FORMEL: A Step Forward in Strength Logging
Authors: Raaen A.M. , Hovem K.A. , Joranson H. , Fjaer E. 
Published: December 2007

Abstract
A new method for estimating in situ mechanical properties from logs has been tested. The method - FORMEL - is based on a new constitutive model, describing processes which occur in rock during mechanical loading.
The method has been compared with results from over 200 rock mechanical tests made on cores, and it compares favorably with direct correlations based on porosity or sonic compressional transit time. It works best for estimating strength at non-zero confining stress, and for porosities below 35%.
Sand strength analysis using FORMEL has been compared with field sand production records, and it is concluded that the method is a valuable tool for sand prediction. A major strength of the method is that it is robust and may be applied with confidence to new wells and fields without re-calibration.

Introduction
A knowledge of in situ rock mechanical parameters is needed for several applications in the petroleum industry. Uses include sand prediction, wellbore stability evaluation, and estimations of compaction and subsidence. The most direct way of obtaining rock mechanical data is from laboratory tests made on cores. However, there are several reasons why other methods are needed: first, core measurements can never provide a continuous strength estimate as a function of depth in a well; second, core tests may be unavailable because of the costs involved or because suitable core material has not been obtained; and third, the effects of stress unloading and core handling upon the quality of rock mechanical tests can be questioned.
This paper is organized in the following way:A short, non-exhaustive introduction is given to some of the previous attempts to determine in situ mechanical properties from logs.A brief explanation of the main elements of the model used in this work are given - the model hereafter being referred to as FORMEL (FORmation MEchanics Logging).Results comparing the FORMEL model with laboratory data are presented for several wells offshore Norway.The model's sensitivity to uncertainty in the input parameters is discussed.Examples of FORMEL for specific wells are shown, and its employment for sand production prediction is discussed.

Logging of mechanical parameters
Mechanical parameters cannot be determined directly from logging tools. Indirect methods (in which the strength and stiffness of the formation are inferred from other properties) must therefore be used.
As the sonic log measures formation stiffness resulting from low-amplitude, high-frequency deformation, it is clear that acoustic logs are prime candidates for incorporation in methods for mechanical properties evaluation.
Two main issues arise from this:How can the low-amplitude, dynamic moduli given by acoustics be related to the large-amplitude, static moduli that are needed?Is there any relation between moduli and strength?
These questions are formidably difficult to answer theoretically, and no one should be offended by the statement that these problems, even today, are far from being solved.
As a result of the lack of established theoretical models, most of the methods suggested for mechanical properties estimation from logs have been empirical. Early attempts simply proposed a cut-off criterion for sand production based on some combination of dynamic moduli (e.g. the product of G and K as used by Tixier et al.).
Schlumberger's Mechpro method went a step further by attempting to predict uniaxial compressive strength from the sonic log. It was based on Deere and Millers correlation between the static Young's modulus E and the uniaxial compressive strength C0. P. 439