Estimation of Groundwater Aquifer Formation- Strength Parameters from Geophysical Well Logs: The Southwestern Coastal Area of Yun-Lin, Taiwan

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1 Energy Sources, Part A, 29:1 19, 2007 Copyright Taylor & Francis Group, LLC ISSN: print/ online DOI: / Estimation of Groundwater Aquifer Formation- Strength Parameters from Geophysical Well Logs: The Southwestern Coastal Area of Yun-Lin, Taiwan B. Z. HSIEH Department of Resources Engineering National Cheng Kung University Tainan, Taiwan G. V. CHILINGAR Environmental Engineering Department University of Southern California Los Angeles, CA, USA M. T. LU Exploration and Production Business Division Chinese Petroleum Corporation Miaoli, Taiwan Z. S. LIN Department of Resources Engineering National Cheng Kung University Tainan, Taiwan Abstract The purpose of this study is to estimate groundwater aquifer formationstrength parameters including shear modulus, bulk modulus, Poisson s ratio, and Young s modulus by using geophysical well logs. A new dispersed-shale index equation was developed by using the natural gamma-ray log and the compensated formation density log to solve a confusing problem of the compaction factor setting in the calculation of sonic porosity for an unconsolidated groundwater aquifer. A useful Poisson s ratio estimation method was employed to estimate a groundwater aquifer s formation-strength parameters when shear-wave transit time data are lacking in groundwater wells. Hydrogeologic parameters are characterized in estimating Address correspondence to Zsay-Shing Lin, Dept. of Resources Engineering, National Cheng Kung University, No. 1 University Road, Tainan City 701, Taiwan. zsaylin@mail.ncku. edu.tw 1

2 2 B. Z. Hsieh et al. formation-strength parameters. Five wells in the southwestern coastal area of Yun- Lin, Taiwan, were logged, and four shallow aquifers were identified from log-derived hydrogeologic characteristics less than 200 m in depth. The formation-strength parameters for aquifers between 310 and 500 m in depth were calculated in two wells because complete formation density and compressional-wave transit time data were available. The results of the aquifer s formation-strength parameters demonstrate that both shear modulus, ranging from 0.15 to psi, and Young s modulus, ranging from 0.40 to psi, increase with depth, whereas bulk compressibility, ranging from 1.2 to psi 1, decreases with increasing depth. Keywords dispersed-shale index, Poisson s ratio, Young s modulus 1. Introduction Geophysical well logging is an ideal method for evaluating formation-strength parameters and hydrogeologic characteristics, not only in providing in-situ and continuous data, but also in obtaining extensive formation information. In addition, the geophysical well logging method can provide economic benefits by saving the cost and time of core analyses and soil/rock mechanical tests. Traditionally, formation-strength parameters such as Poisson s ratio and Young s modulus are obtained from a core triaxial test (Liu, 1992). Recently, there have been studies in estimating formation-strength parameters (Tixier et al., 1975; Anderson et al., 1973; Stein and Hilchie, 1972) and hydrogeologic characteristics using well logging data (Paillet and Crowder, 1996; Temples and Waddell, 1996; Jorgensen, 1991). Temples and Waddell (1996) evaluated the Poisson s ratio and bulk modulus of aquifers by using well logging data from the upper Cretaceous section of Hilton Head Island. They calculated Poisson s ratio from the compressional-wave and shear-wave transit times, and the bulk modulus was estimated from formation density, compressional-wave transit time and shear-wave transit time logs. The measurement of shear-wave transit time in unconsolidated sand is a difficult task even with current technology. Tixier et al. (1975) have developed an empirical correlation without shear-wave transit time to estimate Poisson s ratio based upon the dispersedshale index. They used density porosity and sonic porosity to calculate the dispersedshale index in which the compaction factor was required. However, in unconsolidated or poorly consolidated groundwater aquifers, the estimation of compaction factor is quite subjective. The purpose of this study was to estimate groundwater aquifer formation-strength parameters, including shear modulus, bulk compressibility, Poisson s ratio, and Young s modulus, with a new dispersed-shale index equation. The methodology of the estimation was used to calculate aquifer formation-strength parameters for the southwestern coastal area of Yun-Lin, Taiwan. The results are important for formation subsidence researches and groundwater resources management simulations in Taiwan. 2. Background Theory The formation-strength parameters included in this study are shear modulus, bulk compressibility, Poisson s ratio, and Young s modulus. All of these parameters were calculated from the formation density log data, sonic log data, and natural gamma-ray log data of the aquifer. The calculation equations are described as follows:

