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doi:10.2204/iodp.proc.311.203.2008

Results

Gas hydrate saturation from resistivity

With estimated empirical Archie parameters a, m, and n, Equation 6 can be solved for S_h. The critical unknown parameter in Archie's relation is the in situ R_w, which can be calculated from the equation of state of seawater (Fofonoff, 1985) if the in situ pore water salinity is known, assuming that the pore fluid salt composition is similar to that of seawater. In gas hydrate–free zones, the in situ salinity can be taken as the measured core salinity. However, if gas hydrate was initially present in the core, it would have dissociated upon recovery, thereby freshening the pore water and contaminating the in situ salinity (Kastner et al., 1995; Hesse, 2003), which is the key parameter in determining R_w. A lower estimated in situ salinity would result in a higher R_w, which in turn would erroneously reduce gas hydrate saturation estimates. The main difficulty is in estimating the in situ salinity before gas hydrate dissociation upon core recovery. In this paper, two methods are proposed to solve this problem. Each has advantages and limitations.

Core baseline salinity method

A first solution is to assume a reference no-hydrate salinity profile at each site, corresponding to the highest salinity measurements smoothed over depth (Fig. F4). This trend is referred to as the core baseline salinity (C_cb). In this case, lower-than-baseline core salinity measurements are assumed to be due to freshening by gas hydrate dissociation upon core recovery, and C_cb is used in the calculation of R_w from the equation of state of seawater (Fofonoff, 1985). This approach assumes that there is no pervasive gas hydrate present in the pore space, only local concentrations such as in sandier horizons (i.e., core salinity measurements sample considerable sections where the pore fluid has not been freshened by gas hydrate dissociation).

Once R_w has been calculated from C_cb, a qualitative approach to identify gas hydrate zones is to compare R_t to the R_o that would have been measured if the sediment were fully water saturated (Fig. F6). R_o is calculated from Equation 4, solved for S_h = 0. In Figure F6, zones above the BSR with R_t > R_o are interpreted to contain gas hydrate.

To obtain quantitative estimates of gas hydrate saturation, S_h is calculated from Equation 6 (Fig. F7), with upper and lower bounds on S_h determined from the primary uncertainty associated with the estimated Archie coefficient a. In Figure F7, these results are smoothed by taking a running average over a 10 m interval. The uncertainty in the Archie coefficient a accounts for an average estimated uncertainty in S_h of ±0.07 (one standard deviation).

The important systematic uncertainty in this method is related to the implicit assumption that C_cb is an accurate estimate of the in situ salinity. At most sites, this assumption is probably valid, because the core baseline salinity is near that of seawater (Fig. F4) (i.e., assuming that a gas hydrate–free core sample gives near-seawater salinity is generally reasonable). However, the core salinity measurements at Site U1327 exhibit an anomalous freshened baseline salinity trend relative to the other sites (and nearby cold vent Site U1328; see the "Site U1328" chapter) and therefore represent a special problem in interpretation. At Site U1327, the two end-member interpretations are that the pervasive freshening is either attributed to gas hydrate dissociation upon core recovery or to some other source of freshwater (e.g., rising fresh water from clay dehydration from deep within the accretionary prism). The core baseline salinity method attributes the regional freshening at Site U1327 (from seawater to baseline salinity) to sources other than gas hydrate dissociation. If all or most core samples were in fact freshened by pervasive gas hydrate, this regional gas hydrate would go undetected if the core baseline salinity method is used. The in situ salinity method can estimate pervasive gas hydrate contribution to core pore fluid freshening. However, it involves additional assumptions and uncertainties.

In situ salinity method

An alternative approach that makes no assumptions about in situ salinity is that of Hyndman et al. (1999). With additional assumptions, both gas hydrate saturation and in situ salinity can be estimated: they solve Archie's equation (Equation 6) for S_h simultaneously with

(8)

and

, (9)

where R_sw is the resistivity of seawater (dependent on pressure and temperature, but with fixed seawater salinity concentration [C_sw] taken to be 35), C_core is the core fluid salinity concentration (after dissociation of any in situ gas hydrate), and C_w is the in situ fluid salinity, which is unknown. The physical basis for Equation 9 is the salinity dilution resulting from gas hydrate dissociation upon core recovery. Hyndman et al. (1999) assumed the simplification n = m; their equation is modified here to allow for different values of n and m (Riedel et al., 2005):

, (10)

where R_t is the measured resistivity. For exactness, this calculation requires C_core to be measured from the same physical sample in which resistivity was measured. However, the resistivity data is from nearby downhole logs (from a different hole at the same site). The best approximation available is to take C_core as the C_cb trend. This is somewhat different from the approach of Hyndman et al. (1999), who had less data available. This yields the gas hydrate saturation profiles shown in Figure F8, averaged vertically, over a 10 m window. The in situ salinity method gives systematically higher gas hydrate saturation estimates than the core baseline salinity method but also exhibits a larger standard deviation.

