Parametric Probabilistic Models for Fluid Diffusivity Inversion and Forward Microseismic Generation Using Seismicity Rates

摘要

Fluid diffusivity inversion and injection-induced microseismicity provide useful means of evaluating unconventional reservoirs. When taking into consideration geomechanics, linear poroelasticity equations provide the key connection between diffusion and microseismicity. This work explores microseismicity generation from a probabilistic point of view, embedding uncertainty assessment in its quantification. Bayesian framework serves as the base for probabilistic analysis. The primary objective of this work is to develop a new microseismicity probabilistic model framework that can be used for uncertainty quantification in data analysis as well as to provide forward modeling of microseismicity. Results are tested against real data of Horn Rives shales in Western Canada, and show good prediction of the number of actual microseismicity occurrences against time. The novel probabilistic model is derived from Directed Graphic Model using a statistical learning framework. Stochastic Poisson process combined with a specific rate model is integrated to generate a likelihood function. Both, parameter inference and microseismic event forecast are assisted by Bayesian theorem. The model has an intrinsic statistical learning root, which specifically uses observed microseismic data to update model parameters and then is applied for microseismicity prediction. The model is extended to take into account basic geomechanical principles. Dieterich (1994) relative seismicity rate model is integrated into the aforemantioned probabilistic model. We use a synthetic case to demonstrate how the probabilistic model can be connected with stress and pressure information from geomechanical calculations. The novelty of this study is the development of a probabilistic microseismic prediction model which obeys rate-and-state law based relative seismicity rate constitutive equations. The model inherently considers time dependence of nucleation and fault geomechanics. It can be used for planning purposes in the pre-hydraulic fracturing stage.