SPECIAL 2 SECTION: C O 2 AVO modeling of pressure-saturation effects in Weyburn sequestration JINFENG MA, State Key Laboratory of Continental Dynamics, Northwest University, China IGOR MOROZOV, University of Saskatchewan, Canada The Weyburn Field in southeastern Saskatchewan, Canada (Figure 1) was discovered in 1954 and has been water-flooded since the 1960s. In October 2000, injection of for enhanced oil recovery was started by EnCana, concurrently with a multidisciplinary International Energy Agency Greenhouse Gas (IEA GHG) Monitoring and Storage Project (CO2MSP). In order to monitor injection, storage, and oil recovery, several vintages of 3D and 3D/3-C data were acquired, starting with a baseline survey in December 1999. These time-lapse data sets were used to evaluate the quality and safety of sequestration, and monitor the reservoir pressure front, water flooding, and bypassed oil (White et al., 2004). Several geophysical studies were conducted during Phase I of CO2MSP (White, 2009); however, the potential of the 3D/3-C data sets for monitoring the propagation still has not been fully explored. In this study, we analyze the 3-C data sets to extract the shear-wave properties of the reservoir by using advanced AVO analysis. We focus on using forward modeling to develop AVO attributes that could be used for separating the pore-pressure and saturation effects within the reservoir. In the Weyburn reservoir, crude oil is produced from the Midale beds of the Mississippian Charles Formation (Figure 1c). These beds range from 16 to 28 m in thickness and contain two litho-stratigraphic units: the lower vuggy limestone (8~22 m thick) and the upper marly dolostone (2~12 m). The porosity of the marly zone is high (29%); however, its permeability is low (average ~10 md). Within the vuggy zone, porosity is ~10%, and the average permeability is high (~50 md) (Brown, 2002; White et al., 2004). As a basis for AVO modeling, we used well 102042300614 that was drilled in conjunction with CO2MSP and logged in August 2000. It is near the southwest border of Phase 1A and about 15 m away from a water injection well (Figure 1a). This Parameters Baseline Monitor Temperature 63 C 56 C (52~58 C) Oil API gravity 29 (25~34) 29 (25~34) Gas gravity 1.22 unchanged gravity 1.5249 unchanged Gas/oil ratio 30 L/L unchanged (GOR) Salinity 85,000 ppm NaCl 79,000 ppm NaCl Water resistivity 0.149 ± 0.023 (ohm-m) Oil saturation in Marly zone Oil saturation in Vuggy zone 0.104 ± 0.014 (ohm-m) Average 53% Average 30% Average 35% Average 28% Pore pressure 15 MPa 23 MPa near injector 8 MPa near producer Confining pressure 32~33 MPa unchanged Mineral bulk modulus Mineral shear bulk modulus 83 GPa (Marly 72 GPa (Vuggy 48 GPa (Marly 33.5 GPa (Vuggy unchanged unchanged Clays (shale) moduli 21 GPa (bulk) 7 GPa (shear) unchanged Table 1. Reservoir parameters used in modeling. Figure 1. EnCana s Weyburn seismic monitoring project area: (a) 3D/3-C survey layout and location of well 102042300614 (red); (b) location map in southeastern Saskatchewan; (c) stratigraphic column of Mississippian units. The reservoir is highlighted in cyan. 178 The Leading Edge February 2010
Figure 2. properties calculated by Xu s equations (dashed lines), and the Batzle-Wang equation (solid lines). Red lines = 56 C. Black lines = 63 C. well contains the most complete sets of geophysical logs available to this study; therefore, it is suitable for AVO modeling and can be considered as representative of the reservoir. Rock physics properties of this well were studied earlier (Brown, 2002). Pressure, oil saturation, and other reservoir parameters were measured prior to and during the injection and are listed in Table 1. Note that water saturation for the marly and vuggy zones in this well was recalculated by using Archie s equation and calibrated by MnCl 2 -doping analysis. It was found to be higher than previously estimated. The average saturation in the reservoir injection zone is expected to be around 20% (White et al., 2004). Brown developed a fluid-substitution model and normalincidence synthetic seismograms for the Weyburn reservoir by using reservoir fluid parameters similar to our baseline (Table 1). In the present paper, we extend this analysis to oblique incidence and focus on the fluid-substitution effects on AVO attributes during flooding. The main question