Serge A. Shapiro

Characterization of fluid transport properties of reservoirs using induced microseismicity

We systematically describe an approach to estimate the large-scale permeability of reservoirs using seismic emission (microseismicity) induced by fluid injection. We call this approach seismicity-based reservoir characterization (SBRC). A simple variant of the approach is based on the hypothesis that the triggering front of hydraulically-induced microseismicity propagates like a diffusive process (pore pressure relaxation) in an effective homogeneous anisotropic poroelastic fluid-saturated medium. The permeability tensor of this effective medium is the permeability tensor upscaled to the characteristic size of the seismically active heterogeneous rock volume. We show that in a homogeneous medium the surface of the seismicity triggering front has the same form as the group-velocity surface of the low-frequency anisotropic, second-type Biots wave (i.e., slow wave). Further, we generalize SBRC for 3-D mapping of the permeability tensor of heterogeneous reservoirs and aquifers. For this we apply an approach similar to the geometric optics approximation. We derive an equation describing kinematic aspects of triggering-front propagation in a way similar to the eikonal equation for seismic wavefronts. In the case of isotropic heterogeneous media, the inversion for the hydraulic properties of rocks follows from a direct application of this equation. In the case of an anisotropic heterogeneous medium, only the magnitude of a global effective permeability tensor can be mapped in a 3-D spatial domain. We demonstrate the method on several field examples and also test the eikonal equation-based inversion.

Elastic piezosensitivity of porous and fractured rocks

Understanding the stress dependencies of seismic velocities is important for interpreting a variety of seismic data, ranging from amplitude versus offset (AVO) and velocity analysis to overpressure prediction and 4D seismic monitoring of reservoirs. Sometimes, rather complex forms of these dependencies based on specific models of porous space geometry are used. For example, spherical contacts models (Duffy and Mindlin, 1957; Merkel et al., 2001) Duffy Merkel 2001 and crack contacts models (Gangi and Carlson, 1996; Carcione and Tinivella, 2001) have been used in different studies. Gangi96 However, usually the pore-pressure velocity dependence along with the velocity dependence on the confining pressure are phenomenologically described by the following simple relationship (Zimmerman et al., 1986; Eberhart-Phillips et al., 1989; Freund, 1992; Jones, 1992; Prasad and Manghnani, 1997; Khaksar et al., 1999; Carcione and Tinivella, 2001; Kirstetter and MacBeth, 2001)

Triggering of Seismicity by Pore-pressure Perturbations: Permeability-related Signatures of the Phenomenon

We consider various cases of seismicity, induced by artificial fluid injections in boreholes. Like many other authors, we support the hypothesis that to a large extent the triggering of this seismicity is caused by a diffusive process of the pore pressure relaxation in porous (or fractured), saturated rocks. We show that if this hypothesis is correct, then the spatio-temporal distributions of the seismic events must have several specific features related to the effective permeability of the rock. As a rule the fluid injection-induced seismicity obeys such features. These features can be indications of the diffusive and even hydraulic nature of the seismicity triggering process

Seismogenic index and magnitude probability of earthquakes induced during reservoir fluid stimulations

An important characteristic of seismicity is the distribution of magnitudes of earthquakes. Fluid injection in rocks, aimed to create enhanced geothermal systems (EGS), can sometimes produce significant seismic events (e.g., Majer et al., 2007). This is rarely the case in hydraulic fracturing of hydrocarbon reservoirs. However, in any case the behavior of the seismicity triggering in space and in time is controlled by the process of stress relaxation and pore-pressure perturbation that was initially created at the injection source. This relaxation process can be approximated by pressure diffusion (possibly a nonlinear one) in the pore fluid of rocks (e.g., Shapiro and Dinske, 2009). At some locations the tectonic stress in the Earths crust is close to a critical stress, causing brittle failure of rocks. Increasing fluid pressure in such a reservoir causes pressure in the connected pore and fracture space of rocks to increase. Such an increase in the pore pressure consequently causes a decrease of the eff...

Generalization of Gassmann equations for porous media saturated with a solid material

Gassmann equations predict effective elastic properties of an isotropic homogeneous bulk rock frame filled with a fluid. This theory has been generalized for an anisotropic porous frame by Brown and Korringa’s equations. Here, we develop a new model for effective elastic properties of porous rocks — a generalization of Brown and Korringa’s and Gassmann equations for a solid infill of the pore space. We derive the elastic tensor of a solid-saturated porous rock considering small deformations of the rock skeleton and the pore infill material upon loading them with the confining and pore-space stresses. In the case of isotropic material, the solution reduces to two generalized Gassmann equations for the bulk and shear moduli. The applicability of the new model is tested by independent numerical simulations performed on the microscale by finite-difference and finite-element methods. The results show very good agreement between the new theory and the numerical simulations. The generalized Gass-mann model intro...

