GEOPHYSICS. VOL. 76, NO. 6 (NOVEMBER-DECEMBER 2011); P. O45–O58, 15 FIGS., 2 TABLES. 10.1190/GEO2010-0275.1
Optimal dynamic rock-fluid physics template validated by petroelastic reservoir modeling
Alireza Shahin1, Robert Tatham2, Paul Stoffa3, and Kyle Spikes4
A geologically consistent rock physics model was then used to simulate the inverted seismic attributes. Finally, we conducted a sensitivity analysis of seismic attributes and their crossplots as a tool to discriminate the effect of pressure and saturation. The sensitivity analysis demonstrates that crossplotting of acoustic impedance versus shear impedance should be the most stable way to separate saturation and pressure changes compared to other crossplots (e.g., velocity ratio versus acoustic impedance). We also demonstrated that the saturation and pressure patterns were detected in most of the time-lapse scenarios; however, the saturation pattern is more likely detectable because the percentage in pressure change is often lower than that of the saturation change. Imperfections in saturation and pressure patterns exist in various forms, and they can be explained by the interaction of saturation and pressure, the diffusive nature of pressure, and rapid change in pressure due to production operations.
ABSTRACT Separation of fluid pore pressure and saturation using inverted time-lapse seismic attributes is a mandatory task for field development. Multiple pairs of inversion-derived attributes can be used in a crossplot domain. We performed a sensitivity analysis to determine an optimal crossplot, and the validity of the separation is tested with a comprehensive petroelastic reservoir model. We simulated a poorly consolidated shaly sandstone reservoir based on a prograding near-shore depositional environment. A model of effective porosity is first simulated by Gaussian geostatistics. Well-known theoretical and experimental petrophysical correlations were then efficiently combined to consistently simulate reservoir properties. Next, the reservoir model was subjected to numerical simulation of multiphase fluid flow to predict the spatial distributions of fluid saturation and pressure.
eters such as density (ρ), P-wave velocity (V P ), S-wave velocity (V S ), acoustic impedance (AI), and shear impedance (SI) extracted from prestack seismic data have been used in most recent applications. In doing so, crossplots of the original inverted parameters or their derivatives to other elastic parameters, e.g., λρ (LR) versus μρ (MR), called LMR (Goodway et al., 1997), and elastic impedance (EI) versus AI (Connolly, 1999), are made. Similarly, well-logderived elastic parameters are crossplotted and color-coded with other discriminatory well logs, such as shale fraction and porosity. The well-log analysis allows one to distinguish lithology and fluid classes that guide the classification of the inverted seismic attributes in crossplot domains. Finally, lithology and fluid clusters are back projected from crossplot domains to seismic volumes (Avseth et al., 2005).
INTRODUCTION Seismic reflection data have been used to infer lithology and fluid type from subsurface rocks. Various seismic attributes can be extracted from seismic volumes to qualitatively, semiquantitatively, and quantitatively perform seismic litho-fluid facies classifications. For example, Macrides et al. (2000) use supervised and unsupervised statistical pattern recognition techniques to classify seismic volumes through crossplotting of seismic attributes computed from seismic traces within reservoir intervals. In general, classification techniques based on the seismic observations and/or seismic attributes can be unreliable due to wavelet and tuning effects. To overcome this problem, inverted seismic param-
Manuscript received by the Editor 24 August 2010; revised manuscript received 28 May 2011; published online 9 January 2012; corrected version published online 19 January 2012. 1 Formerly University of Texas, Institute for Geophysics, Austin, Texas, U.S.A.; presently BP North America, Reservoir Geophysics R&D, Houston, Texas, U.S.A. E-mail:
[email protected]. 2 University of Texas, Jackson School of Geological Sciences, Austin, Texas, U.S.A. E-mail:
[email protected]. 3 University of Texas, Institute for Geophysics, Austin, Texas, U.S.A. E-mail:
[email protected]. 4 University of Texas, Geological Sciences, Austin, Texas, U.S.A. E-mail:
[email protected]. © 2012 Society of Exploration Geophysicists. All rights reserved. O45
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The above summary serves as a reference to the current state-ofthe-art technology in classifying seismic volumes into fluid and rock facies. In this paper, we investigate various crossplots to see if the crossplots of inverted seismic attributes can be extended to classify time-lapse seismic signatures. Time-lapse seismic data consists of two or more repeated seismic surveys recorded at different calendar times over a depleting reservoir in primary, secondary, or tertiary recovery phases. The main topic of this paper is to quantitatively associate the changes in time-lapse seismic attributes to the changes in fluid saturation and pressure. This approach has been addressed by several authors in the literature. Some techniques have been proposed to directly invert or transfer time-lapse seismic data to fluid saturation and pressure changes. For example, Landrø (2001) and Landrø et al. (2003) directly inverted time-lapse seismic data for fluid saturation and pressure changes based on an approximate rock physics model and a linearized form of reflection coefficients. Veire et al. (2006) present a stochastic inversion method to discriminate pressure and saturation changes directly from P-P time-lapse AVO data. MacBeth