range of saturation values predicted (-20-80%), the models make easily distinguishable velocity predictions.

Figure 4. (a) The deep resistivity curve vs. depth and three "quick-look" Archie background resistivity estimates, (b) Non-water saturation from "quick-look" Archie method for the background curves shown in (a). The negative saturation values are artifacts and those intervals are ignored in the elastic moduli calculations, (c) Velocity versus depth using curve 2 in (b). Black: log data; gray: baseline model; gray dashed: gas hydrate in fluid; black dashed: gas hydrate in frame, (d) Contact cement model. Black dashed: Scheme "1"; gray dashed: Scheme "2". The gaps in the velocity curves are where the non-water saturation estimate is negative or where a model is not applicable (see Figure 2 and text).

Figure 4. (a) The deep resistivity curve vs. depth and three "quick-look" Archie background resistivity estimates, (b) Non-water saturation from "quick-look" Archie method for the background curves shown in (a). The negative saturation values are artifacts and those intervals are ignored in the elastic moduli calculations, (c) Velocity versus depth using curve 2 in (b). Black: log data; gray: baseline model; gray dashed: gas hydrate in fluid; black dashed: gas hydrate in frame, (d) Contact cement model. Black dashed: Scheme "1"; gray dashed: Scheme "2". The gaps in the velocity curves are where the non-water saturation estimate is negative or where a model is not applicable (see Figure 2 and text).

In our further modeling, we assume the hydrate saturation is given by the middle curve "2" in Figure 4b. The results of applying the "gas hydrate in fluid" and "gas hydrate in solid" models are shown in Figure 4c. Both closely match the velocity data. In contrast, the contact-cement models significantly overestimate the measured velocities (Figure 4d). These modeling results show that in spite of the uncertainty in hydrate saturation estimates, the vastly different predictions of the models allow us to conclude that gas hydrate does not cement the grain contacts at this site.

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