There has quite recently been some discussion regarding the accuracy of gas kick slippage models used in transient flow models. This is not necessarily easy to give a correct answer on. However if pressure build up gradients for a migrating kick in a closed well is used for predicting the kick migration velocity, one can easily obtain a misinterpretation due to the fact that parts of the kick can become suspended in the mud. This was discussed in a paper presented two decades ago (Johnson et al., 1995). The purpose of the paper presented here is to show what kind of uncertainties that are involved in the transient flow modelling process and how that affects the pressure build up gradients. In this paper, a transient numerical model that can be used for simulating two-phase flow will be presented. It is based on the Drift flux model and the one dimensional advection upstream splitting method hybrid scheme (AUSMV). When using transient models for predicting the kick migration time, there are two sources of errors. The first is obvious in the sense that the gas slip parameters are uncertain. However, a less known potential source of error can be numerical diffusion and discretization errors caused by the numerical solver itself. The paper will show how the AUSMV scheme can be made less diffusive by using the slopelimiter concept. The paper will demonstrate that the effect of numerical diffusion can be quite substantial. This will be done by simulating pressure build up in a closed well varying both the slip parameters but also the degree of numerical diffusion. In addition, the simulated effect on the pressure build up when gas get trapped in the mud for lower gas concentrations will also be demonstrated. This paper aims at showing that the uncertainty caused by numerical diffusion can be of the same order as uncertainty in the slip parameters. It will also confirm the results reported in Johnson et al. (1995) by the use of a transient low diffusion flow model.

Bullheading is the process of pumping fluids into the well without circulating back to surface. This operation can be carried out for several reasons. In well control, this can be an alternative well kill approach in situations where conventional kill methods do not apply. When considering the pressurized mud cap drilling technique, bullheading is used for controlling pressures when drilling highly fractured and vugular carbonate formations. Bullheading is also carried out for killing production wells prior to workover operations. For a bullheading operation to be successful one need to ensure that the correct flow rate is chosen to overcome gas migration. This countercurrent to downward flow situation is best described using transient flow simulators to correctly predict what kind of rates and fluid volumes that are required. In addition, a transient flow model can also predict what kind of pressures that will be experienced during the operation to ensure that equipment and fracture pressure limitations are not exceeded. This paper aims at giving an overview of the application and challenges associated with bullheading operations for different type of well operations including the pressurized mud cap drilling technique. Then a mathematical model and a numerical scheme (AUSMV) that can be used for simulating the transient dynamics of a bullheading operation will be described. The drift flux model combined with a slip law will be used. Here special emphasize will be given on describing how we made the numerical scheme second order to reduce effects associated with numerical diffusion. The numerical boundary treatment and handling of flow regime transitions will also be described since one will here alternate between different conditions like cocurrent, countercurrent and downward flow. Two simulation scenarios will be considered. In the first example, a kick scenario will be considered and it will be shown how the transient model can be used to predict the effect of using different bullheading rates when trying to kill the well. Both time and depth variables will be visualized. The model can also predict how large volumes are required for a successful bullheading operation for a given rate. In the second example, it will be shown how the model can be used for simulating the alternating conditions experienced in a pressurized mud cap drilling operation. Here one will have a situation where surface pressure will build up if a kick is migrating in the closed annulus and if the pressure reaches a certain level, the kick has to be bullheaded back into the formation. This process can be repeated several times. The paper will show that the transient model proposed can provide good insight into the dynamics of bullheading and pressurized mud cap drilling. The model seems to be robust in handling the alternating flow conditions. Finally, some words will be said with respect to what is considered as important with respect to improving the modelling.