Seismic hazard due to fluid invasion in hydraulic fracturing, wastewater disposal, and enhanced geothermal systems have become a concern for industry and nearby residents. Some of the challenges associated with the fluid-induced seismic hazard are the estimation of the spatial effects of these industry operations as well as the presence or absence of aftershock triggering. In some cases (e.g. Geysers, California, Hoadley gas field of Alberta), aftershocks triggering do occur, while in other cases (e.g. Soultz‐sous‐Forêts, France), this is not the case. First, to address the spatial effects, using several previously published high-resolution well-log data, we first show that there is a tendency that porosity within the basement resembles fractional Gaussian noise (fGn), while above the basement it resembles fractional Brownian motion (fBm). Based on this observation, we introduce a novel conceptual model of the fluid-induced seismicity in disordered porous media by integrating the notion of fluid diffusion and invasion percolation with spatially correlated permeability and porosity. We find that our model does not only capture the observed variations in frequency-magnitude distribution of seismic events but it also exhibits a much slower decay in seismic activity at large distances for fBm compared to fGn. Second, to address the presence of aftershock triggering, we also introduce nonlinear viscoelastic effects in our model to augment the failure mechanics. This allows us to test whether the presence or absence of aftershocks is coupled to the validity of a time scale separation between fluid dynamics and nonlinear viscoelastic response, for example. Our findings can be directly incorporated in the seismic hazard assessment related to fluid injections.