基于岩石物理分析的叠前弹性反演预测含气砂岩分布_英文_

197 Manuscript received by the Editor June 9, 2011; revised manuscript received September 9, 2011. 1. Energy Resources College of China University of Geosciences, Beijing 100083, China. 2. GNT International Inc., Beijing 100192, China. Gas sand distribution prediction by prestack elastic inversion based on rock physics modeling and analysis APPLIED GEOPHYSICS, Vol.8, No.3 (September 2011), P. 197 - 205, 8 Figures. DOI: 10.1007/s11770-011-0285-1 He Fu-Bang1, You Jun2, Chen Kai-Yuan1 Abstract: Seismic inversion is one of the most widely used technologies for reservoir prediction. Many good results have been obtained but sometimes it fails to differentiate the lithologies and identify the fl uids. However, seismic prestack elastic inversion based on rock physics modeling and analysis introduced in this paper is a signifi cant method that can help seismic inversion and interpretation reach a new quantitative (or semi-quantitative) level from traditional qualitative interpretation. By doing rock physics modeling and forward perturbation analysis, we can quantitatively analyze the essential relationships between rock properties and seismic responses and try to find the sensitive elastic properties to the lithology, porosity, fluid type, and reservoir saturation. Finally, standard rock physics templates (RPT) can be built for specifi c reservoirs to guide seismic inversion interpretation results for reservoir characterization and fluids identification purpose. The gas sand distribution results of the case study in this paper proves that this method has unparalleled advantages over traditional post-stack methods, by which we can perform reservoir characterization and seismic data interpretation more quantitatively and effi ciently. Keywords: Rock physics, seismic response, elastic parameters, elastic inversion, reservoir characterization, modeling Introduction The seismic inversion technique is widely used for oil and gas reservoir prediction. By using different algorithms and methods, it inverts P-waves or converted- wave seismic data and/or gathers into different elastic parameters (acoustic impedance, shear wave impedance, elastic impedance, density, velocity ratio, Poisson’s ratio, and etc.) that can be linked to rock properties (lithology, porosity, pore fl uids, and etc.), which can be further used for reservoir characterization and fluids identification (Fatti, et al., 1994; Gray, et al., 1999; Avseth, et al., 2005). However, different inversion methods have unique features and suitability and inversion results also have ambiguities. Especially when the impedance difference between the reservoir and adjacent formations is small, the regular post-stack inversion does not work or shows some limitation (Avseth, et al., 2005; Li, et al., 2005). In the last several years prestack elastic parameter inversion based on rock physics modeling and analysis experienced a quick development (Xu, et al., 2009; Ye, et al., 2009). This technology has a clearer goal and can produce more accurate results efficiently, which can be helpful for realizing seismic data quantitative interpretation. Seismic rock physics analysis is the critical step in the workfl ow. Seismic rock physics study is a discipline of analyzing the relationships between rock properties and seismic responses. By integrating core data, well logs, 198 Prestack elastic inversion and seismic data, the rock physics analysis aims to study the effects of rock physical parameter changes such as lithologic character, porosity, pore texture, fluid type, and saturation on rock elastic properties, from which the theory and methodology of investigating rock physical properties using seismic responses (the related changes of seismic attributes) has been generated. Rock physics analysis can bridge the rock property parameters and seismic responses and is the foundation for seismic data quantitative interpretation. So far, seismic rock physics analysis is one of the most important study areas for reservoir geophysics and gets more recognition from oil companies and research institutes all over the world (Ødegaard and Avseth, 2004; Avseth, et al., 2005; King, 2005; Huang, et al., 2007; Xu, et al., 2009). The logical and dialectical relationship between rock physics and geophysical responses is elaborated in depth in this paper. The non-replaceable importance and signifi cant contributions of rock physics analysis to quantitative seismic interpretation are also emphasized. Meanwhile, this paper describes in detail the rock physics modeling workflow and analysis, as well as some key points, such as well log quality control and calibration, rock physics model diagnostics, S-wave velocity estimation methods and their suitability, and forward modeling and perturbation to do sensitivity analysis. Eventually