3 Aquifer Formation-Strength Parameters 3 a. Formation-strength Parameters In a homogeneous and isotropic aquifer, the formation shear modulus (G) and bulk compressibility (C b ) can be calculated by knowing compressional-wave transit time ( t C ), formation bulk density (ρ b ), and Poisson s ratio (µ), such as (Tixier et al., 1975): G = Aρ b t 2 c (1) C b = t2 c Bρ b (2) where A = 1 2µ 2(1 µ) B = 1 + µ 3(1 µ) (3) (4) and G = shear modulus, psi; C b = bulk compressibility, psi 1 ; A, B = constants based upon µ, dimensionless; ρ b = bulk density (formation density log reading), gm/cc; t C = compressional-wave transit time, µs/ft; and µ = Poisson s ratio, dimensionless. Young s modulus (E) can be calculated from Poisson s ratio (µ) and the shear modulus (G) with the following equation (Crain, 1986): where E = Young s modulus, psi. E = 2(1 + µ)g (5) b. Poisson s Ratio (µ) and the Dispersed-shale Index (q) Poisson s ratio (µ) in Eqs. (3) to (5) can be calculated using compressional-wave transit time ( t C ) and shear-wave transit time ( t S ) with the following equation (Dewan, 1983): µ = 0.5( t S/ t C ) 2 1 ( t S / t C ) 2 1 (6) where t S = shear-wave transit time, µs/ft. The shear-wave transit time information in the above equation is normally not available in well logging or may be otherwise lacking. Alternatively, Poisson s ratio is estimated using an empirical equation of Poisson s ratio and the dispersed-shale index relationship in an unconsolidated sand formation (Anderson et al., 1973; Tixier et al., 1975): µ = 0.125q (7) where q = dispersed-shale index, fraction. Tixier et al. (1975) calculated the dispersed-shale index (q) from sonic log and formation density log data in hydrocarbon formations using the following equation: q = φ SV φ D φ SV (8)

4 4 B. Z. Hsieh et al. where φ SV = t log t ma t f t ma 1 C p (9) φ D = ρ ma ρ b ρ ma ρ f (10) and φ SV = total porosity derived from sonic log, non-calibrated by shale volume, fraction; φ D = total porosity from density log, non-calibrated by shale volume, fraction; t log = compressional-wave transit time as measured by sonic log, µs/ft; t ma = compressionalwave transit time in formation matrix material, µs/ft; t f = compressional-wave transit time in formation fluids, µs/ft; C p = compaction factor, dimensionless; ρ ma = density of formation matrix material, gm/cc; ρ f = density of formation fluid, gm/cc. The dispersed-shale index (q) calculated from Eq. (8) is suitable for hydrocarbon formations. But, in an unconsolidated groundwater aquifer, the suitable value of the compaction factor (C p ) required in the calculation of φ SV [Eq. (9)] is unclear and subjective. Therefore, the development of a new dispersed-shale index equation for an unconsolidated groundwater aquifer is necessary. The definition of the dispersed-shale index is (Anderson et al., 1973): q = φ t φ e φ t (11) where φ t = total porosity, fraction; φ e = effective porosity, fraction. The dispersed-shale index can be estimated from total porosity (φ t ) and effective porosity (φ e ). The formation porosity can be calculated from the compensated formation density (FDC) log in an unconsolidated aquifer formation where the suitable value of the compaction factor (C p ) required in the calculation of sonic porosity is unclear and subjective (Dewan, 1983). The total porosity can be the original density porosity without calibration by shale volume. The effective porosity (φ e ) can be calculated from the FDC log with calibration by shale volume (Crain, 1986). According to the definition of the dispersed-shale index (Anderson et al., 1973) and the principles of well logging (Crain, 1986; Dewan, 1983), a reasonable dispersed-shale index equation for an unconsolidated groundwater aquifer can be suggested: q = φ D φ D sh φ D (12) where ( ρma ρ b φ D sh = ρ ma ρ f ) ( ) ρma ρ sh V sh ρ ma ρ f (13) V sh = GR log GR min GR max GR min (14) and φ D sh = effective porosity from density log, calibrated by shale volume, fraction; V sh = shale volume, fraction; ρ sh = density of nearby shale, gm/cc; GR log = natural gamma-ray log reading, API units; GR min = the sand base line reading (clean sand), API units; GR max = the shale base line reading (100% shale), API units.

