Particle-laden flows occur in a variety of natural and industrial situations. As particulate suspensions flow through a medium, particles are often retained at constrictions such as pore throats, outlets or orifices. This occurs not only with oversized particles, but also with particles smaller than the constriction. For instance, jams are caused by the formation of particle bridges/arches when several particles attempt to flow through a constriction simultaneously. In many instances the success of an operation depends on our ability to either ensure or stop the flow of particles in the flow stream. Managing the flow of sand into wellbores during hydrocarbon production from poorly consolidated sandstone reservoirs, also referred to as sand control, is one such application in the oil and gas industry. This dissertation presents a multi-pronged effort at modeling the flow of granular suspensions of different concentrations, and through pore openings of different shapes, with two main objectives: (1) predicting the mass and size-distribution of the particles that are produced before jamming, and (2) investigating the underlying factors that influence the onset and stability of particle arches. Since, the dominant interactions and retention mechanisms are concentration dependent, we divided particulate suspensions into three groups based on the volumetric particle concentration ([phi]). High-concentration suspension flows ([phi]>~50%) are dominated by particle-particle interactions. We modeled polydisperse sand packs flowing through screens with rectangular and woven-square openings using 3D discrete element method (DEM). Simulations were validated against experimental data for a wide range of screen opening and sand size distributions. From the experiments and DEM simulations, a new scaling relation is identified, in which the number of different sized particles produced before retention follows a power-law correlation with the particle-to-outlet size ratio. This correlation is explained with a simple probabilistic model of bridging in polydisperse systems and a particle-size dependent jamming probability calculated from experimental data. A new method is presented to estimate the mass and size distribution of the produced solids through screens. The method uses the entire particle size distribution (PSD) of the formation sand, is validated with experimental data and numerical simulations, and provides more quantitative and accurate predictions of screen performance compared to past methods. It is also found that the stability of particle arches is compromised when adjacent outlets are less than three particle diameters away from each other. Low-concentration suspension flows ([phi]<~1%) are dominated by particle-fluid interactions. They were modeled using analytical and stochastic methods to predict sand production through screens with slot and woven-square openings. Analytical expressions were derived for screens with a constant outlet size or with a known outlet size distribution. Monte Carlo simulations showed excellent agreement with the analytical solutions. Based on experiments, we have demonstrated that the models presented here are predictive, provided that an accurate representation of the formation sand PSD and the screen pore size distribution are available. In the intermediate-concentration regime (~1%<[phi]<~50%), the particle trajectories and the flow field are both influenced by each other. The onset of particle bridging due to hydrodynamic forces was studied for monodisperse systems, in a rectangular channel with a single constriction, using coupled computational fluid dynamics (CFD) and DEM simulations. It is shown that the probability of jamming increases with [phi], and there is a critical particle concentration ([phi, superscript asterisk]) for spontaneous bridging. The outlet-to-particle size ratio is the most critical parameter affecting [phi, superscript asterisk]. The effect of inlet-to-particle size ratio, fluid velocity, particle stiffness, particle-to-fluid density ratio, and the effect of convergence in flow geometry were also studied quantitatively. Finally, the application of micro-tomography images in constructing accurate 3D representations and calculating the pore size distribution of complex filter media is demonstrated. A simulation tool is presented that allows one to evaluate the performance of different screens without running expensive and sometimes inconclusive experiments, and enhances our understanding of screen performance. This helps to improve sand screen selection to meet performance criteria under a wide variety of conditions. / text