in this paper, a finite element model is developed for the fully hydro-mechanical analysis of hydraulic fracturing in partially saturated porous media. the model is derived from the framework of generalized biot theory. the fracture propagation is governed by a cohesive fracture model. the flow within the fracture zone is modeled by the lubrication equation. the displacement of solid phase, and...

Hydraulic fracturing is a technique to extract oil and gas from shale formations, obtaining uniform proppant concentration along the fracture key its productivity. Recently, various model predictive control schemes have been proposed achieve this objective. But such controllers require an accurate computationally efficient which difficult obtain given complexity of process uncertainties in rock...