Effect of Formations Compressive Strength on Drill String Vibrations
Authors: Esmaeili Abdolali , Elahifar Behzad , Fruhwirth Rudolf K. , Thonhauser Gerhard 
Published: May 2016

Abstract
Vibrations are known as destructive loads and thus are leading to downhole fatigue failures, severe bottom hole assembly and bit wear and may cause wellbore instabilities. Downhole measurement of vibrations, however, can provide valuable information about downhole conditions and characteristics of the formations drilled. Uniaxial compressive strength is one of the representative characteristics of rock properties. It shows the capacity of a rock to withstand a certain amount of axial loads. Optimizing weight on bit and rotary speed of the drill string are the ways to continue drilling a hole - of course by exceeding uniaxial compressive strength of formations - and to keep rate of penetration in an optimal range during drilling operations. Therefore, it is expected that the axial vibrations change with variations of the uniaxial compressive strength of formations.
Previous experiments with several layered concretes cubes proved that the drill string vibrations are related to the uniaxial compressive strength of concretes. To extend the study in this area, complex rock samples such as sandstone, dolomite and limestone were drilled with optimized ranges of weight on bit and rotary speed of drill string. Experimental drilling operations were conducted using a laboratory drilling rig (CDC miniRig) with a vibration sensor sub attached to the drill string. The uniaxial compressive strength of all samples was measured prior to the experiments. During all experiments, drilling parameters were recorded with a sampling rate of one second and the vibration data with a sampling frequency of 3200 Hz.
Analysis of magnitude and higher order frequency moments of vibration data in combination with the mechanical specific energy demonstrated a change of the drill string's axial vibration measurements due to variations of uniaxial compressive strength. From that it is concluded that the formations can be recognized in real-time by incorporation of the vibration measurements.

Introduction
When talking about drill string vibrations, in most of the time downhole fatigue failure, severe bit wear and reduced rate of penetration come to the mind. Drill string vibrations are inevitable in the drilling operations and lots of researches have been investigated to manage the magnitude of vibrations by designing proper bottom hole assemblies (Macpherson et al., 1993; Chen et al., 2006). However, the vibrations can be utilized as a valuable tool to recognize formations drilled. In most of the cases, the vibrations are caused by bit and drill string interaction with the formations under certain drilling conditions. One of the dominant conditions is formation characteristics (mechanical and petrophysical properties). Uniaxial compressive strength (UCS) is one of the representative characteristic of the formation properties. It shows the capacity of a formation to withstand a certain amount of axial loads. Previous works show that the harder the formation, the bigger the magnitude of the vibrations and vice versa (Esmaeili et. al, 2012). Therefore monitoring vibrations in real-time can advance warning of formation changes.
Myers et al. (2002) explained how the vibration data measured by an accelerometer are related to petrophysical properties of the formations in the Indian Ocean region.
Al-Shuker et. al. (2011) presented changes in drilling dynamics driven by the bit's interaction with the formation can be a near instantaneous indicator of changes in formation characteristics. The key is real-time drilling dynamic measurement at the bit.
Previous works (Esmaeili et al., 2012) presented a close relationship between the mechanical properties of layered concretes cubes and the measured vibrations. The study proved that the vibrations can be used as a tool to recognize the formation changes.