Summary. Severe slugging in pipeline/riser systems was modeled by solving the local instantaneous equations for mass and momentum with a method of characteristics. The results are in good agreement with experimental data obtained in a 0.053-m-diameter flow loop for different pipeline slopes and various flow rates. Introduction The unstable behavior of two-phase flow in pipe systems is encountered frequently in oil production. Examples are the casing heading that occurs in oil wells working at low gas and oil flow rates, the annulus heading of some gas-lift wells, and severe slugging in pipeline/riser systems. Such situations correspond to large-amplitude, long-duration instabilities, which may reduce oil production and damage installations. These large-scale instabilities result from the competition between restoring forces owing to gravity and lift forces linked to gas flow. They have to be distinguished from the small-scale instabilities of the flow itself that arise, for example, in conventional slug flow. Because they probably have the same origin, however, large-scale instabilities are prevented by similar means. This paper focuses on the severe-slugging phenomenon, although the model proposed was also used for annulus heading. Schmidt et al. described a typical unstable periodic cycle (Fig. 1). The first step, slug generation, corresponds to an increase of the pressure in the bottom of the riser. The liquid level does not reach the top of the riser. During this period, the liquid is no longer sup-ported by the gas and begins to fall. As the pressure increases, the gas accumulates in the pipeline, so the riser is supplied by liquid and eventually gas at a lower rate. In the second period, the liquid level is again built up by liquid entering from the bottom of the pipeline. Note that a negative slope is not required to explain this step. For downward flow, a liquid slug is formed at the bottom, so the rise in the liquid level results from liquid flowing alone in the riser. For horizontal flow, the fallback phenomenon does occur, and the rise in liquid level may result from a poor gaseous mixture flowing in the riser. During the second step, slug production, the liquid level reaches the riser outlet, and the liquid slug eventually formed at the bottom of the pipeline is produced until the gas again supplies the riser. This step does not exist for horizontal pipes. In the third step, bubble penetration, gas is again supplied to the riser, so the hydrostatic pressure decreases. As a result, the gas flow rate increases. The fourth step corresponds to "gas blowdown." When the gas produced at the riser bottom reaches the top, the pressure is minimal and the liquid is no longer gas-lifted. The liquid level falls and a new cycle begins. Yocum and Taitel reported on this subject. Schmidt et al., who undertook an extensive investigation of the experimental behavior of pipeline/riser systems, proposed the first model requiring an empirical correlation to calculate liquid fallback. Schmidt et al. later improved the physical model for which four different sets of equations are necessary for slug generation, slug production, bubble penetration, and gas blowdown. Their results are in good agreement for a downward-sloping pipeline. Nevertheless, the model probably cannot adequately cover the full cycle of a horizontal pipe. Pots et al. discussed how to scale a laboratory flow loop to simulate the behavior of a field installation. They mentioned the occurrence of severe slugging with horizontal pipes allow liquid flow rates but suggested flowline undulations as the cause. Taitel's theoretical work dealt with the conditions in which an unstable process occurs and gave solutions for eliminating instability. His study was limited to downward pipe inclination. This paper tries to give a correct physical explanation of flow instability on the basis of experimental investigations and numerical simulations. Long-period instabilities were observed with both downward and horizontal pipes, although with less amplitude in horizontal pipes. A numerical model that solves the same set of equations for the full cycle is proposed. In this first attempt, great care was taken to obtain the right solution for riser behavior from local equations. Only an overall global model was used for the mass balance in the pipe. The solution gives the time variations of the pressures, void fraction, and flow rates, as well as the liquid height in the riser, through the method of characteristics. The predictions are then compared with experimental findings. Experimental Equipment and Procedure To understand the physics of severe slugging, experiments were carried out in a laboratory-scale flow loop made of 0.053-m-ID transparent polyvinyl pipes. The air/water mixture flowed through a 25-m-long horizontal or inclined pipeline and a 13.5-m-long vertical riser (Fig. 2). The pipeline was supported by a pivoting (+/- 8 %) steel frame, and the two pipes were connected through a 0.5-m radius bend. The frame was designed so that bending for a pipe filled with liquid is less than 0.1%. At the pipeline inlet, the fluids were supplied through a Y-junction to prevent disturbances, especially for stratified flow. At the riser outlet, the air/water mixture was separated by gravity in a horizontal vessel working under atmospheric conditions. The separator was designed so that no siphoning occurs between the reservoir and the riser. Water was supplied to the Y-mixer from a pump at a constant flow rate, regardless of the pressure in the pipeline. Air was supplied at a controlled pressure of 500 kPa from a rotary compressor. The gas flow rate was controlled by a manual valve placed close to the mixer and working in a choked condition. The liquid flow rate was measured by a volumetric rotary flowmeter, and a set of three diaphragms covering 0.0005 to 0.1 kg/s was used for the gas flow rate. In both cases, the accuracy was better than +/- 1%. The pipeline was equipped withtwo strain-gauge pressure transducers mounted in the middle and the outlet of the pipe andthree capacitance wires. Instantaneous pressure and liquid height were obtained with an accuracy better than +/-0.5%. In addition, two homemade hot-wire probes were placed in both pipes for flow-pattern recognition. Sixty-eight 30-minute runs, during which the pressures and liquid heights were recorded, were carried out for different gas and liquid flow rates and three different pipe slopes (0, 1, and -1%). The inlet flow conditions are given by the superficial velocity of each phase. For the gas, the velocity is calculated from the mass flow rate using the density at 20 deg. C and 100 kPa. SPEPE P. 299^

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