6n Degrees of Freedom Transient Torque & Drag

When drilling vertical and deviated wells, it is quite common that heavy drill-string vibrations are the source of performance reductions or drilling incidents such as wellbore instabilities, damage to downhole tools or premature wear of drill-pipes. In fact, there are many forms of drill-string vibrations: some are torsional, others are axial or even lateral. But in practice, all three vibration movements may happen simultaneously along the drill-string. It is possible to model the combined effects of axial and torsional oscillations in real-time, but it is much more challenging to include the modelling of lateral displacements and yet be compatible with real-time constraints. Mathematical modelling and downhole measurements indicate that the dynamic movement of drill-strings is also influenced by hydraulic effects (see https://doi.org/10.2118/199678-PA). As drilling fluids are non-Newtonian, thixotropic and visco-elastic, the hydro-mechanical interaction between the drill-pipe and the drilling fluid is complex and needs to be studied in detail. First, we have investigated the impact of drilling fluid in hydrostatic conditions and arrived at a general formulation for the calculation of buoyancy forces on portions of plain and perforated pipes (see https://doi.org/10.2118/204025-PA). We have also found that the Quemada rheological behavior is particularly well-suited to describe the steady state behavior of drilling fluids and we have derived an efficient method for calibrating flow-curves to the Quemada rheological behavior (see https://doi.org/10.1115/OMAE2021-60500). The Quemada rheology is complex and new methods for calculating pressure losses in steady state conditions in pipes and annuli had to be derived (see https://doi.org/10.3390/en13236165). One of the most interesting aspects of the Quemada rheological behavior is that it allows to introduce thixotropic behavior in a very natural way. As thixotropy means that the viscous properties of the fluid depends on its shear history, there is evidently an interesting interaction when there is a transient displacement of the drill-string in the thixotropic fluid. For that reason, we have studied the impact of oscillating flowrates of non-thixotropic and thixotropic non-Newtonian fluids in circular pipes and found that the dynamic response in terms of pressure gradients of thixotropic and non-thixotropic differ substantially. We have developed a transient model of the fluid of such fluids under dynamic conditions (see https://doi.org/10.1115/OMAE2021-61638). While making differential pressure measurements in a flow-loop and comparing the measurements from theoretical calculations based on precise flow-curves made with a scientific rheometer, we have that the more shear thinning is the fluid, the greater is the discrepancy between the measured pressure gradients and the theoretical values. We have traced back the origin of the discrepancy to the default conversions made by Couette rheometers. Indeed, the shear rates and stresses provided by the rheometers utilize the assumption that the fluid is Newtonian, which is not our case. We have developed a correction method for non-Newtonian effects in Couette rheometer and made verified that after correction, the theoretical and measured pressure gradients in a circular pipe are indeed very close. We have at the same time developed a fast and precise method to calibrate the Herschel-Bulkley rheological behavior from pressure gradient measurements in circular pipes (see https://doi.org/10.3390/fluids6040157). The calibration method is inspired by a smart method published by G. Mullineux (https://doi.org/10.1016/j.apm.2007.09.010). For the benefit of the scientific community, the calibration method described by Mullineux (2008) has been implemented in an open-source micro-service (https://github.com/Open-Source-Drilling-Community/Yield-Power-Law-rheology-calibration). The microservice is also accessible here: https://app.digiwells.no/YPLCalibrationFromRheometer/Rheograms. The contribution to the open source community of drilling models is described in a paper that will be available in March 2022 (SPE-208794-MS).

Despite the benefits of using high rotational speed on drilling performance, the systematic use of high top-drive speeds has led to adverse side-effects such as excessive tool-joint wear, wellbore instabilities induced by mechanical shocks, and extreme grinding of drilled-cutting particles resulting in problematic hole cleaning conditions. At any positions along the drill-string, there are 6 degrees of freedom (DOF): one axial, one torsional and four laterals, i.e. two for displacement and two for the direction. The drill-string can be decomposed in n elements, each element having therefore 6 DOF. The primary objective of this project is to develop a 6n DOF transient torque and drag model that is tightly coupled with transient hydraulic and material transport models. The secondary objectives are to develop find automatic calibration methods for the high-fidelity model and to automatically derive a light-weight surrogate model that captures the most important dynamic modes of the full fledge model. The surrogate model can be used in optimization problems. With such a model at hand, it then possible to determine the range of drilling parameters and optimal drilling procedures that minimize drilling events associated with axial, torsional and lateral movements of the drill-string, yet allowing for effective drilling conditions.