et al. (2006) develop a first-order linear formula relating changes in any pair of seismic attributes to changes in pressure and saturation. Shahin et al. (2009 and 2010a) propose seismic timelapse crossplots to directly transfer changes in multicomponent seismic traveltimes and reflection coefficients to changes in fluid saturation and pressure. Some workers make use of inverted elastic parameters (AI and SI changes) to indirectly estimate pressure and saturation changes via crossplotting methods. To summarize, Tura and Lumley (1999) estimate changes in saturation and pressure via crossplotting of inverted AI and SI changes. Cole et al. (2002) propose a grid search method to estimate pressure and saturation by forward modeling of rock and fluid physics. Lumley (2003) proposes a 4D seismic crossplot inversion method using a coordinate transformation and calibration with well data to simultaneously estimate pressure and saturation changes. Andersen et al. (2009) propose a dual crossplotting technology for the seismic facies classification problem. First, a crossplot of the inverted seismic attributes (V P ∕V S versus AI) for the base survey is created and lithofacies are classified accordingly. Second, time-lapse effects are classified via crossplotting of 4D seismic attributes, (Δ½V P ∕V S versus ΔAI), where Δ denotes a change in any parameter due to production between base and monitor surveys. From 4D crossplots, one can classify the seismic volume into different subsets associated with scenarios of changes in pore pressure and/or saturation. Finally, the lithofacies and 4D classes are combined via dual classification to reveal pure and combined 4D effects in pay zones. In spite of the fact that the separation of fluid pore pressure and saturation has been extensively addressed in literature, little attempt has been made to search for an optimal crossplot of inversionderived seismic attributes by performing sensitivity analysis. This kind of study can be barely conducted by real seismic data because high quality seismic data with full offset and bandwidth is required to be accurately inverted for basic elastic parameters, e.g., V P , V S , and ρ. Other attributes are then computed using the basic elastic parameters. Finally, crossplot of various attributes are created to obtain the crossplot maximizing the separation of saturation and pressure, which we call the optimal crossplot. To address the above, we first developed a realistic petroelastic model in which basic petrophysical properties, e.g., effective porosity, effective water
saturation, clay content, etc., have been explicitly attributed to elastic parameters (Shahin et al., 2010b). We then examined the sensitivity of various seismic attributes, simulated via rock physics model and Gassmann fluid substitution, with respect to pore pressure and water saturation. It is shown that AI versus SI should be the optimal crossplot to quantitatively discriminate saturation and pressure changes. The developed petroelastic model is utilized to validate the sensitivity analysis results.
CONSTRUCTING A SYNTHETIC PETROELASTIC RESERVOIR MODEL Geological reservoir model A stacked sand-rich strandplain reservoir architecture has been considered in this study to simulate a realistic geological framework. Strandplains are mainly marine-dominated depositional systems generated by seaward accretion of successive, parallel beach ridges welded onto the subaerial coastal mainlands. They are inherently progradational features and are present on wave-dominated microtidal coasts (Tyler and Ambrose, 1986; Galloway and Hobday, 1996). This sand-rich beach-ridge reservoir architecture is intended to be originally deposited as a clay-free geobody. However, due to postdepositional diagenesis, dispersed clay is produced and is the main factor that reduces porosity and permeability of the reservoir. This model, generated using a Gaussian simulation technique, is part of the comparative solution project, a widely used, large geostatistical model for research on upgridding and upscaling approaches (Christie and Blunt, 2001). We worked with the uppermost 35 layers of the model that is representative of the Tarbert formation, a part of the Brent sequence of middle Jurassic age and one of the major reservoir units in the North Sea. By changing the grid size and smoothing, we modified this model to meet the objectives of this research. Next, we will assign geologically consistent petrophysics information and add facies characterization to develop a more realistic reservoir model comparable to complicated models in the petroleum industry. The model is described on a regular Cartesian grid. The model size is 220 × 60 × 35 in x- (east-west), y- (north-south), and z- (depth) directions, respectively. The grid size is 10 × 10 × 10 m, so the model dimensions are 2200 by 600 by 350 m. The reservoir consists of three facies (Figure 1). Facies A is a fine-grained sandstone with mean grain-size distribution of 80 μm. This facies simulates a low porosity and permeability sandstone reservoir with high clay content. Facies C is a coarse-grained sandstone with mean grain-size distribution of 500 μm. This facies is associated with a sandstone with high porosity and permeability and low clay content. Facies B is a transition facies between facies A and C and corresponds to a medium-grained sandstone with mean grain-size distribution of 250 μm. It is worth noting that a strong correlation between grain size and clay content is reported by several authors (e.g., Saner et al., 1996). This knowledge has been incorporated accordingly into the model by assigning claydependent grain sizes to the three facies in which the higher the clay content, the lower the mean grain-size distribution.
