Computation of Porosity and Saturationin the Vadose Zoneat the Savannah River Site

ABSTRACT

Geophysical logs, penetrometer runs, and core data have been acquired to characterize the shallow sediments of the A/M area at the Savannah River Site, where chlorinated solvents were released to the subsurface. Solvents have migrated through the vadose zone into a shallow aquifer. Logs in the vadose zone, the focus of this paper, have been analyzed to determine porosity, water content, and to flag the clay zones.

The fresh, resistive groundwater complicates the usage of Archie's laws. We use the density and resistivity logs to compute an apparent water resistivity in a sandy unit in the saturated zone. This value is used in the vadose zone, along with the density and guard resistivity logs, to determine saturation. Saturation and the density log are then used to compute porosity and water content in the vadose zone. In addition, the neutron and resitivity logs are used to compute a clay flag.

The calculated logs suggest a three-way partition of vadose-zone lithologies into clay-rich, high-silt/low-clay, and partially saturated sand zones. Clay-rich zones are delineated by low resistivity and/or high neutron porosity. High-silt/low-clay zones occur where resistivity values are moderate and where the formation is saturated or nearly so. Partially saturated sand occurs where moisture content is less than vadose-zone porosity. This three-way division of the vadose zone is believed to be important in terms of contaminant, water, and gas transport.

INTRODUCTION

The A/M area at the Savannah River Site in southeastern South Carolina is currently undergoing characterization and pilot remediation work to locate and recover chlorinated solvents which were released to the subsurface. As part of this characterization effort, subsurface measurements have been obtained by sampling water and core retrieved from wells, by geophysical logging of boreholes, and by cone penetrometer runs. A report by Nelson and Kibler (1995), from which this paper has been excerpted, describes the subsurface data set, examines the groundwater geochemistry and contaminant distribution, and discusses the logs and core data in detail. This paper describes the processing of geophysical logs and their use to estimate porosity and saturation in the vadose zone.

The sequence of Late Cretaceous and Tertiary fluvial/deltaic to shallow marine sediments have been divided into four hydrogeological units (Figure 1). The vadose zone extends from surface to the water table at approximately 150 feet subsurface. Screened intervals sampling the aquifers are also shown in Figure 1. The 'tan clay' represents a major hydrological barrier within the vadose zone, while the 'green clay' separates the M-area aquifer from the Lost Lake aquifer.

PHYSICAL PROPERTY DATA FROM CORE SAMPLES

Physical property measurements on core samples serve three purposes for log analysis. Parameters such as grain density are used directly in computing porosity from a density log. Laboratory determination of porosity and saturation from Shelby-tube samples serve as checks on the results of log-based computations. Delineation of clay minerals aids the interpretation of logs. Nelson and Kibler (1995) examined the results of previously published laboratory measurements; these findings are summarized here.

1. Grain density values range from 2.66 to 2.60 g/cm³, as sediment type progresses from "sandy fat clay" to "poorly graded sand", that is, as grain size increases. The mean grain density of 18 samples is 2.63 g/cm³.

2. Sample analysis shows that 0.39 is a representative value for porosity for samples ranging from sandy clay to poorly graded sand recovered within 200 feet of surface, and that most samples (approximately two-thirds) will have values between 0.35 and 0.42. Any bias in the measurement stems primarily from the effects of sample retrieval and handling. If a systematic bias exists, the porosity values are likely to be low, as sandy materials are prone to consolidation during sampling and handling.

3. The electrical effect of clay in sandstones is expressed by the parameter Qv, which is the volume concentration of clay exchange cations in meq/ml. Qv measures the cation concentration in the pore space and is obtained from measurements of cation exchange capacity and porosity. Mean values of Qv are: sandy fat clay, 0.52; clayey sand, 0.23; silty sand, 0.24; poorly graded sand with silt, 0.13; and poorly graded sand, 0.15. By way of comparison, Waxman and Smits (1968) present Qv values for clean sandstones (porosity~0.22) ranging from 0.02 to 0.08 and for very shaly sandstones (porosity~0.28) ranging from 0.50 to 0.89. Thus, the A/M area samples lie in the middle of the Qv range bracketed by clean sandstones and shaly sandstones.

