Improved Dynamic Modelling of Two-Phase Flow in Well Control Operations

Abstract

This thesis focuses on exploring applications and optimizing transient numerical models for simulating well control situations. The main scope of the research was to find opportunity for improving existing numerical models and to improve the models accordingly. Relevant cases were constructed, simulated with different mathematical models and numerical methods, and the results were compared. The cases constructed were to a large degree motivated from challenges associated with kick handling in subsea back pressure MPD systems and gas in riser unloading events. The models that have been used for evaluating the transient scenarios are the single bubble model and Drift-Flux model. A static analytical model was also developed for kick tolerance evaluations. The first topic studied was kick tolerance evaluation from a probabilistic perspective, using Monte Carlo simulations. By adopting this approach, one can get a probability for whether a certain kick volume can lead to fracturing the formation in the weakest spot. It is also shown how this approach can be useful for analyzing how the uncertainties in each input parameters change the results. The Monte Carlo simulations has, to our knowledge, not been used so far for kick tolerance evaluation. An important matter explored throughout the research was the effect of the numerical diffusion in the results when simulating well control situations and the importance of restricting this effect. We demonstrated how to use different techniques for restricting the numerical diffusion and compared the results between them. This thesis also studies kick behavior when using subsea backpressure MPD systems with oil based mud. In this system, one need to evaluate what will be the maximum surface rates and surface pressure compared to equipment limitations when trying to circulate a certain kick volume directly through the MPD system. The transient flow model for simulating a kick in oil based mud was provided by SINTEF Industry. This model uses the Drift-Flux formulation solved numerically by the predictor-corrector shooting technique. We have used this model to study, for instance, how the results vary when modelling the gas solubility in different ways, how changes in back pressure will impact where free gas will emerge in the riser, the effect of different kick sizes and the impact the circulation rate will have on the maximum flow rates at surface. This thesis has also studied the unloading scenarios that can occur when free gas enters a riser filled with water based drilling fluid. Here the impact of gas suspension, kick sizes and riser geometry on the severity of the unloading was investigated. For these investigations, the explicit AUSMV scheme was used as a numerical solver for the Drift Flux model. The gas slip model used incorporated different flow regimes as well as the effect of suspension where small gas volumes are trapped in the drilling fluid. By using this numerical scheme, we have demonstrated, for example, that the suspension limit has a significant impact on the simulation results, especially when studying whether a riser unloading event might occur or not for certain kick sizes. The suspension limit is often neglected in such models and we advocate the importance of considering this effect in flow models for simulating kicks in WBM. Sensitivity analysis were consistently performed in the publications produced during the Ph.D. The numerical models allowed to explore a gas kick behavior during well control situations and how important parameters affect the results. The thesis also highlights the importance of selecting the appropriate models and the appropriate numerical method for simulating well control situations.