Inference of permeability distribution from injection‐induced discrete microseismic events with kernel density estimation and ensemble Kalman filter

Abstract

Hydraulic stimulation of subsurface rocks is performed in developing geothermal and hydrocarbon reservoirs to create permeable zones and enhance flow and transport in low‐permeability formations. Borehole fluid injection often induces measurable microearthquakes (MEQs). While the nature and source of the processes that lead to triggering of these events is yet to be fully understood, a major hypothesis has linked these events to an increase in pore pressure that decreases the effective compressional stress and causes sliding along preexisting cracks. Based on this hypothesis, the distribution of the resulting microseismicity clouds can be viewed as monitoring data that carry important information about the spatial distribution of hydraulic rock properties. However, integration of fluid‐induced microseismicity events into prior rock permeability distributions is complicated by the discrete nature of the MEQ events, which is not amenable to well‐established inversion methods. We use kernel density estimation to first interpret the MEQ data events as continuous seismicity density measurements and, subsequently, assimilate them to estimate rock permeability distribution. We apply the ensemble Kalman filter (EnKF) for microseimic data integration where we update a prior ensemble of permeability distributions to obtain a new set of calibrated models for prediction. The EnKF offers several advantages for this application, including the ensemble formulation for uncertainty assessment, convenient gradient‐free implementation, and the flexibility to incorporate various failure mechanisms and additional data types. Using several numerical experiments, we illustrate the suitability of the proposed approach for characterization of reservoir hydraulic properties from discrete MEQ monitoring measurements.