4. Water saturation, calculated from measurements of moisture content, is around 0.4 for the four sand classes and around 0.53 for sandy fat clay. Considering possible moisture loss during sample handling, the values for the sands probably represent a lower bound to the in-situ saturations in the vadose zone.

5. Kaolinite is the dominant clay mineral, from 0.60 to 0.97 of a clay sample, with vermiculite (0.01 to 0.28) and illite (<0.07) also present. Smectite is also present, more commonly in the saturated zone than in the vadose zone.

In summary, examination of laboratory measurements of core samples showed that average porosity is 0.39, average grain density is 2.63 g/cm³, kaolinite is the dominant clay mineral, and that minimum water saturation can be expected to be around 0.4.

LOG ACQUISITION AND PROCESSING

Geophysical and cone penetrometer logs from the A/M area consisted of: 1. stress and resistivity logs from 27 cone penetrometer runs; 2. gamma ray logs from 9 holes cased with 4-inch diameter PVC; 3. gamma ray, and electrical resistivity logs from 30 open holes; and 4. gamma ray, neutron, density, and electrical resistivity logs from 10 open holes. This paper focuses on the fourth data set which furnishes the most complete set of logs. Logs were digitized and stored at a spacing of 0.1 feet.

Conversion of neutron logs

Neutron logs were acquired with Century's 9055 tool which uses a 1.0 Curie AmBe source separated by 14 inches (35.6 cm) from the center of a 1" x 6" Helium-3 detector. Tool response is specified as 0 to 10,000 API units to within ±5%. The API system is a single-point system: 1000 API units is assigned to the response of any neutron tool in a water-filled borehole of 7-7/8 inch diameter in Indiana Limestone of 19% porosity. The calibration hole is located at the API test pits in Houston. Each tool supplier develops a transform from API units to porosity for their own neutron tools.

Using calibration information supplied by Century Geophysical, we developed a conversion from countrate (in API units) to neutron porosity:

a + c(lnx) + e(lnx)²

f_n = ---------------------------- (1)

1 + b(lnx) + d(lnx)²

where x is the count rate in API units, lnx is the natural logarithm of x, f_n is the porosity in percent, and the coefficients are given as a function of hole size in Table 1. At porosities less than 30%, the logarithm of count rate increases linearly with decreasing porosity, with uniform behavior as a function of hole size. However, at porosities greater than 30%, the curves for various hole sizes gradually converge to a single point at 100% saturation, requiring the complicated analytical form of equation 1. The form of the optimum fit and its coefficients were determined with commercial software called "Tablecurve". A spline algorithm interpolates to the correct hole diameter.

After conversion of porosity from percent to fractional units, the porosity is adjusted to a sandstone matrix using f_ss = 0.965f + 0.035. This latter correction is required because equation 1 was established for a limestone matrix. The correction was applied because the sediments at the Savannah River Site are sandy rather than calcareous. Final neutron porosity values are given as fractions rather than percent.

Neutrons are moderated (slowed down) by hydrogen at low energies, and are also moderated by the rock matrix at high energies. Neutrons are not slowed down much in air. As a result, neutrons travel farther in partially saturated rock than in saturated rock. Consequently the neutron porosity reading is reduced, an effect which has been called the "excavation effect" by Segesman and Liu (1971) who present the corrections needed for compensated neutron logs from a Schlumberger tool. The corrections are maximum at 50% saturation and increase with increasing porosity. For example, a sandstone of 40% porosity and 50% saturation requires that 8.5% porosity be added to the log reading.

What is the 'excavation effect' for Century's single-detector thermal neutron tool? Fortuitously, the source-to-detector spacing for the near detector in Schlumberger's CNL tool is comparable to the 14-inch spacing of Century's single-detector tool. Figure 19 of Ullo (1981) shows the correction for a 37% porosity clean sand for the near detector of Schlumberger's tool. Ullo shows a porosity correction of 3.3% at 50% saturation, so the correction is less than half that required for the Schlumberger compensated neutron tool. Following Segesman and Liu (1971) and using Ullo's (1981) result, an approximate correction algorithm for the Century neutron tool is,

Df = 0.43 (2f²S_w + 0.04f) (1-S_w) (2)

The correction Df should be added to the reading from a Century tool once the saturation S_w has been established.