5 Aquifer Formation-Strength Parameters 5 c. Aquifer Hydrogeologic Characteristics The theory for estimating formation-strength parameters described above is applied for sand material aquifers. The identification of aquifers from well logs is based on hydrogeologic characteristics, including shale volume, true formation resistivity, effective porosity, and hydraulic conductivity. In this study, the rules for defining a good aquifer by using the calculated results of well logs are constructed. The qualifications of a good aquifer include low shale volume (less than 30%), relatively high true formation resistivity (Rt) comparing with adjacent underlain and overlain formation (qualitative indication of permeability from two types of resistivity logs), good effective porosity (greater than 25%), and high hydraulic conductivity (greater than 10 5 m/s). The shale volume (V sh ) is calculated from the natural gamma-ray (GR) log data by Eq. (14). The true formation resistivity (Rt) can be calculated from a resistivity log with three curves and the appropriate tornado chart: the spherically focused resistivity (RSFL) curve, the medium dual induction resistivity (RILM) curve, and the deep dual induction resistivity (RILD) curve (Asquith and Gibson, 1985). The effective porosity (φ e ) can be calculated from the compensated formation density (FDC) log or the compensated borehole sonic (BHC) log. The result of the porosity calculation, which is not calibrated by shale volume, can be regarded as the total porosity of a formation (Crain, 1986). Generally, if the aquifer contains shaly sand, porosity calculations will be higher. The result of the porosity calculation, which is calibrated by shale volume, can be regarded as the effective porosity of a formation. The effective porosity can be calculated from the compensated formation density (FDC) log and the natural gamma-ray (GR) log by Eq. (13) (Asquith and Gibson, 1985). Formation water resistivity (Rw) is an important factor in well log analysis. In this study, the results of formation water resistivity calculation can be compared with the field measurements collected from the monitoring wells. The calculation of formation water resistivity must be made for clean sand because formation water resistivity is greatly affected by shale-volume content. Formation water resistivity can be calculated from the formation factors (Dewan, 1983). The hydraulic conductivity (K) derived from the permeability (k) can be calculated from logs by the Wyllie and Rose formulas (Wyllie and Rose, 1950; Asquith and Gibson, 1985): k = PC (φ PE )/(Swir SE ) (15) where k = permeability of formation, m 2 ; PC = permeability constant, dimensionless; φ = porosity, fraction; PE = porosity exponent, dimensionless; Swir = irreducible water saturation, fraction; SE = irreducible water saturation exponent, dimensionless; PC, PE, and SE are constant and should be derived from core data and/or pumping test data. Hydraulic conductivity (K) can be obtained from permeability using the following equation: K = k µ f ( ) ρw g g c (16) where K = hydraulic conductivity, m/s; ρ w = density of formation water, Kg/m 3 ; g = gravity acceleration, m/s 2 ; g c = 1.0, Kg m/s 2 /N; µ f = viscosity of formation fluid, Pa s.

6 6 B. Z. Hsieh et al. 3. Regional Geology The study area for estimating formation-strength parameters is located in the southwestern coastal area of Yun-Lin, Taiwan (Figure 1). It is part of the south wing of the Choushui River alluvial fan system, whose deposits consist of unconsolidated sand, silt, and clay from the Choushui River and its tributary. The upper section of the alluvial fan is mostly a gravel formation, whereas the lower section often consists of sand or clay. The sand formations are the major aquifers in this area. All of the sedimentary formations in the investigation area are Pleistocene-Recent in age. In the coastal area of the Choushui River alluvial fan, the shale materials (silt, mud, and clay) were grouped into an aquitard, and the sand materials (fine, medium, and coarse sand) and gravel were grouped into an aquifer. The interlaced shale-material aquitard and the sand-material aquifer were deposited because of alternating transgression and regression. The hydrogeologic structure of this area can be divided into three major aquifers and two major aquitards in the depth interval between the surface and 250 m (Figure 2). The sequence of the structure, in order of increasing depth, is aquifer I, aquitard I, aquifer II, aquitard II, and aquifer III. Both aquifer II and aquifer III are confined aquifers. Confined aquifer II is currently the major water source for civilian use. In the coastal area of the Choushui River alluvial fan, the groundwater level of aquifer II was originally higher than the surface level. Recently, the groundwater levels have rapidly dropped below sea level because of excessive water pumping for civilian use. The decreased groundwater level in the area has caused compaction of the formation and led to serious land subsidence. Confined aquifer III and the deeper aquifers will be the major water source for the future. The formation-strength parameters in the deeper layers (until 500 m) are the most important considerations for formation subsidence researches and the groundwater resource management projects in the future. Figure 1. Study area and well locations of well logs (after Lin et al., 1996).