Petrophysics model The geological model described above is used as the basic model in which petrophysical properties are populated assuming a meaningful petrophysics model. A petrophysics model includes a set of
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Rock-fluid physics and petro-elastic reservoir
Fluid flow simulation combines three fundamental laws governing fluid motions in porous media. These laws are based on conservation of mass, momentum, and energy (Aziz and Settari, 1979). In this research, a commercial finite-difference reservoir simulator, Eclipse 100, is used to replicate a waterflood-enhanced oil recovery on a black oil 2D reservoir containing oil, soluble gas, and water. The reservoir has no water drive. Because of the high-pressure conditions, no gas is produced in the reservoir. Thus, prior to waterflooding, solution gas is the only drive mechanism forcing oil to be produced. This drive is so weak that water injection is required to enhance oil recovery. The same grid block dimensions used to generate the geological model, 10 × 10 × 10 m, were used to simulate fluid flow; hence, mathematical upscaling was not necessary. The capillary pressure data, the relative permeability curves, and PVT (pressure, volume, and temperature) properties of reservoir fluids are borrowed from the Killough (1995) model. Based on this data, the pressure below which the dissolved gas releases from oil, the bubble point, is 2000 psi. For a simulated period of 10 years, the waterflood schedule is simulated by using two injectors at the corners and one producer in the middle of the reservoir. During this period, saturation and pressure values for each reservoir grid block are exported after each
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year. Collecting these databases allows us to analyze the sensitivity of the corresponding seismic elastic parameters to a wide range of changes in fluid saturation and pressure. Figure 5 shows the snapshots of water saturation and pore pressure distributions at the initial reservoir state and after production at different calendar times. At the start of production/injection, water replaced oil near the injectors and a portion of mobile oil will be extracted by the producer. At later time, water will replace more oil, resulting in more produced oil. In other words, behind the waterfronts, the water saturation is increasing monotonically around the injectors, meaning more oil is gradually displaced as more water is injected. In addition, one can clearly see that the behavior of the pressure front is very different from that of the waterfront. Pressure behaves as a wave and propagates very quickly, but water has a mass bulk movement and moves more slowly. Figure 6 shows production data for a period of 10 years throughout the reservoir life. Water injectors penetrate the entire 350 meters of reservoir thickness and are set to a constant water rate of 400 stock tank barrel(STB)/day. The only producer located in the middle of the reservoir also penetrates the whole reservoir thickness and is initially set to a constant oil rate of 750 STB/day. The reservoir initially starts producing oil with a plateau of 750 STB/ day. During this period, volumetric average pressure of the reservoir
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the theoretical and experimental correlations among various sets of petrophysical properties. The model is required to be validated using available well log and core data. Here, the effective porosity model is first generated using Gaussian geostatistics. Clay content and total porosity models are then computed assuming a dispersedclay distribution (Thomas and Stieber, 1975; Marion et al., 1992) (Figure 2a). Horizontal permeabilities in the x- and y-directions are equal and are calculated based on the extension of the dispersedclay model to permeability introduced by Revil and Cathles (1999) (Figure 2b and 2c). Permeability fields depend on porosity, clay content, grain size distribution, and the degree of cementation; subsequently, facies A, B, and C are assigned different trends in permeability-clay content and permeability-porosity domains based on their grain sizes. The vertical permeability field is taken as 25% of the horizontal permeability field for the entire reservoir. So far, the effective and total porosities, clay content and directional permeabilities are modeled using geostatistics and theoretical correlations according to dispersed-clay distribution. Next, we should initialize the reservoir for water saturation and pore pressure. An experimental correlation (Uden et al., 2004) between water saturation and clay content is combined with the dual water model (Best et al., 1980; Dewan, 1983; Clavier, 1984) to compute claybound water (Swb), effective water saturation (Swe), total water saturation (Swt), and oil saturation (So) (Figure 2d). Initial reservoir pore pressure is simulated by assuming a linear hydrostatic gradient from the top to the bottom of the reservoir. Figure 3 summarizes the distributions of petrophysical properties for a 2D cross section in the middle of the 3D reservoir. Figure 4 shows the histogram of petrophysical properties for the entire reservoir volume. Table 1 shows the petrophysical properties of the three facies within the reservoir. Now, a complete set of dynamic and static reservoir parameters has been generated. These will be used to launch a reservoir simulation and to predict time-dependent subsurface distributions of water saturation, pore pressure, and surface well production data.
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Figure 1. Map view of the first upper layer of the 3D reservoir (Christie and Blunt, 2001) showing petrophysical facies (A, B, and C) overlaid on the distribution of effective porosity model. Color scale is effective porosity and the same for all panels. The model is associated with synthetic geologic model and used for the numerical simulation of multiphase fluid flow and rock-physics modeling. The model is defined on a regular Cartesian grid of 10 × 10 × 10 m cells, with 220 × 60 × 35 cells in x (east-west), y (north-south), and z (depth) directions, respectively, for a total dimension of 2200 m × 600 m × 350 m. A 2D cross section from the middle of this 3D model has been selected for this study.
