Liquid–liquid–solid three-phase flow in horizontal wells: flow pattern modeling and dimensionless analysis

The presence of solid particles in horizontal liquid-liquid flows is a common phenomenon encountered in various scientific fields, particularly in petroleum engineering. During production from unconsolidated hydrocarbon zones, sand particles may enter the flow path along with water and oil. The primary issues for sand-producing wells include excessive pressure drops, tubing and pipeline erosion, and reductions in production. Therefore, predicting the critical transport velocity and characterizing the deposition and transport of sand particles in three-phase liquid-liquid-solid flow systems are vital for optimizing and improving flow performance in pipelines. While several researchers have developed models for liquid-liquid and liquid-solid flow systems, liquid-liquid-solid systems have received less attention; as a result, such systems are not yet well understood. An accurate and reliable model to predict the flow regimes in these systems are yet to be developed due to the complexity and uncertainties associated with fluid interactions and their effects on transport of solid particles. To visualize the flow regimes occurred under different conditions, a transparent flow loop system has been developed to facilitate the flow of two liquids (water and oil) alongside with solid particles. In this study, a series of three-phase liquid-liquid-solid flow experiments were conducted using such transparent system with a length of 12 m and a diameter of 30 mm. During multiple tests and experiments, wide range of variables such as solid particle sizes, rates of input particles (ROIP), and water and oil velocities have been considered and their impacts have been evaluated. Five flow patterns were observed in the three-phase liquid-liquid-solid flow: dilute solids at wall (DSAW), concentrated solids at wall (CSAW), moving dunes (MD), stationary bed (SB), and accumulative bed (AB). To better understand the impact of various parameters and to analyze the interaction and competrion between different forces applied under each flow pattern condition three-phase dimensionless Weber and Reynolds numbers have been defined which enables us to accurately predicted the multiphase flow system behavior regardless of the system scale. Such dimensionless numbers have been used to propose an accurate model to predict different flow regimes as well as the transition condition between these flow patterns. A flow pattern map, incorporating key parameters such as flow regime, phase velocity, solid particle properties, and pipe geometry, is also presented. Furthermore, a new mathematical model has been developed to determine the critical deposition velocity with an error of less than 2% which takes into account the impact of multiple influencing factors. The experimental results revealed that at low ROIP (e.g., 40 g/min), solid particle size is the most significant parameter affecting critical deposition velocity. However, at high ROIP (e.g., 220 g/min), particle size has minimal impact and ROIP becomes the dominant factor. Finally, a mathematical model is proposed to predict the flow regime boundaries from stationary bed to accumulative bed flow regimes with an error of less than 5%.