Having solved for S_h in Equation 10, Equation 9 provides a means to calculate C_w , which can then be compared to C_cb to determine if there is regional salinity dilution in the recovered core caused by pervasive gas hydrate occurrence (i.e., to determine whether the C_cb trend is a good estimate of C_w) (Fig. F9). It is first observed that in areas with high gas hydrate saturation, C_w calculated by the in situ salinity method is much higher than C_cb and even reaches unreasonable amounts in some places. This occurs because C_core is taken in Equation 10 to be the C_cb trend , whereas in reality, C_core measurements in these anomalous regions actually show fresher pore waters that do not lie on the background trend (Fig. F9). In other words, if the gas hydrate saturation was calculated at the depth of a freshened core sample using the actual measured fresher core salinity rather than the higher core baseline salinity trend by Equation 9, S_h and C_w would be less. The end result is an overestimation of S_h in areas with higher-than-background gas hydrate saturation, as observed in Figure F8. The method of Hyndman et al. (1999) is limited in areas with heterogeneous gas hydrate distributions because it requires the actual C_core measurement from the same sediment in which the resistivity was measured. However, it does provide a basis for the estimation of an C_wb trend. In areas with background levels of S_h (whether or not they are zero), measurements of C_core lie on the C_cb trend, and the approach provides an accurate estimate of both S_h and C_w because C_cb, in this case, is approximately equal to the measured C_core. So, although the overall S_h and C_w profiles calculated from the in situ baseline approach have inaccurate zones, their C_wb trends are representative of the true in situ salinity. The C_wb trend can therefore be compared to the C_cb trend to determine if there is regional core freshening from gas hydrate dissociation. At Sites U1325, U1326, and U1329, C_wb is well estimated by C_cb to within the uncertainty of the Archie parameters (Fig. F9) (i.e., taking C_cb as the in situ salinity is a good approximation at these sites). Also, there are many pore water samples showing significant freshening throughout the depth intervals, where the calculated C_w is higher than the core baseline salinity, suggesting that the overestimation is simply the result of using the "wrong" core salinity. However, at Site U1327, C_wb is estimated to be slightly higher than C_cb, suggesting a small amount of regional freshening from dissociation upon core recovery may be present. Throughout the depth interval from 150 to 220 mbsf only very little pore water freshening has been seen in the cores; thus, the argument used at Sites U1325 and U1326 does not apply here. The gas hydrate saturation is therefore recalculated at Site U1327 from the core baseline salinity method by using a different estimate of in situ salinity (red line in Fig. F9). This gives slightly higher S_h estimates for this site (Fig. F10). However, as the core hole is a considerable distance from the LWD hole, lateral heterogeneity may be a factor unaccounted for in the above argument, although comparison of the downhole wireline and LWD resistivity logs shows almost identical values around 2 Ωm for the interval in question (150–220 mbsf).

Uncertainty in porosity

So far, gas hydrate saturation has been calculated by using the porosity determined from the LWD density log. The same method as described above is applied here to neutron porosity and core porosity measurements in order to determine the sensitivity of S_h estimates to the type of porosity measurement.

Neutron porosity

New Archie parameters need to be calculated for the resistivity versus neutron porosity relation from a cross plot of these measurements in gas hydrate-free zones (Fig. F5B), giving a = 1.74 ± 0.32 for m fixed at 1.76. This high value for a further suggests that the neutron porosity log values have a positive bias about the true porosity (possibly related to an incomplete correction for bound water content). Furthermore, the sub-BSR zones used in the Archie parameter estimation could potentially have anomalously high porosity values, caused by the influence of free gas below the BSR on the hydrogen concentration. These zones are kept in the analysis because they significantly add to the range of porosities sampled in the empirical calibration.

In contrast, an unconstrained estimation (no fixed m) of Archie parameters gives a = 1.41 and m = 2.09. However, the R² value of the statistical fit to the data points is only 0.7. The Archie functions for the two sets of empirical parameters predict roughly the same formation factor at the porosity of ~55%. The larger m value of 2.09 introduces significant changes in predicted formation factor and thus gas hydrate concentrations for porosities below 45% or above 65%. Using an m-value of 2.09 instead of 1.76 would result in higher gas hydrate concentrations for porosities above 55% and lower concentrations for porosities below 55%.

One way to evaluate the total error in predicted gas hydrate concentrations (ΔS_h) has been shown by Lee and Collett (2001). For any given m-value, ΔS_h can be written as

. (11)

Equation 11 shows that ΔS_h is linearly related to m (i.e., the higher m, the higher the total error in the gas hydrate concentration for constant porosity and gas hydrate concentration). It also shows that the error is higher for smaller gas hydrate concentrations at any given porosity and fixed m-value. Furthermore, the error in porosity is partially cancelled by the uncertainty in the Archie parameter a itself.

