Spatio–Temporal Analysis of Deformation at San Emidio Geothermal Field, Nevada, USA between 1992 and 2010

Deformation has been observed at San Emidio geothermal field in Nevada using geodetic and seismic instruments. These observations point to an interaction between operations at the power plant and stress in the subsurface. In particular, cooling of the reservoir (via injected cooled water) and localized pressure changes (due to pumping and injection) contribute to the stress state at San Emidio. Our WHOLESCALE proposal has been recommended by the Geothermal Technologies Office of the U.S. Department of Energy for negotiation of a financial award. Indeed, the WHOLESCALE acronym stands for “Water & Hole Observations Leverage Effective Stress Calculations And Lessen Expenses”. The goal of the WHOLESCALE project is to simulate the spatial distribution and temporal evolution of stress in a geothermal system. To reach this goal, the WHOLESCALE team proposes to develop a methodology that will incorporate and interpret data from four methods of measurement into a multi-physics model that couples thermal, hydrological, and mechanical (T-H-M) processes over spatial scales ranging from the diameter of a borehole (~0.1 m) to the extent of the entire field (~10 km) and temporal scales ranging from the duration of a micro-seismic event (~1 second) to the typical lifetime of a producing field (3 decades).

By analyzing these data streams, we can take advantage of the perturbations created by pumping operations to infer temporal changes in the state of stress in the geothermal system. For example, we conducted the PoroTomo experiment at the geothermal field at Brady Hot Springs, Nevada . There, a scheduled cessation of both production and injection pumping produced fluid pressure changes as large as 150 kPa (roughly equivalent to 15 m of water) [Patterson et al., 2017] that are associated with microseismic events [Cardiff et al., 2018]. There, "shutdowns in pumping for plant maintenance correlate with increased microseismicity" [Cardiff et al., 2018]. Following these authors, we hypothesize that "extraction of fluids inhibits fault slip by increasing the effective [normal] stress on faults; in contrast, brief pumping cessations represent times when effective [normal] stress is decreased below its long-term average, increasing the likelihood of microseismicity" [Cardiff et al., 2018].
Similar phenomena have been observed at San Emidio. In the month of December 2016, more than 100 discrete micro-seismic events occurred as the power plant and pumping were shut down and subsequently restarted [Warren et al., 2018]. These events are related temporally to recovery during shutdown and spatially clustered around the producing wells.
Such induced seismicity is caused by changes to the state of stress in and around the geothermal reservoir. Indeed, we hypothesize that increasing pore-fluid pressure reduces the effective normal stress acting across preexisting faults and induces micro-seismic events.

