TY - JOUR
AU - Chen,, Xiangyang
AB - Abstract Total water saturation is an important parameter for calculating the free gas content of shale gas reservoirs. Owing to the limitations of the Archie formula and its extended solutions in zones rich in organic or conductive minerals, a new method was proposed to estimate total water saturation according to the relationship between total water saturation, VP-to-VS ratio and total porosity. Firstly, the ranges of the relevant parameters in the viscoelastic BISQ model in shale gas reservoirs were estimated. Then, the effects of relevant parameters on the VP-to-VS ratio were simulated based on the partially saturated viscoelastic BISQ model. These parameters were total water saturation, total porosity, permeability, characteristic squirt-flow length, fluid viscosity and sonic frequency. The simulation results showed that the main factors influencing VP-to-VS ratio were total porosity and total water saturation. When the permeability and the characteristic squirt-flow length changed slightly for a particular shale gas reservoir, their influences could be neglected. Then an empirical equation for total water saturation with respect to total porosity and VP-to-VS ratio was obtained according to the experimental data. Finally, the new method was successfully applied to estimate total water saturation in a sequence formation of shale gas reservoirs. Practical applications have shown good agreement with the results calculated by the Archie model. total water saturation, VP-to-VS ratio, viscoelastic BISQ model, shale gas reservoirs Introduction Shale gas reservoirs have produced considerable amounts of gas worldwide and have become the main unconventional energy source in recent years in China. Water saturation is one of the key parameters for estimating shale gas content, so an accurate method of estimating water saturation is required. The most accurate and reliable methods for determining water saturation are laboratory measurements, such as Dean–Stark on crushed samples (Glorioso and Rattia 2012). However, there are some drawbacks such as limited samples and high costs. The common method of estimating water saturation is logging interpretation, mainly using the Archie formula (Archie 1942), its extended solutions in shaly formations (Simandoux 1963, Poupon and Leveaux 1971, Bassiouni 1994) and other improved methods (Kadkhodaie and Rezaee 2016, Zhang and Xu 2016). Methods based on resistivity and porosity are not always feasible in shale reservoirs rich in organic or conductive minerals (Wu and Aguilera 2012, Mashaba and Altermann 2015). Clay content and kerogen are the two main factors influencing the resistivity of shales. The presence of kerogen as non-conductive materials causes a reduction in rock conductivity that results in underestimation of water saturation (Passey et al1990, Kadkhodaie and Rezaee 2016). Also, the electrical parameters are not easy to determine in the laboratory. Meanwhile the salinity of water saturation may vary a lot from a thousand to a few hundred thousand ppm in the same shale gas formation. So the Archie formula and its extended solutions used in shaly formations do not always work well in shale gas reservoirs. Kadkhodaie and Rezaee (2016) used compensation of kerogen and shale conductivities to develop an effective equation for estimating water saturation in shale gas reservoirs; the equation was independent of electrical parameters and water saturation in the formation, but it requires the total organic carbon (TOC) content based on experimental analysis to be acquired in advance. Zhang and Xu (2016) proposed two new methods to estimate water saturation using the relationship between TOC, core water saturation and calculated water saturation. However, the two methods did not consider that conductive pyrite and other heavy minerals, which are often associated with organic matter, may also decrease the resistivity (Sondergeld et al2010, Glorioso and Rattia 2012). Mavko et al (2005a) used rock physics models to compute the P-wave and S-wave attenuation curves. The results showed that the presence of gas significantly affected the P-wave attenuation. Sun et al (2000) proposed a modified method for estimating P-wave and S-wave attenuation logs from monopole sonic data, and the increase in S-wave attenuation and decrease in P-wave attenuation were related to the oil zones. Mavko et al (2005b) acquired the relationship between VP-to-VS ratio (VP/VS) and P-to-S wave inverse quality factor based on a lot of assumptions. The results showed that the P-to-S wave inverse quality factor increased with increasing VP/VS ratio. Sonic attenuation is an effective way to evaluate the energy loss of a formation and is also one of the important signs of oil and gas. It is shown that the response of the P-to-S wave attenuation ratio is much more sensitive than the P-to-S wave velocity ratio within a nearby formation. However, it is very difficult to calculate the sonic attenuation from the full-wave logging data. Most methods for estimating attenuation are based on the hypothesis that each receiver has the same sensitivity to acoustic attenuation. In fact, many factors affect the estimation of attenuation (i.e. undeterminable borehole fluid attenuation, off-centered tool, geometrical diffusion, disturbance and scattering of waves caused by irregular borehole size and thin-layer formations) (Sun et al2000). However, the velocities of P waves and S waves can be obtained more accurately from the full-wave data. Therefore, this paper uses the P-to-S wave velocity ratio instead of P-to-S wave attenuation ratio to estimate the water saturation. Sun et al (2016) used the VP/VS ratio to identify fluid properties, but few attempts have been made to estimate the water saturation by using this ratio. The basic principle that makes the VP/VS ratio capable of calculating water saturation is based on the fact that the P-wave velocity decreases dramatically when a small amount of gas is present in fluid-filled sand at a fixed porosity of a specific rock skeleton. However, when the gas saturation continues to increase, the P-wave velocity changes gradually (Wu 2000). In a fluid-filled porous medium, fluid has little effect on the shear modulus (Gregory 1976), so the S-wave velocity changes little with the change in gas saturation. In this paper, we propose a new method for estimating total water saturation in shale gas reservoirs based on the relationship between total water saturation, VP/VS ratio and total porosity. Using the viscoelastic BISQ model, the sensitivity of influencing factors for water saturation was analyzed. Firstly, the ranges of the relevant parameters in the viscoelastic BISQ model were estimated in shale gas reservoirs of the studied area. Secondly, the P-wave and S-wave velocities were calculated with the relevant parameters using the BISQ model. The effects of water saturation, porosity, permeability, characteristic squirt-flow length, fluid viscosity and sonic frequency on the VP/VS ratio were then analyzed. The main factors influencing the VP/VS ratio were obtained, which were porosity and water saturation. Finally, the relationship between the VP/VS ratio, porosity and water saturation was obtained, and the empirical equation of water saturation was acquired from the experimental data. The new method was applied well in the YS shale gas field, and it proved to have good agreement with the results from the Archie formula. Mathematical model of water saturation Biot (1956) derived the formula for predicting the theoretical velocity of waves in saturated rock from the properties of the dry rock, which correlated the properties of the pore fluid with the rock mineral skeleton. Murphy et al (1991) proposed the velocity properties of the Gassmann equation: ρVp2=Kp+Kd+43ud 1 ρVs2=ud 2 where Kp=1-KdKma2φKf+1-φKma-KdKma2 3 Kd=Kma(1-β) 4 ud=Uma(1-β). 5 Here VP and VS are the P-wave and S-wave velocities of saturated rocks respectively; Kd and ud are the bulk modulus and shear modulus for dry porous rock skeleton respectively; Kma and Uma are the bulk modulus and shear modulus of the grains respectively; Kf is the bulk modulus of the composite fluid; φ is the porosity; β is the Biot coefficient, which can be written as β = 1 – (1 – φ)3/(1–φ). At a sufficiently low frequency, when the pore fluid is a mixture of gas and water, the bulk modulus of the composite fluid can be estimated as 1/Kf=Sw/Kw+(1-Sw)/Kg 6 where Sw is water saturation, and Kw and Kg are bulk moduli of water and gas respectively. Usually, the gas modulus is 0.05 GPa, which is much smaller than the bulk modulus of brine, which is 2.25 GPa (Tang et al2012). Thus the bulk modulus of the composite fluid is controlled mainly by the gas modulus and gas saturation. When the minerals that make up the rock are fixed, both the bulk and shear moduli of grains are constants. By analyzing the above equations, it can be concluded that the variation of VP/VS ratio is related only to porosity and water saturation, and the ratio can be given as Vp/Vs=f(Sw,φ). 