the technologies of rock physics analysis and prestack elastic parameters inversion were perfectly combined in a case study using real data from one of northwest China’s oil fields. The meaningful and impressive gas sand distribution prediction results proves that the new method introduced in this paper has unparalleled advantages over traditional post stack inversion and can be popularized and applied. Seismic rock physics modeling and analysis Generally, rock physics analysis workflows consist of four parts. They are well log analysis and calibration, rock physics modeling and diagnostics, perturbations and “what if” analysis, as well as seismic response (synthetics, AVO models, and attributes) and parameter sensitivity analysis. Well log analysis and rock physics model diagnostics The seismic rock physics analysis goal is to establish the deterministic relationship between rock physical properties and seismic attributes that can be used to guide more accurate quantitative interpretation of seismic datasets and reservoir prediction. However, high accuracy of seismic and log data are necessary to get correct rock physics analysis results. Many papers can be found to discuss seismic data accuracy but log data accuracy is usually ignored by geophysicists, which will severely affect the calibration and inversion results. In fact, log data accuracy is usually a real problem and the logs do not reflect the actual subsurface geological features because of the effects and limits of log instruments, investigation radius, borehole conditions, mud invasion, and other environmental factors. The logs must be calibrated before use but this calibration can be a little different from the routine environmental correction in two aspects: (1) To pay more attention to acoustic, density, and shear wave velocity log accuracy caused by wellbore breakouts, invasion, cycle skipping, and other reasons from the geophysical point of view; and (2) It is a whole-well calibration rather than a routine interest zone correction and this calibration can give the optimum match between seismic and log data and furthermore is significant to the consequent calibration and inversion. Two criteria used to examine calibrated log accuracy to judge if the logs imaged the actual subsurface geology features and met the rock physics analysis requirements and inversion: (1) the Vp, Vs, and density calibrated logs and their calculations such as P- and S-wave impedance (Zp and Zs), Vp/Vs velocity ratio, or Poisson’ s ratio must agree with the general rock physics laws and models (that is, model diagnostics). For example, on the interest zone density versus P-wave velocity crossplot of one well (see Figure 1), the blue and red line are the Raymer theoretical model lines for clean sand and pure shale and the color bar shows sand volume. Some data points are off the theoretical model range but after correction the abnormal data points were migrated to their corrrect positions inside the model lines. (2) The synthetic generated by the calibrated logs should have an optimum match with seismic traces near the borehole in both kinematics (travel time) and kinetics (amplitude) features. For example, the calibrations between the synthetic seismogram created by corrected logs and the seismic traces near the borehole in the reflections at 0.70, 0.95, and 1.05 seconds in Figure 2 have a significant improvement compared with the match before correction, especially in kinetics features. This signifi cant matching improvement results from the corrections and migrations of the abnormal data points. 199 He et al. Fig. 1 Comparison of before-calibrated (left) and after-calibrated (right) logs of one well. Fig. 2 Comparison of synthetic seismograms generated by before-calibrated (left) and after- calibrated (right) logs with seismic traces near the borehole. Well log calibration from a geophysical point of view is the critical step for rock physics analysis and seismic inversion and the quality of its results determines whether the seismic quantitative interpretation goal can be achieved. Good calibration results have three important contributions to the whole workflow: (1) If after rigorous corrections, the calibrated logs refl ect the actual subsurface geological features, then rock physics analysis and what-if perturbations (forward modeling) can be conducted on the logs to find the sensitive parameters to specific reservoir and fluid types. (2) An optimum match between well logs and seismic, both in kinematics and kinetics behaviors, can be achieved after rigorous calibration. (3) Provide high quality acoustic, density, and shear wave velocity logs to the following seismic inversion. Vs estimation Vs data will be used and involved in the rock physics modeling and elastic inversion. However, usually few shear acoustic