WHOLESCALE PROJECT
Our WHOLESCALE project has been recommended by the Geothermal Technologies Office of the U.S. Department of Energy for negotiation of a financial award 1 . Indeed, the WHOLESCALE acronym stands for "Water & Hole Observations Leverage Effective Stress Calculations And Lessen Expenses".
The goal of the WHOLESCALE project is to simulate the spatial distribution and temporal evolution of stress in a geothermal system. To reach this goal, the WHOLESCALE team proposes to develop a methodology that will incorporate and interpret data from four methods of measurement into a multi-physics model that couples thermal, hydrological, and mechanical (T-H-M) processes over spatial scales ranging from the diameter of a borehole (~0.1 m) to the extent of the entire field (~10 km) and temporal scales ranging from the duration of a micro-seismic event (~1 second) to the typical lifetime of a producing field (3 decades).
The WHOLESCALE team will take advantage of the perturbations created by pumping operations to infer temporal changes in the state of stress in the geothermal system. This rheological experiment will apply the key idea that increasing pore-fluid pressure reduces the effective normal stress acting across preexisting faults. Accordingly, the WHOLESCALE team proposes to collect four types of observational data at San Emidio: (1) Seismology will determine the locations and focal mechanisms of micro-seismic events. A dense array of 3-component seismic instruments will be deployed over the area of the 2016 events during the next planned shutdown of the production wells. Seismic tomographywhen combined with density models estimated from gravimetric surveyswill also provide constraints on material properties such as Poisson's ratio and shear modulus.
(2) Borehole image logs will observe failures in the formation surrounding the well bore to constrain the magnitude and orientation of stress (e.g., Zoback, 2007). If a given fracture is hydraulically conductive, then we infer that it is active under the current state of stress.
(3) Geodesy will measure deformation of the ground surface. At least two continuously operating GPS stations will be installed, one within the subsiding area and one on stable rock outside it. InSAR monitoring will continue.
(4) Hydrology will measure pressure and temperature in multiple boreholes to quantify the propagation of fluid-pressure fronts and changes to effective normal stress.
Each of these four types of observational data is described in detail below. To interpolate and interpret these rich data sets, the WHOLESCALE team will solve the coupled differential equations governing the physics of a fractured, poroelastic medium under stress. We will perform thermo-hydro-mechanical (T-H-M) coupled modeling using a numerical simulator named GEOS [Liu et al., 2018]. Using a combination of the finite-element and finite-volume methods, the GEOS code solves the coupled differential equations governing the flow of fluid and heat as well as the mechanics of the medium deforming under stress. The resulting solution includes the complete stress tensor σ ij as a function of time t at every location (x, y, z) in a large 3-dimensional mesh of the study volume.
In configuring the T-H-M models, the WHOLESCALE team will honor the geologic structure and its material properties. The rock mechanical properties (e.g., Poisson's ratio, density, Young's modulus, thermal expansion coefficient, friction coefficients, effective pressure coefficients) will be measured in samples via laboratory experiments. To account for heterogeneities in mechanical properties over the scale of the reservoir, the WHOLESCALE team will extend the values measured in the lab with information from the borehole logs and the geologic model [Rhodes, 2011] using data-science techniques [e.g., Bayuk et al., 2008]. The GEOS code can account for fluid flow in a porous medium that also includes discrete fractures.
The study site at San Emidio includes a volume with length of ~6 km, width ~5 km, and depth ~2 km. At each point within a mesh of this volume, the resulting numerical solution will determine the complete stress tensor as a function of time as well as its sensitivity to perturbations in the input parameters. The numerical GEOS solution will also calculate modeled values for each of the four types of observable quantities. By optimizing the goodness of fit between the observations and the modeled value calculated by the GEOS simulator, the proposed methodology will seek the model configuration that best fits the data while assessing the uncertainty of the associated reservoir parameters. The result will be a reliable simulation of the spatial distribution and temporal evolution of the full stress tensor σ ij (t, x, y, z) at San Emidio.

EXISTING DATA SETS Seismology
The study area at San Emidio has been seismically imaged using a temporary array deployed in October 2016. The locations of microseismic events and the distribution of emitted seismic energy have been determined [Warren et al., 2018].

Geodesy
Interferometric analysis of synthetic aperture radar images (InSAR) is a geodetic technique that calculates the interference pattern caused by the difference in phase between two images acquired by a satellite radar sensor at two distinct times. The resulting interferogram is a contour map of the change in distance between the ground and the radar instrument. These maps provide a spatial sampling density of ~100 pixels/km 2 , a precision of ~10 mm, a registration accuracy of ~10 m, and an observation cadence of ~1 pass/week [e.g., Massonnet and Feigl, 1998].
Downward deformation of the ground surface (subsidence) associated with geothermal production can be caused by a number of processes, including contraction due to reductions in pore-fluid pressure, thermally-induced contraction, and/or compaction. The same processes can also change the state of stress in the rock matrix sufficiently to induce failure and thus seismicity. At Brady Hot Springs, subsidence rates as high as 20 mm/yr have been measured using InSAR [Ali et al., 2016]. The process driving the observed subsidence is most likely thermal stress caused by injection of cooled brine, based on Bayesian inference with inverse modeling of the InSAR data [Reinisch et al., 2018].
At San Emidio, subsidence at a rate of several mm/yr was measured in the 1990s using InSAR [Eneva et al., 2011;Reinisch, 2019]. For example, Figure 5 shows subsidence at a rate of at least 7 mm/yr at San Emidio. Using nonlinear inversion, Reinisch et al. [2019] "determine that the deformation at San Emidio is well explained by parameterizing the reservoir as a cuboidal sink." Furthermore, "temporal analysis of the volume change rates estimated from individual interferometric pairs using this deformation model suggests a constant rate of volume change of (−1.1 ± 0.1) × 10 4 m 3 /yr between 1992 and 2010, consistent with the time-series analysis in terms of line-of-sight displacement performed by Eneva et al. [12]." .