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In this research study, we deal with a strandplain geological environment filled with poorly consolidated shaly sandstone. As described in the petrophysics model, the clay distribution is dispersed, or pore-filling. The corresponding porosity-clay content model is introduced by Thomas and Stieber (1975). Marion et al. (1992) conducted several laboratory measurements and introduced a topological elastic model for sand-shale mixtures. In their model, clay is a part of the pore fluid; hence, the shear modulus of the mixture is not affected by increasing the clay content. Gassmann theory is then utilized to compute the velocity-porosity trends due to clay content variations. Dvorkin and Gutierrez (2002) present an effective-medium theoretical model for a complete sandy shale and shaly sand sequence assuming pore-filling clay. The model shows similar trends to those observed by Marion-Yin. However, instead of using Gassmann theory, the modified HashinShtrikman lower bound (Dvorkin and Nur, 1996) is used to compute velocity-porosity-clay content relationships. In addition, this model is a stress-sensitive model and includes the effect of pore pressure variations on velocities of the mixture. As a result, we select this rock physics model because it is a comprehensive model. More importantly, it is consistent with our geology and petrophysics models employed. Fluid substitution is the technique of predicting how seismic velocities depend on pore fluids. At the heart of the fluid substitution is Biot-Gassmann’s theory (Gassmann, 1951; Biot,
increases from 3200 to 3920 psi. After 2650 days (7.2 years), this rate is not affordable for the reservoir, so production strategy is intentionally changed to a constant bottom hole pressure (BHP) of 2600 psi for the producer. From this point, the oil rate decreases, and a significant pressure drop is observed. The reservoir always produces above the bubble point pressure (2000 psi); consequently, no gas is produced within the reservoir. However, dissolved gas will be released from live oil at the surface, and gas will be produced with a similar production trend as oil. A small amount of water production occurs from the beginning up to the 2000 days (5.4 years) of production, but afterward it increases significantly. The CPU time for running 10 years of simulation of the 2D reservoir is 240 s.
Rock and fluid physics model By using rock physics modeling, one can transform the petrophysical properties of a reservoir to seismic elastic parameters (Avseth et al., 2005), which can be further used to simulate seismic reflectivity data using a forward seismic modeling algorithm. This process is an essential step in any seismic inversion project aimed at estimating petrophysical properties. In seismic reservoir monitoring, rock physics also plays a significant role. In other words, the numerical simulation of fluid flow, rock physics modeling, and seismic forward modeling can be effectively combined to simulate seismic and production data and, ultimately, to predict the static and dynamic reservoir properties.
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Figure 2. Petrophysics model. (a) The dispersed-clay model for porosity reduction due to increasing of clay content. (b) Horizontal permeability versus clay content. (c) Permeability versus effective porosity. (a-c) Three colors are associated with three facies A (in blue), B (in green), and C (in red). Black dots in (b and c) are projected reservoir points. (d) Fluid saturations versus clay content. Swe, So, Swb, and Swt stand for effective water saturation, oil saturation, clay bound-water saturation, and total water saturation, respectively.
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Rock-fluid physics and petro-elastic reservoir
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Figure 3. Distribution of petrophysical properties for a 2D cross section in the middle of 3D reservoir. The x- and y-axes are the same for all panels and they are reservoir length and thickness in meters, respectively. Each panel is color-coded with the corresponding petrophysical property. The title of each panel shows the scale label as well.
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Figure 4. Histogram of petrophysical properties of the reservoir. Petrophysical facies are overlapped in all domains except in permeability domain where three distinct facies are separated.
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An intermediate step in fluid substitution is to compute the elastic properties of pore fluids. When fluids are compressible, their densities and bulk moduli are functions of pore pressure. In addition, temperature and composition affect fluid bulk moduli and densities. Batzle and Wang (1992) establish a set of empirical correlations that transform pore-fluid properties from engineering to the geophysical domain. Here, these correlations are used to transform PVT (pressure, volume, and temperature) measurements of oil-gas-water to density and bulk modulus. To summarize, combining the Dvorkin-Gutierrez (2002) rock physics model with the fluid physics model (Batzle and Wang, 1992), and using a modified Gassmann theory (Dvorkin et al., 2007), we are able to observe the joint effects of various petrophysical properties on elastic parameters. Consequently, the comprehensive petroelastic model developed in this research can be efficiently used in sensitivity analyses of elastic parameters to petrophysical properties and, ultimately, applied to seismic reservoir
1956). This theory is one of the most stable tools in rock physics and has been widely used in the geoscientist community. However, the use of this theory is questionable in shaly sandstone because clay-bound water (immobile water) in shaly sandstones may prohibit instantaneous equilibrium throughout the pore space when rock is exposed to pore pressure fluctuations induced by a propagating wavefield (Gurevich and Carcione, 2000). To make Gassmann’s equations applicable to shaly sandstone, Dvorkin et al. (2007) present an alternative approach to use effective porosity and effective water saturation instead of their corresponding total values. In their method, a new definition for mineral fractions is derived based on an equivalent-effective medium in which the porous wet shale is treated as part of the grain material. This alternative technique shows greater sensitivity of sediment with respect to fluid replacement compared to that of traditional Gassmann theory based on the total porosity. Here, we employ this alternative Gassmann fluid substitution.
Table 1. Facies petrophysical properties associated with the synthetic reservoir model.
Facies A B C
Total porosity
Effective porosity
Clay content
Effective water saturation
Mean grain size (μm)
Horizontal permeability (mD)
0.11–0.18 0.18–0.25 0.25–0.37
0.01–0.12 0.12–0.22 0.22–0.37
0.25–0.34 0.15–0.25 0.0–0.15
0.45–0.62 0.27–0.45 0.15–0.27
80 250 500
0.37–10 68–1400 6800–91,000
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Figure 5. Snapshots of effective water saturation (left column) and pore pressure (psi) (right column) distributions at initial reservoir state (t0) and after production at different calendar times (three (t3), six (t6), and 10 (t10) years). The x- and y-axes are the same for all panels and they are reservoir length and thickness in meters, respectively. Each panel is color-coded with the corresponding attribute. The title of each panel shows the scale label as well. Blue and black arrows in the panel labeled with Pp (t3) indicate the locations of the injector and producers’ wells.
