Plugging of a hydraulic fracture because of particle bridging in the fracture channel is ubiquitous in drilling operations and reservoir stimulations. The particles transported in the fluid and fracture can aggregate under certain conditions and finally form a plug. The plug reduces the permeability of the flow channel and blocks the fluid pressure from reaching the fracture front, leading to fracture arrest. In this paper, a numerical model is developed to describe the plugging process of a hydraulic fracture driven by a slurry of solid particles in a viscous fluid while accounting for the rock deformation, slurry flow in the fracture channel, fracture propagation, particle transport and bridging. Three dimensionless numbers are derived from the governing equations, which reveal two length scales that control the fracture propagation and particle transport behaviour, respectively. The difference in magnitude between the two length scales implies three limiting regimes for fracture propagation, i.e. static regime, fluid-driven regime and slurry-driven regime, which correspond to fracture arrest, fracture driven by clean fluid, and fracture driven by slurry, respectively. Numerical results show that the fracture will sequentially transition through the static regime, fluid-driven regime and slurry-driven regime as the fracture length increases. The transition between regimes is controlled by the ratio between the two length scales. Simulation results also reveal two plugging modes, with the plug located near the fracture tip region and at the fracture inlet. The transition between the two plugging modes is controlled by the ratio of the length scales and the injected particle concentration.

Large datasets, combined with modeling techniques, provide a quantitative way to estimate when known archaeological sites will be impacted by climatological changes. With over 4,000 archaeological sites recorded on the coast of Georgia, USA, the state provides an ideal opportunity to compare methods. Here, we compare the popular passive “bathtub” modeling with the dynamic Sea Level Affecting Marshes Model (SLAMM) combined with the Marshes Equilibrium Model (MEM). The goal of this effort is to evaluate prior modeling and test the benefits of more detailed ecological modeling in assessing site loss. Our findings indicate that although rough counts of archaeological sites destroyed by sea-level rise (SLR) are similar in all approaches, using the latter two methods provides critical information needed in prioritizing site studies and documentation before irrevocable damages occur. Our results indicate that within the next 80 years, approximately 40% of Georgia's coastal sites will undergo a loss of archaeological context due to wetlands shifting from dry ecological zones to transitional marshlands or submerged estuaries and swamps.