The soft string model has been widely used for torque and drag calculations. Although several modifications have been developed, the standard model in the oil and gas industry is the static soft string model, in which the string is assumed to be motionless and its stiffness is neglected. In order to estimate more realistic and accurate calculation of drillstring loading, not only the acceleration, but also axial stiffness of the string must be considered in force calculations. In this paper, a dynamic, axially-stiff string model is presented for force calculations of drillstring in tripping operations.

The mathematical model is developed to include axial stiffness of the drillstring and acceleration into the soft string model by coupling mass-spring system with the soft string model. Moreover, static friction and drilling fluid drag are taken into account. The drillstring is considered to be a system of coupled oscillators subject to external forces. Then, the motion of the individual oscillator is governed by external forces and the forces applied by its two neighboring elements. In this model, the static friction effect is included as a constraint for initiation of motion.

The drillstring configuration is considered to be drillpipe, drillcollar, and directional assembly. The developed model ("new model") is implemented for tripping-out one stand in two ideal directional wellbores plus one field case wellbore trajectory. Axial force behavior shows a trend of acceleration that is similar to that observed with the previous dynamic soft string model ("previous model": SPE-173084-MS), and the first peak contains the effect of static friction. Displacement at the end of the string shows that the whole drillstring is in motion after few seconds. The axial force using the new model is compared to that (axial force) calculated using the previous model for two different cases. In the acceleration part of the motion, the new model shows a peak about 12% higher than the maximum load in the previous model which is due to the static friction force. In the constant velocity part of the motion, depending on the amount of damping, the new model can show a result similar to that of the previous model.

The new dynamic axially-stiff string model provides a more realistic prediction of hookload, and consequently more realistic loading of the hoisting equipment and fatigue life of the drillstring. Other applications of this model are for wellbore planning, drillstring design, optimization and automation of tripping operations.