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Rock-fluid physics and petro-elastic reservoir
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Production data
The interesting asymmetric trend demonstrates that elastic paracharacterization and monitoring research. We choose to present a meters are more sensitive to pore pressure increase than decrease. sensitivity analysis of seismic attributes and the crossplots of these This suggests that in a time-lapse seismic study, pore pressure deattributes as tools to discriminate the effect of pressure and saturatection should be easier near the injector wells than producers. The tion in a time-lapse seismic study. Further application of using the normalized sensitivities of elastic parameters to pore pressure can petroelastic model developed her can be found in Shahin be expressed in a descending order by V S, V P ∕V S , V P , and ρ, et al. (2011). The corresponding petroelectric model for the reservoir can be respectively. The effectiveness of elastic parameters differs in discriminating efficiently simulated by combining the Thomas and Stieber petrolitho-fluid facies from one another. Figure 9 summarizes various physics model (1975), dual water rock physics model (Best 1980; crossplots of elastic parameters for a wet sandy shale, a water saDewan, 1983; Clavier, 1984), and Arps’ empirical equation (Arps, turated shaly sand, and an oil-saturated shaly sand all at the same 1953) to calculate the free and bound-water resistivity. The joint differential pressure, overburden minus pore pressure. This crossmodeling of the elastic and electrical properties of reservoir rocks plotting using a petroelastic rock model is very instructive in terms will lead to the consistent forward modeling algorithms for joint of identifying the most effective domain to distinguish litho-fluid inversion of seismic and electromagnetic (EM) data. Further applifacies. For example, LR/MR versus LR and V P ∕V S versus AI crosscations of using the petroelectric model can be found in Shahin et al. plots should be the best lithology discriminators for the specific pet(2010a) in which a time-lapse frequency domain controlled-source roelastic model used in this research. However, the presented results EM (CSEM) feasibility study over the 2D reservoir model is simuare not universal, and we suggest examining all crossplots at any lated to investigate the corresponding time-lapse signals. Table 2 summarizes the elastic properties and densities of minerspecific field locations, comparing results, and then making a deals used in this study. Figure 7 illustrates the petroelastic model cision based on optimum crossplot. As mentioned in the discussion of the petrophysics model, three evaluated at initial reservoir conditions. In this figure, (a) shows petrophysical facies are located in the shaly sandstone domain, and a plot of total porosity, V P , and V S versus clay content. Panel there is no sandy shale within the reservoir. In fact, lithology (b) is the rock physics model for a full water saturated rock. On discrimination is not the main concern here. In other words, we (b), the intermediate values of V P and V S on the right lower corner assume that lithology doesn’t change with production over time. of the plot, are associated with clean sandstone. By increasing the clay content, velocities increase because the pore-filling clay stiffens the rock moduli and 1200 Field average pressure(PSIA)[divided by 5] density up to the critical clay concentration at Oil production rate(STB/day) which the entire effective porosity of the sand Gas production rate(MSCF/day) 1000 Water production rate(STB/day) is filled with clay. The highest velocities on CPU time(S) the left upper corner correspond to critical clay concentration. Below this point, both V P and 800 V S decrease by introducing more clay until the point with highest clay content, i.e., pure shale. 600 This phenomenon occurs because quartz grains are replaced with porous clay and decrease the 400 stiffness of the rock. The observed V-shape in the petroelastic domains is a well-known behavior of dispersed-clay distribution in the shaly 200 sandstones. In other words, the discontinuity at the critical clay concentration point creates two 0 different petroelastic domains, shaly sandstone 0 2 4 6 8 10 and sandy shale. Calender time(year) Figure 8 shows the effects of water saturation Figure 6. Simulated production data for a period of 10 years of waterflooding to enand pore pressure on elastic parameters and denhance oil recovery. sity. Panel (a) shows the relative and normalized values of changes in elastic parameters due to changes in water saturation. Because water bulk modulus and density are greater than those of oil, V P , ρ, and V P ∕V S increase when water saturation increases, water replaces oil. In conTable 2. Density and elastic properties of minerals associated trast, V S decreases with increasing water saturation. This is only a with the synthetic reservoir model. density effect because the shear modulus of the rock is unaffected by fluids based on the Biot-Gassmann theory. In descending order, Bulk Shear P-wave S-wave V P ∕V S , V P , ρ, and V S show the corresponding changes of 16, 14, 5, Density modulus modulus velocity velocity 3 and −5 in percent. Panel (b) shows the relative and normalized Constituents (g∕cm ) (GPa) (GPa) (km∕s) (km∕s) values of changes in elastic parameters due to changes in pore pressure. Both V P and V S decrease with increasing pore pressure, Quartz 2.65 37.0 44.0 6.008 4.0748 but V S is more sensitive to pore pressure. Therefore, V P ∕V S inClay 2.41 21.0 7.0 3.4222 1.6440 creases. Density is nearly insensitive to pore pressure variations.
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Shahin et al.
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Consequently, we will evaluate the discriminatory power of various seismic elastic parameters based on a sensitivity analysis and find the optimum time-lapse crossplot to separate the effects of fluid saturation and pressure.