In order to compare the analyses using neutron porosity to those above with density-porosity, we proceed with a fixed m-value of 1.76. Following the protocol outlined above, C_w profiles are calculated from the in situ salinity method at the four sites (Fig. F11). At Sites U1325, U1326, and U1329, C_cb is interpreted to be a good estimate of the true in situ salinity, so the core baseline salinity method is used at these sites to calculate gas hydrate saturation (Fig. F12). At Site U1327, C_wb is again estimated to be slightly higher than C_cb; therefore, C_wb (the better estimate of in situ salinity) is used to calculate S_h from the core baseline salinity method. The uncertainty in a accounts for an average uncertainty in S_h of ±0.09. Neutron porosity-based calculations of S_h generally agree with those obtained from the density porosity to within the calculated uncertainty because the bias in porosity is accommodated by the porosity-specific Archie parameters. This highlights the importance of using empirical Archie parameters calibrated to the specific type of measurement made.

As a check, the Archie analysis is repeated for the neutron porosity, using a neutron porosity profile that is shifted so that its mean at each site is equal to the mean density porosity at that site. This approach eliminates some of the biases inherent in the neutron porosity measurement while preserving structure in the log that might not be present in the density porosity profile. This test gives gas hydrate saturation profiles at all sites that are in agreement with both the density porosity–based estimates and the previous estimate from the (nonshifted) neutron porosity to within the uncertainties estimated from the Archie parameters.

The general conclusion from the neutron porosity analysis is that it yields gas hydrate saturation estimates that are similar to those obtained from the density porosity analysis but with larger uncertainties. Gas hydrate saturation estimates using neutron porosity are not particularly sensitive to the bias toward higher porosities present in the neutron log, so long as the Archie parameters are also calibrated to those biased porosity measurements.

Core porosity

To determine the Archie parameters for the log resistivity versus core porosity data, an average log resistivity value for the 1 m interval corresponding to the core sample depth was calculated for each core sample in gas hydrate–free zones. The spatial correspondence is only approximate, because the core and log data are from different holes ~50 m apart. The resistivity versus porosity data are shown in a Pickett plot (Fig. F5C). With m fixed to 1.76, the best fit to a is 1.43 ± 0.27, a value close to that obtained using the density porosity. Note that the statistical uncertainty in a is greater than that for the log density porosity based relation, probably mainly reflecting the fact that the resistivity and core porosity are measured in different holes. Using a best-statistical fit to the data points without any constraints yields a = 1.57 and m = 1.59 with a very poor R² value of 0.55. For the same reason of comparison, we proceed again with a fixed m-value of 1.76.

The log resistivity data and core porosity trend are used to calculate S_h following the procedure outlined above. Because core porosity measurements are not available at each log sample, a core porosity trend is calculated at each site (Fig. F2B), as a smoothed profile (a least-squares fit) through the core porosity data, using Athy's law, emulating compaction and porosity loss with depth (Athy, 1930):

φ(z) = φ₀e^–z/L, (12)

where z is the depth below seafloor, φ₀ is the porosity at the seafloor, and L is a characteristic decay constant. Equation 9 is then used to calculate the C_w profile from which the C_wb trend is estimated. C_wb is compared to the C_cb trend to assess whether or not C_cb is a good estimate of the true in situ salinity (Fig. F13). C_wb profiles calculated for Sites U1326 and U1327 give trends with slightly greater in situ salinity than C_cb. S_h is then calculated from the core baseline salinity method, using C_wb at Sites U1326 and U1327 and C_cb at Sites U1325 and U1329 (Fig. F14). Uncertainties in Archie parameters account for an average uncertainty in S_h of ±0.08.

Gas hydrate saturation calculated from core porosity and log density porosity are generally in good agreement because S_h profiles calculated from these two porosity measurements have uncertainty bounds that overlap in most areas (Fig. F14). One exception is at Site U1327, where S_h calculated from the core porosity is on average 0.09 greater in the interval of accreted sediments above the BSR (90–225 mbsf). The difference at this site occurs because the porosity profile observed in the log is not well represented by the smoothed Athy-type porosity-depth relation applied to the core data. Although there is no significant overall bias between the log density porosity and the core porosity trend, there are local biases at certain depths (Fig. F2B). In the accreted section above the BSR (90–225 mbsf), with the exception of the high-porosity unit at 120–138 mbsf, the log density porosity is almost exclusively lower than the core porosity trend. Because the Archie parameters (calculated for an average porosity-resistivity relation) are similar for the core and log density porosity, S_h and C_w are biased toward higher values in this interval because of the local porosity bias.

Although the results from the core porosity analysis are reasonable, gas hydrate saturation estimates based on log density porosity measurements are preferred for the following reasons. Core porosities are disadvantaged because (1) they need to use a trend that is smoothed over depth to match the sampling of the resistivity log; (2) they have been measured in samples from different holes than the resistivity data, leading to additional uncertainty caused by interhole variability; and (3) the porosity is measured onboard the ship, after core recovery, rather than in situ.

The log density porosities have the disadvantage that porosity is not measured directly. Porosity is estimated from log density, assuming first that the formation bulk density is well related to the measured electron density and second that the average grain density used in an adequate approximation.

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