To separate and quantify reservoir changes in pressure and saturation from 4D seismic data (Figure 1-7), a good understanding of the impact of reservoir dynamic changes on the elastic properties of the reservoir is a prerequisite. This must involve a quantification of the individual contributions of pressure and saturation effects to the overall 4D seismic response (Figure 2-1). In this context, the quantitative metric is given the name ‘sensitivity’. Sensitivity is specific to the particular dynamic change e.g. pressure sensitivity, water saturation sensitivity, in addition to the particular elastic or seismic attribute derived from the observed 4D seismic data or modelled. For example, moduli, velocities, impedances, time-shifts, amplitudes, AVO gradient, AVO intercept, etc. Sensitivity is a measure of the change in 4D seismic attribute to a unit change of pressure or saturation. In many works concerned with the separation of pressure and saturation changes in 4D seismic data, the sensitivity is often presented as model-driven regression fits, 𝑘𝛼, 𝑘𝜌, 𝐼𝛼, 𝑚𝛼, 𝐼𝛽, and 𝑚𝛽, (Equations 1-1 and 1-2) or data-driven weighting coefficients 𝐶𝑆 and 𝐶𝑃 (Equation 1-13). These weighting or regression terms define the balance between pressure and saturation effects for the inversion, and could be viewed as measures of sensitivity to the independent effects.
Figure 2-1 Sensitivity is a metric for defining the balance between reservoir dynamic changes such as pore pressure and saturations. Colour-filled arrows indicate the 4D impedance response to any of the changes, softening (red /dark red) and hardening (blue/ dark blue). Softening implies a decrease in impedance and hardening implies an increase in impedance. Arrows facing the same direction illustrate the polarity of pressure and saturation changes that are likely to compete against each other during typical production scenarios. For example, in waterflooding, an increase in water saturation, Sw, is accompanied by an increase in pore pressure, and both effects compete against each other. An increase in gas saturation, Sg, (i.e. gas breakout) could also occur, if pressure drops below the bubble point pressure (Falahat et al., 2014), which both compete. Gas injection could also raise pressure as the gas saturation increases, both effects in this case, will reinforce.
Pressure depletion Increasing Sw decreasing Sg
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Rising pressure decreasing Sw Increasing Sg2.1.1 Methods for calibrating sensitivity
Figure 2-2 The three different methods by which the reservoir sensitivity can be estimated. By moving from laboratory measurements on cores, towards rock-physics models constrained by repeat logs and crossing over to the 4D seismic data domain, the analysis is closer to the in-situ conditions and can be argued to be more accurate, modified after Amini (2014)
The techniques for estimating sensitivity are model-driven or data-driven as it is by these two approaches, pressure and saturation changes are separated from 4D seismic data (Figure 2-2) (see also section 1.3). Part of the model-driven approach as popularised by Landrø (2001), involves (1) estimating pressure sensitivity by laboratory analysis on cores where elastic moduli of the rock are measured under different confining pressures, combined with (2) fluid saturation sensitivity using empirical fluid equations, such as Gassmann’s (1951) theory (see section 2.2.1). Although, much of our current knowledge of pressure sensitivity is shaped by laboratory measurements on cores, it is generally acknowledged that such measurements have limited applicability to the in-situ field-scale reservoir response (e.g. Nes, 2000; Eiken and Tøndel, 2005; Alvarez and MacBeth, 2014); contrary to fluid saturation sensitivity which is believed to be adequately explained by Gassmann’s model. Alvarez and MacBeth (2014) discuss the issues associated with laboratory experiments which include: statistical sampling of the cores, time-scale of the production relative to the cycle that pore pressure is cycled in the laboratory, core plug damage, frequency dispersion, evaluation of the effective stress coefficient, geomechanical effects, measuring dry-rock response using the Gassmann model, the role of clays and shales, imperfect stress recovery and stress
Close r to in -situ Inc re asing u n ce rt ai n ty • Quantitative 4D seismic data analysis • Rock-physics models
(and repeat logs) • Core data analysis
Data-driven
asymmetry. Laboratory-based measurements can also be boycotted by using repeat logs- where repeat formation tester (RFT) and elastic logs acquired from the reservoir intervals that have undergone production are used to calibrate the pressure sensitivity. The calibration uses rock-physics equations to model and fit the repeat elastic logs. Repeat logs are however not widely available across fields and such analyses are very limited. An excellent example is given in Fürre et al. (2009) which reports weaker pressure sensitivity than those measured in the laboratory, and found that the log- derived calibration compared favourably with the observed 4D seismic response. Of particular concern with rock physics models are that they are grossly uncertain, time consuming and difficult to calibrate sufficiently (Amini, 2014; Briceno et al., 2016).
Many studies point to 4D seismic data as the measure of “truth” to validate log-derived rock-physics models or laboratory measurements (e.g. Eiken and Tøndel, 2005; Fürre et al. 2009; Amini and MacBeth, 2015; Avseth et al., 2016). The 4D seismic data are a direct and spatially-dense measure of the reservoir’s response over production time. This allows for the investigation of spatial variations in sensitivity, and across monitor times. The data-driven method thus addresses the gaps in rock-physics models using 4D seismic data as an alternative to calibrate the relationship between observed magnitudes of the 4D seismic response and measured magnitudes of pressure and saturation changes induced by production (for example, MacBeth et al., 2006; Landa et al., 2015). Although 4D seismic data measurements better represent the in-situ behaviour of the reservoir rock and associated fluids, it can be argued that the 4D seismic method can be of higher uncertainty than model-driven methods on the basis of non-repeatability noise. This however, depends on individual field acquisition and processing of the 4D seismic data, but the success so far with the data-driven method is promising as they are more reservoir-consistent. The insights gained from rock-physics models are however essential for the quantification and interpretation of 4D seismic signatures.
In this chapter, 4D rock-physics modelling is used to provide background understanding of the variation of sensitivity in sandstones as well as the sensitivity to pressure and fluid saturation changes. Zero-offset 4D amplitudes and time-shifts are modelled to define and quantify the reservoir sensitivity in sandstones. The aim is to guide the interpretation achieved from quantifying the in-situ reservoir’s sensitivity using measured 4D seismic data, to be explored in Chapter 3. Noted earlier in Equations 1-17 and 1-18, the sensitivity depends on the angle of incidence of the 4D seismic data used
for calibration. In Chapter 7 (for example, Figure 7-7) this dependency is shown for the Heidrun field using AVO stacks of the near-offset, mid-offset, far-offset and full-offset to quantify the sensitivity to reservoir changes. It is shown that both the sensitivity to pressure and fluid saturation changes vary with angle of incidence. Also note that full- offset stacks are used to quantify the sensitivity of the various field reservoirs in Chapter 3, and zero-offsets are used in the rock-physics study in this chapter. Ideally, full-offset stack and zero-offset 4D seismic data should be the same after processing, but this is not always true. Seismic acquisitions are strategically designed to image at different offsets, but the propagation effects due to this offset variation are not completely removed in the final processed and stacked (full-offset) 4D seismic data. This means that AVO effects will still interfere and complicate the response observed in the full-offset stack. So, it is to be expected that the sensitivity obtained using zero- offset 4D seismic data will differ from those obtained using full-offset stacks.