7 Then the equation for water saturation with respect to porosity and VP/VS ratio can be obtained. It should be noted that the Gassmann equation is valid only with very low-frequency seismic data (<100 Hz), and the results of the Gassmann equation is worse when the frequency is reaching the sonic logging frequency (104 Hz). So it is necessary to analyze the other factors that affect the VP/VS ratio for sonic logging (Mavko et al2009). Biot theory has shown that elastic waves propagate in saturated porous media with dispersion, but in many cases the velocity dispersions predicted by this theory are lower than the actual ones. Many results show that the squirt flow is the main reason for high dispersion of elastic wave propagation in a fluid medium. The BISQ model was proposed, which related the microscopic jet flow mechanism with the macroscopic characters of solid and fluid (Dvorkin and Nur 1993). The BISQ model has the same advantages as the Biot theory in describing the elastic properties of the pores, moreover it can predict the elastic wave velocity more exactly than the squirt flow theory (Dvorkin and Nur 1993, Yang and Chen 2001, Fang and Yang 2015). Dahl and Spikes (2016) showed that the P and S waves are relatively sensitive to squirt flow. Porosity and water saturation both have significant effects on attenuation and dispersion (Chapman et al2014, Zhang and He 2015). Nie and Yang (2008) suggested that the clay within sandstones was one of the key factors for the high attenuation in clay-bearing sandstones during wave propagation. Nie et al (2008) proposed a generalized viscoelastic BISQ model to take into account the Biot-flow mechanism, the squirt-flow mechanism and the viscoelasticity in clay-bearing sandstones based on Dvorkin's elastic BISQ model. The model could be applied to adequately describe the attenuation coefficient and phase velocity in clay-bearing sandstones with different permeabilities. Nie et al (2012) considered the water saturation and provided an improved viscoelastic BISQ model in partially saturated porous media. The improved model was adequate for predicting the wave velocity and attenuation in different water saturations in clay-bearing sandstones. The phase velocities of P waves and S waves are as follows. Vp1,P2=Re12A1(-B1±B12-4A1C)VS1,S2=Re12A2(-B2±B22-4A2C) 8 where A1=M*ρ22[φFsq+2φη(-iω)] 9 B1=1ρ2Fsqα1+ρ2*ρ2-φρ1*+ρ2*ρ2-M*+Fsqα2φ1+ρaρ2+iωcω+Ω 10 A2=G*ρ22[φη(-iω)] 11 B2=1ρ2-G*1+ρaρ2+iωcω+12Ω 12 Ω=-2η(-iω)φρ1*ρ2+αρaρ2+iωcω 13 C=ρ1*ρ2+ρ1*+ρ2*ρ2ρaρ2+iωcω 14 M*=Me(1+CVδM),δM=MVMe(-iω) 15 Me=λe+2Ge,MV=λV+2GV 16 ρf=Swρw+(1-Sw)ρg 17 ρ1*=ρ1(1+CVδp),ρ2*=ρ2(1+δp),δp=JV(-iω) 18 ρ1=(1-φ)ρs,ρ2=φρf 19 G*=Ge(1+CVδG),δG=GVGe(-iω) 20 ωc=ηφ/kρf 21 CV=Cclaye(1-k/k0) 22 where CV is the viscoelastic parameter correction factor; Cclay is the clay content; k is the permeability; k0 is the reference permeability; ω is the characteristic angular frequency; η is the water viscosity coefficient; δG, δp and δM are the viscoelastic parameters; ρs and ρf are the densities of mixed mineral particles and composite fluid respectively; ρw and ρg are the densities of water and gas respectively; ρa is the additional density caused by the fluid; λe and Ge are the Lamé coefficients; λV and GV are the viscoelastic coefficients; Fsq is the squirt coefficient and is defined as (Dvorkin and Nur 1993) Fsq=F1-2J1(λqR)λqRJ0(λqR) 23 λq2=ρfω2Fφ+ρa/ρfφ+iωcω 24 1F=1Kf+1φKma1-φ-KdKma 25 where R is the average squirt-flow length, which is of the same order of magnitude as the average particle size or the mean fracture length (Mavko et al2009). Estimating key parameters for the viscoelastic BISQ model Shale gas reservoirs tend to be unique and lithologically complex, containing clay, quartz, feldspar, carbonate, pyrite and so on. Conceptually, shale's matrix is comprised of inorganic detritus and kerogen. Curtis (2002) showed that gas was adsorbed onto kerogen and clay-particle surfaces, which accounted for the pore space, and free gas and water was stored in natural fractures and intergranular pores. Prior to estimating water saturation, an appropriate model must be established regarding the distribution in the porous system and the place where the pore-saturating fluids are preferentially retained. In a hypothetical shale gas scenario, different fluids were distributed between kerogen