Computation of porosity from density log.Computation of porosity from density log.

In fully saturated rock, bulk density from the log __b, grain density __g, pore fluid density __w, and porosity f are related by,

__b = __g(1 - f) + __w f (3)

So that a density-derived porosity can be calculated as,

f_d = (__g - __b) / (__g - 1) (4)

In saturated rock, f_d will equal the true porosity, but in unsaturated rock f_d will be less than true porosity.

Filtering of nuclear logsFiltering of nuclear logs

Overlays of gamma-ray logs showed that the fine structure was non-repeatable, and that filtering was required. Experimentation with several filters determined that an 11-point triangular filter preserved depth resolution and improved run-to-run repeatability. Because the log is digitized at 10 points per foot, the filter smooths over 1.1 feet of log. The 11-point filter was also applied to density and neutron logs.

Corrections for normal and guard resistivity logsCorrections for normal and guard resistivity logs.

Normal resistivity logs require correction for borehole fluid resistivity and hole size; separation between the 16-inch and 64-inch logs can be caused by the high contrast between the mud resistivity and formation resistivity. Using a chart from Schlumberger, Scott (1978) wrote a Fortran code to correct the normal logs for the effects of borehole fluid resistivity, hole diameter, and tool diameter. This correction was applied to the logs shown in Figure 2.

The Century 9030 tool contains a guard resistivity sensor consisting of an 8-inch long center current electrode with constant-potential guard electrodes above and below it. Overall length of the three-electrode system is 55 inches; tool diameter is 2.2 inches. Its response range is 0 to 60,000 ohm-m to 5% accuracy. To calculate formation resistivity, the measured resistivity must be multiplied by a factor obtained from a correction chart furnished by Century which depends upon the ratio of measured resistivity R_f to mud resistivity R_m. For an 8-inch diameter hole, the factor ranges from 0.25 for R_f/R_m=0.1 to 1.46 for R_f/R_m=1000. The correction was applied by fitting polynomials to the Century chart and using the caliper measurement to interpolate between curves for varying hole sizes.

Vertical resolution of resistivity logs

Inspection of Figure 2 shows that bed resolution increases progressively from the normal to the guard to the penetrometer logs. For example, a low resistivity bed at 129 feet in MHT-9C is shown by the guard resistivity to be about 2.5 feet thick. The 16-inch normal log defines the thickness adequately, although the bed resistivity response is not as low as the guard resistivity. The 64-inch resistivity shows a bed thickness of about five feet, which is an artifact of the 64-inch spacing rather than the true bed thickness. Note that the 64-inch resistivity reading is not as low as either the guard or 16-inch readings. This example simply illustrates that the 64-inch tool, designed for deeper penetration, is not as effective at either defining bed thickness or measuring bed resistivity as either the 16-inch tool or the guard tool.

Now compare the character of the resistivity curve from the penetrometer run in CPT-007a with that of the resistivity logs from hole MHT-9C (Figure 2). The bed resolution is of course much better than the normal or guard logs because the penetrometer electrode spacing is one inch. There is no effect from mud that requires compensation, and there is no invasion of filtrate into the formation. The only flaw of the penetrometer resistivity is the nearly flat resistivity of 7000 to 8000 ohm-m recorded from 50 to 85 feet. Other than this apparent limitation at very high resistivities, the penetrometer does an excellent job of measuring formation resistivity and resolving thin beds. It is of course limited by the maximum depth attainable by the push mechanism, which at this site was about 160 feet.

Compensation for the effect of clay

To account for the presence of clay in sandstones, Waxman and Smits (1968) derived an empirical model which reduces to Archies law as the pore water becomes sufficiently conductive, but which accounts for a parallel conduction path due to clay counterions as the pore water becomes less conductive. However, the water resistivity in samples supporting the Waxman-Smits model is much less than the water resistivity at Savannah River Site (Figure 3). Consequently the empirical parameter in their model is not adequately constrained for high water resistivity (>2 ohm-m). Our initial intention was to use the W-S model, incorporating the cation exchange capacity data described in a preceding section. However, the inadequacy of the model at high water resistivity made this impractical. Instead, we revert to the use of Archies law, as described in the next subsection. This appoach is tenable because water resistivity is derived from the log data, by computing Rw in saturated sediments below the water table. An apparent Rw acquired in this fashion compensates for whatever effect clays have on water resistivity in the cleaner sands. In other words, we sidestep the issue of explicitly accounting for the effect of clay upon electrical resistivity by making use of a direct in-situ measurement of effective water resistivity and then applying that measurement upwards into the vadose zone.

