Petroelastic approximations for quantitative 4D seismic interpretation
Alvarez Galvez, Erick Raciel
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4D seismic interpretation generally involves analysing changes in amplitude or travel times between a base-line survey (ideally pre-production) and subsequent monitor surveys. Amplitude analysis is commonly performed by calculating the 4D amplitude difference – given by the subtraction of time-shift corrected monitor - base amplitude volumes. This thesis focuses on the development of theoretical approximations that allow explaining, from a physics perspective, the relation between the 4D amplitude signal and production-related changes in pore pressure and fluid saturation. The main objective of finding such approximations is to aid 4D interpretation, by providing physical insights in a quick and intuitive manner that conventional modelling cannot offer. The approximations developed here are expressed in terms of constants and variables with clear physical meaning. This helps in identifying the role that each parameter has in the resulting 4D seismic signal, allowing us to identify those terms with the largest impact and uncertainty. The first conclusion obtained from our derivations is that, except for porosity, the parameters involved act as groups of parameters rather than as individual parameters to form the 4D seismic signal. It is also possible to demonstrate how porosity plays a major role in the magnitude of the 4D signal (this is intuitive for saturation but not for pressure). It was found that, for low porosities, pressure is expected to dominate over saturation and vice-versa. Another important observation is that the magnitude of the rock stress sensitivity determines the polarity of 4D amplitude changes in places where pressure and saturation signals cancel each other (like around injectors). The formulations also allow the analysis of the angle dependence (4D AVO). We observe that, regardless of the type of AVO anomaly of the reservoir in the seismic base line, the 4D AVO signatures behave in a similar way and the role of the overlaying shale in the 4D amplitude variation with angle is minimal. Additionally, previous research has shown that the rock stress sensitivity carries the largest uncertainty and, using the formulations, a methodology was devised to determine a constraint, based on field data observations at injector wells from different fields. The first approximation developed considers a single interface applicable for non-compacting oil reservoirs with no free gas. Subsequent approximations were developed to define the 4D response of fluid contacts, which are applicable to non-compacting reservoirs, including those where free gas is present. The fluid contact equations for the oil-water system were used to develop a technique to estimate residual oil saturation from 4D seismic amplitudes and the method was tested in two North Sea datasets. Finally, an incidental outcome of the new formulations is their potential to be used for 4D seismic inversion to compute pressure and saturation changes. We provide a basic (map-based) implementation of 4D inversion applicable to oil reservoirs with no free gas. The inversion scheme has a straight-forward implementation and requires a minimal amount of a priori information and constraints. It was found that, three angle stacks are required as a minimum to obtain a meaningful inversion result.