Perturbation theory has been used widely in many applications in seismology, more recently for time-lapse studies. Time-lapse studies are cost-effective approaches for monitoring changes in a reservoir due to production or enhanced oil recovery techniques to restore formation pressure and improve the fluid flow over a period of time in a reservoir. By monitoring these changes, time-lapse studies facilitate management of a reservoir and extend the useful life of an oilfield.
Perturbation or, scattering theory is used as a framework to model these difference data in a time lapse study. The baseline survey (before changes) is set as a background medium which undergoes a range of perturbations by the time of the monitor survey (after changes). The study in this thesis focuses on applying the perturbation theory in time-lapse problems to describe the difference data from a baseline survey to a monitor survey in a reservoir. Changes in the pressure or fluid saturation in a reservoir cause changes in seismic parameters such as P-wave and S- wave velocities and density. These changes give rise to difference data between the baseline survey data and monitor survey data. The perturbation quantifies the changes in P-wave and S-wave velocity and density from the time of the baseline relative to the time of the monitor survey.
Time-lapse amplitude variation with offset (AVO) methods are applied to analyze changes in the seismic parameters. A scheme for modelling linear and nonlinear elastic time-lapse difference AVO data for P-P sections (an incident P-wave with reflected P-wave) is formulated. This framework is expressed as perturbation in P-wave and S-wave velocities and density. The perturbations in these parameters are defined such that they can account for the changes in the baseline survey for the wave entering from the cap rock (layer above the reservoir) into the reservoir, and the time-lapse changes in the reservoir. The difference data then, are described as an expansion in orders of both baseline interface properties and time-lapse changes from the time of the baseline survey to the time of the monitor survey. I have also examined this formulation with the numerical data used in the literature for real time-lapse data. To first order the framework for time-lapse difference data is in agreement with Landrø's linear approximation. The higher order terms represent corrections appropriate for large P-wave and S-wave velocity and density contrasts in the reservoir from the time of the baseline survey to the time of the monitor survey. This framework is then expanded to describe the difference data for shear waves and converted waves.
A physical modeling data set is acquired, simulating a time-lapse problem, to validate the theoretical results for P-P data. Physical modelling of geophysical data provides physical property distributions of the Earth which are invariably simpler than the real Earth, and the degree of simplification depends upon the geometry used for the data acquisition. 3D seismic surveys resembling the baseline and monitor surveys are modeled with The University of Calgary Seismic Physical Modelling Facility. Plexiglas, Polyvinyl chloride (PVC), and phenolic slabs are used as proxy materials to simulate the cap rock and reservoir at the time of baseline and monitor survey, respectively. Reflected amplitudes are picked at plexiglas-PVC and plexiglas-phenolic (along the direction of the isotropic plane for phenolic) interfaces and are corrected for geometrical spreading, emergence angle, free surface, transmission loss, and radiation patterns. Results indicate that higher order expansion terms, involving products of elastic time-lapse perturbation and baseline medium perturbation, match laboratory data with significantly reduced error in comparison to linearized forms. We conclude that in many plausible time-lapse scenarios the increase in accuracy associated with higher order corrections demonstrated in this thesis enhances time-lapse modeling.
In the last part of the study, in conjunction with Talisman Energy Inc. part of Repsol Group, a multicomponent time-lapse seismic data set, which was acquired during hydraulic fracturing of two horizontal wells in the unconventional Montney Reservoir at Pouce Coupe Field in the Peace River area, has been used to compare our theoretical results for P-P data. These real data are analyzed to validate derived linear and nonlinear theoretical results for the time-lapse AVO difference during the change in a reservoir from the baseline survey relative to the monitor survey. A well tie has been generated to determine the location of the reservoir on the seismic data at the Montney Formation. Synthetic logs for P-wave and S-wave velocities and density are then generated for the monitor survey. Analyzing the baseline and monitor surveys shows that the nonlinear components of the difference data interpretation scheme do not contribute significantly to estimate time-lapse AVO difference. This is consistent with the fact that the Pouce Coupe data set has a low baseline contrast between the layer above the reservoir and reservoir and a low time-lapse contrast from the baseline survey to the time of the monitor survey. Expanding the field data component of this research, to provide field case studies validating the nonlinear portion of the theory in addition to the linear portion, is a matter of ongoing research which will confirm after this thesis.
View full article as PDF (4.54 Mb)