Probabilistic Models for Kick Tolerance

2021 ◽  
Author(s):  
Martine Kristoffersen ◽  
Dalila Gomes ◽  
Kjell Kåre Fjelde
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Analytical Model ◽  
Flow Model ◽  
Transient Flow ◽  
Simulation Framework ◽  
Gas Distribution ◽  
Fracture Pressure ◽  
Open Hole

Abstract Kick tolerance is an evaluation of how large kick sizes i.e. kick volumes an open hole section can withstand without threatening the formation integrity at the shoe. If a certain kick size cannot be handled safely, the planned open hole section must be shortened, and the casing design must be altered. Three models for calculating the kick tolerances in a well will be compared for a long and short open hole section for various lengths of bottom hole assembly (BHA). The kick tolerance will be performed probabilistically by use of Monte Carlo simulations where important input parameters are considered as distributions. The paper will focus on where the models differ in their results and discuss various opportunities and challenges with using a probabilistic approach. The models will be integrated in a Monte Carlo simulation framework where the major input uncertainties will be pore pressure, fracture pressure and initial gas distribution in the well. The output will be a distribution of the casing pressure load that has to be compared to the fracture pressure distribution which results in a certain probability for fracturing for a given kick size. Only gas kick in water-based mud will be considered. First a transient model based on the single bubble concept was considered and integrated in the Monte Carlo simulation framework. This was first compared against an analytical model which calculates the maximum casing shoe pressure at static shut in conditions. The analytical model considers uncertainty in the initial gas distribution. A transient flow model based on the drift flux model was also considered. Both short and long open hole length were considered. BHA length and kick size were varied. The results show that the transient flow model provides the least conservative results but also the analytical model reduces the probability for fracturing compared to the single bubble model. In most cases, the maximum casing shoe pressure is achieved when kick is located at the BHA. This paper extends the application of methods for reliability-based casing design to also include probabilistic kick tolerances. This is a contribution related to how the well design process can become more risk based. Some challenges related to specification of tolerance requirements, required number of Monte Carlo simulations and computing time will be discussed. It also provides an overview of the differences between the models and which parameters that are most important for the results.

Probabilistic Flow Modelling Approach for Kick Tolerance Calculations

2017 ◽  
Author(s):  
Dalila Gomes ◽  
Knut Steinar Bjørkevoll ◽  
Johnny Frøyen ◽  
Kjell Kåre Fjelde ◽  
Dan Sui ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Pore Pressure ◽  
Flow Model ◽  
Transient Flow ◽  
Probabilistic Approach ◽  
Numerical Approach ◽  
Free Form ◽  
Maximum Pressure ◽  
Fracture Pressure ◽  
Calculation Process

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.

scholarly journals Cheating at Craps

2021 ◽  
Vol 48 (4) ◽  
pp. 53-61
Author(s):  
Andrea Marin ◽  
Carey Williamson
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Modeling And Simulation ◽  
Analytical Model ◽  
Quantitative Evaluation ◽  
Mathematical Analysis ◽  
Simulation Modeling ◽  
Analytical Modeling ◽  
The World ◽  
Simulation Results

Craps is a simple dice game that is popular in casinos around the world. While the rules for Craps, and its mathematical analysis, are reasonably straightforward, this paper instead focuses on the best ways to cheat at Craps, by using loaded (biased) dice. We use both analytical modeling and simulation modeling to study this intriguing dice game. Our modeling results show that biasing a die away from the value 1 or towards the value 5 lead to the best (and least detectable) cheating strategies, and that modest bias on two loaded dice can increase the winning probability above 50%. Our Monte Carlo simulation results provide validation for our analytical model, and also facilitate the quantitative evaluation of other scenarios, such as heterogeneous or correlated dice.

Gibbs-ensemble Monte Carlo simulation of H2–H2O mixtures

2021 ◽  
Author(s):  
Armin Bergermann ◽  
Martin French ◽  
Ronald Redmer
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Giant Planets ◽  
Gibbs Ensemble ◽  
Miscibility Gap ◽  
Ensemble Monte Carlo ◽  
Ensemble Monte Carlo Simulation ◽  
Gibbs Ensemble Monte Carlo

The miscibility gap in H2–H2O mixtures is investigated by conducting Gibbs-ensemble Monte Carlo simulations. Our results indicate that H2–H2O immiscibility regions may have a significant impact on the structure and evolution of ice giant planets.

