Study Group Report 2009: underreamer mechanics (SmartReamer Ltd)
This is the final report on the problem of underreamer mechanics, brought to ESGI68 by SmartReamer Ltd. Click on the link at the bottom to download the full report as a pdf document.

Report coordinator
Marvin Jones (University of Southampton)
David Barton (University of Bristol)
Cameron Hall (University of Oxford)

Executive summary
In the oil and gas industry, an underreamer is a tool used to extend and enlarge the diameter of a previously-drilled bore. The problem proposed to the Study Group is to obtain appropriate mathematical models of underreamer dynamics, in forms that will lead to feasible computation. The modes of dynamics of interest are torsional, lateral and axial. This report describes some initial models, two of which are developed in more detail: one for the propagation of torsional waves along the drill string and their reflection from contact points with the well bore; and one for the dynamic coupling between the underreamer and the drill bit during drilling.

Introduction
In the oil and gas industry, an underreamer is a tool used to extend and enlarge the diameter of a previously-drilled bore. Appropriate mathematical models are needed of underreamer dynamics, in forms that will lead to feasible computation. The modes of dynamics of interest are torsional, lateral and axial. There are various key components to be modelled.

Underreamer: The underreamer may be 12 feet long. It can pass through a pipe, of diameter say 8.75 inches, with its 3 cutter blocks retracted, and then the blocks can be expanded hydraulically to enable it to enlarge the bore to, say 9.875 inches. Further ahead of the underreamer is the leading drill bit, so rock cuttings are already in the mud flow past the underreamer. The cutters are positioned at 120 degrees to each other round the axis, and the main back flow of mud and cuttings past the underreamer goes through the 3 “junk slots" in the circumferential positions between the cutter blocks. A jet of drilling mud is directed through a nozzle ahead of each cutter block in a further attempt to give it clear access to the rock face. It is expected that the main elastic deformation of the underreamer during drilling is in bending.

Cutter blocks: The cutter blocks are mounted with cutting elements made of PDC (polycrystalline diamond compact). These will be subjected to highest loads, vibration and loads will be applied across different points of the cutter blocks.

Drillstring: The drillstring between the surface and the underreamer is so long that it undergoes significant torsional motion. It is rotated at a steady speed at the surface, say 60 or 120 rpm, but the rotation at the underreamer and bit will be unsteady and can have peaks of up to 1000 rpm. There is also up to 50m of drillstring from the underreamer to the bit. The drillstring is free to move within the bore and may make contact at various points along its length. Such points known as torque or drag hotspots could be identified.

Rock and bore: Prior to the passage of the underreamer the rock faces of the bore will already be uneven. The bit is steerable, so the centreline of the bore is generally neither vertical nor straight: it curves and may have horizontal sections.

The nature of the problem
The underreamer dynamics are expected to show various kinds of wear and instabilities depending on both the surface parameters - rotation rate, weight on bit (WoB), flow rate etc. - and on the downhole parameters - formation hardness, wellbore inclination etc. These parameters may adversely affect the underreaming operation and the resulting hole size, concentricity and rugosity. The model should specifically take into account:

• All types of loading and bending moments based on stabilisation points and wellbore contact points.
• Resonant and non-resonant vibration, i.e. torsional, axial, lateral as well as eccentric, sudden, nonresonant vibration modes releasing stored torque.

The model could also be refined to model bit and underreamer wear in varying formations and investigate the effects that differing formation loading would have on both. The main challenge is to construct a model of underreamer dynamics, meeting the above requirements, that can be used both to highlight wear and avoid premature failures due to inherent tool design weak spots or usage related to surface or downhole parameters; and to optimise the rate of penetration and hole cleaning.

Coupled propagation of underreamer and drill bit
One aspect of underreaming explored at the study group was the progression of the underreamer and drill bit through a geological formation of varying resistance. The underreamer and the drill bit are both driven forward by a combination of the thrust from the weight of the drill string and the torque from the rotation supplied at the surface. These two aspects are both necessary when drilling through hard formation; rotation without weight on the bit will not lead to successful drilling, neither will merely pushing through the rock.

Some mathematical modelling of drilling has been done in the past. However, this earlier work only considered an isolated drill bit, rather than a drill bit connected to an underreamer. One opportunity for practical and interesting mathematical modelling is to consider the progression through geological formation of a drill bit connected with an underreamer. Both the underreamer and the drill bit require torque and normal force in order to cut the formation, but the balance of forces between the underreamer and the drill bit will change over time in a manner that should be amenable to analysis.

The lurching progress of the drill-bit and underreamer is depicted below in Figure 1. The reasons for this lurching can be seen more clearly by looking at the length of the material connecting the drill-bit with the underreamer.

As shown in Figure 2, this `spring' slowly extends over a large period of time as the drill-bit moves through the formation faster than the underreamer. Eventually, the extension of the `spring' builds up to the extent that the tensile forces are able to overcome the resistance of the formation around the underreamer and the whole machine lurches forward, accompanied by a rapid decrease in the length of the material connecting the drill-bit with the underreamer.

Figure 1: Progress of drill-bit (shown as continuous line) and underreamer (shown as dashed line). Note that the drill-bit and underreamer become effectively stuck for large periods of time, before breaking through the formation and continuing.

Figure 2: A plot showing the changing length of the material connecting the drill-bit and underreamer over time. This effectively acts as a spring, moderating the forces between the drill-bit and the underreamer.

Click on the link below to view the full report.

Download 'SmartReamer-Underreamer mechanics.pdf' (633 Kb).