TIME-LAPSE ROCK-FLUID PHYSICS TEMPLATES Any change in elastic parameters is considered a function of changes in pore pressure and/or water saturation assuming a noncompacting isothermal reservoir, constant porosity, permeability, and temperature during production. As a result, we are interested in finding an optimal way to separate the effect of fluid saturation and pressure using known seismic attributes. Figure 10 shows a set of V P ∕V S versus AI crossplots computed after six years (t06) of waterflooding. Each crossplot is color-coded with different petrophysical properties including effective porosity, clay content, effective water saturation, and pore pressure. This figure reflects the monotonic variations of porosity, clay content, and water saturation to some degree. Subsequently, quantitative estimation these properties is possible based on the seismic attributes guided by crossplotting of well-log-derived elastic parameters color-coded with other discriminatory well logs such as shale fraction and porosity. This proven technique, called seismic facies classification described earlier, is a necessary step in seismic reservoir characterization
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to distinguish petrophysical facies (here, facies A, B, and C) by crossplotting seismic attributes. In contrast, it is difficult to estimate pore pressure from each individual static crossplot computed at a single time step of waterflooding. Similarly, crossplotting of the other attributes, SI versus AI and LR versus MR (not shown here), confirm that the quantitative estimation of porosity and clay content is possible, but that is uncertain for water saturation and almost impossible for pore pressure. The key question is if we can quantitatively separate changes in water saturation and pore pressure from dynamic or time-lapse crossplots, ΔðV P ∕V S Þ versus ΔAI, ΔSI versus ΔAI, and ΔLR versus ΔMR, where Δ denotes change in any parameter. Figure 11 displays time-lapse changes in pore pressure and water saturation and the associated changes in elastic parameters. Changes in elastic parameters, saturation, and pressure for the base survey (after one year of waterflooding t01) is subtracted from those of the monitor survey (after six years of waterflooding t06) and then normalized using those of the base survey by Δα ¼ ½ðαmonitor − αbase Þ∕αbase × 100, where α denotes any elastic or petrophysical parameter. The percentage of change in pressure is lower than of that of the saturation. Furthermore, the pressure front propagates very fast, but the waterfront has a mass bulk movement and moves slowly. Interpretation of changes in elastic parameters is complicated because of the joint effects of fluid
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Figure 7. Petroelastic model evaluated at reservoir condition. (a) A plot of total porosity, V P and V S versus clay content. (b) The rock physics model, V P and V S versus total porosity, for a full water saturated rock.
Figure 8. (a) Effects of water saturation and (b) pore pressure on density and elastic parameters of reservoir rock. (a and b) The normalized relative changes of density, P- and S-wave velocities, and velocity ratio at different water saturation and pore pressure, respectively.
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Rock-fluid physics and petro-elastic reservoir
Now, we focus our attention on the most favored pressuresaturation discriminator, SI versus AI, and evaluate it for various monitor and base surveys to see if the same observations are valid. Figure 14 and Figure 15 illustrate ΔSI versus ΔAI crossplots for various time-lapse scenarios. As before, changes in AI, SI, Swe, and change in pore pressure (Pp) for the base survey are subtracted
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saturation and pressure. For example, AI increases by increasing water saturation near the injector at the reservoir corner, but AI decreases when pore pressure increases in the vicinity of the same injector. Visual observation shows that some attributes, e.g., LR and ðV P ∕V S Þ, are primarily more sensitive to fluid saturation than pressure, but others, e.g., SI, μ, MR, and V S are significantly more affected by pressure than saturation. Due to the joint effect of fluid saturation and pressure any visual judgment may be misleading. These observations encouraged us to attempt a sensitivity analysis of seismic attributes to changes in fluid saturation and pressure. To separate the effect of fluid saturation and pressure, it is required to find and crossplot a pair of attributes with one attribute most sensitive to saturation and least sensitive to pressure and the other vice versa. Figure 12 displays the results of the sensitivity analysis. Density purely reflects the changes in water saturation, but it is difficult to get reliable estimates of density from a three-term prestack seismic inversion unless near, middle, and far offset data are accessible (Contreras et al., 2007 and Shahin et al., 2008). In descending order, LR, Lambda (L), bulk modulus (Kb), and EI are the main saturation detectors, whereas μ, MR, V S , and SI, are significantly more affected by pressure than saturation. Finally, V P , AI, V P ∕V S , and L/M carry the joint effect of saturation and pressure. Subsequently V P ∕V S versus AI and L/M versus AI crossplots reflect this joint effect as a trend and are not able to provide discrimination as well as those of [LR versus MR] and [SI versus AI] crossplots. This fact can be easily concluded from Figure 13 in which dynamic crossplots are illustrated for the time-lapse scenario displayed in Figure 11. Here, three crossplots of [ΔðV P ∕V S Þ versus ΔAI], [ΔSI versus ΔAI], and [ΔLR versus ΔMR] are displayed. Similar to Figure 11, changes in elastic parameters, saturation, and pressure for the base survey are subtracted from those of a monitor survey and then normalized using those of the base survey. The first and second rows of this figure are color-coded with changes in effective water saturation and pore pressure, respectively. It is clear from the crossplots that pressure and saturation can be separated to some degree. The direction of saturation change is nearly perpendicular to that of pressure change. The directions of separation are neither parallel to the horizontal nor the vertical axes. The linear trend in the [ΔðVp∕VsÞ versus ΔAI crossplot is associated with the fact that both ðV P ∕V S Þ and AI carry the joint effect of saturation and pressure. Therefore, the crossplot of these two attributes is not a good discriminator for saturation and pressure as confirmed by the sensitivity analysis results. In contrast, LR versus MR and SI versus AI crossplots show almost the same discriminatory powers. The range of numbers on the axes of the LMR crossplot is much broader than that of SI versus AI crossplot. However, the scattering of points has the same shape as SI versus AI, i.e., no more value is added when transforming the original seismic attributes, i.e., SI and AI, to other attributes, i.e., LR and MR. Moreover, we must keep in mind that inversion noise will be amplified whenever we attempt to derive other attributes from the original seismic inversion attributes, so SI versus AI not only is the most powerful discriminator, but also is the least noisy one. As a result, the SI versus AI crossplot is selected as the most favored discriminator of saturation and pressure in a time-lapse study and other derived attributes have less or the same discriminatory power as the SI versus AI crossplot.