7 Aquifer Formation-Strength Parameters 7 Figure 2. Hydrogeology structure on profile A (modified from Chiang, 1995). 4. Results and Discussion The collected well logging information of five wells (GH-1, SL-2, PTL-1, THS-5, THS-8) (Figure 1) are the natural gamma-ray (GR) log, the spherically focused resistivity (RSFL) log, the medium dual induction resistivity (RILM) log, the deep dual induction resistivity (RILD) log, the compensated borehole sonic (BHC) log, and the compensated formation density (FDC) log. Also, the well log header for each well includes mud properties, mud salinity, mud conductivity, etc. Based on these well logs, hydrogeologic characteristics such as shale volume (Vh ), porosity (φ), true formation resistivity (Rt), formation water resistivity (Rw), and hydraulic conductivity (K) can be calculated for every well. The hydrogeologic characteristics were first calculated from well logs for five wells. The identification of aquifers was based on the aquifer determinative rules with the calculations of the hydrogeologic characteristics. The formation-strength parameters included shear modulus (G), bulk compressibility (Cb ), Poisson s ratio (µ), and Young s modulus (E), and were estimated for the aquifers in THS-8 and GH-1 wells only, because both the compensated borehole sonic (BHC) log data and the compensated formation density (FDC) log data were available for these wells (Table 1). a. Aquifer Identification and Hydrogeologic Characteristics in Shallow Aquifer Systems In this study, a shallow aquifer system is defined as a formation with a depth less than 200 m. The identification of aquifers is based on characteristics such as low shale volume (Vsh ), high true formation resistivity (Rt), good effective porosity (φe ), and high hydraulic conductivity (K). The criteria for aquifers are as follows: (1) shale volume is less than 30%; (2) effective porosity is greater than 25%; (3) hydraulic conductivity is

8 8 B. Z. Hsieh et al. Table 1 Available log data and calculated parameters for each well Well Depth interval (m) Log data a Calculated parameters b,c SL GR, RSFL, RILM, RILD, BHC V sh, φ, Rt, Rw, K GH GR, RSFL, RILD, BHC V sh, φ, Rt, Rw, K GR, RSFL, RILD, BHC, FDC V sh, φ, Rt, Rw, K, G, C b, µ, E PTL GR, RSFL, RILD, BHC V sh, φ, Rt, Rw, K THS GR, RSFL, RILD, BHC V sh, φ, Rt, Rw, K THS GR, RSFL, RILD, BHC V sh, φ, Rt, Rw, K GR, RSFL, RILD, BHC, FDC V sh, φ, Rt, Rw, K, G, C b, µ, E a Geophysical well logs abbreviation: GR: the natural gamma-ray log; RSFL: the spherically focused resistivity log, ohm-m; RILM: the medium dual induction resistivity log; RILD: the deep dual induction resistivity log; BHC: the compensated borehole sonic log; FDC: the compensated formation density log. b Hydrogeologic characteristics abbreviation: V sh : shale volume, φ: porosity, Rt: the true formation resistivity, Rw: the formation water resistivity, K: hydraulic conductivity. c Formation strength parameters abbreviation: G: shear modulus, C b : bulk compressibility, µ: Poisson s ratio, E: Young s modulus. greater than 10 5 m/s; and (4) indications of permeability from the contrast between the shallow investigation resistivity log (RSFL) curve and the deep investigation resistivity log (RILD) curve. The hydrogeologic characteristics of each well for each aquifer were analyzed. For example, in well GH-1, four aquifers (GH1-F1, GH1-F2, GH1-F3, and GH1-F4) in the range of 20 to 200 m can be identified (Table 2). GH1-F1 is a sand formation from 20 to 51 m deep. There is a thin shaly sand in the upper part of GH1-F1 (at 27 m depth) (Figure 3) in which effective porosity is 23% (Figure 4) and formation resistivity is 16 ohm-m (Figure 5). GH1-F2 is a sand formation in which the formation interval is from 70 to 110 m. There is more shale at the depths of 78 to 80 m, 88, and 100 m in GH1-F2 (Figure 3), which results in lower effective-porosity (Figure 4) and lower hydraulic conductivity (Figure 6). We can infer that the shale formation is a regional aquitard that has not prevented the continuity between the upper and lower aquifers because the hydrogeologic characteristics of the upper and lower aquifers, though divided by the shale formation, are similar. GH1-F3 is a shale-sand interval from 115 to 169 m. There is shale from 137 to 145 m, separating the aquifer into upper and lower parts (Figure 3). The thickness of the upper aquifer is 22 m (115 to 137 m) and the thickness of the lower aquifer is 24 m (145 to 169 m). Though the upper and lower aquifers are divided by a thick shale formation, their hydrogeologic characteristics are similar (Table 2). We can, therefore, infer that the shale formation is a regional aquitard. GH1-F4 is a sand formation between 180 and 200 m. Because the bottom of the logged data is at the depth of 200 m, conditions for depths greater than 200 m are unknown. However, from the trend of the resistivity logs (Figure 5) and the hydraulic conductivity curve (Figure 6), we infer that the bottom of GH1-F4 will be deeper than 200 m. The identification of aquifers and calculation of their hydrogeologic characteristics for the other wells (THS-8, SL-2 THS-5, and PTL-1) between the surface and 200 m were

