Modeling particulate flows in conduits and porous media
Particulate flows exist in a wide range of engineering applications such as drilling and completion operations—from hole-cleaning to well stimulation to sand control. The operations involving particulate flows typically focus on achieving either (1) efficient particle transport or (2) effective particle retention, both of which require a deep understanding of particulate flow behavior under different flow conditions. This dissertation presents novel approaches for modeling particulate transport with the intent to optimize operational efficiency in specific important oilfield applications. The first half of this dissertation focuses on modeling particle transport inside a wellbore. A typical example of such an operation is the pumping of proppant/diverter slurry during a hydraulic fracturing treatment. During the treatment, the particles are moved in a carrier fluid from the wellbore through the perforations and finally into the fractures. The motion of the particles is primarily influenced by the interactions between the fluid phase and the solid phase, and therefore, a precise description of the particle-fluid interactions is essential for modeling the process. The coupling of computational fluid dynamics with the discrete element method (CFD-DEM) approach is adopted for this task. The investigation begins with evaluating the particle transport efficiency (PTE) through a perforation in a horizontal wellbore under various downhole flow conditions. A comprehensive study on the effect of casing, perforation, solid, and fluid properties on PTE is presented. On the basis of the study, empirical PTE correlations are derived and integrated into a multi-cluster hydraulic fracturing model to simulate proppant/diverter transport at a wellbore scale. Simulation results show that because of its high inertia, the transport of proppant is generally much more difficult than the transport of carrier fluid through the perforations. By assuming a simple jamming criterion based on local proppant concentration near the perforations, the heel-biased treatment distribution commonly observed in the field can be accurately reproduced by the model. Recommendations on fracturing job design for promoting an even treatment distribution are also discussed. The second half of the dissertation focuses on modeling particle retention in sand control completions with a special focus on multi-layered metal-mesh screens and gravel packs. A DEM-based approach is developed to evaluate the pore throat size distribution (PoSD) of the sand-retention media. Simulation results show that for a multi-layer plain square mesh (PSM) screen, the overlap, alignment, and relative pore size between individual layers all have a significant impact on the screen’s PoSD. In contrast, only the intra-layer overlap of the filter is important for controlling the PoSD of a multi-layered plain Dutch weave (PDW) screen. For gravel packs, simulation results show that the largest and smallest pore throat sizes are about 1/5 and 1/10 of the effective gravel size for typical gravel sizes used in the field. By using the computed PoSD as an input, an analytical model and a Monte-Carlo model are developed to predict sand production through gravel packs. The modeled PoSD and sand production agree reasonably well with field observations and experimental data. Our approach enables completion engineers to tailor gravel pack designs for different combinations of formation sand size distribution (PSD) and wellbore geometry in a cost-efficient manner.