Application of earth tide analysis in subsurface monitoring
Keywords: Energy Resources Engineering.

Besides the ocean and the atmosphere, the solid Earth is also subject to tidal forces, and the tide-induced deformation of the solid Earth can be observed and utilized to retrieve useful subsurface information. In this work, we illustrated the application of Earth tide analysis in subsurface monitoring by covering topics including extraction of Earth tide signals from downhole pressure data, analysis of extracted tidal signals and computation of amplitudes and phases, analytical relationship between the reservoir tidal response and the theoretical tidal stress for different types of reservoirs, effects of wellbore storage and skin on reservoir tidal responses, the radius of influence of the Earth tide analysis and the atmospheric loading effects. Tidal fluctuations have been observed in downhole pressure measurements for a long time. We studied the application of data spline and the Savitzky--Golay filter (S-G filter) in extracting tidal signals from downhole pressure data. It was found that both algorithms can extract tidal signals effectively with appropriate nodal distance or approximation window size. The data spline and the S-G filter can be combined to extract and smooth the tidal signals. Discrete Fourier transform can be applied to decompose the extracted signals and compute the amplitude and the phase corresponding to a tidal constituent. The application of a phase interpolation approach and the Hanning window can improve the accuracy of the phase estimation. An integrated tidal analysis approach based on data spine, S-G filter, discrete Fourier transform, phase interpolation and the Hanning window was developed to perform the extraction of tidal signals from downhole pressure data, the decomposition of extracted signals into different tidal constituents, and the computation of amplitude ratios and phase shifts. Tidal response models were established to describe the relationship between reservoir and wellbore properties and the tidal information obtained from the extracted signals, including the amplitude ratio and the phase shift. The tidal response models were elaborated under different reservoir and wellbore conditions. For perfectly confined reservoirs without fluid flows, the tidal efficiency and the loading efficiency can be utilized to monitor poroelastic property changes in onshore and offshore reservoirs respectively. One potential application is to monitor the CO2 migration in carbon sequestration projects. The tidal efficiency and the loading efficiency are inversely related with the CO2 saturation in the target reservoir, which was demonstrated with both onshore and offshore field data. General tidal response models were developed for confined reservoirs with only horizontal flows and semiconfined reservoirs with both horizontal and vertical flows. The skin effect and wellbore storage effect were considered in the analytical models. For confined reservoirs, the amplitude ratio and the phase shift were expressed as functions of dimensionless transmissivity, dimensionless wellbore storage, and the skin factor. We found that higher positive skin factor can lead to more negative phase shifts, and a negative skin factor can potentially lead to a phase advance. For semiconfined reservoirs with vertical leakage, the amplitude ratio and phase shift also depend on the magnitude of the vertical leakage. The analytical solution for semiconfined reservoirs indicates that larger vertical leakage can cause smaller amplitude ratio and larger phase advance or smaller phase lag. Based on the analytical solution, the effect of vertical leakage can be separated from that of enhanced permeability around the wellbore, and the phase shift contributed by each of the two effects can be evaluated independently. A tidal response model based on a two-layer radial composite reservoir setting was developed to investigate the effects of radial heterogeneity on the Earth tide analysis. Wellbore storage and skin effects were considered in the tidal response model. The analytical solution indicates that the change in the amplitude ratio gradually decreases as the interface radius increases, and the amplitude ratio eventually converges to a constant value at the radius of influence. The radius of influence of the Earth tide analysis is positively correlated with the effective diffusivity, which was defined as the ratio of the conventional reservoir diffusivity to the tidal frequency. The results given by the analytical model were compared with those from a reservoir simulator, and the radii of influence obtained from the two approaches were consistent. Finally, the effects of atmospheric loading on onshore reservoirs were studied, and an analytical model incorporating both the Earth tide effects and atmospheric loading effects was proposed. The solution to the analytical model provided the combined wellbore pressure response to both effects. The wellbore storage and skin effects were incorporated in the combined model, and it was found that larger wellbore storage or skin effects can result in smaller amplitude and longer time delay of the combined response