pores and the inorganic matrix as shown in figure 1 (Glorioso and Rattia 2012). Using effective porosity to estimate water saturation failed to clearly define the treatment of adsorbed gas in clays, which affects porosity and resistivity logs. Thus it would be unreliable to estimate free gas content using effective porosity and effective water saturation. So Glorioso and Rattia (2012) suggested estimating total water saturation. Figure 1. View largeDownload slide Fluid distribution in porous shale, including natural fractures. Figure 1. View largeDownload slide Fluid distribution in porous shale, including natural fractures. In order to study the major and minor factors influencing the VP/VS ratio in shale gas reservoirs based on the viscoelastic BISQ model, the ranges of the relevant parameters in this model must be estimated. Firstly, the elastic modulus of grains MH has to be estimated from the Hill average equation (Hill 1952) according to the mineral composition. The Hill average equation is often used to estimate the equivalent elastic modulus for a homogeneous matrix with fixed rock components. Secondly, the ranges of relevant parameters can be estimated according to the characteristics of the logging curves and previous research results. Within shales the clay content is highly variable and clays are commonly associated with small grain size (<1/256 mm or <3.9 μm) (Sondergeld et al2010). Also, the pore sizes in shale gas reservoirs are very small (Wang and Reed 2009). Sondergeld et al (2010) suggested that the range of pore dimensions is 5 to 1000 nm from measurements using NMR and mercury injection capillary pressure. Meanwhile, shale gas reservoirs have very low porosity and permeability compared to conventional reservoirs. In the study area, the depth of the shale gas reservoirs is about 2000–2600 m. The temperature of the shale reservoirs is estimated to be 65 °C–77 °C when the surface temperature is 25 °C and the geothermal gradient is 20 °C km–1. Meanwhile, the phenomenon of overpressure is very common, caused mainly by the low compaction mechanism, and the Eaton empirical formula can be used to estimate the pore pressure. When the pore pressure is 50 MPa, the viscosity of water changes from 0.2 × 10–3 to 0.5 × 10–3 Pa s, but it is almost unchanged with increasing pore pressure (Qin and Li 2006). The center frequency of full-wave logging is generally 1000–10000 Hz. Typically, the mineral weight fractions can be obtained based on ECS logging, that is to say, ECS results give the mineral contents of the skeleton. Thus we can estimate the bulk modulus and shear modulus of the grains from the Hill average equation. The estimated results are shown in track 8 of figure 2, and the average bulk and shear moduli are 36 GPa and 29 GPa respectively. Meanwhile, the other relevant parameters are also shown in figure 2. The VP/VS ratio is in the range 1.6–1.7 as acquired by sonic scanner logging. The total porosity (PHIT) varies in the range 0.03–0.08 and the effective porosity (PIGE) varies in the range 0.01–0.06, both from NMR logging. When paramagnetic minerals are not present in the matrix, NMR logging is very useful for measuring porosity independently from the composition of the matrix. The T2 spectral area is proportional to the number of hydrogen nuclei in the pore fluid within the depth of the probe; the corresponding scale factor can be obtained from the porosity and T2 spectral area of the standard samples, so that the area can be converted to the total porosity, which is in good agreement with the result of core analysis (red dots on track 5 in figure 2). Effective porosity can be considered as capillary-bound water plus free fluids, so the T2 cutoff of 3 ms is used to divide the effective porosity. The method is independent of lithology and does not need to calculate the volume of shale. The total water saturation estimated from the Archie formula mainly ranges from 40% to 80%, and the permeability mainly ranges from 0.0001 mD to 0.01 mD from the KSDR model. ECS logging is a geochemical log that quantifies Si, Ca, Fe, S, Ti and Gd plus other elements. The volume of minerals can be obtained from accurate element contents using the empirical relationship, which is based on a large number of core analysis data. The ECS logging results show that in this well the volume fraction of clay is in the range 30%–50% with about the same proportion of sand; the volume fraction of carbonate is small and ranges