Computation of water resistivity, saturation, and bulk volume water

Computation of water resistivity relies upon Archie's empirical law for a rock of porosity f and resistivity R_o saturated with water of resistivity R_w, R_o=R_wf^-m. Substituting R_log for R_o and rearranging this expression, we compute an apparent water resistivity curve R_wa = R_logf^m where the empirical constant m=2. R_log is the guard resistivity or the 16-inch normal resistivity if the guard log is not available.

Saturation S_w is calculated by combining Archies expressions with the density log response. Archies' law relating the resistivity R_t of a partially saturated rock to its saturation is R_t=R_oS_w^-n, where n is the saturation exponent. Combined with Archies' law for a saturated sample, R_o=R_wf^-m,

R_t = R_wS_w^-nf^-m. (5)

The density log in the unsaturated zone will read,

__b = __g(1 - f_v) + S_wf_v__w (6)

where f_v is the porosity in the vadose zone. Solving eqn. 6 for f_v, substituting into eqn. 5, assuming m=n=2, and solving for saturation S_w, we get,

S_w = __g / c , c = (__g - __b)(R_t/R_w)^1/2 + __w (7)

In computing S_w, __g = 2.63 g/cm³, __b is the density log, R_t is either the guard log or the 16-inch normal, and __w = 1.0 g/cm³ for fresh water. R_w is obtained by averaging the water resistivity curve R_wa defined above, within the sandy zones below the water table. By this procedure, R_w includes the excess conduction provided by clay minerals.

The solution of eqn. 6 for porosity in the vadose zone is

f_v = (__g - __b) / (__g - S_w__w) (8)

where S_w has been set to 1.0 wherever it exceeds 1.0 as a result of low values of R_t in eqn. 7.

Finally, water content, here called bulk volume water, (fraction of volume pore water per rock volume), is computed in the vadose zone as the product,

Bvw = S_wf_v (9)

Figure 4 summarizes the computational procedures.

DISCUSSION

Well MHT-9C (Figure 5) was chosen as an example for discussion because it has a complete suite of logs all of which are on scale from surface to total depth. The two right-hand columns contain a summary of the computational results, specifically as the Sw, Clayflag, Bvw, and f_v curves. These four curves suggest a three-way partition of the lithologies in the vadose zone into clay-rich, high-silt/low-clay, and partially saturated sand zones. Clay-rich zones occur where the Clayflag is turned on in response to low resistivity or high neutron porosity. High-silt/low-clay zones occur where Clayflag is off and where the rock is saturated or nearly so (absence of waffle grid). Partially saturated sand occurs where saturation Sw is less than 1, that is, where the waffle grid denotes that moisture content, Bvw, is less than vadose-zone porosity, f_v.

It should be emphasized that the three-way partition relates to pore space properties which are related to lithological and mineralogical properties. Water saturation is related to specific surface area, which in turn is related to grain size and packing. Water saturation is expected to be high in beds with a high fraction of clay-size particles and low in beds comprised of clean, well-sorted sand.

This three-way division of the vadose zone is important in terms of contaminant, water, and gas transport. Clay-rich zones are likely to be much less permeable to all three phases, are likely to "pond" downward-moving dense non-aqueous phase liquid (DNAPL), and are known to contain DNAPL contaminant. High-silt/low-clay zones are likely to block air flow, offer low relative permeability to water and contaminants, and are likely to trap residual contaminant. Partially saturated sands provide the highest relative permeability to water, gas, and contaminant, but are not likely to trap residual contaminant.

We now discuss some specific features of the logs which support this three-way division, and also some of the problem areas which limit the reliability of the results.

