Vadim Lisitsa, Institute of Petroleum Geology and Geophysics (Russia)

KAUST-IAMCS Workshop on Multiscale Modeling, Advanced Discretization Techniques, and Simulation of Wave Propagation

May 7-8, 2011

King Abdullah University of Science and Technology (KAUST)

Thuwal, Kingdom of Saudi Arabia

Finite-Difference Simulation of Seismic Waves Propagation in Multiscale Media: Impact of Cavernous/Fractured Reservoirs (Synthetic Simulation and Field Study)

Authors:

• Vadim Lisitsa, Institute of Petroleum Geology and Geophysics SB RAS, Russia
• Victor Kostin, OAO Intel ZAO, Novosibirsk, Russia
• Galina Reshetova, Institute of Computational Mathematics and Mathematical Geophysics of SB RAS, Novosibirsk, Russia
• Vladimir Tcheverda, Institute of Petroleum Geology and Geophysics SB RAS, Russia
  

One of the key challenges in modern seismic processing is to restore the microstructure of the hydrocarbon reservoir. Recently various techniques have been developed to perform this analysis with the help of scattered seismic waves. Among them, the scattering index presented in (Willis et al., 2006) or a variety of the imaging techniques developed under the generic name of interferometry (see e.g. book of G.Schuster, 2009).

The first step in the development of any inversion/imaging procedure is to simulate accurately the wave field scattered by fractures and caves. The numerical and computer constraints even on very large clusters place limitations on the resolution of the model described. Really, a reservoir beds typically at a depth of 2000 – 4000 meters, which is about 50 – 70 dominant wavelengths. The current practice for the finite-difference simulation of seismic waves propagation at such distances is to use grid cells of 0.05 - 0.1 of a dominant wavelength, usually between 5 - 10 meters. So, one needs to upscale heterogeneities associated with fracturing on a smaller scale (0.01 - 1 meter) and to transform them to an equivalent/effective medium. This effective medium will help reproduce variations in the travel-times and an average change of reflection coefficients but absolutely cancels the scattered waves that are a subject of the above mentioned methods for characterizing fracture distributions.

Thus, the main challenge with a full scale simulation of cavernous/fractured (carbonate) reservoirs in a realistic environment is that one should take into account both the macro- and microstructures. A straightforward implementation of finite difference techniques provides a highly detailed reference model. From the computational point of view, this means a huge amount of memory required for the simulation and, therefore, extremely high computer cost. In particular, a simulated model of dimension 10km × 10km × 10 km, which is common for seismic explorations, with a cell size of 0.5m claims 8×10¹² cells and needs ≈ 350 Tb of RAM.

The popular approach to overcome these troubles is to refine a grid in space only and there are many publications dealing with its implementation (see (Kristek, Moczo and Galis, 2010) for a detailed review), but it has at least two drawbacks:

1. To ensure stability of the finite-difference scheme the time step must be very small everywhere in the computational domain;
2. Unreasonably small Courant ratio in the area with a coarse spatial grid leads to a noticeable increase in numerical dispersion.

Our solution to this issue is to use a mutually agreed local grid refinement in time and space: spatial and time steps are refined by the same factor.

From our numerical experiments we made conclusion that the preferential propagation of scattered energy is along fracture corridors. In order to validate this conclusion for field seismic data there was chosen a well covered by dense enough 3D acquisition system. Following (Pozdnyakov and Tcheverda, 2006) seismic data processing of scattered waves was performed and azimuth distribution of scattered energy estimated and presented in the Fig. 1 (left). At the same time for the well a study of the distribution of cracks was implemented with a special device (Fracture Monitoring System). The results can be seen in Fig. 1 (right). As one can see, both diagrams are similar in their main features.

Fig.1. Azimuthal distribution of scattered energy (left) in comparison with results of Fracture Monitoring System for a well.

References:

1. Kristek, J., Moczo, P. & Galis, M. 2010. Stable discontinuous staggered grid in the finite-difference modelling of seismic motion. Geophysical Journal International 183, 1401-1407.
2. Pozdnyakov V.A., Tcheverda V.A. 2006. 3D Focusing Transformation: Reliable Tool for Imaging of Scattering Objects. 76th Annual Exhibition and Meeting of Society Exploration Geophysicists, 30 Sept. – 05 Oct. 2006, New Orleans, USA.
3. Schuster G. 2009. Seismic interferometry. Cambridge university press, Cambridge.
4. Willis, M., Burns, D., Rao, R., Minsley, B., Toksoz, N. and Vetri, L. 2006. Spatial orientation and distribution of reservoir fractures from scattered seismic energy. Geophysics. 71, O43 - O51.