Multiphase flow is a term used to express a flow that deals with two or more immiscible phases. In the oil and gas production system, multiphase flow can occur in the wellbore and pipelines, and gas-liquid two-phase flow is one of the most common ones. The term flow pattern describes the distribution of each phase in the multiphase flow system. Each flow pattern occurs in certain values of different variables that control the flow behaviors. These variables can be classified into three major categories, operational parameters (i.e., flow rates), geometrical parameters (i.e., pipe diameter and inclination), and the physical properties of the phases (i.e., density, viscosity, and surface tension). For gas-liquid two-phase flow in pipes or wellbores, major flow patterns include segregated flow (SEG), intermittent flow (INT), bubbly (BL, only for vertical or near vertical), and dispersed bubble flow (DB). Intermittent flow is one of the most common flow patterns that occurs in the oil and gas wellbore and pipeline system. For horizontal or inclined pipes, intermittent flow can be further classified into plug flow (PL), slug flow (SL), and pseudo-slug flow (PS). For vertical or near vertical pipe, intermittent flow can be classified into slug flow and churn flow (CH). The focus of this study will be on the two least studied flow patterns namely pseudo-slug and churn flows.
Pseudo-slug flow is considered as a transition flow pattern between conventional slug and segregated flows as the superficial gas velocity increases. It mainly occurs in horizontal or upward inclined pipes. The pseudo-slug flow can be differentiated from the slug flow by having a slug body that does not completely seal the cross-sectional area of the pipe, unlike the conventional slug flow pattern. Churn flow mainly occurs in vertical or near-vertical pipes, and is considered as one of the least investigated flow patterns due to the complexity of its nature. Similar to slug flow, gas pockets flow along with the liquid phase in churn flow but in a more chaotic way. In churn flow, the bullet-shaped Taylor bubbles, a structure that shows a clear bullet-shaped interface on top and occurs typically in conventional slug flow, are distorted because of the relatively higher gas flow rates causing asymmetrical random gas pockets.
Pseudo-slug and churn flows are generally considered as two different flow patterns because of their visual differences. However, some recent experimental studies have shown that they share many similarities. For example, they both have gas penetration through the slug body; they both locate between slug and segregated flow in the flow pattern map; they demonstrate similar time trace signals of liquid holdup equivalent and distribution histogram; their structure velocities are smaller than the one for conventional slug flow. According to the observation from previous experimental studies, we anticipate that pseudo-slug flow gradually changes to churn flow when the inclination angle changes from horizontal to vertical.
Highly inclined pipelines have become common especially in offshore applications, and the wellbore can range from horizontal to vertical with the current advancement in directional drilling. Accurate prediction of the pressure gradient and liquid holdup will be of great importance to the production design. There are several hydraulic models available in the literature for churn flow, while the modeling for pseudo-slug flow has just emerged in recent years. Some of the models predict well for pseudo-slug flow but poorly for churn flow, and vice versa. There is no single model that works well for both pseudo-slug and churn flows. With the current modeling approaches, the user needs to switch the model from pseudo-slug to churn flow when the inclination angle increases from inclined to near vertical to obtain more accurate predictions in liquid holdup and pressure gradient. However, the critical inclination angle corresponding to this flow pattern transition can be gradual and depends on the flowing conditions and is still not clear. Switching the model will also result in discontinuity in model prediction which can lead to problems when coupled with research simulations or uncertainties in facility and production design. In addition, evaluation of these existing models still shows unsatisfactory predictions although they are developed for the targeted flow pattern.
In this study, we developed a simplified unified hydraulic model for pseudo-slug and churn flows, that captures the effects of inclination angle, gas and liquid flow rates, and fluid properties, such as liquid viscosity and gas density, on the liquid holdup and pressure gradient. It removes the need for the user to switch the models as the flow pattern (or inclination angle) changes. The liquid holdup is predicted using the drift-flux model concept, with new correlations for the drift velocity and flow distribution coefficient. The pressure gradient is predicted using two-fluid model with modified gas and liquid shear stresses by considering the additional shear induced by the pseudo-slug/churn structures and the oscillated nature of the liquid film caused by gravity. The model gives the best predictions as compared with other available models in the literature, in terms of predictions for pseudo-slug flow solely, churn flow solely, and both flow patterns.