In reality, downhole conditions are highly unpredictable due to many uncertain and inconsistent factors, such as the uncertainty of the friction and contact between drillstring and bore-hole. As friction and contact are crucial components in torque and drag calculation, it is meaningful and practical to consider their uncertainty. This paper presents a random method for calculation of hoisting drag. Firstly, the finite element method (FEM) is used for hoisting drag calculation of a directional drilling well using Adanoy’s method in the deterministic case. Then two strategies are taken to model the random component in the downhole. The first strategy considers the randomness of the downhole friction. Instead of being a deterministic value, the friction coefficient is considered as Gaussian. The second strategy considers the randomness of contact between drillstring and wellbore. As a result, the drillstring is no longer continuously contacting with the wellbore in the curved section of well profile, which can help avoid overestimating torque and drag. Parametric studies on both strategies are conducted. Monte Carlo (MC) simulation is employed for statistical analysis. The probability density distributions and mean values of drag will be studied. The methodology can be extended into torque or drag calculation in lowering, ream in and ream out drilling conditions. Results from this paper indicate that surface hoisting drag is nearly Gaussian when the friction coefficient is Gaussian. The contact loss leads to considerable reduction in the surface hoisting drag when contact uncertainty is considered. The work of this paper will help estimate the range of surface drag and torque, which allows the well planner to develop a risk assessment for a challenging well trajectory.

A dynamic bottom hole assembly (BHA) model is built with finite element method (FEM) in this paper. This model is used for evaluation the influence of externally added vibration to the BHA system. With this dynamic model along with a general bit-rock interaction formula, the BHA’s motion in axial and torsional directions are examined. Parametric study is carried out by varying the parameters of the applied vibration force, including the mean value, amplitude, angular frequency, and the location of this force excitation. The simulation results indicate that externally applied vibration force is indeed able to improve drilling performance. In particular, the mean value and amplitude of the applied force have a almost linear relation with ROP and WOB. The stresses distributions along BHA are investigated as well.

Based on linear damage accumulation law, this paper investigates the fatigue problem of drill-strings in time domain. Rainflow algorithms are developed to count the stress cycles. The stress within the drill-string is calculated with finite element models which is developed using Euler-Bernoulli beam theory. Both deterministic and random excitations to the drill-string system are taken into account. With this model, the stress time history in random nature at any location of the drill-string can be obtained by solving the random dynamic model of the drill-string. Then the random time history is analyzed using rainflow counting method. The fatigue life of the drill-string under both deterministic and random excitations can therefore be predicted.

Using Euler-Bernoulli beam theory, a finite element model with six degrees of freedom per node is developed for a drill-string assembly. The drill-string is driven by a DC motor on the top and is subjected to distributed loads due to its own weight as well as bit/formation interaction. The model is axial-torsional, lateral-torsional coupled. Under deterministic excitations, the model captures stick-slip behavior in drilling operation. Analysis on its negative effect on drilling performance are made, and potential mitigation measures are also discussed. In random model, the excitations to the drill-bit are modeled as combination of deterministic and random components. Monte Carlo (MC) simulation is employed to obtain the statistics of the response. Two cases of random excitation with different intensities are investigated. The results from MC simulation are compared against that from deterministic case.