9 Aquifer Formation-Strength Parameters 9 Table 2 Hydrogeologic characteristics and aquifer analysis in wells GH-1 and THS-8 GH-1 (20 to 200 m) THS-8 (80 to 200 m) Aquifer Depth (m)/ lithology Characteristics Aquifer Depth (m)/ lithology Characteristics GH1-F m/sand V sh = 18% THS8-F1 N/A N/A φ = 29% Rt = 24 ohm-m Rw = 6.7 ohm-m K = m/s GH1-F m/sand V sh = 11% THS8-F m/sand V sh = 11% φ = 35% φ = 33% Rt = 50 ohm-m Rt = 41 ohm-m Rw = 19.4 ohm-m Rw = 16.8 ohm-m K = m/s K = m/s GH1-F m/sand THS8-F m/sand Upper aquifer V sh = 16% Upper aquifer V sh = 6.3% ( m) φ = 30% ( m) φ = 36% Rt = 43 ohm-m Rt = 50 ohm-m Rw = 12.6 ohm-m Rw = 18.3 ohm-m K = m/s K = m/s Lower aquifer V sh = 16% Lower aquifer V sh = 16% ( m) φ = 30% ( m) φ = 31% Rt = 45 ohm-m Rt = 60 ohm-m Rw = 13.4 ohm-m Rw = 21.2 ohm-m K = m/s K = m/s GH1-F m/sand V sh = 16% THS8-F m/sand V sh = 14% φ = 30% φ = 31% Rt = 45 ohm-m Rt = 50 ohm-m Rw = 14 ohm-m Rw = 20.4 ohm-m K = m/s K = m/s For hydrogeologic characteristics abbreviation, see Table 1. also conducted. The results of aquifer identification show that the sequence of aquifers is the same in the GH-1, THS-8, and SL-2 wells. In these wells, with the exception of THS-8 (THS8-F1) because of unrecorded data from the surface to 80 m (Table 2), four aquifers (F1, F2, F3, and F4) can be identified above the depth of 200 m. There was one shale formation identified in the third aquifer (F3) among the SL-2, GH-1, and THS-8 wells, thus separating the third aquifer into upper and lower sections. In addition, the sequence of aquifers is the same in the THS-5 and PTL-1 wells (Table 3). With the exception of the first aquifer (F1) because of unrecorded log records from the surface to 50 m in both wells, three aquifers (F2, F3, and F4) can be identified above the depth of 200 m. In these wells, the third aquifers (THS5-F3 and PTL1-F3) are single thick aquifers without a shale formation. Since the wells of THS-5 and PTL-1 are along the coast, and the wells of SL-2, GH-1, and THS-8 are closer inland (Figure 1), the difference in the third aquifers shows that there is one shale formation existing in the inland wells (SL-2, GH-1, and THS-8) and that the shale formation disappears gradually as one moves towards the sea (THS-5 and PTL-1). A transgressive sequence can be observed in the aquifer.

10 10 B. Z. Hsieh et al. Figure 3. Shale volume curve for well GH-1. Figure 4. Effective porosity curve for well GH-1. To verify the calculation of the well log analyses in the present study, we compared the results of well log analyses with the available field data from two monitoring wells, such as Shui-Lin and Bo-Zi (Figure 1). In the Shui-Lin monitoring well, the formation water resistivity and hydraulic conductivity, measured from water samples and pumping tests between 191 and 197 m, were 25.6 ohm-m and m/s, respectively (Lin et al., 1996). The well log analysis in the nearby SL-2 well for the corresponding aquifer interval showed formation water resistivity to be 24.5 ohm-m and hydraulic conductivity to be m/s. The well log analysis results in the SL-2 well were approximately the same as the field measurements of the nearby Shui-Lin monitoring well. In the Bo-Zi monitoring well, the formation water resistivity and hydraulic conductivity, measured from water samples and pumping tests between 116 and 146 m, were 22.1 ohm-m and m/s, respectively (Lin et al., 1996). A well log analysis in the nearby PTL-1 well for the corresponding aquifer interval revealed a formation water resistivity of 18.9 ohm-m and a hydraulic conductivity of m/s. In addition, in the Bo-Zi monitoring well, the formation water resistivity and hydraulic conductivity, measured from water samples and pumping tests between 176 and 206 m, were 20.9 ohm-m and m/s, respectively (Lin et al., 1996). The well log analysis results in the nearby PTL-1 well for the corresponding aquifer interval were 15.3 ohm-m for

