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We propose a new model and workflow to predict, quantify and mitigate undesired flowback of proppant from created hydraulic fractures. We demonstrate several field cases in which we predict significant proppant flowback and propose options for mitigation. Mitigation of proppant flowback is based on case- specific changes in the fracturing treatment design and modifications in the well startup schedule that preserve near-wellbore conductivity. The presented workflow integrates four key components of proppant flowback study: (A) simulation of the fracturing job with a high-resolution model of proppant placement inside a fracture; (B) subsequent simulation of flowback from the created fractures equipped by a validated proppant flowback model; (C) a series of laboratory experiments, which quantify the proppant flowback for a wide range of commercial proppants; and (D) an accurate mathematical model, which is validated by the results of laboratory experiments and integrated into a flowback simulator to predict the behavior of injected proppant. Each component is presented with sufficient details to demonstrate its necessity for accurate modeling of a coupled solid-and-fluid flow inside a fracture. The presented theory of proppant pack mobilization is based on the concept of a proppant pack erosion process evolving from free boundaries of proppant packs. The theory confirms that proppant flowback critically depends on flow rate, proppant, fracture, and reservoir parameters. Laboratory experiments on proppant flowback in a cell support these theoretical predictions. The theoretical model of proppant flowback is integrated into the numerical simulator of early-time production from a fractured reservoir and predicts flowback of both injected solids and fluids from a fracture. We show that the combination of the proppant flowback model, laboratory experiments, hydraulic fracturing design tool, and early-time production simulator result in a useful workflow for prediction and mitigation of issues with proppant flowback and production decline. The entire workflow was validated using field cases where proppant flowback was observed. Modeled amounts of flowed back proppant are in good agreement with amounts of proppant observed in the field. Hydraulic fracturing design optimization was performed to minimize or eliminate proppant flowback. The novelty of the proposed study is related to the model of proppant flowback, which accounts for erosion of the proppant pack and is calibrated against unique laboratory experiments. The presented model and proppant flowback mitigation workflow can assist in understanding and mitigating proppant flowback events that can occur during wide range of oilfield operations.

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In this paper, we consider the problem of the free longitudinal vibrations of a beam made of a bimodular material, i.e. an elastic material whose in-tension Young's modulus is a fraction of that under compression. After recalling the exact solutions for an infinite beam and for a beam with fixed ends calculated via the characteristics method, we apply high-resolution methods based on the finite-element approach to solve the nonlinear equation of the motion. In particular, we compare the exact solutions with the numerical solutions calculated using the collocation and least-squares method developed in the present study, the space-time element method, as well as total variation diminishing (TVD) and Newmark methods.

We demonstrate the advantages of a new hydraulic fracturing simulator comprising a fine-scale fracture hydrodynamics and in-situ kinetics model. In contrast to existing commercial modeling tools, it has a sufficient resolution and other functionality for adequate representation of modern stimulation technologies: pulsing injection of proppant, mixtures of multiple fracturing materials (fluids, proppants, fibers, etc.), materials degradation, etc. This simulator accounts for the influence of materials distribution on fracture propagation and calculates fracture conductivity distribution. We coupled it with a production simulation model and established a complete framework for hydraulic fracturing treatment design. In addition to the selection of the pumping schedule, this model can be used to define specifications for novel hydraulic fracturing materials. This is a step change tool for wellbore stimulation and production forecast.