logs are available. Even when there are shear acoustic logs, the quality and accuracy are poor because the shear wave is the subsequent event in shear acoustic log records and is hard to pick accurately. So Vs estimation is essential in most cases. Normally there are two ways to estimate Vs, they are: (1) correlating the measured Vp and Vs from well logs and performing statistical regression to get an empirical function to use. This method is valid when there are good quality measured full wave train acoustic logs 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 Left (1) Normal Right Left (1) Normal Right 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1 5 9 1 5 9 1 5 9 1 5 9 6000 2.5 V p (m /s ) Density (g/cm3) 4000 2000 2 1.5 1 0.8 0.6 0.4 0.2 0 Volume sand (fraction) 6000 2.5 V p (m /s ) Density (g/cm3) 4000 2000 2 1.5 1 0.8 0.6 0.4 0.2 0 Volume sand (fraction) Raymer_Vp_RhoB_clean Raymer_Vp_RhoB_Shale Raymer_Vp_RhoB_clean Raymer_Vp_RhoB_Shale 200 Prestack elastic inversion available in the study area; and (2) using rock physics models for Vs estimation. Seven rock physics models for Vs estimation are available, such as the Greenberg-Castagna, Cemented, Mud Rock, Unconsolidated, Critical Phi, Krief, and Xu- White models. Usually the first four models are used for Vs estimation for high porosity formations and the other three models are normally valid for formations with medium to low porosity (Castagna, et al., 1985; Greenberg and Castagna, 1992; Xu and White, 1995, 1996; Mavko, et al., 2003). Each model has its suitable conditions and limits and three widely used models are briefl y described: 1. Greenberg-Castagna Model Greenberg and Castagna (1992) have given empirical relations for estimating Vs from Vp in multimineralic brine-saturated rocks based on empirical polynomial Vp- Vs relations in pure monomineralic lithologies (Castagna et al., 1993). The Vs in brine-saturated composite lithologies is approximated as: 11 1 0 1 0 1 , 2 i iN NL L j j i ij p i ij p i j i j Vs X a V X a V �� ­ ½ª ºª º § ·° °« » �® ¾¨ ¸« » « »¬ ¼ © ¹° °¬ ¼¯ ¿ ¦ ¦ ¦ ¦ 1 1, L i i X ¦ where L is the number of pure monomineralic lithologic constituents, Xi is the volume fractions of the lithological constituents, aij are the empirical regression coeffi cients, Ni is the polynomial order for constituent i, and Vp and Vs are P- and S-wave velocity (km/s) in composite brine- saturated multimineralic rocks. To estimate Vs from Vp for other fluid saturations, Gassmann’s equation needs to be used in an iterative manner. It includes four steps: 1) Start with an initial guess for Vp-brine (that is, Vp at 100% brine saturation). 2) Calculate Vs-brine corresponding to Vp-brine from the empirical regression. 3) Perform fluid substitution using Vp-brine and Vs- brine in the Gassmann equation to get Vs-fl uid (that is, Vs of any other fl uid saturation, e.g., oil or a mixture of oil, brine, and gas). 4) With the calculated Vs-fluid and the measured Vp- fluid, use the Gassmann relation to get a new estimate of Vp-brine. Check the result against the previous value of Vp-brine for convergence. If convergence criterion is met, stop; if not, go back to step 2 and continue. This method requires prior knowledge of the lithology, porosity, saturation, and elastic moduli and densities of the constituent minerals and pore fl uids. 2. Krief Model The empirical formula of Vp -Vs- ( is porosity) for water saturated rock from the Krief model is similar to the Critical Phi model. For dry rock, the Vp -Vs- empirical formula is: Kdry = Kmineral (1 - β), where Kdry and Kmineral are the bulk moduli of the dry rock and mineral and β is the Biot coeffi cient. Krief et al. (1990) obtained a relation between β and (porosity) using the data of Raymer et al. (1980): ( )(1 ) (1 ) ,m IE I� � where ( ) 3 /(1 ).m I I � The equation can be rewritten as Kdry = Kmineral(1 - )m ( ), and μdry = μmindry (1 - )m ( ). For rocks with any other pore fl uid, the equation can be determined by combining the Krief et al. expression Kdry = Kmineral (1 - β) with Gassmann’s equations or the following simple approximation: 2 min 22 min 2 22 erals fleralp sats flsatp V VV V VV � � � � � � Vs-mineral2 Vp-mineral 2 , where Vp-sat, Vp-mineral, and Vf l are the P-wave velocity of the saturated rock, the mineral, and the pore fl uid and Vs-sat, Vs-mineral are the shear wave velocity of the saturated rock and mineral. This approximate expression can be represented as )( 22 min 22 2 min 2 fleralp flsatp eralssats VV VV VV � � � � �� Vp-mineral Vs-mineral . 