from 5% to 20%, and the pyrite content is less and mainly in the lower part of the shale reservoir. The ECS logging results are in good agreement with the results of core analysis by x-ray diffraction (XRD, pink dots and blue dots on track 9 in figure 2). Thus the appropriate values of the relevant parameters can be estimated as shown in table 1 for the viscoelastic BISQ model in such reservoirs. Figure 2. View largeDownload slide Conventional logging curves, interpretation of reservoir parameters and the mineral components for the shale gas reservoir of well Y1. The track description from left to right is as follows. Track 1: borehole diameter (CAL) and gamma ray (GR); Track 2: compensated neutron logging (CNL), density logging (DEN) and acoustic travelling time (AC); Track 3: array lateral resistivity logging; Track 4: depth; Track 5: core porosity (red dots), total water saturation (SW), total porosity (PHIT) and effective porosity (PIGE); Track 6: permeability (KSDR); Track 7: slowness of compressional (DTCO) and shear (DTSM) waves and VP/VS ratio (VpVs); Track 8: bulk modulus (Kma) and shear modulus (Uma) of mineral particles; Track 9: mineral components (V/V) by ECS logging, and volume fraction of mineral components with results of XRD analysis (clay volume fraction with pink dots and sandy volume fraction with blue dots). Figure 2. View largeDownload slide Conventional logging curves, interpretation of reservoir parameters and the mineral components for the shale gas reservoir of well Y1. The track description from left to right is as follows. Track 1: borehole diameter (CAL) and gamma ray (GR); Track 2: compensated neutron logging (CNL), density logging (DEN) and acoustic travelling time (AC); Track 3: array lateral resistivity logging; Track 4: depth; Track 5: core porosity (red dots), total water saturation (SW), total porosity (PHIT) and effective porosity (PIGE); Track 6: permeability (KSDR); Track 7: slowness of compressional (DTCO) and shear (DTSM) waves and VP/VS ratio (VpVs); Track 8: bulk modulus (Kma) and shear modulus (Uma) of mineral particles; Track 9: mineral components (V/V) by ECS logging, and volume fraction of mineral components with results of XRD analysis (clay volume fraction with pink dots and sandy volume fraction with blue dots). Table 1. Basic parameters and values of the viscoelastic BISQ model. Parameters Kma Uma ρs Kw ρw Kg ρg Unit GPa GPa kg m–3 GPa kg m–3 GPa kg m–3 Value 36 29 2715 2.25 1000 0.05 125 Parameters R Frequency η k φ ρa Sw Unit mm Hz Pa s mD % kg m–3 % Value 2 8000 0.5 × 10–3 0.001 6 420 50 Parameters Kma Uma ρs Kw ρw Kg ρg Unit GPa GPa kg m–3 GPa kg m–3 GPa kg m–3 Value 36 29 2715 2.25 1000 0.05 125 Parameters R Frequency η k φ ρa Sw Unit mm Hz Pa s mD % kg m–3 % Value 2 8000 0.5 × 10–3 0.001 6 420 50 View Large Table 1. Basic parameters and values of the viscoelastic BISQ model. Parameters Kma Uma ρs Kw ρw Kg ρg Unit GPa GPa kg m–3 GPa kg m–3 GPa kg m–3 Value 36 29 2715 2.25 1000 0.05 125 Parameters R Frequency η k φ ρa Sw Unit mm Hz Pa s mD % kg m–3 % Value 2 8000 0.5 × 10–3 0.001 6 420 50 Parameters Kma Uma ρs Kw ρw Kg ρg Unit GPa GPa kg m–3 GPa kg m–3 GPa kg m–3 Value 36 29 2715 2.25 1000 0.05 125 Parameters R Frequency η k φ ρa Sw Unit mm Hz Pa s mD % kg m–3 % Value 2 8000 0.5 × 10–3 0.001 6 420 50 View Large Theoretical modeling results and discussion In order to investigate the main factors influencing the VP/VS ratio, the effects of relevant parameters on this ratio were simulated based on the partially saturated viscoelastic BISQ model. These parameters were porosity, water saturation, permeability, characteristic squirt-flow length, fluid viscosity and sonic frequency. The simulation results are shown in figures 3 and 4. The other parameters were chosen to be the same as in the example of Nie et al (2012), that is, clay content Cclay = 0.4, viscoelastic parameters δG = δp = 0.2, δM = 0.22. The Hill average equation was adopted for estimating the elastic modulus of the composite fluid. Figure 3. View largeDownload slide The effect of porosity. VP/VS ratio versus porosity for total water saturation = 10%, 30%, 50%, 70% and 90%. Figure 3. View largeDownload slide The effect of porosity. VP/VS ratio versus porosity for total water saturation = 10%, 30%, 50%, 70% and 90%. The effect of porosity on VP/VS ratio was examined for water saturation equal to 10%, 30%, 50%, 70% and 90%. Curves of VP/VS ratio against porosity for these five cases are shown in