we are addressing is whether and how pressure and - saturation effects can be separated in AVO intercept-gradient measurements. Fluid substitution model Following Wang et al. (1998), the fluid substation model based on Gassmann s equation was used to estimate the effects of saturation on the elastic moduli within and near the reservoir. The bulk modulus of fluid-saturated porous rock (K sat ) is related to the dry (K dry ) and matrix (K m ) moduli as where φ is the porosity, and all parameters are functions of the depth, denoted z. In Equation 1, K f is the bulk modulus of mixed reservoir fluids. Pore fluids generally consist of water, oil, gas, and, and the bulk modulus of their mixture (1) (K f ) is a function of their relative saturations, temperature, salinity, pore pressure, etc. The shear modulus μ sat = μ dry is considered independent of fluid saturation. Assuming that K m is constant within the marly and vuggy zones, we inverted Equation 1 to obtain the K dry at the current reservoir pressure. Further, pressure-dependence of the dry bulk and shear moduli of the Midale zones was approximated from the results of ultrasonic lab testing. Differential-pressure-related trends K dry (p) and μ dry (p) were measured under confining pressure 23 MPa and pore pressure 15 MPa (Brown, 2002). This confining pressure of 23 MPa was taken as the average of the vertical stress of 32~33 MPa and horizontal stress of 18~22 MPa. Brown derived a polynomial increase of K dry with differential pressure, which we denote K B (p), and a similar dependence for μ dry. Denoting the in-situ differential pressure at baseline conditions as p 0, the pressure-corrected dry bulk modulus then is (2) A similar equation exists for the shear modulus. Here, K dry (z) is estimated from Equation 1, and p is the differential pressure. In our calculations, we took the vertical stress of 32.5 MPa as the confining pressure, which allowed relating the differential pressure in Equation 2 to pore pressure in subsequent fluid-substitution estimates. The quality of Gassmann s fluid substitution is highly dependent on the accuracy of fluid parameters and physical parameters of reservoir rocks. Several selections of the most appropriate models should be made in order to construct an adequate fluid-substitution model. These selections are briefly reviewed below. Constitutive equation for calculating properties. Brown calculated properties using the equation by Batzle and Wang (1992). More recently, Xu (2006) modified these equations to provide more accurate estimates of properties (Figure 2). Note the significant difference in the bulk moduli predicted by these methods, and also the broader minimum in V P shifted to higher pore pressures in Xu s model. February 2010 The Leading Edge 179
Figure 3. Fluid-substituted V P,V S, and density logs (green) and original logs (black) in well 102042300614. V sh is the shale content estimated from the gamma-ray log, and S w is water saturation. The total and effective porosities are shown by blue and black lines, respectively. Fluidsubstituted logs were calculated using pore pressure of 15 MPa and mixed fl uids (40%, 48% brine, and 12% oil). K f of mixed fl uids (green) is assumed constant, whereas K f of in-situ fl uids (black) is variable. Using the effective porosity in Gassmann s equation. Total rock porosity includes isolated pores and the volume occupied by clay-bound water. These volumes cannot be filled by the injected and water. By contrast, effective porosity represents the interconnected pore volume into which fluid substitution can occur, and therefore it (and not the total porosity) should be used as parameter φ in Equation 1. Because the effective porosity is lower than total porosity, its use leads to smaller changes in the elastic parameters. Therefore, timelapse velocity, traveltime, and reflectivity variations estimated by using the effective porosity should be smaller than those derived from total porosity. Shale corrections to matrix modulus of marly dolomite zone. Although the porosity of the marly dolomite zone is high, its permeability is quite low, mainly caused by high shale content within its pores. Shale present within the pores (V sh in Figure 3) effectively reduces the bulk modulus of the reservoir rock matrix (Figure 3). On the other hand, shale content is low within the vuggy