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Figure 9. Various crossplots of elastic parameters for a wet sandy shale, a shaly water saturated sand, and a shaly oil-saturated sand all computed at the same differential stress.
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Shahin et al.
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from those of the monitor survey and then normalized using those of the base survey. Panels in Figures 14 and 15 are color-coded with percentage of changes in effective water saturation and pore pressure, respectively. Time-lapse states are selected in such a way that the most likely scenarios in terms of average pore pressure changes are included. In other words, the following four categories illustrated in Figure 6 have been considered in comparison with different time-lapse scenarios:
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Figure 10. Crossplots for V P ∕V S versus AI computed after six years (t06) of waterflooding. Each crossplot is color-coded with different petrophysical properties, including effective porosity, clay content, effective water saturation, and pore pressure. The title of each panel shows the scale label as well.
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Category (1): The first two years of reservoir life immediately after water flooding. In this period, average reservoir pore pressure increases with calendar time. If the initial reservoir state is called t0, then t01 and t02 are in this category, and they are the reservoir states after two and three years of waterflooding. Category (2): In this period, average reservoir pore pressure is high and constant during two calendar years, which include t02, t03, and t04 in this category. Category (3): In this period, average reservoir pore pressure has a significant drop due to production strategy. It takes two calendar years for the reservoir to reach a
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Figure 11. Time-lapse changes (t06–t01) in fluid pressure and saturation and the associated changes in elastic parameters. The x- and y-axes are the same for all panels and they are reservoir length and thickness in meters, respectively. Each panel is color-coded for the corresponding attribute. The title of each panel shows the scale label as well. Here, changes in AI and SI for the base survey (after one year of waterflooding t01) is subtracted from those of the monitor survey (after six years of waterflooding t06), and then normalized using those of the base survey (t01).
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Rock-fluid physics and petro-elastic reservoir
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stable and constant low pressure level, i.e., category (4). Category (3) includes t04, t05, and t06. Category (4): In this period, average reservoir pore pressure is low and constant during the last four years of waterflooding, which include t06, t07, t08, t09, and t10 in this category.
low average pressure in category (4), but Figure 15b is related to high average pressure in category (2). This phenomenon can be explained by Figure 8b, showing that elastic parameters are more sensitive to pressure changes at high reservoir pressure than at low reservoir pressure states.
As displayed in Figure 14, saturation patterns are well detected in most of the time-lapse scenarios. This is mainly because of the high percentage of change in water saturation, up to 100%, in most of the time-lapse scenarios. Of course, the pattern is not always monotonic, and there are some points scattered between different colors. A typical example is Figure 14d, showing (t02–t01). In a few cases, some points are totally misplaced, e.g., narrow trends in upper right corner of crossplots for Figure 14c. In this case, the base and monitor surveys are located in category (3). As mentioned above, a significant pressure drop (up to −30%) has occurred between these categories, and the imperfection in saturation patterns might be related to this fact to some degree. Pressure patterns in Figure 15 are also well detected in most of the time-lapse scenarios, especially when there is a notable pressure change between the base and monitor surveys. As in the saturation patterns, imperfections exist in the pressure patterns. In addition, the interpretation of the pressure patterns is not as easy as the case for saturation pattern. As an example, a small pressure change (less than 1%) in Figure 15a is well detectable, but the same pressure change in Figure 15b is hardly visible. Figure 15a is associated with VP change(%)
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DISCUSSION In this study, we assume that reasonable estimates of acoustic and shear impedances are already obtained via an accurate prestack seismic inversion algorithm constrained by reliable a priori information from well logs, core data, etc. As is the case for any seismic study, limitations include seismic noise, thickness tuning, poor seismic well tie, and stiff rocks with low porosity. In addition, repeatability in seismic data acquisition and processing, and the low-density contrast between hydrocarbon and injected fluid can limit the success of any seismic time-lapse project. We anticipate that the crossplotting of seismic attributes extracted from prestack inversion of noisy seismic data will be challenging in terms of separation of the saturation and pressure. In inverting conventional P-P seismic data, shear attributes, e.g., SI and MR, are mainly obtained from the gradient part of seismic amplitude and more affected by noise than P-wave attributes, e.g., AI and LR, obtained from the intercept portion of the seismic amplitude. This might limit the discriminatory power of the corresponding crossplot, AI versus SI. In such cases, other discriminator pairs,
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Figure 12. Sensitivity analysis of elastic parameters to changes in fluid saturation and pore pressure. The x- and y-axes are the same for all panels. The x-axes indicates change in water saturation, and the y-axes indicates change in pore pressure (in psi). Each panel is color-coded for the corresponding attribute. The title of each panel shows the scale label as well.