11 Aquifer Formation-Strength Parameters 11 Figure 5. True formation resistivity curve for well GH-1. Figure 6. Hydraulic conductivity curve for well GH-1. formation water resistivity and m/s for hydraulic conductivity. The results of well log analysis in the PTL-1 well were also approximately the same as the nearby field measurements. b. Estimations of Formation-strength Parameters in Deeper Aquifer Systems The THS-8 and GH-1 wells were used to estimate formation-strength parameters because the compensated borehole sonic (BHC) log and the compensated formation density (FDC) log were available for the depth interval between 310 to 500 m (Table 1). In the depth interval between 310 to 500 m in the THS-8 well, six deeper aquifers (THS8-B1, THS8-B2, THS8-B3, THS8-B4, THS8-B5, and THS8-B6) can be identified by using the following well logs or log-derived information: shale volume (Figure 7), effective porosity (Figure 8), natural gamma-rays, resistivity logs (Figure 9), and hydraulic conductivity calculations (Figure 10). The shear modulus (Figure 11), bulk compressibility (Figure 12), Poisson s ratio (Figure 13), and Young s modulus (Figure 14) were calculated for each aquifer. Table 4 shows the results of hydrogeologic characteristic calculations for each aquifer in THS-8. In well GH-1, six aquifers (GH1-C1, GH1-C2, GH1-C3, GH1-C4, GH1-C5, and GH1-C6) can be identified. Table 5 shows the hydro-

12 12 B. Z. Hsieh et al. Table 3 Hydrogeologic characteristics and aquifer analysis in wells THS-5 and PTL-1 THS-5 (50 to 200 m) PTL-1 (50 to 200 m) Aquifer Depth (m)/ lithology Characteristics Aquifer Depth (m)/ lithology Characteristics THS5-F1 N/A N/A PTL1-F1 N/A N/A THS5-F m/sand V sh = 15% PTL1-F m/sand V sh = 15.5% φ = 31% φ = 30.5% Rt = 101 ohm-m Rt = 37 ohm-m Rw = 37.4 ohm-m Rw = 13.1 ohm-m K = m/s K = m/s THS5-F m/sand V sh = 12% PTL1-F m/sand V sh = 10% φ = 32% φ = 34% Rt = 101 ohm-m Rt = 45 ohm-m Rw = 34.6 ohm-m Rw = 18.9 ohm-m K = m/s K = m/s THS5-F m/sand V sh = 14% PTL1-F m/sand V sh = 11% φ = 29% φ = 34% Rt = 100 ohm-m Rt = 39 ohm-m Rw = 17.5 ohm-m Rw = 15.3 ohm-m K = m/s K = m/s For hydrogeologic characteristics abbreviation, see Table 1. geologic characteristics and formation-strength parameter calculations for each aquifer from the depth between 310 to 420 m of GH-1. In this study, the Poisson s ratios derived from the well log data of two wells were between 0.27 and for THS-8 (Figure 13; Table 4) and between 0.27 and for GH-1 (Table 5). Typically, Poisson s ratio for sandy soil ranges between 0.1 and 0.4; for loose sand, between 0.1 and 0.3; for medium-tight sand, between 0.25 and 0.4; and for tight sand, between 0.3 and 0.4 (Liu, 1992). Therefore, the Poisson s ratios derived from well log data for both THS-8 and GH-1 are reasonable for sandy soil. Young s modulus is generally below 10 4 psi for soil and is generally between 10 6 to 10 7 psi for sedimentary rock (Ramiah and Chickanagappa, 1990). The Young s modulus values derived from well log data are between 0.40 and psi for THS-8 (Figure 14; Table 4) and between 0.47 and psi for GH-1 (Table 5). All these Young s modulus values are below the range for sedimentary rock. This is reasonable because the aquifers in THS-8 and GH-1 are all unconsolidated sedimentary rock formations. Therefore, the corresponding shear modulus and bulk compressibility calculations can also be considered reasonable. From the results of formation-strength parameter calculations for each aquifer in THS-8 (Table 4), we can observe that the shear modulus and Young s modulus increase with depth, and that bulk compressibility decreases with depth. In terms of the formation strength of the THS-8 well, the weakest aquifer is THS8-B1 and the strongest is THS8-B6. This result is reasonable because THS8-B6 is the deepest aquifer and THS8- B1 is the shallowest. The general tendency is for formation strength to increase with depth, with the exception of THS8-B5, which is deeper than THS8-B4, but weaker than THS8-B4.