zone, and it is ignored in our model. Following Dvorkin et al. (2007), we replaced the singlemineral K m of dolostone within the marly zone Equation 1 with the effective matrix bulk modulus calculated from the Type of rock Anhydrite Marly dolomite Vuggy limestone V P (m/s) V S (m/s) Density (g/cc) Total porosity 5900.0 3250.0 2.90 0 0 Effective porosity 3600.0 2000.0 2.31 0.29 0.20 5100.0 2900.0 2.56 0.10 0.10 Table 2. Parameters of two-layered models (Figure 5a). mixture of dolostone and shale by using shale parameters given in Table 1. Note that the use of shale corrections reduced the matrix bulk modulus K m within the marly zone, which was assumed constant in previous studies (Figure 3). Finally, in addition to the described elastic moduli and densities, other measured fluid and reservoir parameters (such as temperature, salinity) were considered constant during the modeling described below. AVO forward model and attributes Traditionally, AVO interpretation is based on two-layer or blocked-log models and small-contrast (such as Shuey or Aki-Richards) approximations. However, this is inappropriate for the thin and high-contrast Weyburn reservoir. Our fluid-substitution model incorporates computations derived from well-log measurements made at 0.5-ft intervals throughout the entire zone of interest. This allows detailed calculation of the reservoir response to the finite-bandwidth seismic wavelet. AVO intercept (I) and gradient (G) values were measured from ray-tracing synthetics over the 0 30 range of incidence angles. The full Zoeppritz equation and a zero-phase Ricker wavelet were used to generate the synthetic seismograms. Depth-to-time conversion of well logs was performed at all individual depth readings, which allowed bypassing typical problems related to log and seismic record resampling. In the following, AVO attributes and discriminator are estimated by using different approaches, and a simple - saturation pore-pressure discriminator is proposed and tested. Using the Zoeppritz equation and its approximations. Figure 4 compares the accuracy of small-contrast computations obtained by using Shuey s equation to the exact solution in two-layered models corresponding to the ranges of elastic parameters encountered in the reservoir. The first of these models (Table 2) represents an anhydrite/marly interface, which is the upper boundary of the reservoir. Note the ~10% 180 The Leading Edge February 2010
Figure 4. AVO curves in anhydrite/marly model (Table 2) using the Zoeppritz equation (solid lines) and Shuey s approximation (dashed lines). Black lines = 30% oil and 70% water mixture. Green lines = 18% oil, 72% water, and 10%. differences in the reflectivities at larger ray parameters, which correspond to almost double AVO gradients in the exact solution (Figure 4). Considering that the marly zone is relatively thin (Figure 3) compared to the dominant wavelength, the second end-member model was constructed by removing the Marly zone and placing the anhydrite layer directly above the vuggy zone (Table 2). The strong difference in AVO gradients (Figure 4) shows that Shuey s approximation would lead to incorrect representation of AVO responses. Therefore, the full solution to the Zoeppritz equations should be used for accurate modeling. AVO attributes in well-log based models. AVO attributes of models with realistic depth variations of reflectivity are quite different from those of the conventional two-layered models (Figure 5). Interestingly, in the AVO crossplots, the I, G points computed by using the realistic depth-dependent parameters (Equation 1) are located between those of the anhydrite/marly and anhydrite/vuggy end-member models (Figure 5a). This effect occurs because the half-length of the incident wavelet (~50 m at 40 Hz) exceed the thickness of the reservoir, particularly of its marly zone. When the dominant frequency of the wavelet is increased, a separate reflection from the anhydrite/marly contact becomes observed, and therefore the I,G values approach those of the anhydrite/marly model. Conversely, when the dominant frequency of the wavelet is decreased, the reflectivity from Marly zone becomes relatively insignificant, and the I,G response approaches that of the anhydrite/vuggy model (Figure 5a). By using the well-log-based models, we simulated fluid saturations ranging from 