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Figure 13. Dynamic or time-lapse crossplots associated with production-induced time-lapse changes illustrated in Figure 11, i.e., time-lapse (t06–t01). The colorbar indicated on the top left crossplot is true for all three crossplots in the top row, and it shows change in effective water saturation (Swe) in percent. The colorbar indicated on the lower left crossplot is true for all three crossplots in the bottom row, and it shows change in pore pressure (Pp) in percent.
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Figure 14. Change in effective water saturation for dynamic or time-lapse crossplots associated with production-induced time-lapse changes. The colorbar indicated on the top of each crossplot shows change in effective water saturation (Swe) in percent. The x- and y-axes (change in acoustic and shear impedances, respectively) are the same for all panels. Each panel is titled with the corresponding time-lapse scenario, e.g., panel (a) indicated with t04–t02 means changes in AI and SI for the base survey (after two years of waterflooding t02) is subtracted from those of the monitor survey (after four years of waterflooding t04), and then normalized using those of the base survey (t02).
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Figure 15. Pore pressure change (%) for dynamic or time-lapse crossplots associated with production-induced time-lapse changes. The colorbar on the top of each crossplot shows change in pore pressure (Pp) in percent. The x- and y-axes (change in acoustic and shear impedances, respectively) are the same for all panels. Each panel is titled with the corresponding time-lapse model, e.g., panel (a) indicated with t04–t02 means changes in AI and SI for the base survey (after two years of waterflooding t02) is subtracted from those of the monitor survey (after four years of waterflooding t04), and then normalized using those of the base survey(t02).
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e.g., [V P ∕V S versus AI] may provide more robust separation between pressure and saturation. The constructed petroelastic model represents the realistic distributions of the reservoir and elastic properties, so the discriminatory power of the crossplots can be fairly generalized to other reservoir models. However; structural complexities in reservoirs, e.g., faults, strong layering of shale and sand, etc., may lead to different shapes for the patterns of pressure and saturation than what presented in this paper. In such reservoirs, it is very likely to see reservoir zones only attributed to pressure change or merely affected by changes in fluid saturation. In crossplot domain, these zones will appear as a cloud of points parallel to one of the axes. In the entire paper, we prefer to use the relative quantities rather than absolute values for all the reservoir properties and elastic parameter. By doing so, it is very easy to compare the time-lapse crossplots constructed using various attributes. However, the discussion on relative pressure (measured in percent) may be misleading if we disregard the initial stress state of the reservoir. For instance, if the initial stress state is close to zero effective pressure, a small pressure increase may change the seismic parameters significantly (see a detailed discussion on V P ∕V S ratio versus differential stress in Duffaut et al. (2007).
CONCLUSIONS The geologically consistent petroelastic model developed in this paper explicitly relates petrophysical properties to elastic parameters. It can be generalized as a model for other geological scenarios and, ultimately, applied to quantitative seismic reservoir characterization and monitoring. In addition, this model is well-suited for resistivity modeling aimed to simulate CSEM data. As an example of applications, a sensitivity analysis is performed, and its results are validated by the developed reservoir model. Sensitivity analysis demonstrates that AI versus SI is the most
useful crossplot to quantitatively separate saturation and pressure changes. It is also shown that saturation patterns are detectable in most of the time-lapse scenarios because of the high percentage of change in water saturation, up to 100%. Pressure patterns are also well detected in most of the time-lapse scenarios in particular when notable pressure changes exist between the base and monitor surveys. The percentage in pressure change is often lower than of that of the saturation change in our waterflooded reservoir. Consequently, saturation patterns are more likely to be detected than pressure patterns. However, this does not necessarily mean that pressure patterns in time-lapse scenarios with lower change in percentage of pressure are less predictable. As we demonstrated, a small pressure change (less than 1%) is well detectable in some scenarios, but it is not visible in others, depending on the reservoir pressure state. We show that imperfections exist in both saturation and pressure patterns and they appear in different forms such as mix-scattering and misallocated points preventing monotonic patterns. Some factors causing this phenomenon are the interaction of saturation and pressure, diffusive nature of the pressure front, and rapid change in pressure due to the production operations. Imperfections in saturation patterns can be also addressed by a pressure factor. The behavior of the pressure front during the waterflooding is very different from that of the water front. The distinct pressure behavior results in rapid isopressure equilibrium and makes the pressure and saturation patterns less predictable.
ACKNOWLEDGMENTS We would like to thank the sponsors of the University of TexasAustin EDGER Forum and the Jackson School of Geosciences at the University of Texas at Austin for their support of this research. Alireza Shahin sincerely thanks Carlos Verdin, Larry Lake, Jack Dvorkin, and William Galloway for enlightening discussions on
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reservoir modeling and rock physics. The associate editor, Miguel Bosche, and three anonymous reviewers are acknowlegded for helpful suggestions. A note of special gratitude goes to Schlumberger for providing reservoir simulation software.
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