We study the numerical performance of a continuous data assimilation (downscaling) algorithm, based on ideas from feedback control theory, in the context of the two-dimensional incompressible Navier-Stokes equations. Our model problem is to recover an unknown reference solution, asymptotically in time, by using continuous-in-time coarse-mesh nodal-point observational measurements of the velocity field of this reference solution (subsampling), as might be measured by an array of weather vane anemometers. Our calculations show that the required nodal observation density is remarkably less that what is suggested by the analytical study; and is in fact comparable to the number of numerically determining Fourier modes, which was reported in an earlier computational study by the authors. Thus, this method is computationally efficient and performs far better than the analytical estimates suggest.

This study proposes a novel approach to investigate the diffusion-limited deposition of asphaltenes in flow lines to better understand their nanoscale behavior at interfaces and aid in the development of more accurate remediation methods and modeling tools. Experiments were first designed by flowing asphaltene-in-toluene solutions through capillary polyetheretherketone tubes and imaging their cross-sectional areas using high-resolution scanning electron microscopy. A two-step digital image analysis using machine-learning concepts was applied and consisted of a (1) denoising process by analyzing the local and global bias and variance and (2) binarization process to improve the quality of image segmentation. As a result of polydispersity, particles on the tube surface were categorized into nanoaggregates (1.5–4 nm), small clusters (SCs, 4–10 nm), medium clusters (MCs, 10–20 nm), large clusters (LCs, 20–100 nm), and extra-large clusters (XLCs, >100 nm). A Langmuir adsorption isotherm was measured in toluene with an adsorption free energy of −29 kJ/mol, in agreement with previous work. Nanoaggregates and SCs were the main constituents of the adsorption layer as a result of their high mass diffusivity. A competing behavior between aggregation and adsorption was observed as the asphaltene concentration increased in toluene. Enhanced self-assembly in the bulk phase led to a continuous decrease in the number of adsorbed particles. Adding n-heptane to toluene at different volume ratios prompted the deposition of MCs with a peak in the particle size, number, and mass density observed in the vicinity of the onset of precipitation. These clusters are potential precursors to fouling because they constitute the building blocks of larger particles that grow over time on the surface. Limiting their deposition could be achieved by either increasing the flow rate or introducing chemical inhibitors that promote the formation of larger aggregates in the bulk phase under given flow conditions. The novel insights gained from this study reveal that MC-rich petroleum fluids are more prone to flow assurance challenges and that effective flow enhancers are those that promote the aggregation of MCs into particles that are too large to deposit.

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