100% water to 100% oil and 100%. In the example presented here (Figure 5), the saturation of (denoted S CO2 ) in the mixture was varied from 0 to 100%, and the relative saturations of oil and water were maintained at the ratio of 1:4. This allowed examining the effect of, which is dominant compared to the relative composition of the liquid oil/water mixture. Pore pressures were varied from 7 to 23 MPa, which corresponded to the estimated variation of the pressure from the production to injection wells (Figure 5). When fluids contain even small amounts of, their bulk moduli are strongly affected by the pore pressure. For relatively low pore pressures (~7 MPa) and S CO2 changing from 0 to 1%, the I,G values of the reservoir rapidly move into the area indicated by the yellow ellipse in Figure 5b. Note that the amount of this shift is comparable to the total distance between the 100%-oil and 100%-water cases (Figure 5b). From this area, I,G values move with increasing pressure Figure 5. (a) AVO crossplots from two-layered models and well-log-based models; (b) detail of the well-log model. 40-Hz Ricker wavelet was used. Solid and dashed arrows indicate pore pressure increasing from 7 to 23 MPa, and saturation increasing from 0 to 100%, respectively. Yellow ellipse indicates the area of I,G values converging at low pore pressure. Pink lines and large dot show the discriminator (see text). February 2010 The Leading Edge 181
Figure 6. Principle of discriminator: (a) two zones in the I,G crossplot (compare to Figure 5b); (b) the same zones in the pressuresaturation domain. Figure 7. Dependence of the slope, dg/di, of the discriminator line on: (a) the wavelet frequency and (b) G 0 /I 0 ratio. Blue and black dashed lines give two possible selections for such discriminators picked from the synthetics. The red line is the interpreted optimal discriminator. Note that the discrimination can be performed independently of the absolute amplitudes I 0 and G 0. in a fan-like pattern, generally opposite to the general - saturation trend for S CO2 1 5% (i.e., to the dashed arrow in Figure 5b) and in the direction of the oil/water pore-pressure trend when S CO2 10 100% (solid arrow). By contrast, changes in the oil/water mixture cause subparallel I,G trends that are consistently different from those caused by pore-pressure variations (brown and blue circles in Figure 5b). The pink line in Figure 5b illustrates the proposed approach to AVO classification with respect to the studied pressure-saturation variations. This discriminator line represents the lower bound of the -free distributions and subdivides the I,G plane into two zones denoted A and B (Figure 5b). In terms of the pressure-saturation parameters, these zones are separated by a pressure threshold whose shape can be described by specifying the cutoff saturation level S c and pore pressure p c (Figure 6). By checking the pore-pressure values at which the I,G trends modeled for different S CO2 values cross the discriminator line (Figure 5b), we estimated S c 2% and p c 18 20 MPa. For each of the models (log-based or two-layer), such discriminator lines can be represented by their central points, I 0,G 0 (pink dot in Figure 5b) and slopes, dg/di. If not seeking a precise discrimination of pore pressures (i.e., allowing some vertical position uncertainty in Figure 6b), then a range of slopes can be selected for a fixed central point. This range was picked by eyeball-fitting different straight lines separating the -free and -containing distributions (black and blue lines in Figure 7a). This allowed estimating the uncertainty in I 0, G 0, and dg/di parameters. Further, both I 0,G 0 and dg/di depend on the dominant frequency of the wavelet. By measuring dg/di from models with different frequencies of the incident Ricker wavelet, we estimated its dependence on the frequency (Figure 7a). Finally, by using the uncertainty bounds, a simplified empirical dependence was selected, giving the slope of the discriminator line (red line in Figure 7a). Note that for frequencies >45 Hz, this slope is constant and approximately equal -1.4. Discussion Most interestingly, the slope, dg/di, of the discriminator line can also be represented as a function of the ratio G 0 / I 0 (Figure 7b). This relation is independent of both the frequency and the amplitude of the incident