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Time-Lapse Joint Inversion of Seismic and Resistivity Data during Production of Oil in Carbonate Rocks

A. Revil, M. Karaoulis, and J. Zhang
Colorado School of Mines, Dept. of Geophysics, Golden, CO, USA

Time-lapse joint inversion of geophysical data is required for a number of important problems in geosciences including the management of oil and gas reservoirs and the sequestration of CO2 (e.g., Kowalsky et al., 2006). In some cases, the inclusion of the physics of the monitored process directly in the inversion of the geophysical data can help to reduce the non-uniqueness of the geophysical inverse problem (e.g., Liang et al., 2011). If we consider joint inversion problem of geophysical data alone, there are essentially two types of strategies that can be used, one based on the use of petrophysical models to link geophysical methods (e.g., Hertrich and Yaramanci, 2002; Rabaute et al., 2003; Kowalsky et al., 2006; Woodruff et al., 2010) and one based on the use of structural similarities between the sought physical properties (e.g., Gallardo and Meju, 2003, Linde et al., 2008). Because different rock properties are usually sensitive to different aspects of the texture of porous materials (e.g., fracture versus matrix properties for dual porosity systems), the joint inversion based on petrophysical models may have some difficulties in a certain number of cases while the joint inversion based on the structural similarities (Gallardo and Meju, 2003) may have a better chance to work out the contributions from the different property groups, especially for time-lapse tomography.

Several strategies are also possible for the time-lapse inversion of geophysical datasets. While sequential time-lapse inversion is generally successful (e.g. Karaoulis et al, 2011a), the result is sensitive to the inversion of the first snapshot of the physical process under study. Thus, the traditional approach of inverting separately different snapshots and comparing the results may not be the favoured strategy here. The actively time-constrained (ATC) approach of Kim and Karaoulis (Kim et al., 2009; Karaoulis et al., 2011a, b) seems to be a very suitable approach to invert simultaneously a complete time-lapse geophysical dataset using time as a fourth dimension and using a time-based regularization term into a generalized cost function.

In this presentation, we combine the structural joint inversion and the active time-constrained time-lapse inversion together to invert cross-hole data and we discuss the advantages in combining these two approaches together for the monitoring of partial saturation changes during the production of oil in carbonate reservoirs. This approach will be first illustrated below on a simple problem. A joint time lapse inversion between ERT and GPR is shown by Doetch et al, 2010. In their approach time lapse inversions were used by using the difference inversion (La Brecque and Yang, 2001). This approach minimizes the differences with respect a background model of each time step separately. In our approach, time is introduced to the system and encompasses all space models during the entire monitoring period (global system). The minimized cost function includes a global misfit for all data during the entire monitoring period.

AAPG Search and Discovery Article #120034©2012 AAPG Hedberg Conference Fundamental Controls on Flow in Carbonates, Saint-Cyr Sur Mer, Provence, France, July 8-13, 2012