figure 3. With increasing porosity, the VP/VS ratio gradually increased at a fixed water saturation, and the two obeyed an exponential rule. Meanwhile for a fixed porosity, the VP/VS ratio increased with increasing water saturation. Similarly, in order to investigate the effect of water saturation on VP/VS ratio we examined different relevant parameters. Firstly, we examined a range of porosity equal to 2%, 4%, 6%, 8%, 10% and 12%. At a fixed porosity, the VP/VS ratio increased gradually with increasing water saturation. When there was only a small amount of gas left in fluid-filled pores, the VP/VS ratio increased dramatically. And the two obeyed an exponential rule (figure 4(a)). Secondly, we examined a range of permeability equal to 10–5 mD, 10–4 mD, 10–3 mD and 10–2 mD. At a fixed water saturation, when the permeability changed from 10–5 mD to 10–2 mD, the VP/VS ratio was basically unchanged (figure 4(b)). Thirdly, we examined a range of characteristic squirt lengths equal to 10 nm, 50 nm, 100 nm, 1 mm, 5 mm and 10 mm. The first three represented cases without microfractures, and the latter three represented cases with microfractures. Without microfractures the VP/VS ratio remained essentially unchanged. Similarly, when containing microfractures, the VP/VS ratio had the same characteristics as for a fixed water saturation. However, the VP/VS ratio varied widely between the two cases (figure 4(c)). Fourthly, we examined a range of viscosity equal 0.1 × 10–3 Pa s, 0.5 × 10–3 Pa s and 1 × 10–3 Pa s. At a fixed water saturation, when the viscosity changed from 0.1 × 10–3 Pa s to 10–3 Pa s, the VP/VS ratio was basically unchanged (figure 4(d)). Similarly, when the frequency changed from 103 to 104 Hz, the VP/VS ratio was basically unchanged at a fixed water saturation (figure 4(e)). Figure 4. View largeDownload slide The effect of water saturation. (a) VP/VS ratio versus total water saturation for porosity = 2%, 4%, 6%, 8%, 10% and 12%. (b) VP/VS ratio versus water saturation for permeability = 10–5 mD, 10–4 mD, 10–3 mD and 10–2 mD. (c) VP/VS ratio versus water saturation for squirt-flow length = 10 nm, 50 nm, 100 nm, 1 mm, 5 mm and 10 mm. (d) VP/VS ratio versus water saturation for viscosity = 0.1 × 10–3 Pa s, 0.5 × 10–3 Pa s and 1 × 10–3 Pa s. (e) VP/VS ratio versus water saturation for frequency = 1000 Hz, 5000 Hz and 10 000 Hz. Figure 4. View largeDownload slide The effect of water saturation. (a) VP/VS ratio versus total water saturation for porosity = 2%, 4%, 6%, 8%, 10% and 12%. (b) VP/VS ratio versus water saturation for permeability = 10–5 mD, 10–4 mD, 10–3 mD and 10–2 mD. (c) VP/VS ratio versus water saturation for squirt-flow length = 10 nm, 50 nm, 100 nm, 1 mm, 5 mm and 10 mm. (d) VP/VS ratio versus water saturation for viscosity = 0.1 × 10–3 Pa s, 0.5 × 10–3 Pa s and 1 × 10–3 Pa s. (e) VP/VS ratio versus water saturation for frequency = 1000 Hz, 5000 Hz and 10 000 Hz. The above examples show that for the shale reservoirs in the studied area, the main factors affecting the VP/VS ratio are water saturation and porosity. Whether the reservoirs contain fractures also has an effect on VP/VS ratio, and it has a great influence on the permeability of formation and its characteristic squirt length. Fluid viscosity and full-wave logging frequency have negligible effect on the VP/VS ratio. Based on the above analysis, a relationship can be obtained between VP/VS ratio, porosity and water saturation when the degree of development of fractures in a stratum can be assumed to be consistent: VP/VS=a1φa2Swa3 26 where a1, a2 and a3 are the empirical coefficients to be determined. Taking into account the effects of mineral grains changing, the background value of the VP/VS ratio (VpVs0) is introduced into the equation to counteract the effects of lithological differences; this represents the VP/VS ratio under full water saturation. When the composition of rock minerals changes, the background value should also be adjusted accordingly. Thus the equation for water saturation can be acquired, which can be written as equation (27), in which xa, xm and xn are empirical coefficients. Sw=xa(Vp/Vs/VpVs0)xnφxm 27 The experimental results of the analysis of water saturation show that the average water saturation is 63% and the average gas saturation is 37% in the studied area. Generally the slowness of compressional and shear waves can be obtained through dipole sonic logging, then getting the VP/VS ratio. We have studied the