Porosity

Porosity is remarkably constant throughout the section penetrated by MHT-9C. Excluding the clay-rich zone from 85 to 112 feet, the log-computed porosity, f_v, ranges from 0.34 to 0.55 with a mean of 0.437. Porosity in the saturated zone, 148 to 182 feet, is 0.45, only slightly greater than porosity in the unsaturated zone, 0.43. The log-derived mean of 0.44 is 0.05 higher than the mean porosity of 0.39 obtained from Shelby tube samples, as described in the section on physical property data. The discrepancy of 0.05 could be caused by a grain density value being too high, a density log reading too low, or inadvertent packing of the Shelby tube samples. In any case, both the logs and the core samples show that porosity is remarkably constant within the section.

Indicators of partial saturation

Partial saturation affects both original and computed logs in recognizable ways, as can be observed in Figure 5. Because grain density and porosity do not vary much in these holes, bulk density (in column 1) decreases where saturation decreases. However, bulk density also decreases where clay content is high, so a better indicator is the separation between the two porosity curves derived from the density and neutron logs, f_d and f_n (column 4 of Figure 5, 45-85 feet). In zones of partial saturation, the neutron porosity decreases because there is less hydrogen in the rock. However the density porosity, f_d, increases because the density log decreased due to air-filled pore space. Note that f_v, the porosity estimate which has been compensated for saturation, does not change in the partially saturated zone. The separation between neutron and density logs is commonly used in oil wells to find gas zones.

Another indicator of partial saturation is the apparent water resistivity curve, Rwa, in column 3 of Figure 5. Rwa values are high in partially saturated zones. Although Rwa is compensated for porosity fluctuations, it tracks the guard resistivity closely because porosity variations are relatively small.

Saturation Sw anticorrelates crudely with modal grain size, in column 5, Figure 5, and also with sand and gravel fraction, that is, with 100 minus clay content in column 2. Both modal grain size and sand+gravel increase as surface area decreases. Surface area is the actual control on Sw.

These qualitative indicators concur with the changes in saturation shown by the waffle grid in column 6. The waffle grid shades the area between f_v, from eqn. 8, and Bvw = S_wf_v, from eqn. 9. Thus the waffle grid shows the volume fraction of air in rock, f_v(1 - S_w). The wavy shading shows Bvw, the volume fraction of water in rock.

Gamma-ray log, grain size data, and the tan clay

Although the gamma-ray log correlates fairly well with clay-size fraction (column 2 of Figure 5), exceptions show that it is not a reliable predictor of the clay-size fraction. The most notable exception is the "tan clay" interval (99-110 feet in MHT-9C) which is characterized by low resistivity and high clay-size fraction from sieve analysis. The gamma-ray log does increase at the tan clay in some holes, but in other holes, including MHT-9C, it does not. Likewise the neutron porosity increases in some holes, but it remains relatively unchanged in MHT-9C. The mix of log responses in the tan clay in different holes suggests that clay mineral assemblages vary from hole to hole. Horton (1995) notes that two X-ray diffraction samples from the tan clay zone contain smectite, kaolinite, and minor illite. Using the physical properties of clays (Table 2) to interpret the log responses, we can make some qualitative assertions about clay composition within the tan clay. For example, all logs respond in MHT-7C (not shown), so it is likely that illite (potassium emits gamma rays), smectite (high CEC causes low resistivity), and kaolinite (high water content increases neutron porosity) are all present in significant quantities. Hole MHT-9C, with no gamma response but with pronounced resistivity and neutron responses, is likely to contain smectite and kaolinite, with little illite and heavy minerals. We caution that these associations are speculative and point out the need for coordinated work in clay mineralogy and log analysis.

SUMMARY

Porosity and saturation were calculated from electrical and density logs in the vadose zone. These two properties, combined with additional lithologic insight from the gamma-ray and neutron logs, leads to a three-way separation of vadose zone lithologies based upon their log-derived properties: clay-rich, low-clay, and partially saturated sand zones.

ACKNOWLEDGEMENTS

Ed Rooks of Graves Environmental and Geotechnical Services, Inc., Jackson, South Carolina, supplied information regarding drilling and logging procedures. Brian Peterson of Century Geophysical, Tulsa, Oklahoma, provided information regarding Century's logging tools. M. O'Kelley, of Law Environmental, Atlanta Georgia supplied information on sample analysis. Brian Looney, Carol Eddy-Dilek, and Joe Rossabi of Westinghouse Savannah River Co. provided the logging data and other information from the A/M area.

