Background

All rock physics models require a number of inputs, including porosity and mineralogy. Then there is a host of models to choose from. The procedure of selecting a model based on a training dataset (e.g., well data) has been discussed and utilized in the previous chapters. Once the model is selected, it allows us to explore various “substitution” scenarios, such as lithology, porosity, and reservoir substitution, usually called “what if” perturbations of the original data.

Perhaps the first rock physics substitution equation is that by Gassmann (1951). It is commonly used now to predict the response from a reservoir with a hypothetical “what if” pore fluid from that measured in the well. But can such fluid substitution be conducted directly on the seismic amplitude? Li and Dvorkin (2012) show that it can be done, at least approximately and within a set of assumptions that include establishing a rock physics model relating the elastic properties to porosity and mineralogy. The question posed is whether there are simple recipes that can guide us in predicting a reflection at the shale/gas-sand interface if the reflection at the shale/wet-sand interface is known (and vice versa).

Background

Time-lapse (4D) seismic methods attempt to quantify the difference in the seismic response of the subsurface before and after human interference, mainly hydrocarbon production and fluid injection. Multiple theories and case studies have been published. To mention just a few of them, we refer the reader to Calvert (2005), Osdal et al. (2006), Gommesen et al. (2007), Ebaid et al. (2008), Dvorkin (2008b), Ghaderi and Landrø (2009), Trani et al. (2011), and Ghosh and Sen (2012). The main idea is to interpret the temporal changes observed in the seismic response of the subsurface in terms of hydrocarbon saturation, pore pressure, and temperature in order to ascertain bypassed pockets of hydrocarbons and, eventually, increase the recovery factor.

Perhaps the first glimpse into the physics of time-lapse monitoring was in Nur (1969) where the ultrasonic-wave compressional velocity was measured on a granite sample with just 1.5% porosity as the water was draining from the originally fully saturated sample (Figure 10.1). Later, Wang (1988) discovered that the velocity in rock samples saturated with heavy oil strongly decreases when the samples are heated.

Reflection modeling at an interface: the concept

Forward modeling of seismic reflections at an interface between two elastic half-spaces is a traditional way of setting expectations for the character of seismic traces between the overburden shale and sand reservoir; at gas/oil, gas/water, and oil/water contacts; as well as at various unconformities present in the subsurface. To conduct such computations, the elastic properties of both half-spaces are required. If we know the site-specific transforms between the rock properties and conditions and the elastic properties, we can compute seismic reflections at an interface as a function of porosity, lithology, and fluid. In the next section of this chapter we will review the mathematical apparatus used to compute seismic reflections and then proceed with utilizing these equations for assessing the seismic signatures from the properties of the rock half-spaces forming the interface.

Normal reflectivity and reflectivity at an angle

The reflectivity at an interface between two elastic bodies is defined as the ratio of the reflected wave amplitude to the incident wave amplitude. As the wave strikes the interface, it produces the reflected and transmitted waves (Figure 4.1). Here we will analyze only the reflected P-wave. The incident P-wave can approach the interface in the direction normal to the interface or at a non-zero angle (Figure 4.1). The angle of incidence is defined as the angle between the direction of propagation of the wave front and the direction normal to the interface between the two half-spaces. While a normal-incidence P-wave does not produce S-waves, a P-wave at a non-zero incident angle produces reflected and transmitted S-waves. In the following equations for the P-to-P reflectivity, the properties of the upper interface are marked by subscript “1” while those of the lower interface are marked by subscript “2.”

Introduction

A key challenge faced by geoscientists is to establish and validate the economic potential of a hydrocarbon exploration play using seismic amplitudes. This validation requires the development and implementation of interpretation techniques for calibrating rock properties to seismic data. Quantitative seismic interpretation techniques have been applied with frequent success to predict lithology and fluids in areas with extensive local well control (Avseth et al., 2005). The application of the same techniques is problematic in frontier basins where the nearest well control is some distance away. The main reason is that when interpretation techniques are extrapolated outside their original range of calibration, seismic anomalies cannot be reliably recognized, predicted, and validated.

Validation of recognized seismic anomalies comprises two stages (a) rock-physics-based modeling for amplitude calibration described in this chapter, followed by (b) detailed amplitude interpretation and risk analysis (Chapter 12). This integrated methodology for regional exploration combines rock physics modeling and seismic-based evaluation techniques, allowing the seismic interpreter to predict, quantify, and extrapolate seismic response changes by linking them to rock-property variations and plausible geologic scenarios. This method includes examination of depositional and diagenetic processes to understand the effects of geology on seismic responses as well as possible differences between the interpretation model at the current prospect and that established elsewhere using well control and other known inputs.

Third source of controlled experimental data

Laboratory experiments and well data serve as main sources of controlled experimental data where a number of physical properties are measured on the same samples at varying conditions, such as saturation and pressure. Chapter 2 discusses how these data are used to derive theoretical models as well as establish the relevance of these models to rock types.

Computational rock physics, also called digital rock physics or DRP, is the third such source. The principle of this technique is “image and compute”: image the pore structure of rock and computationally simulate various physical processes in this space, including single-phase viscous fluid flow for absolute permeability; multiphase flow for relative permeability; electrical flow for resistivity; and loading and stress computation for the elastic properties.

The principle of DRP is simple but its implementation is not. It requires at least three main steps: imaging; image processing and segmentation; and physical property simulation.

Three-dimensional imaging of a rock sample is usually performed in a CT scanning machine by rotating the sample relative to an X-ray source. The actual 3D geometry is reconstructed tomographically from these raw data and the image appears in shades of gray. The brightness of a voxel in such a 3D image is directly affected by the effective atomic number of the material and is approximately proportional to its density. For example, dense pyrite will appear bright while less dense quartz will appear light gray. The empty pore space will be black and parts of it illed with, for example, water or bitumen will be dark gray. To image very small features present in shale or micrite in carbonates, even the sharpest CT resolution may not be enough. A different technique, the so-called FIB-SEM, is used where the focused ion beam gradually shaves off thin slices of the sample and the exposed 2D surface is imaged (photographed) by the scanning electron microscope to produce a stack of closely spaced 2D images.