correlation between experimental water saturation, experimental porosity and VP/VS ratio by dipole sonic logging, then obtaining the regression formula, and xa = 0.21, xm = 0.4 and xn = 2.1, with R2 = 0.71. Then using the regression coefficients we have estimated the water saturations, which are in good agreement with water saturations from core analysis shown in figure 5. The figure is a self-checking plot, and the relative range of error is 2% to 20%; the average error is 7.3%. Figure 5. View largeDownload slide Comparison between results of the measured data and estimated water saturation; the two are in good agreement. Figure 5. View largeDownload slide Comparison between results of the measured data and estimated water saturation; the two are in good agreement. Application Figures 6 and 7 show the results of total water saturation of shale gas reservoirs in the YS area with the Archie formula and the new method. The interpretation of sonic velocities and the VP/VS ratio are shown in Track 5. The VP/VS ratio decreases gradually with increasing depth. The total porosity (shown by Track 6) from NMR logging is seen to compare favorably with core data (red dots shown on Track 6). The TOC content (shown by Track 8) is quantified based on the correlation established through the laboratory and density logging, and the estimated TOC content is very consistent with the core data (red dots shown on Track 8). The presence of kerogen and hydrocarbons will increase the resistivity of the rock. The results for their volume fractions shown in Track 11 are obtained using an optimized interpretation of the ECS results, TOC content and well logs. The results show that the reservoirs contain a variable fraction of clay, between 30% and 50%. The main type of clay is illite, with a small amount of chlorite. For the resistivity logging, the larger is the clay fraction, the lower is the rock resistivity. The volume of pyrite (shown on Track 10) in shale gas reservoirs is low, less than 0.02%. However, pyrite in the form of a banded distribution can lead to abnormally low values of resistivity. The presence of conductive minerals has a significant effect on resistivity according to the logging curves. Figure 6. View largeDownload slide Results of estimation of water saturation of well Y1 in the studied area. The track description from left to right is as follows. Track 1: borehole diameter (CAL) and gamma ray (GR); Track 2: compensated neutron logging (CNL), density logging (DEN) and acoustic slowness (AC); Track 3: array lateral resistivity logging (RLA1, RLA2, RLA3, RLA4 and RLA5); Track 4: depth; Track 5: compressional wave slowness (DTCO), shear wave slowness (DTSM) and VP/VS ratio (VP/VS); Track 6: effective porosity (PIGE), total porosity (PHIT) and core porosity (red dots), Track 7: formation permeability by NMR logging (KSDR); Track 8: TOC content (TOC) and core TOC (red dots); Track 9: water saturation by the Archie formula (SW_Archie), water saturation by the new method (SW_Sonic) and core measured data (red dots); Track 10: the volume fraction of pyrite (VPYR); Track 11: ELANPlus volumes. Figure 6. View largeDownload slide Results of estimation of water saturation of well Y1 in the studied area. The track description from left to right is as follows. Track 1: borehole diameter (CAL) and gamma ray (GR); Track 2: compensated neutron logging (CNL), density logging (DEN) and acoustic slowness (AC); Track 3: array lateral resistivity logging (RLA1, RLA2, RLA3, RLA4 and RLA5); Track 4: depth; Track 5: compressional wave slowness (DTCO), shear wave slowness (DTSM) and VP/VS ratio (VP/VS); Track 6: effective porosity (PIGE), total porosity (PHIT) and core porosity (red dots), Track 7: formation permeability by NMR logging (KSDR); Track 8: TOC content (TOC) and core TOC (red dots); Track 9: water saturation by the Archie formula (SW_Archie), water saturation by the new method (SW_Sonic) and core measured data (red dots); Track 10: the volume fraction of pyrite (VPYR); Track 11: ELANPlus volumes. Figure 7. View largeDownload slide Results of estimation of water saturation of well Y2 in the studied area. The track description from left to right is as follows. Track 1: gamma ray (GR) and borehole diameter (CAL); Track 2: compensated neutron logging (CNL), density logging (DEN); Track 3: resistivity logging (RD, RS and RMLL); Track 4: depth; Track 5: compressional wave slowness (DTCO), shear wave slowness (DTSM) and VP/VS ratio (VP/VS); Track 6: effective porosity (PIGN), total porosity (PHIT) and core porosity (red dots), Track 7: formation permeability (PERM); Track 8: TOC content (TOC) and core TOC (red dots); Track 9: water saturation by the Archie formula (SW_Archie) and water saturation by the new method (SW_Sonic); Track 10: the volume fraction of pyrite (VPYR); Track 11: ELANPlus volumes. Figure 7. View largeDownload slide Results of estimation of water saturation of well Y2 in the studied area. The track description from left to right is as follows. Track 1: gamma ray (GR) and borehole diameter (CAL); Track 2: compensated neutron logging (CNL), density logging (DEN); Track 3: resistivity logging (RD, RS and RMLL); Track 4: depth; Track 5: compressional wave slowness (DTCO), shear wave slowness (DTSM) and VP/VS ratio (VP/VS); Track 6: effective porosity (PIGN), total porosity (PHIT) and core porosity (red dots), Track 7: formation permeability (PERM); Track 8: TOC content (TOC) and core TOC (red dots); Track 9: water saturation by the Archie formula (SW_Archie) and water saturation by the new method (SW_Sonic); Track 10: the volume fraction of pyrite (VPYR); Track 11: ELANPlus volumes. In the understratum of shale gas reservoirs in well Y1, the content of organic matter is more than 2%, the borehole condition is better, and the volume fraction of clay is stable compared with the upper formation of shale gas reservoirs. So the resistivity value should increase. However, the deep resistivity appears to be abnormally low, it corresponds to the pyrite enrichment in the lower part of the reservoir, and striped pyrite can greatly reduce the resistivity of shale gas reservoirs. In track 9, water saturation is estimated by the Archie formula (SW_Archie) and by the new method (SW_Sonic). Water saturation is positively correlated with the VP/VS ratio and negatively correlated with total porosity. On the whole, the two trends of water saturation are basically the same, showing that both methods can be used to estimate water saturation. However, the two are quite different in some details, such as pyrite-rich zones. As we can see, in well Y1 the average error relative to the core water saturation is 7.3% by the new method 10.7% by Archie formula. The new method improves the accuracy in calculating the water saturation. In well Y2, in the lower part of the reservoir, we can see the same scenario (i.e. enrichment of pyrite and abnormal low resistivity), and this could result in inaccurate estimation of water saturation by the Archie formula. Conclusions In this paper, the effects of relevant parameters on the VP/VS ratio were simulated on the basis of the viscoelastic BISQ model. The results of the simulation show that the main factors influencing the VP/VS ratio are total porosity and total water saturation. Using these results, a new equation for estimating the total water saturation was proposed based on the relationship between total water saturation, VP/VS ratio and total porosity. Then according to the experimental data, the complete empirical equation was acquired. The new method was successfully applied in the logging data to estimate the water saturation of sequential formation. Compared with the Archie formula, in which it is difficult to determine the electrical parameters and the salinity of water in a formation, the new method provides a simple and effective way to estimate water saturation and avoids many drawbacks in shale gas reservoirs with conductive minerals and non-conductive organic matter. In addition, it does not need the TOC content based on experimental analysis to be acquired in advance. And it is very important for calculating the free gas content, and then estimating the gas initially in-place (GIIP). Acknowledgments The authors would like to thank the National Natural Science Foundation of China (No. 41374124) for their sponsorship and permission to publish the study results. References Archie G E . , 1942 The electrical resistivity log as an aid in determining some reservoir characteristics , Trans. 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TI - A new method for calculation of water saturation in shale gas reservoirs using VP-to-VS ratio and porosity
JF - Journal of Geophysics and Engineering
DO - 10.1088/1742-2140/aa83e5
DA - 2018-02-01
UR - https://www.deepdyve.com/lp/oxford-university-press/a-new-method-for-calculation-of-water-saturation-in-shale-gas-84IUR7Tit0
SP - 224
VL - 15
IS - 1
DP - DeepDyve
ER -