REFERENCES

Ellis, D., Howard, J., Flaum, C., McKeon, D. Scott, H., Serra, O., and Simmons, G., 1988, Mineral logging parameters: nuclear and acoustic, The Technical Review, v. 36, n. 1, p. 38-52.

Horton, R., 1995, X-ray diffraction studies of selected core samples from A/M area, Savannah River Site, South Carolina, USGS Open-file Report, 26p.

Nelson, P.H., and Kibler, J.E., 1995, Geophysical logs and groundwater chemistry in the A/M Area, interim report, Savannah River site, South Carolina, USGS Open-File Report 95-507, 68 p.

Ruhovets, N., and Fertl, W.H., 1981, Digital shaly sand analysis based on Waxman-Smits model and log-derived clay typing, paper V in Transactions Paris Symposium, Soc. Prof. Well Log Analysts, pp. 107-134.

Segesman, F., and Liu, O., 1971, The excavation effect, paper N in Transactions of Twelfth Annual Logging Symposium of Society of Professional Well Log Analysts, 24 p.

Scott, J.H., 1978, A Fortran algorithm for correcting normal resistivity logs for borehole diameter and resitivity, USGS Open-File Report 78-669, 12 p.

Ullo, J.J., 1981, Response of the dual spacing neutron log (CNL) to gas, SPE Paper 10295, 56th Annual Technical Conference of Society of Petroleum Engineers, 11 p.

Waxman, M.H., and Smits, L.J.M., 1968, Electrical conductivities in oil-bearing shaly sands, Soc. Petroleum Engineers Journal, Transactions AIME, v. 243, p. 107-122.

FIGURES

Figure 1. Sketch of sand (open) and clay (lined) layering in upper 270 feet of the A/M area. Also shown are hydrogeologic units, water table at interface between vadose zone and the semiconfined M-area aquifer, and typical placement of well screens A through E. Elevation (feet) is with respect to mean sea level.

Figure 2. Resistivity sensors and logs illustrating resolution of normal (16-inch curve is solid, 64-inch curve is dashed), guard, and penetrometer tools. Electrode spacings are true to the depth scale in feet, but the tool lengths are not. Scales in ohm-m are logarithmic. Penetrometer run CPT-007a is approximately 1500 feet west of MHT-9c.

Figure 3. Ranges of electrical resistivity (conductivity) of core samples and saturant used by Waxman and Smits (1968), and ranges for water samples and a resistivity log from the A/M area.

Figure 4. Sequence of steps for computing saturation, porosity, and water content in the vadose zone. Top row: grain density is assigned a value of 2.63 g/cm³. Second row: density log is smoothed and used with grain density to compute porosity in saturated zone. Third row: resistivity log from guard tool is corrected, then used to compute apparent water resistivity; an average water resistivity is obtained from a depth interval in the saturated zone. Fourth row: Saturation is computed from four inputs and is constrained to not exceed a value of 1.0. Fifth row: Porosity in the vadose zone is computed from four inputs. Sixth row: water content Bvw is computed from porosity and saturation.

Figure 5. Original and computed log curves for well MHT-9C. Original logs, with filtering and borehole corrections, are shown in three lefthand columns, computed curves in three righthand columns. Column 6 (rightmost column) shows porosity at less than 0.5 throughout most of hole; waffle grid shows air-filled porosity and wavy pattern shows water-filled porosity. Water table lies at 148 feet subsurface.

12 13 14 15 16

__b __g(1 - f_v) + S_w f_v __w

S_w = __g / c , c = (__g - __b R_t

R_guard Gamma Ray Clay Gravel

R_wa Sand Caliper Density

f_v = (__g - __b) / (__g - S_w__w)

Bvw = S_w f_n f_d

Modal

Grain 50 100 150

Size

Water Depth (feet)

Table

Clay Flag

air-filled

water-filled

pore space

Resistivity (ohm-m) 7 7000

Porosity 1 0

Saturation 1 0

Porosity 1 0

Density (gm/cc) 1.5 2.5	Gamma (API) 0 250
Caliper 0 (inch) 10