Hydrology
Using absolute stress to predict effective stress acting on failure surfaces requires an understanding of the fluid pressure and its evolution over time. These predictions of fluid pressure, in turn, require an understanding of the subsurface permeability structure that determines subsurface flow pathways and pressure propagation.
Existing evidence from San Emidio indicates that the subsurface is highly heterogeneous and that the fluid-flow pathways are likely controlled by faults, similarly to the permeability structure mapped at Brady during the PoroTomo project [Patterson, 2018]. For example, spatial heterogeneity of permeability can effect fluid flow. Using pumping well records provided by Ormat, we have developed a simple homogeneous analytical model and estimated permeability and storage coefficients by fitting data from a single observation well at San Emidio. However, when performing forward modeling for a second observation well at San Emidio and using the obtained reservoir parameters, a poor match to pressure data was obtained, indicating the influence of heterogeneity.
We plan to image heterogeneity in aquifer permeability using hydraulic tomography, in which pressure-change measurements from a series of pumping tests are recorded at multiple monitoring wells. Then the complete resulting dataset is inverted via a highly parameterized heterogeneous flow model. Observations are available from several existing wells at San Emidio, and additional instrumentation will be installed in other wells as part of the proposed study. We will use changes in flow rates at operational site wells as the impulses consisting of: (1) ceasing all pumping at all wells; (2) restarting pumping operations; (3) pulsed changes to flow rates at individual injection wells; and (4) returning to normal operations.

Borehole indicators of stress
Although limited in spatial extent, boreholes provide direct access to geological and geophysical information used to construct the numerical model and validate the outcomes of the model. Figure 6 shows a resistivity image log collected in an existing well at San Emidio. As evident from the static image (to the right), the change in lithology from the sediments to the underlying andesite is identified by the shallowly dipping plane and change in appearance. Beneath the lithological boundary is a dark, steeply dipping feature resembling the presence of a large-aperture fluid-filled conductive fracture. As these examples illustrate, borehole images provide crucial information about the distribution of fracture orientation, frequency, and its hydraulic state (open conductive vs. healed/sealed).
Borehole images also provide important constraints on the in-situ stress state at the wellbore location. Open conductive fractures gain conductivity because of dilatancy associated with shear slip along the fracture. Since fractures slip only if favorably oriented under the current state of stress, orientation distributions of open and closed fractures provide constraints on the in-situ stress state [Zoback, 2007]. When appropriate stress conditions are met, stress concentrations around the wellbore will create wellbore failures which can also be used to constrain the in-situ stress state at the observed position [Zoback, 2007]. We will also perform laboratory testing of available samples to determine material properties such as density, Young's modulus, and Poisson's ratio. In addition, we will determine the frictional properties that govern the sliding strength of faults and fractures as well as thermal and poroelastic properties that control the stress response of rocks to fluid flow and heat transfer. All of these properties are essential for constraining the numerical modeling.
Analysis of the local stress field in the San Emidio area, based on slip indicators along surface-exposed fault planes, reveals an extensional stress regime with a generally west-northwest trending least principal stress [Rhodes et al., 2010;Rhodes, 2011] (Rhodes, 2011). While this inferred stress is consistent with the normal-faulting system developed in San Emidio and was responsible for the structural development of the field, substantial changes has likely been introduced locally due to heat production in the last two decades. We plan to analyze the available borehole geophysical logs (e.g. gamma ray, density, resistivity, sonic velocity) at San Emidio. These results will help constrain the initial condition of the numerical model before the simulated shut-down of the pumping operations power plant.

CONCLUSION
When comparing cumulative volume change estimated from InSAR data at San Emidio to the cumulative gross production recorded by the operators, we find a strong, positive correlation. "This suggests that deformation at San Emidio was influenced by geothermal production at the site between 1998 and 2010" . As part of the WHOLESCALE project, we will assess the contribution of pressure changes within the modeled reservoir to both vertical deformation (subsidence) and induced seismicity.
The WHOLESCALE project should make an important impact because geothermal operators need quantitative information about the subsurface stress to successfully develop and sustainably manage a geothermal reservoir. The proposed methodology will advance capabilities "to directly measure or infer the stress state" which, as noted in the FOA, "are woefully inadequate, especially away from boreholes" [EERE, 2019]. By reducing the uncertainty of in-situ stress estimates, the WHOLESCALE project should reduce the cost of geothermal energy.

ACKNOWLEDGMENTS
Raw Synthetic Aperture Radar (SAR) data from the Envisat satellite mission operated by the European Space Agency (ESA) are copyrighted by ESA and were provided through the WInSAR consortium at the UNAVCO facility. Raw Synthetic Aperture Radar (SAR) data from the Sentinel-1A satellite mission operated by ESA were available free of charge through the Distributed Active Archive Center (DAAC) at the Alaska Satellite Facility (ASF) and through the Sentinels Scientific Data Hub. This material is based on data services provided by UNAVCO through the GAGE Facility with support from the National Science Foundation (NSF) and National Aeronautics and Space Administration (NASA) under NSF Cooperative Agreement No. EAR-1261833.