3. Xu-White Model Xu and White (1995) developed a theoretical model for velocity estimation in shaley sandstone. The formulation uses the Kuster-Toksöz differential effective medium (DEM) theories to estimate the dry rock P- and S-wave velocities and the low-frequency saturated velocities are obtained from Gassmann’s equation and the high-frequency saturated velocities are calculated using fluid-filled ellipsoidal inclusions in the Kuster- Toksöz model. The total porosity = sand + clay, where sand and clay are the porosities associated with the sand and clay fractions 201 He et al. and they are related to the volumetric sand and clay content. The properties of the solid mineral mixture are estimated by a Wyllie time average of the quartz and clay mineral velocities and arithmetic average of their densities. Then these mineral properties are used in the Kuster-Toksöz equation along with the porosity and clay content to calculate dry rock moduli and velocities. The Xu-White model is valid for estimating the elastic properties of medium-to-low porosity, well-cemented, shaley sandstone media. The estimation error will be bigger when used in shallow strata or layers with a high clay content. Perturbations and sensitivity analysis After the calibration and rock physics model diagnostics, the well logs refl ect the real formation geologic features such as thickness, lithology, porosity, permeability, fl uid types, and saturation and also have a good match with the seismic traces near the borehole. We can then use these calibrated logs and the other calculated elastics parameters to do what-if perturbations analysis for analyzing the seismic response changes with vertical and lateral lithofacies variations, porosity, fluid type, and saturation changes, through which the possible reservoir changes away from the borehole and its seismic responses can be studied and evaluated (Avseth, et al., 2005). Sensitive parameters for the lithologies and fl uid types for a specifi c reservoir might be found through this forward modeling process which could provide theoretical foundation and guidance for predicting oil and gas-bearing reservoirs using rock elastic parameters. dry, and gas sand overlapped each other (7500 to 8500 m/s*g/cm3), so those lithologies cannot be separated by impedance alone. However, a crossplot of multiple elastic parameters, for example, P-wave impedance (Zp) and Vp/Vs velocity ratio with a color bar showing volume of sand, shows better separation among those lithologies. We can use multiple elastic parameters with cross- plotting techniques to build the theoretic rock physics templates for differentiating lithologies and fluid types of the specifi c reservoirs (Figure 3). Prestack elastic parameters inversion In contrast to post-stack seismic impedance inversion, which is applied to a zero-offset or near-offset stacked section to estimate the acoustic impedance of sublayers, prestack inversion uses the full recorded seismic information including near, middle, and far offset data to invert for multiple elastic parameters, such as P wave impedance, shear wave impedance, elastic impedance, Vp/Vs ratio, Poisson’s ratio, density, Lamé’s constant, and etc. Because prestack elastic inversion can produce Vp/Vs-related attributes that are more meaningful for lithologic and fluid identification, it has an advantage over traditional post-stack inversion to handle complicated reservoir characterization. Prestack inversion is normally started with the Zoeppritz equations (Aki and Richards, 1980). Although the Zoeppritz equations can be used to obtain exact plane wave amplitudes of a refl ected P wave as a function of angle, they cannot provide an intuitive understanding of how amplitudes relate to the various physical parameters. Over the years, a number of approximations to the Zoeppritz equations have been made (Aki and Richards, 1980; Shuey, 1985; Gelfand et al., 1986). The Aki and Richards, Shuey, and Gelfand approximations can be reduced to the simple linear equation � � 2sin ,PR R GT T � where R (θ) is the refl ectivity as a function of incidence angle, RP is the P-wave reflectivity at zero offset (the intercept) determined by the acoustic impedance contrast across interfaces, and G is the gradient term which is a function of Poisson’s ratio or Vp/Vs ratio and can include a density term. The linear approximation is good for AVO analysis with incidence angles of 0° to 30°. Clear ly both Zoeppr i tz equat ions and these approximations are related to the angle of incidence. However, seismic data is usually recorded as a function 6000 7000 8000 9000 10000 2.2 2 1.8 1.6 V p /V s P wave impedance (m/s*g/cm3) Gas sand Dry Gaseous water sand 1 0.8 0.6 0.4 0.2 0 Volume sand (fraction) Fig. 3 Lithology differentiation by Vp/Vs - Zp crossplot. Generally, it is difficult to differentiate lithology or fl uid types by only one elastic parameter. For example, in Figure 3, the impedance range of shale, water sand, 202 Prestack elastic inversion of offset rather than incidence angle. We should first transform seismic data from the offset domain to the angle do