wavelet. Therefore, it should be insensitive to the seismic amplitude scaling and could be directly applicable to reflection AVO data. In this type of AVO crossplot, the cases with some should be located below the modeled red curve in Figure 7b. As mentioned above, the described AVO modeling strongly depends on the adopted fluid-substitution model. This sensitivity naturally applies to the proposed discriminator. For example, it can be shown that by using the Batzle-Wang equations instead of Xu s (Figure 2), the discriminator lines could be approximately considered as unchanged, but the corresponding parameters would change significantly, to S c 5% and pc 12 MPa (compared to 2% and 18 20 MPa, respectively, in Figure 6b). Unfortunately, it appears that such sensitivity cannot be overcome or mitigated because it is caused by the strong and fundamental contrasts in mechanical properties of the fluids and dry-rock frame. Further modeling and application to real seismic data in the future should provide additional insights into the utility and stability of this discriminator. Conclusions The application of Xu s equation instead of the Batzle-Wang equation for calculating properties leads to significantly different fluid-substitution models and AVO attributes. The use of effective porosity in place of total porosity and in conjunction with the shale content correction yields reasonable fluid-substitution models. Using fluid-substitution models based on real well logs yields more realistic AVO attributes than those produced from the traditional two-layered or blocked-log models. The use of the exact Zoeppritz equation rather than its approximations is essential for accurate modeling of AVO in carbonate reservoirs. Based on detailed AVO modeling, an empirical pressure saturation discriminator is proposed for the Weyburn reservoir. The discriminator is approximately represented by cut-off saturation (S c 2%) and pore-pressure (p c 18 20 MPa) parameters. It can also be expressed in terms of relative AVO attributes, which makes it independent of the dominant frequency and amplitude of the seismic wavelet. This property should make the proposed discriminator suitable for application to real time-lapse reflection data. 182 The Leading Edge February 2010
Because of the nonlinearity and acute sensitivity of the AVO response to saturation, the modeled Weyburn S c value is low. This may also be similar to other reservoirs. Consequently, it appears that saturations above ~3% may be difficult to differentiate quantitatively from seismic AVO analysis. References Batzle, M. and Z. Wang, 1992, Seismic properties of pore fluids, Geophysics, 57, 1396 1408. Brown, L. T., 2002, Integration of rock physics and reservoir simulation for the interpretation of time-lapse seismic data at Weyburn Field, Saskatchewan, Master s thesis, Colorado School of Mines. Dvorkin, J., G. Mavko, and B. Gurevich, 2007, Fluid substitution in shaley sediment using effective porosity, Geophysics, 72, 3, O1 O8. Wang, Z., M. E. Cates, and R. T. Langan, 1998, Seismic monitoring of flood in a carbonate reservoir: A rock physics study, Geophysics, 63, 1604 1617. White, D. J., K. Hirsche, T. Davis, I. Hutcheon, R. Adair, G. Burrowes, S. Graham, R. Bencini, E. Majer, S. C. Maxwell, 2004, Theme 2: Prediction, Monitoring and Verification of movements, in M. Wilson and M. Monea, eds., IEA GHG Monitoring and Storage Project Summary Report 2000 2004, PTRC, Regina, 2004. White, D. 2009. Monitoring storage during EOR at the Weyburn-Midale Field, The Leading Edge, 28, 838 842. Xu, H., 2006, Calculation of acoustic properties using Batzle- Wang equations, Geophysics, 71, 2, F21 F23. Acknowledgments: We thank David Cooper of EnCana, Don White of Geological Survey of Canada, and Sandor Sule of the University of Saskatchewan for numerous valuable discussions. Thanks to Tom Wilson for his review and comments that improved the quality of this paper. This work is part of Phase II IEA GHG Weyburn Monitoring and Storage Project, sponsored by the Petroleum Technology Research Centre (Regina, Saskatchewan). Ma was also supported by P.R.C. NSFC Grant 40674041, 863 Program Grant 2006AA09Z313, 973 Program Grant 2006CB202208. Morozov was partly supported by Canada NSERC Discovery Grant RGPIN261610-03. Corresponding author: jinfengma2000@yahoo.com.cn February 2010 The Leading Edge 183