Messa and Malavasi (Wear, 2017) systematically reproduced thirteen abrasive jet impingement experiments with CFD-based erosion prediction models and found that the choice of erosion equation dominates the prediction error: none of four correlations (Oka, E/CRC, Huang, DNV-GL) was accurate for all conditions, and even the best-performing Oka model deviated from measured integral erosion ratios by up to a factor of five — a ceiling they attributed to an insufficient physical description of liquid–particle flows and of the impact wear process. The open problem, in the source's own terms, is to deepen the physical description of liquid–particle flows and of the impact wear process so that these deviations are accounted for and the reliability of CFD-based erosion prediction for liquid–solid flows increases. State-of-the-art reviews from 2020, 2021, and 2025, together with the newest mechanistic model proposals through August 2026, indicate that the question remains open: reviews state the field is still not ready for fully physics-based erosion modeling, calibration-based methods remain case-specific, and the newest mechanistic models are active proposals rather than accepted general solutions.

Background

Solid-particle erosion — the progressive loss of wall material caused by impacts of particles carried in a fluid stream — is a life-limiting degradation mechanism in oil-and-gas production (sand transported with produced fluids through chokes, valves, and pipe bends), in hydraulic machinery (sediment-laden water through Pelton and Francis turbines), and in slurry pipelines. In liquid–solid (slurry) flows the prediction problem is harder than in gas–solid flows because the carrier liquid strongly deflects the particles: near a wall the particles decelerate and turn, so they strike at lower velocities and different angles than the free stream would suggest.

The standard engineering prediction tool is the Erosion Prediction Model (EPM) based on computational fluid dynamics (CFD). The turbulent liquid flow is computed with RANS (Reynolds-averaged Navier–Stokes) turbulence closure; particles are tracked through this field, individually or as statistical 'parcels', by integrating a particle equation of motion with sub-models for drag, lift, turbulent dispersion, and wall rebound; finally an erosion equation converts the computed impact velocity, impact angle, and collision frequency at each wall location into a mass-loss rate. Because abrasive sand is non-spherical, the drag sub-model must account for particle shape, commonly through the Haider–Levenspiel correlation, in which the particle sphericity (the surface area of a sphere of equal volume divided by the actual particle surface area) quantifies the shape.

The erosion equation is the weakest link. Well-known candidates of different lineages are: (i) the empirical Oka correlation, fitted to air–sand jet impingement tests, which needs only the target material's density and Vickers hardness number (a standard indentation hardness measure) as material input; (ii) the mechanistic equation of Arabnejad et al., developed at the University of Tulsa's Erosion/Corrosion Research Center (E/CRC), built from cutting and repeated-deformation wear mechanisms but containing coefficients (a wear constant, a threshold velocity, and a deformation-wear factor) that are hard to determine for an arbitrary target material; (iii) Huang's phenomenological model for jet flows; and (iv) the simple correlation embedded in the recommended practice of DNV GL (Det Norske Veritas – Germanischer Lloyd, the classification-society standards body), used industry-wide for sand-erosion screening.

Messa and Malavasi (2017) asked how much of the scatter in published CFD erosion predictions comes from these sub-model and parameter choices, as opposed to the erosion equation itself. They reproduced thirteen abrasive jet impingement experiments from four research groups, spanning different target materials, particle sizes, and flow conditions, systematically varying the turbulence closure, wall restitution coefficients, the forces in the particle equation of motion, the drag model, the particle shape parameter, and the erosion equation. Two findings define the problem. First, the erosion equation dominates: none of the four tested correlations was accurate for all conditions — the E/CRC model tends to overestimate with high sensitivity to its hard-to-set coefficients, the DNV-GL correlation strongly underestimates, Huang's model overestimates, and the Oka model performs best. Second, even for the best model the integral erosion ratio (the ratio between the mass loss of the specimen and the mass of solids coming out of the nozzle) deviates from the measurement by up to a factor of five, which the authors identify as the maximum level of accuracy currently allowed by CFD-based erosion prediction, attributing it to an insufficient physical description of liquid–particle flows and of the impact wear process. The authors frame the jet impingement geometry as a first step toward the more complex flows of oil-and-gas components, and note that self-induced geometry changes during long exposures and the computational cost of Lagrangian particle tracking (the per-particle trajectory integration described above) at higher solid concentrations remain unaddressed.

Problem Statement

The problem, as posed by the source study, is to deepen the physical description of liquid–particle flows and of the particle–wall impact wear process in order to increase the reliability of CFD-based erosion prediction for slurry flows, and in particular to account for the deviations of up to a factor of five in integral erosion ratio that even the best-performing available erosion equation exhibits. The source states this as an open research direction rather than a quantitative acceptance test: it reports that none of the four tested correlations is accurate for all conditions, that 'deviations up to a factor 5 on the integral erosion ratio have to be accounted for', and that this underlines 'the need for further study regarding the physics of both liquid-particle flows and the impact wear process'. It attaches no accuracy threshold, no universality requirement, and no prescribed set of intermediate conclusions to that call.

The setting is the CFD-based Erosion Prediction Model described above, and the quantities of interest are the integral erosion ratio and the erosion scar profile measured in abrasive jet impingement tests of the kind the source reproduced. The open physics concerns both sides of that model: the liquid–particle flow, which sets the impact velocity, impact angle, and collision frequency at the wall, and the impact wear process, which converts them into mass loss. The reliability gap that a deeper physical description is called on to close is the one quantified by the source — deviations up to a factor of five in integral erosion ratio for the best current erosion equation, with none of the available correlations accurate for all conditions. The source treats the jet impingement geometry as the first step before addressing the more complex flows of interest in the oil and gas industry, and identifies two further limitations of current practice that it does not address: the high computational cost of Lagrangian particle tracking at moderate and high solid content, and the neglect of the self-induced geometry changes caused by erosion over long exposures. The problem is to deepen the physical description by a physics-based modification to the Erosion Prediction Model — in the liquid–particle-flow description, in the impact-wear relation that converts impacts into mass loss, or in both — so that the integral-erosion-ratio deviations of up to a factor of five attained by the best current correlation on the source's abrasive jet impingement cases are accounted for; the liquid–particle-flow and impact-wear sides are independent sub-questions that may be deepened separately, and the source leaves the computational cost of Lagrangian particle tracking at moderate and high solid content and the self-induced geometry changes over long exposures unaddressed.

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