Comparison of Experiment With Monte Carlo Simulations on a Reflective Gap Using a Detailed Surface Properties Model

1996 ◽  
Vol 118 (2) ◽  
pp. 388-393 ◽  
Author(s):  
J. Zaworski ◽  
J. R. Welty ◽  
B. J. Palmer ◽  
M. K. Drost
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Grazing Angle ◽  
Incident Radiation ◽  
Monte Carlo Code ◽  
Bidirectional Reflectance Distribution Function ◽  
Bidirectional Reflectance ◽  
Detailed Surface ◽  
Bidirectional Reflectance Distribution

The spatial distribution of light through a rectangular gap bounded by highly reflective, diffuse surfaces was measured and compared with the results of Monte Carlo simulations. Incorporating radiant properties for real surfaces into a Monte Carlo code was seen to be a significant problem; a number of techniques for accomplishing this are discussed. Independent results are reported for measured values of the bidirectional reflectance distribution function over incident polar angles from 0 to 90 deg for a semidiffuse surface treatment (Krylon™ flat white spray paint). The inclusion of this information into a Monte Carlo simulation yielded various levels of agreement with experimental results. The poorest agreement occurred when the incident radiation was at a grazing angle with respect to the surface and the reflectance was nearly specular.

Secondary Fluorescence of 3D Heterogeneous Materials Using a Hybrid Model

2020 ◽  
Vol 26 (3) ◽  
pp. 484-496
Author(s):  
Yu Yuan ◽  
Hendrix Demers ◽  
Xianglong Wang ◽  
Raynald Gauvin
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Analytical Model ◽  
Hybrid Model ◽  
Three Dimensional ◽  
Heterogeneous Materials ◽  
X Ray ◽  
The Monte Carlo Method ◽  
Secondary Fluorescence ◽  
Good Agreement

AbstractIn electron probe microanalysis or scanning electron microscopy, the Monte Carlo method is widely used for modeling electron transport within specimens and calculating X-ray spectra. For an accurate simulation, the calculation of secondary fluorescence (SF) is necessary, especially for samples with complex geometries. In this study, we developed a program, using a hybrid model that combines the Monte Carlo simulation with an analytical model, to perform SF correction for three-dimensional (3D) heterogeneous materials. The Monte Carlo simulation is performed using MC X-ray, a Monte Carlo program, to obtain the 3D primary X-ray distribution, which becomes the input of the analytical model. The voxel-based calculation of MC X-ray enables the model to be applicable to arbitrary samples. We demonstrate the derivation of the analytical model in detail and present the 3D X-ray distributions for both primary and secondary fluorescence to illustrate the capability of our program. Examples for non-diffusion couples and spherical inclusions inside matrices are shown. The results of our program are compared with experimental data from references and with results from other Monte Carlo codes. They are found to be in good agreement.

scholarly journals MONTE CARLO SIMULATION OF ISING MODEL ON DIRECTED BARABASI–ALBERT NETWORK

2005 ◽  
Vol 16 (04) ◽  
pp. 585-589 ◽  
Author(s):  
MUNEER A. SUMOUR ◽  
M. M. SHABAT
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Ising Model ◽  
Monte Carlo Simulations ◽  
Characteristic Time ◽  
Spontaneous Magnetization ◽  
Zero Temperature ◽  
Different Temperatures ◽  
Large Systems ◽  
Ising Spins

The existence of spontaneous magnetization of Ising spins on directed Barabasi–Albert networks is investigated with seven neighbors, by using Monte Carlo simulations. In large systems, we see the magnetization for different temperatures T to decay after a characteristic time τ(T), which is extrapolated to diverge at zero temperature.

scholarly journals RECYCLE OF RANDOM SEQUENCES

1993 ◽  
Vol 04 (03) ◽  
pp. 569-590 ◽  
Author(s):  
NOBUYASU ITO ◽  
MACOTO KIKUCHI ◽  
YUTAKA OKABE
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Random Sequence ◽  
Random Sequences

The correlation between a random sequence and its transformed sequences is studied. In the case of a permutation operation or, in other words, the shuffling operation, it is shown that the correlation can be so small that the sequences can be regarded as independent random sequences. The applications to the Monte Carlo simulations are also given. This method is especially useful in the Ising Monte Carlo simulation.

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