13 Table 4 Hydrogeologic characteristics and formation-strength calculations in the THS-8 well ( m) Aquifer THS8-B1 THS8-B2 THS8-B3 THS8-B4 THS8-B5 THS8-B6 Interval (m) Thickness (m) Hydrogeologic Vsh = 30% Vsh = 21% Vsh = 25% Vsh = 25% Vsh = 22% Vsh = 27% characteristics φ = 23% φ = 27% φ = 26% φ = 25% φ = 26% φ = 22% Rt = 33 ohm-m Rt = 40 ohm-m Rt = 32 ohm-m Rt = 30 ohm-m Rt = 25 ohm-m Rt = 23 ohm-m Rw = 3.54 ohm-m Rw = 3.54 ohm-m Rw = 5.88 ohm-m Rw = 3.54 ohm-m Rw = 3.2 ohm-m Rw = 3.3 ohm-m K = m/s K = m/s K = m/s K = m/s K = m/s K = m/s Shear modulus (10 6 psi) (avg a ) (0.249) (0.252) (0.271) (0.267) (0.264) (0.319) Bulk compressibility (10 6 psi 1 ) (avg) (1.7) (1.83) (1.67) (1.66) (1.73) (1.39) Poisson s ratio (avg) (0.321) (0.302) (0.304) (0.308) (0.304) (0.309) Young s modulus (10 6 psi) (avg) (0.66) (0.66) (0.70) (0.70) (0.69) (0.83) a avg = average. For hydrogeologic characteristics and formation strength parameters abbreviation, see Table 1. 13

14 Table 5 Hydrogeologic characteristics and formation-strength calculations in the GH-1 well ( m) Aquifer GH1-C1 GH1-C2 GH1-C3 GH1-C4 GH1-C5 GH1-C6 Interval (m) Thickness (m) Hydrogeology Vsh = 11% Vsh = 17% Vsh = 13% Vsh = 15% Vsh = 13% Vsh = 8% characteristics φ = 32% φ = 30% φ = 31% φ = 28% φ = 29% φ = 35% Rt = 30 ohm-m Rt = 35 ohm-m Rt = 28 ohm-m Rt = 28 ohm-m Rt = 40 ohm-m Rt = 26 ohm-m Rw = 6.12 ohm-m Rw = 5.33 ohm-m Rw = 4.69 ohm-m Rw = 5.31 ohm-m Rw = 5.84 ohm-m Rw = 6.04 ohm-m K = m/s K = m/s K = m/s K = m/s K = m/s K = m/s Shear modulus (10 6 psi) (avg a ) (0.282) (0.255) (0.27) (0.296) (0.345) (0.239) Bulk compressibility (10 6 psi 1 ) (avg) (1.77) (1.86) (1.85) (1.64) (1.46) (1.93) Poisson s ratio (avg) (0.29) (0.298) (0.287) (0.292) (0.287) (0.301) Young s modulus (10 6 psi) (avg) (0.72) (0.66) (0.70) (0.76) (0.89) (0.62) a avg = average. For hydrogeologic characteristics and formation strength parameters abbreviation, see Table 1. 14

15 Aquifer Formation-Strength Parameters 15 Figure 7. Shale volume of THS-8. Figure 8. Effective porosity of THS-8. c. Dispersed-shale Index Estimation in Groundwater Aquifer In the Anderson et al. (1973) and Tixier et al. (1795) studies, the dispersed-shale index (q) was introduced to calculate Poisson s ratio while the information of shear-wave transit time was lacking or not available. The dispersed-shale index [Eq. (8)] was calculated from sonic porosity (φ SV ) and density porosity (φ D ). In the sonic porosity calculation, the compaction factor (C p ), reflected consolidation and compaction, is the most important parameter for sonic-porosity calculation. Generally, the compaction factor is equal to 1.0 in a consolidated hydrocarbon formation, and varies from 1.0 to as high as 1.8 in unconsolidated groundwater aquifers (Dewan, 1983). In the present study, for the purpose of reflecting the unconsolidated condition, the compaction factor was close to 1.6, and a reasonable sonic porosity can be obtained by Eq. (9). But, in some depth intervals, the sonic porosity was smaller than the density porosity. An unreasonable negatively dispersed-shale index value was estimated by Eq. (8). If we constrained the dispersed-shale index to positive values only, the compaction factor should be adjusted to close to 1.0. A compaction factor close to 1.0 violates the unconsolidated condition, and estimated sonic porosity is generally larger than 50% (the highest value is 68%). Sonic porosity is obviously unreasonably high the compaction factor is close to 1.0 in order to comply with a positive value constraint.

16 16 B. Z. Hsieh et al. Figure 9. Formation resistivity of THS-8. Figure 10. Hydraulic conductivity of THS-8. In addition, in an unconsolidated groundwater aquifer, the suitable value of the compaction factor required both in the calculation of sonic porosity and the dispersed-shale index is unclear and subjective, and the dispersed-shale index equation [Eq. (8)] derived by Tixier et al. (1975) is not suitable for an unconsolidated groundwater aquifer. In this study, a new dispersed-shale index equation [Eq. (12)] for an unconsolidated groundwater aquifer was developed using the definitions of dispersed-shale index (Anderson et al., 1973), the formation density (FDC) log, and the natural gamma-ray (GR) log. The dispersed-shale index is calculated from density porosity (φ D ) and effective density porosity (φ D sh ) in our study. By using this new dispersed-shale index equation for unconsolidated groundwater aquifers, an unreasonably high sonic porosity can be avoided, the problem of compaction factor determination can be reduced, and a reasonable dispersed-shale index can be obtained. 5. Conclusions In this study, aquifer formation-strength parameters were estimated with a new dispersedshale index equation using well logging data. The conclusions based on our results are summarized as follows:

