In recent years, nationally, an average of 193 magnitude ≥3 earthquakes per year were recorded in 2009–2014, with 688 occurring in 2014 alone, swarms of quakes have continued since then. The increased seismicity is limited to a few areas where there with deep injection of fluids from nearby oil and gas operations. Although most injection operations do not cause earthquakes, numerous field cases have shown steady increase of pressure during the produced water re-injection (PWRI) process. This study provides an analytical method for predicting pressure increase during oily water injection and the rock failure conditions for seismic events.

The model derives from mass balance of oil phase in the oil water mixture while considering the oil capture effects by advection, dispersion and adsorption inside the rock. The time-dependent advancement of trapped oil saturation is determined by solving the governing equation for initial condition of oil-free rock and boundary condition of constant oil concentration in the injection water. Also explained and modeled is the effect of oil saturation on the stick/slip rock resistance and the rock strength.

In the oil capture process, size of the near-well zone of trapped oil increases with time – so does the injection pressure. The model predicts maximum oil saturation, size of trapped oil zone and injection pressure increase vs. time. The model is verified by matching laboratory data from core flooding runs. Results show that even a small oil concentration (<500 ppm) could deposit a 10% residual oil bank around the wellbore that would reduce water injectivity by more than 70% and increase injection pressure by 2000 psi. Moreover, the model confirms field observations of the initial rapid increase of oil invasion and injection pressure. Although the injection pressure may eventually stabilize, the process of internal rock "lubrication" with oil would continue.

Two effects may contribute to the rock slippage during the injection process: (1) the trapped oil droplets reduce internal friction in the rock thus lowering its shear strength; and, (2) water injection increases the pore pressure resulting in lower effective stress of the rock. These effects enhance slippage along existing natural fractures and might also initiate new fractures –causing induced seismicity. Results showed that even low injection rates (300 bpd) could trigger earthquake because injection pressure in the near-wellbore region could easily exceed the minimum principal stress (MPS), facilitating the opening of fractures perpendicular to the MPS direction.

The model provides a useful analytical tool to be coupled with geo-mechanical limitations to assess the risk of long-term injection of large volume of produced water. Mechanism and critical conditions for seismic event are described and a method to find geo-mechanical limitations is outlined.

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