The Dynamic Two-Fluid Model OLGA: Theory and Application

Abstract

Summary- Dynamic two-fluid models have found a wide range of application in the simulation of two-phase-flow systems, particularly for the analysis of steam/water flow in the core of a nuclear reactor. Until quite recently, however, very few attempts have been made to use such models in the simulation of two-phase oil and gas flow in pipes. This paper presents a dynamic two-fluid model, OLGA, in dynamic, mining the basic equations and the two-fluid models applied. Predictions of steady-state pressure drop, liquid holdup, and flow-regime transitions are compared with data from the SINTEF Two-Phase Flow Laboratory and from the literature. Comparisons with evaluated field data are also presented. Introduction The development of the dynamic two-phase-flow model OLGA started as a project for Statoil to simulate slow transients associated with mass transport, rather than the fast pressure transients well known from the nuclear industry. Problems of interest included terrain slugging, pipeline startup and shut-in variable production rates, and pigging. This implied simulations with time spans ranging from hours to weeks in extreme cases. Thus, the numerical method applied would have to be stable for long timesteps and not restricted by the velocity of sound. A first version of OLGA based on this approach was working in 1983, but the main development was carried out in a joint research program between the Inst. for Energy Technology (IFE) and SINTEF, supported by Conoco Norway, Esso Norge, Mobil Exploration Norway, Norsk Hydro A/S, Petro Canada, Saga Petroleum, Statoil, and Texaco Exploration Norway. In this project, the empirical basis of the model was extended and new applications were introduced. To a large extent, the present model is a product of this project. Two-phase flow traditionally has been modeled by separate empirical correlations for volumetric gas fraction, pressure drop, and flow regencies, although these are physically interrelated. In recent years, however, advanced dynamic nuclear reactor codes like TRAC, RELAP and CATHARE have been developed and are based on a more unified approach to gas fraction and pressure drop. Flow regular, however, are stiff treated by pressure drop. Flow regular, however, are stiff treated by separate flow-recognize maps as functions of void fraction and mass flow only. In the OLGA approach, flow regimes are treated as an integral part of the two-fluid system. The physical model of OLGA was originally based on diameter data for low-pressure air/water flow. The 1983 data from the SINTEF Two-Phase Flow laboratory showed that, while the bubble/slug flow regime was described adequately, the stratifield /annular regime was not. In vertical annular flow, the produces pressure drops were up to 50 % too high (see Fig. 1). In pressure drops were up to 50 % too high (see Fig. 1). In horizontal flow, the predicted holdups were too high by a factor of two in extreme cases. These discrepancies were explained by the neglect of a droplet field, moving at approximately the gas velocity, in the early model. This regime, denoted stratified- or annular-mist flow, has been incorporated in OLGA 94 and later versions, where the liquid flow may be in the form of a wall layer and a possible droplet flow in the gas core. This paper describes the basic features of this extended two-fluid model, emphasizing its differences with other known two-fluid models. OLGAThe Extended Two-Fluid Model Physical Models. Separate continuity equations are applied for gas Physical Models. Separate continuity equations are applied for gas liquid bulk, and liquid droplets, which may be coupled through interphasial mass transfer. Only two momentum equations are used, however: a combined equation for the gas and possible liquid droplets and a separate one for the liquid film. A mixture energy-consumption equation currently is applied. Conservation of Mass. For the gas phase, 1 (Vg g) = (AVg g vg)+ g+Gg...............(1) t A z For the liquid phase at the wall, 1 V L (V L L) = - (AV L LvL) - g - e+ d+ G L. t A z V L+V D .............................(2) For liquid droplets, 1 V D (V D L) = - (AV D LvD)- g + e - d+G D. t A z V L + V D ...........................(3) In Eqs. 1 through 3, Vg, V L, V D = gas, liquid-film, and liquid-droplet volume fractions, = density, v = velocity, p = pressure, and A = pipe cross-sectional area. g = mass-transfer rate between the phases, e, d = the entrainment and deposition rates, and Gf = possible mass source of Phase f. Subscripts g, L, i, and D indicate gas, liquid, interface, and droplets, inspectively. Conservative Momentum. Conservation of momentum is expressed for three different fields, yielding the following separate 1D momentum equations for the gas, possible liquid droplets, and liquid bulk or film. For the gas phase, x - F D.......(4) For liquid droplets, ( - g ......(5) Eqs. 4 and 5 were combined to yield a combined momentum equation, where the gas/droplet drag terms, F D, cancel out: (Vg t +AV +(V D.........(6) SPEPE P. 171