Summary Underbalanced operations (UBO) are carried out to bypass drilling challenges that could be difficult to resolve by use of conventional drilling techniques. Steady-state multiphase-flow models are used to construct underbalanced-drilling operational windows. These advanced software models are deterministically formulated. It is known that some of the model input parameters, such as the multiphase-flow parameters, friction factors, and reservoir productivity, are subject to uncertainties. Failures to capture these variabilities may introduce some error in the model prediction, resulting in poor well planning and implementation. The purpose of this work is to implement probabilistic modeling of underbalanced drilling by use of a simple steady-state two-phase model. Both predefined uncertain and fixed factors serve as inputs to a pre-existing deterministic model. By applying Monte Carlo simulations, the model predicts outputs that follow a statistical distribution. A sensitivity analysis is conducted to determine the input factor that is most responsible for the uncertainty in the predicted bottomhole pressure (BHP). The results demonstrate that uncertainty modeling can improve underbalanced-drilling design and operations. A more realistic operational window is obtained, ensuring that underbalanced condition is maintained throughout the target section. With a better understanding of uncertainties and the corresponding impacts, well planners can make better decisions regarding well design criteria and safe operational conditions, and avoid huge economic consequences.

Summary Transient flow models play an important role in the planning and follow-up of advanced well operations such as managed pressure drilling (MPD) and underbalanced operations. The most recent trend is a situation whereby flow models and control-engineering algorithms are combined in various settings to control flow parameters. This requires robust flow models and an in-depth understanding of uncertainties in the modeling process. This paper presents a simple and robust transient model that can handle highly dynamic flow systems. The model, the Advection-Upstream-Splitting-Model hybrid scheme, was developed for academic and training purposes. With the model, students can investigate different flow scenarios and pressure-control challenges encountered in general well control, MPD, underbalanced drilling, and automation. The capability of this model to handle highly changing flow scenarios is demonstrated with examples taken from MPD and underbalanced operations. The effect of numerical dissipation on the model predictions is briefly discussed.

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During drilling, there must be an evaluation of the maximum pressure that the formation can handle during a well kill scenario. This will depend on various parameters like fracture pressure, pore pressure, kick volume and several other factors. The depth of the next planned hole section will depend on if a kick of a certain size can be handled safely. This evaluation is often referred to as performing kick tolerances. When starting to drill a section, one will take a leak off test to get an indication of the fracture pressure at the last set casing shoe and this will be important information for the kick tolerance results. For HPHT wells the margin between pore and fracture pressures will be small, and one often has to resort to using transient flow models to perform the kick tolerances. However, there are many uncertain parameters that are affecting the results. Some examples here are pore pressure, type of kick and kick distribution. There is a need for trying to incorporate the uncertainty in the calculation process to give a better overview of possible outcomes. This approach has become more and more popular, and one example here is reliability based casing design. This paper will first describe the kick tolerance concept and its role in well design planning and operational follow up. An overview of all parameters that can affect the results will be given. In water based mud, the gas kick will be in free form yielding higher maximum casing shoe pressures compared to the situation when oil based mud is used where the kick can be fully dissolved. Then it will be shown how both an analytical and a transient flow model can be used in combination with the use of Monte Carlo simulations to generate a probabilistic kick tolerance calculation showing possible outcomes for maximum casing shoe pressure for different kick volumes. Here uncertain input parameters that can affect the calculation result will be drawn from statistical distributions and propagated through the flow model to estimate the casing shoe pressure. Multiple runs will be needed in the Monte Carlo simulation process to generate a distribution of the maximum casing shoe pressure. This will demand a rapid and robust flow model. The resulting maximum casing shoe pressure distribution will then be compared against the uncertainty in the fracture pressure at the last set casing shoe to yield a probability for inducing losses. The numerical approach for predicting well pressures and a schematic of the total calculation process will be given. Emphasis will also be put on discussing how this should be presented to the engineer with respect to visualization and communication. It will also be shown that one of the strengths of the probabilistic approach is that it is very useful for performing sensitivity analysis such that the most dominating factors affecting the calculation results can be identified. In that way, it can help in interpreting and improving the reliability of the kick tolerance simulation results.

Transient flow models play an important role in the planning and follow-up of advanced well operations such as managed pressure drilling and underbalanced operations. The most recent trend is a situation whereby flow models and control engineering algorithms are combined in various settings, to control flow parameters. This requires robust flow models and an in-depth understanding of uncertainties in the modeling process. This paper presents a simple and robust transient model that can handle highly dynamic flow systems. The model, AUSMV scheme, has been developed for academic and training purposes. With the model, students can investigate different flow scenarios and pressure control challenges encountered in general well control, managed pressure drilling, underbalanced drilling, and automation. The capability of this model to handle highly changing flow scenarios will be demonstrated with examples taken from managed pressure drilling and underbalanced operations. The effect of numerical dissipation on the model predictions will be briefly discussed.