Mechanical origin of b-value changes during stimulation of deep geothermal reservoirs

Abstract

The distribution of induced-earthquake magnitudes in deep geothermal reservoirs is a classical tool for monitoring reservoirs. It typically shows some important fluctuations through time and space. Despite being a very crude information (i.e., a scalar quantity) of very complex mechanical stress evolution, understanding these variations could still give us insights into the mechanics of the reservoir. Here, we analyze the output of a simple quasi-static physical model of a single fault and propose a new way to describe bursts that could be compared to seismic events. Our model is an elastic fiber bundle model describing multiple ruptures along a single major fault of the reservoir. It consists of a set of fibers with various strengths, arranged in a planar L×L two-dimensional array, linking together two elastic half-spaces. It mimics a fault zone with various asperities. During load, the fibers break quasi-statically according to a stress threshold distribution. Contrary to classical fiber bundle model, here, when a fiber breaks, it redistributes the load on the surviving fibers through long range elastic interactions. Interestingly, the elasticity of the half-spaces which changes the range of the stress distribution, characterizes two distinct regimes. In a stiff regime, we find an effective ductile deformation regime at large scale since the damage distribution is very difuse. Conversely in softer systems, the distance between two consecutive breaking fibers gets smaller and failure of the interface is localized, exhibiting an effective brittle regime. We analyze two types of burst distributions: a classical one built from the statistics of the broken bonds during each failure step and a new one defines from a waiting time matrix of the fracture front propagation. The first one reproduces several known results for this type of model. The new one evidences the existence of effective creeping advances of the front with statistics that follow a Gutenberg-Richter distribution, in particular, in the ductile regime (stiff systems). We proposed a new definition of bursts in a fault model, based on the local fracture front velocity. We find that b v -values for the distribution of the velocity clusters are very consistent with Gutenberg-Richter distribution of induced seismicity. We link the b v -value fluctuations in the reservoirs to the influence of the velocity threshold level that could be related to recording limitation. b b -values obtained from the broken bond statistics are hardly comparable to seismic events because of the lack of space contiguousness of broken fibers during bursts. In the light of our results, we discuss the implications of b-value changes in geothermal reservoir in terms of fault asperities and normal stress evolution.