Bellows compensators are critical components in pipeline systems, designed to absorb thermal expansions, vibrations, and pressure reflections. Ensuring their operational reliability requires accurate prediction of the stress–strain state (SSS) and stability under internal pressure. This study presents a comprehensive mathematical model for analyzing corrugated bellows compensators, formulated as a boundary value problem for a system of partial differential equations (PDEs) within the Kirchhoff–Love shell theory framework. Two numerical approaches are developed and compared: a finite difference method (FDM) applied to a reduced axisymmetric formulation to ordinary differential equations (ODEs) and a finite element method (FEM) for the full variational formulation. The FDM scheme utilizes a second-order implicit symmetric approximation, ensuring stability and efficiency for axisymmetric geometries. The FEM model, implemented in Ansys 2020 R2, provides high fidelity for complex geometries and boundary conditions. Convergence analysis confirms second-order spatial accuracy for both methods. Numerical experiments determine critical pressures based on the von Mises yield criterion and linearized buckling analysis, revealing the influence of geometric parameters (wall thickness, number of convolutions) on failure mechanisms. The results demonstrate that local buckling can occur at lower pressures than that of global buckling for thin-walled bellows with multiple convolutions, which is critical for structural reliability assessment. The proposed combined approach (FDM for rapid preliminary design and FEM for final verification) offers a robust and efficient methodology for bellows design, enhancing reliability and reducing development time. The work highlights the importance of integrating rigorous PDE-based modeling with modern numerical techniques for solving complex engineering problems with a focus on structural integrity and long-term performance.

Spent water-based drilling fluids generated during technological-well drilling for uranium production are high-solid, chemically heterogeneous suspensions whose treatment is constrained by water scarcity, waste-handling requirements, reagent demand and electrical-energy consumption. This study evaluated a recirculating flow-through disperser that converts pressure-driven flow into controlled nominal velocity gradients and localized contact zones. The laboratory-pilot dataset comprised five high-solid water-based spent-fluid samples, 120 hydrodynamic treatment runs, 216 particle-size-bin observations corresponding to 12 complete distributions, nine mechanical-mixing baseline tests and ten repeated-cycle runs. The investigated range covered nominal Camp–Stein-equivalent velocity gradients of 500–1500 s⁻¹, treatment times of 60–180 s and flocculant dosages of 0–100 g/t dry solids. A 50 L batch was recirculated through a disperser with a cylindrical geometric envelope of approximately 4.75 L. The maximum separation efficiency was 94.20%. The recommended compromise condition (G = 1300 s⁻¹, τ = 150 s and 50 g/t dry solids) achieved 92.15 ± 1.81% separation efficiency, residual aqueous-phase TSS of 125.2 ± 30.0 mg/L, water recovery of 83.84 ± 0.28%, sludge-volume reduction of 59.02 ± 2.11% and wall-plug specific energy consumption of 0.1227 ± 0.0062 kWh/m³. A separate ten-cycle series yielded 0.1245 ± 0.0065 kWh/m³, consistent with the triplicate compromise-mode result. Two-factor response-surface models reproduced the measured G–τ trends and provided prediction intervals for operating-window screening within the investigated fluid class. The findings support coupled energy–separation optimization, rather than selection of the maximum nominal mixing intensity.

The hydrodynamic and tribological characteristics of a sucker-rod pump valve assembly with a modified seat equipped with a turbulizer are investigated. The study aims to extend service life by controlling the flow structure and reducing contact loads in the ball–seat pair. A combined approach is employed, integrating computational fluid dynamics (CFD) simulations with physical experiments. The results show that an increase in turbulence intensity does not lead to a proportional improvement in performance due to energy dissipation; however, an optimal turbulizer geometry is identified that ensures directed swirl flow and efficient transfer of angular momentum. It is established that the theoretical number of ball rotations in oil is 24 over 5 s, whereas the experiment conducted in water yields 30 rotations over the same period, which is attributed to viscosity effects. An empirical relationship is proposed to describe transitions between the “free flow,” “flow with ball,” and “turbulized flow” regimes, taking into account the rheological properties of the fluid; the validity of the model is confirmed by computational experiments. It is demonstrated that reducing contact forces is a more critical factor than maximizing hydraulic efficiency.

Screw compressors are critical equipment in oil and gas production and transportation, where efficiency losses caused by rotor geometry, inlet pressure pulsations, and harsh climatic conditions can accumulate into substantial annual energy penalties and reliability degradation. This study provides a quantitative assessment of these coupled effects within a unified multiphysics framework that combines time-accurate transient CFD simulations based on a fixed Cartesian immersed-boundary formulation with a climate-calibrated offline physics-based digital twin—functioning as a digital shadow with one-way data flow from archival SCADA records—a reduced-order seasonal model with no real-time updating, calibrated against a full calendar year of SCADA records and validated against a held-out cold-season dataset (October–December 2022, T_amb = −15 to +8 °C); summer-period predictions rely on calibrated extrapolation beyond the validation window—an integration not previously demonstrated for oil-flooded screw compressors. Two rotor profile configurations (Type A and Type B) were analyzed to quantify geometry-driven differences in static pressure distribution, leakage tendency, and pulsation sensitivity. Transient suction conditions were modeled using harmonic and quasi-random inlet pressure disturbances to evaluate pressure amplification, phase lag, leakage intensification, and efficiency degradation. Seasonal performance was assessed by integrating temperature-dependent gas properties, oil viscosity behavior, and external heat transfer into an annual climatic load framework. The results show that inlet oscillations are amplified inside the chambers (pressure amplification factor П_p ≈ 1.95; П_p up to 2.3 under quasi-random excitation), reducing mass flow and volumetric efficiency by 8–10% and decreasing polytropic efficiency from 0.78 to 0.69–0.71, while increasing leakage by up to 27% and raising peak contact pressures to 167–171 MPa. Seasonal variability (+30 to −30 °C) increased suction density by 38% but raised drive power by ~9% due to viscosity-driven mechanical losses, producing an energy penalty up to 10.8% and an estimated annual additional consumption of approximately 186 MWh per compressor, decomposed as: cold-season contribution ~113 MWh (±10 MWh, directly field-validated against October–December 2022 SCADA data) and summer-season contribution ~51 MWh (calibrated extrapolation; additional uncertainty unquantified and not included in the ±10 MWh bound). The full annual figure of 186 MWh should be interpreted as a model-based estimate rather than a fully validated result. These findings demonstrate that rotor design optimization and mitigation of nonstationary suction effects, coupled with climate-aware offline physics-based digital shadow operation, represent high-priority levers for improving efficiency and reducing energy penalties in field conditions; reliability implications require further validation against summer-season field measurements.