Maintaining drillstring integrity is one of the main factors in a successful drilling operation. Drillstring integrity failure due to drillpipe fatigue remains to be a major problem. Drillpipe fatigue is caused by cyclic loading of bending (due to dogleg, sagging effect, buckling, and vibration) under rotation, which can lead to pipe twistoff. Collar or pipe off costs the operator millions of dollars to recover due to the cost of nonproductive times, fishing services, cement plugs, sidetracks, bottomhole assembly (BHA) lost in hole, and tool replacements. This failure can cause a significant impact to well cost. For preventive measures, the drilling industry still relies on regular drillstring inspection using nondestructive tests (NDT) to find drillpipe cracks before they grow and the pipe completely twists off downhole or at the minimum, limits the drillstring component's usable time based on the local experience. Until now, there has not been any sensor or method available to monitor the fatigue level of the components. Hence, the industry has a real need for a new method to manage drillstring integrity. Fatigue calculation is a well-established concept and applied in many industries, but not yet fully used to manage drillstring integrity. Several recent digital technology advancements now allow us to implement a fatigue management workflow. Using finite element modeling allows for simulating a fatigue test of connections and portholes in the collar and generates a list of fatigue properties for drillstring components. This method eliminates the expensive and time-consuming fatigue material test. Then, using an integrated dynamic design and analysis platform, allows for simulating the drilling process and calculating the expected loads along the drillstring during the drilling operation. By combining both capabilities in a well planning application makes it possible to calculate expected fatigue life consumed automatically for every designed BHA, which can be connected to an inventory system to select the optimum drillstring components having sufficient fatigue life for the job of interest. When implementing the application, a fatigue life monitoring workflow is also implemented that allows the engineer to monitor fatigue life consumption and take necessary action when it approaches the safety limit. Several technical solutions are required to implement this monitoring workflow, including improving computation speed with the modeling calculation on the cloud and high-performance computing parallel computations, leveraging bending load data from downhole bending sensors to validate and calibrate the modeling, and evaluating historical performance in the maintenance database to continuously refine the workflow. This innovative workflow has been implemented to manage BHA integrity for medium-to-high dogleg severity (DLS). The approaches in managing fatigue life enable risk mitigation for BHA integrity, push kickoffs deeper, shorten the curved sections, and increase reservoir exposure, including reentry applications. This paper presents some field examples that demonstrate how this solution provides drilling operations with a new tool to reduce fatigue failures by predicting expected fatigue life consumed on a job, selecting correct tools, and proactively managing the drilling risks.
Zeckendorf's Theorem states that any positive integer can be written uniquely as a sum of non-adjacent Fibonacci numbers. We consider higher-dimensional lattice analogues, where a legal decomposition of a number n is a collection of lattice points such that each point is included at most once. Once a point is chosen, all future points must have strictly smaller coordinates, and the pairwise sum of the values of the points chosen equals n. We prove that the distribution of the number of summands in these lattice decompositions converges to a Gaussian distribution in any number of dimensions. As an immediate corollary we obtain a new proof for the asymptotic number of certain lattice paths.
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