Characterization of hydraulic properties of rocks using probability of fluid-induced microearthquakes

The use of borehole fluid injections is typical for exploration and development of hydrocarbon or geothermal reservoirs. Such injections often induce small-magnitude earthquakes. The nature of processes leading to triggering of such microseismicity is still not completely understood. Here, we consider induced microseismicity, using as examples two case studies of geothermal reservoirs in crystalline rocks and one case study of a tight-gas sandstone reservoir. In all three cases, we found that the probability of induced earthquakes occurring is very well described by the relaxation law of pressure perturbation in fluids filling the pore space in rocks. This strongly supports the hypothesis of seismicity triggered by pore pressure. Moreover, this opens additional possibilities of using passive seismic monitoring to characterize hydraulic properties of rocks on the reservoir scale with high precision.

Porosity and elastic anisotropy of rocks under tectonic stress and pore-pressure changes

Elastic properties of rocks depend on tectonic stress. Using the theory of poroelasticity as a constraint, we analyze features of these dependencies related to changes in rock pore-space geometry. We develop a formalism describing elastic moduli and anisotropy of rocks as nonlinear functions of confining stress and pore pressure. This formalism appears to agree with laboratory observations. To a first approximation, elastic moduli and seismic velocities as well as porosity depend only on the difference between the confining tectonic stress and pore pressure. However, in general, both the confining stress tensor and the pore pressure must be taken into account as independent variables. The stress-dependent geometry of the pore space fully controls the stress-induced changes in elastic moduli and seismic velocities. Specifically, the compliant porosity plays the most important role, despite the fact that in many rocks the compliant porosity is a very small part of total porosity. Changes in compliant porosi...

Stress sensitivity of elastic moduli and electrical resistivity in porous rocks

Stress dependences of elastic moduli and velocities for anisotropic rocks and electrical resistivity are derived as functions of pore space deformation due to an applied arbitrary load. All dependences have the form of a four-parametric exponential equation V(P) = A + KP − B exp(−DP). The stress dependences are mainly controlled by the tensor of stress sensitivity. One result of our derivations is that if this tensor is isotropic and the rock sample is loaded hydrostatically, the argument D of the exponential term is a universal quantity for all mentioned rock characteristics. We show that laboratory-derived velocity, dilatancy and resistivity measurements as a function of effective pressure support this result.

Finite-difference modeling of wave propagation on microscale: A snapshot of the work in progress

Digital rock methodology combines modern microscopic imagingwithadvancednumericalsimulationsofthephysicalproperties of rocks. Modeling of elastic-wave propagation directly from rock microstructure is integral to this technology. We survey recent development of the rotated staggered grid RSG finite-difference FD method for pore-scale simulation of elastic wavepropagationindigitalrocksamples,includingthedynamic elastic properties of rocks saturated with a viscous fluid. Examination of the accuracy of this algorithm on models with known analytical solutions provide an additional accuracy condition for numerical modeling on the microscale. We use both the elastic and viscoelastic versions of the RSG algorithm to study gas hydratesandtosimulatepropagationofBiot’sslowwave.Weapply RSG method ology to examine the effect of gas hydrate distributions in the pore space of a rock. We compare resulting P-wave velocities with experimentally measured data, as a basis for buildinganeffective-mediummodelforrockscontaininggashydrates. We then perform numerical simulations of Biot’s slow wave in a realistic 3D digital rock model, fully saturated with a nonviscous fluid corresponding to the high-frequency limit of poroelasticity, and placed inside a bulk fluid.The model clearly demonstrates Biot’s slow curve when the interface is open between the slab and bulk fluid.We demonstrate slow wave propagation in a porous medium saturated with a viscous fluid by analyzing an idealized 2D porous medium represented alternating solid and viscous fluid layers. Comparison of simulation results withtheexactsolutionforthislayeredsystemshowsgoodagreementoverabroadfrequencyrange.

Fast location of seismicity: A migration-type approach with application to hydraulic-fracturing data

We propose a new approach for the location of seismic sources using a technique inspired by Gaussian-beam migration of three-component data. This approach requires only the preliminary picking of time intervals around a detected event and is much less sensitive to the picking precision than standard location procedures. Furthermore, this approach is characterized by a high degree of automation. The polarization information of three-component data is estimated and used to perform initial-value ray tracing. By weighting the energy of the signal using Gaussian beams around these rays, the stacking is restricted to physically relevant regions only. Event locations correspond to regions of maximum energy in the resulting image. We have successfully applied the method to synthetic data examples with 20%–30% white noise and to real data of a hydraulic-fracturing experiment, where events with comparatively small magnitudes (<0) were recorded.