Stress Magnitudes From Logs: Effects of Tectonic Strains and Temperature
Authors: Blanton T.L. , Olson J.E. 
Published: December 2007

Abstract
An improved method of calibrating in-situ stress logs has been validated with data from two wells. Horizontal stress profiles are useful for hydraulic fracture design, wellbore stability analysis, and sand production prediction. The industry-standard method of estimating stresses from logs is based on overburden, Poisson's ratio, and pore pressure effects and outputs an estimate of minimum horizontal stress. The model proposed here adds effects of temperature and tectonics and outputs minimum and maximum horizontal stress magnitudes, which are particularly important to the successful completion of horizontal and deviated wells. This method was validated using data collected from a GRI research well and a Mobil well. Seven microfrac stress tests in GRI's Canyon Gas Sands well of Sutton County, TX, provided a means of comparing the predictive capability of different methods. First, one of the seven stress tests was selected as a calibration standard for the stress log. Then the results obtained from the two calibration methods were compared to stress magnitudes from the other six stress tests. This process was repeated using each of the seven stress tests as a calibration standard and comparing predictions to the other six. In every case, the method incorporating tectonic and temperature effects produced significantly more accurate values. In the Mobil well, pre-frac treatment breakdown tests were used to calibrate a log-derived stress profile. While reservoir pressure dominated stress variations, a significant deviation of the log value from the stress-test value in one layer was corrected when the method with tectonics and temperature was used.

Introduction
Advances in well completion technology have made accurate profiles of horizontal stresses more important to successful field development. Data on in-situ stresses have always been important to hydraulic fracture design, wellbore stability analysis, and sand production prediction. More recent work has shown that accurate stress profiles can be used to optimize fracturing of horizontal wells and designing multizone fracture treatments. In fracturing horizontal wells, stress profiles can be used to select zones for the horizontal section that optimize fracture height. For multizone fracturing, the success of advanced limited-entry techniques depends on having accurate profiles of horizontal stresses.

Theory
Conventional Method. The industry-standard method of calculating stresses from logs is based on the following equation:
(1)
The Shmin formula is obtained by solving linear poroelasticity equations for horizontal stress with vertical stress set equal to the overburden and horizontal strains set to zero. Overburden stress, Svert, is determined from an integrated density log. Poisson's ratio, v, is calculated from compressional and shear wave velocities given by an acoustic log.
When independent measures of horizontal stress magnitudes are available from microfracs or extended leak-off tests, the profiles usually need to be shifted to match the measured values, leading to the conclusion that Eq. 1 needs to be calibrated. Typically, this is done by adding a stress term to shift the profile. When measured values are available for several zones, the Poisson's ratio term can be adjusted by a factor to achieve a better fit. For the purposes of this paper, a simple shift is used, as incorporated in the following formula:
(2)
where
(3)
and the primes indicate values for the calibration zone where a measure of the minimum horizontal stress is available. These calibration adjustments have physical implications. Adding a constant to the profile is essentially adding a constant stress, which in some cases has been referred to as a tectonic stress. Adjusting the Poisson's ratio term could be considered a dynamic-to-static conversion. Still these calibrations have more the nature of empirical curve fitting.
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