A one-dimensional mechanistic model for tracking unsteady slug flow.

A novel one-dimensional slug tracking mechanistic model for unsteady, upward gas-liquid slug flow in inclined pipes is presented. The model stems from the first principles of mass and momentum conservation applied to a slug unit cell consisting of a slug body of liquid and a region of stratified flow containing an elongated bubble and a liquid film. The slug body front and rear are treated as surfaces of discontinuity where mass and momentum balances or "jump laws"are prescribed. The former is commonly applied in mechanistic models for slug flow, whereas the latter is typically overlooked, thereby leading to the assumption of a continuous pressure profile at these points or to the adoption of a pressure drop due to the fluid acceleration on a heuristic basis. Our analysis shows that this pressure change arises formally from the momentum jump law at the slug body front. The flow is assumed to be isothermal, the gas is compressible, the pressure drop in the elongated bubble region is accounted for, the film thickness is considered uniform, and weight effects in the pressure from the interface level are included. Besides specifying momentum jump laws at both borders of the slug body, another novel feature of the present model is that we avoid adopting the quasi-steady approximation for the elongated bubble-liquid film region, and thus the unsteady terms in the mass and momentum balances are kept. The present model requires empirical correlations for the slug body length and the elongated bubble nose velocity. The non-linear equations are discretized and solved simultaneously for all the slug unit cells filling the pipe. Timespace variation of the slug body and film lengths, liquid holdup and void fraction, and pressures, among other quantities, can be predicted, and model performance is evaluated by comparing with data in the literature

Prediction of unsteady slug flow in a long curved inclined riser with a slug tracking model

An improved one-dimensional mechanistic model is presented for the prediction of unsteady gas-liquid slug flows in inclined curved pipes, using the slug tracking approach. The equations for mass and momentum conservation are applied to the slug body, liquid film, and elongated bubble regions constituting a slug unit cell. The proposed model can be applied to horizontal or inclined upward flows. Statements of mass conservation result in axial changes of the liquid and gas velocities in the liquid film and elongated bubble. The slug initiation at the inlet is modelled as a random process with slug length variations. Closure relationships for the bubble nose velocity, modified by the wake effect, and the slug frequency for slug initiation are employed. The discretized governing equations are solved fully implicitly, introducing numerical treatments associated with the outlet boundary conditions and the merging of slug units. Of practical interest is an upward gas-liquid slug flow in a catenary riser with a high aspect ratio (length over diameter) being an order of a thousand representing an offshore subsea pipe for the oil and gas production. By considering the pipe initially fully filled with the traveling liquid, the dynamic scenario of the pipe transporting successive slug units is simulated, capturing the continuing evolution of slug flow patterns along the pipe exhibiting the disappearances of liquid slugs due to the bubble coalescences. Spatio-temporal variations of the liquid holdup, the pressure and its gradient, the film and slug lengths, the slug frequency, the velocities of the slug front, bubble nose, liquid in the slug body and film, and of the gas in the elongated bubble are evaluated. The backward flow occurrence in the film zone near the outlet is also predicted due to the pipe inclination. Parametric investigations are performed by specifying the superficial liquid and gas velocities, and comparing the cases of catenary pipes (with variable inclinations) versus inclined and horizontal straight pipes (with fixed inclinations). Results highlight the important effect of gas-to-oil superficial velocity ratio (GOR) in combination with the pipe inclination and curvature effects. Fluctuations of slug flow properties appear to be considerably amplified and more intermittent when increasing the GOR. This observation is important towards regulating the practical flow rates for subsea oil and gas productions as well as designing flexible pipes subject to slug flow-induced vibrations