An adjoint-based formulation leads to a particularly efficient approach for inverting geodetic measurements for the source of the deformation. Specifically, the quantities necessary to iteratively improve the fit to the observations can be computed with just three forward calculations, one to obtain the current residuals, another to solve the adjoint problem, and a third to compute the step length. An inversion algorithm utilizing the adjoint-based gradient is applied to a set of Interferometric Synthetic Aperture Radar (InSAR) data gathered between 2016 and 2018 over the Tulare Basin in California's Central Valley. Because the measured deformation is due to groundwater withdrawal, a penalty function is included in the inversion to avoid placing aquifer volume change in locations that are far from any documented wells. The solution of the inverse problem provides estimates of aquifer compaction that provide a match to the observed range changes while honoring the well data. The solution indicates an average aquifer volume loss of 2.17 (Formula presented.) /year over the two year period from January 2016 to January 2018, encompassing one drought year (2016) and one wet year (2017). This magnitude of lost volume is compatible with the 3.1 (Formula presented.) /year decrease in water volume for the entire Central Valley, estimated from GRACE satellite gravity data.

Objectives/Scope: Steam injection in diatomite reservoirs results in permeability changes owing to fracture propagation, and compaction as a result of thermal effects and pressure changes during injection and production. The purpose of this work is to evaluate these coupled thermal, hydrological, and mechanical (THM) processes over several years of cyclic steam injection and production. A single well model in a diatomite reservoir was created to evaluate these processes at a higher resolution near wellbore than used in a 3-D reservoir-scale model. Methods, Procedures, Process: Simulations include tensile failure, shear failure with simultaneous shear on multiple planes, coupling of porosity and permeability changes with multiphase flow, and diatomite compaction with temperature and effective stress. Initial isotropic horizontal stresses are 1.0375 of vertical (azimuthal average, part of San Joaquin Valley). Injection interval (437-528 m) pressure is fixed, 6.3 MPa, 930 psi (injection), and ~4 MPa (production), with a soak period between injection and production. Three degree dilation on shearing is assumed. To the extent that fracture opening is tensile, fractures close on fluid pressure drop, but shear components remain. Permeability changes due to mechanical failure are simulated using a cubic law. Results, Observations, Conclusions: During injection over multiple cycles, the diatomite surrounding the well is heated to over 250 °C and pressurized by the injected steam. During soak (shut-in) and subsequent production, pressure drops, dropping the boiling point, inducing further vaporization. Geomechanical changes show tensile opening accompanied by a greater amount of shearing. Total shearing increases with each injection cycle, resulting in a greater porosity increase from shearing than tensile opening. Fracture propagation was limited to the diatomite reservoir and did not penetrate the caprock. Novel/Additive Information: Inclusion of an empirical effective stress/temperature diatomite compaction law together with porosity and permeability changes due to mechanical failure more closely models the mechanics of cyclic steaming of diatomite.

A coupled approach, combining the theory of rate- and state-dependent friction and methods from poroelasticity, forms the basis for a quantitative relationship between displacements and fluid leak-off from a growing fracture and changes in the rate of seismic events in the region surrounding the fracture. Poroelastic Green's functions link fracture aperture changes and fluid flow from the fracture to changes in the stress field and pore pressure in the adjacent formation. The theory of rate- and state-dependent friction provides a connection between Coulomb stress changes and variations in the rate of seismic events. Numerical modeling indicates that the Coulomb stress changes can vary significantly between formations with differing properties. The relationship between the seismicity rate changes and the changes in the formation stresses and fluid pressure is nonlinear, but a transformation produces a quantity that is linearly related to the aperture changes and fluid leak-off from the fracture. The methodology provides a means for mapping changes in seismicity into fracture aperture changes and to image an evolving fracture. An application to observed microseismicity associated with a hydrofracture reveals asymmetric fracture propagation within two main zones, with extended propagation in the upper zone. The time-varying volume of the fracture agrees with the injected volume, given by the integration of rate changes at the injection well, providing validation of the estimated aperture changes.