17 Aquifer Formation-Strength Parameters 17 Figure 11. Shear modulus in aquifers of THS-8. Figure 12. Bulk compressibility in aquifers of THS-8. (1) Poisson s ratio is estimated by the dispersed-shale index when lacking shearwave transit time data. This study suggested a reasonable dispersed-shale index equation to avoid the confusing input value of the compaction factor in an unconsolidated groundwater aquifer. (2) The well log data of the five wells (GH-1, SL-2, PTL-1, THS-5, and THS-8) in the southwestern coastal area of Yun-Lin were analyzed. Four aquifers of each well were identified using aquifer characteristics. The hydrogeologic characteristics (shale volume, effective porosity, true formation resistivity, formation water resistivity, and hydraulic conductivity) in each aquifer were calculated. The hydrogeologic characteristics (formation water resistivity and hydraulic conductivity) derived from well logs were compared with field measurements and found to be very close. (3) The formation-strength parameters (shear modulus, bulk compressibility, Poisson s ratio, and Young s modulus) of aquifers in the THS-8 and GH-1 wells between 310 to 500 m deep were calculated using the complete well log data, which included both FDC and BHC data. The log-derived Poisson s ratios and Young s modulus are reasonable for unconsolidated formation. Both the shear modulus, ranging from 0.15 to psi, and Young s modulus, ranging from 0.40 to psi, increase with depth, whereas bulk compressibility, ranging from 1.2 to psi 1, decreases with increasing depth.

18 18 B. Z. Hsieh et al. Figure 13. Poisson s ratio in aquifers of THS-8. Figure 14. Young s modulus in aquifers of THS-8. Acknowledgments Special thanks to Dr. C. Lewis for his discussion and invaluable comments on this study. Thanks also to the China Petroleum Corporation for providing well log data. This work was supported by grants NSC M from the National Science Council of Taiwan and 85EC2A from the Water Resources Agency of the Ministry of Economic Affairs of Taiwan. References Anderson, R. A., Ingram, D. S., and Zanier, A. M Determining fracture pressure gradients from well logs. J. Petrol. Tech. 25: Asquith, G., and Gibson, C Basic Well Log Analysis for Geologists. Tulsa, OK: AAPG. Chiang, C. J Taiwan Groundwater Monitoring Network Choushuichi Alluvial Fan Hydrogeological Investigation Report, Year 1992 to Taipei: Central Geological Survey of the Ministry of Economic Affairs of Taiwan (in Chinese). Crain, E. R The Log Analysis Handbook Volume I Quantitative Log Analysis Methods. Tulsa, OK: PennWell Publishing Company. Dewan, J. T Essentials of Modern Open-Hole Log Interpretation. Tulsa, OK: PennWell Publishing Company. Jorgensen, D.G Estimating geophysical properties from borehole-geophysical logs. Ground Water Monitor. Rev. 11: Lin, Z. S., Chen, S. T., and Lee, C. H Investigation of Stratigraphic Units and Hydrogeological Properties in the Formation of Yun-Lin Subsidence Area. Taipei: Water Resources Agency of the Ministry of Economic Affairs of Taiwan (in Chinese).

19 Aquifer Formation-Strength Parameters 19 Liu, H. S Principles of Geotechnical Engineering. Taipei: Scientific and Technical Publishing Co., Ltd. (in Chinese). Paillet, F. L., and Crowder, R. E A generalized approach for the interpretation of geophysical well logs in ground-water studies theory and application. Ground Water 34: Ramiah, B. K., and Chickanagappa, L. S Handbook of Soil Mechanics and Foundation Engineering, 2nd ed. Rotterdam: A. A. Balkema. Stein, N., and Hilchie, D. W Estimating the maximum production rate possible from friable sandstones without using sand control. J. Petrol. Tech. 24: Temples, T. J., and Waddell, M. G Application of petroleum geophysical well logging and sampling techniques for evaluating aquifer characteristics. Ground Water 34: Tixier, M. P., Loveless, G. W., and Anderson, R. A Estimation of formation-strength from mechanical-properties log. J. Petrol. Tech. 27: Wyllie, M. R. J., and Rose, W. D Some theoretical considerations related to the quantitative evaluation of the physical characteristics of reservoir rock from electrical log data. J. Petrol. Tech. 189: